Core Scouring Dynamics and Gravitational Wave Consequences: Constraints on Supermassive Black Hole Binary Hardening

Abstract

In this paper we perform a multi-messenger investigation of the efficiency of stellar scattering in tightening supermassive black hole binaries by jointly comparing models to the observed galaxy stellar core population and to results of nanohertz gravitational wave observations. Our model uses merger trees from the IllustrisTNG cosmological suite of simulations to predict stellar mass deficits in core galaxies. We take into account dynamical friction, stellar scattering, and gravitational wave emission and compare to the observed relation between core mass deficit and galaxy stellar mass. We find that to match observations, binary hardening in the stellar scattering regime must be about 1.6 times faster than N-body experiments suggest. Most importantly we find that, even assuming a full loss-cone, hardening by stellar scattering alone is insufficient to explain the low frequency turnover seen in the gravitational wave background. This strongly suggests that gas-dynamics play an important role in hardening and provides a reason to be optimistic about electromagnetically visible binary AGN.

Figures (12)

• Figure 1: The luminosity deficit in core galaxies may be estimated by taking the integrated difference between a model of the pre-scoured profile and the observed surface brightness profile. Shown here is an example for the galaxy NGC 4486 (M87). Here, we model the surface brightness profile with the Nuker Law, shown in solid blue (see Eq. \ref{['eq: Nuker']}). Our estimate for the pre-scoured profile, shown in dashdot purple, is a power law with inner logarithmic slope equal to that at the break radius ($R_b$, see Eq. \ref{['eq: Plaw']}). The break radius indicates the distance from the galaxy center where the profile transitions from the shallow inner region to the steep outer region and represents the size of the core.
• Figure 2: Left panel: Mass deficit versus cusp radius for the observed sample of galaxies. The relation is clearly log-linear, with perhaps a weak break at the largest radii. Green diamonds show brightest cluster galaxies, blue circles indicate ellipticals, triangles indicate lenticulars, and the red square is a sole early-type spiral. For reference, M87 is represented by a yellow circle. Right panel: The distribution of logarithmic slopes $\delta$ used to compute the stellar mass deficits, with the peak located at 0.75. This agrees well with the range of 0.7--0.8 2009ApJS..181..486H found for progenitors of core galaxies.
• Figure 3: The top and bottom panels show the star-formation rate and mass histories, respectively, of a TNG300 subhalo in our sample. The pink dashed lines show the snapshots in the simulation where the subhalo underwent a major merger (i.e., $q_\mathrm{gal}\ge1/3$). The gray line marks shapshot number 50, or $z=1$. For our core scouring model we label a merger gas-rich (wet) if an episode of star-formation occurs during or any time after the merger. Conversely, if during and after a merger $\mathrm{sSSF} < 1/3t_H$, where $t_H$ is the Hubble time at the corresponding redshift, the merger is labeled gas-poor (dry). It is only the dry mergers in our model that contribute to core scouring. For this example subhalo, only the two most recent major mergers are considered dry. The preceding merger induced a burst of star formation, and would be a wet merger. Therefore, the wet merger at snapshot 59 would be the first merger considered in the analysis of this subhalo, used to set the inner logarithmic density slope $\lambda_p$ (\ref{['eq:plaw slope']}). Core scouring would then take place during the subsequent dry mergers at snapshots 74 and 89, altering the shape of the nuclear profile. Notice, too, that the mass of the subhalo is unreliable at the snapshot of each merger, so we take the remnant mass to be the mass reported at the subsequent snapshot.
• Figure 4: The plot shows hardening time in years on the y-axis and binary separation in parsecs on the x-axis, decreasing from left to right. The solid purple line shows the total evolutionary track for a representative binary in our model, which is a sum of the dynamical friction (blue dashed line), loss-cone scattering (orange dashed line), and gravitational wave emission (pink dashed line) hardening processes. The dotted line is the dynamical time $\tau_\mathrm{dyn}=r/v_c$ of the host galaxy, for reference. The dark shaded region around the loss-cone scattering curve denotes a range of possible $\hat{H}$ values from $0.1$--$5.0$. The colored shaded regions correspond to the separations where each of the three hardening mechanisms dominates. The opaque orange region shows how inefficient hardening (small values of $\hat{H}$) leads to a smaller range of separations for which stellar scattering dominates the hardening rate, whereas efficient hardening leads to a broader range of separations, shown by the transparent orange. The boundaries of these shaded regions come from the intersection of the lower and upper bounds of the stellar-scattering curves with the dynamical friction and gravitational wave curves. Importantly, the efficiency parameter controls the separation at which gravitational waves dominate angular momentum loss, ultimately impacting the shape of the GWB.
• Figure 5: Mass deficit versus stellar mass for our sample of core galaxies alongside KDE contours generated using a high efficiency factor ($\hat{H}=5.0$) in pink and a low efficiency factor ($\hat{H}=0.1$) in orange. The KDE contours show that the efficiency of stellar hardening is inversely proportional to the amount of stellar mass ejected, as is required by equations \ref{['dadt_lc']} and \ref{['eq: Mej']}. The figure also shows that our model is sensitive to the density of points in the $M_\mathrm{def}$--$M_\star$ plane. Inefficient hardening leads to a denser clustering of points at lower masses not seen at higher efficiencies. The overall slope of the trend also depends sensitively on the hardening efficiency.