High Precision Ringdown Modeling: Multimode Fits and BMS Frames. (arXiv:2110.15922v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Zertuche_L/0/1/0/all/0/1">Lorena Magaña Zertuche</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Mitman_K/0/1/0/all/0/1">Keefe Mitman</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Khera_N/0/1/0/all/0/1">Neev Khera</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Stein_L/0/1/0/all/0/1">Leo C. Stein</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Boyle_M/0/1/0/all/0/1">Michael Boyle</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Deppe_N/0/1/0/all/0/1">Nils Deppe</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Hebert_F/0/1/0/all/0/1">François Hébert</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Iozzo_D/0/1/0/all/0/1">Dante A. B. Iozzo</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Kidder_L/0/1/0/all/0/1">Lawrence E. Kidder</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Moxon_J/0/1/0/all/0/1">Jordan Moxon</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Pfeiffer_H/0/1/0/all/0/1">Harald P. Pfeiffer</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Scheel_M/0/1/0/all/0/1">Mark A. Scheel</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Teukolsky_S/0/1/0/all/0/1">Saul A. Teukolsky</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Throwe_W/0/1/0/all/0/1">William Throwe</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Vu_N/0/1/0/all/0/1">Nils Vu</a>
Quasi-normal mode (QNM) modeling is an invaluable tool for characterizing
remnant black holes, studying strong gravity, and testing GR. Only recently
have QNM studies begun to focus on multimode fitting to numerical relativity
(NR) strain waveforms. As GW observatories become even more sensitive they will
be able to resolve higher-order modes. Consequently, multimode QNM fits will be
critically important, and in turn require a more thorough treatment of the
asymptotic frame at $mathscr{I}^+$. 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 (CCE), an
extraction technique which is known to resolve 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 strain mismatch
improves by a factor of $sim10^5$ when using multimode fitting as opposed to
only fitting the $(2,pm2,n)$ modes. Our most significant result addresses a
critical point that has been overlooked in the QNM literature: the importance
of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the numerical
waveform to that of the QNM model. We show that by mapping the numerical
waveforms$-$which exhibit the memory effect$-$to a BMS frame known as the super
rest frame, there is an improvement of $sim10^5$ in the all-mode strain
mismatch compared to using a strain waveform whose BMS frame is not fixed.
Furthermore, we find that by mapping CCE waveforms to the super rest frame, we
can obtain all-mode mismatches that are, on average, a factor of $sim4$ better
than using the publicly-available extrapolated waveforms. We illustrate the
effectiveness of these modeling enhancements by applying them to families of
waveforms produced by NR and comparing our results to previous QNM studies.
Quasi-normal mode (QNM) modeling is an invaluable tool for characterizing
remnant black holes, studying strong gravity, and testing GR. Only recently
have QNM studies begun to focus on multimode fitting to numerical relativity
(NR) strain waveforms. As GW observatories become even more sensitive they will
be able to resolve higher-order modes. Consequently, multimode QNM fits will be
critically important, and in turn require a more thorough treatment of the
asymptotic frame at $mathscr{I}^+$. 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 (CCE), an
extraction technique which is known to resolve 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 strain mismatch
improves by a factor of $sim10^5$ when using multimode fitting as opposed to
only fitting the $(2,pm2,n)$ modes. Our most significant result addresses a
critical point that has been overlooked in the QNM literature: the importance
of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the numerical
waveform to that of the QNM model. We show that by mapping the numerical
waveforms$-$which exhibit the memory effect$-$to a BMS frame known as the super
rest frame, there is an improvement of $sim10^5$ in the all-mode strain
mismatch compared to using a strain waveform whose BMS frame is not fixed.
Furthermore, we find that by mapping CCE waveforms to the super rest frame, we
can obtain all-mode mismatches that are, on average, a factor of $sim4$ better
than using the publicly-available extrapolated waveforms. We illustrate the
effectiveness of these modeling enhancements by applying them to families of
waveforms produced by NR and comparing our results to previous QNM studies.
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