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

TL;DR

This paper investigates how ultralight dark matter (ULDM) with spins $s=0,1,2$ shapes small-scale structure, focusing on soliton mergers, final halo density profiles, and satellite dynamics. It solves the non-relativistic Schrödinger-Poisson system for multi-component spin states, evolves ensembles of merging solitons, and derives scaling relations that map initial soliton properties to the final core and NFW-tail parameters. The study finds that spin $0$ yields denser, more compact cores with broader tails, while higher spins produce smoother cores and less pronounced interference, resulting in longer dynamical-heating timescales and distinct tidal-disruption behaviours for satellites. By establishing power-law scaling relations linking $N_{ ext{sol}}$ to core densities and tail radii, the authors construct equivalent ULDM haloes across spins for fixed mass or core size, enabling robust cross-spin comparisons and potential observational tests. The work advances a framework to interpret small-scale structure and satellite evolution in ULDM models, with implications for addressing tensions in dwarf-galaxy dynamics and globular-cluster survival, and lays groundwork for incorporating self-interactions in future studies.

Abstract

We explore the impact of spin 0, spin 1 and spin 2 ultralight dark Matter (ULDM) on small scales by numerically solving the Schrödinger-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.

Figures (26)

• Figure 1: Evolution of the ratio $W/\abs{E}$ as a function of $t/\tau_{\text{dyn}}$ for spin $0$, spin $1$ and spin $2$ models with $N_\text{sol}=25$.
• Figure 2: Left panel. Density profiles for each type of spin $s$ simulation in the range $10<N_\text{sol}\leq120$, constructed via spherical averaging. The thin curves denote the density profile for a given $N_\text{sol}$ and different spin-$s$. The solid lines correspond to the radial average of each model and are sorted from top to bottom at small radii for spin $0$ (blue), spin $1$ (red), and spin $2$ (green). The vertical black dashed line represents the spatial resolution. The mass of the ULDM particles is $m_s=2.5\times 10^{-22}$ eV, and the mass of each soliton is $M=5.31\times 10^7 M_{\odot}$. Right panel. Density profile normalised by the maximum density value $\rho_c^f$ as a function of the radius normalised by $r_c^f$. The reference soliton configuration (using $r_c = \rho_c =1$ in \ref{['eq: join_profile']}) is shown for comparison. The ordering at large radii is inverted.
• Figure 3: The solid lines represent the density of dark matter computed directly from simulations, showing the $N_{\text{sol}} = 25$ case. The dashed lines show the best fits obtained from Eq. \ref{['eq: sol']} and Eq. \ref{['eq: nfw']} and the scaling relations discussed in Sec. \ref{['sec: URSDP']}. The solitonic cores are displayed with fainter lines for comparison.
• Figure 4: The normalised core spin $\boldsymbol S_{\text{core}}/N_{\text{core}}$ versus normalised total spin $\boldsymbol S_{\text{tot}}/N_{\text{tot}}$. The bars indicate the standard deviation for all the simulations, and the points represent the binned average data. The trianles correspond to spin $1$ and solid circles to spin $2$.
• Figure 5: Stability test of the stellar system evolved with our particle-mesh $N$-body code. The system remains stable over 1 Gyr, justifying its use as initial conditions for the study of dynamical heating.