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Analytic calculation of dynamical friction for Plummer sphere in ultralight dark matter

O. V. Barabash, T. V. Gorkavenko, V. M. Gorkavenko, O. M. Teslyk, N. S. Yakovenko, A. O. Zaporozhchenko, E. V. Gorbar

TL;DR

This work analyzes dynamical friction on extended bodies moving through ultralight dark matter in a Bose-Einstein condensate, modeling the probe as a Plummer sphere with radius $l_p$. Using linear response theory, it derives analytic expressions for the radial and tangential friction components, reproducing the point-probe limit as $l_p\to 0$ and presenting a detailed calculation of the key quantity $S^{m_l}_{\ell,\ell-1}$ via contour integration. A non-monotonic dependence of the friction on the DM particle mass $m$ is found in the range $10^{-23}$–$10^{-21}$ eV, with finite-size effects increasing for larger $l_p/r_0$ and $m$, offering practical tools for modeling globular clusters and dwarf galaxies in ULDM halos. The results enable efficient, analytic modeling of extended-body orbital dynamics in ULDM and motivate future work on wave-related granulation effects in the outer halos.

Abstract

The dynamical friction force acting on a spatially extended probe (globular clusters and dwarf galaxies) moving in the environment of ultralight bosonic dark matter in the state of the Bose-Einstein condensate is determined. Modeling the probe as a Plumer sphere of radius $l_p$, the radial and tangential components of the dynamic friction force are found in an analytic form, which reduce in the limit $l_p \to 0$ to the corresponding analytic expressions obtained in the literature in the case of a point probe. The dependence of the dynamical friction force on boson particle mass $m$ was analyzed and found to be non-monotonous in the interval $10^{-23} - 10^{-21}$eV.

Analytic calculation of dynamical friction for Plummer sphere in ultralight dark matter

TL;DR

This work analyzes dynamical friction on extended bodies moving through ultralight dark matter in a Bose-Einstein condensate, modeling the probe as a Plummer sphere with radius . Using linear response theory, it derives analytic expressions for the radial and tangential friction components, reproducing the point-probe limit as and presenting a detailed calculation of the key quantity via contour integration. A non-monotonic dependence of the friction on the DM particle mass is found in the range – eV, with finite-size effects increasing for larger and , offering practical tools for modeling globular clusters and dwarf galaxies in ULDM halos. The results enable efficient, analytic modeling of extended-body orbital dynamics in ULDM and motivate future work on wave-related granulation effects in the outer halos.

Abstract

The dynamical friction force acting on a spatially extended probe (globular clusters and dwarf galaxies) moving in the environment of ultralight bosonic dark matter in the state of the Bose-Einstein condensate is determined. Modeling the probe as a Plumer sphere of radius , the radial and tangential components of the dynamic friction force are found in an analytic form, which reduce in the limit to the corresponding analytic expressions obtained in the literature in the case of a point probe. The dependence of the dynamical friction force on boson particle mass was analyzed and found to be non-monotonous in the interval eV.

Paper Structure

This paper contains 5 sections, 53 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Dynamical friction force for circularly moving Plummer sphere
  3. Analytic calculation of $S_{\ell,\ell_1}^{m_l}$
  4. Dependence of dynamical friction force on boson particle mass
  5. Conclusions

Figures (2)

  • Figure 1: Poles of the integrand in $J$ in the complex plane $k$ for $m_l>0$ (left panel) and $m_l<0$ (right panel).
  • Figure 2: Tangential (left panel) and radial (right panel) components of the dimensionless dynamical friction force $\vec{\mathcal{F}}$ given by Eq.\ref{['FDF1']} as a function of the mass of the dark matter particle $m$ in the interval $10^{-23} - 10^{-21}$eV at fixed orbital radius $r_0$ for a point probe and the Plummer sphere for a typical globular cluster in the Fornax dwarf galaxy.