5 Discussion

The presence of the strong Li I $\lambda$ 6708 absorption line in the spectra of stars later than G5 is a good indicator of youth, because Lithium is very efficiently destroyed by convective mixing in the stellar interiors when the temperature at the bottom of the convective layer reaches about 2  $\times~10^6$ (Bodenheimer 1965; D'Antona & Mazzitelli 1994). The capability offered by high-resolution spectroscopy to confirm the PMS nature of X-ray emitting PMS candidates, thourgh the use of Li equivalent width versus $\log{T_{{\rm eff}}}$ diagram, has been shown in previous works (Magazzù et al. 1997; Covino et al. 1997; Wichmann et al. 1999; Alcalá et al. 2000).

With the exception of the star Cru-5, all the Crux stars do show the Li I $\lambda$6708 absorption in their spectra, although the strength of the line in the stars Cru-2E and Cru-2W is comparable to that of the nearby Ca I $\lambda$6717 line, while in all the other stars the lithium line appears much stronger than Ca I.

Figure 7 shows the lithium equivalent width versus effective temperature for the stars in Cru. The upper envelopes for young open clusters adopted by Martín & Magazzù (1998) and by Preibisch et al. (1998) are represented by the continuous and dotted lines, respectively. While the stars Cru-1, Cru-4, Cru-6 and both components of the SB2 Cru-3 fall well above the upper envelope for ZAMS stars, the stars Cru-2E and Cru-2W fall below that boundary. Hence, Cru-2E and Cru-2W are most likely young ZAMS stars. On the other hand, Cru-6 and the SB2 components of Cru-3 lie close to the dividing line between the WTTS and PTTS regions and Cru-1 and Cru-4 fall on the PTTS area. Therefore, it is likely that all these objects are in the post-T Tauri phase.

When comparing the lithium abundance of these stars with that of stars in young clusters, like IC 2602 (see Fig. 8) it is evident that, except for Cru-2E and W and for Cru-5 (which lacks lithium), the other stars should be as young as, or younger than the IC 2602 stars, ie. younger than about 30 Myr.

The fact that the star $\beta$ Crux is a well established proper motion member of the Lower Centaurus-Crux subgroup of the Sco-Cen association, led FL97 to the conclusion that also the six X-ray selected Crux stars are actually members of the low-mass population of the Sco-Cen association. The mean radial velocity and distance of the Lower Centaurus-Crux group reported by de Zeeuw et al. (1999) are +12 km s^-1 and 118 pc respectively. The radial velocity of $\beta$ Crux is +15.6 km s^-1 (Evans 1967). The radial velocity of Cru-1, Cru-4 and Cru-6, as well as the systemic radial velocity of Cru-3 are consistent, within the errors, with the radial velocity of the Lower Centaurus-Crux subgroup, while the radial velocities of Cru-2E and Cru-2W and Cru-5 are inconsistent. Therefore, the latter stars are very likely unrelated to the Sco-Cen association.

Figure 7: Lithium equivalent width versus effective temperature. The thick and dotted lines represent the upper envelope for young open clusters as adopted by Martín & Magazzù (1998) and Preibisch et al. (1998) respectively, while the dashed line indicates the WTTS and PTTS regions as described by Martín (1997).

We can use the luminosities and effective temperatures reported in Table 3 to place the stars in the HR diagram. In Fig. 9 the position of the Crux stars in the HR diagram is compared with the theoretical pre-main sequence evolutionary tracks by Baraffe et al. (1998).

While the stars Cru-1, Cru-3, Cru-4 and Cru-6 fall well above the main sequence, approximately on the same isochrones with ages between 5 and 10 Myrs and masses between 0.3 and 1.2 $M_\odot$, again the stars Cru-2E and 2W and Cru-5 turn out to be unrelated to the other stars. Note also that Cru-5 has a high extinction which indicates that this object is probably a background K-type giant. Moreover, the X-ray - to - optical-flux ( $f_{\rm X}/f_{\rm V}$) ratio of 10^-3.15, reported by PF96 for Cru-2, is in the range -4.4  $< \log{(f_{\rm X}/f_{\rm V})} <-2.8$ for G-K type Pleiades stars (Stauffer et al. 1994), while the other Crux stars have higher $f_{\rm X}/f_{\rm V}$ ratios, which are more consistent with PMS stars. This gives further support to the conclusion that Cru-2E, Cru-2W and Cru-5 are not PMS stars. In addition, the projected rotational velocities of Cru-2E, Cru-2W and Cru-5 (see Table 2) are too low in comparison to those of low-mass PMS stars of similar spectral types.

Figure 8: Lithium abundance versus effective temperature for the Crux stars. The stars of the 30 Myr old cluster IC 2602 by Randich et al. (1997) are also plotted. The dashed line represents the cosmic lithium abundance of 3.3 in the $\log(H)=12$ scale.

Note that for the binary stars Cru-1 and Cru-3, represented with the circled dots in Fig. 9, the luminosities have been corrected as explained in Sect. 3.4. However, as pointed out in that section, it is difficult to determine the luminosity of the components of Cru-1 and hence, it is not possible to separate its individual components in the HR diagram, unless some strong assumptions are made. For instance, that the luminosity ratio of the components is equal to the flux ratio in the K-band and also that the visual pair is indeed a physical binary, in which case the secondary visual component must be about one spectral class later than the primary because it emits 1.8 less flux (see Sect. 4.1). In this case, the age of the components of Cru-1 would fit quite well with that of Cru-3a and b, Cru-4 and Cru-6 (cf. Fig. 9).

Figure 9: Luminosity versus temperature diagram. The Crux stars are represented with the black dots and squares. The binary stars Cru-1 and Cru-3 are represented with the circled dots, while their individual components (connected with the dashed lines) are represented with dots. The theoretical pre-main sequence evolutionary tracks by Baraffe et al. (1998) (for [M/H] = 0, Y= 0.282 and $\alpha =$ 1/ $H_{\rm p} =$ 1.0) are overplotted.

Using the results on the masses derived from the HR diagram, one can speculate on what the orbital period of Cru-1 would be if the projected separation of 0.25 arcsec is indicative of the mean separation. In this case, such separation would correspond to about 27 AU at the distance of 110 pc; from the HR diagram, we derive upper and lower limits of 0.6 $M_\odot$ and 0.38 $M_\odot$ for the total mass of the system respectively. Using Kepler's third law, a period of about 200 years is estimated. We stress, however, that many assumptions have been made and that the mass and age estimates for the components, as well as for the orbital period determination of Cru-1 have to be taken with care until more information regarding the colours of the secondary component will be available.

On the other hand, the dynamical mass of each one of the components of Cru-3ab is a factor of about 1.4 less than the mass inferred from the comparison with the theoretical tracks shown in Fig. 9. This means that, if those PMS tracks are correct, the inclination angle of the system is about 63$^{\circ }$.

We conclude that the stars Cru-1, Cru-3, Cru-4 and Cru-6 are indeed low-mass PMS, associated kinematically and coeval to the Lower Centaurus-Crux subgroup of the Sco-Cen association, and that the stars Cru-2 and Cru-5 are active stars unrelated to the association.

Several other low-mass PMS stars have been found as counterparts of X-ray sources around high-mass stars that are, at the same time, part of an OB or T association. For instance, the RASS found several low-mass PMS stars spread around the Chamaeleon SFR (Alcalá et al. 1995, 1997), some of which were later confirmed to be associated with the B8-type star $\eta$ Cha, forming a cluster (Mamajek et al. 1999, 2000). Also Walter et al. (1998) found a small cluster of PMS stars around $\sigma$ Ori and Pozzo et al. (2000) identified many low-mass PMS star candidates as counterparts of ROSAT X-ray sources in the field around the Wolf-Rayet/O-type star $\gamma$ Velorum.

Since the velocity dispersion in star formation regions is of the order of a few kms^-1 (e.g. Lada & Lada 1991), in a few 10⁷ years the small clusters are dissolved and are no longer recognized as such. Whether Cru-1, Cru-3, Cru-4 and Cru-6 are members of a small aggregate, in which $\beta$ Crux is the massive and central star, is not clear. The star $\beta$ Crux has a radial velocity of +15.6 kms^-1, which means a velocity dispersion relative to Cru-3, Cru-4 and Cru-6 of about 3 kms^-1 (note that the RV of Cru-1, though more consistent with that of $\beta$ Cru, is variable). Assuming a distance of 110 pc, the studied stars would cover the observed spatial extent of about 1 degree in less than 1 Myr, moving with a velocity of 1-2 kms^-1, which is inconsistent with the ages derived from the HR diagram. On the other hand, from their lithium content (see Fig. 8) we know that the Crux stars must be younger than 30 Myr. A 30 Myr population would expand some 30-60 pc, moving with a velocity of 1-2 kms^-1. At a distance of 110 pc such a population would appear completely dispersed. If the velocity dispersion is even higher, as it seems to be the case, the spread of the PMS stars would be even larger. One possibility to explain the existence of a small aggregate would be that molecular material, which maintained the stars bounded during most of the cluster life, was recently cleared up by supernova winds in the same scenario as proposed by Mamajek et al. (1999, 2000) for the $\eta$ Cha cluster. However, the space density of the members of the hypothetical aggregate would be a factor of about three less than in the case of the $\eta$ Cha cluster.

The confirmed PMS stars and $\beta$ Crux do share, however, a common distance and age. Hence, they may be considered as a moving group in a more disperse population of PMS stars in Sco-Cen, rather than a small aggregate. In this case, many more X-ray emitting low-mass PMS stars are expected to be identified distributed on a large sky area as found in previous investigations of the RASS X-ray sources in other star forming complexes. The proper motion studies by de Zeeuw et al. (1999) revealed indeed a large number of objects with coherent proper motion in the Lower Centaurus-Crux subgroup. Therefore, we concur with the most plausible conclusion by FL97 that the stars detected in the PF96 ROSAT pointing, and confirmed here to be low-mass PMS stars, are just a few objects in a much larger loose group of low-mass PMS stars, which are members of the Lower Centaurus-Crux subgroup of the Sco-Cen association.