Resonant interactions between orbiting bodies that amplify gravitational wave emissions.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.
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.
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.
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.
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.
| f_reh | variable | Gravitational wave knee frequency at reheating — frequency hertz |
| T_reh | variable | Reheating temperature — temperature kelvin |
| h | variable | Dimensionless Hubble constant (H0/100 km/s/Mpc) — hubble constant dimensionless |
| \Omega_{\rm GW} | variable | Gravitational wave energy density parameter — energy density parameter |
| \Delta\rho/\rho | variable | Density contrast (relative density perturbation) — density contrast |
| \propto | operator | Indicates proportionality between the left and right sides — proportional to |
| R_B | variable | Bondi radius — radius metre |
| M | variable | mass of the central object — mass kilogram |
| c_s | variable | sound speed of the surrounding medium — sound speed metre per second |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| h_0 | variable | gravitational wave strain amplitude — strain |
| ε | variable | ellipticity — ellipticity |
| I_zz | variable | moment of inertia about rotation axis — moment of inertia kilogram metre squared |
| f_GW | variable | gravitational wave frequency — frequency hertz |
| d | variable | distance to source — distance metre |
| G | constant | Newton's constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| h̃_L | variable | Lensed gravitational wave signal in frequency domain — gravitational wave strain |
| f | variable | Gravitational wave frequency — frequency hertz |
| μ_j | variable | Magnification factor of image j — magnification |
| Δt_j | variable | Time delay of image j relative to source — time delay second |
| n_j | variable | Morse index of image j — morse index |
| h̃_src | variable | Unlensed source gravitational wave signal — gravitational wave strain |
| ∑ | operator | Sum over lensed images — summation |
| e^{...} | operator | Complex exponential encoding phase shifts — exponential |
| \gamma | variable | Ratio of observed to Newtonian gravitational acceleration |
| g | variable | Observed gravitational acceleration — acceleration metre per second squared |
| g_N | variable | Newtonian gravitational acceleration — acceleration metre per second squared |








