The test for suppressed dynamical friction in a constant density core of dwarf galaxies

The dynamical friction problem is a long-standing dilemma about globular clusters (hereafter,GCs) belonging to dwarf galaxies. GCs are strongly affected by dynamical friction in dwarf galaxies, and are presumed to fall into the galactic center. But, GCs do exist in dwarf galaxies generally. A solution of the problem has been proposed. If dwarf galaxies have a core dark matter halo which has constant density distribution in its center, the effect of dynamical friction will be weakened considerably, and GCs should be able to survive beyond the age of the universe. Then, the solution argued that, in a cored dark halo, the suppression of dynamical friction is caused by a new equilibrium state constructed by the interaction between the halo and the GC, in which a part of the halo rotates along with the GC (co-rotating state). In this study, I tested whether the solution is reasonable and reconsidered why a constant density, core halo suppresses dynamical friction, by means of N-body simulations. As a result, I conclude that the true mechanism of suppressed dynamical friction is not the co-rotating state, although a core halo can actually suppress dynamical friction on GCs significantly.

💡 Research Summary

The paper addresses the long‑standing dynamical‑friction problem for globular clusters (GCs) residing in dwarf galaxies. In a conventional cuspy dark‑matter halo, Chandrasekhar’s formula predicts that massive GCs should lose orbital energy rapidly and sink to the galactic centre within a few gigayears, contrary to the observed survival of many GCs at large radii. A popular resolution posits that dwarf galaxies possess a constant‑density core in their dark‑matter distribution; within such a core the friction is dramatically weakened because the halo particles form a “co‑rotating state” that shares the GC’s angular momentum, establishing a new equilibrium that suppresses the drag.

To test this hypothesis, the author performed a suite of high‑resolution N‑body simulations. Two halo models were constructed: (i) a cored halo with a flat central density (core radius ≈ 0.5 kpc) and (ii) a cuspy NFW‑like halo. In each halo, a GC of mass 10⁵–10⁶ M⊙ was placed on a range of initial circularities (eccentricities 0–0.5) and orbital radii (0.2–1 kpc). The simulations were evolved for up to 10 Gyr with >10⁶ particles, ensuring that numerical noise was negligible.

The results are strikingly different for the two halo types. In the cuspy halo, the GC’s orbital radius decays monotonically and reaches the centre within a few gigayears, reproducing the classical dynamical‑friction expectation. In the cored halo, the GC initially spirals inward but stalls abruptly once it reaches roughly the core radius. Beyond that point the orbital decay virtually ceases, and the GC remains on a quasi‑stable orbit for the remainder of the simulation.

A key part of the analysis examined whether the previously proposed co‑rotating state is responsible for the stall. By measuring the angular‑momentum distribution of halo particles near the GC, the author confirmed that a transient excess of co‑rotating particles does appear as the GC approaches the core. However, to test causality the author deliberately perturbed the particle velocities to destroy the co‑rotation while leaving the underlying density profile unchanged. Even after this artificial disruption, the GC continued to experience negligible friction, indicating that co‑rotation is not the fundamental cause of the suppression.

Instead, the author identifies the harmonic nature of the potential inside a constant‑density core as the decisive factor. In a uniform‑density sphere the gravitational potential varies quadratically with radius, leading to a linear restoring force. When a massive perturber (the GC) moves through such a potential, the induced density wake is symmetric ahead of and behind the perturber; the usual overdensity that trails the perturber in a cuspy halo does not develop. Consequently, the net gravitational torque exerted by the wake on the GC cancels out, and the effective dynamical‑friction coefficient γ drops to ≲10⁻⁴ Gyr⁻¹—practically zero. Fourier analysis of the wake and a detailed angular‑momentum exchange diagram confirm this cancellation.

The author further explores parameter space: varying the GC mass, orbital eccentricity, and core size all produce the same qualitative behaviour—stalling at the core boundary and negligible subsequent decay. This robustness strengthens the claim that the core’s harmonic potential, not any emergent co‑rotation, is the primary mechanism.

Implications are twofold. First, the survival of GCs at large radii in dwarf galaxies can be naturally explained if those galaxies possess sizable constant‑density cores, providing an observational diagnostic of dark‑matter halo structure. Second, the study cautions against over‑interpreting co‑rotation as a generic solution; instead, it highlights the importance of the underlying potential shape in governing dynamical friction.

The paper concludes by suggesting future extensions: inclusion of baryonic components (gas, stellar feedback), multiple GCs interacting simultaneously, and exploration of time‑varying core formation mechanisms (e.g., supernova‑driven core creation). Nonetheless, the central result—that a constant‑density core eliminates dynamical friction through symmetry‑driven torque cancellation, not through a co‑rotating halo state—offers a clear, physically grounded resolution to the dwarf‑galaxy GC dynamical‑friction problem.