Preferential Accretion onto the Secondary Black Hole Strengthens Gravitational Wave Signals

TL;DR

This work tackles the discrepancy between the observed nanohertz GWB amplitude and theoretical expectations by proposing preferential accretion onto the secondary SMBH during galaxy mergers. Using an observationally grounded framework that ties galaxy mergers to SMBH properties through the velocity-dispersion function and the $M_\bullet-\sigma$ relation, the authors model how differential accretion alters SMBH mass ratios and increases the rate of major SMBH mergers, thereby boosting the GWB. They show that even modest total SMBH mass growth ($\Delta M_{\bullet,tot}/M_{\bullet,tot} \approx 10\%$) can bring the predicted GWB into agreement with NANOGrav's measurements, with stronger effects at higher redshift for LISA and JWST-relevant populations and a shortened time to detect individual continuous-wave SMBH binaries in PTA data. The results highlight circumbinary-disk accretion as a key factor shaping GW signals across cosmic time and motivate further observational constraints on SMBH mass-ratio evolution during mergers. The approach provides a concrete, testable link between galaxy-scale processes and GW signals detectable by PTAs, LISA, JWST, and LIGO/Virgo/KAGRA.

Abstract

Pulsar timing arrays have recently found evidence for nanohertz gravitational waves that are consistent with being produced by a cosmological population of binary supermassive black holes (SMBHs). However, the amplitude of this gravitational wave background is larger than predicted from theoretical and empirical models of SMBH binary populations. We investigate preferential accretion onto the secondary, less massive SMBH of the binary as a potential solution to this discrepancy. We carry out the first observationally-based analysis of the effect of preferential accretion on the SMBH binary population, and we find that preferential accretion onto the secondary SMBH increases the binary SMBH mass ratio, causing many minor galaxy mergers to lead to major SMBH mergers. The fraction of SMBH mergers that are major mergers increases by a factor of 2-3 when preferential accretion is included. Further, we find that only a small amount of preferential accretion (10% total SMBH mass growth) is needed to bring the predicted gravitational wave background amplitude into agreement with observations. Preferential accretion has an even larger effect on gravitational wave signals detected by LISA, which will probe SMBH binaries at higher redshifts where the environment is more gas-rich, and can also help explain the rapid build up of overmassive black holes at high redshifts observed by the James Webb Space Telescope. It also shortens the time to the first detection of an individual SMBH binary emitting continuous waves. Preferential accretion strengthens the gravitational wave signals produced by any binary embedded in a circumbinary disk, including LIGO sources.

Figures (4)

• Figure 1: The relationship between the final binary SMBH mass ratio ($q_{\bullet, f}$, the mass ratio at $\sim$mpc separations) and the initial SMBH mass ratio ($q_{\bullet, i}$, the mass ratio at kpc-scale separations) for different models of accretion. Here, $q_{\bullet, i}$ is derived from the mass ratio of the galaxy pair. For no accretion (solid black line), the SMBH mass ratio does not evolve. However, models of preferential accretion onto the secondary SMBH drive $q_{\bullet, f}$ higher, as shown for observationally-based estimates of 10% (blue solid line) and 20% (orange solid line) cumulative growth of the total SMBH mass $M_{\bullet, tot}$. The dotted line shows $q_{\bullet, f} = 0.25$, which denotes the cut-off between minor SMBH mergers (below the dotted line) and major SMBH mergers (above the dotted line). We highlight that the differential accretion models bring many SMBH binaries from what would be considered a minor SMBH merger event ($0.1 \leq q_{\bullet} < 0.25$) into the classification for a major SMBH merger event ($0.25 \leq q_{\bullet} \leq 1$).
• Figure 2: Fraction of SMBH binaries as a function of $q_{\bullet,f}$, the final SMBH mass ratio when the binary enters the pulsar timing gravitational wave band ($\sim$mpc separations), for the population of $0.1 \le q_{gal} \le 1$ galaxy mergers. Solid lines show the median values over 1000 realizations, while the shaded regions show the $1\sigma$ errors. The no accretion model (black line) is where the SMBH mass ratio is derived from the galaxy mass ratio and there is no further SMBH mass growth ($q_{\bullet,f}=q_{\bullet,i}$). The models of preferential accretion onto the secondary SMBH, for observationally-based estimates of 10% (blue line) and 20% (orange line) cumulative growth of the total SMBH mass $M_{\bullet,tot}$, drive the fraction of SMBH binaries higher for higher SMBH mass ratios. The dotted vertical line at $q_{\bullet,f}=0.25$ marks the dividing line between minor SMBH mergers (to the left) and major SMBH mergers (to the right). When compared to the no accretion model, the model of 10% (20%) total SMBH mass growth increases the fraction of major SMBH mergers from 22% to 41% (57%).
• Figure 3: Probability distribution functions of the predicted GWB amplitude for models of no SMBH accretion (black), differential accretion with 10% total SMBH mass growth (blue), and differential accretion with 20% total SMBH mass growth (orange). The SMBH binary evolution timescale is set to 1.8 Gyr, the median timescale found for the differential accretion model we use here DU20.1SI20.1. The brown diamond data point shows the median measured value for the GWB amplitude found in NANOGrav's 15-year data set, with error bars showing the $90\%$ credible region AG23.1. The top panel (a) is only for major galaxy mergers ($q_{gal} \geq 0.25$), while the bottom panel (b) is for both major and minor galaxy mergers ($q_{gal} \geq 0.1$). While the no accretion models are similar in the two panels, the other two models change significantly when minor galaxy mergers are included because preferential accretion can turn minor galaxy mergers into major SMBH mergers (see Figure \ref{['fig2']}). We note that the model with 10% total SMBH mass growth due to differential accretion with the inclusion of minor mergers has a median value that most closely matches the median value constrained from pulsar timing array data.
• Figure 4: Predicted values of the GWB amplitude for models with no SMBH accretion (black), as well as models of preferential accretion onto the secondary SMBH with total SMBH mass $M_{\bullet,tot}$ growth of 10% (blue) and 20% (orange). Each line shows the median values over 1000 realizations, with the shaded regions denoting the $1\sigma$ errors. For clarity we show only one shaded, $1\sigma$ error region per panel: zero (left, gray), 10% (middle, blue), and 20% (right, orange) total SMBH mass growth. The SMBH binary evolution timescale $T_{evol}$, which is the timescale for the SMBH binary to evolve from $\sim$kpc separations to $\sim$mpc separations, is allowed to vary. The dotted vertical line illustrates $T_{evol}=1.8$ Gyr, the median timescale found for the model of differential SMBH mass accretion that we use DU20.1SI20.1. The dashed brown horizontal line shows the median amplitude of the GWB found in NANOGrav's 15-year data set (brown shaded area is the $90\%$ credible region; AG23.1). We find that even small amounts (10%) of differential accretion onto the SMBH binary amplify the amplitude to values consistent with the current constraints from NANOGrav.