Influence of conservative corrections on parameter estimation for extreme-mass-ratio inspirals

TL;DR

This paper develops an improved waveform model for extreme-mass-ratio inspirals (EMRIs) that includes conservative self-force corrections, enhancing parameter estimation accuracy and assessing the significance of higher-order effects.

Contribution

The paper introduces a new numerical kludge waveform model for EMRIs that incorporates conservative self-force corrections derived from post-Newtonian comparisons, which was not done before.

Findings

Conservative corrections slightly improve parameter estimation accuracy.

Omitting conservative corrections generally results in small errors for most systems.

First-order self-force calculations may be sufficient for accurate parameter estimation.

Abstract

We present an improved numerical kludge waveform model for circular, equatorial EMRIs. The model is based on true Kerr geodesics, augmented by radiative self-force corrections derived from perturbative calculations, and in this paper for the first time we include conservative self-force corrections that we derive by comparison to post-Newtonian results. We present results of a Monte Carlo simulation of parameter estimation errors computed using the Fisher Matrix and also assess the theoretical errors that would arise form omitting the conservative correction terms we include here. We present results for three different types of system, namely the inspirals of black holes, neutron stars or white dwarfs into a supermassive black hole (SMBH). The analysis shows that for a typical source (a 10 solar mass compact object captured by a one million solar mass SMBH at signal to noise ratio of 30) we expect to determine the two masses to within a fractional error of ~0.0001, measure the spin parameter q to ~0.00003 and determine the location of the source on the sky and the spin orientation to within 0.001 steradians. We show that, for this kludge model, omitting the conservative corrections leads to a small error over much of the parameter space, i.e., the ratio R of the theoretical model error to the Fisher Matrix error is R<1 for all ten parameters in the model. For the few systems with larger errors typically R<3 and hence the conservative corrections can be marginally ignored. In addition, we use our model and first order self-force results for Schwarzschild black holes to estimate the error that arises from omitting the second-order radiative piece of the self-force. This indicates that it may not be necessary to go beyond first order to recover accurate parameter estimates.