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

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.