Non-parametric uncertainties in the dark matter velocity distribution

TL;DR

This paper explores how uncertainties in the dark matter velocity distribution affect direct detection limits, introducing a Bayesian prior and a novel approximation to marginalize over these uncertainties, with minimal impact for masses above 60 GeV.

Contribution

It develops a new method to incorporate velocity distribution uncertainties into dark matter detection analyses, bridging halo-dependent and halo-independent approaches.

Findings

Limits are robust above 60 GeV mass.

Uncertainty can weaken limits by less than an order of magnitude.

Anisotropic distributions can weaken limits by up to two orders of magnitude.

Abstract

We investigate the impact of uncertainty in the velocity distribution of dark matter on direct detection experiments. We construct an multinomial prior with a hyperparameter $\beta$ that describes the strength of our belief in an isotropic Maxwell-Boltzmann velocity distribution. By varying $\beta$, we interpolate between a halo-independent and halo-dependent analysis. We present a novel approximation for the marginalisation of this prior that is applicable to any counting experiment. With this formula, we investigate the impact of the uncertainty in limits from XENON1T. For dark matter masses greater than about 60 GeV, we find extremely mild sensitivity to the distribution. Below about 60 GeV, the limit weakens by less than an order of magnitude if we assume an isotropic distribution in the galactic frame. If we permit anisotropic distributions, the limit further weakens, but at most by about two orders of magnitude. Lastly, we check the impact of parametric uncertainties and discuss the possible inclusion and impact of our technique in global fits.