Fuzzy Dark Matter and Dark Matter Halo Cores

Abstract: Whereas cold dark matter (CDM) simulations predict central dark matter cusps with densities that diverge as $\rho$(r)$\sim$ 1/r observations often indicate constant density cores with finite central densities $\rho_0$ and a flat density distribution within a core radius r$0$. This paper investigates whether this core-cusp problem can be solved by fuzzy dark matter (FDM), a hypothetical particle with a mass of order m$\approx$10$^{-22}$eV and a corresponding de Broglie wavelength on astrophysical scales. We show that galaxies with CDM halo virial masses M${vir} \leq 10^{11}$M$_{\odot}$ follow two core scaling relations. In addition to the well known universal core column density $\Sigma_0 \equiv \rho_0 \times$r$0$ = 75 M${\odot}$pc$^{-2}$ core radii increase with virial masses as r$0 \sim$ M${vir}^{\gamma}$ with $\gamma$ of order unity. Using the simulations by Schive et al. (2014) we demonstrate that FDM can explain the r$0$-M${vir}$ scaling relation if the virial masses of the observed galaxy sample scale with formation redshift z as M$_{vir}\sim$(1+z)$^{-0.4}$. The observed constant $\Sigma_0$ is however in complete disagreement with FDM cores which are characterised by a steep dependence $\Sigma_0 \sim$r$_0^{-3}$, independent of z. More high-resolution simulations are now required to confirm the Schive et al. simulations and explore especially the transition region between the soliton core and the surrounding halo. If these results hold, FDM can be ruled out as the origin of observed dark matter cores and other physical processes are required to account for their formation.