5 Masses, distances and evolutionary times

The derived atmospheric parameters were compared to two sets of evolutionary tracks (from the Geneva group, Schaller et al. 1992; and the Padua group, Salasnich et al. 2000) to estimate stellar masses and evolutionary times ${T_{\rm evol}}$ (see Fig. 3) by interpolation. The results do not depend on the model grid used. Derived masses differ by less than 0.1$M_{\odot}$ and evolutionary lifetimes by less than 4 Myr (except PG 1610+239: 17 Myr). Errors for the evolutionary lifetimes in Table 6 include errors propagated from uncertainties in atmospheric parameters as well as from the use of the two model sets.

The distance has been calculated from mass, effective temperature, gravity and the dereddened apparent magnitude of the stars:

$$d = 1.11 \sqrt{\frac{M_{\star}F_V}{g}\times 10^{0.4V_0}} {\rm [kpc]}$$

where ${M_{\star}}$ is the stellar mass in $M_{\odot}$, g is the gravity in cm  $\rm {s^{-2}}$, F_V is the model atmosphere flux at the stellar surface in units of $10^8{\,}{\rm {erg \ cm^{-2}{ }\,s^{-1}{ }\,\AA^{-1}}}$ and V₀ is the dereddend apparent visual magnitude.