As part of a global analysis of deep star counts to constrain scenarii of galaxy formation and evolution, we investigate possible links between the galactic spheroid and the dark matter halo. A wide set of deep star counts at high and intermediate galactic latitudes is used to determine the large scale density law of the spheroid. Assuming a power density law, the exponent, flattening, local density and IMF slope of this population are estimated. The estimation is checked for robustness against contamination of star counts by the thick disc population. Contamination effects are derived from a model of population synthesis under a broad variety of thick disc parameters. The parameter fit is based on a maximum likelihood criterion. The best fit spheroid density law has a flattening of 0.76, a power index of 2.44. There is a significant degeneracy between these two parameters. The data are also compatible with a slightly less flattened spheroid (c/a = 0.85), in combination with a larger power index (2.75). A flatter spheroid (c/a = 0.6) with a power index of 2 is not excluded either. We also constrain the spheroid IMF slope alpha to be 1.9 +/- 0.2, leading to a local density of 1.64 10$^{-4}$ stars pc$^{-3}$ and a mass density of 4.15 10$^{-5}$ Msun pc$^{-3}$. With this slope the expected mass density of brown dwarfs in the halo makes a negligible part of the dark matter halo, as already estimated from microlensing surveys. So, as star count data progresses in depth and extent, the picture of the spheroid star population that comes out points to a shape quite compatible with what we know about the distribution of baryonic dark matter if it is made of stellar remnants, suggesting a common dynamical origin.
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