8 Estimation of the number of RR Lyrae stars in Sgr

Figure 10: Luminosity-metallicity relation for Dsph of the Local group. Data have been taken from Mateo (1998). The dashed line corresponds to the best fit to the data points. The filled circle corresponds to the estimated luminosity of Sgr if this galaxy had lost 50$\%$ of its mass since its formation. The open triangle represents the first luminosity estimate of this galaxy (Ibata et al. 1995). The vertical dotted line (shifted by 0.02 dex for clarity) encompasses the different estimates of Mateo et al. (1998).

Using the results from Paper I, it is possible to estimate the total number of RRab stars in Sgr. The best fit to the core of Sgr corresponds to an exponential with a scale-length of 4.1$^{\circ}$ on the main axis and a central density of 139 RRab per square degree. Assuming an axis ratio of 3:1 (Ibata et al. 1995), we get $\sim$4200 RRab in the main body of Sgr. This estimate is only a lower limit for Sgr since we did not consider the nearly flat profile in the outer region of the main body (Paper I). Irwin (1999) estimated that Sgr lost 50$\%$ of its mass through tidal stripping. This implies that the number of RRab stars associated with Sgr could be as high as $\sim$8400.

Provided RRab stars are good tracers of light in Sgr, we can estimate a lower limit to the total luminosity of this galaxy using the luminosity function (LF) published by Mateo et al. (1995). Their LF is complete down to $M_ V\sim4.5$ mag. For fainter magnitudes we extend the LF with the Bulge LF (Holtzman et al. 1998). This should not significantly alter the result since most of the light is emitted by brighter stars. The field of Mateo et al. contains five RRab stars. Rescaling the RRab number density to the integrated luminosity and assuming a distance modulus of (m-M)₀=17.0 to Sgr yields -4.9 mag per RRab. It results that $M_V{\rm (Sgr)}< -$13.9 ^+0.4_-0.6 mag, where the uncertainties represent the poissonian uncertainty in the RRab counts. Again, if we assume 50$\%$ mass loss, the total magnitude of Sgr before stripping would be $\sim$-14.7 mag.

Previous estimates have continuously increased the luminosity of Sgr as new extensions of this galaxy were discovered, with estimations ranging from $M_V\sim -$13.0 (Ibata et al. 1995) to $M_V\sim -$14.6 mag (Mateo et al. 1998). Our estimation seems to favor the higher luminosity of Sgr. The metallicity of the dominant population in Sgr is estimated to be [Fe/H]$\sim -$1.1 dex (Mateo et al. 1995). An absolute luminosity of $\sim -$14.7 mag for Sgr would be consistent with the empirical magnitude-metallicity relationship for Dsph galaxies, as shown in Fig. 10.