Galactic disc heating by density granulation in fuzzy dark matter simulations

Fuzzy dark matter (FDM), an attractive dark matter candidate comprising ultralight bosons (axions) with a particle mass $m_a\sim10^{-22}$ eV, is motivated by the small-scale challenges of cold dark matter and features a kpc-size de Broglie wavelength. Quantum wave interference inside an FDM halo gives rise to stochastically fluctuating density granulation; the resulting gravitational perturbations could drive significant disc thickening, providing a natural explanation for galactic thick discs. Here we present the first self-consistent simulations of FDM haloes and stellar discs, exploring $m_a=0.2-1.2\times10^{-22}$ eV and halo masses $M_\text{h} = 0.7-2.8\times10^{11}$ M$_\odot$. Disc thickening is observed in all simulated systems. The disc heating rates are approximately constant in time and increase substantially with decreasing $m_a$, reaching $dh/dt \simeq 0.04$ ($0.4$) kpc Gyr$^{-1}$ and $d\sigma_z^2/dt \simeq4$ ($150$) km$^2$s$^{-2}$Gyr$^{-1}$ for $m_a=1.2$ ($0.2$) $\times10^{-22}$ eV and $M_\text{h} =7\times10^{10} \text{M}_\odot$, where $h$ is the disc scale height and $\sigma_z$ is the vertical velocity dispersion. These simulated heating rates agree within a factor of two with the theoretical estimates of Chiang et al., confirming that the rough estimate of Church et al. overpredicts the granulation-driven disc heating rate by two orders of magnitude. However, the simulation-inferred heating rates scale less steeply than the theoretically predicted relation $d\sigma^2_z/dt \propto m_a^{-3}$. Finally, we examine the applicability of the Fokker-Planck approximation in FDM granulation modelling and the robustness of the $m_a$ exclusion bound derived from the Galactic disc kinematics.