Exploring Ultralight Dark Matter Self-Coupling via the Gravitational Wave Background

Abstract

Supermassive black hole (SMBH) binary mergers are a primary source of the stochastic gravitational wave background (SGWB) in the nanohertz band, now being actively probed by pulsar timing arrays (PTAs). We investigate how ultralight dark matter (ULDM) with a quartic self-interaction, forming solitonic cores around SMBHs, modifies the SGWB through dynamical friction on the inspiralling binary. Solving the Gross--Pitaevskii--Poisson (GPP) equations numerically for halo masses $M_{\mathrm{halo}}\sim 10^{13}{M}_{\odot }$, we compute self-consistent solitonic density profiles across a range of dimensionless self-coupling parameters $\hat{\lambda }$, covering both attractive and repulsive self-interactions. We find that soliton-induced dynamical friction imprints a characteristic suppression feature in the GW strain spectrum, whose frequency location and depth are sensitive to both the ULDM mass $m$ and the coupling $\hat{\lambda }$. For SMBH masses $M_{\bullet }\sim 10^{8.5}{M}_{\odot }$ and ULDM masses in the range $m\sim (3\times 10^{-22}-2\times 10^{-21})\mathrm{eV}$, current PTA observations from NANOGrav, EPTA, and PPTA may place qualitative limits on the attractive and repulsive self-coupling of ULDM particles. ULDM masses exceeding $\sim 1.6\times 10^{-21}\mathrm{eV}$ are independently excluded by soliton accretion-timescale constraints. These results demonstrate that the nanohertz GW spectrum provides a complementary probe of ULDM self-interactions, operating in a regime distinct from conventional particle-scattering or rotation-curve analyses.

15 pages, 8 figures, Version accepted in Journal of Physics G: Nuclear and Particle Physics