Gravitational Radiation Reaction and Inspiral Waveforms in the Adiabatic Limit

We describe progress evolving an important limit of binaries in general relativity: stellar mass compact objects spiraling into much larger black holes. Such systems are of great observational interest. We have developed tools to compute for the first time the radiation from generic orbits. Using global conservation laws, we find the orbital evolution and waveforms for special cases. For generic orbits, inspirals and waveforms can be found by augmenting our approach with an adiabatic self-force rule due to Mino. Such waveforms should be accurate enough for gravitational-wave searches.

Figure 1

Top: Average CPU time per mode versus number of processors $N$ for two strong field orbits. Our scaling shows $T_{\mathrm{CPU}}\propto 1/N$. The typical CPU time per mode is short, though eccentric orbits are about 5–10 times slower than circular. Bottom: Flux ${\dot{E}}_l$ (defined in the text) versus $l$ for an orbit with $p=4$, $e=0.5$, $\iota =45°$, and black hole spin $a=0.9M$.

Figure 2

Gravitational waveform for several strong field orbits; all are for a hole with spin $a=0.9M$, and have $p=4$. Top: eccentricity $e=0.5$, inclination $\iota =45°$. Middle: $e=0$, $\iota =45°$. Bottom: $e=0.5$, $\iota =0°$. Orbital parameters, particularly eccentricity, richly influence the harmonic structure.