This paper is part of a global analysis of star counts developed to constrain consistently scenarii of galaxy formation and evolution.The central tool of this approach is the "Besançon" model of population synthesis. This model is gradually tuned to fit an increasing number of observational constraints while keeping compatibility with previous fits and theoretical prescriptions. In the present paper we address the problem of the halo (dark or visible) by trying to compare the properties of the spheroid population (the visible halo) with the dark matter halo, as traced by microlensing at high galactic latitudes and by the rotation curve. If the dark matter is made at least partly of stellar remnants, as shown by recent statistics of microlensing at high galactic latitudes (Aubourg et al., 1993; Alcock et al., 1997; Alcock et al., 1998), the density trend of this matter should be close to a power law with index of 2 (as expected from a flat rotation curve). It is natural to think of a similar shape for the stellar spheroid.
Constraints on the overall shape of the dark halo are poor. Cosmological simulations of halo formation generally predict that halos are flattened by about c/a 0.7 (Rix, 1996). But the axis ratio depends on how much the halo matter is dissipative, the more dissipative, the flatter the halo. Direct determinations of the dark matter distribution in polar ring galaxies show flattened halos with c/a 0.5 (Sackett et al., 1994; Rix, 1996).
Concerning the spheroid population, most previous analyses suggest rather steep density slopes with power indices between 3.0 and 3.5. However, these analyses are based on rather small samples of well identified tracers. The estimated flattening also cover a wide range between 0.6 to 1.0:
The distribution of galactic globular clusters appears to be well fitted by a power law density with index and flattening of 1 (Harris, 1976; Zinn, 1985). Hawkins RR Lyrae observations (1984) showed with a flattening of 0.9. Saha (1985), using a spherically symmetric model, found out to 25 kpc but then the RR Lyrae density falls off more rapidly beyond 25 kpc. Another study of RR Lyrae by Wetterer (1996) showed that a spherically symmetric model yields whereas an ellipsoidal distribution yields . Sluis (1998) counted blue horizontal branch (BHB) stars and RR Lyrae and found and . Still from BHB star counts, Sommer-Larsen (1987) derived and up to 40 kpc, Preston (1991) found that increases from 0.5 to 1 up to 20 kpc with . Soubiran (1993) showed that is compatible with the kinematical behavior of a star sample near the north galactic pole. K dwarf counts with HST yield and (Gould et al., 1998). All of these studies were based on a few hundred objects at most.
In order to find new constraints on the spheroid density law, we undertook a photometric and astrometric sample survey in various galactic directions. We complemented these data with existing deep photometric star counts in several high and intermediate latitude fields. Most such counts contain large numbers of halo dwarfs, but they cannot be distinguished from thick disc dwarfs by their colours but at faint magnitudes. Since no large optical surveys were available at magnitude fainter than 20, we used heterogeneous data coming from various studies (often of extragalactic aim) in various photometric systems.
The population synthesis model used here permits to perform a global analysis of these heterogeneous data, since observational data can be simulated in each field with the true observational conditions (photometric system, errors and selection effects). The synthetic approach allows also to estimate the biases and expected contaminations by other populations.
In Sect. 2 we describe the model of population synthesis and external constraints on the spheroid population. In Sect. 3 we describe the data sets and the comparison method. In Sect. 4 we discuss the results and their implications for the dark matter halo.
© European Southern Observatory (ESO) 2000
Online publication: June 30, 2000