Binary Black Hole Coalescence

Two black holes spiraling, merging, and ringing — animated in real time on the accurate post-Newtonian trajectory of IMRPhenomD, with the emitted gravitational-wave field rendered as it propagates outward in the equatorial plane.

Khan, Husa, Hannam, Ohme, Pürrer, Forteza, Bohé · 2016 · arXiv:1508.07253  ·  Buonanno, Iyer, Ochsner, Pan, Sathyaprakash · 2009 · arXiv:0907.0700
MODEL CLASS  CALIBRATED WAVEFORM MODEL  trajectory from IMRPhenomD; the wave field is drawn in the equatorial plane
65
Mtot · M☉
1.22
mass ratio q
-0.02
χeff
62
Mf · M☉
0.69
χf
275
fRD · Hz
Spacetime · Equatorial Plane · m = 2 Quadrupole Emission

Two horizons on the inspiral trajectory · GW field at retarded time

Black-hole positions integrated from the post-Newtonian equations of motion. The emitted gravitational-wave field is rendered on a 256×256 grid using the m=2 quadrupole formula evaluated at t − R/c; the two-armed spiral pattern is the asymptotic wave structure at large radius. Time control at bottom; cameras at left; instantaneous source state at right.

Camera

Source state · live

t−0.000 s
r / M10.0
v = (Mω)1/30.20
fGW35 Hz
|h(r=100M)|0.0
Coordinates use the total mass M = M1+M2 as both length and time unit; multiply by GM/c3 = 320 μs to recover physical units for this source.
Adiabatic inspiral
ISCO crossing
Plunge
Merger
Ringdown · l=m=2,n=0
h+ − +
t = 0.000 M · 0.0 ms

Coalescence proceeds through three regimes the animation labels in real time. The adiabatic inspiral is what the post-Newtonian series describes — orbital separation shrinking slowly relative to the orbital period as energy is radiated away. The plunge begins near the innermost stable circular orbit (ISCO of the effective Kerr geometry) where the perturbative expansion breaks down and the bodies fall together over a few dynamical times. The ringdown is the single remnant black hole's quasi-normal mode oscillation, decaying exponentially at the Berti+ 2009 (l = m = 2, n = 0) Kerr frequency. Every transition is computed from the source parameters, not pre-scripted; if you change q or χ in the sliders below, the phase markers move along with the trajectory.

Source parameters

Five aligned-spin parameters

65 M☉
log scale · 10 – 3160 M☉ · sets the physical-time scaling
1.22
PhenomD trained for q ≤ 18 · q > 4 enters higher-mode regime
+0.32
Aligned with L̂ · changes inspiral length and final spin
-0.44
Aligned with L̂ · range [−0.99, +0.99]
0.20
v = (Mω)1/3 at animation start · lower = more cycles, slower

Boundary of validity

What is and isn't modelledread this

The post-Newtonian trajectory is integrated as TaylorT4 to 3.5 PN with the dominant spin-orbit term at 1.5 PN. The merger and ringdown geometry is constructed from the verified Husa+ 2016 final-spin and Healy+ 2014 final-mass fits and the Berti+ 2009 Kerr quasi-normal-mode table — these are the same fits used by the IMRPhenomD waveform model and reproduce GW150914's remnant parameters to within 5%. The animation is geometric, not photometric — the dark sphere is the apparent horizon, the bright ring is the photon sphere (r = 1.5 rS in Schwarzschild, slightly modified for Kerr), and the colored wave field is the m = 2 quadrupole strain at the retarded time. No Kerr lensing of the background, no relativistic beaming of the photon ring.

Aligned spin only

Spins are constrained to ±L̂. Precession (in-plane spin components) would tilt the orbital plane and introduce amplitude modulation; that is not in the model.

precession not modelled
Mass ratio q ≤ 18

Outside this domain PN extrapolates and the remnant fits degrade. EMRIs (q ~ 10⁴) need Teukolsky-perturbation models.

q = 1.22 · inside training region
Spin magnitude |χ| ≤ 0.85

Final-spin fit was trained on |χ1,2| ≤ 0.85. Higher values extrapolate and the apparent horizon visualization (drawn at r = MBH(1+√(1−χ²))) shrinks toward the maximally rotating limit.

|χ|max = 0.44 · well inside
Geometric, not photon-lensed

Real BBH visualizations from SXS / NASA SVS apply Kerr ray-tracing to render the photon ring with general-relativistic lensing of the background star field. Here the BH is drawn as a dark sphere with a bright photon-sphere ring; the colored field outside is the GW strain, not light.

no Kerr lensing
Equatorial wave slice only

The colored plane is the z = 0 slice of the asymptotic GW field. Off-plane the m = 2 amplitude scales as (1+cos²ι)/2, so an edge-on observer (ι = 90°) sees half the equatorial amplitude. The colorbar uses arbitrary units with global rescaling.

equatorial m=2 only
Plunge interpolation

Between v ≈ 0.55 (ISCO) and the moment of common horizon formation the trajectory is an analytic interpolation, not full numerical relativity. This is the regime where a real production tool would call NRSur7dq4 or read SXS waveform data.

analytic plunge bridge

References

  • Buonanno, A., Iyer, B. R., Ochsner, E., Pan, Y., Sathyaprakash, B. S. 2009, Phys. Rev. D 80, 084043 — TaylorT4 / TaylorF2 post-Newtonian equations of motion to 3.5 PN — arXiv:0907.0700
  • Khan, S., Husa, S., Hannam, M., Ohme, F., Pürrer, M., Forteza, X. J., Bohé, A. 2016, Phys. Rev. D 93, 044007 — IMRPhenomD frequency-domain inspiral-merger-ringdown approximant — arXiv:1508.07253
  • Husa, S., Khan, S., Hannam, M., Pürrer, M., Ohme, F., Forteza, X. J., Bohé, A. 2016, Phys. Rev. D 93, 044006 — Final-spin fit "FinalSpin0815" (eq. 3.6) — arXiv:1508.07250
  • Healy, J., Lousto, C. O., Zlochower, Y. 2014, Phys. Rev. D 90, 104004 — Final-mass and recoil fits from non-precessing BBH NR — arXiv:1406.7295
  • Berti, E., Cardoso, V., Will, C. M. 2006, Phys. Rev. D 73, 064030; Berti, E., Cardoso, V., Starinets, A. O. 2009, Class. Quantum Grav. 26, 163001 — Kerr quasi-normal-mode frequencies and damping times — arXiv:gr-qc/0512160, arXiv:0905.2975
  • Damour, T., Iyer, B. R., Sathyaprakash, B. S. 2001, Phys. Rev. D 63, 044023 — TaylorT4 family of time-domain templates — arXiv:gr-qc/0010009
  • Boyle, M. et al. 2019, Class. Quantum Grav. 36, 195006 — SXS Visualizations Group and the modern numerical-relativity reference catalog — arXiv:1904.04831
  • Abbott, B. P. et al. (LIGO–Virgo Collaboration) 2016, Phys. Rev. Lett. 116, 061102 — GW150914 (Mtot ≈ 65 M☉, q ≈ 1.22, χeff ≈ −0.06, DL ≈ 410 Mpc) — arXiv:1602.03837
  • Abbott, R. et al. 2020, Phys. Rev. Lett. 125, 101102 — GW190521 (detector-frame Mtot ≈ 250 M☉) — arXiv:2009.01075
  • Abbott, R. et al. 2020, Phys. Rev. D 102, 043015 — GW190412 (q ≈ 3.6) — arXiv:2004.08342