BANYAN. IV. FUNDAMENTAL PARAMETERS OF LOW-MASS STAR CANDIDATES IN NEARBY YOUNG STELLAR KINEMATIC GROUPS—ISOCHRONAL AGE DETERMINATION USING MAGNETIC EVOLUTIONARY MODELS

As defined in this paper, a bona fide member is one that has all XYZUVW parameters known from parallax, RV, and proper motion measurements consistent with a high membership probability to a given YMG, as determined by various tools such as Bayesian inference (Malo et al. 2013; Gagné et al. 2014) and the convergent point analysis (Rodriguez et al. 2014, 2013). A bona fide member is also required to display youth indicators. The most common indicator is the presence of Li, but this diagnostic is restricted to early M dwarfs younger than a few 10⁷ yr since Li is rapidly depleted, especially in fully convective stars (Randich et al. 2001). For older early M dwarfs, the location in the color–magnitude diagram is the only way to constrain their age. In Paper II, we showed that bona fide low-mass members of YMGs show unusually high X-ray luminosities and rotational velocities, which can be used as independent youth indicators in the age range of ∼10–100 Myr. Spectroscopic evidence of low-gravity (e.g., Na i, K i; Riedel et al. 2014; Gorlova et al. 2003) is another useful youth indicator for mid-late M dwarfs.

In summary, the youth of low-mass stars can be assessed through the following indicators: unusually high luminosity (bolometric, X-ray, and UV when available) compared to old stars of the same temperature (spectral type), unusually high rotational velocity, Li detection (depending on spectral type and age) and the gravity-sensitive Na i and K i lines. Because the interpretation of the observed luminosity is different in the case of an unresolved multiple system, RV monitoring and high-contrast imaging should be pursued to identify binary systems within the proposed bona fide members.

The RV measurements of Paper II combined with recent parallax measurements enable the identification of three new bona fide members. The proposed three new bona fide members are all in the βPMG: J2033−2556 (M4.5V), J2010−2801 (M2.5+M3.5), and J2043−2433 (M3.7+M4.1). They all have a membership probability (P_{v + π}) greater than 90%, high X-ray luminosity typical of βPMG members and they also show signs of low gravity (Riedel et al. 2014). J2033−2556 has multi-epoch RV measurements ruling out a binary system with good confidence.

We highlight six other candidates with known parallax whose membership is either ambiguous or uncertain for various reasons. Due to these reasons, we take the conservative approach of excluding these targets from the results presented in this paper.

2MASSJ01351393−0712517 is a spectroscopic binary (M4.5V) identified in Paper II as a strong candidate member of Columba, but a recent parallax measurement (Shkolnik et al. 2012) yields a higher, though still ambiguous, membership probability (P_{v + π}) of 76% in favor of βPMG. While this star remains a good young star candidate, its membership is not firm enough to declare it a bona fide member of βPMG.

2MASSJ01365516−0647379 (M4V+L0V) is a visual binary that satisfies all criteria to be a bona fide member of βPMG. However, the atmosphere models fitting analysis presented in Section 3.1 yields an effective temperature of ∼3500 K that appears to be too high for an M4V (∼3100 K) even though its bolometric luminosity (log  L_bol = −2.2 L_☉) is consistent with a βPMG membership. At such a luminosity and temperature this star should show some Li, but it does not.

2MASSJ14252913−4113323 is an M2.5V spectroscopic binary with a strong membership probability in βPMG. This binary was first proposed to be a potential member of TWA (with a marginal kinematic fit) by Riedel et al. (2014) using the equivalent width (EW) Lithium absorption and the Na i 8200 index. However, as discussed in Paper II, this object is relatively distant (67 pc) and youth indicators (Nai, Li) are consistent with a membership to an association significantly younger than βPMG, perhaps the Scorpius–Centaurus complex (de Zeeuw et al. 1999). While this star is certainly young, its membership is doubtful enough to not declare it a bona fide member of βPMG.

HIP 11152 is an M3Ve with a high membership probability to βPMG. However, the derived T_eff = 3906 ± 20 K (Pecaut & Mamajek 2013) is too hot for a star of this spectral type; Pecaut & Mamajek (2013) derived a spectral type of M1V for this star. At this temperature, the star appears under-luminous for a membership in βPMG. Furthermore, no Li is detected in this star, which is incompatible with all other βPMG members of similar T_eff that show some Li. If this star is an M3Ve, it most likely has a T_eff of ∼3100 K close to the Li boundary transition.

2MASSJ00233468+2014282 and 2MASSJ23314492−0244395 are candidate members (K7V(sb2), M4.5V) with a membership probability (P_v) under 90%. These stars are good young star candidates, but their membership remains too low to consider them in this analysis.

Since 2010, 54 young star candidates were observed with ESPaDOnS, a visible-light echelle spectrograph at Canada-France-Hawaii Telescope (CFHT).⁷ Observations were done using the "star+sky" mode combined with the "slow" and "normal" CCD readout mode. The spectra have a resolving power R ∼ 68,000 and covers the 3700–10500 Å spectral domain over 40 orders. The observations were obtained with individual exposures of 60–1800 s depending on the target brightness, yielding typical signal-to-noise ratios (S/Ns) of ∼80–120 per pixel (2.6 km s⁻¹).

All observations were processed by CFHT using UPENA 1.0, an in-house software that calls the Libre-ESpRIT pipeline (Donati et al. 1997). We used the processed spectra with the unnormalized continuum and the automatic wavelength solution inferred from telluric lines.

Since no telluric standards were observed within the same night as the science targets, telluric correction was achieved using 40 A0V spectroscopic standards secured from other ESPaDOnS programs available through the CFHT data archive. The telluric correction involves the following steps. First, we find the spectroscopic standard obtained through atmospheric conditions as close as possible to that of the target star. This choice is done by performing a linear combination of several telluric standards minimizing the ratio of absorption depth for several prominent telluric lines. Second, hydrogen absorption lines are removed from the telluric standard spectrum by fitting and dividing out a Voigt profile to each line. Finally, the target spectrum is divided by the corrected telluric standard spectrum, followed by the division of a blackbody curve with the effective temperature of the chosen spectroscopic standard.

In order to compare ESPaDOnS spectra with atmosphere models, the spectra were flux-calibrated by integrating target spectra with appropriate spectral response curves and scaling the results to match the apparent fluxes of the target star through various photometric bands. The apparent magnitudes came from various sources: SDSS-DR9 (Ahn et al. 2012), UCAC4-APASS (Zacharias et al. 2013), Tycho (Høg et al. 2000), DENIS (Epchtein et al. 1997), Riedel et al. (2014), or Koen et al. (2002, 2010). The relative spectral response curves, effective wavelengths and zero points were taken from the Filter Profile Service,⁸ and APASS filter transmission curves were kindly provided by Dr. Helmar Adler.

Fundamental stellar parameters, namely the effective temperature (T_eff), surface gravity (log  g), metallicity ([M/H]), and stellar radius (R), were determined by fitting atmosphere models to our spectra. The derivation of the stellar radius requires a distance estimate which, when a parallax is not available, is taken to be the statistical distance (d_s) inferred from the method explained in Paper I.

We adopted the same spectral fitting analysis presented in Mohanty et al. (2004a) and Mentuch et al. (2008), which consists of restricting the analysis to spectral regions strongly sensitive to surface gravity and effective temperature, namely the Na i and K i lines (see Table 1).

As stated in Reylé et al. (2011) and Mann et al. (2013), the TiO opacity database is not complete for the BT-Settl models used here, hence TiO bands were not included in our analysis. Moreover, the Na i line at 589 nm is strongly affected by chromospheric emission lines, which may lead to a biased estimate of the effective temperature.

The candidate spectra were fitted with the BT-Settl atmosphere models (Allard et al. 2012) using solar abundances from Asplund et al. (2009). These models are available for temperatures between 400 and 70,000 K, log g between −0.5 and 5.5 and metallicity between −4.0 and +0.5. For the purpose of our analysis, the atmosphere models considered were restricted to T_eff between 2700 and 5000 K, log g between 4.0 and 5.5 and [M/H] between −0.5 and +0.3, in steps of 100 K, 0.5 dex, 0.3 dex, respectively.

We have linearly interpolated atmosphere models separated by 100 K to construct a model grid with 50 K resolution in T_eff; analogous averaging of models separated by 0.5 dex yields a grid with 0.25 dex resolution in log g. The metallicity was interpolated at a value of −0.25 dex using the −0.5 and +0.0 atmosphere models. This procedure was done to improve the numerical precision of the fitting procedure, as shown in Mohanty et al. (2004b)

Prior to the fitting procedure, all target spectra were corrected for their heliocentric RV as measured in Paper II and the model spectra were convolved with a Gaussian kernel to match the resolving power and with a rotational broadening profile to match the measured vsin i (see Paper II and Table 2) of the targets.

The best model fit was determined by minimizing the goodness-of-fit parameter G_k defined by Cushing et al. (2008) as

$$\begin{equation} G_{k} = \sum _{i=1}^{n} W_{i} \left(\frac{F_{{\rm obs},i}-C_{k}F_{k,i}}{\sigma _{{\rm obs},i}} \right)^{2}, \end{equation} \tag{ 1 }$$

where F_obs,i is the observed flux at wavelength i, σ_{obs, i} is the associated uncertainty, F_{k, i} is the synthetic model flux for the same wavelength, and W_i is the weight applied at each wavelength.

The parameter C_k is set to minimize G_k and corresponds to the value of (R/d)² where R is the stellar radius and d the distance to the given star. The subscript k refers to a model with a given set of T_eff, log g and [M/H].

Uncertainties on the derived fundamental parameters were determined as in Casagrande et al. (2006, 2008) through Monte Carlo simulations; by repeating the above fitting procedure 51 times, each time with a different random realization of the observed spectrum within the measurement errors (distance, flux calibration, and Gaussian noise on each spectral pixel). Typical uncertainties are 40 K, 0.15 dex, 0.05 R_☉ for T_eff, log g and R, respectively.

The bolometric flux (F_bol) was estimated by integrating the best atmosphere model, which depends on T_eff, log g, and metallicity at the best radius found. The bolometric luminosity given by L_bol = 4πd²F_bol was derived from the statistical distance when parallax measurement was not available. The inferred parameters for all candidate stars are given in Table 2. Figure 1 presents a comparison between observations and the best-fitting atmosphere model for the βPMG candidate member GJ 2006 B.

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For the purpose of validating our analysis, the same method was applied to five stars (GJ 880, GJ 205, HIP 67155 (GJ 526), GJ 687, GJ 411) with known parallax and fundamental parameters determined independently by Boyajian et al. (2012), Mann et al. (2013), and Pecaut & Mamajek (2013). The spectrum of HIP 67155 is from the CADC, but it was also obtained with ESPaDOnS and we applied the same analysis procedure described above. As before, since no telluric standards were observed with the target observations, the same procedure described in Section 2.1 was used to find the best telluric standard. As the ESPaDOnS CCD was replaced between semesters 2010B and 2011A, we selected telluric standards observed with the same CCD as the observations.

Figure 2 presents our estimated effective temperatures and radii compared to the literature measurements. There is a good correlation between all estimates with a standard deviation of 3% and 5% for T_eff and R, respectively.

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Our spectroscopic data includes the Li resonance line at 6707.8 Å, a very important age indicator in young stars. The lithium EW was measured using the following procedure. All spectra were first corrected for their respective heliocentric velocity.

Then the Li absorption feature was fitted between 6990 and 6710 Å with a two-parameter function: the two parameters are the slope of the local continuum and the depth of the assumed Gaussian absorption feature. The width of the assumed Gaussian absorption feature was set to the rotational velocity of the star (measured in Paper II) after convolution with the instrumental profile determined by fitting a Gaussian to a slow rotator featuring a high lithium EW. Uncertainties were determined through a Monte Carlo analysis, i.e., by adding random Gaussian noise to the data and repeating the fitting procedure above. Figure 3 presents examples of Li absorption lines spanning a wide range of rotational velocities and EW strengths. The resulting Li EW are given in Table 2. The reported uncertainties are statistical only and do not take into account possible systematic uncertainties associated with the location of the local continuum that may be biased by the faint ∼20 mÅ Fe line at 6707.4 Å located ∼4 spectral resolution elements away from the lithium line. For this reason, we adopt a conservative 5σ criterion for reporting upper limits.

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Figure 5 presents the H-R diagram for our sample of bona fide members (top panel) as well as young bona fide members from the literature whose fundamental parameters were estimated by Pecaut & Mamajek (2013). Only stars with parameters accurate to better than 5σ are considered. The bottom panel is the same diagram but for the candidate members only. Several of our candidates are multiple systems, including several visual binaries, the majority of them uncovered through our RV survey (Paper II). The bolometric luminosities of these systems, given in Table 2, include all components. For the purpose of comparing them with single stars, we made the simplified assumption that they are equal-luminosity systems, hence their luminosity was reduced by a factor of two in Figure 5. This approximation is reasonable since the median flux ratio of the visual binaries uncovered in Paper II is 0.72.

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Figure 5 also includes a sample of old M dwarfs whose fundamental parameters were determined interferometrically by Boyajian et al. (2012). The sample is complemented by two field stars with measured parallax from Shkolnik et al. (2012) and archival ESPaDOnS spectra to which our analysis could be applied for deriving their fundamental parameters. As shown in Figure 5, the inferred bolometric luminosities and T_eff for the old stars we analyzed agree reasonably well with the old sequence. Thus, we can be confident that our analysis is viable for deriving fundamental parameters of our young star candidates.

Older stars in Figure 5 are compared with 4 Gyr Dartmouth magnetic and non-magnetic evolutionary models. For the non-magnetic case, one can note a discrepancy of about 0.1 dex in log L_bol between observations and evolutionary models for T_eff > than 3500 K. The disagreement is somewhat larger for lower T_eff and has been noted before by Boyajian et al. (2012) using other models (e.g., Baraffe et al. 1998). Interestingly, a magnetic α − Ω model with a field strength between 1 and 2 kG (as typically observed; Reiners 2012) provides a very good fit to the observations. One of main results of this work is that the inclusion of a magnetic field in evolutionary models provides a better fit to observations for K5V to M5V stars.

The young star data of Figure 5 are also compared with young isochrones of 5, 10, and 20 Myr for magnetic models of 2.5 kG. Note that the 100 Myr isochrone is very close (∼0.1 dex above at T_eff = 3400 K) to the 4 Gyr isochrone. In general, there is a trend in Figure 5 (top panel) where young bona fide members show higher luminosities compared to older (field) stars. The trend is also as expected within moving groups in the sense that, at a given T_eff, candidate members of βPMG (10–20 Myr), are more luminous (∼0.5 dex) compared to older ABDMG members (∼70–120 Myr). Moving groups of intermediate ages (THA, COL; ∼20–40 Myr) are also over luminous compared to ABDMG but they share similar luminosities with βPMG members.

We also note that, qualitatively, a single isochrone does not provide a good fit for all T_eff. This is particularly obvious for βPMG for which a ∼20 Myr old isochrone appears to fit the data reasonably well for T_eff greater than ∼3500 K whereas an isochrone younger than 5 Myr appears to better fit the data at lower T_eff. We shall come back to this point in Section 6.1. The same trend is also seen for late-type members of ABDMG that appear over-luminous for their expected age, and for the candidate members sample (bottom panel).

To complete this analysis, we present in Figure 6 the T_eff–radius diagram for the same samples used to construct the H-R diagram. All young star candidates show inflated radii compared to MS stars, which is not surprising since the radius is effectively derived from the luminosity. The same trend observed in the H-R diagram is also seen here, in that βPMG members have radii that are not consistent with a single isochrone. Late-type (T_eff < 3500 K) stars have radii typically a factor of ∼2 larger than early-type members, which is consistent with the over luminosity factor of ∼4 (0.6 dex) observed in the H-R diagram (see Figure 5).

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The main results of this analysis are the following: (1) as expected, bona fide members with known parallax show over luminosity, hence apparent inflated radii, compared to MS stars, and (2) no single theoretical isochrone can fit the observed fundamental parameters for low-mass members of βPMG.

βPMG is one of the youngest, nearest, and best studied comoving groups in the solar neighborhood. The age of this group remains somewhat uncertain, though it is likely to be between 8 and 40 Myr. Soderblom et al. (2013) presents a recent review of the various age estimates for βPMG along with the pros and cons of the various methods used thus far. In summary, four different methods have been used: isochronal age, kinematic age, the LDB method, and the Li abundance.

Using the H-R diagram method, Barrado y Navascués et al. (1999) and Zuckerman et al. (2001) determined an isochronal age of 20 ± 10 Myr and 12$^{+8}_{-4}$ Myr, respectively. The kinematic age method consists of tracing back the orbits of all members in time and finding when the volume of the group was smallest (i.e., when pairs of stars appeared to be closest to one another or to the group). Traceback ages of 11–12Myr have been calculated by Ortega et al. (2002) and Song et al. (2003) while Makarov (2007) found a wider age range of 22 ± 12 Myr using the flyby technique. Kinematic age methods have the distinct advantage of being independent of stellar models. On the other hand, they rely on the crucial—and not necessarily correct—assumption that all members are coeval and that the group formed within a relatively small volume at birth. This method cannot be used reliably for groups (older than 50 Myr) as uncertainties in space velocities translate into large positional extent at birth. Furthermore, kinematic age methods suffer somewhat from subjectivity in that the method only works for some selected members. The third method, LDB, makes use of the fact that Li is rapidly depleted in low-mass stars and massive brown dwarfs, which in turn translates into a very sharp luminosity boundary between stars with and without Li. The LDB method (Bildsten et al. 1997; Jeffries 2006) is probably one of the most reliable methods for aging clusters as it relies on relatively simple physics and it is weakly dependent on the evolutionary models used (Soderblom et al. 2013). The first LDB age estimate of 20 Myr for βPMG was reported by Song et al. (2002), based on the observation of the binary system HIP 112312 (M4V + M4.5V) whose primary shows a strong Li EW while the companion does not. Song et al. (2002) argued that theoretical pre-MS evolutionary models were not able to simultaneously match the observed luminosity and the Li depletion pattern for both components and concluded that LDB ages are systematically overestimated. Recently, Binks & Jeffries (2014) determined an LDB age of 21 ± 4 Myr based on several Li EW measurements. Finally, the Li abundance can also be used to derive the age through comparison with evolutionary and atmosphere models. Macdonald & Mullan (2010) used this method to infer an age of ∼40 Myr for βPMG.

The results presented in this work give us the opportunity to derive both an isochronal age from low-mass stars and a new estimate of the LDB age due to new Li measurements. Moreover, our high-resolution spectroscopic observations provide useful constraints for identifying multiple systems that could affect the interpretation of the results.

6.1.1. Isochronal Age from Low-mass Stars

Here, we use the Darmouth evolutionary models to estimate the age of all stars with good fundamental parameters, i.e., the same sample of bona fide members used for constructing the H-R diagram in Figure 5. Figure 7 shows the estimated age for all stars as a function of T_eff, for non-magnetic and magnetic α − Ω models (1 and 2.5 kG).

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Figure 7 provides a different way to illustrate that a single isochrone cannot match all of the observations. It also shows that the isochronal age depends on the magnetic field strength assumed. Table 4 gives a summary of various average age estimates for stars with effective temperature higher than or below 3500 K. First, we focus on the results using non-magnetic models. All stars with T_eff higher than ∼3500 K show a similar and average age of 15 ± 1 Myr while those with T_eff < 3500 K are best fitted with an age of 4.5 ± 0.5 Myr; those values were obtained by excluding all 5σ outliers. Using the larger sample including candidates without parallax yields ages of 21 ± 3 Myr for T_eff > 3500 and 5 ± 1 Myr for T_eff < 3500 K. This discrepancy in age was also noted by Binks & Jeffries (2014) using Siess (Siess et al. 2000) evolutionary models (see their Figure 2) and Yee & Jensen (2010) showed the same results using three different models (see their Figure 3).

Table 4. βPMG Age from Several Indicators

Method	Derived Sample Age (Myr)
	With π	All
Isochrone T > 3500 (no B field)	15 ± 1	21 ± 3
Isochrone T < 3500 (no B field)	5 ± 1	5 ± 1
Isochrone T > 3500 (1 kG)	24 ± 4	27 ± 3
Isochrone T < 3500 (1 kG)	6 ± 1	6 ± 1
Isochrone T < 3500 (2.5 kG)	14 ± 1	16 ± 2
LDB with binary	30 ± 2	...
LDB without binary	26 ± 3	...

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Figure 7 shows that the age estimate does not vary monotonically with T_eff and instead shows an abrupt transition around ∼3500 K. This systematic age difference with T_eff (or mass) is probably not inherent to an age spread within the βPMG. While such an age dispersion is certainly possible, if not expected (Soderblom et al. 2013; see also Section 6.1.2), there is no good reason to expect very low-mass stars to be systematically younger than most massive ones. One can exclude ages as young as 4 Myr since all M dwarfs would be Li-rich at that age, which is not the case.

If the age is not responsible for the observed excess luminosity in very low-mass stars, what could be the cause? One possibility is that those stars could be equal-luminosity unresolved binary systems that would be very difficult to detect spectroscopically. This binary hypothesis is far from satisfactory since it can account for only half of the observed luminosity excess and would imply that the binary frequency is higher at lower masses. It is unlikely that it could be the case.

A more attractive alternative is to invoke the effect of magnetic field on evolutionary models, in particular the α − Ω dynamo model for which the bolometric luminosity appears quite sensitive to magnetic field strength. As shown in Table 4 and Figure 7, magnetic models tend to increase the inferred age. For stars with T_eff < 3500 K, the age is increased from ∼5 to ∼15 Myr. This latter age is certainly much more probable than the former for βPMG. The apparent age difference between stars below and higher than T_eff ∼ 3500 K could thus be explained if early-type stars have magnetic field strengths systematically lower compared to late-type ones. Using the compilation of magnetic field measurements of Reiners (2012),⁹ one finds that old K0V–K5V stars have an average magnetic field of 0.20 ± 0.1 kG compared to 2.6 ± 0.9 kG for M0V–M5V. Thus, there is a very significant trend for the magnetic strength to increase between K and M stars. However, this trend seems to disappear for young stars. Instead, using the same compilation, this time for PMS, one finds average magnetic field strengths of 2.2 ± 0.7 kG and 2.4 ± 0.8 kG for young K and M stars, respectively.

The main conclusion from this discussion is that ignoring magnetic field systematically underestimates the ages derived from isochrones. The data presented here compared to the Darmouth magnetic evolutionary models suggests an isochronal age for βPMG likely between 15 and 28 Myr (Bf = 1 kG for T > 3500 K).

6.1.2. An Age Gradient in βPMG?

The age derived above is an average value for the whole association and does not allow for a likely age spread. As discussed in Soderblom et al. (2013), the characteristic timescale τ_SF for the duration of a star formation event over a region of length scale l should be

$$\begin{eqnarray*} &&\tau _{{\rm SF}}\sim l_{{\rm pc}}^{1/2}\,\,{\rm Myr}. \end{eqnarray*}$$

Taking the current membership of βPMG and fitting an ellipsoid to the Galactic positions XYZ of all members, one can estimate a characteristic radius of the group defined as R_c ∼ (abc)^1/3, where a, b, and c are the fitted semi-major axes of the ellipsoid. One finds R_c ∼ 14 pc or τ_SF ∼ 5 Myr. Thus, from a theoretical point of view, βPMG members are expected to show an age spread of the order of ∼5 Myr.

There are two βPMG bona fide members for which magnetic field strengths are available; these measurements can be used for estimating the isochronal age of these individual stars based on magnetic evolutionary models. Those two stars are HIP 102409 (AU MIC), with a magnetic field strength, Bf, of 2.3 kG (Saar 1994), and HIP 23200 (Gl 182), with Bf = 2.5 kG (Reiners & Basri 2009). Only AU MIC is labeled in Figure 7, since Gl 182 has a measured bolometric luminosity under our 5σ criterion. The magnetic α − Ω model (Bf = 2.5 kG) predicts an age of ∼29 ± 3 Myr for AU MIC and ∼26 ± 10 for GJ 182; the latter estimate requires a small extrapolation since our grid of magnetic α − Ω models does not extend beyond T_eff = 3800 K.

Interestingly, both AU MIC and GJ 182 have a similar T_eff within ∼200 K and yet their Li EW differ by more than a factor of three. Indeed, as shown in Table 2, AU MIC (T_eff = 3642 ± 22 K) has a relatively low Li EW (80 mÅ) compared to other βPMG members of similar effective temperature, for instance GJ 182 (270 mÅ; T_eff = 3866 ± 18 K) and HIP 23309 (360 mÅ; T_eff = 3884 ± 17 K). An age difference provides a natural explanation to account for such a large difference in Li EW. This trend for AU MIC to have a relatively low Li-EW compared to other βPMG of similar T_eff may be an indication that AU MIC is somewhat older than a typical member of the βPMG.

6.1.3. The Lithium Depletion Boundary Age

Li is rapidly depleted in young low- and very low-mass stars, which in turn translates into a very sharp luminosity boundary between stars with and without lithium measurements. Using a K-band color-magnitude diagram and Li EW measurements, both from the literature and new observations, Binks & Jeffries (2014) determined an LDB age of 21 ± 4 Myr for βPMG. Here, we repeat this analysis using a slightly different methodology. As before, we work in the L_bol–T_eff plane and we use a maximum likelihood method for determining the LDB luminosity and its uncertainty. Figure 8 presents the H-R diagram of all stars considered for the LDB analysis; this figure is similar to Figure 5, except that stars are color coded to discriminate those with (blue symbols) and without lithium (red symbols). As usual, we treat the two samples separately: one with measured parallaxes and the other complemented with strong candidate members lacking parallaxes. All stars considered for the LDB analysis are identified in Table 2. The sample includes all data available from the literature including new observations presented here. Figure 8 shows three kinds of objects: (1) K5V–K7V dwarfs with radiative cores and convective envelopes which still have high EW Li, (2) early-M dwarfs which may have radiative cores or be fully convective objects without lithium, and (3) late-type fully convective M dwarfs with lithium detection.

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The bolometric luminosity L₀ at which the LDB occurs was determined using a maximum likelihood function. Let $L_i^a$ be the measured bolometric luminosity of the i^th target in the sample of n stars with Li and $L_i^b$ be the measured bolometric luminosity for the i^th stars in the sample of m stars without Li. The true bolometric luminosity of each star is characterized by a probability density function, f(l):

$$\begin{eqnarray*} &&f(l) = \frac{1}{\sigma _i\sqrt{2\pi }} e^{ -\frac{1}{2} \left(\frac{l-l_i}{\sigma _i} \right)^2}, \nonumber \end{eqnarray*}$$

where σ_i is the luminosity measurement uncertainty. Let P^a be the probability that all stars with lithium have a true luminosity above L₀, P^b be the corresponding probability that stars without lithium have a true luminosity below L₀, and $\mathcal {L} (L_0)$ be the probability density function for L₀, the LDB luminosity. We have,

$$\begin{eqnarray*} &&\mathcal {L} (L_0)=P^aP^b \end{eqnarray*}$$

with

$$\begin{eqnarray} &&P^a (L>L_0) = \prod _{i}^{n}\int _{L_0} ^{\infty } f \left(l_i^a \right) dl \nonumber \\ &&P^b (L<L_0) = \prod _{i}^{m}\int _{-\infty } ^{L_0} f \left(l_i^b \right) dl. \end{eqnarray} \tag{ 2 }$$

Applying this methodology yields the most probable value and uncertainty for L₀, which can then be compared with theoretical predictions from the Darmouth models (see Figure 9) to derive the corresponding LDB age. Here, we adopt the same definition as Binks & Jeffries (2014) for L₀, the luminosity at which 99% of the initial Li abundance is depleted. Using the whole sample with parallax (11 stars) yields L₀ = −1.59 ± 0.06 L_☉ for a corresponding age of 30 ± 2 Myr. The LDB age is potentially sensitive to the luminosity correction applied to binary systems, especially those that happen to be close to L₀. Excluding binary systems from the sample (five stars left) yields L₀ = −1.49 ± 0.08 L_☉ for an age of 26 ± 3 Myr. We adopt this value as the best LDB estimate since it is less likely affected by uncertainties associated with binarity.

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Our LDB age of 26 ± 3 Myr is consistent with the value of 21 ± 4 Myr derived by Binks & Jeffries (2014) using a different methodology and different evolutionary models. This is another illustration that the LDB age is relatively insensitive to the choice of evolutionary models, magnetic or not. It is encouraging that LDB age estimates for βPMG are in good agreement with the isochronal age range between 15 and 28 Myr.

One should caution that the LDB age is not without systematic uncertainties associated with ill-understood Li depletion processes like rotation (Bouvier 2008; da Silva et al. 2009), magnetic field (Chabrier et al. 2007) and early accretion history (Baraffe et al. 2009). It has been suggested that strong differential rotation at the base of the convective envelope may be responsible for enhanced Li depletion in solar-type slow rotators (Bouvier 2008). Finally, accretion activity could potentially enhance lithium depletion rate during the first few Myr of star formation, in which case the LDB age should be regarded as an upper limit. Both the LDB method and magnetic evolutionary models yield a consistent age for βPMG of 26 ± 3 Myr.

We can apply the same analysis to other groups (Columba, THA, and Argus) albeit with less accuracy, since there are fewer candidates with the required measurements than in βPMG (see Table 2). Since the data is sparse, we combined all three groups together assuming that they have approximately the same age, which is probably not inaccurate given they all share age estimates between 20 and 40 Myr. The sample comprises 12 stars, of which six have parallax measurements. As for βPMG, we divide the sample between early- (T > 3500 K) and late-type (T < 3500 K) stars. The best isochrone fits yield 21 ± 4 Myr for (T > 3500 K) and 10 ± 3 Myr for (T < 3500 K). Again, the same trend is observed for late-type stars having relatively young ages. The age inferred from early-type stars is consistent with age estimates of these groups in the literature.

Since no late-type members with Li was found for these groups, only lower limits can be set for the average LDB age. Figure 10 shows the H-R diagrams of the group. The significant number of late-type stars with undetected lithium, spanning a wide range of luminosity provides a useful lower limit for L₀. Using the same maximum likelihood method described above, one can define a 3σ lower limit for L₀ at which there is a probability of finding 99.7% of stars above L₀. This limit is L₀ < −2.29 L_☉  corresponding to a lower limit age of ∼79 Myr.

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If we take into account only candidates of THA and COL, excluding the ARG member, the 3σ lower limit for L₀ is −2.04 L_☉  corresponding to a lower limit age of ∼50 Myr. These lower limits are consistent with the fact that it is very likely βPMG is younger than those associations.