High Precision Ringdown Modeling: Multimode Fits and BMS Frames

Abstract

Quasi-normal mode (QNM) modeling is an invaluable tool for studying strong gravity, characterizing remnant black holes, and testing general relativity. To date, most studies have focused on the dominant (2, 2) mode, and have fit to standard strain waveforms from numerical relativity. But, as gravitational wave observatories become more sensitive, they can resolve higher-order modes. Multimode fits will be critically important, and in turn require a more thorough treatment of the asymptotic frame at I + . The first main result of this work is a method for systematically fitting a QNM model containing many modes to a numerical waveform produced using Cauchy-characteristic extraction, which is known to exhibit memory effects. We choose the modes to model based on their power contribution to the residual between numerical and model waveforms. We show that the all-mode mismatch improves by a factor of ∼ 10 5 when using multimode fitting as opposed to only fitting (2, ±2, n) modes. Our second main result addresses a critical point that has been overlooked in the literature: the importance of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the simulated gravitational wave to that of the QNM model. We show that by mapping the numerical relativity waveforms to the super rest frame, there is an improvement of ∼ 10 5 in the all-mode strain mismatch in the presence of memory, compared to using the strain whose BMS frame is not fixed. We illustrate the effectiveness of these modeling enhancements by applying them to families of waveforms produced by numerical relativity, and comparing our results to previous studies.

Measuring quasi-normal mode amplitudes with misaligned binary black hole ringdowns

“…The short-lived nature of the overtones means they can only be constrained at early times when unmodeled contributions are larger. Recent work has featured fits to the overtones [7,18,21,25]. However, as discussed in LKAH, we find the fits to the n = 1 overtones are only robust over a small fraction of the parameter space (for nearly aligned sources I ≤ 20 • with large spin a ≥ 0.9M ).…”

“…As shown in Ref. [25], 96% of the ringdown power can be described with just the ( , m, n) = (2, 2, ≤ 2) modes. However, as discussed in LKAH and recently Ref.…”

“…These definitions signify how the wavefronts circulate along the azimuthal direction, following Ref. [25]. The notion of a "standard set" of late-time ringdown modes thus ceases to be a useful concept when one begins modeling black hole mergers with highly misaligned components.…”

Angular emission patterns of remnant black holes

“…Potentially, subtractions of the late ringdown residuals [24] could help improve the fitting in the range of 40 ≲ t offset =M ≲ 50. We do not conduct such subtraction because it is not well motivated, and the small impact from the residuals [91] does not quantitatively change the resulting transition time and minimum distance in our analysis. Recent studies show that using the Cauchycharacteristic extraction and mapping to the super-rest frame would be a proper approach to obtain the memory-free waveform [90,91].…”

Nonlinear effects in the black hole ringdown: absorption-induced mode excitation

“…In contrast, for typical mergers, sums consisting purely of (linear) QNMs have been shown to provide a good fit to numerical relativity from surprisingly early times 2 [24][25][26][27][28][29][30] (although this does not automatically imply that the solution itself is linear). It therefore remains to be understood to what degree nonlinear mode interactions are present in astrophysical mergers: it has been proposed that the formation of a common horizon "hides" nonlinearities from asymptotic observers [31], or that the black-hole potential "filters" nonlinear features out of the signal.…”