EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 656 (December 2021) A&A, 656 (2021) A149 Full HTML
Free Access
Issue
A&A
Volume 656, December 2021
Article Number A149
Number of page(s) 18
Section Galactic structure, stellar clusters and populations
DOI https://doi.org/10.1051/0004-6361/202141747
Published online 16 December 2021

© ESO 2021

1. Introduction

During the last years, a large number of young and intermediate-age stellar clusters (with ages of up to about two billion years) have been discovered in the Magellanic Clouds (MCs) that exhibit extended main-sequence turnoffs (eMSTOs, Mackey & Broby Nielsen 2007; Milone et al. 2009, 2018; Li et al. 2017). The youngest of these (τ ≤ 700 Ma) also display split main sequences (MSs, Bastian et al. 2017; Correnti et al. 2017; Li et al. 2017; Milone et al. 2018), similar to those observed in the old globular clusters of the Milky Way (MW). These features are not a peculiarity of the MCs clusters alone, but have recently been found in Galactic open clusters as well (Marino et al. 2018a; Cordoni et al. 2018; Piatti & Bonatto 2019; Li et al. 2019; Sun et al. 2019). This fact, which appears to be quite common, leads us to critically reconsider the assumption that colour-magnitude diagrams (CMDs) of open clusters can be reproduced by a single isochrone as a consequence of an unique and homogeneous stellar population, as has been thought until now. This has led, for instance, to the use of the so-called isochrone cloud to fit the CMDs of clusters displaying an eMSTO (Johnston et al. 2019).

It has been observed that the magnitude of the eMSTO/split MS phenomenon is related to the cluster age (Niederhofer et al. 2015; Cordoni et al. 2018), which would imply that it is caused by an evolutionary effect. Stellar rotation is accepted as the main cause (Marino et al. 2018b; Sun et al. 2019). Observed and synthetic CMDs were compared, and based on this, split MSs have been explained by the coexistence of two stellar populations with different rotation rates (D’Antona et al. 2015; Milone et al. 2016). One of them, which includes about two-thirds of the total MS stars, consists of fast rotators and forms the so-called red MS (rMS), while the other one, the blue MS (bMS), is composed of the slow-rotating stars. Additionally, in the area of the CMDs around the MSTO, fast rotators are brighter than the slow ones. This picture has been directly confirmed directly through measurements of projected rotational velocities (v sin i) in eMSTO stars in the two MCs (Dupree et al. 2017; Marino et al. 2018b) and in MW open clusters (Sun et al. 2019).

However, rotation alone is not always able to explain the observational behaviour. In certain situations, an age spread resulting from a prolonged star formation history or multiple star formation episodes is also required (Goudfrooij et al. 2017; Gossage et al. 2019). Nonetheless, this is not the case for open clusters, whose mass is well below the mass considered necessary to create multiple populations (Krumholz et al. 2019; Gratton et al. 2019). Alternatively, according to D’Antona et al. (2017), the rotational braking that is due to tidal interactions between the components of close binaries from a single stellar population of coeval stars may also produce a distribution of rotational velocities capable to reproduce the eMSTOs and split MSs observed in the CMDs. A greater number of observations are necessary to elucidate and constrain the role of each of these mechanisms, or of any other mechanism that is still hidden underneath it. This will allow us to fully understand this phenomenon.

Here we report the analysis of a large sample of stars that are on the MS and are giants in the nearby and poorly studied open cluster Stock 2. This is a dispersed cluster discovered by Stock (1956) and is located in the Orion spiral arm, [α(2000) = 2h15m, δ(2000) = +59°16′, ℓ = 133.334°, b = −1.694°1], roughly on the same line of sight as the double cluster h & χ Persei, but considerably closer to the Sun. However, despite its proximity, the physical parameters for this cluster such as age or chemical composition are not precisely known. According to the literature (Stock 1956; Krzeminski & Serkowski 1967; Robichon et al. 1999; Spagna et al. 2009), the distance to Stock 2 ranges between 300 and 350 pc, although the most recent studies, based on the second Gaia data release, place it at about 400 pc (Cantat-Gaudin et al. 2018; Reddy & Lambert 2019). The average reddening is E(B − V) ≈ 0.35, but it appears to be variable across the cluster field (Krzeminski & Serkowski 1967; Spagna et al. 2009; Ye et al. 2021).

The age is still not precisely known. On the one hand, the cluster might be coeval or slightly older than the Pleiades (100–275 Ma, e.g., Krzeminski & Serkowski 1967; Robichon et al. 1999; Reddy & Lambert 2019; Ye et al. 2021), but on the other hand, Sciortino et al. (2000) found from the analysis of the cluster X-ray luminosity function that its age is similar to that of the Hyades (τ ≃ 625 Ma). Based on the TO region shape and the distribution of the giants on the CMD, Spagna et al. (2009) reported an age within the 200–500 Ma range. Thus, the age of Stock 2 is still a debated issue and represents a challenging task. Recently, Reddy & Lambert (2019) performed the first detailed spectroscopic analysis of this cluster so far. They took high-resolution spectra of three red giants, from which they estimated a solar-like mean metallicity ([Fe/H] = −0.06  ±  0.03) and the chemical abundances for 23 elements. Ye et al. (2021) obtained a similar value ([Fe/H] = −0.04  ±  0.15) from LAMOST medium-resolution spectra of almost 300 likely members. They also found that Stock 2 is a massive cluster (≈4000 M⊙).

This paper is part of the Stellar Population Astrophysics (SPA) project, which is an ongoing Large Programme running on the 3.6-m Telescopio Nazionale Galileo (TNG) at the Roque de los Muchachos Observatory (La Palma, Spain). The SPA is an ambitious project whose aim is to reveal the star formation and chemical enrichment history of the Galaxy, obtaining an age-resolved chemical map of the solar neighbourhood and the Galactic thin disc. More than 500 nearby representative stars are being observed at high resolution in the optical and near-infrared bands by combining the High Accuracy Radial velocity Planet Searcher in North hemisphere spectrograph (HARPS-N) and GIANO-B spectrographs (see Origlia et al. 2019, for more details on SPA). In this work, we combine high-resolution spectroscopy, archival photometry, and the Gaia early third data release (Gaia-eDR3, Gaia Collaboration 2016, 2021) in order to investigate the properties of Stock 2. We pay special attention to the upper MS and MSTO. The analysis of stellar parameters, CMDs, and the lithium abundance are of great importance to constrain the cluster age. The paper is structured as follows. In Sect. 2 we present our observations and explain the criteria we followed to select our targets. Then, we describe our spectral analysis in Sect. 3 and display the results we derived: radial velocities, atmospheric parameters, and chemical abundances. The determination of the extinction and the analysis of the CMDs are detailed in Sects. 4 and 5, respectively. The discussion and comparison of our results with the literature are conducted in Sect. 6. Finally, we summarise our results and present our conclusions in Sect. 7.

2. Observations and target selection

With the aim of studying the cluster and determine its properties, we observed a sample of representative stars among the bona fide members (with an assigned membership probability of P = 1) from Cantat-Gaudin et al. (2018). The only exception is the brightest giant, star g1, for which Cantat-Gaudin et al. (2018) reported a membership probability of P = 0.8. We initially targeted the giants to determine the cluster metallicity and detailed abundances, as we did for other clusters in SPA. We mainly selected red clump stars for this so that the sample would be as homogeneous as possible (see Casali et al. 2020; Zhang et al. 2021). These stars, orange circles in Fig. 1, are labelled ‘g’ in Table 1. By examining the Gaia-DR2 CMD (because Gaia-eDR3 was not available when we prepared our observations), we realised that the cluster exhibited an eMSTO/split MS. This was not clearly visible in pre-existing photometry because of field contamination. In order to study this, we also selected the brightest stars in the upper MS as targets, which are close to the turn-off (TO) point (green triangles in Fig. 1 and labelled ‘to’ in Table 1), as well as MS stars. We followed three different sequences to sample the blue MS (bMS, blue circles and ‘b’), red MS (rMS, red circles and ‘r’), and the upper envelope of the MS, which is the region that is mostly populated by binary and multiple stars (black circles and ‘u’). The numbering used throughout this paper for each of these series consists of assigning a sequential number beginning with the brightest star. In total, we acquired high-resolution spectra for 46 stars in several observational runs that are described below (see Table 1).

thumbnail Fig. 1.

G/(GBP − GRP) diagram for Stock 2. Members from Cantat-Gaudin et al. (2018) are marked with light brown dots. Stars observed with CAOS in this work are represented with green triangles while those observed with HARPS-N appear as circles with different colours, as explained in the text.

Table 1.

Observation log.

2.1. Spectroscopy

We used HARPS-N (Cosentino et al. 2014) to observe the ten cluster giants on 5 and 6 November 2018. HARPS-N is an échelle spectrograph mounted at the 3.6 m TNG telescope at El Roque de los Muchachos Observatory (La Palma, Spain). It is fibre-fed from the Nasmyth B focus and covers the wavelength range from 3870 Å to 6910 Å, providing a resolving power of R = 115 000. Still with the same equipment, we then took spectra for 24 MS stars from 16 to 19 December 2018 and from 13 to 15 January 20192. The instrument pipeline was used to reduce these spectra.

We completed the TNG observations by collecting additional spectra for the 14 brightest stars of the upper MS around the TO point. Observations were carried out between 29 and 31 October 2020 with the Catania Astropysical Observatory Spectropolarimeter (CAOS, Spanò et al. 2006; Leone et al. 2016). CAOS is an échelle spectrograph mounted on the 0.91 m telescope at M. G. Fracastoro station (Serra La Nave, Mt Etna (Italy)), which provides a resolution of R = 55 000. It is fibre-fed from the Cassegrain focus and covers the wavelength range from 3875 Å to 6910 Å in 81 orders. These spectra were reduced by employing the IRAF3 packages following standard procedures. The log of the observations can be found in Table 1. This table displays the spectrograph we used, the heliocentric Julian day at mid exposure (HJD), the exposure time (texp, which is the sum of all exposures of the same star), an estimate of the average signal-to-noise ratio per pixel achieved at 6500 Å (S/N), and the HD (or Tycho, or 2MASS) designation (Name).

2.2. Archival data

As mentioned above, we started our investigation based on the work conducted by Cantat-Gaudin et al. (2018). From the analysis of Gaia-DR2 data, they identified 1209 members for Stock 2. In the astrometric space, they located the cluster at (μα*, μδ, ϖ) = (15.966, −13.627, 2.641) ± (0.650, 0.591, 0.076). It clearly stands out from the background (as shown in Fig. 2, which highlights the stars we observed). According to the spatial distribution of its members (Fig. 3), Cantat-Gaudin et al. (2018) placed the cluster centre at α(2000) = 2h15m25.44s, δ(2000) = +59°31′19.2″, at a distance Δ(α, δ) = (25.4s,15.3′) from the nominal value. Stock 2 is a dispersed cluster, and half of its members (r50) are found within a radius of 1.03° around the centre. The most distant members are positioned almost 4° away. As a result, none of the photometric datasets in the literature covers its entire extension. For this reason, we resorted to all-sky photometric surveys to complement our spectroscopy and the Gaia data. We used JHKS magnitudes from the 2MASS catalogue in the near-infrared wavelength (Skrutskie et al. 2006) as well as BVg′r′i′ optical bands from the APASS catalogue (Henden et al. 2016). For the brightest stars for which the APASS photometry is not reliable we also made use of the values listed in the ASCC2.5 catalogue (Kharchenko & Roeser 2009) in some cases. The combination of all these data allowed us to analyse the CMDs of the cluster, as we explain in Sect. 5. All the astrometric and photometric data available for the stars observed in this work are summarised in Tables A.1 and A.2 of the paper.

thumbnail Fig. 2.

Proper-motion diagram in the field of Stock 2. The ellipse (dashed brown line) is centred on the average proper motions of the cluster and has semi-axes of four times the sigmas of the μα* and μδ distributions of the cluster members according to Cantat-Gaudin et al. (2018). It represents the cluster extent in astrometric space. Grey dots represent field stars, and the remaining symbols are the same as in Fig. 1.

thumbnail Fig. 3.

Sky region around Stock 2. Grey dots show sources with G ≤ 16 mag within a radius of 240′ around the cluster nominal centre (magenta cross). Cluster members identified by Cantat-Gaudin et al. (2018) are represented by black points, and the cluster centre derived from them is shown by the white cross. Coloured circles and green triangles are the objects observed in this work (see Fig. 1) with the HARPS-N and CAOS spectrographs, respectively. The overdensities visible at RA ∼ 35° and Dec ∼ 57° correspond to the h & χ Per double cluster.

3. Spectral analysis

3.1. Radial velocity

We started the spectroscopic analysis by measuring the heliocentric radial velocity (RV) of the observed objects. For this purpose, we cross-correlated our spectra against synthetic templates by employing the task FXCOR, which is contained in the IRAF packages. When we examined the cross-correlation function (CCF), we identified some multiple systems (SB2 or SB3) among the stars forming our sample: r4, u1, and u2. In the upper sequence, we therefore found only two binaries out of the six candidates, although the remaining four might be single-lined systems (SB1). Additionally, star u3 might also have a close companion because it shows a discrepant Ruwe4 Gaia parameter for a single source (≈3.3). For the remaining single stars, the results are listed in the last column of Table 2. The RVs clearly show a large dispersion, with values ranging from −16.5 to +15.7 km s−1. This is likely a consequence of the v sin i distribution. While for slow rotators (e.g., giants and stars in the lower MS) precise RVs can be determined, for rapid rotators, this is not the case. This is specially relevant for the hottest stars in our sample, which are located at the upper MS close to the TO point. These stars are of spectral type A. In addition to rotating rapidly, they display far fewer features in their spectra, which broadens and reduces the intensity of the CCF peak. To calculate the average RV for the cluster, we therefore only took the stars into account whose v sin i < 50 km s−1. Based on 21 members, we thus derived an average value of RV = 7.5 ± 3.3 km s−1. On the other hand, Gaia-DR2 (eDR3 does not provide new values) gives the RV for 194 objects among the members listed in Cantat-Gaudin et al. (2018). The average value, after applying a 3σ clipping filter to ignore outliers, is RVGDR2 = 9.5 ± 3.3 km s−1 (which becomes 8.0 km s−1 if the error-weighted mean is calculated instead). If we consider only the giants, the weighted average of our values is RV = 7.9 ± 1.4 km s−1 (where we have assumed the weighted standard deviation as uncertainty), which is in close agreement with the above estimate.

Table 2.

Stellar parameters derived for the single stars.

3.2. Atmospheric parameters

To determine the stellar atmospheric parameters of our targets, we used the ROTFIT code (Frasca et al. 2006) adapted to the SPA project workframe, as was done previously (see e.g., Frasca et al. 2019; Casali et al. 2020). The code provides not only atmospheric parameters such as effective temperature (Teff), surface gravity (log g), and iron abundance ([Fe/H], as a proxy of the metallicity), but also an estimate of the spectral type (SpT) and the projected rotational velocity (v sin i). We note that the last item is a key parameter for the research we conducted here. ROTFIT is based on a χ2 minimisation of the difference between the target spectrum and a grid of templates. This difference is evaluated in 28 spectral segments of 100 Å each. Then, the final parameters are obtained by averaging the results of the individual regions, weighting them according to the χ2 and the information contained in each spectral segment. As template spectra, we selected a collection of high-resolution spectra of real stars with well-known parameters taken with ELODIE (R = 42 000). This grid of templates is the same as was used in the Gaia-ESO Survey by the Catania node (Smiljanic et al. 2014; Frasca et al. 2015). A more detailed description of our method can be found in Frasca et al. (2019).

For all the single stars, the results are displayed in Table 2. We obtained an average solar metallicity of [Fe/H] = 0.00 ± 0.08 for this cluster, which was calculated as the weighted mean of the values for the spectra analysed with ROTFIT. The error reflects the standard deviation of the individual values around the cluster mean.

ROTFIT is optimised to be used with FGK-type targets. For hotter stars, we therefore used a different approach based on a grid of synthetic spectra computed as described in Sect. 3.3, for which we adopted an opacity distribution function (ODF) computed for solar abundances. To determine Teff and log g, we used the wings and cores of Balmer lines, while a region around the Mg IIλ4481 line was used to derive the v sin i. The rapid stellar rotation strongly broadens the spectral lines and they also become shallow, which makes them very difficult to measure. We therefore chose to adopt [Fe/H] = 0.

3.3. Chemical abundances

In order to calculate the elemental abundances of our (single) targets, we made use of the spectral synthesis technique (Catanzaro et al. 2011, 2013), as we already did within the SPA project previously (Frasca et al. 2019). As a starting point, we took the atmospheric parameters obtained with ROTFIT to compute 1D local thermodynamic equilibrium (LTE) atmospheric models with the ATLAS9 code (Kurucz 1993a,b). Then we generated the corresponding synthetic spectra using the radiative transfer code SYNTHE (Kurucz & Avrett 1981). As an optimisation code, we exploited ad hoc IDL routines based on the amoeba minimisation algorithm to determine the best solution by minimising the χ2 of the differences between the synthetic and observed spectra. To confirm the validity of the input parameters, we let them vary at this point. We always found that the best solution is consistent with the ROTFIT values reported in Table 2. We therefore adopted them for the subsequent analysis. After we confirmed the parameters, we started to determine the abundances. We focused our analysis on 39 spectral regions of 50 Å each between 4400 and 6800 Å. In this way, we derived the chemical abundances of 22 elements with an atomic number up to 56: C, O, Na, Mg, Al, Si, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Y, Zr, and Ba. For the hottest stars, those around the TO point observed with CAOS, it was not possible to provide reliable abundances. These A-type stars, with effective temperatures above 8000 K, rotate with moderate-to-high velocities, which prevents the analysis of the few spectral lines that are observed in their spectra. the bluest part of the spectra is not sufficiently well exposed even for classification purposes, therefore we took the spectral types from the SIMBAD database.

Individual abundances for each star are listed according to the standard notation A(X) = log [n(X)/n(H)] + 12 in Tables A.3 and A.4 for MS stars and giants, respectively. Additionally, the cluster mean abundances for each element, in terms of [X/H], are reported in Table 3. They were calculated by means of the weighted average of each star, using the individual errors as weight. The abundances are expressed referring to the solar value that we obtained by applying the same procedure to a HARPS-N spectrum of Ganymede (see Table 5 in Frasca et al. 2019).

Table 3.

Average chemical abundances ([X/H]) for Stock 2 obtained with SYNTHE.

With the exception of the hottest and fast rotating stars for which we can not measure its abundance, we found an average [Fe/H] = −0.13 ± 0.08. This value is slightly lower than that derived by using ROTFIT, but it is still compatible within the errors. For clarity, we adopted the weighted mean of both values (obtained from ROTFIT and SYNTHE, respectively) as the iron content of the cluster, that is, [Fe/H] = −0.07 ± 0.06.

We find that the abundances derived from giants and dwarfs are compatible within the errors for all the elements except for Ba and Sr, which are clearly overabundant in giants (0.48 and 0.38 dex, respectively), and Co, which is only marginally overabundant. For the remaining elements, no significant discrepancies are seen. The differences for Na, V, and Cu are ≥0.15 dex, but they are still consistent with each other. Stock 2 shows solar weighted-mean ratios for α-elements ([α/Fe] = 0.04 ± 0.05, without including the O) and iron-group elements ([X/Fe] = 0.03 ± 0.03). For the heaviest elements without Sr and Ba, the cluster exhibits a supersolar ratio ([s/Fe] = 0.17 ± 0.04).

4. Reddening and SED fitting

With the aim of determining the interstellar extinction (AV) of our sources as well as the luminosity (L), we resorted to the spectral energy distribution (SED) fitting method. From publicly available optical and near-IR photometric data, we built the corresponding SED, which was fitted with BT-Settl synthetic spectra (Allard 2014). For each target, we assumed its Gaia-eDR3 parallax as well as the atmospheric parameters (Teff and log g) obtained in Sect. 3.2, leaving the stellar radius (R) and AV as free parameters. These parameters were then obtained by χ2 minimisation, and the stellar luminosity was calculated as L = 4 π R2 σ T eff 4 $ T_{\textrm{eff}}^4 $. An example of this fitting is shown in Fig. 4. The errors on AV and R are found by the minimisation procedure considering the 1σ confidence level of the χ2 map, but we also took the error on Teff into account.

thumbnail Fig. 4.

Top: example of an SED fitting (star g8). Bottom:χ2-contour map of the fitting. The red contour corresponds to the 1σ confidence level.

The AV values thus obtained are reported in Table 4. We provide results for 42 stars, whose AV range from 0.37 to 1.93 mag, with an average of AV = 0.84±0.34, where the error is the standard deviation. This extinction corresponds to E(B − V) = 0.27 ± 0.11 when a standard reddening law with RV = 3.1 is assumed. The high dispersion confirms the existence of a noticeable differential reddening across the observed field, as described in previous studies (Krzeminski & Serkowski 1967; Spagna et al. 2009). Our value is indeed compatible within the errors with the value most frequently accepted for the cluster, E(B − V)≈0.35 (Ye et al. 2021).

Table 4.

Results of the SED fitting.

Alternatively, we evaluated the reddening from the colour excess definition, that is, by comparing observed and intrinsic colours for each star. For this purpose, we used the 2MASS photometric data shown in Table A.2 because they are more suitable than the optical values: they are less strongly affected by extinction. The intrinsic colours were adopted from the spectral types (Table 2) according to the calibrations of Straižys & Lazauskaitė (2009). In this way, we obtained an average cluster reddening of E(B − V) = 0.26 ± 0.11 from 43 stars, which shows an excellent agreement with the value derived from the SED fitting. This agreement is especially remarkable considering that photometric calibrations do not take the effect of the rotational velocity on the colour into account.

5. Colour-magnitude diagrams

With the aim of investigating the age of the cluster, we combined archival photometry with the spectroscopy obtained in this work. We made use of the most widespread procedure, the so-called isochrone-fitting method. It consists of finding the age-dependent model, isochrone, that best reproduces the cluster evolutionary snapshot reflected in its CMD. In a first step, it was necessary to construct the CMD. We did this in three different photometric systems (optical, 2MASS, and Gaia-eDR3), highlighting our targets in Fig. 5 according to the criterion described in Sect. 2. We took advantage of the reddening obtained previously (E(B − V) = 0.27, Sect. 4) to draw the following diagrams: MV/(B − V)0, MKS/(J − KS)0, and G/(GBP − GRP). Individual distances derived from the inversion of their parallaxes were also taken into account. Individual zero-point offset corrections, with an average value of about −33 μas, were applied to the published Gaia-eDR3 parallaxes following the recommendations outlined by Lindegren et al. (2021). In a second step, we then drew PARSEC isochrones (Bressan et al. 2012) for different ages computed at the metallicity found in this work ([Fe/H] = −0.07, see Sect. 3.3). With the intention of ensuring the reliability of the fit, we selected from the list of members identified by Cantat-Gaudin et al. (2018) only those with a sufficiently high membership probability (i.e. P ≥ 0.7). Additionally, we imposed a quality cutoff on this sample, taking only the objects whose error on parallax is below 0.1 mas, that is, objects with an uncertainty smaller than 5%. We considered 1016 cluster members with Gaia-eDR3 photometry. We cross-matched our member list with the APASS (Henden et al. 2016) and 2MASS (Skrutskie et al. 2006) catalogues and then selected only the stars with good-quality photometry. In the first case, this meant stars with errors on both V and (B − V) < 0.1 mag, while in the second case, this meant only the stars without any ‘U’ photometric flag. In total, we retrieved 409 and 955, respectively. The resulting diagrams are displayed in Fig. 5.

thumbnail Fig. 5.

Colour-magnitudes diagrams for Stock 2 in three different photometric systems. Left: MV/(B − V)0, photometric data from the APASS catalogue. Centre:MKS/(J − KS)0 (2MASS). Right: G/(GBP − GRP) (Gaia-eDR3). Colours and symbols are the same as in Fig. 1. The green line and the shaded area are the best-fitting isochrone within the uncertainties (log τ = 8.65 ± 0.15).

When building the first CMD (MV/(B − V)0), we immediately realised the incorrect positions of the brightest stars, which included many of our targets. For these stars, the APASS photometry provides errors above one magnitude or even not quantified errors. With this purpose, we resorted to the ASCC2.5 catalogue (Kharchenko & Roeser 2009), from which we took V and (B − V) for stars brighter than V = 10 after scaling both photometric datasets5. Then we dereddened the CMD (left panel of Fig. 5) by applying individual corrections to the stars for which we have spectra and the average value to the remaining stars. Finally, we plotted the isochrone that best reproduces the CMD based on a visual inspection, from which we obtained a log τ = 8.65 ± 0.15 for the cluster (equivalent to an age of 450 ± 150 Ma). In this case, the error reflects the interval of isochrones that gives a good fit. With this age, the MSTO stellar mass is ≈2.8 M⊙. In general, stars occupy positions close to the isochrone, and only the TO stars seem to lie slightly away from it.

The fit is for the 2MASS CMD is quite good and all stars match the isochrone rather well, with the exception of the star g1. It is the brightest in the cluster and lies at a position away from the rest of the giants. Because it is so bright, it is close to saturation, and its photometry, flagged in the catalogue as ‘EDD’, has errors in each band of about 0.2 mag. Therefore its anomalous (J − K) colour could simply be an instrumental effect. Some residual dispersion is still observed for the MS stars although the correction for reddening was applied; moreover, in the NIR, the reddening is lower than at optical wavelengths and should play a minor role in the CMD. After the reddening correction, no clear eMSTO/split MS is apparent in the CMD. Giants show a dispersion in magnitude greater than it would be expected from their atmospheric parameters, which are very similar to each other.

In the last diagram, the Gaia-eDR3 CMD, the isochrone (and not the stars as in the previous CMDs) was reddened using the average extinction obtained in Sect. 4 because the dereddening of the Gaia photometry is not a trivial task. A distance modulus of 7.87 was applied, which corresponds to the distance derived by Cantat-Gaudin et al. (2018). The fit is also good, and the stars lie along the isochrone.

6. Discussion

One of the objectives of this research was to determine the age of the cluster. Now, based on Gaia-eDR3 individual parallaxes for the cluster members and the extinction derived from the SED fitting, we were able to build suitable CMDs, in which the cluster age was obtained through the isochrone-fitting method. By analysing the dereddened 2MASS CMD, which is less strongly affected by the interstellar dust than the CMDs at optical wavelengths used in past works, we can asses that Stock 2 is a moderately young open cluster of 450 ± 150 Ma. This means that it is somewhat younger than the Hyades and clearly older than the Pleiades. This confirms the results of Spagna et al. (2009) and Sciortino et al. (2000) over previous studies (e.g., Krzeminski & Serkowski 1967).

The RVs obtained by us are in general compatible within the errors with those found in the literature, as displayed in Table 5 for stars in common with Mermilliod et al. (2008), who measured RVs for red giants in open clusters, and Reddy & Lambert (2019). Although Mermilliod et al. (2008) claimed binarity for g3 and g9, we did not see any feature in their spectra that might confirm this, as Reddy & Lambert (2019) concluded as well. However, given the discrepancies for the latter, perhaps it might be a long-period variable. Figure 6 shows the stars for which we have derived their RV compared, when possible, to the values obtained by Gaia-DR2. We highlight the excellent agreement for the slow rotators, especially in the case of giant stars. For fast rotators, as we already noted, our errors are instead very large and the results are not very reliable; for most of them, Gaia-DR2 does not provide any RV.

thumbnail Fig. 6.

Comparison of the RVs obtained in this work (symbols and colours as in previous figures) with those of Gaia-DR2 (open squares). The dashed line shows the average cluster value, RV = 8.0 km s−1.

Table 5.

Comparison of the RV (km s−1) derived in this work and in the literature.

Regarding the atmospheric parameters, as already mentioned, Reddy & Lambert (2019) conducted the only spectroscopy-based paper devoted to Stock 2. Their study is based on high-resolution spectra (R = 60 000) of three of the cluster giants. These stars, which have also been observed by us, are g3 (numbered as 43 in their work), g4 (1011), and g9 (1082). Our temperatures and metallicities are slightly higher but still in agreement with their values within the errors. Instead, gravities are only marginally compatible. The two datasets are compared in Table 6. These discrepancies can probably be explained by different methods that were used. In this work, we employed spectral fitting, while their approach was based on the equivalent width (EW) analysis.

Table 6.

Comparison of the atmospheric parameters derived in this work with those of the literature.

With the aim of confirming the consistency of our results, we plot the Kiel and HR diagrams in Fig. 7. The former is a reddening-free diagnostic, whereas in the latter, extinction has been taken into account when the luminosity was calculated. The location of the stars in the HR diagram is better than in the Kiel diagram, where gravities lie at a distance with respect to those of the isochrone around 0.2 dex, as we reported in the comparison with results from Reddy & Lambert (2019). Additionally, TO stars show a large dispersion in this diagram. This is very likely a consequence of the poor accuracy of the gravity determinations for these A-type stars, which rotate moderately or fast. In the HR diagram, these stars are placed more closely clustered around the TO point, as expected. The fit is also better for MS stars and is especially good for giants, which fall on the isochrone.

thumbnail Fig. 7.

Kiel and HR diagrams for Stock 2. Symbols and colours are the same as in Fig. 5.

6.1. Chromospheric emission and lithium abundance

For stars cooler than about 6500 K and with an age from a few ten to a few hundred Ma, the level of magnetic activity (e.g., the emission in the cores of lines that formed in the chromosphere) and the atmospheric lithium abundance can be used to estimate the age (see e.g., Jeffries 2014; Frasca et al. 2018, and references therein). The best diagnostics of chromospheric emission in the wavelength range covered by HARPS-N are the Ca II H&K and Balmer Hα lines. However, the S/N at 3900 Å is very low, so that we can only use Hα for this purpose. The templates produced by ROTFIT with rotationally broadened spectra of non-active, lithium-poor stars were subtracted from the observed spectra of the targets to measure the excess emission in the core of the Hα line ( E W H α em $ EW_{\mathrm{H\alpha}}^{em} $) and the equivalent width of the Li Iλ6708 Å absorption line (EWLi), removing the blends with nearby lines.

Figure 8 shows an example of the subtraction procedure we used to measure the equivalent width of the Hα and lithium lines, E W H α em $ EW_{\mathrm{H\alpha}}^{em} $ and EWLi. These quantities were measured on the subtracted spectra by integrating the residual emission and absorption profiles, as shown by the green dashed areas in Fig. 8. They are reported in Table 7.

thumbnail Fig. 8.

Subtraction of the non-active, lithium-poor template (red line) from the spectrum of Stock2 r8 (black dots), which reveals the chromospheric emission in the Hα core (blue line in the bottom panel) and emphasises the Li Iλ6708 Å absorption line, removing the nearby blended lines (top panel). The green hatched areas represent the excess Hα emission (bottom panel) and Li I absorption (top panel) that were integrated to obtain E W H α em $ EW_{\mathrm{H\alpha}}^{em} $ and EWLi, respectively.

Table 7.

Li Iλ6708 Å equivalent widths and lithium abundance for targets cooler than 7000 K.

A simple method for obtaining an estimate of a star’s age independent of that derived from isochrones is to compare its position in a diagram that plots lithium abundance, A(Li), versus Teff with the upper envelopes of clusters with a known age. We calculated the lithium abundance, A(Li), from our values of Teff, log g, and EWLi by interpolating the curves of growth of Lind et al. (2009), which span the Teff range 4000–8000 K and log g from 1.0 to 5.0 and include non-LTE corrections. In Fig. 9 we show the lithium abundance as a function of Teff along with the upper envelopes of the distributions of some young open clusters shown by Sestito & Randich (2005). In addition to the large errors of A(Li), which take into account both the Teff and EWLi errors, Fig. 9 shows that all the targets are located close to or below the Hyades upper envelope, compatible with an age ≈600 Ma. The only exception is the coldest target, b8, which lies between the upper envelopes of the Pleiades (≈100 Ma) and NGC 6475 (≈300 Ma). This suggests an age ≲300 Ma for this star. However, for stars with Teff > 6000 K, the upper envelopes are very close to each other, which hampers the estimation of the cluster age with this method. Lithium abundances for colder stars, where the envelopes separate more, would be extremely useful in clarifying this point. Unfortunately, the combination of very high resolution and telescope size did not permit us to reach the low MS. Hopefully, large samples of fainter stars will be acquired, for instance by the survey WEAVE (Dalton et al. 2020), which is due to start soon at the 4.2 m William Herschel Telescope.

thumbnail Fig. 9.

Lithium abundance as a function of Teff. The upper envelopes of A(Li) for IC 2602 (age ≈ 30 Ma), the Pleiades (≈100 Ma), NGC 6475 (≈300 Ma), and the Hyades (≈600 Ma) clusters adapted from Sestito & Randich (2005) are overplotted.

6.2. Galactic metallicity gradient

Open clusters are good tracers of the radial metallicity distribution of the Galaxy (i.e. the so-called Galactic gradient). To determine how the metallicity derived for Stock 2 in this work compares with the general gradient, we collected a sample of homogeneously analysed clusters from the Gaia-ESO iDR5 and iDR6 (Baratella et al. 2020; Magrini et al. 2021) and the APOGEE DR16 surveys (Donor et al. 2020). From the latter, we only took clusters with data derived from two or more stars and closer than 15 kpc. In addition, open clusters from Alonso-Santiago et al. (2017, 2018, 2019, 2020) were also added to the sample, along with those previously investigated within the SPA project (Frasca et al. 2019; D’Orazi et al. 2020; Casali et al. 2020; Zhang et al. 2021). We gathered more than one hundred clusters for this comparison, ten of which are in common in different datasets. Figure 10 shows the location of Stock 2 in the Galactic gradient. Galactocentric distances were taken from Cantat-Gaudin et al. (2018), who obtained their distances from the Gaia-DR2 parallaxes, taking as a reference for the solar value R⊙ = 8.34 kpc. The metallicity in terms of iron abundance was referenced to A(Fe) = 7.45 dex (Grevesse et al. 2007). The metallicity found in this work is compatible with that expected for its position.

thumbnail Fig. 10.

Radial metallicity gradient from open clusters studied in the framework of the Gaia-ESO (Baratella et al. 2020; Magrini et al. 2021, red circles) and APOGEE (Donor et al. 2020, green circles) surveys. Other similar clusters analysed by Alonso-Santiago et al. (2017; 2018; 2019; 2020, blue circles,) are also added, together with those previously investigated in the SPA project (Frasca et al. 2019; D’Orazi et al. 2020; Casali et al. 2020; Zhang et al. 2021, orange circles). Black lines link results for the same cluster provided by different authors. The star represents Stock 2.

6.3. Chemical composition and Galactic trends

We compared our results for the abundances (separately for MS stars and giants) to those of Reddy & Lambert (2019), with which we have 17 chemical elements in common. For the comparison, the values from Reddy & Lambert (2019) were scaled to our solar references. Figure 11 shows the differences of the abundance ratios ([X/H]), this work minus those from the literature. As expected, the differences are smaller for giants (Δ[X/H] = 0.07 dex on average) than for MS stars (0.12 dex). With the only exception of Y, the chemical composition of all the giants is fully compatible with that obtained by Reddy & Lambert (2019). On the other hand, the abundances for Na, V, Co, Zn, Y, and Ba are somewhat different for MS stars.

thumbnail Fig. 11.

Differences between our mean abundances for giants and MS stars and those by Reddy & Lambert (2019). The error bars are the quadratic sum of the uncertainties reported in the two studies for each element.

Finally, as we have done above in relation to the metallicity gradient, we compared the abundances obtained in this work with those of the comparison clusters selected before. We completed the sample by adding the Gaia-ESO DR4 abundances (Magrini et al. 2017, 2018) for the clusters in common with Magrini et al. (2021). We have up to 18 chemical elements in common with them, for which the ratios [X/Fe] versus [Fe/H] are displayed in Fig. 12 for 16 chemical elements. The remaining 2 elements are O and Ba, but because the measure of the abundances is conditioned by the evolutionary state of the stars (see Sect. 3.3) for these elements, we discarded them from the comparison. In general, the chemical composition of Stock 2 is compatible with that of the Galactic thin disc, as supported by the agreement with the observed chemical trends traced by more than one hundred open clusters. Only the abundance of Cu is sligthtly below these trends, but it is still compatible with them.

thumbnail Fig. 12.

Abundance ratios [X/Fe] vs. [Fe/H]. Symbols and colours are the same as in Fig. 10. The dashed lines indicate the solar value.

6.4. Rotational velocity, reddening, and eMSTO

We investigated the relation between v sin i and the eMSTO phenomenon. As mentioned in Sect. 2, we selected our targets following three different sequences along the MS in the CMD of Fig. 1: blue, red, and the upper envelope. About 40% of all the stars observed in this work rotate rapidly (with v sin i > 100 km s−1). Table 2 shows that the fastest rotators are found among the brightest stars in each sequence in general, but a large scatter of velocities is also detected. According to the literature (Dupree et al. 2017; Marino et al. 2018b; Sun et al. 2019), the bMS should be populated by stars that rotate more slowly than those in the rMS. However, this is not what we observe in this work. Significant differences are not found in the mean v sin i of either sequence. In addition, for the single stars in the group in which we expected to find binaries (the upper envelope sequence), their v sin i are smaller than in the two other series, although they are redder even than the rMS stars (see Table 8).

Table 8.

Mean projected rotational velocities (km s−1) and reddening in MS stars. N is the number of stars in each category.

To interpret this phenomenon, the contribution of the reddening should not be ignored. The average cluster value obtained in this work is compatible within the errors with that expected for its position according to the extinction maps obtained by Lallement et al. (2019). However, as noted above, its value varies considerably across the cluster field. For illustrative purposes only, we map in Fig. 13 the distribution of AG in the cluster region from its members. Because Gaia-eDR3 does not provide these values, we took them from Gaia-DR2. For slightly more than half of the members identified by Cantat-Gaudin et al. (2018), specifically, for 673 stars, AG was available. In order to derive individual values for the remaining objects, we calculated them as the distance-weighted average of the values of the five closest members. After we estimated the AG for all the members, we started to construct the chart. In a first step, a grid of points covering the spatial distribution of the cluster members was generated. These points were spaced every 30″ in both RA and Dec. In a second step, the AG of all the members distant up to 3′ from each point was then averaged. The resulting spatial distribution of the cluster members, colour-coded according to their AG, is shown in Fig. 13. It displays how variable the reddening is across the cluster field. This is likely the result of the low Galactic latitude and the large extension that it occupies on the sky.

thumbnail Fig. 13.

Interstellar extinction (AG) towards Stock 2, as traced by the cluster members.

For each of the sequences into which we grouped our MS stars, we calculated the average v sin i and AV. These quantities, together with their standard deviations, are quoted in Table 8. Although our sample is not statistically large, our data suggest that rotational velocity cannot explain the observed eMSTO, but reddening is most likely responsible for it.

7. Conclusions

We have conducted this research in the framework of the SPA project with the aim of continuing to improve our knowledge of the solar neighbourhood. This work is focused on Stock 2, a nearby and little-studied open cluster. We studied it in detail from high-resolution spectroscopy complemented with archival photometry and Gaia-eDR3 data. Our sample is by far the largest to date. It is composed of 46 bona fide members that include both giants and MS stars. In order to study the eMSTO phenomenon, we selected the brightest of the MS stars around the TO point and many others following three different sequences to cover the spread observed in the CMDs.

We found three double-spectrum binaries in our sample. For the remaining stars, we measured their radial and projected rotational velocities and derived the extinction and their atmospheric parameters. In addition, we carried out the chemical analysis for 29 stars observed with HARPS-N, providing the abundances of 22 elements.

We found that half of the MS stars are fast rotators, with v sin i > 100 km s−1. However, the distribution of slow and fast rotators along the bMS, rMS, and uMS sequences is random. This discards the rotational velocity as the cause of the observed eMSTO. Additionally, cluster members are disseminated over a wide region of the sky (up to ≈13° × 8°), and differential reddening plays an important role in shaping the CMDs. We found an average reddening in the cluster field of E(B − V) = 0.27 ± 0.11. Its large dispersion (consistent with the Gaia-DR2 value, E(GBP − GRP) = 0.40 ± 0.18) confirms the existence of a variable reddening across the field of Stock 2.

The reddening also makes it difficult to obtain an accurate age for the cluster. However, from the isochrone-fitting on the dereddened 2MASS CMD, which is the least affected by extintcion, we derived a value of 450 ± 150 Ma. This age implies a mass at the MSTO of ≈2.8 M⊙. The analysis of the abundance of lithium indicates an age similar to that of the Hyades (∼600 Ma), although the coolest observed member could be as young as 300 Ma. Spectroscopic observations of a larger sample of members with a lower Teff is needed to settle this point. We expect very useful data from large spectroscopic surveys that will start in the near future, such as WEAVE. The cluster RV derived from the giants is ≈8.0 km s−1. Stock 2 shows a solar-like metallicity, [Fe/H] = −0.07 ± 0.06, which is fully compatible within the errors with that expected for its Galactocentric distance.

Finally, we performed a detailed study of the cluster chemical composition by determining the abundances of C, odd-Z elements (Na and Al), α-elements (O, Mg, Si, S, Ca, and Ti), iron-peak elements (Sc, V, Cr, Mn, Co, Ni, Cu, and Zn), and s-elements (Sr, Y, Zr, and Ba). The chemical composition of MS stars is compatible within the errors with that of the giants. The differences are only significant for Co and particularly for Ba and Sr; the abundances of Ba and Sr are clearly higher in giants. We conclude our research by claiming that its chemical composition is consistent with that of the thin disc. This is supported by the values of its ratios [X/Fe] that are on the Galactic trends displayed by open clusters in the Gaia-ESO and APOGEE surveys. Finally, the cluster shows solar-like mean ratios for the α ([α/Fe] = 0.04 ± 0.05) and the iron-peak [iron-peak/Fe] = 0.03 ± 0.03 elements, and for the heaviest elements (without the Ba and Sr abundances), it exhibits a mild overabundance with respect to the Sun, [s/Fe] = 0.17 ± 0.04.

1

Nominal coordinates according to the WEBDA database, https://webda.physics.muni.cz/

2

We used GIARPS, i.e. the combination of GIANO and HARPS-N, but we use only HARPS-N spectra here because they are more efficient for the warm MS stars. GIANO spectra will be used in forthcoming papers.

3

IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under the cooperative agreement with the National Science Foundation.

5

By employing almost one hundred stars with good-quality photometry in both catalogues, we found average differences (ASCC2.5 minus APASS) of Δ V = −0.040 and Δ(B − V) = −0.005 mag.

Acknowledgments

We thank the anonymous referee for her/his suggestions which have helped to improve this paper. We acknowledge the support from the Italian Ministero dell’Istruzione, Università e Ricerca (MIUR). We thank the TNG personnel for help during the observations. This work has made use of 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. This research has made use of the Simbad database, operated at CDS, Strasbourg (France). This publication also made use of 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. GC acknowledges support from the European Research Council Consolidator Grant funding scheme (project ASTEROCHRONOMETRY, G.A. n. 772293, http://www.asterochronometry.eu).

References

  1. Allard, F. 2014, in Exploring the Formation and Evolution of Planetary Systems, eds. M. Booth, B. C. Matthews, & J. R. Graham, 299, 271 [Google Scholar]
  2. Alonso-Santiago, J., Negueruela, I., Marco, A., et al. 2017, MNRAS, 469, 1330 [NASA ADS] [CrossRef] [Google Scholar]
  3. Alonso-Santiago, J., Marco, A., Negueruela, I., et al. 2018, A&A, 616, A124 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  4. Alonso-Santiago, J., Negueruela, I., Marco, A., et al. 2019, A&A, 631, A124 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  5. Alonso-Santiago, J., Negueruela, I., Marco, A., Tabernero, H. M., & Castro, N. 2020, A&A, 644, A136 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  6. Baratella, M., D’Orazi, V., Carraro, G., et al. 2020, A&A, 634, A34 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  7. Bastian, N., Cabrera-Ziri, I., Niederhofer, F., et al. 2017, MNRAS, 465, 4795 [NASA ADS] [CrossRef] [Google Scholar]
  8. Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127 [NASA ADS] [CrossRef] [Google Scholar]
  9. Cantat-Gaudin, T., Jordi, C., Vallenari, A., et al. 2018, A&A, 618, A93 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  10. Casali, G., Magrini, L., Frasca, A., et al. 2020, A&A, 643, A12 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  11. Catanzaro, G., Ripepi, V., Bernabei, S., et al. 2011, MNRAS, 411, 1167 [CrossRef] [Google Scholar]
  12. Catanzaro, G., Ripepi, V., & Bruntt, H. 2013, MNRAS, 431, 3258 [NASA ADS] [CrossRef] [Google Scholar]
  13. Cordoni, G., Milone, A. P., Marino, A. F., et al. 2018, ApJ, 869, 139 [CrossRef] [Google Scholar]
  14. Correnti, M., Goudfrooij, P., Bellini, A., Kalirai, J. S., & Puzia, T. H. 2017, MNRAS, 467, 3628 [NASA ADS] [Google Scholar]
  15. Cosentino, R., Lovis, C., Pepe, F., et al. 2014, in Ground-based and Airborne Instrumentation for Astronomy V, eds. S. K. Ramsay, I. S. McLean, H. Takami, SPIE Conf. Ser., 9147, 91478C [Google Scholar]
  16. Dalton, G., Trager, S., Abrams, D. C., et al. 2020, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, SPIE Conf. Ser., 11447, 1144714 [NASA ADS] [Google Scholar]
  17. D’Antona, F., Di Criscienzo, M., Decressin, T., et al. 2015, MNRAS, 453, 2637 [NASA ADS] [Google Scholar]
  18. D’Antona, F., Milone, A. P., Tailo, M., et al. 2017, Nat. Astron., 1, 0186 [CrossRef] [Google Scholar]
  19. Donor, J., Frinchaboy, P. M., Cunha, K., et al. 2020, AJ, 159, 199 [NASA ADS] [CrossRef] [Google Scholar]
  20. D’Orazi, V., Oliva, E., Bragaglia, A., et al. 2020, A&A, 633, A38 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  21. Dupree, A. K., Dotter, A., Johnson, C. I., et al. 2017, ApJ, 846, L1 [NASA ADS] [CrossRef] [Google Scholar]
  22. Frasca, A., Guillout, P., Marilli, E., et al. 2006, A&A, 454, 301 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Frasca, A., Biazzo, K., Lanzafame, A. C., et al. 2015, A&A, 575, A4 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  24. Frasca, A., Guillout, P., Klutsch, A., et al. 2018, A&A, 612, A96 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  25. Frasca, A., Alonso-Santiago, J., Catanzaro, G., et al. 2019, A&A, 632, A16 [NASA ADS] [EDP Sciences] [Google Scholar]
  26. Gaia Collaboration (Prusti, T., et al.) 2016, A&A, 595, A1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  27. Gaia Collaboration (Brown, A. G. A., et al.) 2021, A&A, 649, A1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  28. Gossage, S., Conroy, C., Dotter, A., et al. 2019, ApJ, 887, 199 [NASA ADS] [CrossRef] [Google Scholar]
  29. Goudfrooij, P., Girardi, L., & Correnti, M. 2017, ApJ, 846, 22 [CrossRef] [Google Scholar]
  30. Gratton, R., Bragaglia, A., Carretta, E., et al. 2019, A&ARv, 27, 8 [Google Scholar]
  31. Grevesse, N., Asplund, M., & Sauval, A. J. 2007, Space Sci. Rev., 130, 105 [Google Scholar]
  32. Henden, A. A., Templeton, M., Terrell, D., et al. 2016, VizieR Online Data Catalog, II/336 [Google Scholar]
  33. Jeffries, R. D. 2014, EAS Pub. Ser., 65, 289 [CrossRef] [EDP Sciences] [Google Scholar]
  34. Johnston, C., Aerts, C., Pedersen, M. G., & Bastian, N. 2019, A&A, 632, A74 [EDP Sciences] [Google Scholar]
  35. Kharchenko, N. V., & Roeser, S. 2009, VizieR Online Data Catalog, I/280B [Google Scholar]
  36. Krumholz, M. R., McKee, C. F., & Bland-Hawthorn, J. 2019, ARA&A, 57, 227 [NASA ADS] [CrossRef] [Google Scholar]
  37. Krzeminski, W., & Serkowski, K. 1967, ApJ, 147, 988 [NASA ADS] [CrossRef] [Google Scholar]
  38. Kurucz, R. 1993a, ATLAS9 Stellar Atmosphere Programs and 2 km/s grid. Kurucz CD-ROM No. 13. Cambridge, 13 [Google Scholar]
  39. Kurucz, R. L. 1993b, in IAU Colloq. 138: Peculiar versus Normal Phenomena in A-type and Related Stars, eds. M. M. Dworetsky, F. Castelli, & R. Faraggiana, ASP Conf. Ser., 44, 87 [Google Scholar]
  40. Kurucz, R. L., & Avrett, E. H. 1981, SAO Special Report, 391 [Google Scholar]
  41. Lallement, R., Babusiaux, C., Vergely, J. L., et al. 2019, A&A, 625, A135 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  42. Leone, F., Avila, G., Bellassai, G., et al. 2016, AJ, 151, 116 [NASA ADS] [CrossRef] [Google Scholar]
  43. Li, C., de Grijs, R., Deng, L., & Milone, A. P. 2017, ApJ, 844, 119 [CrossRef] [Google Scholar]
  44. Li, C., Sun, W., de Grijs, R., et al. 2019, ApJ, 876, 65 [Google Scholar]
  45. Lind, K., Asplund, M., & Barklem, P. S. 2009, A&A, 503, 541 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  46. Lindegren, L., Bastian, U., Biermann, M., et al. 2021, A&A, 649, A4 [EDP Sciences] [Google Scholar]
  47. Mackey, A. D., & Broby Nielsen, P. 2007, MNRAS, 379, 151 [NASA ADS] [CrossRef] [Google Scholar]
  48. Magrini, L., Randich, S., Kordopatis, G., et al. 2017, A&A, 603(A2), 1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  49. Magrini, L., Spina, L., Randich, S., et al. 2018, A&A, 617, A106 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  50. Magrini, L., Lagarde, N., Charbonnel, C., et al. 2021, A&A, 651, A84 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  51. Marino, A. F., Milone, A. P., Casagrande, L., et al. 2018a, ApJ, 863, L33 [NASA ADS] [CrossRef] [Google Scholar]
  52. Marino, A. F., Przybilla, N., Milone, A. P., et al. 2018b, AJ, 156, 116 [NASA ADS] [CrossRef] [Google Scholar]
  53. Mermilliod, J. C., Mayor, M., & Udry, S. 2008, A&A, 485, 303 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  54. Milone, A. P., Bedin, L. R., Piotto, G., & Anderson, J. 2009, A&A, 497, 755 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  55. Milone, A. P., Marino, A. F., D’Antona, F., et al. 2016, MNRAS, 458, 4368 [NASA ADS] [CrossRef] [Google Scholar]
  56. Milone, A. P., Marino, A. F., Di Criscienzo, M., et al. 2018, MNRAS, 477, 2640 [Google Scholar]
  57. Niederhofer, F., Georgy, C., Bastian, N., & Ekström, S. 2015, MNRAS, 453, 2070 [NASA ADS] [CrossRef] [Google Scholar]
  58. Origlia, L., Dalessandro, E., Sanna, N., et al. 2019, A&A, 629, A117 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  59. Piatti, A. E., & Bonatto, C. 2019, MNRAS, 490, 2414 [NASA ADS] [CrossRef] [Google Scholar]
  60. Reddy, A. B. S., & Lambert, D. L. 2019, MNRAS, 485, 3623 [NASA ADS] [CrossRef] [Google Scholar]
  61. Robichon, N., Arenou, F., Mermilliod, J.-C., & Turon, C. 1999, A&A, 345, 471 [NASA ADS] [Google Scholar]
  62. Sciortino, S., Micela, G., Favata, F., Spagna, A., & Lattanzi, M. G. 2000, A&A, 357, 460 [NASA ADS] [Google Scholar]
  63. Sestito, P., & Randich, S. 2005, A&A, 442, 615 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  64. Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163 [NASA ADS] [CrossRef] [Google Scholar]
  65. Smiljanic, R., Korn, A. J., Bergemann, M., et al. 2014, A&A, 570, A122 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  66. Spagna, A., Cossu, F., Lattanzi, M. G., & Massone, G. 2009, Mem. Soc. Astron. It., 80, 129 [Google Scholar]
  67. Spanò, P., Leone, F., Bruno, P., et al. 2006, Mem. Soc. Astron. It. Suppl., 9, 481 [Google Scholar]
  68. Stock, J. 1956, ApJ, 123, 258 [NASA ADS] [CrossRef] [Google Scholar]
  69. Straižys, V., & Lazauskaitė, R. 2009, Balt. Astron., 18, 19 [NASA ADS] [Google Scholar]
  70. Sun, W., de Grijs, R., Deng, L., & Albrow, M. D. 2019, ApJ, 876, 113 [NASA ADS] [CrossRef] [Google Scholar]
  71. Ye, X., Zhao, J., Liu, J., et al. 2021, AJ, 161, 8 [NASA ADS] [CrossRef] [Google Scholar]
  72. Zhang, R., Lucatello, S., Bragaglia, A., et al. 2021, A&A, 654, A77 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]

Appendix A: Additional material

Table A.1.

Gaia-eDR3 astrometric data and distance from the nominal cluster centre for the stars that we observed spectroscopically.

Table A.2.

Photometry for the stars that we observed spectroscopically.

Table A.3.

Chemical abundances, expressed as A(X) = log[n(X)/n(H)]+12, for MS stars in Stock 2.

Table A.4.

Chemical abundances, expressed as A(X) = log[n(X)/n(H)]+12, for giants in Stock 2.

All Tables

Table 1.

Observation log.

In the text
Table 2.

Stellar parameters derived for the single stars.

In the text
Table 3.

Average chemical abundances ([X/H]) for Stock 2 obtained with SYNTHE.

In the text
Table 4.

Results of the SED fitting.

In the text
Table 5.

Comparison of the RV (km s−1) derived in this work and in the literature.

In the text
Table 6.

Comparison of the atmospheric parameters derived in this work with those of the literature.

In the text
Table 7.

Li Iλ6708 Å equivalent widths and lithium abundance for targets cooler than 7000 K.

In the text
Table 8.

Mean projected rotational velocities (km s−1) and reddening in MS stars. N is the number of stars in each category.

In the text
Table A.1.

Gaia-eDR3 astrometric data and distance from the nominal cluster centre for the stars that we observed spectroscopically.

In the text
Table A.2.

Photometry for the stars that we observed spectroscopically.

In the text
Table A.3.

Chemical abundances, expressed as A(X) = log[n(X)/n(H)]+12, for MS stars in Stock 2.

In the text
Table A.4.

Chemical abundances, expressed as A(X) = log[n(X)/n(H)]+12, for giants in Stock 2.

In the text

All Figures

thumbnail Fig. 1.

G/(GBP − GRP) diagram for Stock 2. Members from Cantat-Gaudin et al. (2018) are marked with light brown dots. Stars observed with CAOS in this work are represented with green triangles while those observed with HARPS-N appear as circles with different colours, as explained in the text.
In the text
thumbnail Fig. 2.

Proper-motion diagram in the field of Stock 2. The ellipse (dashed brown line) is centred on the average proper motions of the cluster and has semi-axes of four times the sigmas of the μα* and μδ distributions of the cluster members according to Cantat-Gaudin et al. (2018). It represents the cluster extent in astrometric space. Grey dots represent field stars, and the remaining symbols are the same as in Fig. 1.
In the text
thumbnail Fig. 3.

Sky region around Stock 2. Grey dots show sources with G ≤ 16 mag within a radius of 240′ around the cluster nominal centre (magenta cross). Cluster members identified by Cantat-Gaudin et al. (2018) are represented by black points, and the cluster centre derived from them is shown by the white cross. Coloured circles and green triangles are the objects observed in this work (see Fig. 1) with the HARPS-N and CAOS spectrographs, respectively. The overdensities visible at RA ∼ 35° and Dec ∼ 57° correspond to the h & χ Per double cluster.
In the text
thumbnail Fig. 4.

Top: example of an SED fitting (star g8). Bottom:χ2-contour map of the fitting. The red contour corresponds to the 1σ confidence level.
In the text
thumbnail Fig. 5.

Colour-magnitudes diagrams for Stock 2 in three different photometric systems. Left: MV/(B − V)0, photometric data from the APASS catalogue. Centre:MKS/(J − KS)0 (2MASS). Right: G/(GBP − GRP) (Gaia-eDR3). Colours and symbols are the same as in Fig. 1. The green line and the shaded area are the best-fitting isochrone within the uncertainties (log τ = 8.65 ± 0.15).
In the text
thumbnail Fig. 6.

Comparison of the RVs obtained in this work (symbols and colours as in previous figures) with those of Gaia-DR2 (open squares). The dashed line shows the average cluster value, RV = 8.0 km s−1.
In the text
thumbnail Fig. 7.

Kiel and HR diagrams for Stock 2. Symbols and colours are the same as in Fig. 5.
In the text
thumbnail Fig. 8.

Subtraction of the non-active, lithium-poor template (red line) from the spectrum of Stock2 r8 (black dots), which reveals the chromospheric emission in the Hα core (blue line in the bottom panel) and emphasises the Li Iλ6708 Å absorption line, removing the nearby blended lines (top panel). The green hatched areas represent the excess Hα emission (bottom panel) and Li I absorption (top panel) that were integrated to obtain E W H α em $ EW_{\mathrm{H\alpha}}^{em} $ and EWLi, respectively.
In the text
thumbnail Fig. 9.

Lithium abundance as a function of Teff. The upper envelopes of A(Li) for IC 2602 (age ≈ 30 Ma), the Pleiades (≈100 Ma), NGC 6475 (≈300 Ma), and the Hyades (≈600 Ma) clusters adapted from Sestito & Randich (2005) are overplotted.
In the text
thumbnail Fig. 10.

Radial metallicity gradient from open clusters studied in the framework of the Gaia-ESO (Baratella et al. 2020; Magrini et al. 2021, red circles) and APOGEE (Donor et al. 2020, green circles) surveys. Other similar clusters analysed by Alonso-Santiago et al. (2017; 2018; 2019; 2020, blue circles,) are also added, together with those previously investigated in the SPA project (Frasca et al. 2019; D’Orazi et al. 2020; Casali et al. 2020; Zhang et al. 2021, orange circles). Black lines link results for the same cluster provided by different authors. The star represents Stock 2.
In the text
thumbnail Fig. 11.

Differences between our mean abundances for giants and MS stars and those by Reddy & Lambert (2019). The error bars are the quadratic sum of the uncertainties reported in the two studies for each element.
In the text
thumbnail Fig. 12.

Abundance ratios [X/Fe] vs. [Fe/H]. Symbols and colours are the same as in Fig. 10. The dashed lines indicate the solar value.
In the text
thumbnail Fig. 13.

Interstellar extinction (AG) towards Stock 2, as traced by the cluster members.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.