Waveforms for circular inspiral into Kerr black holes. *Curator's note: These waveforms were developed using Scott Hughes' black hole perturbation theory code (the "Teukolsky code"). There are two major steps in this process: (1) Repeatedly solving the Teukolsky equation to compute the fluxes of energy and angular momentum and the instantaneous wavestrain sourced by geodesic orbits. The code Hughes has developed for this is described in the following paper: S. A. Hughes, Phys Rev D 61, 084004 (2000). Hughes has been finding errors in this paper (none catastrophic so far...) at the rate of one per year since then: S. A. Hughes, Phys Rev D 63, 049902(E) (2001) S. A. Hughes, Phys Rev D 65, 069902(E) (2002) S. A. Hughes, Phys Rev D 67, 089901(E) (2003) (2) Taking a data set produced by the Teukolsky code and stitching together a quasistationary sequence to build the worldline followed by an inspiraling body, plus the associated inspiral waveform. The techniques and code for doing this are presented in S. A. Hughes, Phys Rev D 64, 064004 (2001) ------------------------------------------------------------------------ About this data: as described in the papers referenced above, these waves are computed in a harmonic/multipole decomposition of the perturbation to the background Kerr spacetime. In step 1 of this process (repeatedly solving the Teukolsky equation), as many orders are kept as are needed in order for a numerical convergence criterion to be met; see the 2000 PRD paper for discussion of this criterion. This means that more multipoles are used the deeper we get into the strong field of the black hole. In step 2, we use _all_ of the available harmonics/multipoles to compute the inspiral trajectory. However, we only use some subset of those harmonics/multipoles to make the waveform. This was largely to make the code run faster. High order harmonic/multipole contributions to the wavestrain rapidly become uninteresting at least at the level of making plots and audio files (which was the original purpose of producing these waves). ------------------------------------------------------------------------ The data file names encode the case they describe: iota_{i}_{ratio}_{lmax}_{kmax}.wave i: initial inclination angle (definition of inclination given in papers by Hughes) ratio: mass ratio of the system, M_{bh}/m_{small body}. The only data available right now has M/m = 1e4. lmax, kmax: the maximum values of the multipole index l and harmonic index k used to construct the waveform; see papers by Hughes for further details. The data on AstroGravs has lmax = {2, 4} and kmax = {2, 4}. (One exception: when iota = 0, k = 0 is the only allowed k index.) ------------------------------------------------------------------------ Data is available for only two values of black hole spin, so far: a/M = 0.998 (the value one obtains when spinup by thin disk accretion is buffered by retrograde photon capture from a hot photosphere; see K S Thorne 1974, ApJ 191, 507); a/M = 0.3594 (the value at which the horizon rotation frequency is identical to the orbital frequency at the innermost stable circular orbit; this is a natural spin value assuming magnetic braking by field lines that thread the horizon and the inner parts of an accretion disk). ------------------------------------------------------------------------ Each .wave file contains the following data columns: t r iota hpl_0 hcr_0 hpl_1 hcr_1 hpl_2 hcr_2 hpl_3 hcr_3 t is time (units explained below) r is orbital radius in units of M (the big black hole mass) iota is inclination angle hpl_0 is hplus viewed down the hole's spin axis hcr_0 is hcross viewed down the hole's spin axis hpl_1 is hplus viewed at 30 degreees to the hole's spin axis hcr_1 is hcross viewed at 30 degreees to the hole's spin axis hpl_2 is hplus viewed at 60 degreees to the hole's spin axis hcr_2 is hcross viewed at 60 degreees to the hole's spin axis hpl_3 is hplus viewed in the hole's equator hcr_3 is hcross viewed in the hole's equator t is given in somewhat goofy units. To get t in units of the big black hole mass, multiply t by the mass ratio (10000 for this data set). The reason for this is that M*M/m is the natural timescale for radiation reaction to significantly affect the binary; my code thus uses this number as its natural timestep. The various wavestrains are normalized such that their values are close to 1. To get values that would be measured by a gravitational wave detector, multiply by G m/(c^2 D) (where m is the mass of the inspiraling object, and D is distance to the binary). Note that certain data files were removed at the request of Scott Hughes because of lousy behavior in the time series. This behavior appears to be due to an interpolator bug that will be fixed when these files are superseded by improved data from Hughes' updated Teukolsky code.