phenomenon

gravitational wave resonance

Resonant interactions between orbiting bodies that amplify gravitational wave emissions.
25 related articles · 6 formulas

Description

Gravitational wave resonance is a phenomenon where orbiting bodies, such as neutron stars or black holes, interact with each other in a way that amplifies the emission of gravitational waves. This occurs when the orbital frequency of the system matches a natural resonant frequency of the bodies themselves, causing them to deform and oscillate more strongly. The effect can significantly enhance the energy lost to gravitational radiation, speeding up the inspiral of the binary system and producing stronger signals than would be expected from a simple point-mass model.

History

The concept of tidal resonance in binary systems was explored in the 1970s and 1980s, with key contributions from theorists like Peter Goldreich and Scott Tremaine in the context of planetary moons, and later applied to neutron star binaries by researchers such as Lars Bildsten and Curt Cutler in the 1990s.

How it works

In a binary system, each body has its own natural oscillation modes, similar to how a bell rings at specific frequencies. As the two bodies orbit each other, their gravitational pull causes tidal deformations. When the orbital frequency sweeps through one of these natural frequencies, the deformation is amplified — the body 'rings' like a struck bell. This resonant oscillation extracts extra orbital energy, which is radiated away as gravitational waves. The effect is strongest during the final moments before merger, when the orbital frequency rapidly increases through a range of resonant frequencies.

In practice

Resonance effects are crucial for accurately modeling gravitational wave signals from neutron star binaries, helping detectors like LIGO and Virgo extract precise information about the stars' internal structure and equation of state.

Fun fact

The resonance can be so strong that it causes the neutron star to deform into a prolate (cigar-like) shape, dramatically increasing the gravitational wave amplitude just before merger.

Concept graph →

Formulas

$$f_{\rm reh} \propto T_{\rm reh}$$
Gravitational wave knee frequency scales with reheating temperature.
What is in the formula
f_rehvariableGravitational wave knee frequency at reheating — frequency hertz
T_rehvariableReheating temperature — temperature kelvin
f_{\rmreh}\simeq3.8*10^{-8}(\frac{t_{\rmreh}}{\rmgev}){\rmhz} · 2605.00735v1
$$h^2 \Omega_{\rm GW} \propto \left(\frac{\Delta\rho}{\rho}\right)^2$$
Gravitational wave amplitude scales with density contrast squared.
What is in the formula
hvariableDimensionless Hubble constant (H0/100 km/s/Mpc) — hubble constant dimensionless
\Omega_{\rm GW}variableGravitational wave energy density parameter — energy density parameter
\Delta\rho/\rhovariableDensity contrast (relative density perturbation) — density contrast
\proptooperatorIndicates proportionality between the left and right sides — proportional to
h^2ω_{\rmgw}^{\rmpeak}\sim10^{-8}\frac{δρ^2}{ρ_f^2} · 2607.24734v1
$$R_B = rac{2GM}{c_s^2}$$
Radius where gravitational energy equals thermal energy.
What is in the formula
R_BvariableBondi radius — radius metre
Mvariablemass of the central object — mass kilogram
c_svariablesound speed of the surrounding medium — sound speed metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
r_b=\frac{2gm_{bh}}{c_s^2} · 2606.02700v1
$$h_0 = \frac{4\pi^2 G}{c^4} \frac{\varepsilon I_{zz} f_{\rm GW}^2}{d}$$
The amplitude of gravitational waves from a rotating ellipsoid.
What is in the formula
h_0variablegravitational wave strain amplitude — strain
εvariableellipticity — ellipticity
I_zzvariablemoment of inertia about rotation axis — moment of inertia kilogram metre squared
f_GWvariablegravitational wave frequency — frequency hertz
dvariabledistance to source — distance metre
GconstantNewton's constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
h_0=\frac{4π^2g}{c^4}\frac{\varepsiloni_{zz}f_{\rmgw}^2}{d} · 2606.05082v1
$$\tilde{h}_L(f) = \sum_j |\mu_j|^{1/2} e^{2\pi i f \Delta t_j - i\pi n_j} \tilde{h}_{\rm src}(f)$$
Lensed gravitational wave signal sum over images.
What is in the formula
h̃_LvariableLensed gravitational wave signal in frequency domain — gravitational wave strain
fvariableGravitational wave frequency — frequency hertz
μ_jvariableMagnification factor of image j — magnification
Δt_jvariableTime delay of image j relative to source — time delay second
n_jvariableMorse index of image j — morse index
h̃_srcvariableUnlensed source gravitational wave signal — gravitational wave strain
∑operatorSum over lensed images — summation
e^{...}operatorComplex exponential encoding phase shifts — exponential
\tilde{h}_l(f)=\sum_{j=1}^{n_{\rmimg}}|μ_j|^{1/2}\exp[2πifδt_j-iπn_j]\tilde{h}_{\rmsrc}(f;θ_s) · 2607.03885
$$\gamma = \frac{g}{g_N}$$
Ratio of observed to Newtonian gravitational acceleration.
What is in the formula
\gammavariableRatio of observed to Newtonian gravitational acceleration
gvariableObserved gravitational acceleration — acceleration metre per second squared
g_NvariableNewtonian gravitational acceleration — acceleration metre per second squared
γ=\frac{g}{g_n}=\frac{v^2/r}{g_nm_{{tot}}/r^2} · 2607.14450

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