The Gravitational-wave Background from Massive Black Holes in the ASTRID Simulation

Abstract Recent pulsar timing array (PTA) observations detected nanohertz gravitational waves, likely originating from massive black hole binaries (MBHBs). The detected amplitude is unexpectedly higher than inferred from the electromagnetic measurements. We present new gravitational-wave background (GWB) results from the ASTRID simulation. Its large volume and on-the-fly dynamics for massive black holes (MBHs) provide new insights into the MBHB population, offering a more accurate assessment of its contribution to the observed GWB. ASTRID predicts a GWB from MBHBs of h c = 2.8 × 10 −15 , or ∼45% of the observed amplitude at ∼4 nHz with a slope consistent with f −2/3 , and h c = 2.5 × 10 −16 with h c ∝ f −1.6 at ∼30 nHz. These predictions remain below current PTA constraints but align with empirical models based on the observed MBH mass functions. By comparison, TNG300 with postprocessed MBH dynamics yields a range between 70% and 90% (20% and 30%) of the observed levels at low (high) frequencies. At low frequencies, ASTRID predicts that the bulk of the GWB originates from MBHBs with masses M tot = 1–3 × 10 9 M ⊙ peaking at z ≈ 0.3, consistent with TNG300. Notably, both simulations predict significant contributions from minor mergers ( q < 0.2) by up to ∼40%. By tracing the full merger trees of local MBHs in ASTRID, we show that they generate gravitational waves at ∼10%–80% of the maximum signal assuming no accretion and recent equal-mass mergers. Finally, we demonstrate the importance of on-the-fly MBH dynamics, the lack of which leads to 3–5 times excessive mass growth by merger, and a boost to the GWB prediction from this overestimated mass function, especially at high frequencies.