The final seven-component model fits all photometric profiles with a mean relative error 0.7 per cent, and the rotation curve from 2 kpc to 24 kpc with the relative error 2 per cent. Therefore, the model is in good agreement with both data sets. The model describes well also the velocity dispersion data, the distribution of globular clusters and young stars + gas. The parameters of the final model (the axial ratio, the harmonic mean radius, the total mass of the population, M, the structural parameters, and N, and the dimensionless normalizing constants, h and B-luminosities and colour indices) are given in Table 3, a colon designates fixed parameters. The final model is represented by solid lines in Figs. 1 - 7.
Table 2. Model parameters
Table 3. Calculated descriptive functions
The total luminosity of M 81 is calculated to be the optically visible mass the corresponding ratio The mass-to-light ratio of both disk-like components (disk + flat) together is of all spheroidal components (nucleus+core+bulge+halo) together Total luminosity of the spheroid is .
Table 4 presents some descriptive functions calculated for our final model. where is the gravitational potential, is the gradient of the gravitational potential in the radial direction (in the units of . is the effective inner mass, defined as a point mass in the centre of the galaxy, having the same gravitational attraction at R as the subsystem. The quantity is the local ratio in the B-colour derived by dividing the effective mass and the effective luminosity in a shell limited by the radii R and . The radii are in kiloparsecs, the masses in units of the ratios in solar units.
The calculated local mass-to-luminosity ratios are given in Fig. 13. A clear difference between the visible and dark matter begins at the distance 11 kpc.
The mass-to-light ratio within the Holmberg radius 19 kpc is . The radius at which the masses of dark matter and visible matter become equal is 26 kpc. These numbers indicate that the DM concentration around M 81 is significantly smaller than around M 31. However, because the extent of DM is larger than for M 31 the ratio of the total mass and visible mass is in both cases nearly the same ( for M 81).
© European Southern Observatory (ESO) 1998
Online publication: June 18, 1998