Open Access
Issue
A&A
Volume 664, August 2022
Article Number A70
Number of page(s) 64
Section Galactic structure, stellar clusters and populations
DOI https://doi.org/10.1051/0004-6361/202141114
Published online 05 August 2022

© F. J. Galindo-Guil et al. 2022

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

One of the most fundamental parameters necessary for the characterisation of any astrophysical object, from planets, stars, and galaxies up through the whole universe, is age. There are only two true pillars holding up the scale of astrophysical age. The first is the age of the Sun, which comes from radiometric measurements of the oldest Solar System material, which yields 4.55 ± 0.07 Ga (see Patterson 1956 or the recent value 4.5672 ± 0.6 Ga from Amelin et al. 2002). The second is the age of the universe, with an estimate of 13.8 Ga, based on the Lambda cold dark matter cosmological model (ΛCDM, Planck Collaboration VI 2020).

All other ages are subject to significant uncertainties, and their determinations face multiple observational and theoretical challenges. Ages are generally better determined in stellar associations1 than in isolated stars and, more precisely, open clusters are very convenient for this purpose. They usually provide a significant sample of objects when testing the hypothesis that they were born simultaneously from the same molecular cloud and with an identical composition. Two excellent and complete summaries of techniques for estimating ages in ensembles of stars can be found in Mermilliod (2000) and Soderblom (2010).

There are several methods and techniques aimed at assigning ages at present, however, each of them is valid within a specific age interval. Ages can vary as much as 50% depending on the technique, as in the case of stellar associations with ages below 150 Ma (see Stauffer et al. 1995a or Barrado y Navascués et al. 1999a). Even when using the same technique, there can be broad variations depending solely on the different grids of theoretical models.

Several features and characteristics are taken into account when deriving ages in stellar associations. The isochrone fitting technique is the most widely used since it covers all ages and masses, making use of colour-magnitude or Hertzsprung–Russell diagrams (HRDs). The turn-off isochrone fitting consists of reproducing the morphology of the cluster sequence close to the turn-off region, which is where stars are approaching the end of hydrogen burning at their core. The pre-main-sequence (PMS) isochrone fitting consists of reproducing the position of PMS stars in the cluster. However, there are significant deviations between ages derived using PMS stars still contracting onto the main sequence, and high-mass ones that have already evolved away from it (Lyra et al. 2006; Naylor 2009). These differences can be due to the effects of binarity and rotation of the upper main-sequence stars (Mermilliod 2000) or due to the fact that the effective temperatures predicted by current PMS evolutionary models are overestimated due to the magnetic fields and star-spots (D’Antona et al. 2000; Stauffer et al. 2003; Jackson & Jeffries 2014b; Franciosini et al. 2022). The rotation of massive stars increases the estimated age of a stellar association about 25% (Meynet & Maeder 2000), with this effect being more pronounced in younger associations, such as Alpha Persei and the Pleiades, than in older ones such as Coma Berenices, Praesepe, or the Hyades (Maeder 1971). The isochrone fitting ages estimated from models that take into account the magnetic field are systematically higher than those estimated from models that ignore this effect (Malo et al. 2014b).

There are other methods used to derive stellar ages. The kinematic age technique is based on the motions of a group of stars due to its expansion from their birthplace without experiencing any forces (see the seminal works from Ambartsumian 1947, 1949; Blaauw 1946, 1964; and the subsequent works with a refined methodology: Brown et al. 1997b or Miret-Roig et al. 2018). This technique is applicable to stellar associations younger than 20 Ma (Soderblom 2010).

The Strömgen photometric system uvbyβ allows us to derive effective temperatures and surface gravities for BAF-type stars and they are used to estimate the age comparing with theoretical evolutionary tracks (see Song et al. 2001; David & Hillenbrand 2015). Also, the strength of gravity-sensitive spectrophotometric features is an age proxy in stellar associations within the 5 to 15 Ma range, with an uncertainty of 2 Ma (Lawson et al. 2009). Another technique, namely, gyrochronology, derives ages for main-sequence and low-mass stars using their rotation periods and colours, for ages older than 600 Ma (Barnes 2007). Finally, the white dwarf cooling age exploits the slope and position of its thermal evolution relative to the main-sequence with an age range of validity from 150 Ma to 4 Ga (De Gennaro et al. 2009).

The lithium depletion boundary (LDB) is a technique that allows for an independent age determination for a stellar association (Basri et al. 1996), valid for values between 20 to few hundred Ma. It is based on the presence or absence of lithium in low-mass stars and brown dwarfs (Rebolo et al. 1992). Lithium burns inside the stellar nucleus (D’Antona & Mazzitelli 1984) and stars with masses below about 0.3 M are fully convective. The convection makes that the lithium surface abundance to decrease with age, and for low-mass objects, the decay is very rapid. For masses below ∼0.07 M (depending on the evolutionary theoretical model), the core temperature is never hot enough to destroy it, and its abundance (both internal or in the stellar or sub-stellar atmosphere) remains the same. The burning process is so fast and depends so strongly on mass that there is a sharp boundary between lithium-rich and lithium-poor members (D’Antona & Mazzitelli 1994; Bildsten et al. 1997; Ushomirsky et al. 1998). The LDB technique was successfully applied to the Pleiades (Stauffer et al. 1998a) and Alpha Persei (Stauffer et al. 1999) clusters, and since then, this method has been used in a dozen of stellar associations.

Similarly to other model-dependant techniques, the LDB age is also affected by possibly assumptions made in the input physics of the stellar models it relies on (Jeffries & Naylor 2001; Burke et al. 2004; Tognelli et al. 2015). The expected uncertainties on LDB age depends on the luminosity of the star at the LBD, ranging from about 3% percent for faint old stars to about 15% for brighter young stars (Burke et al. 2004; Tognelli et al. 2015). In addition, the LDB technique is indirectly affected by other uncertainties: (a) stellar distances, (b) the contamination by field stars, (c) the transformation from observational quantities, magnitude, and colours, as well as theoretical ones such as bolometric luminosities and effective temperatures (Jeffries & Naylor 2001), (d) the presence of binaries or multiple systems, (e) the magnetic activity and rotation of the objects (Soderblom et al. 1993; Chabrier et al. 2007; Malo et al. 2014b), (f) the identification of a significant number of low-mass cluster members within a small magnitude range, and (g) the low quality and/or low resolution of the used stellar spectra.

The availability of photometric all-sky or wide sky surveys, such as Gaia DR2 (Gaia Collaboration 2018a), SDSS (Alam et al. 2015), 2MASS (Skrutskie et al. 2006), WISE (Cutri 2013), or Pan-STARRS (Chambers et al. 2017) has signalled the dawning of a new era and allowed us to address several of the factors mentioned above from a new perspective. The high-quality astrometric data of Gaia DR2 represent a significant advance for at least three reasons: they allow us (a) to calculate, for the first time, individual distances for each low-mass cluster member, (b) to refine the membership criteria, and in some cases (c) to determine whether an object is a multiple system. Furthermore, the use of wide-area multi-wavelength imaging surveys with ranges from ultraviolet to infrared allows us to calculate the total flux of each object without assuming any monochromatic bolometric correction, which is a noteworthy source of systematic uncertainties in the LDB age. Empirical bolometric corrections are derived from main-sequence stars and our objects have different logg values; in addition, bolometric corrections vary as a function of metallicity, especially for temperatures less than 3000 K (Jeffries & Naylor 2001; Burke et al. 2004; Tognelli et al. 2015).

In this work, we present, for the first time, a homogeneous analysis for all the stellar associations with former LDB ages aimed at creating a complete set of an LDB age scale. This analysis includes new photometric data in a broad range of wavelengths, individual accurate parallaxes from Gaia DR2, and the effects of metallicity and gravity. The work is structured as follows. In Sect. 2, we introduce the stellar associations under consideration. We provide information of the data and evolutionary models used in Sect. 3. Section 4 shows the method scheme in detail. We analyse each stellar association, explain additional information from literature, identify outliers, and locate the LDB in Sect. 5. Section 6 covers the effects of systematic uncertainties on the derived LDB including a comparison between the LDB ages and those derived from other techniques. Section 7 presents our conclusions. Additional material is presented in the Appendices. In Appendix A, we made all the plots for each stellar association available, along with the vector point diagrams (VPDs), parallax distributions, and HRDs. In Appendix B, we show the effect on the LDB of the adopted reddening. A short description for some objects belonging to the Beta Pictoris moving group are given in Appendix C, and a brief study of the 32 Ori moving group in Appendix D. Partial tables with data (names, astrometry, lithium equivalent widths, photometry, and quantities calculated) are given in Appendix E.

2. Stellar associations sample

For our study, we considered twelve stellar associations with a previous LDB age estimation. Nine of them are young open clusters and three are moving groups. Table 1 includes the main properties of the studied targets that are briefly discussed below.

Table 1.

Data from the literature for the twelve stellar associations with LDB ages.

2.1. Alpha Persei

Alpha Persei is an open cluster located at a distance of 175 pc with an age of 71 Ma (Gaia Collaboration 2018b) and with chemical composition values ranging from [Fe/H] = −0.054 ± 0.046 dex (Boesgaard & Friel 1990) to [Fe/H] = +0.18 dex (Pöhnl & Paunzen 2010). Mermilliod et al. (2008) noticed the existence of a extended co-moving stream of stars, recently confirmed and characterised by Nikiforova et al. (2020). The age ranges between 50 Ma to 80 Ma: 51.3 Ma (Mermilliod 1981), 52 Ma assuming E(B − V) = 0.055 mag (Makarov 2006), 80 ± 10 Ma (Prosser 1992), and Ma, assuming (m − M)0 = 6.21 mag and AV = 0.28 mag (Bossini et al. 2019).

Regarding the LDB technique, Basri & Martín (1999a) computed a lower age limit of 66 Ma based on one object, AP270. Stauffer et al. (1999) using a large sample, calculated 90 ± 10 Ma assuming 176 pc and AI = 0.17 mag, E(R − I)C = 0.07 mag. Later, Barrado y Navascués et al. (2004) recomputed it and yielded 85 ± 10 Ma assuming (m − M)0 = 6.23 mag and E(B − V) = 0.096 mag. Finally, Burke et al. (2004) derived 87 ± 9 Ma, using a (m − M) = 6.23 ± 0.10 mag and AI = 0.17 ± 0.04 mag.

2.2. NGC 1960 (M 36)

NGC 1960 is a northern hemisphere open cluster located at 1157 pc (Cantat-Gaudin et al. 2018a) with an estimated age of 25 Ma (Bossini et al. 2019, assuming mag and AV = 0.657 mag). Several works have determined the distance, age, and reddening of NGC 1960: ≤22.4 Ma (Mermilliod 1981), Ma, assuming (m − M)0 = 10.6 ± 0.2 mag (1318 ± 120 pc) and E(B − V) = 0.25 ± 0.02 mag (Sanner et al. 2000), 25 Ma assuming 1330 pc and E(B − V) = 0.22 mag (Sharma et al. 2006), 20 Ma using and E(B − V) = 0.20 mag (Mayne & Naylor 2008), and finally Ma and Ma (Bell et al. 2013). Jeffries et al. (2013) calculated a LDB age of 22 ± 4 Ma, assuming a distance modulus of 10.33 mag ( pc) and E(B − V) = 0.20 mag.

2.3. IC 4665

IC 4665 is located at 346 pc (Gaia Collaboration 2018b), with an age of Ma (Bossini et al. 2019) and a metallicity of [Fe/H] = −0.03 ± 0.04 (Dias et al. 2002). The age ranges between 25 to 50 Ma: 36.3 Ma (Mermilliod 1981), 25 ± 5 Ma (Manzi et al. 2008) 36 ± 9 Ma, assuming a distance of 360 ± 12 pc and 42 ± 12 Ma, with a distance of 357 ± 12 pc (Cargile & James 2010), and between 31 to 34 Ma (Randich et al. 2018).

Manzi et al. (2008) computed an LDB age of Ma, assuming 370 ± 50 pc and E(B − V) = 0.18 mag (AIc = 0.333 mag). Randich et al. (2018) re-calculated the LDB age, Ma, using (m − M)0 = 7.82 ± 0.25 mag and E(B − V) = 0.226 ± 0.080 mag.

2.4. NGC 2547

NGC 2547 is located in the Vela complex (Eggen 1986) at 394 pc with E(B − V) = 0.040 mag, an age of Ma (Gaia Collaboration 2018b), and a metallicity of [Fe/H] = −0.16 ± 0.09 (Dias et al. 2002). The NGC 2547 age ranges between 14 Ma to 57 Ma: 14 ± 4 Ma and 55 ± 25 Ma (Jeffries & Tolley 1998, using a distance modulus of 8.1 mag and E(B − V) = 0.06 mag), an age range between 20 to 35 Ma (Naylor et al. 2002, assuming a distance modulus range of 8.00 − 8.15 mag), two age ranges, from 32 to 50 Ma and from 63 ± 30 to 75 ± 25 Ma, depending on the technique (Lyra et al. 2006, assuming E(B − V) = 0.03 ± 0.02 mag and 390 ± 25 pc), 38 Ma and Ma (Naylor 2009, assuming (m − M)0 = 8.03 mag and E(B − V) = 0.04 mag), 36–40 Ma (Randich et al. 2018), and Ma (Bossini et al. 2019 assuming (m − M)0 = 7.98 mag, and AV = 0.124 mag.

Oliveira et al. (2003) made the first attempt to locate the LDB resulting in an age range between 35−54 Ma. Later, Jeffries & Oliveira (2005) calculated an LDB age of 34 − 36 Ma, assuming (m − M)0 = 8.10 ± 0.10 mag and E(B − V) = 0.06 ± 0.02 mag. Burke et al. (2004) calculated an age of 38 ± 7 Ma, using (m − M) = 8.15 ± 0.15 mag and AI = 0.05 ± 0.03 mag. Finally Randich et al. (2018) re-calculated the LDB age using (m − M)0 = 7.81 ± 0.25 mag and E(B − V) = 0.080 ± 0.024 mag: Ma.

2.5. IC 2602

IC 2602, the brightest Southern Hemisphere open cluster, is located at a distance 152 pc (6.571 ± 0.007 mas), E(B − V) = 0.031 mag, with an age of Ma (Gaia Collaboration 2018b) and [Fe/H] = −0.05 ± 0.05 (Randich et al. 2001).

The age ranges between 25 to 63.2 Ma. Other values are: 36.3 Ma (Mermilliod 1981), 25 Ma and 35 Ma (Stauffer et al. 1997 depending on the technique), Ma (Naylor 2009, assuming a distance modulus of 5.88 mag, 150 pc and E(B − V) = 0.02 mag), 29–32 Ma (Randich et al. 2018), and Ma (Bossini et al. 2019, assuming (m − M)0 = 5.91 mag and AV = 0.10 mag).

Dobbie et al. (2010) computed an LDB age of Ma assuming (m − M)0 = 5.86 ± 0.1 mag (149 pc), and E(B − V) = 0.035 mag. Randich et al. (2018) recalculated the LDB age using a distance modulus of 5.85 ± 0.10 mag and E(B − V) = 0.068 ± 0.025 mag: Ma.

2.6. IC 2391

This cluster is located at a distance of 152 pc (6.597 ± 0.007 mas), E(B − V) = 0.030 mag, with an age of Ma (Gaia Collaboration 2018b) and [Fe/H] = −0.03 ± 0.07 (Randich et al. 2001). It is an open cluster with similar age and distance to IC 2602 (Stauffer et al. 1997), but they are located in different sky regions, see Fig. 1. Several works have studied both clusters in a parallel way: Stauffer et al. (1997), Randich et al. (2001), and D’Orazi & Randich (2009).

thumbnail Fig. 1.

Projected positions for IC 2391 (black pluses are members from Gaia Collaboration 2018b and green triangles objects from the LDB sample) and IC 2602 (blue crosses are members from Gaia Collaboration 2018b and red circles sources from the LDB sample).

The IC 2391 age ranges between 25 to 50 Ma: 36.3 Ma (Mermilliod 1981), 25 to 35 Ma isochrone fitting age (Stauffer et al. 1997), 40–45 Ma (Randich et al. 2018) and Ma, assuming (m − M)0 = 5.91 mag and AV = 0.09 mag (Bossini et al. 2019).

The LDB age was initially estimated by Barrado y Navascués et al. (1999a): 53 ± 5 Ma, assuming AI = 0.02 mag and (m − M)0 = 5.95 ± 0.1 mag. A further refinement in Barrado y Navascués et al. (2004) produced a value of 50 ± 5 Ma, assuming the same distance and E(B − V) = 0.06 mag. Burke et al. (2004) calculated an age of 48 ± 5 Ma, using a (m − M) = 5.95 ± 0.10 mag and AI = 0.02 ± 0.02 mag. Randich et al. (2018) re-computed the LDB age using (m − M)0 = 5.82 ± 0.10 mag and E(B − V) = 0.088 ± 0.027 mag: Ma.

2.7. The Pleiades

The Pleiades cluster is located at 136 pc (7.364 ± 0.005 mas), E(B − V) = 0.045 mag, and an age of Ma (Gaia Collaboration 2018b). Metallicity values, [Fe/H], range from −0.034 ± 0.024 (Boesgaard & Friel 1990) to 0.06 ± 0.06 (Gebran & Monier 2008). Excellent summaries of previous works can be found in Stauffer et al. (2007), Bouy et al. (2015) and Lodieu et al. (2019a).

Although it has been widely studied, its distance and age have been a matter of controversy, ranging the distance between 115 to 140 pc, depending on the work and the technique used: 115.9 ± 2.7 pc (van Leeuwen & Hansen Ruiz 1997), 131.8 ± 2.5 pc (Pinsonneault et al. 1998), 139.1 ± 3.5 pc (Southworth et al. 2005), 120.2 ± 1.9 pc assuming E(B − V) = 0.04 mag (van Leeuwen 2009), 136.2 ± 1.2 pc (Melis et al. 2014), and pc (Galli et al. 2017). The age ranges between 70 to 150 Ma: 77.6 Ma (Mermilliod 1981), 150 Ma (Mazzei & Pigatto 1989) 100 Ma, assuming (m − M)0 = 5.60 mag and E(B − V) = 0.04 mag (Meynet et al. 1993), 70 ± 10 Ma (Stauffer et al. 1995b)2, Ma, assuming (m − M)0 = 5.35 mag and E(B − V) = 0.02 mag (Naylor 2009), 132 ± 2 Ma (Bell et al. 2014), Ma (Cargile et al. 2014), Ma, assuming (m − M)0 = 5.67 mag and AV = 0.14 mag (Bossini et al. 2019), and Ma, assuming E(B − V) = 0.045 mag (Lodieu et al. 2019a).

Basri et al. (1996) attempted to determine the LDB age and reported a lower limit of ∼115 Ma based on the detection of lithium in the binary system PPL-15 (Basri & Martín 1999b). Later, the exhaustive study of Stauffer et al. (1998b), yielded a value of 125 ± 8 Ma assuming (m − M)0 = 5.60 mag and AI = 0.06 mag. In addition, Barrado y Navascués et al. (2004) re-calculated the value at 130 ± 20 Ma, whereas Burke et al. (2004) re-calculated an age of 126 ± 11 Ma, both using a (m − M) = 5.60 ± 0.10 mag and AI = 0.06 ± 0.03 mag. Finally, Dahm (2015) derived an age of 112 ± 5 Ma, assuming 136.2 ± 1.2 pc (Melis et al. 2014) and AV = 0.12 mag, AI = 0.06 mag, AJ = 0.03 mag, and AK = 0.01 mag.

2.8. Blanco 1

Blanco 1 is located at 237 pc with E(B − V) = 0.001 mag and an age of Ma (Gaia Collaboration 2018b)3. It has an estimated metallicity of [Fe/H] = +0.03 ± 0.074 (Netopil et al. 2016). The age ranges between 90 to 200 Ma: 90 ± 25 Ma (Panagi & O’dell 1997), 80 ± 20 Ma (Cargile et al. 2009, assuming 240 ± 10 pc and E(B − V) = 0.016 mag), Ma (Bossini et al. 2019, assuming (m − M)0 = 6.876 mag and AV = 0.031 mag), and Ma (Cargile et al. 2014).

Cargile et al. (2010) identified the LDB at log Lbol = −2.94 ± 0.12 L or log Lbol = −2.90 ± 0.09 L (depending on monochromatic bolometric corrections) and determined an age of 132 ± 24 Ma, assuming a distance modulus of 6.58 ± 0.12 mag and E(I − Ks) = 0.02 mag (AI = 0.03 mag). Later, Juarez et al. (2014) used empirical activity corrections to investigate the effects of magnetic activity on the LDB age. They updated the LDB age to Ma, and taking into account the activity, they gave a value of Ma.

2.9. The Hyades

The Hyades cluster is the nearest open cluster to the Sun, 45 pc (de Bruijne et al. 2001). It has an estimated age of 625 ± 50 Ma (Perryman et al. 1998) and [Fe/H] = +0.127 ± 0.022 (Boesgaard & Friel 1990). Metallicity ranges from [Fe/H] = +0.05 ± 0.05 (Gebran et al. 2010) to [Fe/H] = +0.13 ± 0.05, derived using 61 sources (Netopil et al. 2016). Additional information can be found in Perryman et al. (1998) and Lodieu et al. (2019b). Recently, Meingast & Alves (2019) and Röser et al. (2019) reported the detection of the tidal tails. The age ranges between 500 to 1200 Ma: 661 Ma (Mermilliod 1981), an age range between 500 to 1000 Ma (Eggen 1998), 648 ± +45 Ma (De Gennaro et al. 2009), 800 Ma (Brandt & Huang 2015), Ma (Gaia Collaboration 2018b), and Ma (Lodieu et al. 2019b). Martín et al. (2018) identified the LDB in the Hyades and derived an age of 650 ± 70 Ma. More recently, Lodieu et al. (2018) re-analysed the age adding to the study the source 2M0418 and inferred an age range of 580–775 Ma (mean of 700 Ma) from the bolometric luminosity, and 580–950 Ma (mean of 760 Ma) from the effective temperature.

2.10. Beta Pictoris moving group

The Beta Pictoris moving group, hereafter BPMG, named after the star β Pictoris, is a 20 ± 10 Ma co-moving group of stars (Barrado y Navascués et al. 1999b) with a metallicity of [Fe/H] = −0.01 ± 0.08 (Viana Almeida et al. 2009). Several studies have addressed the BPMG age with different results: 20 ± 10 Ma (Barrado y Navascués et al. 1999b), Ma (Zuckerman et al. 2001), 11.5 Ma (Ortega et al. 2002), ∼12 Ma (Song et al. 2003), 15 Ma (Torres et al. 2006), 22 ± 12 Ma (Makarov 2007), an age range between 13 ± 5 Ma to 21 ± 9 Ma (Mentuch et al. 2008), 22 ± 3 Ma (Mamajek & Bell 2014) 24 ± 3 Ma (Bell et al. 2015) 40 Ma (Macdonald & Mullan 2010), an age range between 15 and 28 Ma (Malo et al. 2014b), Ma (Miret-Roig et al. 2018) which was updated to Ma (Miret-Roig et al. 2020).

Song et al. (2002) estimated the LDB in < 20 Ma. Then, Binks & Jeffries (2014) added to the study eight low-mass members and re-calculated the age: 21 ± 4 Ma with an additional model-dependent uncertainty of ±1 Ma. Messina et al. (2016), after de-correlating the lithium equivalent width from the rotation period, calculated an age of 25 ± 3 Ma using the hot side of the LDB. Finally, other LDB ages have also been calculated: ≥30 Ma (Yee & Jensen 2010), 26 ± 3 Ma (Malo et al. 2014b) and 22 ± 6 Ma (Shkolnik et al. 2017).

2.11. Tucanae-Horologium moving group

At first, the Tucanae-Horologium moving group (THMG) was identified as two separate associations: the Tucanae association (Zuckerman & Webb 2000) with ten co-moving stars placed at a distance ∼45 pc, and the Horologium association (Torres et al. 2000) located at ∼60 pc. Viana Almeida et al. (2009) reported a metallicity of [Fe/H] = −0.03 ± 0.05 using nine members. The age ranges between 5–45 Ma: 40 Ma (Zuckerman & Webb 2000), ∼30 Ma (Torres et al. 2000), an age range between 10–30 Ma (Stelzer & Neuhäuser 2000), ∼20 Ma (Kraus et al. 2014), 45 ± 4 Ma (Bell et al. 2015), and Ma (Miret-Roig et al. 2018). Kraus et al. (2014) confirmed 129 new late-type members with spectral types between K3 to M6 and these authors calculated an LDB age of 40 Ma.

2.12. 32 Ori moving group

The 32 Ori moving group (32 Ori MG, also known as Mamajek 3), was noticed as a group of X-ray-bright late-type stars from the ROSAT All-Sky Survey (Alcalá et al. 2000) with similar proper motions and moving with the massive binary 32 Ori (B5V+B7V). Mamajek (2007) defined the moving group with about ten sources and estimated an age of 25 Ma (with no technique specifically given).

Bell et al. (2015) calculated an isochronal fitting PMS age of Ma adopting a distance of 91.86 ± 2.42 pc for all the stars. With the new census, Bell et al. (2017) calculated a PMS isochronal fitting age of 25 ± 5 Ma using E(B − V) = 0.03 ± 0.01 mag (AV = 0.10 ± 0.03 mag) and the kinematic or trigonometric distances derived for each source.

Bell et al. (2017) calculated an LDB age of 23 ± 4 Ma using E(B − V) = 0.03 ± 0.01 mag (AV = 0.10 ± 0.03 mag) and the kinematic or trigonometric distances derived for each source. They combined both results, PMS age and LDB age, and released an age of 24 ± 4 Ma (±4 Ma statistical and ±2 Ma systematic).

3. Data and evolutionary models

3.1. Initial census for the stellar associations

Most of the open clusters we analysed here are included in the Gaia Collaboration (2018b), so we have built the initial sample of cluster members with data from that work. There are two exceptions: NGC 1960 and 32 Ori MG. For these two, we selected the members from Cantat-Gaudin et al. (2018a) for NGC 1960 and Bell et al. (2017) for the 32 Ori MG.

We created a new list restricting to only members with measured lithium equivalent widths and close to the expected LDB, hereafter referred to as the LDB sample (see Table E.5). The selected members must satisfy the following requirements: they should have available spectral data with enough resolving power (ℛ > 1000) and a moderate signal-to-noise ratio (S/R > 20) around the lithium feature located at 6707.8 Å (see Fig. A.2 from Bayo et al. 2011). Unfortunately, the lithium data for the same cluster are not homogeneous, as they have been obtained by several authors using different analyses and with spectra with different resolving power or signal-to-noise ratio. We compiled the dataset using the astronomical databases Astrophysics Data System (ADS, Murray et al. 1992), SIMBAD (Egret et al. 1991), and VizieR (Ochsenbein et al. 2000).

3.2. Gaia DR2: parallaxes, proper motions, and photometry

The second Gaia (Gaia Collaboration 2016) data release, hereafter Gaia DR2, is an all-sky survey catalogue with celestial positions and G photometry for approximately 1.7 × 109 sources; for 1.3 × 109 of those sources, parallaxes and proper motions are also available (Gaia Collaboration 2018a). The quality and quantity of data released by Gaia DR2 are unprecedented. However, we should take into account some caveats related to the astrometry: (a) all the sources have been considered as single stars; so, if an object is a multiple system it likely lacks an astrometric solution or its value is corrupted; (b) some sources have negative parallaxes (see Luri et al. 2018); and (c) objects with separations ∼0.2 − 0.3″ and not resolved in Gaia DR2 can contain spurious parallax values with small uncertainties.

The Gaia DR2 catalogue includes photometry in three optical bands G, GBP, GRP, with a bright limit of G ≈ 3 mag and a limiting magnitude of G = 21 mag (Evans et al. 2018). The analysis from Maíz Apellániz & Weiler (2018) reports a systematic linear trend in the photomotric system, for the range G ∈ [6, 16] mag, estimated to be 3.5 ± 0.3 mmag mag−1 These values can be greater in crowded regions, in the vicinity of bright sources, and at values of G ≥ 19 mag. This mainly affects GBP and to a lesser extent GRP. Smart et al. (2019) indicated that for their sample of cool dwarfs (with spectral types ranging from M8 to T6), GBP is heavily affected. So, our faintest and furthest sources might suffer from overestimation in this band. The flux-excess factor (named +photbprpexcessfactor+ and included in the catalogue) gives a quantitative indication of this effect and can be used to filter out unreliable values (see recommendations from Evans et al. 2018).

We queried the Gaia DR25 archive without imposing any restriction, cross-matching the positions on the sky (right ascension and declination) from our sources using a 2.5″ radius. When finding two or more sources for the same input, we made certain which counterpart was the correct one and we carefully investigated the images and the entries using ESASky (Baines et al. 2017) and Aladin (Bonnarel et al. 2000). We followed a different approach for the Hyades and the MGs because we lost a lot of sources in the cross-matching. This was due to two factors: (a) the proximity and high proper motion of the sources, and (b) our input positions on the sky are in epoch 2000, while Gaia DR2 uses as reference epoch 2015.5. In such cases we identified each source using the 2MASS source name and the SIMBAD database, then we checked with ESASky and Aladin whether there was a Gaia DR2 counterpart or not. Once we knew the Gaia DR2 name, we obtained the rest of the quantities, astrometric and photometric data from the archive. Throughout this work, we performed the analysis with the Gaia DR2 data. However, we carried out an additional check with the Gaia EDR3 data (Gaia Collaboration 2021).

3.3. Photometry

We gathered photometric data from the literature. For each association, these came from studies carried out with different telescopes and instruments and, therefore, with heterogeneous uncertainties and different completeness and limiting magnitudes Additionally, we gathered data from all-sky or wide-area multi-wavelength imaging surveys, with ranges from the ultraviolet to the infrared, using, whenever possible, the Virtual Observatory SED Analyzer (VOSA, Bayo et al. 2008), together with the SIMBAD and VizieR databases. We cross-matched the celestial position of each source with the catalogues provided using a matching radius of 3.0″. The catalogues adopted for the analysis are the following: Tycho-2 (Høg et al. 2000) BTVT bands; 2MASS (Cutri et al. 2003) JHKs bands; CMC 14 (Evans et al. 2002) r band; DENIS (DENIS Consortium 2005) iJKs bands; UKIDSS (Lawrence et al. 2007) bands ZYJHKs; APASS DR9 (Henden et al. 2009) BVgri bands; GALEX (Bianchi & Team GALEX 2000) FUVNUV bands; WISE (Cutri 2013) W1 W2 W3 W4 bands; IPHAS DR2 (Barentsen et al. 2014) riHα bands; SDSS DR12 (Alam et al. 2015) ugriz bands; VPHAS DR2 (Drew et al. 2016) ugri bands; and Pan-STARRS1 (Chambers et al. 2017) gP1rP1iP1zP1yP1 bands. As described in Sect. 3.2, here we also checked all the images to avoid any misidentification. We show the collected photometric bands in Appendix E.

3.4. Evolutionary theoretical models and LDB

To estimate the LDB age, we used the luminosity-age relationships from: (a) Burke et al. (2004), calculated by assuming a solar metallicity of Z = 0.0188 and Y = 0.27; and (b) Tognelli et al. (2015) with Z = 0.013 and Z = 0.0166. In both the cases, the LDB has been defined as the model in which lithium is depleted by a factor of 100 from its initial value. Moreover, we took the mass-tracks or the isochrones provided from other works and calculated the LDB bolometric luminosity-age relationships as well as the point where lithium has been depleted by a factor of 100: (c) Burrows et al. (1993, 1997) calculated it on the basis of solar metallicities (Anders & Grevesse 1989; d) D’Antona & Mazzitelli (1994) calculated it based on solar metallicities (Anders & Grevesse 1989), using the Canuto & Mazzitelli (1991) convection model and opacities from Alexander et al. (1983); (e) BT-Settl models (Allard et al. 2012) using [M/H] = 0.0 (following Asplund et al. 2009); and (f) Siess et al. (2000) using solar composition Z = 0.02, These relationships also provide other stellar parameters: mass, radius, surface gravity and effective temperature.

Also, we used isochrone models from Tognelli et al. (2011), and a Zero Age Main Sequence from Stahler & Palla (2005), to identify background, foreground sources or multiple systems in the HRDs.

4. Method

We built an HRD to locate the LDB in each stellar association, including only those sources with a moderate signal-to-noise ratio (S/N > 20), in the region of the lithium absorption line. The way we derived the bolometric luminosities will be discussed in Sect. 4.3. According to Kraus et al. (2014), the LDB determined using bolometric luminosities or bolometric magnitudes is more unambiguous due to their large dynamical range over which it varies across the relevant age scales. Thus, we demarcated the LDB in terms of bolometric luminosity.

To estimate subsequent quantities, we first need to estimate the distance of the cluster. To do this, using the member list we evaluated the median distance and size of each open cluster constructing a kernel density estimation7 (KDE) function, as suggested in Luri et al. (2018). Following this method, we obtained the mode parallax (ϖmode), the median, the weighted median, the weighted variance, the quartiles, the 2.5th percentile, and the 97.5th percentile. Finally, we calculated distances at different percentiles with d = 1/ϖ. In Table 2 we provide the estimated parallaxes together with the calculated distances for each stellar association. As an example, Fig. 2 shows the parallax probability density function (PDF) for Alpha Persei. Unlike open clusters, the sources belonging to BPMG, THMG, and 32 Ori MG are positioned across a wide range of distances (see Table 1 and Malo et al. 2013). For this reason, we avoided calculating the average value and we used the distance (parallax) available for each source.

thumbnail Fig. 2.

Parallax PDF for the Alpha Persei members (taken from Gaia Collaboration 2018b). The modelled PDF is shown in gray and a superimposed histogram in blue. The two magenta vertical dotted lines point the 2.5th and 97.5th percentiles; the two cyan vertical dashed lines point the quartiles and the the red vertical line shows the mode of the PDF. The small vertical black lines below the horizontal axis (below y = 0.0) show the parallaxes of each source.

Table 2.

Parallax distributions from the initial sample of cluster members using a KDE based on Gaia DR2 data.

4.1. Outliers based on proper motions and parallaxes

The accurate proper motions and parallaxes obtained from Gaia DR2 allowed us remove possible outliers in the different LDB samples. As an example, Fig. 3 shows the proper motion vector point diagram (VPD) for the Alpha Persei with sources from the LDB sample and the comparison sample. Several sparse sources do not share proper motions with the rest, so we considered them, based on visual inspection, as outliers and were discarded as members. We plotted the proper motions as ellipses because we took into account the uncertainties and the correlation coefficients between them, as recommended in Brown et al. (1997a) (see Lindegren et al. 2016, 2018; Luri et al. 2018 and examples in Cantat-Gaudin et al. 2018b). Similarly, we compared the parallaxes, see Fig. 4 for Alpha Persei. We discarded in the LDB analysis the sources with parallaxes outside the range delimited by the values at the 2.5th and 97.5th percentiles, taking into account the uncertainties of the individual measurements. This values are shown with a grey filled area and the quartiles with a red superimposed area. The lack of radial velocities with enough resolving power for all objects in all associations prevents us from performing a further complete analysis using positions, parallaxes, proper motions, and radial velocities. We proceeded in the same way in all the open clusters. The figures can be found in Appendix A.

thumbnail Fig. 3.

VPD for Alpha Persei. Top: blue dashed ellipses are the members taken from Gaia Collaboration (2018b); red ones are the LDB sample objects. Five sources (AP296, AP310, AP313, AP317, and AP322) possess a proper motion different from that of the rest of the members. AP272 is also shown (see the text). Uncertainties in the proper motions and its correlations are taken into a account and shown as ellipses. All data have been taken from the Gaia DR2 catalogue. Bottom: zoom on the previous plot.

thumbnail Fig. 4.

Parallaxes for 17 selected Alpha Persei sources close to the LDB. The grey filled area shows the parallax distribution from Gaia Collaboration (2018b) between the percentiles 2.5th and 97.5th, while the distribution quartiles are delimited by a red filled area superimposed. All the parallaxes have been taken from the Gaia DR2 catalogue. The standard deviation (STD), the weighted mean, and the median of the LDB sample are also displayed.

4.2. Distances from parallaxes

One of the innovations of this work is the inclusion of individual distances for each object. The conversion of d = 1/ϖ might not be used to assess the distance and to deal with this issue. Previous works (see Maíz Apellániz 2005; Bailer-Jones 2015; Luri et al. 2018) suggested that we derive distances as an inference problem using a Bayesian approach. Thus, we inferred the distance of each source individually, drawn from the parallax using the Kalkayotl code (Olivares et al. 2020) after 10 000 iterations. We tested all prior families (see Olivares et al. 2020) and found that the Gaussian prior proves to be the one most suited to describe the parallax distribution. The Gaussian prior is defined by two parameters: the +priorloc+ and the +priorscale+. The +priorloc+ is the open cluster distance value taken from Gaia Collaboration (2018b) or Cantat-Gaudin et al. (2018a) and the +priorscale+ is five times the maximum radius of the open cluster (Olivares et al. 2020).

We assumed the same prior for all objects belonging to the same stellar association. For each open cluster, we calculated the maximum radius using the comparison lists, comparing their sky-positions with the sky-position of the centre derived from Gaia Collaboration (2018b) (priv. comm. F. van Leeuwen). On the other hand, in the MGs, the members are distributed in a wide range of distances without being grouped or ‘clustered’ in a particular area of the sky. For instance, BPMG members are located between 9 and 73 pc, THMG members between 36 and 71 pc (see Malo et al. 2013) and 32 Ori MG members between 71 and 131 pc (see Bell et al. 2017). We chose the median value of the distance for the +priorloc+, and a +priorscale+ of 200 (roughly two times the larger distance). In Table E.1 we show the priors used in the calculations.

We obtained a distance distribution for each source where the maximum-a-posteriori describes the distance of the object (dMAP), and the two values at the 2.5th and 97.5th percentiles determine its minimum and maximum distances (dmin and dmax).

For those objects without parallaxes or with negative values, we assumed the distribution corresponding to the association they belong. The parallax is the mode of the PDF, ϖmode, and the uncertainties are the values at the 2.5th and the 97.5th percentiles. We calculated the distances and the uncertainties by taking the reciprocal of the parallax values. Regarding 32 Ori MG, we proceeded differently. We took all the members from Bell et al. (2017) and calculated the parallax PDF. In this way, we realized that several sources are outliers, and we considered a sub-sample of objects with parallaxes in the range of ϖ ∈ (8.0, 11.0) mas. We used this sub-sample to derive the 32 Ori MG distance. We did not apply this procedure to BPMG and THMG due to the wide range of parallaxes of their members.

Other works, such as that of Lodieu et al. (2019b), determine parallaxes for the faintest Hyades objects. We computed distances from these parallaxes in the same way as before, by using the same prior (see Table E.1). Table 2 lists the values of the parallaxes (mode, KDE), the percentiles, and the derived distance with its uncertainties for each analysed stellar association.

4.3. Bolometric luminosities and effective temperatures

The bolometric luminosity and effective temperatures were evaluated reconstructing the spectral energy distribution (SED) of each analysed source. To do this, we relied on the several photometric bands in order to have a complete coverage of the stellar spectra in a broad range of wavelengths. We used the data of the photometric surveys listed in Sect. 3.3.

The SED was built using the VOSA tool (Bayo et al. 2008). In a first step, VOSA brings together all the photometric values of each source and transforms the magnitudes into fluxes. The total observed flux is computed adding all the photometric bands. When measurements of overlapping bands are taken, VOSA estimates the overlapping wavelength regions and weights the fluxes accordingly to avoid overestimating the total flux. In addition, each photometric value is de-reddened taking into account the values of AV8 and the extinction law from Indebetouw et al. (2005). Secondly, VOSA compares the flux values with synthetic photometry from several grids of theoretical spectra, using a χ2 test and determines which model reproduces the observed data. Thirdly, the best-fitting model infers the flux in the wavelength range where there are no data, calculates the final total flux for the source (Ftot), its uncertainty (Ferr), and its stellar parameters with their respective uncertainties. Blue and infrared excesses are not taken into account, and the analysis does not include UV or u bands.

We used two sets of theoretical models to fit the SEDs: Kurucz (Castelli et al. 1997) and BT-Settl (Allard et al. 2013) grids. Both grids and the range of validity of each one have been studied before (see Bouy et al. 2015; Barrado et al. 2016; Bayo et al. 2017; Solano et al. 2019, 2021). We restricted the parameters to: Teff ≥ 4500 K for Kurucz models and Teff ≤ 4500 K for BT-Settl, where they work best. We fixed the metallicity to the value of each association, see Table 1, and the surface gravity to the fair value of log g = 4.5 dex, except for the Hyades members where we assumed log g = 5.0 dex. This assumption is in line with the BT-Settl evolutionary models (Allard et al. 2012): very low-mass stars with masses from 0.006 to 1.4 M and ages between 10 Ma to 1 Ga, have log g ∈ [4.4, 5.3] dex. From an empirical point of view, Reid & Hawley (2005) pointed out that the values for M0–M5 spectral types are ranged log g ∈ [4.5, 5.0] dex. Based on our previous experience with VOSA, we fixed these values to explore the effective temperature range more effectively9. A large number of photometric bands, as well as the wide spectral range they cover, allows us to say that the vast majority of the Ftot from the object comes from observations (≥70%) and not from any model. We checked all the SEDs to detect and avoid spurious photometric bands, false detections, or contamination due to background sources. We fitted a cubic spline over the five best models, minimizing the χ2 in order to avoid the discrete values in Teff returned by VOSA (Barrado et al. 2016). The analysis of the uncertainties on our calculated bolometric luminosities and effective temperatures, as well as the assumed values for metallicity, surface gravity, and reddening, are discussed in Sect. 6.

We calculated bolometric luminosities using Lbol = 4πd2Ftot, where Ftot is the total observed flux obtained from VOSA, and d is the distance of the object. In the case of sources with parallaxes, we calculated bolometric luminosities generating a Gaussian random sample of Ftot considering its uncertainty Ferr, and using its distance distribution as we mentioned in Sect. 4.2. The maximum-a-posteriori of this distribution is the Lbol and the 2.5th and 97.5th percentiles determine its uncertainties.

4.4. LDB loci determination

Previous works (Jeffries & Oliveira 2005; Juarez et al. 2014 or Binks & Jeffries 2014) have defined the LDB loci in the HRD, (Teff LDB, Lbol LDB) as the mid-point between the coldest lithium-poor source and the hottest lithium-rich one (in terms of effective temperature) and the faintest lithium-poor source and the brightest lithium-rich one (in terms of bolometric luminosity).

Using the LDB samples defined previously, we discarded all the non-members (NM) using the Gaia data and confirmed multiple systems (hereafter CMS, such as spectroscopic binaries) that contribute to blur the LDB for this analysis. We took the faintest lithium-poor object and considered all the sources whose bolometric luminosities were in the interval between Lbol 97.5th and Lbol 2.5th. Likewise, we did the same for the brightest lithium-rich object. Some objects can be considered as multiple systems because of their location in the HRD or analogous diagrams. However, there is no explicit confirmation of whether they are10. In this case, we have performed the LDB analysis considering both cases: (a) assuming it is a single star, (b) or it is a multiple system and was excluded in the determination of the LDB.

Applying this procedure, we obtain (for any stellar association) a sample of n-sources close to the LDB locus. In some cases (IC 2602, Blanco 1), we can select only two sources, a lithium-poor and a lithium-rich one, and this is insufficient for the analysis. We would require at least two lithium-poor sources and two lithium-rich ones. Thus, the resulting sub-samples should have at least four sources.

To estimate the LDB and quantify the uncertainty associated, we used a jackknife method with a bootstrap re-sampling. We split the sub-sample of n sources into n sets containing all but one source: the first set contains all but source 1, the second set contains all but source 2, and so forth. For each set, we generated 10 000 simulated bootstrap samples. A bootstrap sample contains n − 1 bolometric luminosities, one from each source. They were generated using a Gaussian random value of the Ftot considering its uncertainty ΔFtot, and a random value of the distance derived from its distribution (Sect. 4.2).

We calculated the LDB luminosity as the equal middle point between the bolometric luminosity of the faintest lithium-poor object and the brightest lithium-rich object. The result is a bolometric luminosity distribution of the LDB loci obtained from all the simulations, where the LDB is located at the mode, and the uncertainties are given at 16th and 84th percentiles, as we show in Fig. 5. Finally, we derived ages using the evolutionary models presented in Sect. 3.4. Also, we determined the Teff LDB as the mid-point in terms of effective temperature between the coldest lithium-poor source and the hottest lithium-rich one. We estimated an uncertainty due to the models of ±71 K based on the mean squared error of the two sources. As an example, we show in Fig. 6 the HRD for Alpha Persei with the LDB sample, the comparison sample, and our estimated Lbol LDB. Similar figures for the remaining stellar associations are shown in Appendix A.

thumbnail Fig. 5.

Bolometric luminosity PDF for the Alpha Persei LDB, after run 60 000 bootstrap samples, see Sect. 4.4. We show all the sample distribution as a blue histogram, and we model a PDF with all the values in grey. We highlight the mode of the PDF with a red line and the percentiles at 16th and 84th with two red dashed ones.

thumbnail Fig. 6.

HRD and the LDB for Alpha Persei. Left: symbols are as follows: green solid circles are lithium-rich sources and magenta triangles lithium-poor ones, both from our LDB sample; empty large broken black circles are suspected multiple systems; over-imposed big black crosses are sources discarded as members after this work; and grey points are known members from Gaia Collaboration (2018b). Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 80 Ma. The figure also includes 70 Ma isochrones from: D’Antona & Mazzitelli (1994; black dashed line), Tognelli et al. (2011; orange dashed dot line), Siess et al. (2000; red dotted line), and a Zero Age Main Sequence from Stahler & Palla (2005; the green solid line). Right: zoom on the left plot. A black horizontal line marks the Lbol LDB, together with the 16th and 84th percentiles (dotted lines). Alpha Persei is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). For clarity, members from Gaia Collaboration (2018b) are not shown.

5. Analysis of the LDB

In the following subsections, we analyse in detail each stellar association and locate its LDB. We apply the method presented in Sect. 4. The results are summarised in Table 3 and Fig. 7.

thumbnail Fig. 7.

Location of the LDB for all studied stellar associations and its relation with the age. We show bolometric magnitudes of the LDB for each stellar association as horizontal lines (several colours). Uncertainties are not shown for clarity. The lines that cross diagonally from the lower left corner to the upper right one correspond to different LDB models: the dashed black line is the D’Antona & Mazzitelli (1994) LDB, the dashed dotted brown thicker line is the Burrows et al. (1997) LDB, the dashed dotted green thinner line is the Burke et al. (2004) LDB, the dotted red line thicker corresponds to the Pisa LDB (Tognelli et al. 2015), the dotted red line thiner correspond to the Siess et al. (2000) LDB and the blue line is the BT-Settl LDB (Allard et al. 2013).

Table 3.

LDB loci in terms of Lbol, Teff and the ages derived using several evolutionary models.

5.1. Alpha Persei

We collected sources from former works around the LDB (with Ks > 12.0 mag). In total, our compilation includes 17 sources: nine without lithium and six with it, from Stauffer et al. (1999) (first work with a complete census of members around the LDB); one with lithium, AP270, from Basri & Martín (1999a) and one without lithium, AP272, from Zapatero Osorio et al. (1996).

Photometric data from previous works were used: RcIcKs (Stauffer et al. 1999; Barrado y Navascués et al. 2002), and F814W and F785L from the Hubble Space Telescope (Martín et al. 2003). In addition, we recovered VIc from Prosser (1992, 1994), and RcIc from Deacon & Hambly (2004). All the sources have parallaxes and proper motions in Gaia DR2.

Stauffer et al. (1999) included remarks about some sources: AP317 could be a background star or a possible member; AP322 (2MASSJ 03330848+4937550) is likely to be a non-member; and AP323 and AP325 could be binary systems.

The proper motions (Fig. 3) and parallaxes (Fig. 4) suggest that AP310 at 7.518 mas and AP317 at 11.573 mas, are foreground objects that do not belong to Alpha Persei, whereas we confirmed that AP322 is a background source with ϖ = 4.083 ± 0.426 mas. AP272 looks like a foreground object, 6.389 mas, but its proper motion could agree with the rest of the members. Its position on the HRD does not affect the LDB locus. AP313 shows a discrepant proper motion but a parallax (5.419 mas) consistent with the members from the comparison sample, so we considered it as a non-member. Lastly, Stauffer et al. (1999) surmised that AP325 was a binary system, and we considered it as a suspected multiple system due to its HRD location (Fig. 6).

Stauffer et al. (1999) located the LDB with the sources AP323 (lithium-rich but probably a binary system), AP310 (lithium-poor) and AP300 (lithium-rich), and they estimated a Mbol LDB = 11.40 mag (Lbol LDB = 2.168 × 10−3L). However, Barrado y Navascués et al. (2004) assume that the LDB is defined by AP310, AP322, and AP300 and located the LDB at Mbol LDB = 11.31 mag (Lbol LDB = 2.355 × 10−3L). With the new analysis, we located the LDB at L, and Teff LDB = 2 857 ± 71 K (see the HRD in Fig. 6).

Although we considered AP323 and AP325 as suspected binaries, they may play a vital role in the LDB loci, therefore it would be necessary to study their multiplicity more reliably.

5.2. NGC 1960 (M 36)

We created the LDB sample collecting 32 members from Jeffries et al. (2013). We used gri photometric data from Jeffries et al. (2013), and from our database (Galindo-Guil et al., in prep.). The source 4165 is the only one without a counterpart in Gaia DR2. Candidate members identified as 3028, 3590, and 3596 have counterparts, but lack parallaxes and proper motions, and the source 3081 possesses negative parallax. Jeffries et al. (2013) point out that 3080 shows evidence of being a binary system, and 3081 (the brightest object with lithium) could have depleted the ∼99% of its initial lithium content.

From the VPD (Fig. A.1 left), we considered as non-members 2188, 2249, 2663, 3080, and 3150. Other sources, namely, 1859, 1871, 2696, and 3073, are inside the bulk of the confirmed members by the narrowest of margins. We discarded 1269, 1859 and 2703 in the location of the LDB, because lie outside the percentiles of the parallax PDF (see Fig. A.1 right). We note that 2171 is almost outside the percentiles of the parallax PDF, and 3612 possesses a large parallax uncertainty; 3081 has negative parallax, and the bolometric luminosity was calculated based on the distance derived from the comparison sample.

We note that the abrupt transition between lithium-poor and lithium-rich objects is not visible in NGC 1960, (see the HRD in Fig. A.2a), and compared with other stellar associations (see Sects. 2.3, 2.4 and subsequent sections). Jeffries et al. (2013) locate the LDB with three lithium-rich objects: 3080, 3081, and 3596 at L. However the combination of undetected binary systems, photometric uncertainties and contamination, prevented them to detect a reliable LDB loci. Two out of the three lithium-rich sources, 3596 and 3081, do not have individual parallaxes in Gaia DR2, so we assumed the mean distance to the cluster (see Table 2), and we considered 3080 as a non-member because of its proper motion.

The scarcity of lithium-rich sources and the poor astrometric quality of the data (due to the faintness of the sources) did not allow us to derive a bona fide LDB age. In any case, we proceeded in the same way as we did with Alpha Persei. We located the LDB at L, and Teff LDB = 3 123 ± 71 K, see Fig. A.2a. However, if we consider the three lithium-rich objects (3080, 3081 and 3596) as multiple systems and discard them, then the faintest lithium-poor source, 4165, gives an upper limit in the LDB location at Lbol LDB < 16.27 × 10−3L and at Teff LDB < 3016 K (see Fig. A.2b). This object would push the minimum age to Ma. (see Fig. A.2b).

NGC 1960 needs a deeper photometric survey followed by a spectroscopic study to determine lithium abundances in fainter objects than our LDB sample. This is because the abrupt transition between lithium-poor and lithium-rich objects is not visible in contrast to other associations. Our LDB loci might be a tentative one, and we do not discard the possibility that it could be a possible upper limit.

5.3. IC 4665

We recovered data from different works: 39 members from Manzi et al. (2008), 13 members from Prosser (1993) and Jeffries et al. (2009) and 15 members only from Jeffries et al. (2009). All sources from Manzi et al. (2008) and some from Jeffries et al. (2009) have been detected previously in Prosser (1993), Giampapa et al. (1998) and de Wit et al. (2006). Manzi et al. (2008) did not provide equivalent widths of lithium for their faintest members, they highlighted the presence or absence of lithium and classified them in three categories: ‘Y’ for a lithium-rich source, ‘N’ for a lithium-poor one, and ‘?’ when the signal-to-noise ratio did not allow to confirm or reject the presence of lithium. Our LDB sample comprises a total of 67 sources and all of them have counterparts in Gaia DR2. P333 (with lithium) and P373 (without lithium) lack parallax and proper motion measurements. In addition, we collected photometric data in filters ICFHT12 and zCFHT12 (de Wit et al. 2006) and VIc (Jeffries et al. 2009).

The proper motions are illustrated in Fig. A.3 and parallaxes in Fig. A.4. In terms of proper motions, we rejected: JCO1-530, JCO3-285, JCO3-357, JCO4-337, JCO9-120, P002, P030, P059, P065, P139 P215, P290, P331, P377, P398, and P411. Some objects lie outside the percentiles of the parallax PDF. Then, A.09.30.47, JCO4-337, P396, and P398 were considered foreground objects, while JCO1-530, JCO2-213, JCO3-285, P002, P059, P065, P139, P215, P290, P331, and P377 were taken as background sources; P344 is on the borderline of the bulk of the proper motions but we still considered it as a member.

P065, P290, P313, and P315 show variable radial velocities or evidence for a double line system, or both (Manzi et al. 2008); consequently, we considered them as multiple systems. We note that P344, as in the case of P313, could be a multiple system because both share close positions in the HRD (see Fig. A.5) and have similar parallax values, so it is considered a suspected multiple system. A.09.30.14 and P238 are marked as ‘?’ in Manzi et al. (2008) and their lithium detection is uncertain. Then, P372 and P344 are marked as ‘Y?’ (Manzi et al. 2008) and we treated them as lithium-rich objects.

Manzi et al. (2008) locate the LDB between the sources P350 (lithium-poor) and P338 (lithium-rich) at L. We located the LDB by considering two different scenarios. In the first one, we considered P344 as a single source (Fig. A.5c), while the second scenario, we considered P344 as a suspected multiple system (Fig. A.5d). In the first scenario, we located the LDB at L and Teff LDB = 3110 ± 71 K, while the second scenario resulted in L and with equal Teff LDB. For this open cluster, we decided to apply this second scenario.

We remark that the four objects, A.09.30.14, P238, P372, and P344, located around the LDB, must be studied in detail with high-quality spectra to determine their lithium abundances. Also, it would be interesting to have parallaxes for P333 (with lithium) and P373 (without lithium).

5.4. NGC 2547

We took the sample of 52 radial velocity members from Jeffries & Oliveira (2005) as our LDB sample. We collected photometric data in BVIc filters from Naylor et al. (2002), RcIcZ from Jeffries et al. (2004) and the Spitzer photometric bands 3.6 μm, 4.5 μm, 5.8 μm 8.0 μm, and 24 μm from Gorlova et al. (2007). All the sources have counterparts in Gaia DR2 with parallax and proper motion measurements.

Jeffries & Oliveira (2005) identified six possible multiple systems: JO-21, JO-27, JO-30, JO-31, JO-39, and JO-56. In addition, three of them, (JO-27, JO-30, and JO-31) together with JO-26, are lithium-rich objects located at brighter luminosities than the LDB (see Figs. 5–7 from Jeffries & Oliveira 2005). So, JO-26 could be an unresolved multiple system, and it was excluded from our calculation.

The analysis of the proper motions and the parallax distribution (see Fig. A.6) allowed us to affirm that JO-26 and JO-30 are non-members; JO-27 and JO-31 could be multiple systems or fast rotators. We note that JO-62 has a very high uncertainty in proper motions; and JO-02, JO-07, JO-37, JO-45, and JO-57 are near the borders of the bulk of previous members. Overall, the objects that we considered as non-members based on proper motions are JO-26 and JO-30; those based on parallaxes: JO-45, JO-57, and again JO-30.

Jeffries & Oliveira (2005) located the LDB at L. We located the LDB at L and Teff LDB = 3004 ± 71 K (see Fig. A.7).

5.5. IC 2602

We selected 14 sources from Dobbie et al. (2010). Six of them are lithium-rich objects and six are lithium-poor. Dobbie et al. (2010) considered two objects: 10420419-6404236 and 10443357-6415455 as possible members, and the rest as bona fide members. From Dobbie et al. (2010), we have recovered photometric data in the band Ic/IwpESO845. However, we did not use them in our SED fitting, given the large uncertainties in their photometric values, as the authors pointed out. All the sources have a counterpart in Gaia DR2, but 10452984-6444543 lacks parallax and proper motions.

10443357-6415455 is considered as possible member by Dobbie et al. (2010) and we confirmed that it is a background object due to its parallax (see Fig. A.8 right). Then, 10370251-6444416 can also be considered as a background object. Besides, Dobbie et al. (2010), suggest that two sources could be binary systems or young interlopers due to their positions above the cluster sequence in the colour-magnitude diagram, and with clear lithium detections: 10452984-6444543 and 10391188-6456046. The position of 10391188-6456046 in the HRD (Fig. A.9) indicates that it may be an equal-mass binary system. 10452984-6444543 is detected in Gaia DR2 but without astrometric solution, for this reason and taking into account its HRD position, we suggest that it is a suspected multiple system. We note that Gaia DR2 has revealed that this source has a fainter background counterpart, 5239800972309874176, located at 1.8″, with a parallax of 0.6386 ± 0.5577 mas. The fact that it is only identified in Gaia DR2 suggests that the photometric data released in previous surveys are a combination of two sources. Finally, 10452984 and 10391188 are two suspected binaries that need solid confirmation about their multiplicity. Dobbie et al. (2010) located the LDB between 10430890-6356228 and 10430236-6402132, at MJ = 8.26 ± 0.23 mag (L). We located the LDB at L and Teff LDB = 2926 ± 71 K.

5.6. IC 2391

We collected a total of 28 sources from our previous works (Barrado y Navascués et al. 1999a, 2001, 2004; Boudreault & Bailer-Jones 2009). We added some objects to the LDB sample: CTIO-106, CTIO-202, and CTIO-205, which are members but lack lithium feature measurements because the low-quality spectra do not allow us to discern the presence or absence of it (Barrado y Navascués et al. 2004). We used our photometric data VRcIcZ from Barrado y Navascués et al. (2001) and we collected VRcIc from Patten & Pavlovsky (1999). All the sources have a counterpart with proper motions and parallaxes in Gaia DR2. Our membership criterion is in contrast to that of Boudreault & Bailer-Jones (2009), who considered as members objects without the Hα line in emission: 20-001, 20-009, 20-024, and 20-029. Below, we will see that these sources can be considered outliers due to their parallax, proper motions, or both. Furthermore, they suggest that values of EW Li < 0.1 Å, as it happens with 20-009 and 20-014 (see their Table 6), indicate the presence of the lithium feature at 6708 Å. However they do not provide a reliable measurement of the equivalent width. In the same way, we go on to see that these sources are outliers.

From Barrado y Navascués et al. (1999a); Barrado y Navascués et al. (2004), we collected some remarks about some objects: PP-07 and CTIO-206 could be possible binaries or outliers; CTIO-062 is a lithium-rich source (also studied in Boudreault & Bailer-Jones 2009 with name 20-022); the lithium detection of CTIO-077 is quite uncertain (Barrado y Navascués et al. 2004), but we considered it as a lithium-rich object.

We confirmed two foreground objects: PP-07 and 20-024, along with eight background sources: CTIO-017, CTIO-059, 20-001, 20-009, 20-012, 20-014, 20-018, and 20-029 (see Fig. A.10 right). We show the proper motions from IC 2602 and IC 2391 LDB samples in the same VPD, Fig. A.10 left. There are ten sources that we considered as non-members because they are far away from the bulk of the members: 20-001, 20-009, 20-012, 20-014, 20-018, 20-024, 20-029, CTIO-017, CTIO-0 59, and PP-07; these are the same objects that are not members in terms of parallaxes. We note that there is a crowded region in the VPD around μα ⋅ cos(δ) = − 12.9 and μδ = 11.5 mas yr−1, with six sources: PP-07, CTIO-017, 20-001, 20-017, 20-018, and 20-029.

In addition, CTIO-062 (20-022), a lithium-rich member (Barrado y Navascués et al. 2004; Boudreault & Bailer-Jones 2009), has proper motions and parallax similar to other members, as well as Hα in emission, but it is located below the cluster sequence in the HRD. It shows a fainter bolometric luminosity than other members with the same effective temperature, so it could be an outlier. The objects without measurements of the lithium feature (CTIO-106, CTIO-202, CTIO-205, and 15-005) are not relevant in the LDB determination, except for CTIO-205 that could be a multiple system due to its position in the HRD. CTIO-081 could also be a multiple system (see the HRD, Fig. A.11). According to Boudreault & Bailer-Jones (2009), the lithium-poor M7.5 dwarf 15-005 fulfils our membership criteria, but due to its position in the HRD and its spectral type, it would be expected to have lithium. The reason for the non-detection is the low signal-to-noise ratio of the spectrum (S/N = 8.3). We considered this object a member with doubtful detection, although it does not affect the LDB location. Lastly, CTIO-077, a member with an uncertain lithium detection (Barrado y Navascués et al. 2004), considered as a lithium-rich object, is not key in the determination of LDB loci.

Barrado y Navascués et al. (1999a) located the LDB between the sources PP-14, CTIO-096, and CTIO-038 at Mbol LDB = 10.29 mag (Lbol LDB = 6.026 × 10−3L). Subsequently, Barrado y Navascués et al. (2004) located the LDB at Mbol LDB = 10.24 mag (Lbol LDB = 6.31 × 10−3L). We located the LDB at L and Teff LDB = 2956 ± 71 K.

5.7. The Pleiades

We selected 35 sources from different works: Marcy et al. (1994), Rebolo et al. (1996), Oppenheimer et al. (1997), Stauffer et al. (1998b,a) and Dahm (2015), together with photometry and lithium quantities from the DANCe database (Bouy et al. 2015; Barrado et al. 2016 and other works: Steele et al. 1993; Bouvier et al. 1998; Zapatero Osorio et al. 1999; Martín et al. 2000; Stauffer et al. 2007). With the exception of Roque 5 and Roque 25, the rest of the sources have a counterpart in the Gaia DR2 catalogue; and with the exception of CFHT-Pl-18 and MHObd 3, all the sources have parallaxes and proper motions11.

Olivares et al. (2018) studied the probability of a source being an equal-mass binary and eight sources fulfil their criterion: HCG 509, HHJ 6, HHJ 3, PPL-15, PPL-15, Roque 13, MHObd 3, CFHT-Pl-12, and CFHT-Pl-16. Some of these sources are confirmed binary systems: CFHT-Pl-12 (Bouy et al. 2006), CFHT-Pl-18 (Martín et al. 1998), PPL-15 (Basri & Martín 1999b), and HCG 509 (Stauffer et al. 2020). Others are possible suspected binaries: PPL-1 with a strong absorption lithium feature, HHJ-6 and BPL-169 (Stauffer et al. 1998b), and Roque 12 (which might be an eclipsing binary brown dwarf as suggested by Scholz et al. 2020, based on a single eclipse).

Martín et al. (2000) claimed that the lithium-rich source CFHT-Pl-16 could be an unresolved binary (with identical components) or it could be a non-member. PPL-14 was observed once during a flare event (see Table 1, Stauffer et al. 1995a). Dahm (2015) studied its radial velocity, compatible with the cluster, and its membership. We suggest that MHObd 3 is a suspected multiple system due to the absence of astrometric solution in Gaia DR2 and its position in the HRD (Fig. A.14a), as previously suggested Stauffer et al. (1998b). Two sources, MHObd 1 and MHObd 3, present low signal-to-noise ratio lithium detections (Stauffer et al. 1998b,a), which would indicate that they are brown dwarfs or, at least, transition objects that have burned most of its initial lithium. IPL 43 has a low signal-to-noise ratio spectrum near 6700 Å that precludes an assessment of the lithium equivalent width (Dahm 2015). Another significant aspect is the three lithium-poor objects studied by Martín et al. (2000): Roque 12 (spectral type M7.5), Roque 5 (M9) and Roque 25 (L0), all of them fainter than the LDB assumed by us (see the HRDs, Fig. A.14). This fact might be due to the low quality of the spectra.

From the parallax distribution, Fig. A.13, we discarded as members HCG 332, HCG 509, Calar 3, MHObd 1, and CFHT-Pl-12. About HCG 332 (HHJ 339) and HCG 509 (HHJ 430), Oppenheimer et al. (1997) suggested that they could simply be foreground weak-line T Tauri stars with the same proper motion and only a parallax measurement could make the membership assertion more certain. Thus, they are not members of the Pleiades as Stauffer et al. (2020) recently confirmed. CFHT-Pl-15, HCG 332, and HCG 509 have proper motions that are very different from the rest of the objects, as we show in Fig. A.12. Furthermore, HCG 509, HCG 332, CFHT-Pl-15, and CFHT-Pl-18 are non-members12 due to the low membership probabilities in the DANCe catalogue (Bouy et al. 2015; Olivares et al. 2018) and in the work of Stauffer et al. (2020). In short, we show all the remarks of each object in Table E.5.

Stauffer et al. (1998b) located the LDB with the sources CFHT-Pl-10 and CFHT-Pl-11, at Mbol LDB = 11.99 mag (Lbol LDB = 1.259 × 10−3L). On the other hand, Barrado y Navascués et al. (2004) located the LDB with the sources CFHT-Pl-09, CFHT-Pl-10, Roque 16 (CFHT-Pl-11), and Teide 2 (CFHT-Pl-13), at Mbol LDB = 12.14 mag (Lbol LDB = 1.096 × 10−3L). Dahm (2015) located the LDB at MJ = 9.73 ± 0.05 mag (L), assuming the distance from Melis et al. (2014). We located the LDB at L and Teff LDB = 2728 ± 71 K.

The lithium feature in Roque 5, Roque 12, Roque 25, and IPL 43 needs to be studied in more detail. MHObd 3 lacks astrometric solution in Gaia DR2 and requires a further study in terms of membership due to its position in the HRD (Fig. A.14) and its lithium content. MHObd 1 was considered a non-member based on its parallax, even though this one is not very different from the previous members. It likely belongs to the tidal tail of the Pleiades.

5.8. Blanco 1

We selected 15 sources: 9 members studied both in Cargile et al. (2010) and Juarez et al. (2014); 1 member studied only in Cargile et al. (2010) and 5 members only studied in Juarez et al. (2014). We did not find any counterpart to B1opt-6335 in any catalogue; consequently, our sample ultimately contains 14 objects. Five targets have lithium detection and the rest lack any. We took the coordinates for each source from Moraux et al. (2007) since it was not possible to find the counterparts using the coordinates from Juarez et al. (2014). We gathered photometric bands: Icz from Moraux et al. (2007), and BV from Cargile et al. (2009) for the object JC0-F18-88.

All the objects have a counterpart in Gaia DR2, except the faintest object CFHT-BL-49. Then, CFHT-BL-36 has a negative parallax, ϖ = −0.28 ± 1.35, and CFHT-BL-45 is detected in Gaia DR2 but lacks astrometric solution.

From the VPD, Fig. A.15 left, we discarded as members CFHT-BL-29 and CFHT-BL-36. We also note that sources CFHT-BL-38 and CFHT-BL-43 have large uncertainties; CFHT-BL-16, CFHT-BL-36, and CFHT-BL-38 have parallaxes outside the percentiles of the parallax PDF (see Fig. A.15) and we considered them as non-members. We note that although CFHT-BL-43 is within the parallax distribution, it has huge uncertainties. All the objects from Juarez et al. (2014) have a radial velocity within the range of 2 to 10 km s−1 in 3σ (see Fig. 4 from Juarez et al. 2014), however, some objects are not within this range in 1σ. Under this criterion, CFHT-BL-22, CFHT-BL-25, CFHT-BL-29, CFHT-BL-36, and CFHT-BL-45 fall into the category of non-members. Lastly, we note that CFHT-BL-22 shows lithium in its spectrum even though it is hotter and brighter than other lithium-poor objects (beyond effective temperature and bolometric luminosity uncertainties). It fulfils the proper motion, distance membership criterion and, according to Juarez et al. (2014), it is currently depleting lithium.

Cargile et al. (2010) delimited the LDB between CFHT-BL-24 and CFHT-BL-38, at . Juarez et al. (2014) used the sources CFHT-BL-22 and CFHT-BL-38 to establish the LDB boundaries, so the updated Blanco 1 LDB is located at (L). We located the LDB at and Teff LDB = 2746 ± 71 K (see the HRD, Fig. A.16b). If we discarded those sources whose radial velocities are not within the range proposed by Juarez et al. (2014) in 1σ (see text above and Fig. A.16c), we located the LDB at and Teff LDB = 2746 ± 71 K. We consider the last criterion because it contains the cleanest sample. There are few objects around the LDB and it would be interesting to perform a monitoring process with a wealth of objects.

5.9. The Hyades

We gathered 34 sources from different works: 12 sources from Hogan et al. (2008), from which 6 have a spectrum to determine if they are lithium-rich objects (Martín et al. 2018); 1 source from Pérez-Garrido et al. (2017), the L5 lithium-rich brown dwarf 2MASS J04183483+2131275 (2M0418, Lodieu et al. 2018) and 21 sources from Bouvier et al. (2008), of which only CFHT-Hy-10, CFHT-Hy-11, CFHT-Hy-12, CFHT-Hy-13, CFHT-Hy-19, CFHT-Hy-20, and CFHT-Hy-21 have spectra, but do not cover the lithium feature. It is important to note that Hya10 is not considered a definitive lithium-rich object in Martín et al. (2018) due to its poor detection. Nevertheless, we studied both situations, lithium-rich and lithium-poor object, intending to examine the location of the LDB and possible variations. In short, there are only lithium measurements for 7 objects. From our selection, Hya09, Hya10, Hya12, 2M0418, CFHT-Hy-20, and CFHT-Hy-21 do not have a counterpart in Gaia DR2, whilst, Hya02, Hya04, Hya05, Hya07, Hya11, and CFHT-Hy-16 do have a counterpart but lack proper motions and parallaxes due to their faintness.

We collected additional data from different works: proper motions and distances from Hogan et al. (2008); photometric bands IzJHK and proper motions from Bouvier et al. (2008); photometric data in the J band, proper motions and distances from Lodieu et al. (2014); proper motions from Pérez-Garrido et al. (2017); spectrophotometric distances calculated using the photometry from Martín et al. (2018); and ground based parallaxes and proper motions from Lodieu et al. (2019b).

We considered in our study CFHT-Hy-19 (19 in Fig. A.17) and CFHT-Hy-20 (20 in Fig. A.17) as foreground sources. In addition, we noted that CFHT-Hy-21 (21) and Hya11 have large uncertainties. We did not rule out any source from the VPD because all sources fall within the bulk of previous members.

On the question of distances and parallaxes, different works carried out calculations with different approaches: spectroscopic distances based on an absolute magnitude versus spectral type relationship (Lodieu et al. 2014; Pérez-Garrido et al. 2017; Martín et al. 2018), or from the proper motion of the object and the cluster velocity (see Eq. (3) from Hogan et al. 2008). We followed the same method that we used before for the open clusters with the Gaia DR2 data (see Sect. 4.3). We show all the information in Appendix E.

Martín et al. (2018) located the LDB between the lithium-poor Hya11 and the lithium-rich sources Hya09 and Hya12 at L They calculated bolometric luminosities of the sources assuming calibrations for field L dwarfs to avoid any dependence on the distance. Later, Lodieu et al. (2018) added the lithium-rich source 2M0418 and locate the LDB at L. We located the LDB at L, and Teff LDB = 2021 ± 71 K (see Fig. A.18b). If we considered that Hya10 is not a lithium-rich object (see text above), the LDB location does not change, only the uncertainties change slightly: L (Fig. A.18c).

The Hyades is the only stellar association whose LDB is placed at L spectral types. Another fact is that all sources except 2M0418 does not have the Hα feature in emission. It would be interesting to study whether this effect takes place in L spectral type objects in younger associations and establish whether it can be an indicator of age.

5.10. Beta Pictoris moving group

We took a sample of 127 sources, all M dwarfs, collected from Shkolnik et al. (2017). This work is our starting point because it gathers information about multiple systems, possible outliers, and equivalent widths of the lithium feature. We cross-matched the 127 sources with Gaia DR2, by visual inspection using ESASky.

Our final LDB sample contains 138 sources. Some of them have several counterparts associated in the Gaia DR2 catalogue, and they may be multiple systems. In some cases, the multiple system is only well resolved in Gaia DR2 (with individual parallaxes, proper motions and photometric bands), for instance, 20085368 (Fig. 8). Consequently, the object is a merge of several sources and its stellar parameters are affected. These objects are considered multiple systems in our study (marked as ‘CMS’ in Table E.5). In others, the initial source has several associated background objects, and they might contaminate the photometry of the main object, for instance, 18420438 (Fig. 8). We can also have a combination of both cases: a multiple system only well resolved in Gaia with several associated background objects, for instance, 05015881 (Fig. 8) or 03393700. The photometric data are probably blended and could have erroneous stellar parameters. We marked them as contaminated photometry (CP) in Table E.5. Finally, we searched other works to identify additional multiple systems in our LDB sample: Mason et al. (2001), Beuzit et al. (2004), Bergfors et al. (2010), and successive references.

thumbnail Fig. 8.

2MASS RGB images of three remarkable sources belonging to BPMG. The main source, 2MASS catalogue, is shown with a purple cross, the Gaia DR2 counterparts are shown with green squares and proper motions- with cyan dotted lines. Top: 20085368 is a binary system resolved with Gaia DR2. Medium: 18420438 is a source whose photometry may be contaminated by a background source. Bottom: 05015881 is a binary system whose photometry is resolved in Gaia DR2 and there is a very close background source.

Only three sources, (01112542, 03323578, and 0524191413) do not have a counterpart in Gaia DR2 and nine lack astrometric solutions. All the information related to binary, multiple systems, and background sources associated with any object that belongs to our LDB sample is shown in the Appendix C.

The members are sparse and spread over the sky, located between 9–73 pc (Malo et al. 2013), so there is not any over-density in the sky and we cannot discard any member based on their VPD. Initially, we did not discard any source based on their parallaxes. Nevertheless, some of them might be outliers because they have significantly smaller parallaxes than other members: 03255277, 03370343, 11493184, 15063505, and 18435838.

We show in the HRD, Fig. A.19, that most of the sources follow the main sequence and recognise the region delimited by the lithium-poor sources. The faintest ones give an idea of the suspected LDB, which is illustrated in Fig. A.19b. There may be several explanations of why a lithium-rich source lies above the single star locus in a HRD, (e.g. multiplicity, high rotational velocities, or activity) and there is an explanation of why a lithium-poor source lies below the single star locus: it is probably a field star, older than the association (a non-member). There are six lithium-poor objects below the main sequence; three of them are: 01365516, 05363846, and 23512227, which are located at fainter bolometric luminosities than the suspected LDB and they might be non-members. In contrast, the distribution of lithium-rich sources along the main sequence is blurred. After discarding multiple systems and sources with possible contaminated photometry (see Fig. A.19b), we identified eight lithium-rich sources brighter than the suspected LDB: 05082729, 20333759, 00501752, 17173128, 18030409, 02450826, 18011345, and 05061292. Two of them have undergone high activity periods: 05082729 with Lx/Lbol = −3.19 and 2033375914, with Lx/Lbol = −3.15 exhibited a strong X-ray to bolometric luminosity (Messina et al. 2017) and the multi-epoch radial velocity measurements (see Malo et al. 2014b) have ruled out its binary nature. This object suffered a flare with a magnitude increase of ΔV = 3.29 mag. The rest of sources are above the suspected LDB, three with Lbol ∼ 50–60 × 10−3L (00501752, 17173128, and 18030409) and the other three with Lbol ∼ 30 × 10−3L (02450826, 18011345, and 05061292). We may need further analysis to find out if they are outliers or if their positions are related to other effects, for instance, multiplicity.

Song et al. (2002) located the LDB between the lithium-poor WW PsA (22445794) and the lithium-rich Tx PsA (22450004), with both sources constituting the wide binary system HIP 112312, at . Binks & Jeffries (2014) located the LDB as a rectangular region separating lithium-poor from lithium-rich sources in several colour-magnitude diagrams and calculated from the position of the central points of the boxes at . Malo et al. (2014b), using a maximum likelihood method for determining the LDB in terms of bolometric luminosity, located it at log(Lbol LDB/L) = − 1.49 ± 0.08 (). Finally, Shkolnik et al. (2017) added new members and refined the LDB age (following the same procedure as Kraus et al. 2014 in THMG; see Sect. 2.11), but these authors did not find a clear gap in luminosities where there are lithium-poor and lithium-rich objects, They identified the LDB at MK LDB = 5.6 ± 0.4 mag, at , where there are an equal number of lithium-poor and lithium-rich sources, with eight stars in each group.

We located the LDB at and Teff LDB = 3095 ± 71 K, using the following sources: 20083784, 00482667, 00193931, 18092970, 22450004, 22085034, 04480085, 04480258, 00194303, 23314492, 01303534, 05061292, 18011345, 21200779, 02450826, 21384755, 20333759, 05015665, 19300396, 05082729, 01351393, 22445794, 17173128, 02175601, 13215631, 18030409, 00501752, 05335981, 18055491, 21100535, 06131330, and 18151564, (see Fig. A.19c). However, if we take into account the faintest lithium-poor sources, we can locate the LDB at and Teff LDB = 2986 ± 81 K, see Fig. A.19d. In this scenario, we discarded all the lithium-rich sources above the suspected LDB. All of them are bona-fide members, but two sources undergone high activity periods and the rest could be considered as multiple systems (see previous paragraphs). In this case, the LDB locus is located at cooler effective temperatures and fainter bolometric luminosities ΔLbol = 25.35 × 10−3L, which leads to a 7 to 10% Ma age variation. A comparison of both criteria reveals a difference in the LDB locus of a 119% in terms of bolometric luminosity and a 36% in terms of effective temperature. We decided to use the first scenario because there is no reason to rule out the lithium-rich sources.

In addition, several blended objects require actual bolometric luminosity and effective temperature estimations. In addition, there are nine lithium-rich objects in the HRD region where lithium content should have been depleted: 02272804, 02450826, 00501752, 18011345, 17173128, 18030409, 05061292, 05082729, and 20333759, so further data are required to determine exactly how the multiplicity or activity in the X-Rays domain (or, perhaps, erroneous membership classification) might be associated with this effect. Due to the proximity of these objects, the quality of the astrometric parallax is quite good. A new membership assignment using excellent astrometric and spectroscopic data as Miret-Roig et al. (2020) for less massive objects might resolve this jigsaw puzzle.

5.11. Tucanae-Horologium moving group

We collected a total of 110 sources with parallax measurements from Gaia DR2, all of them confirmed as members, with spectral type M and lithium information taken from Kraus et al. (2014). We have followed the same criteria as them to determine whether the object is lithium-rich or not: one lithium-rich object has EWLi > 0.100 Å and one lithium-poor object has EWLi < 0.100 Å. We gathered all the photometric data through VOSA.

There are two binary systems confirmed through spectroscopic data (Kraus et al. 2014): 020701764406380 and 045153034647309. We deemed these objects as multiple systems, marked as ‘CMS’ in Table E.5. Two sources deviate in the HRD (Fig. A.20): 03050976-3725058 (5.465 mas, 178 pc) and 21354554-4218343 (0.735 mas, 563 pc), they are located quite above the rest of sources, so we considered them as non-members. The source 22444835-6650032 might be a multiple system due to its position in the HRD. Other sources with a similar spectral type (our source spectral type is M4.8) have bolometric luminosities half of that of our source. However, Gagné et al. (2015) and Schneider & Shkolnik (2018) do not suggest anything related to possible multiple systems.

Kraus et al. (2014) quantified the location of the LDB at Mbol = 9.89 ± 0.10 mag, L. They defined the LDB identifying the limit where equal numbers of lithium-depleted and lithium-bearing stars encroach onto the opposite side of the boundary. We located the LDB in the same way as we did in the rest of associations at L and Teff LDB = 2935 ± 71 K (see Fig. A.20b). If we assumed that 22444835-6650032 is a multiple system, the LDB location changes in terms of bolometric luminosity: L, a change of 15% in terms of bolometric luminosities that produces an age increase of 2 and 6 Ma (6 and 10%) depending on the evolutionary model used (see Fig. A.20c). This last case is the one we selected.

The membership selection from Kraus et al. (2014) based on lithium measurements might introduce a bias in the location of the LDB (see Section 5 from that work). A possible solution would be to carry out a new membership assignment, as we propose for the BPMG low-mass objects.

5.12. 32 Ori moving group

To assess the LDB, we collected 33 M dwarfs from Bell et al. (2017). However, this number rises to 36 thanks to the multiplicity of three sources discovered after we cross-matched our input catalogue with Gaia DR2. Then, we have THOR-14Aa (3341625121978020736) and THOR-14Ab (3341625126275164032) instead of THOR 14A; THOR-17Aa (3389908598860532096) and THOR-17Ab (3389908598858685696) instead of THOR-17A; and THOR-40a (3341538436655619840) and THOR-40b (3341538436653898240) instead of THOR-40. THOR-14Aa and THOR-14Ab are two sources in Gaia DR2 with different astrometric parameters, unlike the rest of the photometric surveys, where they are blended. The bolometric luminosity is obtained with the total observed blended flux and calculated at both distances. All the sources have a counterpart in the Gaia DR2 catalogue, but THOR-17Aa, THOR-17Ab, THOR-18, THOR-35, THOR-36, THOR-40a and THOR-40b lack of parallaxes and proper motions.

Previous works (Bell et al. 2017; Murphy et al. 2020) reported additional information that we took into account. THOR-17A (so THOR-17Aa, and THOR17Ab), THOR-18, THOR-21, THOR-26, and THOR-37 showed strong He Iλ 5876 Å and 6876 Å emission lines. There are several confirmed spectroscopic binaries: THOR-18, THOR-31 (a binary system), THOR-33 (a 5″ visual binary), and recently, Murphy et al. (2020) reported that THOR-42 (2MASS J05525572-0044266) is a young eclipsing binary comprising two pre-main sequence M dwarfs with combined spectral type M3.5. Some objects are suspected spectroscopic binary systems: THOR-15 and THOR-37; and others are considered fast rotators: THOR-05, THOR-07, THOR-23, and THOR-34.

32 Ori MG members are located in a bounded sky area (as we show in Fig. 9), unlike other MGs (see SACY by Torres et al. 2006 or Malo et al. 2013). We performed a similar analysis to the one done with the open clusters, We discarded those sources that have parallaxes outside the interval ϖ ∈ (8.0, 11.0) mas: THOR-27 (a background source), along with three foreground sources, 2MASS J05053333+0044034, THOR-33, and THOR-34. We did not discard any source in the VPD because none of these sources are placed outside the area described by other members (as can be checked in Fig. A.21. With regard to 2MASS J05053333+0044034 (plotted as 05053333), THOR-33, and THOR-34, they show discrepant proper motions.

thumbnail Fig. 9.

Location of all 32 Ori MG sources (red circles from Bell et al. 2017), together with the Hyades (purple triangles), the Pleiades (blue squares), and Taurus members (grey pluses from Ducourant et al. 2005). The Hyades and the Pleiades members are taken from Gaia Collaboration (2018b).

Bell et al. (2017) located the LDB with the sources THOR-30 (lithium-poor object) and THOR-32 (lithium-rich object) at . We located the LDB at and Teff LDB = 3135 ± 71 K, see Fig. A.23b.

Stauffer et al. (2020) found that HCG 332 (HHJ 339) and HCG 509 (HHJ 430), as described in Sect. 2.7, share space motions that match those of 32 Ori MG. The inclusion of these objects in our analysis does not affect to the LDB loci, because HCG 509 is a binary system (Stauffer et al. 2020) and HCG 332 is fainter than the LDB. We also show these objects in the HRD, Fig. A.23b. In addition, THOR-35 and THOR-36 lack parallaxes and are key objects around the LDB. So, it would be interesting to obtain parallaxes for them.

Finally, we studied the possibility that 32 Ori MG is made up of two populations, see the details in the Appendix D. Briefly, from our analysis we distinguished two populations: 32 Ori MG-Pop 1 with a LDB located at and Teff LDB = 3157 ± 71 K (Fig. A.23c); and 32 Ori MG-Pop 2 with a LDB located at and Teff LDB = 3098 ± 71 K (Fig. A.23d). In addition we did an extra analysis. The 32 Ori MG sources belong to two different stellar groups from Kounkel & Covey (2019): Theia 133 and Theia 370. We located the LDB at and Teff LDB = 3139 ± 71 K, for Theia 133 (Fig. D.3a); and and Teff LDB = 3087 ± 71 K, for Theia 370 (Fig. D.3b).

6. LDB error budget

In this section, we discuss the sources of error in our LDB loci and their derived ages. We study the accuracy of our derived stellar parameters, the importance of reddening in the LDB location, and we compare our LDB ages with those derived using other techniques. We also discuss some caveats in obtaining our estimations.

6.1. Accuracy of the stellar parameters

In order to estimate the accuracy of our stellar parameters, both assumed and calculated (metallicity, surface gravity, reddening, effective temperature, and distance), we made a comparison with the values from Anders et al. (2019)15 and from Randich et al. (2018). In addition, we employed two grids of model atmospheres to study their effect on the derivation of the total flux of each object.

6.1.1. Comparison with Anders et al. (2019)

Anders et al. (2019) derived stellar parameters, distances, and reddenings for 285 × 106 stars down to G = 18 mag, using the StarHorse code (Queiroz et al. 2018) and combining photometric catalogues and parallaxes from Gaia DR2. We calculated the difference between the StarHorse stellar parameters and the ones we either assumed or derived. We applied four filters to the StarHorse dataset: the first one with all the sources in common, the second one with a clean sub-sample that fulfils SH_GAIAFLAG=“000” and SH_OUTFLAG=“00000” (see Anders et al. 2019 for an explanation), the third one only shows the members after our work, and the fourth one is the clean sub-sample of the previous one. We provide the results grouped into stellar associations in Table E.2. No object was found in the case of the NGC 2547 LDB sample, only two objects from Alpha Persei and the Pleiades, and only the hotter and brighter objects with Teff > 3100 K, from IC 4665 and Blanco 1. On the other hand, the least massive objects with later spectral types were found due to their proximity in the youngest (32 Ori MG and BPMG) and oldest (the Hyades) associations.

We assumed a homogeneous metallicity for all the objects in a stellar association given by the mean value (the values are shown in Table 1). Some of them are not tabulated in the models, so we have taken the closest one. Our fixed values and those calculated with StarHorse agree.

A comparison of the two approaches reveals that the fixed value of log g = 4.5 for all the objects is consistent. However, we discern that the StarHorse values in the Hyades, the oldest association, are close to log g = 5.0 dex instead of log g = 4.5 dex. We calculated the stellar parameters of the Hyades using log g = 4.5 and log g = 5.0 dex. The total flux, Ftot, is not affected by the change. The differences in terms of percentages are 0.7%, with a standard deviation of 3%. This fact is not reflected in the Teff, as the calculated values using log g = 5.0 dex are hotter by 26 K on average (with standard deviation 115 K). So, we fixed log g = 5.0 dex for the Hyades and log g = 4.5 dex for the rest of the associations.

The comparison between our calculated distances and that in StarHorse must be done carefully. While Anders et al. (2019) re-calibrated the parallaxes and their uncertainties (see further explanation in Table 1 and Sect. 2), we decided not to apply any corrections. The Gaia DR2 parallaxes show several systematic uncertainties on a small scale (depending on magnitude, colour, and position) and on a large scale (as the global parallax zero-point offset of −0.029 mas, see further explanations from Arenou et al. 2018; Lindegren et al. 2018). These last two papers suggest treating the parallax zero-point as an adjustable parameter, adding that this is not always possible for very small samples or when the distance is nearly constant in the sample, as in a stellar cluster. So, we decided not to apply this global offset in our analysis16. Even so, we tested the impact of this offset in Sect. 6.3.

Concerning the distance calculations, Anders et al. (2019) adopted a Bayesian approach using elaborate priors with the aim of estimating distances for a complex variety of objects in all the Milky Way (priors include information about stellar evolutionary models and density laws for the main components of the Milky Way as the thin and thick disc, bulge, and halo, as well as the broad metallicity and age ones for those components). By contrast, our goal is to calculate the distance of an object (as well as possible) belonging to a stellar association, thus, we used a suitable Gaussian prior (see Sect. 4.2 for the explanation). Here, StarHorse gives the distance values in the 5th, 16th, 50th and 95th percentiles, where dist50 is considered the main estimator of the distance, and the uncertainties are given by dist16 and dist84. In our case, the maximum-a-posteriori is the main estimator of the distance, and the 2.5th and 97.5th percentiles give the uncertainties. However, in Fig. 10, all the uncertainties were determined at 16th and 84th percentiles, showing a good agreement between both methods. The most significant discrepancies are found at distances dMAP > 950 pc. The poorest agreement is found in objects from NGC 1960 and IC 4665, which are the furthest associations. The NGC 1960 sample only contains four objects, two of them with low quality as it is shown by the StarHorse flags. The IC 4665 sample contains a a large number of sources considered as non-members after this work. These objects have systematically higher StarHorse distances than our calculated values. As a result of the comparison, we can conclude that this effect affects non-member background objects.

thumbnail Fig. 10.

Comparison of our calculated distances, dMAP and those derived with StarHorse (Anders et al. 2019).

Therefore, the mere fact of using the Bayesian approach is not enough to calculate reliable distance measurements. We assumed that all the objects belong to the open cluster and chose a prior accordingly. While bona fide members have accurate distances, the background objects and outliers with parallaxes higher than 20% are likely to be biased, as we see when making comparisons with StarHorse results. This suggests that it is necessary to discard outliers using the parallaxes instead of the calculated distances.

Another quantity, namely, interstellar reddening, affects the stellar parameters and in particular, the effective temperature. We show our results for the effective temperatures with those from StarHorse together with the reddening, AV in Fig. 11. We note that Teff is our calculated effective temperature, and teff50 is the StarHorse effective temperature at 50th percentile. As a matter of fact, we can distinguish three different zones depending on the effective temperature: (1) zone A with Teff < 3200 K, populated by the objects that are considered in the LDB location, (2) zone B with Teff ∈ (3200, 3700) K, and (3) zone C with Teff > 3700 K. In zone A, there is no significant difference between the two effective temperatures ΔTeff = −9 K (standard deviation 127 K) and a ΔAV = −0.20 mag (standard deviation 0.34 mag). There are objects from all the stellar associations included, but there is a greater presence of objects from the Hyades, BPMG, and THMG. One implication of this is the possibility that the best match corresponds to those objects with very low or null values of AV, for instance, the Hyades, THMG, and BPMG. In zone B, we measured an offset of ΔTeff = −330 K (standard deviation 468 K) and ΔAV = −0.63 mag (standard deviation 0.76 mag), and we systematically found lower values than those from StarHorse. In zone C, in overall terms, there is an offset of ΔTeff = −440, on average (standard deviation 710 K), and ΔAV = −0.68 mag on average (standard deviation 0.79 mag). We observed two trends: objects very close to the 1:1 line with small differences between Teff and AV, and a second group with ΔTeff > 500 K. In the latter case, most of the objects are from IC 4665 and THMG.

thumbnail Fig. 11.

Comparison of effective temperatures derived in Anders et al. (2019) and from VOSA. Top: Ssources from the LDB samples. Note we did not find any NGC 2547 counterpart in StarHorse. Bottom: only those sources considered as members after this work.

The four NGC 1960 sources with counterparts in StarHorse are located inside the range of Teff ∈ (3600, 4500) K and teff50 > 4500 K. In the range of Teff ∈ (3250, 3600) K and teff50 > 4500 K, there are only sources from IC 4665, BPMG, THMG, and 32 Ori MG. In brief, sources with Teff < teff50 have values of the extinction AV5017 greater than the ones we have assumed. We distinguish three zones depending on their tendency even though there is no definitive explanation. The Teff − AV relation might be affected by the use of synthetic photometry from the Kurucz grid together with the extinction law used in StarHorse, the differential reddening in some stellar associations (e.g. the Pleiades: see Breger 1986; Stauffer & Hartmann 1987; Gibson & Nordsieck 2003a,b) or both.

6.1.2. Comparison with Randich et al. (2018)

We compared our results with those obtained in Randich et al. (2018). In this work they employ the stellar parameters obtained from the Gaia-ESO Survey, GES (Gilmore et al. 2012), and derive reddening values comparing several grids of models with various colour-magnitude diagrams. We calculated the difference between their values and ours, for the four associations, we have in common: IC 4665, NGC 2547, IC 2602, and IC 2391 (see Table E.3). As with the StarHorse values, the assumed log g = 4.5 dex is consistent, although we seem to have an offset of −0.36 ± 0.61 dex.

These authors E(B − V) values are systematically higher than ours, of about 0.0477 mag, with a standard deviation of 0.0093 mag. This value is within the Gaia Collaboration (2018b) uncertainties for the excess. As we will see in Sect. 6.2 and Appendix B, higher reddening values produced hotter effective temperatures. Figure 12 shows a temperature offset of approximately 200 K, probably caused by the values E(B − V). Our effective temperature values were obtained from the SED after applying the assumed E(B − V) value, while values from Randich et al. (2018) are obtained from particular lines in the spectrum (Damiani et al. 2014).

thumbnail Fig. 12.

Comparison of effective temperatures derived in Randich et al. (2018) and from VOSA. Top: all the sources are members from Gaia Collaboration (2018b) with counterpart in Randich et al. (2018). Bottom: only sources considered as members after this work from the LDB samples with counterpart in Randich et al. (2018).

6.1.3. Impact of different model atmosphere grids on the total flux.

The amount of flux inferred from just one colour using grids of models is huge in typical bolometric corrections. In contrast, VOSA offers a panchromatic bolometric correction based on the numerous photometric bands collected and their uncertainties (included in the quantity Ferr, see Sect. 3.3). VOSA releases the Fobs/Ftot for all adjustments. This value is higher than 0.7 in our objects, so less than 30% of the total flux comes from model atmospheres. As such, we do not expect a large effect due to the adopted synthetic spectra. Besides the effective temperature, synthetic spectra depend also on surface gravity and metallicity. For these parameters, we assumed constant values, namely, [Fe/H] = 0.0 and log g = 4.5 dex (log g = 5.0 dex for the Hyades), consistent with what has been done in previous works (see Sects. 6.1.1 and 6.1.2). It is likely that it does not increase the uncertainty in the Ftot estimation. However, to check the impact of the adopted spectra in the determination of bolometric luminosity, we compared the results obtained using two different grids of model atmospheres.

Our reference grid is the BT-Settl (Allard et al. 2012, see Sect. 4.3). We compared it with the MARCS grid (Gustafsson et al. 2008), using the standard metallicity class ([Fe/H] = 0.0) and logg = 4.5 dex18. We calculated the Ftot in the wavelength range common to both models: from 1300 Å to 20 μm. The results for models with Teff ∈ [2500, 3500] K are given in Table 4, where Ftot is the integrated flux, ΔFtot is the difference of fluxes of the MARCS and BT-Settl models, and %Δ is the difference in percentage terms. The maximum difference is 5%, being less than 1% in most cases. Moreover, these effects are even smaller because in most of the targets the flux between u and Ks (and up to the W2 photometric band) is determined by the observations only, and not by any model. Thus, we did not find any significant difference between the two grids in the effective temperature range of the LDB.

Table 4.

Differences in fluxes between MARCS and BT-Settl model atmosphere.

6.2. Effects of reddening in the LDB

The reddening values vary greatly from one work to another for the same stellar association. Even if the same technique is used to calculate it, the isochrone fitting, the result is quite sensitive to the set of stellar models used to derive it, (see e.g. Gaia Collaboration 2018b; Randich et al. 2018; Bossini et al. 2019). In our analysis, we used the values of the reddening computed by Gaia Collaboration (2018b), whenever possible, neglecting the uncertainties19. We used these values in order to compare age values determined with the same reddening and different technique (see Sect. 6.4).

Different methodologies reveal different reddening values, and a kaleidoscope study from diverse perspectives would be interesting. Another effect that may be related is differential reddening, as occurs in the Pleiades (see Sect. 6.1.1), but that is beyond the scope of this work.

In order to quantify and make a rough estimate of how different values affect the location of the LDB (see Appendix B), we studied Alpha Persei assuming two very different single reddening values: AV = 0.279 mag (Gaia Collaboration 2018b) and AV = 0.055 mag (Bossini et al. 2019). We chose this open cluster because the LDB is very clearly located. All the calculations are presented in Appendix B. If we assume AV = 0.055 mag, the LDB locus is at: L and Teff LDB = 2806 ± 71 K, which it means a variation of Lbol LDB of about −0.24 × 10−3L. So, the LDB is located at fainter luminosities, cooler effective temperatures, and the resulting age is older: Ma (BT-Settl model from Allard et al. 2012). Table B.2 shows the age differences between models. If we make a comparison with the ages determined using AV = 0.279 mag, we find age differences ranging from 3 to 6 Ma (about 3 to 9%). However a more in-depth and systematic study of this variable is needed for each stellar association.

6.3. Effects of the parallax zero-point offset in the LDB

We studied how the inclusion of the Gaia DR2 global parallax zero-point offset (see Arenou et al. 2018; Lindegren et al. 2018) affects the the average stellar association distance and its LDB. In addition, we studied possible differences between Gaia DR2 and EDR3.

We tested the impact of the global parallax zero-point offset on the average stellar association distance by adding +0.029 mas to all parallaxes before performing our distance estimation. For the Hyades, we obtained dmode = 47.368 pc and the values at the 2.5th, 25th, 75th, and 97.5th percentiles are 60.684, 50.761, 44.412, and 36.530 pc, respectively (see Table 2). In the case of more distant stellar associations such as Alpha Persei, we calculated dmode = 173.571 pc with 2.5th, 25th, 75th, and 97.5th percentile values of 186.653, 178.254, 170.162, and 161.682 pc; and for the Pleiades we obtained dmode = 135.352 pc with percentile values of 146.899, 138.571, 132.554, and 124.234 pc. In these cases, the zero-point offset carries a change of up to a maximum of 1 pc. However the effect is larger in the most distant NGC 1960, with a dmode = 1165.908 pc and percentile values of 1455.688, 1241.557, 1103.338, 978.990 pc, which makes it a 40 pc closer.

In addition, we tested their impact on the derived Lbol LDB. We found that the effect is negligible for the Hyades L, and the Pleiades: L, where the LDB loci changes ΔLbol LDB = 0.001 × 10−3L, less than 0.1%. After we applied the offset, we located the LDB for Alpha Persei at L, which implies ΔLbol LDB = 0.04 × 10−3L fainter, and a change of 1.4% in Lbol LDB. The most pronounced case is that of NGC 1960 because it is the cluster with the smaller parallax and the most distant. After adding the offset, NGC 1960 it is placed 40 pc nearest and we located the LDB at L that implies an LDB loci ΔLbol LDB = 0.199 × 10−3L smaller, and account for a 0.84% change in Lbol LDB. We conclude that the effect produced by zero-point offset parallax on the LDB locus is more pronounced for more distant stellar associations. However, it is not the predominant source of the uncertainty.

To conclude this analysis, we studied the effect of Gaia EDR3 parallaxes on the Alpha Persei distance and its LDB location. We obtained a dmode = 173.840 pc, with the following values at the 2.5th, 25th, 75th, 97.5th percentiles: 190.660, 179.165, 169.287, 160.242 pc. In this case, the distance is 0.62 pc closer (Δdmode). We do not see a substantial change in the location and size of Alpha Persei using the Gaia EDR3 parallaxes, although the parallax uncertainties are smaller in EDR3. We also checked the effect on the LDB location. We obtained: L, which implies an LDB loci ΔLbol LDB = 0.125 × 10−3L brighter, and account for a 4.1% change in Lbol LDB. Furthermore, the age decreases by 0.9 Ma: Ma, using the BT-Settl models.

6.4. Comparison between ages: several models and techniques

We locate the LDB in terms of the bolometric luminosity. The choice is due to the large dynamic range over which it varies in relevant age scales. We have found that the Lbol LDB and Teff LDB produce different age values. In Table 3, we present our calculated Lbol LDB and Teff LDB, and the age estimated using Lbol LDB and several grids of evolutionary models. In addition, as a test, we have calculated the Teff LDB from the previously estimated age (between parentheses in Table 3). The purpose of that is to highlight the differences between the ages estimated from the Lbol LDB and the Teff LDB (see Song 2016). This effect is significantly larger at brighter Lbol LDB (younger stellar associations) and we also show an evolutionary model dependence. A possible explanation is that the radii of these objects are larger than predicted by the models (Berger 2006; López-Morales 2007; Ribas et al. 2008), of up to 14 ± 2% for a given bolometric luminosity for a sample of fast-rotating pleiades (Jackson et al. 2018). The rotation, accretion, and magnetic fields are effects that may be involved in this fact. In summary, it is necessary to determine precisely how radii affect effective temperatures and bolometric luminosities and, hence, the LDB.

What can be clearly seen in Table 3 and Fig. 13 are the differences between ages calculated with different grids of evolutionary models, so there is a clear dependence. Any grid of models starts with a different equation-of-state, opacities, nuclear reaction rates and hypothesis, such as the convection model or the model atmosphere and leads to these age differences. We find several general remarks: (a) the Pisa and Siess LDB give ages younger than BT-Settl LDB; (b) the largest differences, 12 Ma, are found at Mbol ∈ [8.0, 9.5] mag, around 20 Ma, and account for 50% of the age, as we show for the BPMG with the Burrows and BT-Settl models.

thumbnail Fig. 13.

Radar chart with LDB ages estimated using several evolutionary grid models. The age values showed as filled circles and connected with dashed lines are the same as Table 3. We also show the mean age value (thin solid line) and its standard deviation (the shadow region) for each association.

We compared the LDB age scale derived using the BT-Settl luminosity-age relation with other age values (see Table 1) in Fig. 14. In general, the LDB ages are older than those estimated using a different method. When we compare our LDB ages with previous works using the same methodology, (as first pointed out Basri et al. 1996; Stauffer et al. 1998b) there is still some discrepancy, although not so pronounced. This result is probably related to the use of (a) different grid of models to derive ages, (b) individual parallaxes and to the fact that we discarded multiple systems together with foreground and background objects, and (c) in some cases, different reddening values.

thumbnail Fig. 14.

Comparison between our LDB age and the age estimated using other techniques. Left: sges derived from the isochrone fitting technique. The ages come from: Gaia Collaboration (2018b; blue diamonds), Bossini et al. (2019; purple squares), and Mermilliod (1981; gray circles). Middle: ages derived from the Pre Main-Sequence isochrone fitting technique. Orange diamonds represent PMS isochrone fitting ages: the Pleiades, BPMG, THMG and 32 Ori MG, Bell et al. (2013, 2014, 2015); and IC4665, Cargile & James (2010). Brown squares are the rest of PMS isochrone fitting ages: NGC 1960, Bell et al. (2013); IC 4665, Manzi et al. (2008); NGC 2547, Naylor & Jeffries (2006); IC 2602 and IC 2391, Stauffer et al. (1997); Alpha Persei, Prosser (1992); the Pleiades, Stauffer et al. (1995b); Blanco 1, Cargile et al. (2009); BPMG and THMG, Torres et al. (2006); and 32 Ori MG, Mamajek (2007). Right: LDB ages derived from previous works. See the references in Table 1, its legend, and Sect. 2.

On the other hand, we noted that the Pleiades PMS isochrone age from Bell et al. (2014) fits well with our LDB age because these models were re-calculated using this fact as input; Gaia Collaboration (2018b) provided two age values for Blanco 1. From the main-sequence turn-off, they obtained an age of Ma. However, if they used the LDB age of Ma (Juarez et al. 2014), they would reproduce the lower main sequence, with a marginal fit to the upper main sequence. We show both values in Fig. 14.

A summary is presented in Table 5. Also, concerning studies on active stars, e.g. Reiners (2012), works like Malo et al. (2014b) partly resolved the age inconsistency between LDB and isochrone-fitting age for the BPMG. It would be interesting to extend this study to the rest of the associations.

Table 5.

Properties of the Lithium Depletion Boundary for the 12 stellar associations.

In Fig. 15 we plot our LDB ages together with other ages calculated with other techniques for a selection of stellar associations. Here, we also see the differences in age between the different techniques. It is worth noting that in some cases, parameters like reddening and distance are completely different from those used in our work. This fact may be the reason for the age discrepancies.

thumbnail Fig. 15.

Radar charts with ages in [Ma] calculated using different techniques: ‘LDB’ refers to our calculated ages using the BTSettl (see Table 3); ‘Gyr’ is the gyrochronology ages (Cargile et al. 2014); ‘ISO’ is isochrone fitting ages (Gaia Collaboration 2018b); ‘PMS’ is PMS isochrone fitting ages from several works: IC 2602 (Stauffer et al. 1997); Alpha Persei (Prosser 1992); the Pleiades (Stauffer et al. 1995b). Then, ‘Grav” is the gravity ages (David & Hillenbrand 2015); ‘WD’ is the ages derived using the white dwarf cooling sequence age: Alpha Persei and the Pleiades (Lodieu et al. 2019a); the Hyades (Lodieu et al. 2019b). Left: age range ∈[0, 800] Ma. Right: zoom onto the age range ∈[0, 160] Ma.

7. Conclusions and summary

The origin of the data and membership selection is very different for each stellar association and this fact can result in bias effects on the location of the LDB. In the case of the BPMG (such us Torres et al. 2006 or Shkolnik et al. 2017) and the THMG (Kraus et al. 2014), the membership selection was based on lithium measurements, so it is very likely that it might be a bias. We have tried to mitigate this possible effect by studying the membership of these objects based on the Gaia DR2 data: positions, parallaxes, and proper motions.

In line with our aim of creating a complete set of LDB age scale and following the example of Mermilliod (1981), we present a systematic and homogeneous study of twelve stellar associations. Our main results are as follows:

  1. Twelve stellar associations with former LDB ages have been thoroughly studied conducting a careful and extensive bibliographic review to recover additional data to determine possible outliers, as well as multiple systems and sources with unique features that can affect the LDB location.

  2. We calculated individual distances for each source using a Bayesian statistic approach (Kalkayotl), and derived individual bolometric luminosities and effective temperatures for 500 sources, from their SEDs, using Gaia DR2 data including photometric data in a broad range of wavelengths, as well as the effects of metallicity and surface gravity. All the SEDs and images in several photometric bands were checked individually to determine special features.

  3. We fine-tuned previous memberships using individual parallaxes and proper motions from Gaia DR2, in addition to an HRD. The LDB has been determined using a jackknife method with a bootstrap re-sampling that takes into account the bolometric luminosities distributions of objects.

  4. We derived LDB ages using different theoretical evolutionary models. The discrepancies between them are due to the input physics. Also, we found a discrepancy between the ages derived using bolometric luminosities and those derived using effective temperatures. Since the ages from the bolometric luminosities are more robust to variations of AV than the rest, we have selected them as the reference set.

  5. Our work reveals Lbol LDB values that are more precise than former ones in general terms, because our method is quite robust since we statistically determine them. Nevertheless, it is affected when: (a) the sequence of M-dwarfs (or L-dwarfs) objects is scarce, for instance, there are few objects with spectroscopic measurements that allow us to discern their lithium abundance; and (b) the sources that determine the LDB have larger bolometric luminosities uncertainties due to larger parallax uncertainties. In specific terms, our calculated Lbol LDB are in agreement with former ones for IC 4665, NGC 2547, IC 2602, IC 2391, the Pleiades, and Blanco 1. In contrast to earlier calculations, for the BPMG, the 32 Ori MG, Alpha Persei, and the Hyades, our Lbol LDB calculation is brighter. On the other hand, we found fainter Lbol LDB for NGC 1960 and THMG. All these discrepancies are mainly due to a new membership assignment, the update distance determination from individual parallaxes, or both – as in the case of the 32 Ori MG, NGC 1960, THMG, Alpha Persei, or the Hyades.

  6. We identified two peaks in the parallax distribution of the 32 Ori MG members. Besides, we checked that the 32 Ori MG members belong to two different stellar groups: Theia 133 and Theia 370, after Kounkel & Covey (2019). Finally, we located a tentative LDB and age for Theia 133 and Theia 370.

  7. The final results are summarized in Table 5, where the best age determinations are listed. Those were derived homogeneously and provide a well established relative age scale.

Based on the theoretical calculations (Bildsten et al. 1997; Ushomirsky et al. 1998), we would expect an abrupt transition between lithium-poor and lithium-rich objects. Nevertheless, this is not always the case, as we have found in our study of several stellar associations. One possible explanation may be the presence of unresolved multiple systems that could affect the interpretation and location of the LDB loci. Another explanation is that other phenomena or mechanisms come into play. The accretion, the rotation, and the magnetic fields (all correlated with each other) prevent lithium depletion or generate different abundances for stars with the same mass (see Soderblom et al. 1993; Chabrier et al. 2007; Somers & Pinsonneault 2014; Jackson & Jeffries 2014a; Barrado et al. 2016; Bouvier et al. 2018). Although only a few works have studied the LDB with some of these effects in mind (Malo et al. 2014b; Juarez et al. 2014; Messina et al. 2016), it would be interesting to extend it to the other associations, and to carry out a study focussed on the multiplicity around the LDB. The stellar collision or the engulfment of a planetary object by a main star or brown dwarf (Abia et al. 2020; Israelian et al. 2001), or the accretion of planetesimals leaving lithium abundance abnormalities in the atmosphere of the main object (Kaiser et al. 2021) might be another possible scenario. However, it remains to be seen how the change in the lithium abundance, the stellar parameters may be quantified, and how common these phenomena may be overall.

In a future work, we will analyse the LDB loci in terms of effective temperature and bolometric luminosity together, and we will incorporate data to help explain and quantify the effects of rotation and magnetic fields in the LDB age. It would be interesting to apply the Malo et al. (2014b) procedure to the rest of the associations, and check if the inconsistency is resolved between LDB and isochrone-fitting ages. It is necessary to populate some areas of the Lbol LDB range and study stellar associations, with ages ranging between that of the Pleiades and the Hyades, such as Praesepe or Coma Berenices (see Martín et al. 2020). There are no significant variations in our results based on the Gaia EDR3 data. However, we plan to update these results following the launch of Gaia DR3 in 2022.


1

We use the term stellar association to refer both to open clusters and moving groups. A moving group is a stream of stars with common age and motion through the Milky Way and with no overdensity of stars discernible in any region (Zuckerman & Song 2004). An open cluster is a group of gravitationally bound stars that shows a clear concentration above the surrounding stellar background (Moraux 2016).

2

The uncertainty is an estimate from their Figs. 5c and 5d.

3

They also report an age of Ma, but with this value the lower main sequence is poorly fitted.

4

This metallicity value has been a matter of controversy, see: Westerlund et al. (1988), Edvardsson et al. (1995) and Ford et al. (2005).

6

In the Tognelli et al. (2015) models, [Fe/H] = 0.0 correspond to Z = 0.013, and [Fe/H] = +0.1 to Z = 0.016. We estimated the ages for Alpha Persei and the Hyades using Z = 0.016 and for the rest Z = 0.013, due to their metallicities, see Table 1.

7

We used the library scikit-learn (Pedregosa et al. 2011) to calculate it.

8

The AV were calculated from E(B − V) with RV = 3.1.

10

Throughout this work, we call these objects suspected multiple systems.

11

CFHT-Pl-9 and MHObd 6 are the same source (Stauffer et al. 1998b and Bouvier et al. 1998) even though the SIMBAD database treats them as two independent sources. We carried out a visual check of the charts from Stauffer et al. (1998b) and Bouvier et al. (1998) to confirm it. Also the counterpart of CFHT-Pl-10 in 2MASS catalogue is 2MASS J03443231+2525181.

12

Olivares et al. (2018) use a membership probability threshold p = 0.84 (the one with higher accuracy and only for classification purposes). On the other hand, Bouy et al. (2015) use a threshold of p = 0.75.

13

These objects are not extremely faint and cool, have a counterpart in other surveys like 2MASS, and the SEDs do not have strange behaviours. The most plausible reason that they do not appear in Gaia DR2 is that the astrometric solution does not converge, because they are multiple systems.

14

Also known as SCR J2033-2556 AB.

15

We accessed the data via the Gaia mirror archive at the Leibniz-Institut für Astrophysik Potsdam: https://gaia.aip.de/, using the Gaia DR2 source_id.

16

Other works, as Meingast et al. (2021), do not apply the parallax-offset value, because it is a global average and can be significantly different on local scales.

17

AV50 is the StarHorse line-of-sight extinction at λ = 5420 Å, AV, 50th percentile.

19

Extinction values from Gaia Collaboration (2018b) have an uncertainty of ΔE(B − R) = 0.04 mag.

Acknowledgments

A special thanks to Alcione Mora for his help with the Gaia data, Floor van Leeuwen for his help with the size of the clusters, Ana María Álvarez García, María Teresa Galindo Guil and Irene Pintos-Castro for their comments and suggestions, Agnes Monod-Gayraud for her careful reading of the manuscript and English corrections, and the anonymous referee for the comments that helped to improve the quality of this manuscript. FJGG acknowledges support from Johannes Andersen Student Programme at the Nordic Optical Telescope. This research has been funded by the Spanish State Research Agency (AEI) Project No.PID2019-107061GB-C61 and No. MDM-2017-0737 Unidad de Excelencia “María de Maeztu” – Centro de Astrobiología (INTA-CSIC); AB acknowledges support by ANID, – Millennium Science Initiative Program – NCN19_171 and BASAL project FB210003, and from FONDECYT Regular 1190748; VOSA, developed under the Spanish Virtual Observatory project supported from the Spanish MINECO through grant AyA2017-84089; the astronomical java software TOPCAT (Taylor 2005) and STILTS (Taylor 2006); NASA’s Astrophysics Data System Bibliographic Services; ESASky, developed by the ESAC Science Data Centre (ESDC) team and maintained alongside other ESA science mission’s archives at ESA’s European Space Astronomy Centre (ESAC, Madrid, Spain); the SVO Filter Profile Service (http://svo2.cab.inta-csic.es/theory/fps/) supported from the Spanish MINECO through grant AyA2014-55216; data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement; The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation; the SIMBAD database, operated at CDS, Strasbourg, France; Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University; data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration; data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation

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Appendix A: Parallaxes distributions, VPDs, and HRDs for all the stellar associations

In this appendix, we present the parallax distributions the VPDs and the HRDs for all the stellar associations. In some cases, we studied different possibilities of locating the LDB and for these, we present different HRDs, that is, a different one for each location.

thumbnail Fig. A.1.

VPD and parallaxes for NGC 1960. Left: VPD, for NGC 1960. Blue dashed ellipses are the members taken from Cantat-Gaudin et al. 2018a; red ellipses are our LDB sample. The rest is the same as in Fig. 3 but for NGC 1960. Right: same as in Fig. 4 but for NGC 1960.

thumbnail Fig. A.2.

HRDs and the LDB for NGC 1960. (a) Same as Fig. 6. Cyan squares are lithium-rich sources without Gaia DR2 parallaxes and purple stars are lithium upper limits or lithium-poor sources without Gaia DR2 parallaxes, both from our LDB sample (see Section 4.2); empty large black circles are confirmed multiple systems and broken lines are suspected multiple systems; over-imposed big black crosses are sources discarded as members after this work. Moreover, grey points are known members from Cantat-Gaudin et al. (2018a). Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one corresponds to 30 Ma. The figure includes: a 20 Ma and a 30 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed line), a 25 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line), a 30 Ma isochrone from Siess et al. 2000 (red dotted line) and a Zero Age Main Sequence from Stahler & Palla 2005 (green solid line). (b) Zoom on the left plot. A black horizontal line marks the Lbol LDB, together with the 16th and 84th percentiles (dotted lines). NGC 1960 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). An extensive dashed horizontal green line indicates a possible LDB upper limit (see Section 5.2).

thumbnail Fig. A.3.

VPD for IC 4665. Left: Details are the same as in Fig. 3 but for IC 4665. Right: Zoom on the left figure.

thumbnail Fig. A.4.

Parallaxes for IC 4665 members close to the LDB. Details are the same as in Fig. 4 but for IC 4665.

thumbnail Fig. A.5.

HRDs and the LDB for IC 4665. (a) the same as in Figs. 6 and A.2 but for IC 4665. The violet crosses are sources with undetected or dubious lithium detections due to their low resolution spectrum or other technical disabilities. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 30 Ma. The figure includes: a 20 Ma and a 30 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed lines), a 25 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line), a 30 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the previous plot around the LDB with all the source names. (c) A black horizontal line marks the Lbol LDB, together with the 16th and 84th percentiles (dashed lines), following the first scenario, see Section 2.3. (d) Same as (b), but the the Lbol LDB is located following the second scenario, see Section 2.3. It is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

thumbnail Fig. A.6.

VPD and parallaxes for NGC 2547. Left: Same details as in Fig. 3 but for NGC 2547. Right: Same as in Fig. 4 but for NGC 2547.

thumbnail Fig. A.7.

HRDs and the LDB for NGC 2547. (a) the same as in Fig. 6 and A.2 but for NGC 2547. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue lines to 40 and 50 Ma. The figure includes: a 30 Ma and a 50 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed lines), a 35 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line), a 40 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the (a) plot around the 52 radial velocity members from Jeffries et al. (2004) sample. (c) Zoom around the LDB. NGC 2547 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). We show the names of all the objects but not the uncertainties (for the purposes of clarity).

thumbnail Fig. A.8.

VPD and parallaxes for IC 2602. Left: Same details as in Fig. 3 but for IC 2602. Source 10443357 possesses a proper motion far different than the rest of members. Right: Same as in Fig. 4 but for IC 2602.

thumbnail Fig. A.9.

HRDs and the LDB for IC 2602. (a): The same as in Fig. 6 but for IC 2602. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 50 Ma. The figure includes 50 Ma isochrones from: Siess et al. 2000 (red dotted line), D’Antona & Mazzitelli 1994 (black dashed line). (b): Zoom on the (a) plot with the LDB. IC 2602 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

thumbnail Fig. A.10.

VPD for IC 2391 and IC 2602 members and parallaxes for IC 2391. Left: Same details as in Fig. 3 but for IC 2391 and IC 2602. Some objects have uncertainties smaller than the size of the markers. Black dotted ellipses are the IC 2391 members and blue dashed ellipses are the IC 2602 members, green solid ellipses are the IC 2391 LDB sample objects, and red solid ellipses are the IC 2602 LDB sample objects. Right: The same as in Fig. 4 but for IC 2391.

thumbnail Fig. A.11.

HRDs and the the LDB for IC 2391. (a) The same as in Fig. 6 but for IC 2391. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 60 Ma. The figure includes: a 50 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed line), a 60 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the left plot with the location of the LDB. IC 2391 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

thumbnail Fig. A.12.

VPD for the Pleiades. Left: Same details as in Fig. 3 but for the Pleiades. Light grey plus symbols are the Taurus-Auriga members taken from the Ducourant et al. (2005) proper motions catalogue. Right: Zoom on the left figure.

thumbnail Fig. A.13.

Parallaxes for the Pleiades members close to the LDB. Same details as in Fig. 4 but for the Pleiades.

thumbnail Fig. A.14.

HRDs and the LDB for the Pleiades. (a) The same as in Fig. 6 but for the Pleiades. In addition, grey points are known members from Gaia Collaboration (2018b), and sienna points from Bouy et al. (2015). Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 120 Ma. The figure includes: a 100 and 200 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed lines), and a 120 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the previous plot with the location of the LDB. The Pleiades is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

thumbnail Fig. A.15.

VPD and parallaxes for Blanco 1. Left: Same details as in Fig. 3 but for Blanco 1. Right: Same as in Fig. 4 but for Blanco 1. We note that CFHT-BL-36 has got negative parallax.

thumbnail Fig. A.16.

HRDs and the LDB for Blanco 1. (a) Same as in Fig. 6 but for Blanco 1. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 120 Ma. The figure includes: a 120 Ma isochrone from Siess et al. 2000 (red dotted line), a 100 and a 200 Ma from D’Antona & Mazzitelli 1994 (black dashed lines). The rest of the symbols follow the same convention as previous HRDs. (b) Zoom on the left plot close to the LDB. The Blanco 1 age is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (c) Same as (b), but the LDB is located after discarding sources whose radial velocities are not within the 1σ radial velocity criterion, see Section 2.8. The tri-down symbols are over-imposed in the non-members following this criterion. The Blanco 1 age is Ma (BT-Settl models from Allard et al. 2012).

thumbnail Fig. A.17.

VPD and parallaxes for the Hyades. Left: Same as in Fig. 3 but for the Hyades. We have added proper motions for the LDB sample sources from: Hogan et al. 2008 (purple filled circles); Lodieu et al. 2014 (grey triangles with their uncertainties); Pérez-Garrido et al. 2017 (the 2M0418, the black plus symbol); Lodieu et al. 2019b (orange stars with their uncertainties). Right: Same as in Fig. 4 but for the Hyades. We have added parallax values from Lodieu et al. (2019b) in blue, (above the black dashed line).

thumbnail Fig. A.18.

HRDs and the LDB for the Hyades. (a) The same as in Fig. 6 but for the Hyades. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 700 Ma. (b) Zoom on the previous plot close to the LDB. (c) Same as the previous plot but, we considered that Hya10 has an unclear lithium detection. The Hyades is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

thumbnail Fig. A.19.

HRDs and the LDB for the BPMG. (a) The same as in Fig. 6 but for the BPMG. Empty large black broken line circles are suspected multiple systems or sources with associated background objects and photometric data blended in some bands. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 20 Ma. Uncertainties are not shown in order to gain clarity, although in the bolometric luminosities are usually smaller than the symbols, with the exception of some sources without parallaxes. The figure includes 20 Ma isochrones from: D’Antona & Mazzitelli 1994 (black dashed line), Siess et al. 2000 (red dotted line), and a 17 Ma from Tognelli et al. 2011 (orange dashed dot line). (b) Zoom on the (a) plot around the LDB. The size of lithium-poor sources has been increased to locate the LDB. The area delimited by them is marked with gray thick dashed lines. Some remarkable sources are labelled. (c) Same as the previous plot with the LDB locus determined following the first scenario. Since we focus on the sole aim of locating the LDB, we do not show: sources that are confirmed or suspected multiple systems; sources with two or several associated objects (third configuration) with photometric data blended in some bands; non-members; sources with undetected lithium feature; and objects without parallaxes. Effective temperatures uncertainties are shown in some lithium poor objects in order to gain clarity, Bolometric luminosities uncertainties are smaller than the size of the symbols. The BPMG is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (d) Same as the previous plot with the LDB locus determined following the second scenario.

thumbnail Fig. A.20.

HRDs and the LDB for the THMG. (a) Same as in Fig. 6 but for THMG. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 50 Ma. The figure includes 50 Ma isochrones from: D’Antona & Mazzitelli 1994 (black dashed line), and Siess et al. 2000 (red dotted line). It also includes a 40 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). (b) Zoom on the (a) plot around the LDB following the first scenario. To retain clarity, we have only drawn the effective temperature uncertainties and the names for the sources that defined the LDB and two additional sources. The uncertainties in the bolometric luminosities are usually smaller than the size of the symbols. (c) Same as (b), but the LDB is located following the second scenario (Section 2.11). The THMG is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

thumbnail Fig. A.21.

VPDs for the 32 Ori MG. Left: The red ellipses are all 32 Ori MG members (Bell et al. 2017); the black filled triangles are Hyades members and the blue squares are Pleiades members, (both from Gaia Collaboration 2018b); and the light grey plus symbols are the Taurus-Auriga members taken from Ducourant et al. (2005). The size of the symbols is greater than the size of the uncertainties (shown as ellipses). Right: Zoom on the previous plot.

thumbnail Fig. A.22.

Parallaxes for the 32 Ori MG members close to the LDB. Same as in Fig. 4 but for the 32 Ori MG. We removed the ‘THOR-’ prefix of each object from the name.

thumbnail Fig. A.23.

HRDs and the LDB for the 32 Ori MG. (a) The same as in Fig. 6 but for 32 Ori MG. Empty black diamonds correspond to fast rotators. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue lines to a 20 and 30 Ma. The figure includes 20 Ma isochrones from Siess et al. 2000 (red dotted line), and D’Antona & Mazzitelli 1994 (black dashed line). It also includes a 18 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). (b) Zoom on the previous plot around the LDB. We added the sources HCG 332 and HCG 509 (see Section 2.12). The 32 Ori MG is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (c) Zoom on the LDB for 32 Ori MG population 1, see Appendix D. The 32 Ori MG population 1 is Ma (BT-Settl models from Allard et al. 2012). (d) Zoom on the LDB for 32 Ori MG population 2, see Appendix D. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 30 Ma. The figure includes: a 25 Ma isochrone from Siess et al. 2000 (red dotted line), a 20 Ma isochrone from D’Antona & Mazzitelli 1994 (black dashed line), and a 20 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). The 32 Ori MG population 2 is Ma (BT-Settl models from Allard et al. 2012).

Appendix B: Variation of the LDB with the reddening

We adopted two very different reddening values for Alpha Persei: AV = 0.279 mag from Gaia Collaboration (2018b), and mag from Bossini et al. (2019) with (m − M)0 = 5.824 mag, 146 pc.

We studied the variation of the stellar parameters, Lbol and Teff, with both reddening values. We proceeded in the same way as in the whole article: we created two input files for VOSA, one with AV = 0.279 mag and other with AV = 0.055 mag. We show the results in Figure B.1 and in Table B.1.

thumbnail Fig. B.1.

Comparison between stellar parameters for Alpha Persei LDB sample using two different reddenings for the objects AV = 0.259 mag and AV = 0.055 mag. Top: Comparative analysis between effective temperatures shown as a 1:1 line and a dashed one shifted 75 K. Bottom: Comparison between bolometric luminosities.

Table B.1.

Stellar properties for the Alpha Persei LDB sample derived using two different reddening values.

A reddening of AV= 0.279 mag produced brighter luminosities and hotter effective temperatures than AV = 0.055 mag: a median offset of 0.21 × 10−3L with standard deviation of ±0.53 × 10−3L, and a systematic median offset of 79 K with standard deviation of ±28 K. In terms of percentages these changes were: 6.3% in bolometric luminosities (reaching a maximum of 8.3%) and 2.2 % in Teff. This change also affects the location of the LDB: using AV = 0.279 mag we found L and Teff LDB = 2 857 ± 74 K; using AV = 0.055 mag we found L and Teff LDB = 2 806 ± 71 K (Table B.2). The HRD show the changes (Figure B.2).

thumbnail Fig. B.2.

HRDs around the Alpha Persei LDB sample using two different reddening values. the blue isochrones correspond to BT-Settl models (Allard et al. 2013), with ages of 1, 10, 80, 100 Ma, and 1 Ga, where the thick one corresponds to a 80 Ma. We also show the Zero Age Main Sequence (Stahler & Palla 2005) as the green solid line. We have used the same symbols and standards than previous HRDs. Left: Reddening used is AV = 0.279 mag. It is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). Right: Reddening used is AV = 0.055 mag. It is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

Table B.2.

Alpha Persei LDB loci in terms of Lbol, Teff and the ages derived using several evolutionary models.

We conclude that a higher level of reddening produces an LDB at brighter bolometric luminosities and hotter effective temperatures and, therefore, younger ages. Ages obtained using the two reddening values with different evolutionary models for Alpha Persei are shown in Table B.2 We estimated that a decrease of 80% in AV produces an increase in age between 3 and 6 Ma depending on the model. These variations may not be the same in stellar associations such as the Hyades (older and closer) or NGC 1960 (younger and further).

Appendix C: Discussion of individual objects from BPMG

In this appendix, we provide information and remarks about some objects of the BPMG LDB sample. Some of them are visual binaries or multiple systems only resolved in Gaia DR2 and their bolometric luminosities are a combination of two or several sources in all photometric bands (except for Gaia). In these cases, we calculated the bolometric luminosities with the photometric bands as are given in the catalogues using the parallax of each of the components.

00164976 has a counterpart in Gaia DR2, 386050700157461760, without an astrometric solution.

00275023 (2MASS J 00275023-3233060, GJ 2006 A) and 00275035 (2MASS J 00275035-3233238, GJ 2006 B) form a wide binary system.

01071194 has a counterpart in Gaia DR2, 2353128266975662080, without an astrometric solution.

01112542 is a lithium-rich binary system (GJ 3076 AB, LP 467-16) with a separation between the two main components of 0.41″ (Beuzit et al. 2004) or 0.293 ± 0.002″ (Janson et al. 2012). The system lacks a counterpart in Gaia DR2.

01132817 is a binary system that is only resolved in Gaia DR2, composed of 4988735051246293504 (01132817a with ϖ = 19.95 mas) and 4988735051245195008 (01132817b with ϖ = 19.67 mas), both components with similar proper motions and are separated by 1.549″.

01535076 is a binary system resolved in Gaia DR2: 5143033331902438656 (01535076a ϖ = 29.54 mas) and 5143033331901973888 (01535076b ϖ = 29.53 mas) with a separation of 2.792″.

02335984 is a binary system resolved in Gaia DR2: 5132219016567875200 (02335984a, G = 13.53 mag and ϖ = 12.41 mas) and 5132219012272775808 (02335984b, G = 13.54 mag without parallax and proper motions). It was previously identified by Bergfors et al. (2010).

02365171 (GSC 08056-00482 with 25.742 mas) was considered as a possible outlier (Shkolnik et al. 2017) but we have discarded this possibility.

02485260 is classified as a single line binary (Malo et al. 2014a and Shkolnik et al. 2017).

03323578 lacks counterpart in Gaia DR2.

03363144 has a ϖ = 22.04 mas and was considered as a possible outlier (Shkolnik et al. 2017), but we have discarded this possibility

03393700 has associated three sources in Gaia DR2: 244734761312058240, with 0.38 mas, 244734765606605824 without parallax and the right counterpart 244734765608363136 with ϖ = 24.8 mas, a spectroscopic binary (Skinner et al. 2018).

04593483 (V1005 Ori) is a spectroscopic binary (Elliott et al. 2014).

05015881 is a double system (Song et al. 2003) or a quadruple system (HIP 23418 ABCD, see Malo et al. 2013). Mason et al. (2018) calculated a separation between the two main components of 1.234″. Two components are resolved in the Gaia DR2: GJ 3322A (3291643148740384128, LP 476-207 A, 05015881a) and GJ 3322B (3291643148741783296, LP 476-207 B, 05015881b). Song et al. (2003) found that the combined system HIP 23418 shows prominent emission lines of Na D λ5890 Å and λ5896 Å, He Iλ5876 Å and λ6876 Å, and Hα.

05241914 lacks counterpart in Gaia DR2, 2MASS J 05241914-1601153 probably because it is a binary system, M4.5+M5.0, with a separation of 0.639 ± 0.001″ (Bergfors et al. 2010). Lithium has been detected in the binary system (unresolved spectra from Malo et al. 2013 and Binks & Jeffries 2014).

05320450 (2MASS J 05320450-0305291, V1311 Ori) has a counterpart in Gaia DR2: 3216729573251961856 (ϖ = 28.94 mas) and it is identified as a lithium rich member in da Silva et al. (2009) just like Malo et al. (2013). Binks & Jeffries (2016) also detected lithium but they did not considered it as a member. Finally, Janson et al. (2012) reported this object as a binary system, M2V+M3.5V, with a separation of 0.216 ± 0.003″.

10172689 (5355751581627180288 with ϖ = 51.00 mas) could be contaminated by other background sources (5355751585943066880 with ϖ = 0.08 ± 0.26 mas and 5355751585947981568 with ϖ = 1.13 ± 1.20 mas) and other source detected in 2MASS: 10172697-5354200 (5355751585943068416 with ϖ = 0.58 ± 0.13 mas).

13545390 (5845972349875278720 ϖ = 43.76 mas) has associated the background object Gaia DR2 source 5845972349858754688 (ϖ = 0.09 mas).

15385679 is located in a very crowded region. It has associated two Gaia DR2 sources: the rigth one 5882581895192805632 (ϖ = 25.471 mas) and a background source 5882581929553337216 (ϖ = 0.896 mas).

16572029. There are three sources related that can contaminate the main one 5935776714456619008 (ϖ = 19.75 mas): 5935776714456617984 (ϖ = 0.41 mas) and 5935776714412775552 (ϖ = −0.35 mas).

17150219 is located in a very crowded region and three sources can contaminate the main object 5978985558581221760 (ϖ = 38.59 mas): 5978985562916750976 (ϖ = 0.05 mas) 5978985562873939456 (ϖ = 1.63 mas).

17173128 (HD 155555C, 5811866358170877184 with ϖ = 32.95 mas) the photometry might be contaminated with the ghosts from HD 155555, by a near background source (5811867835635129728 with ϖ = −0.14 mas located at 4.48″) or both. 17173128 together with 2MASS J 17172550-6657039 (V824 Ara, HIP 84586) take part in a multiple system.

17292067 is a source without parallax and proper motions, perhaps it is due to two sources detected in 2MASS very near: 17292067-5014529 and 17292064-5014574.

18142207 the main source, 4045698732855626624 (ϖ = 13.99 mas) could be contaminated by a background source 4045698737270604288 (ϖ = 1.57 mas).

18420483 the main source 6649786646225001984 (ϖ = 19.33 mas) could be contaminated by a background source 6649786646219487744 (ϖ = 0.01 mas).

18435838 is a lithium-rich object that has associated four counterparts in Gaia DR2: 6730618549223057664 (7.07 mas) the bright and main one, 6730618549223057920 (0.12 mas), 6730618549211759104 (-1.03 mas), and 6730618549211759232 (0.58 mas). Its parallax indicates that it is a background object, and it is very likely that the bolometric luminosity is a combination of the four sources. This object must be treated with caution. We considered it as a non-member and as a multiple system.

18465255. 18465255 (6631685008336771072, ϖ = 19.78 mas) could be contaminated by a background source, 6631685008335769728 (ϖ = 1.26 mas).

18471351. 18471351 (4071532308311834496, ϖ = 16.8 mas) could be contaminated by a background source, 4071532312630649344 (ϖ = −0.29 mas).

19082195. 19082195 (4088823159447848064, ϖ = 14.4 mas) could be contaminated by a background source, 4088823163758008192 (ϖ = 1.46 mas).

19102820 is a binary system formed by two sources separated by 0.424″ (Janson et al. 2017), both sources are resolved in Gaia DR2 and both without parallaxes: 4080460377082576128 (19102820a, the closest source 19102820a with G = 12.07 mag) 4080460381377496832 (19102820b with G = 19.42 mag).

19260075. 19260075 (6643851448094862592, ϖ = 20.82 mas) could be contaminated by a background source, 6643851448094200320 (ϖ = −0.33 mas).

19560294 (1RXS J195602.8-320720, 6747467431032539008 with ϖ = 18.02 mas) is a spectroscopic binary (Elliott et al. 2014).

20004841. 20004841 (6366726276822544768, ϖ = 33.96 mas) could be contaminated by a background source, 6366726276820119040 (ϖ = 0.23 mas).

20085368 is a multiple system with two sources associated, a possible binary resolved with Gaia DR2 separated 1.426″: 20085368a (6697858840776095616 with ϖ = 22.22 mas) and 20085368b (6697858840773435776 with ϖ = 22.43 mas).

20100002 (SCR J2010-2801) is a source without parallax and proper motions, this is probably because it is a double line binary (Malo et al. 2014a).

20434114 is a visual binary (Shkolnik et al. 2009) as we can confirm using Gaia DR2 data: 20434114a (6806301370519190912 with ϖ = 22.81 mas) and 20434114b (6806301370521783552 with ϖ = 23.51 mas).

20415111 (AT Mic, HD 196982) is a binary system formed by two sources (Torres et al. 2006): 20415111a (6792436799475128960, TYC-7460-137-1) and 20415111b (6792436799477051904, TYC-7460-137-2) both resolved in Gaia DR2 and Tycho-2, but not resolved in other surveys as 2MASS or WISE.

20560274 (AZ Cap, HD 358623) is a binary system formed by two sources separated by 2.181″ (Janson et al. 2017) and also it is resolved in Gaia DR2: 20560274a (6882838031331951488 with ϖ = 21.77 mas) and 20560274b (6882838031330569856 with ϖ = 21.62 mas). Also there is a very close background object: it is only detected in Gaia DR2: 6882838031330568960, with ϖ = 0.64 mas.

21374019 (WDS J21376+0137AB, RX J2137.6+0137) is a binary system (Mason et al. 2001) and perhaps due to that lacks of parallax and proper motions in Gaia DR2.

23353085 has counterpart in Gaia DR2, 2392233119572232064, but lacks parallax and proper motions.

Appendix D: 32 Ori MG as one or two associations

In this appendix, we report on a significant aspect of 32 Ori MG. In contrast to other stellar associations, the moving group appears to be composed of two sub-samples. First, we calculated the parallax PDF of the known members as it is explained in Section 4.1. We realized that some of them are non-members due to the parallax: 2MASS J05572121+0502158 (ϖ = 0.325 mas) and TYC 4767-689-1 (ϖ = 1.759 mas) are background sources; 2MASS J05053333+0044034 (ϖ = 21.255 mas), THOR-33 (ϖ = 25.944 mas) and THOR-34 (ϖ = 26.069 mas) are foreground sources. We removed them and re-did the parallax PDF.

We carried out this process twice and the results are shown Figure D.1. After the first and the second iteration, we can see two maximums in the parallax PDF: around 8.93 mas and 10.21 mas and after the second iteration in 8.95 mas and 10.19 mas. It appears that the population of 32 Ori MG is composed of two populations. This fact is also remarkable with the distances released by Bell et al. (2017). We divided the two populations based on parallaxes: population 1 with ϖ < 9.52 mas and population 2 with ϖ > 9.52 mas.

thumbnail Fig. D.1.

Parallax PDF for the 32 Ori MG known members (taken from Bell et al. 2017). The modelled PDF is shown in gray and a superimposed histogram in blue. The cyan vertical dashed lines point the percentiles of the raw data at the 2.5th, 25th, 50th, 75th, and 97.5th. The magenta vertical dotted lines point the same percentiles as before but calculated from the modelled KDE. The red vertical line shows the mode of the PDF. The small vertical black lines below the horizontal axis (below y = 0.0) shows the parallaxes of each source. Top: All the previous known members from Bell et al. (2017). Middle: First iteration. Bottom: Second iteration.

We do not see any trend across both figures in terms of the sky distribution and the VPD of the two populations in Fig. D.2. We calculated the parallax PDF using a width validated with cross-validation, but this value may produce these two maximums in the parallax PDF and we must be cautious with our results.

thumbnail Fig. D.2.

Spatial distribution and VPD for the 32 Ori MG members. Top: Spatial distribution of the known members from Bell et al. (2017), after removing some outliers. The two populations based on parallaxes are shown. Bottom: VPD of the 32 Ori MG, sub-sample red squares are population 1 (ϖ < 9.52 mas) and blue circles population 2 (ϖ > 9.52 mas). Black dashed ellipses are the Pleiades members taken from Gaia Collaboration 2018b and the light grey plus symbols are the Taurus-Auriga members taken from Ducourant et al. (2005). The proper motion data have been taken from the Gaia DR2 catalogue, with the exception of the Taurus sample that comes from Ducourant et al. (2005).

In any case, we located the LDB for each sub-sample. We located the LDB at and Teff LDB = 3 157 ± 71 K for population 1 (Figure A.23c). The large uncertainties are due to the scarcity number of sources. For population 2, we located the LDB at L and Teff LDB = 3 098 ± 71 K (Figure A.23d). However, the LDB might be located at fainter bolometric luminosities due to the scarcity of sources. The Lbol LDB may be able to reach 23.418 × 10−3L, which would result in an age increase of about 2 Ma.

We carried out an extra analysis to analyse the 32 Ori MG population. We crossmatched the 32 Ori MG sources with the stellar groups identified in Kounkel & Covey (2019) work. The sources from Bell et al. (2017) belong to two different stellar groups: Theia 133, with logage = 7.74419 (55 Ma) and ϖ = 6.376 mas, and Theia 370, with logage = 8.16773 (147 Ma) and ϖ = 6.552 mas. This outcome is contrary to our previous naive population division based on parallaxes. Following the Kounkel & Covey (2019) membership criterion, we determined the LDB for these stellar associations. For Theia 133, we located the LDB at and Teff LDB = 3 139 ± 71 K. However, the uncertainties are underestimated due to the source scarcity between the faintest lithium-poor source, THOR-14B and the lithium-rich one, THOR-17B, so, the LDB would be located at , see Figure D.3a. In the same way, for Theia 370 we located the LDB at and Teff LDB = 3 087 ± 71 K, (Figure D.3b). The Lbol LDB uncertainties are underestimated, as is also the case with Theia 133, and the updated LDB would be .

thumbnail Fig. D.3.

HRDs and the LDB for Theia 130 and Theia 370. All the symbols and lines follow the same convention as Figure A.23. The blue lines correspond to a isochrones of 1, 10, 30, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), where the thick one corresponds to a 30 Ma. The figure includes a 20 Ma isochrone from D’Antona & Mazzitelli 1994 (black dashed line). (a): Theia 133. The figure includes a 20 Ma isochrone from Siess et al. 2000 (red dotted line) and a 18 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). Theia 133 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (b): Theia 370. The figure includes a 25 Ma isochrone from Siess et al. 2000 (red dotted line) and a 20 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). Theia 370 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

There are still many unanswered questions about the real existence of this moving group: the two peaked parallax distribution together with the evidence of two stellar groups as Kounkel & Covey (2019) released. To develop a full picture of the 32 Ori MG, we need additional membership kinematic studies.

Appendix E: Additional tables

Table E.1.

Priors used in the distance calculation with Kalkayotl.

Table E.5, available at the CDS, includes calculated and collected stellar parameters for each object from each LDB sample. Parallaxes and proper motions were taken from Gaia DR2. Here, ‘ρμα *  μδ’ is the correlation between proper motion in right ascension and proper motion in declination; ‘EW Li’ is the equivalent width of Li I at 6 707.8 Å, with its reference ‘Ref.’. Equivalent width of a lithium-poor object is given by an upper limit or without any measure; if this is the case, then it is shown as ‘-’. There are some objects that have undetermined lithium content because the data retrieved from the literature have low resolving power, low signal-to-noise ratio, or bad quality or they do not cover this part of the spectrum. These objects are marked with ‘⋯’. The label ‘Li rich’ indicates whether it is a lithium-rich or lithium-poor object based on ‘EW Li’: ‘Y’ indicates a lithium-rich object, ‘N’ indicates a lithium-poor object and ‘?’ indicates an object with undetermined lithium content. ‘Other’ means other remarks of the source: ‘EL’ means strong emission line object, ‘F’ is a flaring object, ‘FR’ is a fast rotator, ‘NM’ is no member (based on this work), ‘SuB’ suspected binary or multiple system, ‘CMS’ is a confirmed binary or multiple system. Then, ‘dMAP’, ‘dmin’, and ‘dmax’ are the distances for each object. If a source lacks a parallax, proper motions, or both in Gaia DR2 or it has a negative parallax, we indicated the distances with ‘-’.

We complete this appendix with tables that gather photometric bands for each stellar association, with the exception of THMG and 32 Ori MG, where all the photometric bands were recovered using VOSA. The values in parentheses have not been taken into account in the SED fitting.

Table E.2.

Comparison between stellar parameters derived with VOSA and StarHorse.

Table E.3.

Comparison between stellar parameters derived with VOSA and from GES (Randich et al. 2018).

Table E.5.

Photometry for the Alpha Persei members retrieved from the literature.

Table E.6.

Photometry for the NGC 1960 members retrieved from the literature.

Table E.7.

Photometry for the IC 4665 members retrieved from the literature.

Table E.8.

Photometry for the NGC 2547 members retrieved from the literature.

Table E.9.

Photometry for the IC 2602 members retrieved from Dobbie et al. (2010).

Table E.10.

Photometry for the IC 2391 members retrieved from the literature.

Table E.11.

Photometric bands recovered from several works and the literature for the Pleiades LDB sample, part I.

Table E.12.

Photometry for the Pleiades members retrieved from the literature, part II.

Table E.13.

Other identifiers for the Pleiades LDB sample.

Table E.14.

Photometry for the Blanco 1 members retrieved from the literature.

Table E.15.

Photometry for the Hyades members retrieved from the literature.

Table E.17.

Stellar properties for the Hyades LDB sample. Quantities obtained from Hogan et al. (2008).

Table E.18.

Stellar properties for the Hyades LDB sample. Quantities obtained from Lodieu et al. (2014).

Table E.19.

Stellar properties for the Hyades LDB sample. Quantities obtained from Martín et al. (2018).

Table E.20.

Stellar properties for the Hyades LDB sample. Quantities obtained from Lodieu et al. (2019b).

Table E.21.

Other identifiers for the 32 Ori MG LDB sample.

All Tables

Table 1.

Data from the literature for the twelve stellar associations with LDB ages.

Table 2.

Parallax distributions from the initial sample of cluster members using a KDE based on Gaia DR2 data.

Table 3.

LDB loci in terms of Lbol, Teff and the ages derived using several evolutionary models.

Table 4.

Differences in fluxes between MARCS and BT-Settl model atmosphere.

Table 5.

Properties of the Lithium Depletion Boundary for the 12 stellar associations.

Table B.1.

Stellar properties for the Alpha Persei LDB sample derived using two different reddening values.

Table B.2.

Alpha Persei LDB loci in terms of Lbol, Teff and the ages derived using several evolutionary models.

Table E.1.

Priors used in the distance calculation with Kalkayotl.

Table E.2.

Comparison between stellar parameters derived with VOSA and StarHorse.

Table E.3.

Comparison between stellar parameters derived with VOSA and from GES (Randich et al. 2018).

Table E.5.

Photometry for the Alpha Persei members retrieved from the literature.

Table E.6.

Photometry for the NGC 1960 members retrieved from the literature.

Table E.7.

Photometry for the IC 4665 members retrieved from the literature.

Table E.8.

Photometry for the NGC 2547 members retrieved from the literature.

Table E.9.

Photometry for the IC 2602 members retrieved from Dobbie et al. (2010).

Table E.10.

Photometry for the IC 2391 members retrieved from the literature.

Table E.11.

Photometric bands recovered from several works and the literature for the Pleiades LDB sample, part I.

Table E.12.

Photometry for the Pleiades members retrieved from the literature, part II.

Table E.13.

Other identifiers for the Pleiades LDB sample.

Table E.14.

Photometry for the Blanco 1 members retrieved from the literature.

Table E.15.

Photometry for the Hyades members retrieved from the literature.

Table E.17.

Stellar properties for the Hyades LDB sample. Quantities obtained from Hogan et al. (2008).

Table E.18.

Stellar properties for the Hyades LDB sample. Quantities obtained from Lodieu et al. (2014).

Table E.19.

Stellar properties for the Hyades LDB sample. Quantities obtained from Martín et al. (2018).

Table E.20.

Stellar properties for the Hyades LDB sample. Quantities obtained from Lodieu et al. (2019b).

Table E.21.

Other identifiers for the 32 Ori MG LDB sample.

All Figures

thumbnail Fig. 1.

Projected positions for IC 2391 (black pluses are members from Gaia Collaboration 2018b and green triangles objects from the LDB sample) and IC 2602 (blue crosses are members from Gaia Collaboration 2018b and red circles sources from the LDB sample).

In the text
thumbnail Fig. 2.

Parallax PDF for the Alpha Persei members (taken from Gaia Collaboration 2018b). The modelled PDF is shown in gray and a superimposed histogram in blue. The two magenta vertical dotted lines point the 2.5th and 97.5th percentiles; the two cyan vertical dashed lines point the quartiles and the the red vertical line shows the mode of the PDF. The small vertical black lines below the horizontal axis (below y = 0.0) show the parallaxes of each source.

In the text
thumbnail Fig. 3.

VPD for Alpha Persei. Top: blue dashed ellipses are the members taken from Gaia Collaboration (2018b); red ones are the LDB sample objects. Five sources (AP296, AP310, AP313, AP317, and AP322) possess a proper motion different from that of the rest of the members. AP272 is also shown (see the text). Uncertainties in the proper motions and its correlations are taken into a account and shown as ellipses. All data have been taken from the Gaia DR2 catalogue. Bottom: zoom on the previous plot.

In the text
thumbnail Fig. 4.

Parallaxes for 17 selected Alpha Persei sources close to the LDB. The grey filled area shows the parallax distribution from Gaia Collaboration (2018b) between the percentiles 2.5th and 97.5th, while the distribution quartiles are delimited by a red filled area superimposed. All the parallaxes have been taken from the Gaia DR2 catalogue. The standard deviation (STD), the weighted mean, and the median of the LDB sample are also displayed.

In the text
thumbnail Fig. 5.

Bolometric luminosity PDF for the Alpha Persei LDB, after run 60 000 bootstrap samples, see Sect. 4.4. We show all the sample distribution as a blue histogram, and we model a PDF with all the values in grey. We highlight the mode of the PDF with a red line and the percentiles at 16th and 84th with two red dashed ones.

In the text
thumbnail Fig. 6.

HRD and the LDB for Alpha Persei. Left: symbols are as follows: green solid circles are lithium-rich sources and magenta triangles lithium-poor ones, both from our LDB sample; empty large broken black circles are suspected multiple systems; over-imposed big black crosses are sources discarded as members after this work; and grey points are known members from Gaia Collaboration (2018b). Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 80 Ma. The figure also includes 70 Ma isochrones from: D’Antona & Mazzitelli (1994; black dashed line), Tognelli et al. (2011; orange dashed dot line), Siess et al. (2000; red dotted line), and a Zero Age Main Sequence from Stahler & Palla (2005; the green solid line). Right: zoom on the left plot. A black horizontal line marks the Lbol LDB, together with the 16th and 84th percentiles (dotted lines). Alpha Persei is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). For clarity, members from Gaia Collaboration (2018b) are not shown.

In the text
thumbnail Fig. 7.

Location of the LDB for all studied stellar associations and its relation with the age. We show bolometric magnitudes of the LDB for each stellar association as horizontal lines (several colours). Uncertainties are not shown for clarity. The lines that cross diagonally from the lower left corner to the upper right one correspond to different LDB models: the dashed black line is the D’Antona & Mazzitelli (1994) LDB, the dashed dotted brown thicker line is the Burrows et al. (1997) LDB, the dashed dotted green thinner line is the Burke et al. (2004) LDB, the dotted red line thicker corresponds to the Pisa LDB (Tognelli et al. 2015), the dotted red line thiner correspond to the Siess et al. (2000) LDB and the blue line is the BT-Settl LDB (Allard et al. 2013).

In the text
thumbnail Fig. 8.

2MASS RGB images of three remarkable sources belonging to BPMG. The main source, 2MASS catalogue, is shown with a purple cross, the Gaia DR2 counterparts are shown with green squares and proper motions- with cyan dotted lines. Top: 20085368 is a binary system resolved with Gaia DR2. Medium: 18420438 is a source whose photometry may be contaminated by a background source. Bottom: 05015881 is a binary system whose photometry is resolved in Gaia DR2 and there is a very close background source.

In the text
thumbnail Fig. 9.

Location of all 32 Ori MG sources (red circles from Bell et al. 2017), together with the Hyades (purple triangles), the Pleiades (blue squares), and Taurus members (grey pluses from Ducourant et al. 2005). The Hyades and the Pleiades members are taken from Gaia Collaboration (2018b).

In the text
thumbnail Fig. 10.

Comparison of our calculated distances, dMAP and those derived with StarHorse (Anders et al. 2019).

In the text
thumbnail Fig. 11.

Comparison of effective temperatures derived in Anders et al. (2019) and from VOSA. Top: Ssources from the LDB samples. Note we did not find any NGC 2547 counterpart in StarHorse. Bottom: only those sources considered as members after this work.

In the text
thumbnail Fig. 12.

Comparison of effective temperatures derived in Randich et al. (2018) and from VOSA. Top: all the sources are members from Gaia Collaboration (2018b) with counterpart in Randich et al. (2018). Bottom: only sources considered as members after this work from the LDB samples with counterpart in Randich et al. (2018).

In the text
thumbnail Fig. 13.

Radar chart with LDB ages estimated using several evolutionary grid models. The age values showed as filled circles and connected with dashed lines are the same as Table 3. We also show the mean age value (thin solid line) and its standard deviation (the shadow region) for each association.

In the text
thumbnail Fig. 14.

Comparison between our LDB age and the age estimated using other techniques. Left: sges derived from the isochrone fitting technique. The ages come from: Gaia Collaboration (2018b; blue diamonds), Bossini et al. (2019; purple squares), and Mermilliod (1981; gray circles). Middle: ages derived from the Pre Main-Sequence isochrone fitting technique. Orange diamonds represent PMS isochrone fitting ages: the Pleiades, BPMG, THMG and 32 Ori MG, Bell et al. (2013, 2014, 2015); and IC4665, Cargile & James (2010). Brown squares are the rest of PMS isochrone fitting ages: NGC 1960, Bell et al. (2013); IC 4665, Manzi et al. (2008); NGC 2547, Naylor & Jeffries (2006); IC 2602 and IC 2391, Stauffer et al. (1997); Alpha Persei, Prosser (1992); the Pleiades, Stauffer et al. (1995b); Blanco 1, Cargile et al. (2009); BPMG and THMG, Torres et al. (2006); and 32 Ori MG, Mamajek (2007). Right: LDB ages derived from previous works. See the references in Table 1, its legend, and Sect. 2.

In the text
thumbnail Fig. 15.

Radar charts with ages in [Ma] calculated using different techniques: ‘LDB’ refers to our calculated ages using the BTSettl (see Table 3); ‘Gyr’ is the gyrochronology ages (Cargile et al. 2014); ‘ISO’ is isochrone fitting ages (Gaia Collaboration 2018b); ‘PMS’ is PMS isochrone fitting ages from several works: IC 2602 (Stauffer et al. 1997); Alpha Persei (Prosser 1992); the Pleiades (Stauffer et al. 1995b). Then, ‘Grav” is the gravity ages (David & Hillenbrand 2015); ‘WD’ is the ages derived using the white dwarf cooling sequence age: Alpha Persei and the Pleiades (Lodieu et al. 2019a); the Hyades (Lodieu et al. 2019b). Left: age range ∈[0, 800] Ma. Right: zoom onto the age range ∈[0, 160] Ma.

In the text
thumbnail Fig. A.1.

VPD and parallaxes for NGC 1960. Left: VPD, for NGC 1960. Blue dashed ellipses are the members taken from Cantat-Gaudin et al. 2018a; red ellipses are our LDB sample. The rest is the same as in Fig. 3 but for NGC 1960. Right: same as in Fig. 4 but for NGC 1960.

In the text
thumbnail Fig. A.2.

HRDs and the LDB for NGC 1960. (a) Same as Fig. 6. Cyan squares are lithium-rich sources without Gaia DR2 parallaxes and purple stars are lithium upper limits or lithium-poor sources without Gaia DR2 parallaxes, both from our LDB sample (see Section 4.2); empty large black circles are confirmed multiple systems and broken lines are suspected multiple systems; over-imposed big black crosses are sources discarded as members after this work. Moreover, grey points are known members from Cantat-Gaudin et al. (2018a). Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one corresponds to 30 Ma. The figure includes: a 20 Ma and a 30 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed line), a 25 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line), a 30 Ma isochrone from Siess et al. 2000 (red dotted line) and a Zero Age Main Sequence from Stahler & Palla 2005 (green solid line). (b) Zoom on the left plot. A black horizontal line marks the Lbol LDB, together with the 16th and 84th percentiles (dotted lines). NGC 1960 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). An extensive dashed horizontal green line indicates a possible LDB upper limit (see Section 5.2).

In the text
thumbnail Fig. A.3.

VPD for IC 4665. Left: Details are the same as in Fig. 3 but for IC 4665. Right: Zoom on the left figure.

In the text
thumbnail Fig. A.4.

Parallaxes for IC 4665 members close to the LDB. Details are the same as in Fig. 4 but for IC 4665.

In the text
thumbnail Fig. A.5.

HRDs and the LDB for IC 4665. (a) the same as in Figs. 6 and A.2 but for IC 4665. The violet crosses are sources with undetected or dubious lithium detections due to their low resolution spectrum or other technical disabilities. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 30 Ma. The figure includes: a 20 Ma and a 30 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed lines), a 25 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line), a 30 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the previous plot around the LDB with all the source names. (c) A black horizontal line marks the Lbol LDB, together with the 16th and 84th percentiles (dashed lines), following the first scenario, see Section 2.3. (d) Same as (b), but the the Lbol LDB is located following the second scenario, see Section 2.3. It is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. A.6.

VPD and parallaxes for NGC 2547. Left: Same details as in Fig. 3 but for NGC 2547. Right: Same as in Fig. 4 but for NGC 2547.

In the text
thumbnail Fig. A.7.

HRDs and the LDB for NGC 2547. (a) the same as in Fig. 6 and A.2 but for NGC 2547. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue lines to 40 and 50 Ma. The figure includes: a 30 Ma and a 50 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed lines), a 35 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line), a 40 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the (a) plot around the 52 radial velocity members from Jeffries et al. (2004) sample. (c) Zoom around the LDB. NGC 2547 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). We show the names of all the objects but not the uncertainties (for the purposes of clarity).

In the text
thumbnail Fig. A.8.

VPD and parallaxes for IC 2602. Left: Same details as in Fig. 3 but for IC 2602. Source 10443357 possesses a proper motion far different than the rest of members. Right: Same as in Fig. 4 but for IC 2602.

In the text
thumbnail Fig. A.9.

HRDs and the LDB for IC 2602. (a): The same as in Fig. 6 but for IC 2602. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 50 Ma. The figure includes 50 Ma isochrones from: Siess et al. 2000 (red dotted line), D’Antona & Mazzitelli 1994 (black dashed line). (b): Zoom on the (a) plot with the LDB. IC 2602 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. A.10.

VPD for IC 2391 and IC 2602 members and parallaxes for IC 2391. Left: Same details as in Fig. 3 but for IC 2391 and IC 2602. Some objects have uncertainties smaller than the size of the markers. Black dotted ellipses are the IC 2391 members and blue dashed ellipses are the IC 2602 members, green solid ellipses are the IC 2391 LDB sample objects, and red solid ellipses are the IC 2602 LDB sample objects. Right: The same as in Fig. 4 but for IC 2391.

In the text
thumbnail Fig. A.11.

HRDs and the the LDB for IC 2391. (a) The same as in Fig. 6 but for IC 2391. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 60 Ma. The figure includes: a 50 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed line), a 60 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the left plot with the location of the LDB. IC 2391 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. A.12.

VPD for the Pleiades. Left: Same details as in Fig. 3 but for the Pleiades. Light grey plus symbols are the Taurus-Auriga members taken from the Ducourant et al. (2005) proper motions catalogue. Right: Zoom on the left figure.

In the text
thumbnail Fig. A.13.

Parallaxes for the Pleiades members close to the LDB. Same details as in Fig. 4 but for the Pleiades.

In the text
thumbnail Fig. A.14.

HRDs and the LDB for the Pleiades. (a) The same as in Fig. 6 but for the Pleiades. In addition, grey points are known members from Gaia Collaboration (2018b), and sienna points from Bouy et al. (2015). Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 120 Ma. The figure includes: a 100 and 200 Ma isochrones from D’Antona & Mazzitelli 1994 (black dashed lines), and a 120 Ma isochrone from Siess et al. 2000 (red dotted line). (b) Zoom on the previous plot with the location of the LDB. The Pleiades is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. A.15.

VPD and parallaxes for Blanco 1. Left: Same details as in Fig. 3 but for Blanco 1. Right: Same as in Fig. 4 but for Blanco 1. We note that CFHT-BL-36 has got negative parallax.

In the text
thumbnail Fig. A.16.

HRDs and the LDB for Blanco 1. (a) Same as in Fig. 6 but for Blanco 1. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 120 Ma. The figure includes: a 120 Ma isochrone from Siess et al. 2000 (red dotted line), a 100 and a 200 Ma from D’Antona & Mazzitelli 1994 (black dashed lines). The rest of the symbols follow the same convention as previous HRDs. (b) Zoom on the left plot close to the LDB. The Blanco 1 age is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (c) Same as (b), but the LDB is located after discarding sources whose radial velocities are not within the 1σ radial velocity criterion, see Section 2.8. The tri-down symbols are over-imposed in the non-members following this criterion. The Blanco 1 age is Ma (BT-Settl models from Allard et al. 2012).

In the text
thumbnail Fig. A.17.

VPD and parallaxes for the Hyades. Left: Same as in Fig. 3 but for the Hyades. We have added proper motions for the LDB sample sources from: Hogan et al. 2008 (purple filled circles); Lodieu et al. 2014 (grey triangles with their uncertainties); Pérez-Garrido et al. 2017 (the 2M0418, the black plus symbol); Lodieu et al. 2019b (orange stars with their uncertainties). Right: Same as in Fig. 4 but for the Hyades. We have added parallax values from Lodieu et al. (2019b) in blue, (above the black dashed line).

In the text
thumbnail Fig. A.18.

HRDs and the LDB for the Hyades. (a) The same as in Fig. 6 but for the Hyades. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 700 Ma. (b) Zoom on the previous plot close to the LDB. (c) Same as the previous plot but, we considered that Hya10 has an unclear lithium detection. The Hyades is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. A.19.

HRDs and the LDB for the BPMG. (a) The same as in Fig. 6 but for the BPMG. Empty large black broken line circles are suspected multiple systems or sources with associated background objects and photometric data blended in some bands. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 20 Ma. Uncertainties are not shown in order to gain clarity, although in the bolometric luminosities are usually smaller than the symbols, with the exception of some sources without parallaxes. The figure includes 20 Ma isochrones from: D’Antona & Mazzitelli 1994 (black dashed line), Siess et al. 2000 (red dotted line), and a 17 Ma from Tognelli et al. 2011 (orange dashed dot line). (b) Zoom on the (a) plot around the LDB. The size of lithium-poor sources has been increased to locate the LDB. The area delimited by them is marked with gray thick dashed lines. Some remarkable sources are labelled. (c) Same as the previous plot with the LDB locus determined following the first scenario. Since we focus on the sole aim of locating the LDB, we do not show: sources that are confirmed or suspected multiple systems; sources with two or several associated objects (third configuration) with photometric data blended in some bands; non-members; sources with undetected lithium feature; and objects without parallaxes. Effective temperatures uncertainties are shown in some lithium poor objects in order to gain clarity, Bolometric luminosities uncertainties are smaller than the size of the symbols. The BPMG is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (d) Same as the previous plot with the LDB locus determined following the second scenario.

In the text
thumbnail Fig. A.20.

HRDs and the LDB for the THMG. (a) Same as in Fig. 6 but for THMG. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 50 Ma. The figure includes 50 Ma isochrones from: D’Antona & Mazzitelli 1994 (black dashed line), and Siess et al. 2000 (red dotted line). It also includes a 40 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). (b) Zoom on the (a) plot around the LDB following the first scenario. To retain clarity, we have only drawn the effective temperature uncertainties and the names for the sources that defined the LDB and two additional sources. The uncertainties in the bolometric luminosities are usually smaller than the size of the symbols. (c) Same as (b), but the LDB is located following the second scenario (Section 2.11). The THMG is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. A.21.

VPDs for the 32 Ori MG. Left: The red ellipses are all 32 Ori MG members (Bell et al. 2017); the black filled triangles are Hyades members and the blue squares are Pleiades members, (both from Gaia Collaboration 2018b); and the light grey plus symbols are the Taurus-Auriga members taken from Ducourant et al. (2005). The size of the symbols is greater than the size of the uncertainties (shown as ellipses). Right: Zoom on the previous plot.

In the text
thumbnail Fig. A.22.

Parallaxes for the 32 Ori MG members close to the LDB. Same as in Fig. 4 but for the 32 Ori MG. We removed the ‘THOR-’ prefix of each object from the name.

In the text
thumbnail Fig. A.23.

HRDs and the LDB for the 32 Ori MG. (a) The same as in Fig. 6 but for 32 Ori MG. Empty black diamonds correspond to fast rotators. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue lines to a 20 and 30 Ma. The figure includes 20 Ma isochrones from Siess et al. 2000 (red dotted line), and D’Antona & Mazzitelli 1994 (black dashed line). It also includes a 18 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). (b) Zoom on the previous plot around the LDB. We added the sources HCG 332 and HCG 509 (see Section 2.12). The 32 Ori MG is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (c) Zoom on the LDB for 32 Ori MG population 1, see Appendix D. The 32 Ori MG population 1 is Ma (BT-Settl models from Allard et al. 2012). (d) Zoom on the LDB for 32 Ori MG population 2, see Appendix D. Thin blue lines correspond to isochrones of 1, 10, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), while the thick blue one to 30 Ma. The figure includes: a 25 Ma isochrone from Siess et al. 2000 (red dotted line), a 20 Ma isochrone from D’Antona & Mazzitelli 1994 (black dashed line), and a 20 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). The 32 Ori MG population 2 is Ma (BT-Settl models from Allard et al. 2012).

In the text
thumbnail Fig. B.1.

Comparison between stellar parameters for Alpha Persei LDB sample using two different reddenings for the objects AV = 0.259 mag and AV = 0.055 mag. Top: Comparative analysis between effective temperatures shown as a 1:1 line and a dashed one shifted 75 K. Bottom: Comparison between bolometric luminosities.

In the text
thumbnail Fig. B.2.

HRDs around the Alpha Persei LDB sample using two different reddening values. the blue isochrones correspond to BT-Settl models (Allard et al. 2013), with ages of 1, 10, 80, 100 Ma, and 1 Ga, where the thick one corresponds to a 80 Ma. We also show the Zero Age Main Sequence (Stahler & Palla 2005) as the green solid line. We have used the same symbols and standards than previous HRDs. Left: Reddening used is AV = 0.279 mag. It is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). Right: Reddening used is AV = 0.055 mag. It is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text
thumbnail Fig. D.1.

Parallax PDF for the 32 Ori MG known members (taken from Bell et al. 2017). The modelled PDF is shown in gray and a superimposed histogram in blue. The cyan vertical dashed lines point the percentiles of the raw data at the 2.5th, 25th, 50th, 75th, and 97.5th. The magenta vertical dotted lines point the same percentiles as before but calculated from the modelled KDE. The red vertical line shows the mode of the PDF. The small vertical black lines below the horizontal axis (below y = 0.0) shows the parallaxes of each source. Top: All the previous known members from Bell et al. (2017). Middle: First iteration. Bottom: Second iteration.

In the text
thumbnail Fig. D.2.

Spatial distribution and VPD for the 32 Ori MG members. Top: Spatial distribution of the known members from Bell et al. (2017), after removing some outliers. The two populations based on parallaxes are shown. Bottom: VPD of the 32 Ori MG, sub-sample red squares are population 1 (ϖ < 9.52 mas) and blue circles population 2 (ϖ > 9.52 mas). Black dashed ellipses are the Pleiades members taken from Gaia Collaboration 2018b and the light grey plus symbols are the Taurus-Auriga members taken from Ducourant et al. (2005). The proper motion data have been taken from the Gaia DR2 catalogue, with the exception of the Taurus sample that comes from Ducourant et al. (2005).

In the text
thumbnail Fig. D.3.

HRDs and the LDB for Theia 130 and Theia 370. All the symbols and lines follow the same convention as Figure A.23. The blue lines correspond to a isochrones of 1, 10, 30, 100 Ma, and 1 Ga from the BT-Settl models (Allard et al. 2013), where the thick one corresponds to a 30 Ma. The figure includes a 20 Ma isochrone from D’Antona & Mazzitelli 1994 (black dashed line). (a): Theia 133. The figure includes a 20 Ma isochrone from Siess et al. 2000 (red dotted line) and a 18 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). Theia 133 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012). (b): Theia 370. The figure includes a 25 Ma isochrone from Siess et al. 2000 (red dotted line) and a 20 Ma isochrone from Tognelli et al. 2011 (orange dashed dot line). Theia 370 is Ma old using the BT-Settl bolometric luminosity-age relationship (Allard et al. 2012).

In the text

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