Comprehensive Assessment of the Too-Big-to-Fail Problem

TL;DR

This study uses a semi-analytical model and large statistical samples to evaluate the too-big-to-fail problem in dark matter haloes, revealing significant discrepancies with observations if the satellite galaxy inventory is complete down to low velocities.

Contribution

It introduces a new statistical method for assessing the TBTF problem and demonstrates the importance of large samples and proper data analysis in this context.

Findings

Only 1.4% of MW-sized haloes match the MW satellite data above 15 km/s.

The fraction drops below 0.0005 when considering satellites down to 8 km/s.

Discrepancies suggest potential issues with ΛCDM or the need for baryonic effects.

Abstract

We use a semi-analytical model for the substructure of dark matter haloes to assess the too-big-to-fail (TBTF) problem. The model accurately reproduces the average subhalo mass and velocity functions, as well as their halo-to-halo variance, in N-body simulations. We construct thousands of realizations of Milky Way (MW) size host haloes, allowing us to investigate the TBTF problem with unprecedented statistical power. We examine the dependence on host halo mass and cosmology, and explicitly demonstrate that a reliable assessment of TBTF requires large samples of hundreds of host haloes. We argue that previous statistics used to address TBTF suffer from the look-elsewhere effect and/or disregard certain aspects of the data on the MW satellite population. We devise a new statistic that is not hampered by these shortcomings, and, using only data on the 9 known MW satellite galaxies with $V_{\rm max}>15{\rm kms}^{-1}$, demonstrate that $1.4^{+3.3}_{-1.1}\%$ of MW-size host haloes have a subhalo population in statistical agreement with that of the MW. However, when using data on the MW satellite galaxies down to $V_{\rm max}=8{\rm kms}^{-1}$, this MW consistent fraction plummets to $<5\times10^{-4}$ (at 68% CL). Hence, if it turns out that the inventory of MW satellite galaxies is complete down to 8km/s, then the maximum circular velocities of MW satellites are utterly inconsistent with $\Lambda$CDM predictions, unless baryonic effects can drastically increase the spread in $V_{\rm max}$ values of satellite galaxies compared to that of their subhaloes.