Galactic models with massive coronae IV. The Andromeda galaxy, M 31

Stellar populations in spiral galaxy M 31 are studied by using modelling. The method is based on the assumptions that 1) the galaxy is in a steady state, 2) galactic populations are physically homogeneous, and 3) equidensity surfaces of the galactic populations are similar concentric ellipsoids or can be represented as sums of such ellipsoids. All available observational data on surface photometry from U to K bands, rotation velocities, stellar velocity dispersions, distribution and kinematics of globular clusters, as well as the distribution of the young stellar component and gas have been collected. These data are used to decompose the galaxy into a central nucleus, a metal-rich core and a bulge, a metal-poor halo, an old stellar disk, a young gaseous-stellar population and a massive dark corona. Each population is characterized by its ellipticity, radius, mass, luminosity, structure parameter, and colour indices. We show how the multi-dimensional parameter space of M 31 subsystems can be split into several nearly independent regions with lower dimensionality. This enables us to calculate the values of the parameters in several steps. The sensitivity of the population parameters to various observational data is analysed. The density distribution parameters, colour indices and mass-to-light ratios of these populations are derived and mass distribution functions of M 31 and its subsystems are calculated. The mean mass-to-luminosity ratio in the optically visible parts of the galaxy is found to be M/L_B_=4.8+/-1.5M_sun_/L_sun_, and the ratio of the total mass to the visible one M_T_/M_vis_=43. The local M/L ratio at the outer edge of the area to which the surface photometry data apply resulting from a best-fit model is 2500.