Singular value decomposition in parametrised tests of post-Newtonian theory

Various coefficients of the 3.5 post-Newtonian (PN) phasing formula of non-spinning compact binaries moving in circular orbits is fully characterized by the two component masses. If two of these coefficients are independently measured, the masses can be estimated. Future gravitational wave observations could measure many of the 8 independent PN coefficients calculated to date. These additional measurements can be used to test the PN predictions of the underlying theory of gravity. Since all of these parameters are functions of the two component masses, there is strong correlation between the parameters when treated independently. Using Singular Value Decomposition of the Fisher information matrix, we remove this correlations and obtain a new set of parameters which are linear combinations of the original phasing coefficients. We show that the new set of parameters can be estimated with significantly improved accuracies which has implications for the ongoing efforts to implement parametrised tests of PN theory in the data analysis pipelines.Comment: 17 pages, 6 figures, Accepted for publication in Classical and Quantum Gravity (Matches with the published version

Implications of binary black hole detections on the merger rates of double neutron stars and neutron star-black holes

We show that the inferred merger rate and chirp masses of binary black holes (BBHs) detected by advanced LIGO (aLIGO) can be used to constrain the rate of double neutron star (DNS) and neutron star - black hole (NSBH) mergers in the universe. We explicitly demonstrate this by considering a set of publicly available population synthesis models of \citet{Dominik:2012kk} and show that if all the BBH mergers, GW150914, LVT151012, GW151226, and GW170104, observed by aLIGO arise from isolated binary evolution, the predicted DNS merger rate may be constrained to be $2.3-471.0$~\rate~ and that of NSBH mergers will be constrained to $0.2-48.5$~\rate. The DNS merger rates are not constrained much but the NSBH rates are tightened by a factor of $\sim 4$ as compared to their previous rates. Note that these constrained DNS and NSBH rates are extremely model dependent and are compared to the unconstrained values $2.3-472.5$ \rate~ and $0.2-218$ \rate, respectively, using the same models of \citet{Dominik:2012kk}. These rate estimates may have implications for short Gamma Ray Burst progenitor models assuming they are powered (solely) by DNS or NSBH mergers. While these results are based on a set of open access population synthesis models which may not necessarily be the representative ones, the proposed method is very general and can be applied to any number of models thereby yielding more realistic constraints on the DNS and NSBH merger rates from the inferred BBH merger rate and chirp mass.Comment: 5 pages, no figures, 4 tables, v2: matches published versio

Generic bounds on dipolar gravitational radiation from inspiralling compact binaries

Various alternative theories of gravity predict dipolar gravitational radiation in addition to quadrupolar radiation. We show that gravitational wave (GW) observations of inspiralling compact binaries can put interesting constraints on the strengths of the dipole modes of GW polarizations. We put forward a physically motivated gravitational waveform for dipole modes, in the Fourier domain, in terms of two parameters: one which captures the relative amplitude of the dipole mode with respect to the quadrupole mode ($\alpha$) and the other a dipole term in the phase ($\beta$). We then use this two parameter representation to discuss typical bounds on their values using GW measurements. We obtain the expected bounds on the amplitude parameter $\alpha$ and the phase parameter $\beta$ for Advanced LIGO (AdvLIGO) and Einstein Telescope (ET) noise power spectral densities using Fisher information matrix. AdvLIGO and ET may at best bound $\alpha$ to an accuracy of $\sim10^{-2}$ and $\sim10^{-3}$ and $\beta$ to an accuracy of $\sim10^{-5}$ and $\sim10^{-6}$ respectively.Comment: Matches with the published versio

Radiation reaction in the 2.5PN waveform from inspiralling binaries in circular orbits

In this Comment we compute the contributions of the radiation reaction force in the 2.5 post-Newtonian (PN) gravitational wave polarizations for compact binaries in circular orbits. (i) We point out and correct an inconsistency in the derivation of Arun, Blanchet, Iyer, and Qusailah. (ii) We prove that all contributions from radiation reaction in the 2.5PN waveform are actually negligible since they can be absorbed into a modification of the orbital phase at the 5PN order.Comment: 7 pages, no figures, submitted to CQ

Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order

[abridged] Although gravitational radiation causes inspiralling compact binaries to circularize, a variety of astrophysical scenarios suggest that binaries might have small but nonnegligible orbital eccentricities when they enter the low-frequency bands of ground and space-based gravitational-wave detectors. If not accounted for, even a small orbital eccentricity can cause a potentially significant systematic error in the mass parameters of an inspiralling binary. Gravitational-wave search templates typically rely on the quasi-circular approximation, which provides relatively simple expressions for the gravitational-wave phase to 3.5 post-Newtonian (PN) order. The quasi-Keplerian formalism provides an elegant but complex description of the post-Newtonian corrections to the orbits and waveforms of inspiralling binaries with any eccentricity. Here we specialize the quasi-Keplerian formalism to binaries with low eccentricity. In this limit the non-periodic contribution to the gravitational-wave phasing can be expressed explicitly as simple functions of frequency or time, with little additional complexity beyond the well-known formulas for circular binaries. These eccentric phase corrections are computed to 3PN order and to leading order in the eccentricity for the standard PN approximants. For a variety of systems these eccentricity corrections cause significant corrections to the number of gravitational wave cycles that sweep through a detector's frequency band. This is evaluated using several measures, including a modification of the useful cycles. We also evaluate the role of periodic terms that enter the phasing and discuss how they can be incorporated into some of the PN approximants. While the eccentric extension of the PN approximants is our main objective, this work collects a variety of results that may be of interest to others modeling eccentric relativistic binaries.Comment: 49 pages, 4 figures. Submitted to Phys. Rev. D. Supplementary materials available at http://link.aps.org/supplemental/10.1103/PhysRevD.93.124061. V2: minor updates to match published versio