Gravitational-wave signatures of mirror (a)symmetry in binary black hole mergers: measurability and correlation to gravitational-wave recoil

TL;DR

The paper investigates whether the net circular polarization of gravitational waves from binary black-hole mergers, quantified by $V_{ m GW}$, correlates with intrinsic source properties. It defines $V_{ m GW}$ as the gravitational Stokes parameter and shows it vanishes for mirror-symmetric configurations, becoming nonzero when spins are misaligned and precession occurs. It derives and tests a near-linear relation between $V_{ m GW}$ and the remnant recoil helicity, supported by NR simulations across precessing and eccentric binaries. It further demonstrates that $V_{ m GW}$ can be measured unbiasedly in injections using the NRSur7dq4 surrogate at high SNR (${ m SNR} obreak[≈] 50$), with implications for probing BH-formation channels, cosmological parity, and potential new physics in gravity.

Abstract

Precessing binary black-hole mergers can produce a net flux of circularly-polarized gravitational waves. This imbalance between left- and right-handed circularly polarized waves, quantified via the Stokes pseudo-scalar $V_{\rm GW}$, originated from mirror asymmetries in the binary. We scan the parameter space of black-hole mergers to investigate correlations between $V_{\rm GW}$ and chiral magnitudes constructed out of the intrinsic parameters of the binary. To this end, we use both numerical-relativity simulations for (quasi-circular) and eccentric precessing mergers from both the SXS and RIT catalogues, as well as the state-of-the-art surrogate model for quasi-circular precessing mergers NRSur7dq4. We find that, despite being computed by manifestly different formulas, $V_{\rm GW}$ is linearly correlated to the helicity of the final black hole, defined as the projection of its recoil velocity onto its spin. Next, we test our ability to perform accurate measurements of $V_{\rm GW}$ in gravitational-wave observations through the injection and recovery of numerically simulated signals. We show that $V_{\rm GW}$ can be estimated unbiasedly using the surrogate waveform model NRSur7dq4 even for signal-to-noise ratios of nearly 50, way beyond current gravitational-wave observations.

Figures (11)

• Figure 1: Example of a BBH that remains invariant under a mirror transformation with respect to the separating plane. The picture represents one instant of time during the inspiral. The arrows denote the individual spin vectors of the two BHs, each one labelled as 1 and 2. As a consequence of the spacetime mirror symmetry, the Stokes parameter (Eq. \ref{['eq:VGW']}) vanish dRetal20sanchis2023precessing.
• Figure 2: Example of a BBH that fails to be invariant under mirror transformations. The lack of spacetime mirror symmetry, produced as a consequence of the misalignment of the two BH spin vectors, leads to Stokes parameter (Eq. \ref{['eq:VGW']}) that differ from zero.
• Figure 3: Recovery of the GW Stokes $V_{\rm GW}$ parameter for numerically simulated signals. Posterior distributions of the GW Stokes $V_{\rm GW}$ parameter, obtained from the recovery of numerically simulated signals, for eight different BBHs observed at three inclinations, indicated at the top of each plot. The right (left) violins correspond to signal-to-noise ratios of 17 (50). The coloured dashed lines on each distribution enclose the 90% credible intervals, and the common red dashed line denotes the true $V_{\rm GW}$ value computed from the simulation. The acronym "SD" refers to the value of the Savage-Dickey ratio evaluated at $V_{\rm GW} = 0$, as detailed in Eq. \ref{['eq:SDratio']}.
• Figure 4: Linear correlation between the helicity $\mathscr{h}$, the transverse recoil velocity $K^J$, and the gravitational Stokes parameter $V_{\rm GW}$. The $x$ and $y$ axes show, respectively, the projections of the recoil velocity $\vb*{K}$ onto the total angular momentum direction $\vu*{J}$ and onto the final BH spin direction $\vu*{a}_{\rm f}$. The latter quantity can be understood as proportional to the helicity $\mathscr{h}=\langle \vu*{K}, \vu*{a}_{\rm f} \rangle$ of the remnant black hole. The colour denotes the value of $V_{\rm GW}$: red (blue) indicates positive (negative) values, which agree with the signs of $K^J$ and $\mathscr{h}$. The points correspond to an ensemble of 500000.0 BBHs drawn from a population with uniform masses and isotropic spins measured at a reference time $t_{\rm ref} = -100\,M$. All three quantities are computed from GW strains generated from the NRSur7dq4 model. The grey contours overlaying the points denote the (2D) $\{1,\ 2,\ 3\}\,\sigma$ levels of the distribution, representing the density of the population on this plane.
• Figure 5: Strong linear correlation of $V_{\rm GW}$ with $K^J$ and $K\,h$ in the SXS and RIT catalogues. In the left panel, it is showing the 2018 BBH simulations in the SXS catalogue, including eccentric and precessing binaries. For each of them, we compute the projection of the recoil velocity $\vb*{K}$ along the $\vb*J$ direction at $t = -100\,M$, against the Stokes parameter $V_{\rm GW}$. Their strong linear correlation is shown by the grey dashed line and the narrow violet shaded area, which denote the best-fit line and its 95% confidence interval. The green circles highlight the eccentric binaries, which have eccentricity greater than 0.001 at the reference time of the simulation. To echo Fig. \ref{['fig:linear_relation']}, we colour each point by the rescaled helicity $K\,\mathscr{h}$ of the remnant BH. In the right panel, we plot the helicity $K\,\mathscr{h}$ against $V_{\rm GW}$ for the 1880 binaries in the full RIT catalogue, in which 824 of them are eccentric binaries which are circled in green. From both catalogues, it is evident that both of them share a similar slope, and their $y$-intercepts are compatible with 0.000.