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Dynamical friction for circular orbits in self-interacting ultralight dark matter and Fornax globular clusters

Hyeonmo Koo, Jae-Weon Lee

Abstract

We investigate the impact of repulsive self-interaction in ultralight dark matter (ULDM) on dynamical friction in circular orbits in ULDM halos and its implications for the Fornax dwarf spheroidal (dSph) galaxy's globular clusters. Using the Gross-Pitaevskii-Poisson equations, we derive the dynamical friction force considering soliton density profiles for both non-interacting and strongly self-interacting ULDM. Our results show that self-interactions reduce the dynamical friction effect further than both the non-interacting ULDM and standard cold dark matter models. Furthermore, we derive the low Mach number approximation to simplify the analysis in the subsonic motion, where the tangential component of dynamical friction dominates. Applying these findings to the Fornax dSph, we calculate the infall timescales of globular clusters, demonstrating that strong self-interaction can address the timing problem more effectively. We constrain the parameter space for ULDM particle mass and self-coupling constant, which are consistent with other constraints from astronomical and cosmological observations.

Dynamical friction for circular orbits in self-interacting ultralight dark matter and Fornax globular clusters

Abstract

We investigate the impact of repulsive self-interaction in ultralight dark matter (ULDM) on dynamical friction in circular orbits in ULDM halos and its implications for the Fornax dwarf spheroidal (dSph) galaxy's globular clusters. Using the Gross-Pitaevskii-Poisson equations, we derive the dynamical friction force considering soliton density profiles for both non-interacting and strongly self-interacting ULDM. Our results show that self-interactions reduce the dynamical friction effect further than both the non-interacting ULDM and standard cold dark matter models. Furthermore, we derive the low Mach number approximation to simplify the analysis in the subsonic motion, where the tangential component of dynamical friction dominates. Applying these findings to the Fornax dSph, we calculate the infall timescales of globular clusters, demonstrating that strong self-interaction can address the timing problem more effectively. We constrain the parameter space for ULDM particle mass and self-coupling constant, which are consistent with other constraints from astronomical and cosmological observations.
Paper Structure (12 sections, 42 equations, 3 figures, 2 tables)

This paper contains 12 sections, 42 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. ultralight dark matter models and their soliton profiles
  3. Dynamical friction
  4. Ultralight dark matter over-density from Madelung formalism
  5. Calculation of dynamical friction force
  6. Low-Mach number approximation of dynamical friction coefficient
  7. Dynamical friction coefficient for non-interacting limit
  8. Application to Fornax globular clusters
  9. Infall timescale for leading-order approximation
  10. Summary
  11. Validity of the Thomas-Fermi limit through dimensional analysis
  12. Evaluating leading-order term in $S_{\ell,\ell-1}^m$

Figures (3)

  • Figure 1: Tangential DF coefficients for $\ell_q \mathcal{M}=3$ (red), 2 (blue), and their leading-order term (black dashed). For subsonic motion (shaded region), this term could mainly illustrates the behavior of full-order calculation, better for lower $\ell_q \mathcal{M}$.
  • Figure 2: Contours of infall timescales 5, 10, 20 Gyr for full-order (solid) and leading-order (dashed) calculations are plotted in the $(m_\phi,~\lambda)$ parameter space for GC3 (left) and GC4 (right). The shaded regions correspond to the central density of Fornax dSph, satisfying $\rho_c \geq 10^{-3},~10^{-2},~10^{-1},~1 \ M_\odot / \mathrm{pc}^3$.
  • Figure 3: Direct comparison between the full-order infall timescales of GC3 (solid) and GC4 (dotted).