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Astron. Astrophys. 335, 449-462 (1998)

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5. Results

The final seven-component model fits all photometric profiles with a mean relative error 0.7 per cent, and the rotation curve from [FORMULA] 2 kpc to [FORMULA] 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, [FORMULA] the harmonic mean radius, [FORMULA] the total mass of the population, M, the structural parameters, [FORMULA] and N, and the dimensionless normalizing constants, h and [FORMULA] 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]

Table 2. Model parameters



[TABLE]

Table 3. Calculated descriptive functions


The total luminosity of M 81 is calculated to be [FORMULA] the optically visible mass [FORMULA] the corresponding [FORMULA] ratio [FORMULA] The mass-to-light ratio of both disk-like components (disk + flat) together is [FORMULA] of all spheroidal components (nucleus+core+bulge+halo) together [FORMULA] Total luminosity of the spheroid is [FORMULA].

Table 4 presents some descriptive functions calculated for our final model. [FORMULA] where [FORMULA] is the gravitational potential, is the gradient of the gravitational potential in the radial direction (in the units of [FORMULA]. [FORMULA] 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 [FORMULA] is the local [FORMULA] ratio in the B-colour derived by dividing the effective mass and the effective luminosity in a shell limited by the radii R and [FORMULA]. The radii are in kiloparsecs, the masses in units of [FORMULA] the [FORMULA] 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 [FORMULA] 11 kpc.

[FIGURE] Fig. 13. Local mass-to-luminosity ratios for visible matter only and for visible + dark matter

The mass-to-light ratio within the Holmberg radius [FORMULA] 19 kpc is [FORMULA]. 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 [FORMULA] is in both cases nearly the same ([FORMULA] for M 81).

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998
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