6 The Cepheids as distance calibrators

Cepheids variables are the principal distance indicators upon which the calibration of the extragalactic distance scale currently rests, and one of the most nagging contributors to uncertainty in that scale is the Galactic Cepheid calibration (see Feast & Walker 1987 for a review). Using all the available photometric and spectroscopic data, we have determined the reliable reddening as well as distance values to the cluster. They can therefore be used to refine the zero-point of the extragalactic distance scale, since three Cepheids are members of this cluster. Sandage et al. (1999) have shown that the PLR is $<\!\!M_v\!\!>\ = - 2.82 ~{\rm Log}~ P + C1$; where C1 is the zero-point and it needs to be determined precisely. The periods and average $<\!\!V\!\!>$ magnitudes of the Cepheids present in this cluster are listed in Table 6. These $<\!\!V\!\!>$ magnitudes and the present determination of distance and reddening to the NGC 7790 are used to determine their $<\!\!M_v\!\!>$ values (see Table 6). These along with the periods used in the PLR, allow to determine the values of C1 for all Cepheids as indicated in Table 6. The average value ( $-1.31\pm0.1$) of C1 agrees very well with the value of -1.34 given by Sandage et al. (1999) using theoretical models for solar metallicity. However, a lower metallicity for the NGC 7790 Cepheids will not change the value as according to Sandage et al. (1999) the luminosity dependence on metallicity is very week ( $\frac{{\rm d}M_v}{{\rm d}[{\rm Fe/H}]} = - 0.081$). Periods of the Cepheids can also be used to determine their ages. Romeo et al. (1989) estimated an age of 120 Myr for the Cepheids of NGC 7790 using the period-age relation derived from those stellar evolutionary models where convective core overshooting and mass loss are taken into account. Thus the age of the Cepheids is consistent with the age of the cluster derived by fitting of isochrones in the M_v, (B-V)₀ diagram (see Fig. 7).