Interactive gravitational wave demonstration for spin and eccentricity
Every binary black hole radiates the same basic chirp, so the parameters we measure have to be hidden somewhere in its shape. The tool below lets you drag the mass ratio, the effective spin and the precessing spin of a binary and compare the waveform against a pinned reference. Every waveform is an SEOBNRv5 model in dimensionless units:
- time is measured in units of the total mass $M$, with $t=0$ at the peak of $\lvert h_{22}\rvert$;
- the phase is set to zero at that peak, so two waveforms can be compared cycle by cycle;
- dimensionless amplitude $r h_{22}/(M\nu)$ plotted, the amplitude is divided by the symmetric mass ratio $\nu = q/(1+q)^2$ to make comparison easier.
Open interactive explorer in full-screen ↗
How it is made
The page cannot run a waveform model live, so it carries a precomputed grid: 9 values of $q$
(log-spaced from 1 to 8), 7 values of $\chi_{\rm eff}$, 9 values of $\chi_p$ and 7 values of $e$, generated with
pyseobnr (SEOBNRv5HM for aligned spins,
SEOBNRv5PHM once $\chi_p > 0$, SEOBNRv5EHM once $e > 0$). Rather than storing inertial-frame modes, it stores the
co-precessing modes $(2,2)$, $(2,1)$, $(3,3)$, $(3,2)$, $(4,4)$, $(4,3)$ together with the Euler
angles of the frame rotation. In that frame every amplitude and phase is smooth, so the browser can
interpolate them in $\log q$ and $\chi_{\rm eff}$ and then rotate, with Wigner $D$-matrices, to the
frame of the total angular momentum $\mathbf{J}$, from which the inclination $\iota$ is measured
(this frame barely moves, which is what makes the interpolation physical; what it cannot resolve
between grid nodes is the orbital phase at merger relative to the precession cycle, equivalent to a
different initial in-plane spin azimuth),
- note that this approximation might have some slight incorrect ringing at high $q\sim8$ and high $\chi_p$, but for the bulk of the parameter space this is correct
