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ABSTRACT Self-interacting dark matter (SIDM) has been proposed to solve small-scale problems in CDM cosmology. In previous work, constraints on the self-interaction cross-section of dark matter have been derived assuming that the self-interaction cross-section is independent of velocity. However, a velocity-dependent cross-section is more natural in most theories of SIDM. Using idealized N-body simulations without baryons, we study merging clusters with velocity-dependent SIDM. In addition to the usual rare scattering in the isotropic limit, we also simulate these systems with anisotropic, small-angle (frequent) scatterings. We find that the collisionless brightest cluster galaxy (BCG) has an offset from the DM peak that grows at later stages. Finally, we also extend the existing upper bounds on the velocity-independent, isotropic self-interaction cross-section to the parameter space of rare and frequent velocity-dependent self-interactions by studying the central densities of dark matter-only isolated haloes. For these upper-bound parameters, the DM-BCG offsets just after the first pericentre in the dark matter-only simulations are found to be ≲10 kpc. On the other hand, because of BCG oscillations, we speculate that the distribution of BCG offsets in a relaxed cluster is a statistically viable probe. Therefore, this motivates further studies of BCG off-centring in hydrodynamic cosmological simulations.
Sabarish et al. (Sat,) studied this question.