Analytical Waveform Approximations and Parameter Sensitivity in Gravitational-Wave Models
Year: 2026
Type: preprint
Abstract: How do the total mass and the mass ratio shape the mathematical form of the gravitational wave emitted by an inspiralling compact binary? We answer this question within the post-Newtonian (PN) approximation of general relativity, using the chirp time per unit frequency \(dt/df\), a quantity unaffected by the arbitrary time and phase offsets of the signal. In the variables \((\mathcal{M},\eta)\), the chirp mass fixes the leading law \(dt/df\propto\mathcal{M}^{-5/3}f^{-11/3}\), and the mass ratio enters through sensitivity coefficients \(s_k(\eta)\), which we give in closed form to 2.5PN. Their signs alternate between the 1PN correction and the radiative tail. As a result, the mass-ratio sensitivity of the chirp changes sign at \(v_\star=(743-1386\eta)/(2016\pi)\) to leading order, that is at \(f_\star\simeq16.6\text{--}111\ \mathrm{Hz}\ (M_\odot/M)\). This relation is stable under truncation to within 7% and lies below the observed band for essentially all known sources. The same coefficients govern a closed-form cycle budget. They also explain why the tail term reverses the sign of the chirp--mass--mass-ratio correlation in a Fisher-matrix analysis and reduces \(\sigma_\eta\) by factors of 2--4. A phase-coherence bound shows that the Newtonian chirp is adequate only in the last 2--26% of the frequency range below the innermost stable circular orbit.
Source: Preprints.org
Author: Doni Nurdiansyah
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224619258