Self-interacting dark matter solves the final parsec problem of supermassive black hole mergers

TL;DR

This paper proposes that self-interacting dark matter can facilitate supermassive black hole mergers by providing dynamical friction to overcome the final parsec barrier, also affecting the gravitational wave spectrum.

Contribution

It introduces the idea that dark matter self-interactions resolve the final parsec problem and influence gravitational wave signals from SMBH mergers.

Findings

Self-interacting dark matter can bridge the final parsec in SMBH mergers.

Collisionless cold dark matter disrupts the dark matter spike, preventing merger.

Velocity-dependent self-interactions fit GW data and solve small-scale structure issues.

Abstract

Evidence for a stochastic gravitational wave (GW) background, plausibly originating from the merger of supermassive black holes (SMBHs), is accumulating with observations from pulsar timing arrays. An outstanding question is how inspiraling SMBHs get past the "final parsec" of separation, where they have a tendency to stall before GW emission alone can make the binary coalesce. We argue that dynamical friction from the dark matter (DM) spike surrounding the black holes is sufficient to resolve this puzzle, if the DM has a self-interaction cross section of order $\,$cm$^2$/g. The same effect leads to a softening of the GW spectrum at low frequencies as suggested by the current data. For collisionless cold DM, the friction deposits so much energy that the spike is disrupted and cannot bridge the final parsec, while for self-interacting DM, the isothermal core of the halo can act as a reservoir for the energy liberated from the SMBH orbits. A realistic velocity dependence, such as generated by the exchange of a massive mediator like a dark photon, is favored to give a good fit to the GW spectrum while providing a large enough core. A similar velocity dependence has been advocated for solving the small-scale structure problems of cold DM.