Warm, not Fuzzy: Generalized Ultralight Dark Matter Limits from Milky Way Satellites

TL;DR

This paper extends limits on ultralight scalar dark matter particle mass by analyzing Milky Way satellite data, accounting for wave interference effects and free-streaming suppression in the matter power spectrum.

Contribution

It introduces a generalized model for ultralight dark matter with a peaked power spectrum and derives new constraints on particle mass considering wave interference and free-streaming effects.

Findings

Lower bound on dark matter mass: >6×10^{-18} eV for certain wavenumbers.

Wave interference effects can weaken constraints for smaller wavenumbers.

Constraints depend on the peak wavenumber of the dark matter power spectrum.

Abstract

We generalize lower limits on the dark matter (DM) particle mass $m$ derived from Milky Way (MW) satellite galaxy abundances to scenarios in which DM is an ultralight scalar field produced with a field power spectrum peaked at a subhorizon wavenumber $k_*$. In these models, the DM field free-streams similar to warm dark matter while also exhibiting significant small-scale wave interference effects. The resulting dimensionless density power spectrum shows two effects: (i) free-streaming suppression at $k_{\rm fs}\sim k_{\rm eq}/[(k_*/a_{\rm eq}m)\ln(a_{\rm eq}m/k_*)]$; (ii) Poisson-like enhancement related to wave interference, at $k\gtrsim10^{-2}k_*$, which saturates near the Jeans scale $k_{\rm J}\sim k_{\rm eq}/(k_*/a_{\rm eq}m)$. Comparing these predictions with established constraints on a free-streaming cutoff in the linear matter power spectrum from the MW satellite population, we obtain $m>6\times10^{-18}\,{\rm eV}\,(k_*/10^4\,{\rm Mpc}^{-1})$ for $k_*>10^4\,{\rm Mpc}^{-1}$ at 95\% confidence. For smaller $k_*$, Poisson-noise enhancement on MW satellite scales weakens the constraint, yielding $m>6\times10^{-18}\,{\rm eV}\,(k_*/10^4\,{\rm Mpc}^{-1})^2$ for $k_*<10^4\,{\rm Mpc}^{-1}$ at 95\% confidence.