Heating and scattering of stellar distributions by ultralight dark matter

TL;DR

This study investigates how ultralight dark matter (ULDM) halos heat embedded stellar populations via wave-induced density fluctuations. Using Schrödinger-Poisson simulations and analytic approximations, the authors quantify four systematic effects: heating by the central soliton, stellar self-gravity, tidal stripping of halos, and tidal-field suppression when the stellar cluster is small compared to the de Broglie wavelength. They validate a quasi-particle framework far from the core, demonstrate the need for soliton-aware modeling near the core, and show that heating rates scale as $f_\mathrm{ULDM}^2$ in the outer halo while becoming mass-independent inside the core. The results illuminate how these effects modify heating-driven ULDM constraints and identify key areas for future work, including tidal disruption studies and regimes where the stellar cluster size is much smaller than the de Broglie wavelength.

Abstract

Due to wave interference, an ultralight light dark matter halo has stochastic, granular substructures which can scatter stars, leading to the heating of stellar distributions. Studies of this phenomenon have placed lower bounds on the ultralight dark matter mass. In this paper we investigate a number of relevant systematic effects, including: (1) the heating by the central soliton, (2) the self-gravity of the stars, (3) the suppression of heating in a tidally stripped halo, and (4) the tidal field suppression of heating when the stellar cluster is much smaller than the de Broglie wavelength. The first three effects are quantified by studying the dynamics of stellar particles in Schrodinger-Poisson simulations of ultralight dark matter halos, while the last effect is studied using analytic approximations.

Figures (16)

• Figure 1: Evolution of an ultralight dark matter field halo. Initial conditions are produced using the eigenmode method and then simulated using the full nonlinear Schrödinger-Poisson equations. Columns show three simulation snapshots. The top and bottom rows show density slices and projections, respectively. The halo is relatively stable throughout its evolution, although the soliton moves randomly around the center. Here the ULDM mass is $m_{22} = 5$, the scale radius is $R_s = 2 \, \mathrm{kpc}$, and scale density is $\rho_0 = 1.89 \times 10^{6} \, \mathrm{M_\odot / kpc^3}$. Slight azimuthal alignments visible in the first snapshot are due to the finite number of eigenfunctions used at initialization. They relax after a few time steps of the simulation.
• Figure 2: Halo density profiles used in halo generation. The target profile, red, is given as a combination of a cuspy NFW profile, green, beyond the core radius and a core profile, blue, inside the core radius. The constructed profile, black, is composed of the best fit sum of weighted eigenmodes of the Hamiltonian given by the potential from the target density profile. Here the ULDM mass is $m_{22} = 5$, the halo profile scale radius is $R_s = 2 \, \mathrm{kpc}$, and scale density is $\rho_0 = 1.89 \times 10^{6} \, \mathrm{M_\odot / kpc^3}$.
• Figure 3: Left: the log density of an ultralight dark matter halo. The red dots superimposed on the density show the projected position of stellar particles. Center: distribution of stellar particle radii embedded in the halo at two different snapshots. Right: Half-light radius of stellar particles overtime. We can see the half-light radius of the particles increases overtime consistent with the heating from the ultralight dark matter halo. In this simulation $m_{22} = 5$ and $f_\mathrm{ULDM} = 0.5$ ($f_\mathrm{ULDM}$ defined in equation \ref{['eqn:define_f']}).
• Figure 4: Halos constructed with different values of $\epsilon_\mathrm{max}$. Left: a halo containing only the central soliton and a few of the next lowest eigenmodes. The granularity is the outer halo is entirely absent. Center: a halo containing the soliton and low energy modes. The granularity in the density has begun to develop, particularly in the vicinity of the core. Right: the benchmark halo. The granular structure is present throughout the halo. $\epsilon_\mathrm{max} \equiv E_\mathrm{max} / |E_0|$ is the maximum energy as a fraction of the ground state energy. Eigenmodes with energy exceeding $E_\mathrm{max}$ are removed in the halo construction.
• Figure 5: Left: the log density of an ultralight dark matter halo. The red dots overlayed on the density show the projected position of stellar particles. Right. Change in half-light radius of stars embedded in evolving ultralight dark matter is plotted (black). This is compared with the same distribution of stars evolving in the analogous NFW profile (red) and in a "frozen" ultralight dark matter halo (green). The latter two simulations do not experience any heating or change in the half-light radius.