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

Hamish Silverwood, Sofia Sivertsson, Pascal Steger, Justin I. Read, Gianfranco Bertone

Published 2015-07-30Version 1

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 terms describing the couplings of vertical-radial and vertical-axial motions. Using MultiNest we can then fit a dark matter mass profile to tracer density and velocity dispersion data, and derive credible regions on the 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 crucial 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 overestimation of the dark matter density.