5 Discussion

5.1 Radial velocity: binarity

Lithium detections guarantee youth and the very likely membership of our sample in the $\sigma$Orionis cluster. With radial velocities we may be able to study possible multiplicity. However, the large uncertainties and having only one epoch of observations for the majority of the targets prevent us from carrying out a detailed analysis. In general, the radial velocities in Table 3 are in the interval 30-50kms^-1. Walter et al. (1998) obtained radial velocities of 104 pre-main sequence stars within 30$^\prime$ from the $\sigma$Orionis star. These authors find a sharp distribution peaking at around 25kms^-1 and covering a range from 10kms^-1 up to 50kms^-1. Our measurements are in full agreement with this wide radial velocity survey. Figure 17 depicts our radial velocities against Imagnitudes. Neither drift nor an increasing dispersion are obvious at the faintest magnitudes, indicating that the very low mass stars and brown dwarfs of $\sigma$Orionis are not yet affected by internal dynamical evolution, and that these objects still share the bulk motion of the group.

Figure 17: Radial velocities against I magnitudes. SOri45 is not included in the figure (see text).

Only the brown dwarf SOri45 clearly shows a rather discrepant radial velocity, which differs by more than 2.5$\sigma$ with respect to the cluster mean velocity. With a mass estimated at around 0.02$M_{\odot}$ (Béjar et al. 1999), SOri45 is the smallest object in our sample. It might belong to another kinematical group of young stars, like the Taurus star-forming region or the Gould Belt. On the basis of its multi-wavelength photometry and spectroscopy, SOri45 is probably not a member of Taurus. The distance modulus to Taurus is 5.76 (Wichmann et al. 1998), which would make SOri45 incredibly overluminous by 2.2mag in the HR diagram. Guillout et al. (1998) and Alcalá et al. (2000) have shown that the distribution of candidate members of the Gould Belt for the particular direction towards Orion lies at 200-300pc from the Sun and well to the southwest of the Orion A cloud. This is relatively far away from $\sigma$Orionis (>55pc). SOri45 fits the photometric and spectroscopic sequences of the $\sigma$Orionis cluster very nicely (Béjar et al. 1999, 2001), supporting its location in the Orion complex. Furthermore, this brown dwarf displays strong H$\alpha$ emission and lithium in its atmosphere, which is typical of ages much younger than that of the Gould Belt (30-80Myr, Alcalá et al. 2000; Moreno et al. 1999), and it does not show a radial velocity consistent with membership in either Taurus or the Gould Belt. Alternatively, SOri45 might be a runaway object of the $\sigma$Orionis cluster resulting from encounters with other cluster members; it may have been dynamically ejected from the multiple system where it originated (Kroupa 1998; Portegies Zwart et al. 1999; Reipurth & Clarke 2001; Boss 2001), or SOri45 might be a brown dwarf close binary. So far none of these hypotheses can be discarded. Further radial velocity measurements are needed to assess the possible binary nature. If SOri45 is proved to be a spectroscopic binary, the dynamical masses of the components will be valuable for testing theoretical evolutionary tracks at very young ages and substellar masses.

From Fig. 10 we observe that r053820-0237 (M5) appears remarkably overluminous with respect to the cluster photometric sequence. In addition, its radial velocity is the largest amongst our measurements. These two properties suggest that this star is an equal mass binary.

   
5.2 The age of the $\sigma$Orionis cluster

We do not observe from Fig. 16 that our $\sigma$Orionis targets have undergone appreciable lithium destruction. Actually, the Li I curves of growth that neatly reproduce the observations are those computed with the "initial'' lithium abundance. More massive F- and G-type stars in the Orion complex have similar lithium contents (Cunha et al. 1995). The lower envelope to the distribution of the Li I pEWs shown in Fig. 16 could be described by the logN(Li)=1.9 curve of growth, i.e., lithium depleted by about one order of magnitude. We shall discuss the likely age of the $\sigma$Orionis cluster on the basis of no lithium destruction, and depletions by factors of 3 (logarithmic abundance of $\sim$2.5dex) and 10 (logarithmic abundance of 2.0dex).

Figure 18: Surface curves for lithium depletions by factors of 3 (logN(Li)=2.5, upper panel) and 10 (logN(Li)=2.0, lower panel) as a function of age and mass. Models are taken from D'Antona & Mazzitelli (1994, dashed line), D'Antona & Mazzitelli (1997, dotted line), Pinsonneault et al. (1990, solid line) and Baraffe et al. (1998, dash-dotted line).

According to various evolutionary models available in the literature, very low mass stars (M$\le$0.3$M_{\odot}$) burn lithium very efficiently by one order of magnitude at ages older than 15Myr (D'Antona & Mazzitelli 1994, 1997; Pinsonneault et al. 1990; Baraffe et al. 1998). Stars with masses in the interval 0.5-0.8$M_{\odot}$ do it in a shorter time scale. This is summarized in Fig. 18, which shows surface curves for a given lithium abundance as a function of age and stellar mass. The age of the $\sigma$Orionis cluster will be constrained by late-K and early-M stars. More massive members (M$\ge$0.9$M_{\odot}$) need longer times to deplete some lithium, so they are not useful for our purposes.

Lithium depletion by a factor of 10 will impose a rather conservative upper limit on the age of the cluster. From Fig. 18 we infer that this upper limit is around 10Myr (based on Baraffe et al. 1998 and Pinsonneault et al. 1990 models), because this is the time required by 0.6-0.8$M_{\odot}$-stars to consume their lithium from initial abundance down to logN(Li)=2.0. Models by D'Antona & Mazzitelli (1994, 1997) predict values that are twice as young, i.e., around 5Myr. However, since no lithium depletion is apparent in any cluster member, it seems reasonable to establish shorter upper limits. If we adopt the surface curve corresponding to a factor of 3 lithium depletion, the plausible oldest age of the $\sigma$Orionis cluster is 8Myr (as given by Baraffe et al. 1998 and Pinsonneault et al. 1990 models). We have also inspected the lithium depletion tracks provided by Proffitt & Michaud (1989) and Soderblom et al. (1998) obtaining very similar values. Our result fully agrees with the maximum age expected for the central, most massive cluster star to blow up as a supernova (Meynet et al. 1994). $\sigma$Orionis low mass stars span an age range similar to that of the early-type members, i.e., the low and high mass populations are essentially coeval. Similar upper limits are found for other associations in Orion, like the star-forming region around the $\lambda$Orionis star (7-8Myr, Mathieu et al. 2001), and Orion WTT stars (Alcalá et al. 1998). We could adopt as the mean cluster age the oldest isochrone for which lithium is still preserved within 0.2dex across the entire mass range. This occurs at roughly 2-4Myr considering all models, a result in full consistency with previous analysis of theoretical isochrone fitting to the observed photometry (Béjar et al. 1999).

An additional constraint to the age of the cluster comes from the ratio of CTT stars to WTT stars. Based on strong H$\alpha$ emission and the presence of forbidden emission lines, this ratio turns out to be in the range 30-40% in $\sigma$Orionis. Follow-up observations of our targets (mid-infrared, radio) are, however, desirable to confirm the presence of circumstellar disks. The ratio obtained in $\sigma$Orionis is slightly smaller than that of younger regions, like the area around the Orion Molecular Cloud (ratio $\ge$40%, 1-3Myr, Rebull et al. 2000), and considerably larger than the one of older clusters and associations, like the Sco-Cen OB association (ratio of 11%), whose population of CTT stars, WTT stars and post-TTauri stars has been investigated by Martín (1998). This author defines post -TTauri stars as young, late-type stars that are burning lithium and display moderate H$\alpha$ emission. The average age of the whole Sco-Cen OB association is in the range 5-15Myr, as determined by de Geus et al. (1989). We do not find evidence for the existence of post-TTauri stars in $\sigma$Orionis, and hence, this cluster is essentially younger than the Sco-Cen OB association.