Measuring spin precession from massive black hole binaries with gravitational waves: insights from time-domain signal morphology

TL;DR

The paper tackles the challenge of robustly measuring spin precession in high-mass binary black holes using time-domain gravitational-wave inference. It employs the NRSur7dq4 IMR surrogate and defines spins via $\chi_{eff}$ and $\chi_p$, analyzing GW190521-like signals across varying SNR, total mass, and extrinsic angles to map how information about precession accumulates over time. Key findings show that, at high post-peak SNR, ringdown alone can constrain $\chi_p$, while longer inspirals at lower masses can reveal precession from the inspiral; extrinsic orientations modulate measurability but do not require fine-tuning, and the informative waveform features vary across signals. The results underscore that spin precession in heavy BBHs is detectable across multiple morphologies and will improve with next-generation detectors, enabling deeper insights into BBH formation channels.

Abstract

Robustly measuring binary black hole spins via gravitational waves is key to understanding these systems' astrophysical origins, but remains challenging -- especially for high-mass systems, whose signals are short and dominated by the merger. Nonetheless, events like GW190521 show that strong spin precession can indeed be gleaned. In this work, we track how spin precession imprints on simulated high-mass binary black hole signals cycle-by-cycle using time-domain inference. We investigate a suite of signals, all with the same spins and (near-unity) mass ratio -- yielding identical spin evolution -- but different signal-to-noise ratios (SNRs), total masses, and extrinsic angles, all of which affect the observed waveform morphology. We truncate each signal at various times and infer source parameters using only the data before or after each cutoff. The resultant posterior allows us to identify which time segments of each signal inform its spin precession constraints. We find that at a sufficiently high post-peak SNR ($\sim 20$), spin precession can be constrained by the NRSur7dq4 waveform model when just the post-peak data (i.e., ringdown) are visible. Similarly, at a large enough pre-cutoff SNR ($\sim 10$), spin precession can be constrained using only pre-peak data (i.e., inspiral); this occurs for signals with detector-frame total mass $\lesssim 100 M_{\odot}$ at GW190521's full-signal SNR. Finally, we vary the inclination, polarization, and phase angles, finding that their configuration need not be fine-tuned to measure spin precession, even for very high-mass and short signals with two to three observable cycles. We do not find that the same morphological features consistently drive precession constraints: in some signals, precession inference hinges on the relationship between a loud merger and quiet pre-merger cycle, as was the case for GW190521, but this is not generically true.

Figures (13)

• Figure 1: Evolution of posteriors for representative cutoff times for GW190521 and its $\mathrm{max.}\,\mathcal{L}$ waveform, exemplifying that the $\mathrm{max.}\,\mathcal{L}$ waveform behaves similarly to the real data, both for the full signals and as a function of cutoff time. Each row shows different segments of data analyzed: the top row shows the full segment of real data (gray) and the full $\mathrm{max.}\,\mathcal{L}$ waveform (black), while subsequent rows show results from data before (blue) and after (orange) different cutoff times: $t_{\rm cut}= \{-25.6, -2.4, 4.9, 24.4,30.5\}\,M$ from top to bottom. The lighter shaded histograms correspond to the real GW190521 data, while the darker empty histograms are for the $\mathrm{max.}\,\mathcal{L}$ waveform. JSDs between the two posteriors are given in inset text on each plot. First column: The whitened $\mathrm{max.}\,\mathcal{L}$ waveform from the full analysis (black) along with the whitened LLO data (gray). The blue/orange shaded regions highlight the data informing the same-color posteriors in the remaining columns, and the black-dashed vertical line is the cutoff time. Second through fourth columns: Marginalized posteriors on the detector-frame total mass $M$, mass ratio $q$, and effective precessing spin $\chi_\mathrm{p}$ inferred from each segment of data. Priors on each parameter are represented by the gray-dotted histograms and vertical red lines mark the true values for the $\mathrm{max.}\,\mathcal{L}$ waveform (Table \ref{['tab:GW190521_maxL_params']}). See Ref. animation_figure01 for an animation of this figure, including more cutoff times.
• Figure 2: Evolution of the $\chi_\mathrm{p}$ posterior for the GW190521 $\mathrm{max.}\,\mathcal{L}$ waveform at different full-signal optimal network SNRs: $\rho_{\rm full}=$ 15 (green), 20 (yellow), 30 (pink), and 40 (red). Top row: Whitened strain $\hat{h}$ in LLO. The gray hatched shading hides data excluded from a given analysis. Bottom row: Posteriors for $\chi_\mathrm{p}$ inferred from the non-shaded data in the corresponding column in the top row. The prior is shown as gray dotted, while the black dashed vertical line is the true value. Louder signals have more sharply peaked $\chi_\mathrm{p}$ posteriors at all times. The $\rho_{\rm full}=30$ and $40$ waveforms retain some information about $\chi_\mathrm{p}$ in the post-peak data alone (third column). See Ref. animation_figure02 for an animation of this figure, including more cutoff times and SNRs.
• Figure 3: Information about $\chi_\mathrm{p}$ in the ringdown of the $\mathrm{max.}\,\mathcal{L}$ waveform at different SNRs. These signals have $\rho_{\rm pp}=25,30,40,50,75,100$, which correspond to full-signal SNRs of $\rho = 30.5, 36.5, 48.7, 60.9, 91.4, 121.8$. For reference, the $\mathrm{max.}\,\mathcal{L}$ waveform has $\rho_{\rm pp} = 11.4$. Top panel: Posteriors on $\chi_\mathrm{p}$ from the post-peak data ($t > 0\,M$) for different post-peak SNRs (different colors). The ringdown alone has measurable information about $\chi_\mathrm{p}$, as the posteriors are not consistent with the prior (gray dotted). Bottom panel: JSD between the $\chi_\mathrm{p}$ posterior and prior from data after different cutoff times (horizontal axis) for different SNRs (different colors). The whitened strain of each signal in LLO is plotted above, with the upper axis labeling the fraction of $\rho_{\rm pp}$ remaining after $t_\mathrm{cut}$. The two points circled in gray are an example of posteriors with comparable JSDs originating from signals with different SNRs. For loud enough signals, $\chi_\mathrm{p}$ can be measured up to late times of $20\,M$ into the ringdown.
• Figure 4: Waveforms and inference results for signals with different detector-frame total masses but the same SNR: $M=80\,M_\odot$ (magenta), $100\,M_\odot$ (pink), $120\,M_\odot$ (purple), $270\,M_\odot$ (dark blue), and $500\,M_\odot$ (light blue). First row: Whitened waveforms in LLO, with the time axis plotted in units of seconds. Second row: Whitened waveforms in LLO, with the time axis plotted in units of detector-frame total mass. Since all other parameters are the same, the waveform cycles line up when plotted in units of $M$. Cutoff times $t_i \in \{ -21.8, -0.8, 12.8, 18.0, 24.1\}\,M$, corresponding to specific peaks/troughs of the signals, are labeled with vertical black dashed lines. Third and fourth rows:$\chi_\mathrm{p}$ posteriors for the pre- and post-cutoff analyses for each signal (corresponding colors to top two rows). We exclude the full-signal analysis results, as they are indistinguishable from the pre-$t_5$ results. Fifth row: SNR accumulation over time for the different signals. See Ref. animation_figure04 for an animation of this figure, including more cutoff times and masses.
• Figure 5: JSD between the pre-cutoff $\chi_\mathrm{p}$ posterior and the prior versus the pre-cutoff SNR for different total masses (colors) and a range of cutoff times. The gray dashed line is the global line of best fit across all masses. The horizontal black dashed line marks the threshold we define for an informative posterior, $\mathrm{JSD} \gtrsim 10^{-2}$. The inset zooms in on the informative region, with lines of best fit for each mass individually (colored dashed lines).