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

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3. Subsystems in M 81

The general review of the stellar populations in our Galaxy can be found in textbooks by Mihalas & Binney (1981) and Gilmore et al. (1990) and in reviews by Hodge (1989), Majewski (1993). In the present section we describe the populations as they can be distinguished in external galaxies (cf. reviews by van den Bergh 1975, Hodge 1989) with special emphasis on M 81. For every population we emphasize what parameters of a subsystem are determined independently and thereafter kept fixed in the final best-approximation process.

3.1. The nucleus

Ho et al. (1996) divided the nucleus of M 81 into a narrow-line region and a broad-line region. In the narrow-line region they discriminated a lower density "halo" with a radius [FORMULA]  pc and denser "core" with a radius about 0.1-1 pc. For broad-line region crude estimates gave the radius [FORMULA]  pc. The mass of broad-line region was estimated to be [FORMULA]. According to Bower et al. (1996) the broad-line component originates most likely from the elliptical accretion disk. This interpretation is consistent with HST [FORMULA] image of the nucleus obtained by Devereux et al. (1997) and with VLBI observations by Bietenholz et al. (1996). Thus we suppose the broad-line region to be a gas disk surrounding a point mass (black hole). Further we will neglect the gas disk mass and take into account only the black hole (BH) mass.

Now we may estimate the mass of the larger stellar component (narrow-line region) which we call here the nucleus. One constraint is the stellar velocity dispersion 250 km/s measured by Bower et al (1996) using the HST FOS camera at the galactocentric distance [FORMULA] 2.6 pc. We take this value as the mean line-of-sight velocity dispersion of the nucleus. The radius of the nucleus as well as the structure parameter and the luminosity is derived from the surface photometry of the central regions of M 81. The surface photometry of the nuclear region with the highest angular resolution is done by Crane et al. (1993) with HST FOC (f/96). From his photometric profile we obtain for the radius of the nucleus [FORMULA] [FORMULA]  pc, the luminosity [FORMULA] [FORMULA] and structure parameter [FORMULA] [FORMULA] With sufficient precision the nucleus can be taken as spherical (i.e. axial ratio [FORMULA] 1.).

The mass of the nucleus was determined using formula (8) of the Appendix. For [FORMULA] this relation gives [FORMULA] and [FORMULA]. This mass-to-light ratio is obviously too large for any stellar population. For this reason we study also a model where the [FORMULA] ratio of the nucleus was taken as an upper limit for an old metal-rich population (Bressan et al. 1994, Worthey 1994) [FORMULA], giving [FORMULA] and hence [FORMULA].

Although the nucleus is a prominent structural feature in galaxies, dynamically it is quite independent of the remaining subsystems. Thus we keep the parameters [FORMULA], N, [FORMULA], [FORMULA], [FORMULA] of the nucleus fixed during the final approximation procedure. More detailed structure of the nucleus and a central point source is beyond the scope of the present paper.

3.2. The core and the bulge

In general, the spheroidal parts of galaxies are not physically homogeneous (Rose 1985, Morrison & Harding 1993).

It is convenient to define the bulge consisting of stars with normal (solar) metal content. This is one of the most prominent structural features of galaxies. In several nearby galaxies, in the inner regions of spheroids, a sudden increase in metallicity (Cohen 1979, Delisle & Hardy 1992, O'Connell et al. 1992, Davidge 1997) has been detected. In the case of M 81 this kind of increase was most strong inward of 0.3-0.5 kpc. Thus we separate a metal-rich core from the bulge.

The problem of discriminating between the core and the bulge is a complicated one and will be discussed in Sect. 4.2. All the parameters of the core and the bulge have been determined during the final approximation process.

3.3. The halo

By `halo' we mean a spheroidal metal-poor population II subsystem, typical representatives of which are old stars (like RR-Lyrae variables) and low metallicity globular clusters (GC). In M 81 there are no observations on the distribution of old star populations at present. Hence we must confine ourselves to the observations of GC.

The first effort to compile a sample of GC was made by Georgiev et al. (1991a, 1991b) on the basis of 6m (Russia) and 2m (Bulgaria) telescope plates. They estimated also B-V colour indices. However, in the present study we do not use their observations, because, as it was mentioned by the authors, the mean (B-V) colour of their sample is nearly [FORMULA] redder than it could be expected. Taking into account quite moderate seeing [FORMULA] this sample may contain distant galaxies.

We use the sample of GC candidates selected by Perelmuter & Racine (1995) from CFHT plates and Mayall 4m telescope CCD frames. Resulting surface density distribution of GC candidates is given in Fig. 6 by open circles.

[FIGURE] Fig. 6. The distribution of globular clusters in M 81. The observations by Perelmuter & Racine (1995) are presented by open circles. The continuous line gives our best-fit model distribution for the halo.

We estimated the flatness of GC subsystem from their Fig. 17 and found that the apparent axial ratio is [FORMULA] giving us the true axial ratio [FORMULA]. Thus the GC system in M 81 is not very spherical (the same holds also for galaxies M 87 and M 31 modelled by us earlier (Papers III and IV).

Only old metal-poor GCs can be considered as test particles of the halo subsystem. Metallicity gradient of GC in Perelmuter & Racine's sample is weak with an exception of the innermost point at [FORMULA] 1.2 kpc, thus we may conclude that in outer regions the contribution of bulge clusters is weak. In addition, the metallicity distribution of M 81 GC does not exhibit two-peaked distribution as is observed in some other galaxies (see Secker et al. 1995, Zepf et al. 1995, Elson & Santiago 1996) and their mean [FORMULA] 0.7 nearly coincides with the M31 halo cluster sample (Racine 1991, Reed et al. 1994). Thus we can expect that with possible exception of innermost clusters the Perelmuter & Racine's GC sample can be used as test particles of the halo subsystem.

The observed cluster distribution is well approximated by our density distribution law (Appendix, Eq. 1) with the parameters [FORMULA] and [FORMULA]  kpc. The mean colour indices for the M 81 cluster population are [FORMULA] [FORMULA].

For the mean velocity dispersion of GC population Perelmuter et al. (1995) derived 152 km/s. We use this value also in our model as an input parameter. Although this value is the halo object's dispersion, it is not determined by the halo mass only. GCs do not form even an approximately dynamically independent subsystem but lie in the gravitation field of the whole galaxy. Very important are the contributions due to disk and dark matter corona masses. Hence, in order to use the GC mean velocity dispersion the virial theorem for multicomponent systems must be used (Paper IV, App. A, Eq. (A8)).

As an independent value, related to mass, we use the mass-to-light ratio of GCs. According to the models by Pryor & Meylan (1993) the mean M/L ratio of GC in our Galaxy is [FORMULA] [FORMULA] We take this value as a reasonable first approximation also for M 81 halo.

These values of the referred above GC population parameters ([FORMULA], N, [FORMULA], [FORMULA], [FORMULA], [FORMULA]) are taken as fixed halo parameters in the final approximation process.

3.4. The extreme flat subsystem

Young stars and gas contribute most to the flat subsystem. The HI surface density distribution from observations made by Gottesman & Weliachew (1975) and Rots (1975) were converted to units [FORMULA], reduced to total HI mass [FORMULA] [FORMULA] (Appleton et al. 1981, Yun et al. 1994) and averaged. The [FORMULA] surface densities from observations by Brouillet et al. (1988, 1991) and Sage & Westphal (1991) were converted also to units [FORMULA] and averaged. 1 Composed in this way [FORMULA] surface density distribution gives the total [FORMULA] mass [FORMULA] [FORMULA]. (Outside [FORMULA]  kpc no [FORMULA] measurements are available. We extrapolated the data to this region. Corresponding additional uncertainties were included in the total mass error.) Thereafter the HI and [FORMULA] surface densities were added. The resulting surface density distribution of the gas is given in Fig. 7 by filled circles. The total gas mass is [FORMULA] [FORMULA].

[FIGURE] Fig. 7. The surface density distribution of the flat subsystem. Open circles and vertical scale units on the left-hand side - stellar component, filled circles and units on the right-hand side - gas component, solid curve - best-fit model distribution.

To obtain the stellar component distribution, we used the surface brightness distribution of spiral arms (Schweizer 1976), observations of OB-associations (Ivanov 1992) and HII regions (Hodge & Kennicutt 1983, Petit et al. 1988). The distributions of OB-associations and HII regions were deprojected "face on" and the number surface densities in concentric rings were calculated. Thereafter the distribution of surface brightness of spiral arms, the number surface density distribution of OB associations and HII regions were averaged. Resulting stellar component distribution is given in Fig. 7 by open circles (the vertical scale corresponds to the Schweizer's B-colour surface brightness measurements of spiral arms).

The total mass of young stars is derived by using the empirical Schmidt star formation law. If the power in the Schmidt law is [FORMULA] the characteristic star formation time is [FORMULA] 4.8 Gyr and the present star formation rate in M 81 is [FORMULA]. If [FORMULA] 2 then [FORMULA] 0.6 Gyr and SFR = [FORMULA] (this value is more consistent with SFR = [FORMULA] determined by Hill et al. (1995) from UV emission). The mean of these two values gives the mass of stars with ages less than 1 Gyr [FORMULA] [FORMULA].

Therefore, the total mass of the flat subsystem of M 81 is [FORMULA] [FORMULA] [FORMULA]. The distribution of stars and gas of this population (Fig. 7) is well represented by the density distribution law (1) (see Appendix) with parameters [FORMULA]  kpc, [FORMULA] [FORMULA] [FORMULA]. For the flattening of the subsystem we take as in our Galaxy [FORMULA] 0.02, for colour indices we take the values derived by Schweizer (1976) [FORMULA], [FORMULA], [FORMULA].

These values will be used in the least-square fit as fixed parameters for the flat subsystem.

3.5. The disk

It is convenient to define the disk as consisting of stars with normal metallicity but with quite different ages (the mean age is about [FORMULA] As for the flat subsystem, we allow a toroidal structure for the disk, i.e. central density minimum. Otherwise it is difficult to model a minimum of the rotation velocity at 1 kpc (Einasto et al. 1980a; Rohlfs & Kreitschmann 1980). In determining the disk mass we do not assume the "maximum disk". Therefore we do not fix the disk parameters first. The problem of discrimination between the disk mass and possible dark matter amount in our model will be discussed in Sect. 4.3.

In the Milky Way there is probably, in addition to an ordinary old disk, an additional thick disk (e.g. Gilmore et al. 1995). As an hypothesis, this gives a sufficient reason to study the possible existence of a thick disk in M 81. Unfortunately, during the preliminary model construction we found that due to inclination of M 81 ([FORMULA]) the model is insensitive to analyse the vertical structure of the disk in detail. For this reason, we did not include a thick disk component in further modelling.

3.6. The massive corona

On the basis of very different observations it can be concluded that masses of galaxies are larger than it follows from a simple assumption of constant mass-to-light ratio. Large masses in the outer parts of galaxies result from the rotation velocities remaining constant at large galactocentric distances (Freeman 1993), from the thermal emission of hot gas detected in X-rays (Fabbiano 1989), from gravitational lensing effects (Blandford & Narayan 1992, Fort & Mellier 1994) etc. In the case of M 81 the mass distribution at largest distances is determined from the kinematics and distribution of M 81 satellite galaxies. We assume the corona to be spherical ([FORMULA] 1).

To decide what galaxies form a bound group is not easy even when radial velocities of satellite galaxies are known (e.g. discussion in Huchtmeier & Skillman 1995). In our modelling we used the sample of 17 satellite galaxies with measured radial velocities from the study by van Driel et al. (1998) who gave the mean velocity dispersion of M 81 group [FORMULA] 114 km/s. We approximated cumulative satellite spatial distribution with the density distribution formula (2) (see Appendix) with parameters [FORMULA] [FORMULA]  kpc, [FORMULA] [FORMULA]. Although the formal error in [FORMULA] is not big, in reality it is coupled with the disk mass, allowing a wide range of possible disk masses. We will study the coupling of disk mass and the corona parameters in Sect. 4.3.

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© European Southern Observatory (ESO) 1998

Online publication: June 18, 1998