A non-parametric method for measuring the local dark matter density

TL;DR

This paper introduces a non-parametric, noise-reducing method for measuring local dark matter density using stellar kinematic data, accounting for the tilt term and avoiding numerical differentiation.

Contribution

The paper presents a novel one-dimensional method that incorporates the tilt term and reduces numerical noise in estimating dark matter density from stellar kinematics.

Findings

The method successfully estimates dark matter density from mock data.

Ignoring the tilt term leads to systematic underestimation.

The approach is effective for tracers up to 1 kpc above the disc.

Abstract

We present a new method for determining the local dark matter density using kinematic data for a population of tracer stars. The Jeans equation in the $z$-direction is integrated to yield an equation that gives the velocity dispersion as a function of the total mass density, tracer density, and the tilt term that describes the coupling of vertical and radial motions. We then fit a dark matter mass profile to tracer density and velocity dispersion data to derive credible regions on the vertical dark matter density profile. Our method avoids numerical differentiation, leading to lower numerical noise, and is able to deal with the tilt term while remaining one dimensional. In this study we present the method and perform initial tests on idealised mock data. We also demonstrate the importance of dealing with the tilt term for tracers that sample $\gtrsim 1$ kpc above the disc plane. If ignored, this results in a systematic underestimation of the dark matter density.