3D Black Hole & Neutron Star Mergers

Two black holes, or two neutron stars, spiral in as they radiate gravitational waves. The readout tracks the wave frequency in hertz, the strain and the energy radiated.

Loading compact-object merger (WebGL 2.0)

Binary black holes and neutron stars spiral together as they radiate gravitational waves. The inspiral here is a Newtonian circular orbit shrinking under the leading-order (Peters) radiation-reaction formula, played back faster than real time. The merger and ringdown are a scripted animation. It is not a numerical-relativity or post-Newtonian solver.

Binary Black Holes

GW150914-like masses (5-80 Msun). The inspiral stops at a = 6 GM/c^2.

Neutron Star Mergers

GW170817-like masses (1.0-2.3 Msun), stopping at contact for 12 km stars. No tides are modelled.

Kilonova Ejecta

BNS runs end with an ejecta burst. Colours are illustrative; no nuclear network is computed.

Physical Readouts

GW frequency in Hz, strain at a reference distance and radiated binding energy, from the formulas below.

Technical Details

What Is Computed

Units are G = c = 1 with total mass M = 1, so separation is in GM/c^2 and time in GM/c^3. The orbit is circular and Newtonian; its separation shrinks under the leading-order (2.5PN, Peters 1964) radiation-reaction formula, which integrates exactly:

da/dt  = -(64/5) * eta / a^3      eta = m1*m2/(m1+m2)^2
a(t)^4 = a0^4 - (256/5) * eta * t
omega  = a^(-3/2)                 (Kepler)

f_GW = 2 * omega/(2*pi) / (M * G*Msun/c^3)       [Hz]
h    = 4 * eta * (G*M/c^2) / (a * D)             (face-on quadrupole amplitude)
E_rad / (M c^2) = (eta/2) * (1/a - 1/a0)          (Newtonian binding energy)

Each run starts at twice the stopping separation (6 GM/c^2 for black holes, contact of two 12 km stars for neutron stars) and is played back so the inspiral takes about 30 seconds at speed 1; the readout shows how much real time one second represents. Higher post-Newtonian terms, spins, tides, the plunge, the merger itself and the ringdown are not modelled: everything after the stopping separation is a scripted animation, and spin only turns the decorative glow ring.

R-Process Nucleosynthesis (background)

When neutron stars merge, they eject neutron-rich material that undergoes rapid neutron capture (r-process), creating elements heavier than iron. The demo does not compute this; the ejecta colours only label the peaks below:

R-Process PeakMass NumberElementsYe Threshold
First PeakA ~ 80Se, Br, Kr< 0.40
Second PeakA ~ 130Te, I, Xe< 0.30
Third PeakA ~ 195Au, Pt, Os< 0.20
ActinidesA ~ 250U, Th, Pu< 0.15

Controls

  • Mass Sliders: Adjust primary and secondary masses (Msun)
  • Type Toggle: Switch between BBH and BNS binaries
  • GW Rings: One expanding ring per gravitational-wave cycle, brightness scaled by strain
  • Trails Toggle: Show/hide orbital path history
  • Speed Slider: Control simulation time scale
  • Orbit: Click and drag to rotate camera view
  • Zoom: Scroll to zoom in/out

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