6 Stellar masses, ages and kinematics

6.1 Masses and ages

As described in Sect. 3.2, the stellar mass is required in the determination of the gravity from the Hipparcos parallax. With the derived temperature and absolute magnitude, the mass was estimated from the stellar position in the $M_{V} - \mbox{${\rm log} T_{\rm eff}$ }$ diagram (see Fig. 4) by interpolating in the evolutionary tracks of VandenBerg et al. ([1999]), which are distributed in metallicity with a step of $\sim 0.1$ dex. These new tracks are based on the recent OPAL opacities (Rogers & Iglesias [1992]) using a varying helium abundance with [$\alpha$/Fe] = 0.30 for $\mbox{\rm [Fe/H]}\leq -0.3$ and a constant helium abundance (Y=0.2715) without $\alpha$ element enhancement for $\mbox{\rm [Fe/H]}\geq -0.2$. Figure 4 shows the position of our program stars with $-0.77<\mbox{\rm [Fe/H]}<-0.66$ compared to the evolutionary tracks of Z = 0.004 ( $\mbox{\rm [Fe/H]}=-0.71$). The errors in $T_{\rm eff}$, M_V, and [Fe/H] translate to an error of $0.06~M_{\odot}$ in the mass.

Figure 4: The positions of our program stars with $-0.77<\mbox{\rm [Fe/H]}<-0.66$ compared to the evolutionary tracks ofVandenBerg et al. ([1999]) with $\mbox{\rm [Fe/H]}=-0.71$

Figure 5: The positions of our program stars with $-0.77<\mbox{\rm [Fe/H]}<-0.66$ compared to the isochrones of VandenBerg et al. ([1999]) with $\mbox{\rm [Fe/H]}=-0.71$

Stellar age is an important parameter when studying the chemical evolution of the Galaxy as a function of time. Specifically, the age is useful in order to interpret abundance ratios as a function of metallicity. In this work, the stellar age was obtained simultaneously with the mass from interpolation in the evolutionary tracks of VandenBerg et al. ([1999]). It was checked that practically the same age is derived from the corresponding isochrones. As an example, a set of stars are compared to isochrones in Fig. 5. The error of the age due to the uncertainties of $T_{\rm eff}$, M_V, and [Fe/H] is about 15% ( $\sigma(\log \tau)$ = 0.07) except for a few stars, which have relatively large errors of the Hipparcos parallaxes.

6.2 Kinematics

Stars presently near the Sun may come from a wide range of Galactic locations. Information on their origin will help us to understand their abundance ratios. Therefore, stellar space velocity, as a clue to the origin of a star in the Galaxy, is very interesting.

The accurate distance and proper motion available in the Hipparcos Catalogue (ESA [1997]), combined with stellar radial velocity, make it possible to derive a reliable space velocity. Radial velocities from the CORAVEL survey for 53 stars were kindly made available by Nordström (Copenhagen) before publication. These velocities are compared with our values derived from the Doppler shift of spectral lines. A linear least squares fit for 40 stars (excluding the suspected binaries) gives:

$$RV =0.997\left(\pm0.002\right)RV_{\mathrm{CORAVEL}}+0.26\left(\pm0.12\right) \mbox{\rm\,km\,s$^{-1}$ }.$$

The rms scatter around the relation is 0.72 kms^-1, showing that our radial velocities are as accurate as 0.5 kms^-1. Hence, our values are adopted for stars not included in the CORAVEL survey.

The calculation of the space velocity with respect to the Sun is based on the method presented by Johnson & Soderblom ([1987]). The correction of space velocity to the Local Standard of Rest is based on a solar motion, (-10.0, +5.2, +7.2) kms^-1 in (U, V, W), as derived from Hipparcos data by Dehnen & Binney ([1998]). The error in the space velocity arising from the uncertainties of distance, proper motion and radial velocity is very small with a value of about $\pm 1$ kms^-1.

The ages and space velocities derived in the present work are generally consistent with EAGLNT. But the more accurate absolute magnitude, as well as the new set of theoretical isochrones, in our study should give more reliable ages than those determined by EAGLNT based on the photometric absolute magnitude and the old isochrones of VandenBerg & Bell ([1985]). This situation is also true for space velocities with our results based on distances and proper motions now available from Hipparcos.