The universe at faint magnitudes. I - Models for the galaxy and the predicted star counts

Abstract

A detailed model is constructed for the disk and spheroid components of the Galaxy from which the distribution of visible stars and mass in the Galaxy is calculated. The application of star counts to the determination of galactic structure parameters is demonstrated. The possibility of detecting a halo component with the aid of star counts is also investigated quantitatively. The stellar luminosity functions and scale heights are determined from observations in the solar neighborhood. The global distribution of matter is assumed, based on studies of other galaxies, to be an exponential disk plus a de Vaucouleurs spheroid. The spheroid luminosity function is found to have the same shape as the disk luminosity function over the range of absolute magnitudes (+4 to + 12) that contributes significantly to the star counts for mV ≤ 30. The density of spheroid stars in the solar neighborhood is 1/800 of the value for the disk. The star counts calculated using the density variation of a de Vaucouleurs spheroid are consistent with the available data; the counts predicted with the aid of a Hubble law are inconsistent with observations at more than the two-sigma level of significance. The variations of the calculated star densities with apparent magnitude, latitude, and longitude agree well with the available star count data for the observationally well studied range of 4 ≲ mV ≲ 22. The calculated (B - V) color distributions are also in good agreement with existing data. The color data also indicate that QSOs comprise only a few percent of the total number of stellar objects to mV = 22 (mB = 22.5). The spheroid component is found to be approximately spherical. The scale lengths of the Galaxy model and computed total luminosity and M/L ratios for the disk and spheroid are in agreement with observations of other Sbc galaxies. Illustrative Fig. and a table of interesting characteristics (such as the mass and luminosity contained within various radii and the escape velocity) are provided. Further ground-based observations at attainable faint magnitudes (mV ≤ 23 mag) would be important. Star counts and (B - V) colors in several widely separated selected fields would permit a more accurate determination of the disk scale length and the spheroid star density and ellipticity. The most effective regions in which to make these observations are specified. The Galaxy model of the disk and spheroid is used to predict the star densities (in B and V) that may be observable with the aid of the Space Telescope down to very faint magnitudes. The stellar density to mV = 28 from the disk and spheroid is predicted to be 104 stars per square degree at the galactic pole. The predicted star counts are insensitive to many of the model parameters, although drastic changes in the shape of the luminosity function outside the presently determined magnitude range could produce measurable departures from the predicted star counts at faint magnitudes. The rotation curve computed solely from the disk and spheroid components decreases beyond about 10 kpc from the center of the Galaxy. A halo with even a relatively small mass density in the Solar neighborhood (ρHalo (Sun) = 0.01 Msun pc-3) can give rise to a flat rotation curve. The stellar content of such a halo would be revealed by observations with Space Telescope cameras if the halo consists of main sequence stars with MV ≲ 19.0 mag (existing observations imply MVMS ≳ 14.0 mag) or faint white dwarfs with MVWD ≲ 17.5 mag (existing observations imply MVWD ≳ 13.0 mag). Existing data imply (M/L)Halo ≳650 (Solar Visual units). The results for V magnitudes are described in the main text; the corresponding results for B magnitudes are summarized in Appendix A. A table of predicted differential and integrated star counts for both V and B magnitudes is given in Appendix B. Simple formulae that reproduce to an accuracy of 15% the predicted model star densities as a function of magnitude, latitude, and longitude are also provided in Appendix B.