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 $k_{\ast }$. 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 $k_{\mathrm{f}\mathrm{s}}\sim k_{\mathrm{e}\mathrm{q}}\mathrm{/}[(k_{\ast }\mathrm{/}{a}_{\mathrm{e}\mathrm{q}}m)\ln (a_{\mathrm{e}\mathrm{q}}m\mathrm{/}{k}_{\ast })]$; (ii) Poisson-like enhancement related to wave interference, at $k\gtrsim {10}^{-2}{k}_{\ast }$, which saturates near the Jeans scale $k_{\mathrm{J}}\sim k_{\mathrm{e}\mathrm{q}}\mathrm{/}(k_{\ast }\mathrm{/}{a}_{\mathrm{e}\mathrm{q}}m)$. Comparing these predictions with established constraints on a free-streaming cutoff in the linear matter power spectrum from the MW satellite population, we obtain $m>6\times {10}^{-18}\mathrm{e}\mathrm{V}(k_{\ast }\mathrm{/}{10}^4{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1})$ for $k_{\ast }>{10}^4{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ at 95% confidence. For smaller $k_{\ast }$, Poisson-noise enhancement on MW satellite scales weakens the constraint, yielding $m>6\times {10}^{-18}\mathrm{e}\mathrm{V}(k_{\ast }\mathrm{/}{10}^4{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}{)}^2$ for $k_{\ast }<{10}^4{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ at 95% confidence.