[Paper Review] Early galaxy evolution from deep wide field star counts. I. The spheroid density law and mass function

A. C. Robin, C. Reylé+1 more|arXiv (Cornell University)|Apr 7, 2000

Astronomy and Astrophysical Research3 citations

TL;DR

This study uses deep wide-field star counts from high and intermediate galactic latitudes to constrain the spheroid's density law and initial mass function (IMF), finding a moderately flattened (c/a = 0.76) power-law density profile with index 2.44 and a stellar IMF slope of 1.9 ± 0.2. The results suggest the spheroid's mass distribution is compatible with a baryonic dark matter halo composed of stellar remnants, supporting a common dynamical origin for visible and dark matter components.

ABSTRACT

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 αto 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.

Motivation & Objective

• To determine the large-scale density law of the galactic spheroid using deep wide-field star counts.
• To estimate the spheroid's local density, power-law index, flattening, and IMF slope through maximum likelihood fitting.
• To assess the robustness of results against contamination from the thick disc population.
• To evaluate the compatibility of the spheroid's mass distribution with the dark matter halo, particularly as traced by microlensing and rotation curves.
• To test whether the spheroid's properties support a common dynamical origin with baryonic dark matter in the form of stellar remnants.

Proposed method

• A revised version of the Besançon population synthesis model is used to simulate star counts under realistic observational conditions, including photometric systems, errors, and selection effects.
• The model incorporates four Galactic components: thin disc, thick disc, halo (spheroid), and bulge, with adjustable parameters for each.
• A maximum likelihood criterion is applied to fit the observed star counts across multiple high- and intermediate-latitude fields.
• Contamination from the thick disc is quantified using synthetic models with varied thick disc parameters (e.g., local density, scale height, IMF slope), including extreme cases to test robustness.
• The analysis compares observed colour-magnitude distributions with model predictions to isolate the spheroid contribution, especially in the blue peak at faint magnitudes.
• Degeneracy between spheroid parameters and thick disc contamination is assessed by testing models with higher-than-standard thick disc densities and scale heights.

Experimental results

Research questions

• RQ1 What is the true power-law index and flattening of the galactic spheroid's density distribution, based on deep wide-field star counts?
• RQ2 How significant is the contamination from the thick disc population in the blue peak of star counts, and how does it affect spheroid parameter estimation?
• RQ3 What is the initial mass function (IMF) slope of the spheroid, and what does it imply for the local stellar and mass density?
• RQ4 Is the spheroid's mass distribution consistent with the dark matter halo, particularly as inferred from microlensing surveys and rotation curves?
• RQ5 Can the spheroid's properties be reconciled with a baryonic dark matter component made of stellar remnants such as white dwarfs and brown dwarfs?

Key findings

• The best-fit spheroid density law has a power-law index of 2.44 and a flattening (c/a) of 0.76, indicating a moderately flattened, extended distribution.
• A significant degeneracy exists between flattening and power-law index, with alternative solutions including c/a = 0.85 and index 2.75, or c/a = 0.6 and index 2.0, all within 2σ confidence.
• The spheroid IMF slope is constrained to α = 1.9 ± 0.2, yielding a local stellar density of 1.64 × 10⁻⁴ stars per cubic parsec.
• The resulting mass density of the spheroid is 4.15 × 10⁻⁵ M☉ pc⁻³, with negligible contribution from brown dwarfs to the dark matter halo.
• The spheroid's mass distribution is compatible with a baryonic dark matter halo composed of stellar remnants, supporting a common dynamical origin with the observed dark matter halo.
• Contamination from the thick disc is found to be small under standard model assumptions, and overestimation of thick disc parameters would only strengthen the conclusion of a flat spheroid with low power-law index.