Generic extreme mass-ratio inspiral

Generic orbits are characterized by three numbers which set their orbital geometry: The “semi-latus rectum” p; the eccentricity e; and the inclination I. Precise definitions of p and e can be found in a good book on classical mechanics; for our purposes, it is useful to note that the semimajor axis of an elliptical orbit (the Newtonian limit of these models) is related to p and e by

$$ a = p/(1 - e^2). $$

The results presented here today are quite out of date; our ability to model systems like this has advanced considerably since we first developed these waveform models. These sounds are based on rather crude kludge models, which were introduced by various of us about 15 years ago as a stopgap in order to explore how measuring EMRI signals while better models were produced. Much better models now exist, and we are likely to update these sounds accordingly in the not-too-distant future.

In the cases we present here, we have put $$p = 5GM/c^2$$ and have set the black hole spin to 95% of the maximum. We then vary eccentricity and inclination to see how changing the orbit’s geometry changes the waves.

Eccentricity e = 0.2, inclination I = 25°: waveform

Eccentricity e = 0.7, inclination I = 25°: waveform

Eccentricity e = 0.95, inclination I = 25°: waveform

Eccentricity e = 0.95, inclination I = 60°: waveform

The character of the waves changes quite dramatically as the eccentricity is increased. For high eccentricity, the wave consists of a series of “pops” as the small body passes through periapsis, and is quiet as it goes back out to apoapsis. The pops come closer together as the system evolves, since GW backreaction reduces the system’s eccentricity. In these kludges, many of the systems become completely circular before the system merges. Though the shrinking eccentricity is correct, shrinking to e = 0 is known to be an incorrect artifact of the kludge.

The major effect of inclination is to change the point at which the smaller body’s orbit becomes unstable and it plunges into the big black hole. The two sounds for e = 0.95 are nearly identical, but the more highly inclined one shuts off sooner. The higher the orbit’s inclination, the more rapidly this feature is encountered.

In all these cases, the system’s mass ratio is set to 10,000:1. Setting the total mass to roughly 100 solar masses makes the audio signal correspond roughly to the band of the human ear. The sound files correspond to the “plus” polarization of the systems’ waveforms, and they are “viewed” in the equatorial plane of the parent black hole.