Spectroscopy for asymmetric binary black hole mergers

Open Access

Spectroscopy for asymmetric binary black hole mergers

Jahed Abedi, Collin D. Capano, Shilpa Kastha, Alexander H. Nitz, Yi-Fan Wang, Julian Westerweck, Alex B. Nielsen, and Badri Krishnan

Phys. Rev. D 108, 104009 – Published 6 November 2023

Abstract

We study Bayesian inference of black hole ringdown modes for simulated binary black hole signals. We consider to what extent different fundamental ringdown modes can be identified in the context of black hole spectroscopy. Our simulated signals are inspired by the high-mass event GW190521. We find strong correlation between mass ratio and Bayes factors of the subdominant ringdown modes. The Bayes factor values and time dependency, and the peak time of the (3,3,0) mode align with those found analyzing the real event GW190521, particularly for high-mass ratio systems.

Received 6 September 2023
Accepted 12 October 2023

DOI:https://doi.org/10.1103/PhysRevD.108.104009

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

General relativity Gravitation Gravitational waves

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Jahed Abedi ^1,2,3,*, Collin D. Capano ^4,2,3, Shilpa Kastha^5,2,3, Alexander H. Nitz⁶, Yi-Fan Wang ^7,2,3, Julian Westerweck ^2,3,8, Alex B. Nielsen¹, and Badri Krishnan^9,2,3

¹Department of Mathematics and Physics, University of Stavanger, NO-4036 Stavanger, Norway
²Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Callinstraße 38, 30167 Hannover, Germany
³Leibniz Universität Hannover, 30167 Hannover, Germany
⁴Department of Physics, University of Massachusetts, Dartmouth, Masschusetts 02747, USA
⁵Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁶Department of Physics, Syracuse University, Syracuse, New York 13244, USA
⁷Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, 14476 Potsdam, Germany
⁸Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
⁹Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

^*jahed.abedi@uis.no

Article Text

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Issue

Vol. 108, Iss. 10 — 15 November 2023

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Images

Figure 1
A comparison of the final mass, mass ratio and SNR of samples from IMR analyses of GW190521, using the NRSur7dq4 [60] (Left) and IMRPhenomTPHM (Right) [61] waveform model. The solid lines in the plots represent the 50% and 90% credible contours. The dots’ color represents the samples’ SNR. Notably, the NRSur7dq4 results exhibit a second mode with higher SNR at larger mass ratio, which agrees with the findings from the ringdown analysis.
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Figure 2
Bayes factors $B_{220, 221}^{modes}$ for various models with the indicated modes in real GW190521 data. These are calculated relative to the stronger of the two models containing either only the (2,2,0) or both the $(2, 2, 0) + (2, 2, 1)$ modes. The dashed lines show where the (3,3,0) mode peaks. As depicted in this figure, the Bayes factor strongly supports the presence of both the (2,2,0) and (3,3,0) modes over either the (2,2,0) mode alone or a combination of the (2,2,0) and (2,2,1) modes, with an estimated value of $56 \pm 1$ at $t_{ref} + 6 ms$ .
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Figure 3
Results of the ringdown analysis for simulated signals of set $A$ in terms of Bayes factors as shown in Fig. 2. Set $A$ consists of 100 injections drawn from the GW190521 IMR-posterior samples. The injected signals use the IMRPhenomTPHM waveform model. Both columns show the same injection parameters, but either using all modes implemented in IMRPhenomTPHM (left, Signal subset) or only the 22 mode (right, Control subset). Top row: highest mass ratio injection, $q = 19.2$ Center row: injection with (3,3,0) Bayes factor closest to that for GW190521, $q = 8.8$ . Bottom row: lowest mass ratio injection of set $A$ , $q = 1.1$ . The ringdown analysis method and selection of modes are identical for all results shown. The dashed lines show where the (3,3,0) mode Bayes factor for GW190521 peaks in Fig. 2. This figure illustrates that as the mass ratio increases within the Signal injection set (left panel), our analysis patterns of multiple modes-encompassing peak time, Bayes factor values, etc., increasingly mirrors the pattern seen in GW190521 (illustrated in Fig. 2). Conversely, when we conduct an equivalent analysis on the Control injections (right panel), featuring only the 22 mode, we find no similarity to the observed pattern.
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Figure 4
Results of the ringdown analysis of set $A$ , using as templates the $(2, 2, 0) + (3, 3, 0)$ quasinormal modes. Set $A$ has 100 injections drawn from the GW190521 IMR-posterior samples which use the IMRPhenomTPHM waveform model. The injections’ mass ratio ranges from $q = 1.1$ to $q = 19.2$ . For visibility, we display only 17 randomly selected injections of the total 100, uniformly distributed in mass ratio. Injections for the left panel have all modes of IMRPhenomTPHM, while those for the right panel have only the 22 mode. The ringdowm analysis method and template modes are identical for left and right. The red curve represents the result from the $(2, 2, 0) + (3, 3, 0)$ analysis for GW190521 and dashed lines show where its Bayes factors peak. In the left panel, this figure demonstrates that as the mass ratio increases in the Signal injections, our analysis pattern-encompassing the peak time, Bayes factor values, etc., for $(2, 2, 0) + (3, 3, 0)$ progressively aligns with the pattern observed in GW190521 (illustrated in red). In contrast, conducting a similar analysis on the Control injections (right panel), which feature only the 22 mode, reveals no resemblance to the observed pattern. This figure prominently demonstrates the robust support from the Bayes factor for the existence of both $(2, 2, 0) + (3, 3, 0)$ modes over either (2,2,0) or $(2, 2, 0) + (2, 2, 1)$ modes at $\sim t_{ref} + 6 ms$ specifically for high-mass ratio systems.
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Figure 5
The same as Fig. 4 for the 10 injections of set $B$ . These are low-mass ratio injections (set $B$ ), and neither the Signal (left panel) nor the Control (right panel) injections exhibit similarity to the pattern observed in GW190521 (illustrated in red). For these low-mass ratio injections, the Bayes factors indicate no support for the existence of both $(2, 2, 0) + (3, 3, 0)$ modes.
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Figure 6
Set $A$ simulated signals: Bayes factors $B_{220, 221}^{220 + 330}$ for the $(2, 2, 0) + (3, 3, 0)$ model, maximized over time, vs mass ratio of the corresponding injection. Bayes factors are again calculated with respect to the stronger of the two models consisting of either the (2,2,0) or the $(2, 2, 0) + (2, 2, 1)$ modes. The vertical dashed line shows the Bayes factor for GW190521. The colorbar represents the time of the peak (3,3,0) Bayes factor relative to the reference time. Left: injections with all IMR modes (Signal). Right: the same injections with only the 22 IMR mode (Control). For high-mass ratio systems (set $A$ ), the peak time and Bayes factor values for the Signal injections (left panel) are shifted towards those obtained for GW190521 (dashed vertical line), compared to those of the Control injections (right panel).
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