© ESO, 2011

1. Introduction

Rotation period measurements in open clusters and young associations provide a fundamental source of information on the angular momentum evolution of late-type stars. Stars in a cluster represent the most homogeneous sample (in age, initial chemical composition, and interstellar reddening) that can be empirically identified and are therefore essential for our understanding of stellar evolution. The identifications of young nearby stellar loose associations (e.g., Torres et al. 2008; Zuckerman & Song 2004, and references therein) have further extended the homogeneous stellar samples on which the early phases of stellar evolution can be investigated effectively. Nearby young associations are valuable targets for the characterisation of the stellar rotation and of the link with other stellar and environment properties. Like open clusters, in fact, physical association allows us to study ensembles of stars with similar age and native environment and reduce the uncertainties due to intrinsic dispersion (still of unknown origin) of rotation period, light elements abundance, and magnetic activity. Such systems are targets of several dedicated studies like spectral characterisation and searches for planets and circumstellar discs (e.g. Torres et al. 2006; Setiawan et al. 2008; Chauvin et al. 2010; Carpenter et al. 2009).

In recent years, a number of valuable monitoring projects of young and intermediate-age open clusters (see, e.g., Herbst & Mundt 2005; Herbst et al. 2007; Hodgkin et al. 2006; von Braun et al. 2005) have provided enough data for statistical analyses of the rotational evolution of solar-like stars. Irwin & Bouvier (2009) report a compilation of 3100 period measurements available then. More recent measures of photometric rotation periods include those of 575 stars in M 37 by Hartman et al. (2009), 368 Pleiades stars by Hartman et al. (2010), 122 stars in M 37 by Messina et al. (2008), 38 stars in M 11 by Messina et al. (2010a), 46 stars in Coma Berenicis by Collier Cameron et al. (2009), and 55 stars in M 34 by James et al. (2010). Extensive survey work in clusters at 1–2 Myr, mainly the Orion Nebula Cluster (ONC) and NGC 2264, have established the initial distribution of rotation rates in low-mass stars (Stassun et al. 1999; Herbst et al. 2001; Rebull 2001; Makidon et al. 2004; Lamm et al. 2004). Herbst & Mundt (2005) estimate that 50–60% of the stars on convective tracks are released from any locking mechanisms very early on and spin-up as a consequence of their contraction in the pre-main sequence (PMS), and these stars account for the rapidly rotating young main sequence stars. The other 40–50% lose substantial amounts of angular momentum during the first few million years, and end up as slowly rotating main sequence stars. The duration of the rapid angular momentum loss phase is  ~5–6 Myr, which is roughly consistent with the lifetime of discs estimated from infrared surveys of young clusters. This supports the hypothesis that the interaction with a circumstellar disc drains angular momentum from the star, thus delaying its spin up for the (variable) duration of its lifetime (e.g., Haisch et al. 2001). This process is not understood in detail yet (see, e.g., Collier Cameron & Campbell 1993; Shu et al. 1994; Matt et al. 2010) and is usually modelled by means of very simplified assumptions, e.g., the disc-locking hypothesis (Köenigl 1991; Collier Cameron et al. 1995) or accretion-driven stellar wind (e.g., Matt & Pudritz 1995).

The initial distribution of rotation rates and the strong rotational regulation in the first  ~5 Myr are deemed responsible for the dispersion of rotation periods at a given mass seen in individual young clusters from the PMS until the age of the Hyades. For the Hyades, a narrow correlation between the B − V colours and the rotation periods of F, G, and K stars has been found (Radick et al. 1987). A small scatter of the individual stellar rotation rates about the mean period-colour relation has also been found on M 37 (Messina et al. 2008; Hartman et al. 2009), M 35 (Meibom et al. 2009), and Coma Berenicess (Collier Cameron et al. 2009). The convergence of the spin rates in  ~600 Myr is a consequence of the strong dependence on stellar rotation rate of the angular momentum loss via a thermally driven magnetically channelled wind (e.g., Mestel & Spruit 1987; see also Weber & Davis 1967; Kawaler 1988; Chaboyer et al. 1995a,b). For such a convergence to occur at the age of the Hyades, the timescale for coupling the stars radiative interior to its outer convective zone must also be significantly shorter than the Hyades age (see, e.g., Collier Cameron et al. 2009).

The relationship between age, rotation, and activity has been a crucial topic of stellar evolution over the past 40 years. Angular momentum loss due to stellar winds is generally thought to be responsible for the Skumanich (1972) law, but the exact dependence of rotational velocity on age is not entirely clear, and it relies on the assumed stellar magnetic field geometry and degree of core-envelope coupling (Kawaler 1988; Krishnamurthi et al. 1997). Empirical age-rotation relations have been proposed to determine the age of stars, a method referred to as gyrochronology (e.g., Barnes 2003, 2007; Mamajek & Hillenbrand 2008; Collier Cameron et al. 2009; Barnes 2010). Empirical age-activity relations have also been proposed, though these do not always find activity decaying with time quite as simply as predicted by the Skumanich law (e.g., Feigelson et al. 2004; Pace & Pasquini 2004; Giampapa et al. 2006).

The determination of stellar rotational periods in large samples of stars of different ages and mass is also crucial for understanding the relationships with stellar properties and their close surroundings. It is also expected that the dissipation timescale of circumstellar discs is related to the processes of planets formation (e.g. Bouvier 2008). On the other hand, the presence of planets may in turn influence the stellar rotational evolution. Recently, Pont (2009) has investigated the influence of tidal interaction with close-in giant planets (Hot Jupiters), and Lanza (2010) studied the role of Hot Jupiter interaction with the coronal magnetic field in the stellar angular momentum loss rate via a magnetised wind.

Open clusters also represent a unique testbed for studying the Li depletion with age and its relationships with stellar rotation (e.g., Sestito & Randich 2005; Jeffries & Oliveira 2005; Randich et al. 2005). In fact, stellar rotation plays a role in shaping the internal circulation, which in turn affects the abundance of light elements that are easily destroyed in the stellar interior (Li, Be, B). A survey of Li abundances in young stellar associations has been carried out by da Silva et al. (2009), who also studied the relationships with age and vsini.

While significant progress has been attained in the last few years, thanks to several dedicated projects or as a by-product of high-precision photometric planet-transit surveys, our knowledge of the rotation evolution of late-type stars remains incomplete, so firm confirmation of the correlations proposed above is still needed. RACE-OC (Rotation and ACtivity Evolution in Open Clusters) is a long-term project designed to study the evolution of the rotational properties and the magnetic activity of late-type members of stellar open clusters with ages between 1 to about 600 Myr (Messina 2007; Messina et al. 2008, 2010a). In Messina et al. (2010b, hereafter Paper I), we considered stellar associations at distances closer than 100 pc and ages younger than about 100 Myr from the list of Torres et al. (2008). These are TW Hydrae, β Pictoris, Tucana/Horologium, Columba, Carina, and AB Doradus associations. They span ages between 8 and 100 Myr and, therefore, allow us to study the angular momentum evolution close to the crucial phase of dissipation of circumstellar discs and planet formation. In Paper I, we determined rotational periods for 144 of 204 late-type members of these associations. A clear indication of evolution with time of rotational period and of its photometric signatures (e.g., photometric amplitude of light curve) has been observed. The goal of the present paper is to complete the study of the associations identified by Torres et al. (2008), determining the rotational properties of members of ϵ Chamaeleontis, Octans, and Argus associations (~6, 20, and 40 Myr, respectively), with mean distances between 110 and 150 pc.

In Sect. 2, we present the sample considered in the present study. In Sect. 3, we describe the photometric data that are used in our analysis. In Sect. 4, we describe our procedure for the rotation period search. In Sect. 5, we present our results. Conclusions are given in Sect. 6. In the Appendix we present the results on periods for a few revisited targets in Paper I.

2. The sample

The sample of our investigation is taken from the compilation of Torres et al. (2008), which includes an updated analysis of the membership of nearby associations younger than 100 Myr. We selected the following associations that have mean distances beyond 100 pc: ϵ Chamaeleontis, Octans, and Argus. These associations are reported with ages in the range  ~6 to  ~40 Myr (cf. Table 1).

The ϵ Chamaeleontis association was discovered and characterised by Frink et al. (1998). We selected 15 late-type members: 14 are high-probability members from the compilation of Torres et al. (2008) and one is a recently added member by Kiss et al. (2011) as part of the RAVE (Radial Velocity Experiment) project. Given the possible connection with ϵ Chamaeleontis, as first suggested by Mamajek et al. (1999), we also compiled a list of all (15) late-type members of the η Chamaeleontis cluster from Torres et al. (2008), whose age is estimated as around 4–9 Myr. Four cluster members with good kinematic data were found as high-probability members of the ϵ Cha association. In the following analysis we consider both η and ϵ Cha members as coeval with an age of  ~6 Myr, but we continue to use different symbols to distinguish them.

The Octans association was discovered within the SACY project (Torres et al. 2003). Owing to its mean distance of about 140 pc and the small number of members with trigonometric parallax, the accuracies on distance of individual members and age (~20 Myr) are poorer than for other associations found with the same approach and the discovered members mostly have G spectral type. Torres et al. (2008) give an updated list of members of this association from which we selected a sample of 12 members with spectral type later than F.

The Argus association was also discovered by Torres et al. (2003) in the SACY survey. Based on the convergence method and following the suggestion of Makarov & Urban (2000), they found that the kinematic properties of the members of the IC 2391 open cluster are in good agreement with their proposed Argus members. Torres et al. (2008) give an updated list of members of both Argus and IC 2391 members. Finally, we also considered the new candidates members of young associations recently identified by Kiss et al. (2011) from RAVE data and by Desidera et al. (2011). From these lists, we compiled a sample of 57 members (27 Argus stars and 30 stars in IC 2391) with spectral type later than F.

From the initial list of 121 known stellar members, we selected 99 late-type stars (spectral types later than F or colours consistent with a late spectral type) that are suitable for the photometric search of rotational modulations. In Table 1 we list name, abbreviation, age, and mean distance of the associations under study (Torres et al. 2008), together with the number of known members and late-type members selected for period search. Most of the spectroscopic information (spectral types, projected rotational velocity vsini) is from SACY database (Torres et al. 2006). In the case of IC 2391 cluster, vsini values come from da Silva et al. (2009) and Marsden et al. (2009). Additional bibliography for individual targets is given in Appendix A.

Furthermore, to complete the analysis of the associations studied in Paper I, we considered the photometry becoming available in the Wide Angle Search for Planets (SuperWASP) archive for the stars of TW Hydrae, β Pictoris, Tucana/Horologium, Columba, Carina and AB Doradus associations. The new rotation periods of the associations studied in Paper I and retrieved from SuperWASP photometry are reported in Appendix B.

3. Data

3.1. The ASAS photometry

As in Paper I, most of the present analysis is based on data from the All Sky Automated Survey (ASAS) (Pojmanski 1997, 2002). The ASAS project is monitoring all stars brighter than V = 14 at declinations δ <  +28°, with typical sampling of 2 days. The ASAS archive¹ ensures long-term monitoring since it contains data from 1997 to date. A short-term monitoring might hamper the identification of the correct rotational period. Since the configuration of active regions, which is responsible for the light rotational modulation, evolves with time, such a long time-span is particularly suitable for our purposes.

The linear scale at focal plane is 16 arcsec/pixel. The FWHM of stellar images is 1.3–1.8 pixels. Aperture photometry through five apertures is available in the ASAS catalogue. The choice of the aperture adopted in our analysis was made star by star by selecting the aperture giving the highest photometric precision (i.e., the minimum average magnitude uncertainty).

3.2. The SuperWASP photometry

The SuperWASP project (Pollacco et al. 2006) recently released the first public data archive (Butters et al. 2010)². Light curves from 2004 to 2008 for both the northern and southern observatories are included. Temporal and spatial coverage is irregular, but extended enough to make a systematic search for photometric timeseries of our targets meaningful. The observing procedure includes sequences up to nine hours long for stars at the most favourable sky declinations with a sampling of about ten minutes. The SuperWASP data have therefore a better sensitivity to periods  ≲ 1 d than the ASAS data. We then checked the availability in SuperWASP archive of data for both the targets studied in this paper as well those we studied in Paper I. To further complete Paper I analysis, we also checked the availability of ASAS and SuperWASP photometry for the new candidates members of young MG identified by Kiss et al. (2011). Our analysis is based on the processed flux measurements obtained through application of the SYSREM algorithm (Tamuz et al. 2005). SuperWASP observations were collected in 2004 without any light filter, the spectral transmission defined by the optics, detector, and atmosphere. Starting from 2006 they were collected through a wide band filter in the 400–700 nm. Owing to differences in spectral bands with respect to the standard Johnson V ASAS data, we decided to analyse the SuperWASP data independently without merging these with ASAS data.

3.3. Data from the literature

Literature period determinations, including those listed in ASAS Catalogue of Variable Stars (ACVS) and the search for variable stars from SuperWASP data (Norton et al. 2007), were considered and compared to our measurements when available. These are listed in Tables 2–4. Three cases of discrepant results are discussed individually in Appendix A.

4. Photometry rotation period search

The rotational period search procedure is described in Paper I. Here we briefly summarise it. The analysis makes use of the Lomb-Scargle periodogram (Scargle 1982). The light curves of late-type active stars are typically characterised by changes in amplitude and shape with timescales of a few months or even shorter (see, e.g., Messina et al. 2004). These are due to the finite lifetime of active regions, consisting of either dark spots or bright faculae, and to differential rotation. Additional photometric variability is observed on timescales shorter and longer than the rotation period because of flares and magnetic cycles. This variability pattern causes the application of the Lomb-Scargle periodogram to the whole light curve to fail the detection of the rotational period in some cases. Therefore, in addition to analysing the whole timeseries (which is typically 8-yr long for ASAS data and 4-yr long for SuperWASP data), we performed the period search on light-curve segments not exceeding two months.

The determination of the false alarm probability (FAP) is a crucial issue for evaluating the significance of detected periodicities. The existence of significant correlations between data that are collected on shorter timescales than the stellar variability does not allow safely making the assumption that each observed data point is independent of the others (Herbst & Wittenmyer 1996; Stassun et al. 1999; Rebull 2001; Lamm et al. 2004). To overcome this difficulty, we follow the bootstrap approach proposed by Herbst et al. (2002). For each light curve segment, we scramble 1000 times the day numbers of the Julian Day (JD) while keeping photometric magnitudes and the decimal part of the JD unchanged. Then we perform the period search on each fake randomised dataset, comparing the power of the highest peak to that observed on the real dataset to obtain the FAP. We adopt a confidence level larger than 99% (FAP  < 0.01) as detection threshold for a significant detection.

Finally, to successfully identify the true rotational periodicity, it is necessary to consider aliases, which might have even higher power than the true period. The spectral window function is inspected to disentangle aliases (1-d peak, beat periods between the star’s rotation period (P) and the data sampling). The uncertainties in the period determination were derived following Lamm et al. (2004).

For each target we report (Tables 2–4) the detected rotation period, together with the number of segments in which such a period was derived, with a confidence level higher than 99%. In some cases, however, the same period was found in other segments with a confidence level below 99%, but the lightcurve still showed a clear rotational modulation with this very period.

We therefore also report the number of segments in which the lightcurve, when phased with the detected rotation period, shows a smooth sinusoidal variation; in this case, the average residual in the sinusoidal fit of the light curve is smaller than the light-curve amplitude. The number of segments in which the period was found with a confidence level higher than 99% and/or the number of segments in which the phased lightcurve show average residuals lower than its amplitude can be used to estimate the robustness of the period determination. When vsini measurements are also available, a consistency check can be performed with the equatorial velocity, which can be derived from the rotational period and an estimate of the stellar radius. We use this information to classify the detected periods according to their reliability.

Periods derived in at least five segments, or in less than five but with an independent confirmation from the literature, and that are consistent with vsini will be referred to as confirmed periods (C). Periods derived in less than five segments that are consistent with vsini and that produce mean residuals in the sinusoidal fit less than the light-curve amplitude in at least five segments will be referred to as likely periods (L). Periods derived in less than five segments that produce mean residuals in the sinusoidal fit less than the light-curve amplitude in less than five segments, or with only 1–2 determinations in the literatures, or that are inconsistent with vsini will be referred to as uncertain periods (U).

5. Results

The results of our investigation are summarised in Table 1, where we report the total number of confirmed periodic members (and the total number of confirmed + likely + uncertain in paretheses), the number of periodic members with period adopted from the literature, new periods determined from this study (and periods revised by us with respect to earlier literature values).

We determined 45 confirmed rotation periods (31 of which are new determinations), 11 likely, 24 uncertain (10 of which are taken from the literature). Eleven of 80 periodic stars were already known from the literature and we could confirm their rotation period, whereas we revised it for 3 stars (RECX 1, RECX 11, and CD-48 2972, see Appendix A). The rotation periods of 19 stars remain unknown, for three of which we have data neither in ASAS, in SuperWasp, nor in the literature, whereas for 16 we find non-periodic variability. In Tables 2–4 we report the results of a period search in some detail for the members of individual associations. As in Paper I, the results of the period search for close spectroscopic binaries whose rotation might be altered by the tides of their companions is here reported. However, they are excluded from the rotational distributions and also when computing the mean and median values in the subsequent sections. In Table B.2, we list the rotation periods for each periodic target, together with uncertainties and normalised powers, determined in the individual time-series segments.

The light curves of all stars for which either the ASAS or the SuperWASP photometry allowed us to determine the rotation period are plotted in Figs. B.7–B.23.

5.1. Colour-magnitude diagrams

Following the approach of Paper I, we use the M_V vs. V − I CMD and a set of low-mass PMS evolutionary tracks to derive masses and radii. Owing to the targets distances, on average larger than 100 pc, and their young ages, especially in the case of the ϵ/η Cha members, the observed colours may suffer from reddening arising either from interstellar or circumstellar material. We have investigated on the possible colour excess of all targets and derived the intrinsic colours for the subsequent analysis. V magnitudes are taken from ASAS because the long-term monitoring gives the possibility of measuring the brightest magnitude over a long time range, i.e. the value corresponding to the observed minimum spot coverage. In most cases, the ASAS V-magnitudes are found to be brighter than those reported in the references below.

ϵChamaeleontis. Colours are taken either from Torres et al. (2006) or Alcalà et al. (1995) both in the Johnson-Cousins photometric system. All but two members (GSC 9235-01702 and CD − 74712) are found to be affected by reddening (see Tables B.3–B.5). The colour excess of each target is determined by comparing the observed V − I colour with the V − I colour corresponding to the spectral type of a standard dwarf star. The A_V extinction is derived from E(V − I) using the relations of Mathis (1990). We find that the A_V extinction ranges from 0.1 to 1.8 mag. A study by Knude & Hog (1998) based on the Hipparcos and Tycho data found that in the Chamaeleon region the interstellar extinction in the distance range of our targets never exceeds A_V ~ 0.15 mag. Therefore, the derived reddening, in agreement with the very young age of the ϵ Cha members, likely arises from circumstellar rather than from interstellar material.

ηChamaeleontis. Colours in the Johnson-Cousins photometric system and spectral types in the present paper are taken from Lawson et al. (2001, 2002). A study by Westin (1985) has found the interstellar reddening for this cluster to be unimportant. This result is also confirmed by Mamajek et al. (2000) who found the V − I colour of members to be consistent with the inferred spectral type.

Octans. The observed colours are taken from Torres et al. (2006) and are found to be consistent with the spectral types; therefore, no reddening correction is applied. We adopt the V − I colour corresponding to the target’s spectral type for four stars missing V − I measurements. Only one star (TYC 7066 1037 1) with measured V − I colour shows an excess that we corrected as described above.

Argus. V − I colours are taken from Torres et al. (2006). We adopt the colours corresponding to the spectral type of standard dwarf stars for 14 members that lack V − I measurements. Only one star (TYC 8561 0970 1) with measured V − I colour shows an excess that we corrected as above.

IC2391. Colours in the Johnson-Cousins photometric system are taken either from Patten & Simon (1996) or from Platais et al. (2007). In the latter case only B − V is measured and V − I is inferred from spectral type. The mean reddening towards IC 2391 is estimated to be close to zero (Patten & Simon 1996) and no correction was made for interstellar reddening. Only one star (PMM 1759) needed to be corrected to make V − I consistent with spectral type.

In general, as expected from variability arising from spots and/or faculae, the V-magnitude variability amplitude in our targets never exceeds  ~0.3 mag. The only deviating star is PMM 8145 whose variability amplitude reaches  ~2 mag. In this case, however, there is a close, very bright nearby star (o Vel, V = 3.6 mag Δα = 2 arcsec, Δδ = 70 arcsec) and therefore CCD saturation affecting the PMM 8415 time-series cannot be ruled out.

Vmagnitudes, B − V, and U − B colours (flagged with A_V when corrected for reddening), absolute magnitudes, distances and vsini values from the literature are listed in Tables B.3–B.5.

The reddening-corrected CMDs of the studied associations are plotted in Figs. 1, 2 together with the Baraffe et al. (1998) evolutionary tracks and the CMDs of three well-studied open clusters of known age for reference: α Persei (~70 Myr), the Pleiades (~110 Myr), and NGC 2516 (~150 Myr).

As in Paper I, we estimate masses and radii comparing positions in the CMD with the Baraffe et al. (1998) evolutionary tracks. The stellar radius (R) allows us to make a comparison between vsini and the equatorial velocity v_eq = 2πR/P (where P is the rotation period) to check the consistency between the two and derive the stellar inclination. Derived masses and radii are listed in Tables B.3–B.5.

5.2. v sin i vs. equatorial velocity

All but five of the periodic variables in our sample have known projected equatorial velocities (vsini). In Fig. 3, we compare vsini and v_eq, by delineating the loci of vsini = v_eq, corresponding to equator-on orientation, and vsini = π/4 v_eq, corresponding to a randomly orientated rotation axis distribution. In Fig. 3 all periodic (confirmed, likely, and uncertain) targets are plotted. The major uncertainty in the equatorial velocity is the radius estimate. The reported vsini uncertainties are on average 10%. Only four stars (GSC 9419-01065 in ϵ Cha, CD-582194 and CPD-621197 in Argus, and PMM 351 in IC 2391) (flagged with an apex c in Tables 2 and 4 and plotted with circled symbols in Fig. 3) have inconsistent vsini/v_eq (i.e., much larger than unity). These cases are discussed in Appendix A.

In Table 5, for each association we report the average  ⟨ sini ⟩  ± σ, the correlation coefficient r from the linear Pearson statistics between vsini and v_eq, where the labels a and b indicate the significance level of the correlation coefficient. The significance level represents the probability of observing a value of the correlation coefficient greater than r for a random sample with the same number of observations and degrees of freedom.

It is interesting to note that all association members have mean inclinations that are inconsistent with the value (π/4) expected for a completely randomly orientated rotational axis distribution. Specifically, all association members tend to appear almost equator-on to the observer. This behaviour, which was also exhibited by the six other associations within 100 pc analysed in Paper I, may arise from some bias rather than being real. A bias in the member selection is unlikely, since the association members were identified in larger samples selected on the basis of their X-ray emission, which is not affected by the inclination of the rotation axis. On the contrary, a bias towards equator-on members may be more likely. In fact, we find that members with unknown rotation periods exhibit on average vsini systematically smaller than members with uncertain, likely, and confirmed periods, respectively. In the specific case of Argus/IC 2391, which is the most numerous association in the present paper, we find that members with unknown periods have  ⟨ vsini ⟩  = 15.1 km s^-1 with respect to  ⟨ vsini ⟩  = 33.8 km s^-1 exhibited by members with confirmed periods. In the case of the AB Dor association studied in Paper I we find  ⟨ vsini ⟩  = 8.2 km s^-1 for stars with unknown period against  ⟨ vsini ⟩  = 25.9 km s^-1 for members with confirmed periods. From the former case, we can infer that about 20% of stars, whose average vsini is about half that of equator-on stars, is still missing in the vsini versus v_eq plot of Argus/IC 2391. Therefore, a bias towards stars with high values of inclination is present, which are those that show larger-amplitude light modulation and that are most favoured for the rotation period determination. We may also suppose that our derived radii are all systematically underestimated, likely from effects of high magnetic activity and fast rotation, as found by, e.g., Chabrier et al. (2007) and Morales et al. (2009). This makes v_eq systematically small with respect to the measured vsini. Nonetheless, these two quantities are found to be strongly correlated (see Table 5) differently than expected in the case of random distribution of axes. This finding certainly deserves further investigation to take all possible observation biases into account so is beyond the scope of the present paper.

5.3. ϵ/η Chamaeleontis

We determined the rotation periods for 11 stars in ϵ Cha, of which there are ten new and one already known in the literature. The rotation periods of another two stars were retrieved from the literature. For stars in η Cha, we retrieved 12 rotation periods, of which seven were retrieved from the literature. For ϵ and η Cha we therefore have a total of 25 periods available, 14 confirmed, 1 likely, and 10 uncertain. In the left panel of Fig. 4, we plot with filled blue bullets and red squares the members of ϵ and η Cha, respectively, with confirmed periods. Small-size filled symbols represent likely periods, whereas small-size open symbols are used for uncertain periods.

Members of ϵ Cha with confirmed periods have all M ≥ 0.8 M_⊙. Their periods have a mean P_mean = 4.35 d and a median P_median = 3.97 d. Members of η Cha with confirmed periods have all but one M ≥ 0.8   M_⊙. Their periods have P_mean = 4.67 d and P_median = 4.84 d, although only derived from four stars. If ϵ and η Cha are considered together as a coeval system, we obtain P_mean = P_median = 4.45 d.

5.4. Octans

Of 12 late-type members to the Octans association, we determine the rotation periods of ten stars (eight of which are confirmed periods, and two are likely periods). The Octans rotation period distribution is plotted in the right panel of Fig. 4. Owing to the very small number of known late-type members, the period distribution upper bound is not sufficiently defined. All confirmed periodic members in our study have masses M ≥ 0.8   M_⊙ and the mean and median periods turned out to be P_mean = 1.46 d and P_median = 1.61 d.

Octans is the most distant association (~140 pc) and, owing to the small number of members with accurate trigonometric parallax, its age is the most uncertain in our sample. As for the other associations, the Octans members were selected by SACY on the basis of their X-ray emission in the ROSAT Bright Survey. However, the detected members of Octans are at the detection limit of that survey. Therefore, it is likely that only the most active and, therefore, fast rotating members have been detected. That means that our sample of periodic stars is biased, the detection of only the fastest rotating stars being favoured. Therefore, the bias towards the faster rotators, together with the uncertainty on age, makes the Octans mean and median rotational periods quite unreliable, which must be taken into account in our analysis of the rotation period evolution reported in Fig. 7.

5.5. Argus/IC 2391

Among the three associations under analysis, Argus has the largest number of late-type members, 27 Argus stars plus 30 additional stars in the IC 2391 cluster. We determine the rotation period of 45 members. However, only for 23 members, which are plotted in Fig. 5, are the rotation periods confirmed.

We overplot the empirically determined functions computed according to Barnes (2003) and describing the loci of the upper/lower bounds of the α Persei period distribution for main-sequence stars. The Argus/IC 2391 upper bound is very close to the dashed line, which is computed for a nominal age of 70 Myr, suggesting an age for Argus/IC 2391, slightly older than the quoted age of 40 Myr. Considering confirmed periods only, we found P_mean = P_median = 2.27 d for Argus, P_mean = 2.36 d, and P_median = 3.03 d for IC 2391. In both cases all stars have mass M > 0.8   M_⊙. When all members (Argus/IC 2391) are considered, together P_mean = 2.43 and P_median = 2.30 d. Although quoted with the same age, we see, either in Fig. 5 or from the above mean values, that the distribution of rotation periods of IC 2391 stars appears slightly different from that of Argus stars, with more slow rotators in the cluster. This difference may arise from the different selection criteria adopted to search for members. Argus members are identified on the basis of their X-ray emission and are all present in the ROSAT Bright Source Catalog (Voges et al. 1999). Conversely, the IC 2391 members are selected from a variety of sources, without X-ray preselection. Since fast rotators have brighter coronal luminosities and the mean distance of Argus asociation members is 106 pc, compared to  ~ 145 pc for IC 2391, we expect that the census of association members is biased toward the most active and fast-rotating stars (see Desidera et al. 2011).

5.6. Rotation-photospheric activity connection

Following Paper I, we have extracted for each periodic target the V-band maximum peak-to-peak light curve amplitude ever observed in the available time series that are plotted in Fig. 6. For the older associations under analysis, Octans and Argus/IC 2391, the photometric variability mostly arises from the presence of cool spots on the stellar photosphere. In the case of ϵ/η Cha, a contribution from hot spots, arising from accretion processes, cannot be ruled out. The largest amplitudes are observed in the youngest association at an age of about 6 Myr where the presence of circumstellar material (as inferred from the observed colour excess) and related accretion phenomena are still expected. The lowest amplitudes are observed in the Octans association with an assumed age of about 20 Myr. The apparent age dependence of the light curve amplitude at fixed rotation and mass will be discussed in a forthcoming paper (Messina et al., in prep.).

5.7. Rotation period evolution

In Fig. 7, we plot the results of our period search in the nine associations under study, where we show the rotation period variation of low-mass stars versus age in the 0.8–1.2 M_⊙ range. We plot the rotation periods listed in Tables 2–4 of this paper, and in Tables 3–8 of Paper I, complemented with the updated values listed in Table B.1 of this paper. We overplot the median and mean rotation periods computed for each association (or coeval associations as explained by the labels) considering only the confirmed rotation periods to which we assign the same weight. We also add the mean and median rotation periods of ONC (Herbst et al. 2002), NGC 2264 (Rebull et al. 2002; Lamm et al. 2004), α Persei, and the Pleiades, whose rotation periods are taken from the compilation of Messina et al. (2003, and references therein).

In Table 6 we report for each cluster/association the number of confirmed periods used to derive the mean and median values, as well as the KS significance levels that consecutive (at increasing ages) measured period distributions are drawn from the same distribution according to Kolmogorov-Smirnov tests (see, e.g., Sect. 14.3 of Press et al. 1992). Period distribution variations that are not statistically significant have KS values close to unity, while statistically significant variations have KS values close to zero.

The newly added mean and median values at 6 Myr (ϵ/η Cha) and 40 Myr (Argus/IC 2391) confirm the trend of period evolution with age found in Paper I. From 1 to 9 Myr, the mean and median periods slowly decrease, but the KS values remain rather high, which indicate that indeed the period distributions do not change significantly. This behaviour is consistent with a locking mechanism operating in this age range. From 9 to 30 Myr both mean and median periods decrease and the KS values indicate a statistical significant variation in this case. The decrease in mean and median periods is monotonic, with only the period distribution of Octans deviating from this trend. However, as discussed in Sect. 5.4, the sample of known Octans late-type components is expected to be rather incomplete and biased towards fast rotators, which could explain the rather low mean and median periods compared with adjacent values. Furthermore, the Octans age uncertainty is considerably larger than for the other associations. For the 0.8–1.2 M_⊙ range, our analysis is therefore consistent with a considerable disc-locking before 9 Myr, followed by a moderate but unambiguous spin-up from 9 to 30 Myr, consistent with stellar contraction towards the ZAMS.

Variations between 30 and 70 Myr are rather doubtful. The KS test indicates that there is no significant variation between 30 and 40 Myr. On the other hand, the KS test indicates a significant variation between 40 and 70 Myr, but while the median indicates a significant spin-up, the mean remains approximately constant. Between 70 and 110 Myr the KS test indicates a significant variation and both mean and median periods increase. This situation may be due to the heterogeneity of the sample: all stars with masses above 1 M_⊙ are expected to complete their contraction toward the ZAMS at ages earlier than about 30 Myr, but stars with lower mass will end the contraction towards the ZAMS later on (around 70 Myr for a star of 0.8 M_⊙). The unambiguous spin-down from 70 to 110 Myr is consistent with all stars in the 0.8–1.2 M_⊙ mass range having entered the MS phase and therefore the angular momentum evolution being dominated by wind-braking.

6. Conclusions

We have performed a rotation period search for all late-type members of the nine young (< 100 Myr) associations known to date for which either ASAS or SuperWASP data are available. We supplemented such information with rotation periods retrieved from the literature to derive a catalogue that contains (considering also the new periods listed in Table B.1) a total of 241 rotation periods. We have established quality criteria for classifying the derived period based on the frequency of period determination in various light-curve segments, independent measurements retrieved from the literature, and consistency with vsini. Based on such criteria, three quality levels are proposed: confirmed, likely, and uncertain. Our catalogue contains 171 confirmed, 44 likely, and 26 uncertain periods. The rotation period remains unknown for the remaining 50 late-type members. Thanks to the newly determined period distributions at  ~ 6,  ~ 30, and  ~ 40 Myr, our catalogue allows a better empirical description of angular momentum evolution of stars with masses from 0.8 to 1.2 M_⊙ and with ages from 1 to 100 Myr.

The catalogue is used to build rotation period distributions vs. colours for each association in the 0.8–1.0 M_⊙ mass range. Excluding Octans, which is likely to be affected by a strong selection bias toward shorter periods, the average and median periods are found to essentially decrease from the ONC age (~1 Myr) untill the α Persei age (~70 Myr). The two-sided KS test indicates that indeed the period distributions do not change much from 1 to 9 Myr, while variations are statistically significant from 9 to 30 Myr. This increase in the average rotation rate with age is consistent with the contraction of the stars toward the ZAMS, which is contrasted by disc-locking at an early stage. The situation from 30 to 70 Myr is rather uncertain, probably because of the heterogeneity of our sample, in which stars of different mass reach the ZAMS at different ages. From α Per (70 Myr) to the AB Dor/Pleiades (110 Myr) both mean and median periods increase with the KS test, indicating a statistically significant variation.

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Acknowledgments

The extensive use of the SIMBAD and ADS databases operated by the CDS centre, Strasbourg, France, is gratefully acknowledged. We used data from the WASP public archive in this research. The WASP consortium comprises of the University of Cambridge, Keele University, University of Leicester, The Open University, The Queen’s University Belfast, St. Andrews University, and the Isaac Newton Group. Funding for WASP comes from the consortium universities and from the UK’s Science and Technology Facilities Council. The Authors would like to thank Dr. G. Pojmański for the extensive use we made of the ASAS database. We are grateful to the Referee Dr. James for his valuable comments that allowed us to significantly improve our analysis and its presentation.

References

Online material

Appendix A: Individual stars

A.1. ϵ + η Cha

GSC 9419-01065: the rotation period derived from our analysis is P = 8.0 d. Although the flux rotational modulation is clearly found in more than five segments; however, the computed v_eq = 2πR/P is inconsistent with the measured vsini = 18.0 km s^-1 (Torres et al. 2006), so this period is considered uncertain. However, we note that the only available vsini measurement has quite a large  ± 30% uncertainty. More accurate determinations would be desiderable to confirm the correctness of the current vsini value.

HD 104237E: the ASAS photometry did not allowed us to infer any periodicity. We adopted the period of P = 2.45 d detected by Feigelson et al. (2003), which combined with the estimated radius gives an equatorial velocity consistent with the measured vsini. This star belongs to a quintuple system, where the brightest component is the Herbig Ae star HD 104237. Feigelson et al. (2003) found a reddening A_V = 1.8 ± 0.3 that likely arises from material within the parent stellar system, the reddening of other members associated to ϵ Cha being small or even absent.

GSC 9416-1029: Doppmann et al. (2007) report a period of P = 5.35 d that likely represents the system’s orbital period. The available ASAS photometry of this star, which is quite inaccurate owing to the target’s faintness, shows evidence of a period P = 5.50 d in two of nine time segments. In the case this is the correct rotational period, which would imply a rotational/orbital synchronisation, which is quite a surprising circumstance at an age of about 6 Myr.

GSC 9235-01702: it has very recently been discovered to be a member of ϵ Cha by Kiss et al. (2011) as part of the RAVE project. From the ASAS photometry, we found the same rotation period as found by Bernhard et al. (2009), based on the same ASAS data.

RECX 1 (EG Cha): we detect a rotation period P = 4.5 d in 12 of 15 time segments, which is twice the period reported by Lawson et al. (2001). An inspection of Fig. 2 of Lawson et al. (2001) shows that their phased light curves in both 1999 and 2000 seasons exhibit significant magnitude phase dispersion.

RECX 11 (EP Cha): we found a period P = 4.84 d in 7 of 12 time segments with confidence level over 99% and no evidence of any power peak at the period P = 3.95 d discovered by Lawson et al. (2001) in 1999 (P = 3.69 d in 2000). Again, an inspection of their phased light curves shows significant dispersion

RECX 12 (EQ Cha): the star shows two significant periods in Lawson et al. (2001), P = 1.25 d and P = 8.55 d. The star is a close binary, so they might represent the rotational periods of the two components. Our analysis allowed us to detect only the shorter period that is adopted in the present analysis.

RECX 15 (ET Cha): is a classical T Tauri star, with evidence of on going accretion (Lawson et al. 2002). The large amplitude variations (up to 0.44 mag) are likely driven by accretion hot spots.

A.2. Octans

CD-58 860: we find two periods, P = 1.612 d and P = 2.610 d, in eight out of ten time segments with comparable levels of confidence. However, the longer period, once combined with stellar radius, determines a ratio vsini/v_eq slightly greater than unity. Therefore, in the present analysis we adopt P = 1.612 d.

CD-43 1451: this star is also present in the SuperWASP archive. However, neither from the ASAS nor from the SuperWASP database we could determine the rotation period, but only the presence of light variability.

HD 274576: the period P = 2.22 d is found in nine out of ten time segments of ASAS photometry and in two out of two SuperWASP observation seasons, and it is fully consistent with the measured vsini. We note that in both the ASAS and SuperWASP timeseries another period P = 1.824 d is also found with a very high confidence level, although it is smaller than the earlier, in almost all time segments, which is also consistent with vsini.

TYC 7066 1037 1: the period P = 2.47 d is found in 6 out of 14 time segments of ASAS photometry and in three out of five segments of SuperWASP photometry.

A.3. Argus and IC 2391

HD 5578 (BW Phe): is a close visual binary. We found two rotation periods of comparable power, P = 1.461 d and P = 3.15 d, in most time segments. The shorter period is assumed to be the star’s rotation period, since it is the only one consistent with a vsini/v_eq ≤ 1.

CD-56 1438: we detect a period P = 0.24 d in only one segment that may conciliate with the very high vsini.

CD-28 3434: the P = 3.82 d period is very well established and also detected in three out of three time segments of SuperWASP data, as well in the complete timeseries. Although no vsini is available to check consistency with v_eq, it is considered a confirmed period.

HD 61005: has been suggested to be a likely member of the Argus association (Desidera et al. 2011). Although its P = 5.04 d period is found in only three time segments of the ASAS timeseries, it was confirmed by the period search carried out in the Tycho and Hipparcos photometry (Desidera et al. 2011), so it is considered confirmed in the present analysis.

CD-39 5883: the period is detected in two out of nine segments of ASAS photometry and in five out of five segments of WASP data as well in the complete timeseries and is consistent with vsini/v_eq ≤ 1.

CD-58 2194: the most significant period is P = 5.16 detected in four time segments as well in the complete timeseries. However, it is inconsistent with the high vsini. It may be the beat of the P = 0.55 d period detected in only one season. This period is therefore considered uncertain.

CD-57 2315: it is variable, but no periodicity was found.

CPD-62 1197: the most significant period is P = 1.26 d which is found in seven out of nine segments. However, it leads to a vsini/v_eq ~ 2 and therefore it will not be considered in the following analysis. Another significant period is P = 0.82 d, which is, however only detected in three out of nine segments, so it is classified as uncertain.

TYC 7695 0335 1: the same P = 0.39 d is found in three out of nine ASAS segments and in four out of four segments of SuperWASP data.

HD 85151A: is a close visual binary. The P = 0.97 d is only found in the ASAS complete timeseries, but in five out of five time segments of SuperWASP data.

CD-65 817: is a close visual binary.

HD 310316: is a close visual binary.

CD-74 673: is a spectroscopic binary with an orbital period P = 614 d (Guenther et al. 2007).

CD-52 9381: the most significant period is P = 5.19 d detected in six out of nine time segments, as well in the complete series. However, a P = 0.89 d is also detected and reported in the ACVS. The shorter one is consistent with vsini/v_eq ≤ 1, and it is considered as a confirmed period.

PPM 351: the most significant period is P = 1.931 d that is found in six out of nine segments; however, it gives vsini/v_eq > 1. Another detected period is P = 0.69 d, which is, however, found in only three out of nine segments, so it is considered uncertain.

PMM 1083 (V365 Vel): our period determination is in good agreement with the earlier determination by Patten & Simon (1996). Two different vsini values are reported in the literature, vsini = 43 km s^-1 from Marsden et al. (2009) and vsini = 67 km s^-1 from Platais et al. (2007). However, only the first is consistent with vsini/v_eq ≤ 1.

PMM 1820 (V366 Vel): our period determination is in good agreement with the earlier determination by Patten & Simon (1996).

PMM 4413: is an SB2 with an orbital period P = 90.6 d (Platais et al. 2007) whose components have measured vsini of 8.6 and 8.4 km s^-1, which give consistent vsini/v_eq ratios.

PMM 4467 (V364 Vel); PMM 4902; PMM 5884 (V377 Vel): our period determinations are in good agreement with the earlier determinations by Patten & Simon (1996).

PPM 8145: unlike stars whose variability arises from dark spots, this star spends most of its time in its fainter state. The variability likely arises from magnitude outbursts. It shows the largest variability amplitude (~2 mag) in our sample. The reference magnitude, differently than other stars, is probably the faintest one.

PMM 4902 (V379 Vel): although detected in only three time segments, it is considered confirmed because its period is confirmed by the literature value (Patten & Simon 1996).

PPM 2182: we found two significant periods, P = 3.28 d and P = 1.437 d. However, both are not consistent with vsini/v_eq ≤ 1, being vsini = 78 km s^-1 (da Silva et al. 2009) and therefore are considered uncertain.

Appendix B: New/revised periodicities in young associations studied in Paper I

The availability of SuperWASP light curves allowed us to revisit some of the targets studied in Paper I. We found SuperWASP timeseries for 71 targets listed in Paper I. For the seven candidate members of β Pic and Tuc/Hor newly proposed by Kiss et al. (2011), we retrieved SuperWASP timeseries for two of them and ASAS time series for the remaining five. Unfortunately, of 78 targets the data on nine stars turned out to be too sparse to be suitable for a meaningful period search. The analysis of the 69 timeseries allowed us to discover (i) 15 new periods (5 of which likely), (ii) to confirm 35 periods, and (iii) to revise 13 periods. Finally, for six stars we could not detect any period. Three of them were also found non periodic in Paper I, two were found periodic in only 1 or 2 ASAS time segments, and one had only one literature determination. Our results are summarised in Table B.1.

Concerning the revised periods, the previous determinations reported in Paper I were either based on literature values (1 target), had inconsistent vsini/v_eq ratio (4 targets), or were beat periods detected in less than five time segments (5 targets), or detected in five or more segments (3 targets). Based on this result for the period revision of a few targets in Paper I, in the present work we decided to consider a rotation period to be well established (confirmed) if detected in five or more time segments or in fewer, but with an independent determination from the literature.

In the following we update the results presented in Paper I including new results based on Super WASP and on a more conservative period selection.

TW Hydrae We found SuperWASP data for eight targets in TW Hya and confirmed the rotation periods of four targets, and determined three new periods. However, only one out of the three newly periodic targets (TWA 20) is a confirmed TWA member, the other two having been rejected or needing to be confirmed. The rotation period of TWA 23, although detected in three out of five time segments, has a critical value close to the data 1-day observation sampling. Therefore, even if reported in this work, it needs additional observations to be confirmed, therefore, we classify it as uncertain. The data of TWA 3 were quite sparse to be suitable for a period search.

To summarise, we have so far derived confirmed periods for 15 out of 17 certain late-type members of TW Hya. Rotation periods of TWA 3A and TWA 3B are still unknown.

βPictoris Data for 13 β Pic targets are available in the SuperWASP database, five of which have been recently identified as β Pic members by Kiss et al. (2011). For seven targets we confirm the period determined in Paper I. For the other six we determined previously unknown period, five of them classified as confirmed, the other one (J01071194-1935359) as likely.

To summarise, we derived confirmed periods for 29 of the 37 late-type members of β Pic. For a further three stars we determined likely periods, whereas for only one star we have an uncertain period. The rotation periods of four stars still remain unknown.

Tucana/Horologium Data for 19 Tucana/Horologium targets are available in the SuperWASP database, two of which have been recently identified as Tucana/Horologium members by Kiss et al. (2011). For nine targets we confirm the rotation periods determined in Paper I. For one target (J01521830-5950168) we determined the previously unknown period that we classify as uncertain.We revised the period of HIP 21632, which was taken from the literature in Paper I and based on Hipparcos photometry, and the period of TYC 8852 0264 1 whose earlier determination led to inconsistent vsini/v_eq ratio. This star was excluded in Paper I from rotation period evolution analysis also because it is a rejected member. SuperWASP data of six targets were quite sparse and unsuited for period search. Data of HD 25402 were suited but did not allow any period detection.

To summarise, we derived confirmed periods for 22 of 29 late-type members of Tucana/Horologium. Two stars have rotation periods still to be confirmed. Rotation periods of five stars HIP 490 HIP 6856, TYC 8489 1155 1, AF Hor, and HIP 16853 are still unknown.

Columba Data for 12 Columba targets are available in the SuperWASP database. For four targets we confirm the rotation period determined in Paper I. For two targets we determined the previously unknown period that we classify as confirmed. We revised five rotation periods. The revised period of TYC 7100 2112 1 now gives consistent vsini/v_eq ratio. The other four revised periods were in Paper I either beat periods or detected in four or fewer time segments, whereas they are now well established. Data of HIP 25709 were too sparse to allow a period determination.

To summarise, we derived confirmed periods for 20 of 23 late-type members of Columba. TYC 6457 2731 1 and TYC 5346 132 1 still have unknown periods. The period of HIP 25709 is classified as likely.

Carina We did not find any SuperWASP data for the Carina late-type members. We derived confirmed periods for 14 of 21 late-type members. Four stars have the period classified as likely. The periods of TYC 8584 2682 1, HD107722 is still unknown. TYC 8586 2431 1 has period leading inconsistent vsini/v_eq ratio.

AB Doradus Data for 26 AB Doradus targets are available in the SuperWASP database, and for three targets we determined the previously unknown period (one classified as confirmed, and two as likely). For 11 targets we confirm the rotation period determined in Paper I. We revised six periods, and did not detect any periodicity of five stars although the timeseries are suitable for the period search. The observations of one target are too sparse for period search. The rotation period of HIP 116910 reported in Paper I revealed itself to be the beat period of the confirmed P = 1.787 d discovered in SuperWASP data. The periods of TYC 7059 1111 1 and TYC 7598 1488 1 reported in Paper I led to inconsistent vsini/v_eq ratio, whereas the updated period solved the inconsistency. The period of TYC 7064 0839 1, TYC 7605 1429 1, and TYC 7627 2190 1 reported in Paper I were detected in less than five time segments, whereas the new periods are classified as confirmed.

To summarise, we derived confirmed periods of 29 of 64 late-type members of AB Doradus. Twenty members have periods classified as likely. The rotation period of 15 members is still unknown.

In Figs. B.1–B.3 we plot the updated rotation period distributions in the young associations studied in Paper I, where the newly discovered and the revised rotation periods are plotted with squared and squared crossed symbols, respectively, whereas circled symbols represent the rotation periods of the new candidate members proposed by Kiss et al. (2011).

Similarly, in Fig. 6 we plot the updated distributions of light curve amplitudes versus rotation period in the young associations studied in Paper I.

We notice that both rotation periods and light curve amplitudes of the newly proposed members by Kiss et al. (2011) agree with the values of the other confirmed association members. This evidence gives further support to their assigned membership.

All Tables

All Figures