A Study of Warm Dark Matter, the Missing Satellites Problem, and the UV Luminosity Cut-Off

TL;DR

This paper extends warm dark matter predictions below the velocity dispersion cut-off to address the Missing Satellites Problem and UV luminosity cut-off, aligning theory with observations and deriving the Tully-Fisher relation from first principles.

Contribution

It introduces an extension of the Press-Schechter formalism for warm dark matter to lower masses, providing new insights into satellite counts and luminosity limits.

Findings

Predictions match observed satellite counts.

Predictions align with UV luminosity cut-off constraints.

Derived the Tully-Fisher relation from fundamental principles.

Abstract

In the warm dark matter scenario, the Press-Schechter formalism is valid only for galaxy masses greater than the "velocity dispersion cut-off". In this work we extend the predictions to masses below the velocity dispersion cut-off, and thereby address the "Missing Satellites Problem", and the rest-frame ultra-violet luminosity cut-off required to not exceed the measured reionization optical depth. We find agreement between predictions and observations of these two phenomena. As a by-product, we obtain the empirical Tully-Fisher relation from first principles.