method

gravitational wave parameter estimation

Using gravitational wave observations to measure properties like eccentricity and test spacetime geometry.
27 related articles · 6 formulas

Description

Gravitational wave parameter estimation is the process of extracting physical properties of astrophysical sources from the detected gravitational wave signals. This includes measuring parameters like the masses, spins, and eccentricity of merging black holes or neutron stars, as well as testing the predictions of general relativity. Accurate parameter estimation is crucial for understanding the population of compact objects and for probing the nature of gravity in strong-field regimes.

History

The field developed in the 1990s with the planning of gravitational wave detectors, and became a practical reality after the first detection in 2015. Since then, continuous improvements in waveform models and computational methods have refined the accuracy of parameter estimation.

How it works

The process involves comparing the observed gravitational wave signal with a bank of theoretical waveforms generated from general relativity or alternative theories. Using Bayesian inference, the likelihood of each set of parameters is computed, and posterior distributions are obtained. Techniques like matched filtering and Markov Chain Monte Carlo methods are employed to efficiently explore the parameter space and find the best-fit values with uncertainties.

In practice

This is used in all gravitational wave observatories (LIGO, Virgo, KAGRA) to identify the source properties of each event, and in future space-based detectors like LISA to study extreme mass ratio inspirals and cosmological sources.

Fun fact

The eccentricity of a binary system can be measured from gravitational waves, providing clues about the dynamical environment where the system formed, such as dense star clusters.

Concept graph →

Formulas

$$ds^2 = -e^{2\rho} dt^2 + e^{2\lambda} dr^2 + r^2 d\Omega^2$$
Metric for spherically symmetric spacetime in general coordinates.
What is in the formula
ds^2variablespacetime interval — spacetime interval metre squared
dtvariablecoordinate time differential — time differential second
drvariableradial coordinate differential — radial coordinate differential metre
dΩ^2variablesolid angle element squared — solid angle element squared
ρvariablemetric function of r and t — metric function
λvariablemetric function of r and t — metric function
rvariableradial coordinate — radial coordinate metre
ds^2=-e^{2ρ}dudv+r^2dω^2 · 2605.00780v1
ds^2=-a(r)dt^2+b(r)^{-1}dr^2+r^2(dθ^2+\sin^2θdφ^2) · 2605.09521v1
$$R_g = \frac{GM}{c^2}$$
Characteristic scale near event horizon for distance measurement.
What is in the formula
R_gvariableGravitational radius — gravitational radius metre
MvariableMass of the gravitating object — mass kilogram
GconstantFundamental constant quantifying the strength of gravity — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantUniversal speed limit for massless particles and information — speed of light = 299792458 metre per second
r_g=\frac{gm}{c^2} · 2606.25636
$$a_0 = \frac{e E_0}{m_e c \omega}$$
Dimensionless parameter comparing electron oscillation energy to rest mass.
What is in the formula
a_0variablerelativistic intensity parameter (normalized vector potential) — relativistic parameter
E_0variablepeak electric field amplitude of the laser — electric field volt per metre
ωvariableangular frequency of the laser — angular frequency radian per second
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
m_econstantmass of an electron at rest — electron mass = 9.1093837015e-31 kilogram
cconstantuniversal speed limit of light in vacuum — speed of light = 299792458 metre per second
a_0=\frac{ee_0}{m_ecω}=\frac{\sqrt{i[\rmw/cm^2]λ^2[μm^2]}}{1.38*10^{18}}\ge1 · 2607.00505
a_0=\frac{ee_0}{m_ecω} · 2607.00505v1
$$\mathcal{M} = \frac{(m_1 m_2)^{3/5}}{(m_1+m_2)^{1/5}}$$
Mass parameter determining gravitational wave chirp.
What is in the formula
MvariableChirp mass — mass kilogram
m_1variableMass of first object — mass kilogram
m_2variableMass of second object — mass kilogram
\mathcal{m}=\frac{(m_1m_2)^{3/5}}{(m_1+m_2)^{1/5}} · 2607.01372v1
m_{c,z}=\frac{(m_{1,z}m_{2,z})^{3/5}}{(m_{1,z}+m_{2,z})^{1/5}} · 2607.03885
$$b = q \sqrt{1 + \frac{2GM}{q v_{\infty}^2}}$$
Impact parameter for gravitational scattering.
What is in the formula
bvariableimpact parameter — impact parameter metre
qvariabledistance of closest approach in absence of gravity — distance metre
Mvariablemass of the gravitating body — mass kilogram
v_infinityvariablespeed of the test particle at infinity — velocity metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
sqrtoperatortakes the square root of the argument — square root
b=q\sqrt{1+\frac{2gm_\odot}{qv_\infty^2}} · 2607.04216
$$\sin \theta = \frac{q}{r} \sqrt{ \frac{1 + 2GM/(q v_{\infty}^2)}{1 - 2GM/(r v_{\infty}^2)} }$$
Angle for gravitational scattering trajectories.
What is in the formula
thetavariabledeflection angle — angle radian
qvariabledistance of closest approach in absence of gravity — distance metre
rvariableradial distance from the gravitating body — distance metre
Mvariablemass of the gravitating body — mass kilogram
v_infinityvariablespeed of the test particle at infinity — velocity metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
sinoperatortrigonometric sine function — sine
sqrtoperatortakes the square root of the argument — square root
\sinθ_c=\frac{q}{r}\sqrt{\frac{1+2gm_{\odot}/(qv_{\infty}^2)}{1-2gm_{\odot}/(rv_{\infty}^2)}} · 2607.04216v1

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