Circular extreme mass-ratio inspiral

These correspond to an EMRI which initially has zero eccentricity. An orbit which starts circular stays circular, which makes computing its GWs relatively simple. This is an idealized limit, but nicely illustrates the dynamics of these binaries and the character of their waves. (And, there are some astrophysical scenarios which make very small eccentricity plausible. Because such waves are relatively simple to model, they may be easier to measure as compared to the generic case.)

In the sounds linked below, the two GW polarizations are encoded in stereo: “plus” polarization is in one ear, “cross” is in the other. You can sometimes hear a cool evolution in the two polarizations, especially as the end is approached. Also, note that there are two angles describing the waves: Orbital plane and viewing angle. Orbital plane describes how the orbit is tilted with respect to the equator of the black hole (where the “equator” is 90° from the spin axis); the viewing angle describes the system’s orientation to our line of sight. Zero degrees viewing angle means that we are viewing in the equatorial plane of the binary.

We organize the cases we show by the spin of the larger body, focusing on two spins motivated by particular evolutionary scenarios. In all cases, the mass ratio is set to 10,000:1, and the total mass is adjusted so that the system’s signal is in the band of the human ear. This yields a total mass of about 100 solar masses for the 99.8% cases, and about 60 solar masses for the 35.94% cases.

Spin 99.8% of maximum

99.8% of maximum spin is a good “astrophysical” limit. 100% of maximum is the mathematical limit. However, a 1974 analysis by Kip Thorne shows that when a black hole accretes hot matter, its spin saturates at 99.8% of maximum. The reason is the hot accreting matter radiates a roughly isotropic glow of photons, and those photons carry both energy and angular momentum. The capture cross section for counter-rotating photons is significantly larger than that for co-rotating photons. The retrograde angular momentum of the counter-rotating photons buffers the spin at 99.8% maximum. Thorne’s model uses a very thin disk of material, now regarded as unlikely to be astrophysically relevant. When thicker disk models are used, the spin is buffered to an even smaller value. But 99.8% is still a nice value to stand in for the largest spin likely to be found in nature.

Spin 35.94% of maximum

In many models for the evolution of black hole spin during accretion, there is magnetohydrodynamic coupling of the hole to accreting material. For rapid spin, the hole spins faster than the orbital frequency at the inner edge of an accretion disk; this coupling tends to slow down those holes. For slow spin, the disk spins faster than the hole; this coupling speeds up those holes. 35.94% of maximum is the point at which the inner edge and the hole rotate at exactly the same frequency. As such, it describes “slow” rotation in a model where a hole’s spin evolution is driven by accretion.

These sounds were all made by UROP alumna Pei-Lan Hsu using code written by Hughes.