Gravitational-wave measurements of the mass and angular momentum of a black hole

Journal Article · Wed Nov 15 04:00:00 EST 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.3194· OSTI ID:5179828

Echeverria, F ^[1]

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1. Theoretical Astrophysics, California Institute of Technology, Pasadena, California 91125 (US)

A deformed black hole produced in a cataclysmic astrophysical event should undergo damped vibrations which emit gravitational radiation. By fitting the observed gravitational waveform {ital h}({ital t}) to the waveform predicted for black-hole vibrations, it should be possible to deduce the hole's mass {ital M} and dimensionless rotation parameter {ital a}=({ital c}/{ital G})(angular momentum)/{ital M}{sup 2}. This paper estimates the accuracy with which {ital M} and {ital a} can be determined by optimal signal processing of data from laser-interferometer gravitational-wave detectors. It is assumed that the detector noise has a white spectrum and has been made Gaussian by cross correlation of detectors at different sites. Assuming, also, that only the most slowly damped mode (which has spheroidal harmonic indices {ital l}={ital m}=2) is significantly excited---as probably will be the case for a hole formed by the coalescence of a neutron-star binary or a black-hole binary---it is found that the one-sigma uncertainties in {ital M} and {ital a} are {Delta}{ital M}/{ital M}{approx equal}2.2{rho}{sup {minus}1}(1{minus}a){sup 0.45}, {Delta}{ital a}{approx equal}5.9{rho}{sup {minus}1}(1{minus}a){sup 1.06}, where {rho}{approx equal}{ital h}{sub {ital s}}({pi}fS{sub h}){sup {minus}1/2} (1{minus}{ital a}){sup {minus}0.22}. Here {rho} is the amplitude signal-to-noise ratio at the output of the optimal filter, {ital h}{sub {ital s}} is the wave's amplitude at the beginning of the vibrations, {ital f} is the wave's frequency (the angular frequency {omega} divided by 2{pi}), and {ital S}{sub {ital h}} is the frequency-independent spectral density of the detectors' noise. These formulas for {Delta}{ital M} and {Delta}{ital a} are valid only for {rho}{approx gt}10. Corrections to these approximate formulas are given in Table II.

• OSTI ID: 5179828
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Journal Name: Physical Review (Section) D: Particles and Fields; (USA) Vol. 40:10; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
ASTROPHYSICS
BLACK HOLES
GRAVITATIONAL RADIATION
GRAVITATIONAL WAVE DETECTORS
INTERFEROMETERS
LASERS
MASS
MEASURING INSTRUMENTS
NEUTRON STARS
PROBABILITY
RADIATION DETECTORS
RADIATIONS
SIGNAL-TO-NOISE RATIO
STARS