An analytical model of surface mass densities of cold dark matter haloes - with an application to MACHO microlensing optical depths

TL;DR

This paper develops an analytical model to quantify biases in surface mass density estimates of dark matter haloes caused by assuming spherical symmetry, with implications for microlensing studies of MACHOs.

Contribution

It introduces an analytical model for surface density scatter due to halo triaxiality and substructure, improving the accuracy of light propagation modeling in dark matter haloes.

Findings

Triaxiality causes up to ±70-80% scatter in surface densities.

Subhaloes increase scatter, especially in galaxy-sized haloes.

The model helps assess the reliability of simplified halo models.

Abstract

The cold dark matter (CDM) scenario generically predicts the existence of triaxial dark matter haloes which contain notable amounts of substructure. However, analytical halo models with smooth, spherically symmetric density profiles are routinely adopted in the modelling of light propagation effects through such objects. In this paper, we address the biases introduced by this procedure by comparing the surface mass densities of actual N-body haloes against the widely used analytical model suggested by Navarro, Frenk and White (1996) (NFW). We conduct our analysis in the redshift range of 0.0 - 1.5. In cluster sized haloes, we find that triaxiality can cause scatter in the surface mass density of the haloes up to sigma_+ = +60% and sigma_- = -70%, where the 1-sigma limits are relative to the analytical NFW model given value. Subhaloes can increase this scatter to sigma_+ = +70% and sigma_- = -80%. In galaxy sized haloes, the triaxial scatter can be as high as sigma_+ = +80% and sigma_- = -70%, and with subhaloes the values can change to sigma_+ = +40% and sigma_- = -80%. We present an analytical model for the surface mass density scatter as a function of distance to the halo centre, halo redshift and halo mass. The analytical description enables one to investigate the reliability of results obtained with simplified halo models. Additionally, it provides the means to add simulated surface density scatter to analytical density profiles. As an example, we discuss the impact of our results on the calculation of microlensing optical depths for MACHOs in CDM haloes.