3 Parameter determinations

3.1 Radial velocity and ${v\,{sin}\,i}$

Due to the serious problems with the cross-disperser positioning during the February 1999 observations, no radial velocity determinations were possible from the CASPEC spectra.

Determinations of radial velocity, RV, and projected rotational velocity, ${v\,{sin}\,i}$, were obtained using instead the FEROS spectra, and in the case of the SB2 Cru-3 also the CORALIE data, by means of cross-correlation analysis. Given the large spectral coverage achievable with FEROS and CORALIE, the cross-correlation of the target and template spectra was performed after rebinning the spectra to a logarithmic wavelength scale, in order to eliminate the dependence of Doppler shift on the wavelength (Simkin 1974). Moreover, only parts of the spectra free of emission lines and/or not affected by telluric absorption lines were considered. Therefore, the NaI D, and H$\alpha$ lines as well as wavelengths longer than about 7000 Å  have been excluded from the cross-correlation analysis. The result of the cross-correlation is a correlation peak which can be fitted with a Gaussian curve. The parameters of the Gaussian, center position and full-width at half-maximum (FWHM) are directly related to RV and ${v\,{sin}\,i}$, respectively. The method of the correlation has been fully described by Queloz (1995), and Soderblom et al. (1989). More details about the calibration procedure can be found in Appendix A of Covino et al. (1997). The measured RV and ${v\,{sin}\,i}$  determinations for the program stars are reported in Fig. 1 and Table 2. The typical measured errors are of the order of 1 km s^-1 and 1.5 km s^-1 for RV and ${v\,{sin}\,i}$  respectively.

Figure 2: Comparison of the IR colours of the Crux stars (dots) with those of normal field stars (+) and IRAS sources ($\times$) in star forming regions. The solid line represents the colours of normal field dwarfs from Bessel & Brett (1988). The arrow indicates the normal reddening vector.

3.2 Spectral types and effective temperatures

Exploiting the large spectral range covered by the CASPEC and FEROS spectra, we could assign spectral types to the target stars following the procedure described in Covino et al. (1997) and Alcalá et al. (2000).

For the stars earlier than K7, an estimate of the effective temperature has been performed using the calibrations between the Na I D lines equivalent width and $\log{T_{{\rm eff}}}$ for luminosity class V given by Tripicchio et al. (1997), while for cooler stars the relationship between the K I $\lambda$7699 equivalent width and $\log{T_{{\rm eff}}}$ for luminosity class V, reported in Tripicchio et al. (1999), was used.

The derived effective temperatures are consistent, within the errors, with those derived using the calibration between spectral type and effective temperatures (e.g. de Jager & Nieuwenhuijzen 1987). The spectral type and effective temperature for the Crux stars are reported in Table 3.

3.3 H$\alpha$ and Li equivalent widths and Li abundances

H$\alpha$ and Li I 6708 Å  line equivalent widths were determined from the normalized CASPEC and FEROS spectra by integration of the line, interpolating linearly the continuum on both sides of the line.

The main source of error on these measurements comes from the uncertainty in the placement of the photospheric continuum. For each spectrum, at least three individual measurements of W(H$\alpha$) and W(Li) were obtained by setting the continuum at different positions. The mean estimated error of W(Li) is 10 mÅ  in most cases, while for W(H$\alpha$) the error is about 10%. For the stars later than M1, in which the continuum placement is difficult because of photospheric absorption bands, the uncertainty of W(Li) may be as high as 25 mÅ.

Lithium abundances, in the usual scale $\log(H)=12$, were derived from the W(Li) and $T_{{\rm eff}}$ values using the non-LTE curves of growth given by Pavlenko & Magazzù (1996), assuming $\log{g}=4.5$.

The main source of error on the derived $\log{N({\rm Li})}$ values is the uncertainty in the effective temperature. The estimated mean uncertainties on $T_{{\rm eff}}$ are on the order of $\Delta T_{{\rm eff}}\approx$ 150 K. Taking this and a mean error of about 15 mÅ  in W(Li) into account, we estimate a mean error on the order of 0.15 to 0.2 dex in $\log{N({\rm Li})}$. However, the assumption of $\log~g$ = 4.5 affects significantly the lithium abundance determination, in the sense that a lower surface gravity yields a higher lithium abundance. In particular, for stars with $\log{T_{{\rm eff}}}$ less than about 3.7 ($\approx$5000 K) and $\log{W({\rm Li})}$ greater than about 2.5 ($\approx$320 mÅ), the difference in $\log{N({\rm Li})}$ may rise to 0.3 dex, when assuming $\log{g}$ = 3.5. Hence, assuming $\log{g}~= 3.5$ would result in higher lithium abundances than when assuming $\log{g}=4.5$. Thus we adopt the most conservative value, $\log{g}$ = 4.5, which might eventually lead to an underestimation of the abundance. In the case of the spectroscopic binary Cru-3, we used the method reported in Covino et al. (2001) in order to determine the weighting factors and correct for the contribution of each binary component to the observed total continuum. Since the two components are quite similar, the weighting factor is practically 0.5 for each of them.

The H$\alpha$ and lithium equivalent widths W(Li), as well as the lithium abundances are reported in Table 3. We adopt the convention that positive equivalent widths indicate absorption lines. By comparison with the values reported in Table 1 of FL97, we notice that the strength of the H$\alpha$ emission line of Cru-1, Cru-3 and Cru-6 is quite variable, as it is expected in active, young stars.

 

 

Table 3: Derived parameters for the stars in the Crux sample.

Crux	SpT	$\log{T_{{\rm eff}}}$	$W_{\rm H\alpha}$	$W_{\rm Li}$	$N_{\rm Li}$	$A_{\rm V}$	$\log{L}$
		[K]	[Å]	[mÅ]			[$L_{\odot}$]
1	M3	3.532	-6.50	0.395	1.04	0.13	-0.85
2E	G9	3.719	1.94	0.150	2.60	0.00	-0.14
2W	K3	3.671	0.94	0.230	2.33	0.00	-0.22
3a	K5	3.644	-0.48	0.460	2.82	0.63	-0.10
3b	K5	3.644	-0.52	0.480	2.89	0.63	-0.10
4	M4	3.517	-5.80	0.420	1.17	0.07	-0.92
5	K4	3.657	1.00	-	-	1.25	-0.67
6	M1	3.564	-3.20	0.570	2.14	0.10	-0.60

3.4 Bolometric luminosities

The methods described in Alcalá et al. (1997) were used to calculate the bolometric luminosities, assuming that the six Crux stars are located at the same distance as the B0.5IV type star $\beta$ Cru, i.e. 110 pc (Perryman et al. 1997). A normal interstellar extinction law was assumed in order to derive the intrinsic colours and reddening. The interstellar extinction, $A_{\rm V}$, and the stellar luminosities are reported in Table 3.

The stellar luminosities calculated in this way are over-estimated for the binary stars. For equal binary components, one can derive the individual luminosities simply by subtracting $\log\,2$ to the total luminosity. The luminosities derived in this way for the components of Cru-3 are reported in Table 3; in the case of Cru-1, it is more difficult to estimate the individual luminosities, because there is no information on the individual spectral types or colours. As a first approximation, one can assume that the luminosity ratio of the components is the same as the flux ratio measured in the K band (see Sects. 2.2 and 4.1), and hence subtract $\log~(1 + 1/1.8)$ and $\log~(1+1.8)$ to the logarithmic total luminosity, for the primary and secondary components respectively.