Ultralight Dark Matter Constraints from NanoHertz Gravitational Waves

Abstract

We investigate the impact of ultralight dark matter (ULDM) on the mergers of supermassive black holes (SMBH) and the resulting stochastic gravitational wave background. ULDM is based on exceptionally light particles and yields galactic halos with dense central solitons. This increases the drag experienced by binary SMBH, decreasing merger times and potentially suppressing gravitational radiation from the binary at low frequencies. We develop semi-analytic models for the decay of SMBH binaries in ULDM halos and use current pulsar timing array (PTA) measurements to constrain the ULDM particle mass and its fractional contribution to the dark matter content of the universe. We find a median ULDM particle mass of $7. \times 10^{-22}$ eV and show that scaling relations suggest that the drag remains effective at relatively low ULDM fractions, which are consistent with all other constraints on the model. Consequently, future pulsar timing measurements will be a sensitive probe of any ULDM contribution to the overall dark matter content of the universe.

Figures (8)

• Figure 1: (Top) Central densities as a function of time for an equal mass binary (blue), a binary with mass ratio $1:3$ (orange), and a stationary central black hole (green); the total SMBH mass is $10 M_s$. For the equal mass case, the initial radius is 0.015pc; the unequal mass case has 0.03pc and 0.01pc; $r_c\approx 0.0296$pc. The central densities of the binaries oscillate but are near the single black hole value. (Bottom) Radial density profiles at $t\sim 0.264$kyr.
• Figure 2: Posterior distribution of model parameters with 68% and 95% confidence interval contours for the realistic model. Reported values correspond to the medians and their 68% credible intervals.
• Figure 3: Posterior distribution for the simple model; other settings match those of Figure \ref{['fig:posterior1']}.
• Figure 4: The joint posterior for the ULDM particle mass and fraction is shown alongside existing constraints, as summarized in Ref. Lazare:2024uvj. Dark blue and blue lines show 68 and 95% confidence intervals, respectively; the realistic and simple models are shown with solid and dashed lines, respectively.
• Figure 5: The dark blue line corresponds to the best-fit spectra for the realistic ULDM model; the dashed blue line represents the simple model. The purple line is the gravitational wave-only model from Agazie2023. Grey violins are the 15-year NANOGrav data. Shaded regions around the lines highlight the 95% credible regions.