The dark matter density at the Sun's location

TL;DR

This paper tackles the challenge of estimating the local dark matter density $\rho_\odot$ without resorting to global Galactic mass modeling. It introduces a model-independent method based on centrifugal equilibrium, modeling the Milky Way as a Freeman exponential disk plus a spherical DM halo and deriving an analytic expression for $\rho_\odot$ in terms of local observables such as the angular velocity $\omega$, the RC slope $\alpha_\odot$, the disk fraction $\beta$, and the disk-halo geometry via $r_{\odot D}$. The authors obtain a central value $\rho_\odot = 0.43$ GeV cm$^{-3}$ with uncertainties dominated by $\alpha_\odot$ and $r_{\odot D}$, and show that corrections for halo oblateness and disk thickness are small. The method avoids the degeneracies of global mass modeling and provides a readily updateable framework as measurements improve, making the result particularly useful for interpreting direct and indirect dark matter searches. Overall, the work delivers a reliable, analytic estimate of the local DM density anchored in local kinematics rather than global Galactic modeling.

Abstract

We derive the value of the dark matter density at the Sun's location (rho_0) without globally mass-modeling the Galaxy. The proposed method relies on the local equation of centrifugal equilibrium and is independent of i) the shape of the dark matter density profile, ii) knowledge of the rotation curve from the galaxy center out to the virial radius, and iii) the uncertainties and the non-uniqueness of the bulge/disk/dark halo mass decomposition. The result can be obtained in analytic form. It explicitly includes the dependence on the relevant observational quantities and takes their uncertainties into account. By adopting the reference, state-of-the-art values for these, we find rho_0 = 0.43(11)(10)GeV/cm3, where the quoted uncertainties are respectively due to the uncertainty in the slope of the circular-velocity at the Sun location and the ratio between this radius and the length scale of the stellar exponential thin disk. We obtain a reliable estimate of rho_0, that, in addition, is ready to take into account any future change/improvement in the measures of the observational quantities it depends on.

Figures (3)

• Figure 1: Effect of the DM halo oblateness $q$.
• Figure 2: Effect of the disk thickness $z_0$.
• Figure 3: Different estimates of the circular velocity of the Milky Way, resulting from the global mass model of cu09. These are obtained from the gravitational potential (solid line), the HI terminal velocities Malhotra95 (blue points), and velocity dispersions xue08 (black points).