High-Accuracy Mass, Spin, and Recoil Predictions of Generic Black-Hole Merger Remnants

We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to interpolate the remnant mass, spin, and recoil velocity in the seven-dimensional parameter space of precessing black-hole binaries with mass ratios $q\le 2$, and spin magnitudes ${\chi }_1$, ${\chi }_2\le 0.8$. For precessing systems, our errors in estimating the remnant mass, spin magnitude, and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude (improvement is also reported in the extrapolated region at high mass ratios and spins). In addition, we also model the remnant spin and kick directions. Being trained directly on precessing simulations, our fits are free from ambiguities regarding the initial frequency at which precessing quantities are defined. We also construct a model for remnant properties of aligned-spin systems with mass ratios $q\le 8$, and spin magnitudes ${\chi }_1$, ${\chi }_2\le 0.8$. As a byproduct, we also provide error estimates for all fitted quantities, which can be consistently incorporated into current and future gravitational-wave parameter-estimation analyses. Our model(s) are made publicly available through a fast and easy-to-use Python module called surfinBH.

Figure 1

Quasicircular binary BH merger problem viewed as a scattering process via a “Feynman” diagram. Time flows to the right. All quantities are well defined in the asymptotically flat region far from the interaction (merger).

Figure 2

Errors in predicting remnant mass, spin, kick magnitude, and kick direction for nonprecessing binary BHs with mass ratios $q\le 8$, and spin magnitudes ${\chi }_1$, ${\chi }_2\le 0.8$. The direction error is the angle between the predicted vector and a fiducial vector, taken to be the high-resolution NR case and indicated by a ${}^{\star }$. The square (triangle) markers indicate median (95th percentile) values. Our model surfinBH3dq8 is referred to as 3dq8. The black histogram shows the NR resolution error while the dashed histograms show errors for different existing fitting formulae.

Figure 3

Errors in predicting the remnant mass, spin magnitude, spin direction, kick magnitude, and kick direction for precessing binary BHs with mass ratios $q\le 2$, and spin magnitudes ${\chi }_1$, ${\chi }_2\le 0.8$. Our model, surfinBH7dq2, is referred to as 7dq2. The black histogram shows the NR resolution error while the dashed histograms show errors for different existing fitting formulae. In the bottom-right panel we show the distribution of kick magnitude vs error in kick direction.

Figure 4

Left panel: Errors for surfinBH7dq2 in predicting remnant properties when the spins are specified at an orbital frequency of $f_0=10\mathrm{Hz}$, for different total masses. Right panel: Errors for surfinBH7dq2 when extrapolating to higher mass ratios, with the spins specified at $t=-100M$. The labels on the horizontal axis indicate the range of mass ratios being tested. Note that the distributions in these plots are normalized to have a fixed height, not fixed area.