Damping of dynamical friction force in self-interacting ultralight dark matter and Fornax timing problem

TL;DR

This study investigates how a damping term in the generalized Gross-Pitaevskii-Poisson description of ultralight dark matter alters dynamical friction acting on globular clusters in the Fornax dwarf spheroidal. By deriving and solving the dynamical friction force with damping, and constructing consistent ULDM density profiles that feature a soliton core plus an isothermal envelope matched to observations, the authors assess GC3’s infall times under various ULDM masses and self-interaction strengths. They find that the damping term typically reduces friction and that, depending on the formation radius and regime (Gaussian vs Thomas–Fermi), the Fornax timing problem can be alleviated for specific ULDM masses, with GC3’s 12 Gyr lifetime achievable in some parameter sets. Overall, the work links ULDM microphysics, core–envelope halo structure, and dynamical friction in a way that yields testable implications for Fornax and similar systems.

Abstract

The dynamics of globular clusters in the Fornax dwarf galaxy pose a challenge for the standard cold dark matter (CDM) and can be used to test other models of dark matter. We study this dynamics in the context of ultralight bosonic dark matter model, accounting for the damping term in a generalized Gross-Pitaevskii equation. Employing analytic formulas for the dynamical friction force, the infall time and evolution of globular clusters are compared in the cases with and without the damping term. It is argued that the damping term plays an important role for the Fornax timing problem in ultralight dark matter models.

Figures (5)

• Figure 1: The dependence of $s$-wave scattering length $a_s$ (in meters) on the mass of the ULDM particle $m$ defined by Eq. \ref{['eq: TF constraint']} for $m> 10^{-21}$ eV and Eq. \ref{['eq: first mass-radius relation']} for $m<10^{-21}$ eV. The dashed vertical line separates the Gaussian density (left) from the TF (right) density approximation.
• Figure 2: Panel a) Fornax mass density profiles $\rho_{DM}$ (in $kg/\textrm{m}^3$). At the inflection points, the soliton dark matter density is stitched together with the NFW density profile. Panel b) Fornax rotation curves for the TF and Gaussian density distributions of ULDM soliton.
• Figure 3: The tangential component of the dimensionless dynamical friction force $\mathcal{F}_t$ as a function of distance from the Fornax dwarf galaxy center for several values of the ULDM boson mass: panel a) taking into account the damping term, panel b) neglecting the damping term ($\xi=0$).
• Figure 4: The trajectory $r(t)$ of the globular cluster GC3 as a function of time in the Gaussian regime and several values of the ULDM boson mass in the range $3.09\cdot 10^{-22}$ eV $<m<$$7\cdot 10^{-22}$ eV with its initial position panel a) $r_0=1$ kpc and panel b) $r_0=1.5$ kpc. The black horizontal line indicates the current position of GC3.
• Figure 5: The trajectory $r(t)$ of the globular cluster GC3 as a function of time in the Thomas-Fermi regime for several values of the ULDM boson mass in the range $10^{-21}$ eV $<m<$$3\cdot 10^{-21}$ eV with its initial position panel a) $r_0=1$ kpc and panel b) $r_0=1.5$ kpc. The black horizontal line indicates the current position of GC3.