Dwarf galaxies united by dark bosons
Alvaro Pozo, Tom Broadhurst, George F. Smoot, Tzihong Chiueh, Hoang Nhan Luu, Mark Vogelsberger, Philip Mocz
Abstract
Low-mass galaxies in the local group are dominated by dark matter and comprise the well-studied ``dwarf spheroidal'' (dSph) class, with typical masses of ${10}^{9}--{10}^{10}{M}_{\ensuremath{\bigodot}}$ and also the equally numerous ``ultrafaint dwarfs'' (UFDs), discovered recently, that are distinctly smaller and denser with masses of only ${10}^{7}--{10}^{8}{M}_{\ensuremath{\bigodot}}$. This bimodality amongst low-mass galaxies contrasts with the scale-free continuity expected for galaxies formed under gravity, as in the standard cold dark matter model for heavy particles. Within each dwarf class we find the core radius ${R}_{c}$ is inversely related to velocity dispersion $\ensuremath{\sigma}$, quite the opposite of standard expectations, but indicative of dark matter in a Bose-Einstein state, where the uncertainty principle requires ${R}_{c}\ifmmode\times\else\texttimes\fi{}\ensuremath{\sigma}$ is fixed by Planck's constant, $h$. The corresponding boson mass, ${m}_{b}=h/{R}_{c}\ensuremath{\sigma}$, differs by one order of magnitude between the UFD and dSph classes, with ${10}^{\ensuremath{-}21.4}\text{ }\text{ }\mathrm{eV}$ and ${10}^{\ensuremath{-}20.3}\text{ }\text{ }\mathrm{eV}$, respectively. The two-boson species is reinforced by parallel relations seen between the central density and radius of UFD and dSph dwarfs, respectively, each matching the steep prediction, ${\ensuremath{\rho}}_{c}\ensuremath{\propto}{R}_{c}^{\ensuremath{-}4}$, for soliton cores in the ground state. Furthermore, soliton cores accurately fit the stellar profiles of UFD and dSph dwarfs where prominent, dense cores appear surrounded by low-density halos, as predicted by our simulations. Multiple bosons may point to a string theory interpretation for dark matter, where a discrete mass spectrum of axions is generically predicted to span many decades in mass, offering a unifying ``axiverse'' interpretation for the observed ``diversity'' of dark matter dominated dwarf galaxies.