Internal kinematics of dwarf galaxies orbitally moving in ultralight dark matter

TL;DR

This paper investigates how torques act on dwarf galaxies orbiting the Milky Way in ultralight dark matter (ULDM) halos and how these torques influence internal kinematics. The authors model dwarfs as deformed Plummer spheres on circular orbits with a misalignment angle $\theta$ and derive analytic expressions for two main torques: (i) the dynamical-friction torque arising from ULDM linear response, including a damping term with strength $\xi$ and a sound speed $c_s$, and (ii) the tidal torque generated by the Milky Way potential. They show that the tidal torque, quantified by a dimensionless $T_g$, dominates the inner ULDM friction torque $T_{inner}$ by about 3–4 orders of magnitude for the dwarfs studied, implying tides primarily govern the internal kinematics, with the inner torque only becoming relevant in mergers or nearly coalescing systems. The study also finds that the tidal torque yields a misalignment-dependent restoring force near equilibrium, leading to small-angle oscillations with frequencies $\omega$ and periods ranging from a few hundred Myr to several Gyr, depending on the dwarf’s structure and orbit. These results have implications for interpreting dwarf galaxy kinematics in the Milky Way halo and motivate future work on non-circular or large-amplitude rotations and more detailed dynamical modeling.

Abstract

For dwarf galaxies modeled as deformed Plummer spheres and orbitally moving in ultralight dark matter halo of the Milky Way, the torque induced by the dynamical friction force is determined. The impact of this torque, as well as the torque produced by the gravitational force of the Milky Way, on the internal kinematics of dwarf galaxies is studied. Possible oscillations of dwarf galaxies caused by the tidal torque and misalignment of dwarf galaxies with respect to their equilibrium position are investigated and the corresponding frequencies and periods of oscillations are found.

Figures (3)

• Figure 1: Schematics of the plane of an orbiting dwarf galaxy modeled as a deformed Plummer sphere.
• Figure 2: Dimensionless inner torque $T_\text{inner}$ as a function of angle $\theta$ for dwarf galaxies UmiI, UmaI, FnxI, CarI, and WilI.
• Figure 3: Left panel: Dimensionless tidal torque $T_g$ as a function of $\theta$ for dwarf galaxies UmiI, UmaI, FnxI, CarI, and WilI. Dashed lines correspond to the linear approximation $T_g=-\alpha\,\theta$ with values of $\alpha$ listed in Table \ref{['tab:2']}. Right panel: Dimensionless tidal torque $T$ as a function of $r_0/l_p$ for $a=2$, $b=0.8$, $\theta=0.2$ rad (black solid line) and $\theta=0.5$ rad (red dashed line) with points defined numerically using Eq. (\ref{['T']}) and the straight lines are linear approximations.