Self-Interacting Dark Matter Solves the Final Parsec Problem of Supermassive Black Hole Mergers

Area of Science:

• Astrophysics
• Cosmology
• Particle Physics

Background:

• Pulsar timing arrays suggest a stochastic gravitational wave (GW) background, likely from supermassive black hole (SMBH) mergers.
• A key challenge is understanding how SMBH binaries overcome the 'final parsec problem' where inspiral stalls before GW emission alone can cause coalescence.

Purpose of the Study:

• To investigate if dynamical friction from dark matter (DM) spikes can resolve the final parsec problem for SMBH binaries.
• To explore the implications of DM self-interactions on the GW spectrum.

Main Methods:

• Theoretical modeling of dynamical friction exerted by DM spikes on inspiraling SMBH binaries.
• Analysis of the GW spectrum resulting from SMBH mergers under different DM models (collisionless vs. self-interacting).

Main Results:

• Dynamical friction from a self-interacting dark matter (SIDM) spike, with a self-interaction cross-section around 1 cm²/g, can facilitate SMBH binary coalescence.
• This mechanism naturally explains the observed softening of the stochastic GW background spectrum at low frequencies.
• Collisionless cold dark matter (CDM) is insufficient as it disrupts the DM spike.

Conclusions:

• Self-interacting dark matter provides a viable solution to the final parsec problem for SMBH mergers.
• The properties of SIDM, particularly its velocity dependence, are crucial for matching current GW observations and potentially resolving small-scale structure issues in cosmology.