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#### Spectroscopy of binary black hole ringdown using overtones and angular modes

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##### Citation

Forteza, F. J., Bhagwat, S., Pani, P., & Ferrari, V. (2020). Spectroscopy of binary
black hole ringdown using overtones and angular modes.* Physical Review D,* *102*:
044053. doi:10.1103/PhysRevD.102.044053.

Cite as: https://hdl.handle.net/21.11116/0000-0006-72D5-9

##### Abstract

The black hole uniqueness and the no-hair theorems imply that the quasinormal

spectrum of any astrophysical black hole is determined solely by its mass and

spin. The countably infinite number of quasinormal modes of a Kerr black hole

are thus related to each other and any deviations from these relations provide

a strong hint for physics beyond the general theory of relativity. To test the

no-hair theorem using ringdown signals, it is necessary to detect at least two

quasinormal modes. In particular, one can detect the fundamental mode along

with a subdominant overtone or with another angular mode, depending on the mass

ratio and the spins of the progenitor binary. Also in the light of the recent

discovery of GW190412, studying how the mass ratio affects the prospect of

black hole spectroscopy using overtones or angular modes is pertinent, and this

is the major focus of our study. First, we provide ready-to-use fits for the

amplitudes and phases of both the angular modes and overtones as a function of

mass ratio $q\in[0,10]$. Using these fits we estimate the minimum

signal-to-noise ratio for detectability, resolvability, and measurability of

subdominant modes/tones. We find that performing black-hole spectroscopy with

angular modes is preferable when the binary mass ratio is larger than $q\approx

1.2$ (provided that the source is not located at a particularly disfavoured

inclination angle). For nonspinning, equal-mass binary black holes, the

overtones seem to be the only viable option to perform a spectroscopy test of

the no-hair theorem. However this would require a large ringdown

signal-to-noise ratio ($\approx 100$ for a $5\%$ accuracy test with two

overtones) and the inclusion of more than one overtone to reduce modelling

errors, making black-hole spectroscopy with overtones impractical in the near

future.

spectrum of any astrophysical black hole is determined solely by its mass and

spin. The countably infinite number of quasinormal modes of a Kerr black hole

are thus related to each other and any deviations from these relations provide

a strong hint for physics beyond the general theory of relativity. To test the

no-hair theorem using ringdown signals, it is necessary to detect at least two

quasinormal modes. In particular, one can detect the fundamental mode along

with a subdominant overtone or with another angular mode, depending on the mass

ratio and the spins of the progenitor binary. Also in the light of the recent

discovery of GW190412, studying how the mass ratio affects the prospect of

black hole spectroscopy using overtones or angular modes is pertinent, and this

is the major focus of our study. First, we provide ready-to-use fits for the

amplitudes and phases of both the angular modes and overtones as a function of

mass ratio $q\in[0,10]$. Using these fits we estimate the minimum

signal-to-noise ratio for detectability, resolvability, and measurability of

subdominant modes/tones. We find that performing black-hole spectroscopy with

angular modes is preferable when the binary mass ratio is larger than $q\approx

1.2$ (provided that the source is not located at a particularly disfavoured

inclination angle). For nonspinning, equal-mass binary black holes, the

overtones seem to be the only viable option to perform a spectroscopy test of

the no-hair theorem. However this would require a large ringdown

signal-to-noise ratio ($\approx 100$ for a $5\%$ accuracy test with two

overtones) and the inclusion of more than one overtone to reduce modelling

errors, making black-hole spectroscopy with overtones impractical in the near

future.