Classical models of elliptical galaxies were found from luminosity profiles and were calibrated using either central velocity dispersions, or motions of companion galaxies. Models of spiral galaxies were constructed using rotation velocities. A natural generalisation of classical galactic models is the use of all available observational data - photometric data on the distribution of colour and light, and kinematical data on the rotation and/or velocity dispersion. Further, it is natural to include into models data of all major stellar populations, such as the bulge, the disk, the halo, as well as the flat population in spiral galaxies, consisting of young stars and interstellar gas.
All principal descriptive functions of galaxies (circular velocity,
gravitational potential, projected density) are simple integrals of
the spatial density. Therefore it is natural to apply for the spatial
density
(a)
of galactic populations a simple generalised exponential expression
(Einasto 1965):
 |
(1) |
where a is the semi-major axis of the isodensity ellipsoid, a0 is the effective radius of the population, and N is a structural parameter, determining the shape of the density profile. This expression (called the Einasto profile) can be used for all galactic populations, including dark halos. The case N = 4 corresponds to the de Vaucouleurs density law for spheroidal populations, N = 1 corresponds to the exponential density law for disk.
To combine photometric and kinematic data, mass-to-light ratios of galactic populations are needed. Luminosities and colours of galaxies in various photometric systems result from the physical evolution of stellar populations that can be modelled. Detailed models of the physical and chemical evolution of galaxies were constructed by Tinsley (1968). Combined population and physical evolution models were calculated for a representative sample of galaxies by Einasto (1972). It is natural to expect, that in similar physical conditions the mass-to-luminosity ratio Mi / Li of the population i has similar values in different stellar systems (star clusters, galactic populations). Thus star clusters and central cores of galaxies can be used to estimate Mi / Li values for the main galactic populations.