Heating of Milky Way disc Stars by Dark Matter Fluctuations in Cold Dark Matter and Fuzzy Dark Matter Paradigms

Abstract: Although highly successful on cosmological scales, Cold Dark Matter (CDM) models predict unobserved over-dense \squote{cusps} in dwarf galaxies and overestimate their formation rate. We consider an ultra-light axion-like scalar boson which promises to reduce these observational discrepancies at galactic scales. The model, known as Fuzzy Dark Matter (FDM), avoids cusps, suppresses small-scale power, and delays galaxy formation via macroscopic quantum pressure. We compare the substructure of galactic dark matter halos comprised of ultra-light axions with masses $10^{-24} \mathrm{eV} \leq m_a \leq 10^{-18} \mathrm{eV}$ to conventional CDM results. Besides self-gravitating subhalos, FDM includes additional substructure in the form of non-virialized over-dense wavelets formed by quantum interference patterns which provide a more efficient source of heating to galactic discs than do subhalos. We find that, in the solar neighborhood, wavelet heating is sufficient to give the oldest disc stars a velocity dispersion in excess of $30 \: \mathrm{km} \: \mathrm{s}^{-1}$ within a Hubble time if all energy delivered to the disc goes into velocity dispersion. Furthermore, we calculate the radius-dependent disc velocity dispersion and corresponding scale height caused by the heating of dynamical substructure in both CDM and FDM with the determination that these effects will produce a flaring that terminates the Milky Way disc at $15 - 20 \: \mathrm{kpc}$. Although the source of thickened discs is not known with any certainty, the heating due to perturbations caused by dark substructure cannot exceed the total disc velocity dispersion. Therefore, this work provides a lower bound on the FDM particle mass of $m_a > 0.57 \times 10^{-22} \mathrm{eV}$. FDM wavelets should be considered a viable mechanism for producing the observed disc thickening with time.