# Generic wave models

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}).

In the cases we present here, we have chosen to put

*p*= 5

*GM*/

*c*

^{2}for all the binaries, and we 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°: p5_e0.2_i25_a0.95_hp

Eccentricity

*e*= 0.7, inclination

*i*= 25°: p5_e0.7_i25_a0.95_hp

Eccentricity

*e*= 0.95, inclination

*i*= 25°: p5_e0.95_i25_a0.95_hp

Eccentricity

*e*= 0.95, inclination

*i*= 60°: p5_e0.95_i60_a0.95_hp

Notice that 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 out to apoapsis. The pops come closer together as the system evolves, since GW backreaction reduces the system's eccentricity. (In these crude simulations, many of the systems become completely circular before the system merges. Though the shrinking eccentricity is correct, the shrinking to

*e*= 0 is now known to be an artifact of the kludge used here. This will be updated as we expand our catalog of sounds!) 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. Notice that 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 that feature is encountered.

As with the circular waves, the system's mass ratio is set to 10,000:1 in all cases; the total mass was then adjusted so that it lies nicely in the band of the human ear. The total mass of the system turns out to be roughly 100 solar masses in these cases. 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.