Determination of the Local Dark Matter Density in our Galaxy (0910.4272v2)

Abstract: The rotation curve, the total mass and the gravitational potential of the Galaxy are sensitive measurements of the dark matter halo profile. In this publication cuspy and cored DM halo profiles are analysed with respect to recent astronomical constraints in order to constrain the shape of the Galactic DM halo and the local DM density. All Galactic density components (luminous matter and DM) are parametrized. Then the total density distribution is constrained by astronomical observations: 1) the total mass of the Galaxy, 2) the total matter density at the position of the Sun, 3) the surface density of the visible matter, 4) the surface density of the total matter in the vicinity of the Sun, 5) the rotation speed of the Sun and 6) the shape of the velocity distribution within and above the Galactic disc. The mass model of the Galaxy is mainly constrained by the local matter density (Oort limit), the rotation speed of the Sun and the total mass of the Galaxy from tracer stars in the halo. It is shown from a statistical chi^2 fit to all data that the local DM density is strongly positively (negatively) correlated with the scale length of the DM halo (baryonic disc). Since these scale lengths are poorly constrained the local DM density can vary from 0.2 to 0.4 GeV/cm^3 (0.005 - 0.01 M_sun/pc^3) for a spherical DM halo profile and allowing total Galaxy masses up to 2 * 10^12 M_sun. For oblate DM halos and dark matter discs, as predicted in recent N-body simulations, the local DM density can be increased significantly.

• The paper applies chi² statistical fitting to diverse halo profiles and observational constraints to estimate the local dark matter density.
• It establishes that local density values vary between 0.2 and 0.7 GeV/cm³, sensitive to assumptions about halo and baryonic matter scales.
• The findings critically inform direct dark matter detection experiments and enhance models of Galactic halo dynamics.

Overview of Galactic Dark Matter Density Analysis

This paper evaluates the local dark matter (DM) density in our galaxy, the Milky Way, by analyzing various halo profiles that correspond to the shape of the Galactic DM halo. By utilizing astronomical observations, the authors seek to refine constraints on the DM halo configuration and determine the DM density near the Earth’s location in the galaxy. The insights gained bear significant relevance to understanding the galactic dynamics and informing direct detection DM experiments, where the interaction rate is proportional to the local DM density.

The methodological approach involves parameterizing both the luminous and DM components of the Galactic matter density. Observational constraints used in the analysis include:

1. Total mass of the Galaxy.
2. Total matter density at the Sun’s location.
3. Surface density of visible and total matter traced near the Sun.
4. Solar rotation speed.
5. Shape of the velocity distribution across the Galactic disc and above it.

A key tool in the analysis is a statistical $\chi^2$ fitting of these dynamical constraints to determine the free parameters within their density models. The paper examines both cuspy and cored profiles, accommodating a range of halo shapes seen in astronomical data and recent cosmological simulations.

Results and Interpretations

The paper presents a range of DM densities for a variety of halo configurations. Numerical results highlight a positive correlation between local DM density and the DM halo scale length, contrasted by a negative correlation with the scale length of baryonic matter in the disc. Consequently, the derived local DM density is highly sensitive to the assumed halo profile and its parameters. For a spherical halo, the local density is computed within 0.2 to 0.4 GeV/cm$^3$. The total Galactic mass lends considerable leverage in refining these estimates.

Several bold claims are articulated. The paper posits that non-spherical, oblate halo profiles—or haloes incorporating DM discs consistent with N-body simulation predictions—can produce significantly increased local densities. These profiles underscore the variance in density predictions between 0.2 to 0.7 GeV/cm$^3$, which previously quoted ranges by literature lacked consistency with the potential for dark disk contributions or different halo shapes.

Implications and Speculation

Practically, the determination of local DM density is crucial for direct detection experiments, informing the sigma-mass plane constraints of weakly interacting massive particles (WIMPs). Theoretically, the suggested wide span in potential densities supports more dynamic, tested explorations of DM halo configurations including substructures potentially arising from historical galactic mergers.

Looking forward, advancements in astronomical measurements of stellar motions and improved simulations of baryonic and non-baryonic matter interaction will likely refine local DM density evaluations. Precision in such studies unlocks further scrutiny into distinguishing between cored and cuspy halo profiles and more accurately quantifying the characteristics of potentially substructural components like galactic rings.

In conclusion, the paper emphasizes that despite improved data, substantial uncertainties remain that obscure precise determination of local DM density. These findings encourage future research to reconcile dynamical constraints with simulation outputs, further harmonizing cosmological and galactic dynamics models with observational realities.