Gravitational Waves from Inspiralling Compact Binaries: Partial 3.5 PN Modes, Higher Order Stationary Phase Approximation

Abstract

For both data analysis and validation of numerical waveforms we need to know the Post-Newtonian (PN) waveforms as accurately as possible. Comparison between PN waveforms and numerical waveforms is implemented by projecting the waveforms onto spin weighted spherical harmonics and comparing the individual components. I am focusing on the inspiral part of non-spinning coalescing compact binary (CCB) system, as they are the most promising sources for laser interferometric detectors. To compute the spherical harmonic modes (h^{lm}s) for inspiralling compact binaries (ICBs) we need to know the source multipole moments of the system. Earlier investigations have calculated the spherical harmonic modes for 3 PN accurate gravitational waveform and some modes for l=2,3, at 3.5 PN accuracy. My aim is to go half a PN order further and calculate spherical harmonic modes for 3.5 PN accurate full waveform for non-spinning ICBs. To this end, I discuss the accuracy of the source multipole moments which will contribute to 3.5 PN waveform. By doing literature survey I have checked the availability of these moments and listed the available ones. I show that with the available source moments we can calculate spherical harmonic modes(h^{lm}s) with full 3.5 PN accuracy, only for modes l=2,3 when l+m is even, for l=5 when l+m is odd and for l>=6. With the available source multipole moments as inputs, I have written a mathematica code, which gives spherical harmonic modes for 3.5 PN accurate waveform as a function of l and m. This new code also reproduces the spherical harmonic modes till 3 PN order consistent with the earlier work. Finally I display the spherical harmonic modes for l=5 when l+m is odd and for l=6 to l=9 which are obtained in this work and are new. Extreme mass ratio inspirals (EMRIs) are one of the important sources for evolved laser interferometric space antenna (eLISA). Recent works have calculated the 22 PN waveforms for extreme mass ratio binaries (EMRIs) using the black hole perturbation theory. Vijay et al have calculated the Fourier transform of gravitational waveform for EMRIs to 22 PN order using the leading stationary phase approximation (SPA). The SPA can be improved by computing the next order correction terms. In the second part of my project, I find the first order correction terms to the Fourier transform of the gravitational waveform for EMRIs.