A new method for extracting gravitational wave:
BH ringdown mode search using Auto-Regressive method
Hisaaki Shinkai 真貝寿明 （大阪工大）(Osaka Institute of Technology)
hisaaki.shinkai@oit.ac.jp

Outline & Summary

The ring-down part of gravitational waves in the ﬁnal stage of merger of compact objects tells us the nature of strong gravity which can be used for testing
the theories of gravity. The ring-down wave, however, fades out in a very short time with a few cycles, and hence it is challenging for gravitational wave
data analysis to extract the ringdown frequency and its damping time scale.
We develop a new method, the autoregressive modeling (AR) approach, which extracts waveform by ﬁtting a linear function from bare data. It works wellfor small number of data points, and does not require any templates. After obtaining the best parameters using mockdata, we applied this method for blackhole merger events of the LIGO/Virgo/KAGRA O3 catalog (GWTC-3). We ﬁnd that for high SNR events, we can extract ring-down waves properly.
The identiﬁed ringdown modes are around those reported in GWTC-3, i.e. no signiﬁcant deviations from the modes predicted by general relativity.
This method should work for extracting higher modes of ring-down waves, but we do not ﬁnd them yet.

Motivation & O3 data

Mockdata Comparison
LVK arXiv:2111.03606

Towards testing gravity theories ⇒GWTC-3 (O3b)Ringdown-part extraction is a keyMerger()[ ­]

continued

Mockdata preparation

SXS data + shifted ringdown injection + aLIGO noise
modiﬁed after t̲merger (set A)
60 setmodiﬁed before/after t̲merger (set B) 60 set

Ringdown

Inspiral// / /_ _  _// ///  /MethodNakano+, PRD99 (2019) 124032

Auto-Regressive modelvs Short FFTsegment = 1/16 sec = 256 points

sampling rate=4096
h(t)ringdown search
60 mockdata
shift = 1/512 sec = 8 points
The order M can be ﬁxed at 2〜8.
Even for short segment,
AR model shows precise powerspectrum.

P(f)
ARFFT

freq.

[mock data, SNR=40, inspiral part]

Results
GW150914

GW150914
Hanford (SNR=20.6)

H100_SpectrogramARR

f 220 = 271.8 Hz, f 221 = 266.0 Hz, f 222 = 254.7 Hz
f 210 = 380.7 Hz, f 211 = 225.7 Hz, f 200 = 252.8 Hz

f 330 = 430.9 Hz, f 331 = 427.4 Hz, f 332 = 421.1 Hz
f 320 = 387.9 Hz, f 310 = 351.1 Hz, f 300 = 320.3 Hz

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ACKNOWLEDGMENTS
This work was supported by JSPS KAKENHI Grant No. JP17H06358 (and also JP17H06357) [A01: Testing gravity theories using gravitational waves, as a part of the innovative research area, "Gravitational wave physics andastronomy: Genesis"], by JSPS KAKENHI Grant No. JP18K03630 [Non-linear dynamics in the modiﬁed gravity theories as a test of string theory] and by No. 19H01901 [New directions in gravitational-wave data analysis: bothin computing algorithms and hardwares including its outreach activities].

http://www.oit.ac.jp/is/shinkai/

The IAU General Assembly 2022 @ Busan Korea, 2022/August 2-11