Although highly successful on cosmological scales , Cold Dark Matter ( CDM ) models predict unobserved over-dense ‘ 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 and density fluctuations of galactic dark matter haloes comprised of ultra-light axions to conventional CDM results .
Besides self-gravitating subhaloes , FDM includes non-virialized over-dense wavelets formed by quantum interference patterns which are an efficient source of heating to galactic discs .
We find that , in the solar neighborhood , wavelet heating is sufficient to give the oldest disc stars a velocity dispersion of \sim \SI { 30 } { \kilo \meter \per \second } within a Hubble time if energy is not lost from the disc , the velocity dispersion increasing with stellar age as \sigma _ { D } \propto t ^ { 0.4 } in agreement with observations .
Furthermore , we calculate the radius-dependent velocity dispersion and corresponding scale height caused by the heating of this dynamical substructure in both CDM and FDM with the determination that these effects will produce a flaring that terminates the Milky Way disc at \SIrange { 15 } { 20 } { \kilo \parsec } .
Although the source of thickened discs is not known , the heating due to perturbations caused by dark substructure can not exceed the total disc velocity dispersion .
Therefore , this work provides a lower bound on the FDM particle mass of m _ { a } > \SI { 0.6 e - 22 } { \electronvolt } .
Furthermore , FDM wavelets with this particle mass should be considered a viable mechanism for producing the observed disc thickening with time .