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

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 $k_{\ast }$. In these models, the DM field free-streams similarly to warm DM while also exhibiting significant small-scale wave interference effects. The resulting dimensionless density power spectrum shows two effects: (i) free-streaming suppression at $k_{\mathrm{fs}}\sim k_{\mathrm{eq}}/[(k_{\ast }/a_{\mathrm{eq}}m)\ln (a_{\mathrm{eq}}m/k_{\ast })]$; (ii) Poisson-like enhancement related to wave interference at $k\gtrsim 10^{-2}{k}_{\ast }$, which saturates near the Jeans scale $k_{\mathrm{J}}\sim k_{\mathrm{eq}}/(k_{\ast }/a_{\mathrm{eq}}m)$. Comparing these predictions with established constraints on a free-streaming cutoff in the linear matter power spectrum from the MW satellite population and assuming that warm ultralight DM does not change the form of the galaxy--halo connection relative to cold DM, we obtain $m>6\times 10^{-18}\mathrm{eV}(k_{\ast }/10^4{\mathrm{Mpc}}^{-1})$ for $k_{\ast }>10^4{\mathrm{Mpc}}^{-1}$ at 95% confidence. For smaller $k_{\ast }$, Poisson-noise enhancement on MW satellite scales weakens the constraint, yielding $m>6\times 10^{-18}\mathrm{eV}(k_{\ast }/10^4{\mathrm{Mpc}}^{-1}{)}^2$ for $k_{\ast }<10^4{\mathrm{Mpc}}^{-1}$ at 95% confidence.

9 pages, 3 figures; updated to published version

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