Scaling relations, dynamical heating and tidal disruption in spin $s$ ultralight dark matter models

Abstract

We explore the impact of spin 0, spin 1 and spin 2 ultralight dark Matter (ULDM) on small scales by numerically solving the Schr\"odinger-Poisson system using the time-split method. We perform simulations of ULDM for each spin, starting with different numbers of identical initial solitons and analyse the properties of the resulting haloes after they merge. Our findings reveal that higher spin lead to broader, less dense haloes with more prominent Navarro-Frenk-White (NFW) tails, a characteristic that persists regardless of the number of solitons involved. Additionally, we study the process of dynamical heating for these haloes, and find that the heating time-scale for higher spin increases order an of magnitude compared to the spin 0 case. Then, we identify scaling relations that describe the density profile, core-NFW of spin~$s$ ULDM haloes as a function of the number of initial solitons $N_{\text{sol}}$. These relations allow us to construct equivalent haloes based on average density or total mass, for arbitrarily large $N_{\text{sol}}$, without having to simulate those systems. We simulate the orbit of an ULDM satellite in a constructed halo treated as an external potential, and find that for host haloes having the same average density, the disruption time of the satellite is as predicted for a uniform sphere regardless of the spin. However, satellites orbiting haloes having the same mass for each spin, result in faster disruption in the case of spin 0, whereas for haloes having the same core size result in faster disruption in the case of spin 2.