The Gravitational Wave Background from Massive Black Holes in the ASTRID Simulation

Abstract: Recent pulsar timing array (PTA) observations have 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 dynamical friction for 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 $h_c=2.8\times10^{-15}$, or $\sim45\%$ of the observed amplitude at $\sim 4\,{\rm nHz}$ and $h_c=2.5\times10^{-16}$ ($5\%$) with $h_c\propto f^{-1.6}$ at $\sim 30\,{\rm nHz}$. These predictions remain below current PTA constraints but align with previous empirical models based on the observed MBH mass functions. By comparison, TNG300 with post-processed MBH dynamics yields a range between $70-90\%$ ($20\% - 30\%$) of the observed levels at low (high) frequencies. At low frequencies, ASTRID predicts that the bulk of the GWB originates from MBHB with masses $M_{\rm tot}=1-3\times 10^9\,M_\odot$ peaking at $z\approx 0.3$, consistent with TNG300. Notably, both simulations predict significant GWB contribution from minor mergers ($q<0.2$) by up to $\sim 40\%$. By tracing the full merger trees of local MBHs in ASTRID, we show that they generate GWs at $\sim 10\%-80\%$ 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 similar boost to the GWB prediction.