Intermediate-mass-ratio-inspirals in the Einstein Telescope. II. Parameter estimation errors

TL;DR

This paper evaluates how accurately the Einstein Telescope can measure parameters of intermediate-mass-ratio inspirals using two waveform models, providing detailed estimates of measurement errors for various system configurations.

Contribution

It introduces a comprehensive analysis of parameter estimation errors for IMRIs with two advanced waveform models, including spin effects, using Fisher Matrix and Monte Carlo methods.

Findings

Parameter estimation errors can reach fractional accuracies of 0.001 for masses and 0.0003 for spins.

Sky localization can be achieved within 0.003 steradians, and luminosity distance within 10%.

Results depend on the detector network configuration and source parameters.

Abstract

We explore the precision with which the Einstein Telescope (ET) will be able to measure the parameters of intermediate-mass-ratio inspirals (IMRIs). We calculate the parameter estimation errors using the Fisher Matrix formalism and present results of a Monte Carlo simulation of these errors over choices for the extrinsic parameters of the source. These results are obtained using two different models for the gravitational waveform which were introduced in paper I of this series. These two waveform models include the inspiral, merger and ringdown phases in a consistent way. One of the models, based on the transition scheme of Ori & Thorne [1], is valid for IMBHs of arbitrary spin, whereas the second model, based on the Effective One Body (EOB) approach, has been developed to cross-check our results in the non-spinning limit. In paper I of this series, we demonstrated the excellent agreement in both phase and amplitude between these two models for non-spinning black holes, and that their predictions for signal-to-noise ratios (SNRs) are consistent to within ten percent. We now use these models to estimate parameter estimation errors for binary systems with masses 1.4+100, 10+100, 1.4+500 and 10+500 solar masses (SMs), and various choices for the spin of the central intermediate-mass black hole (IMBH). Assuming a detector network of three ETs, the analysis shows that for a 10 SM compact object (CO) inspiralling into a 100 SM IMBH with spin q=0.3, detected with an SNR of 30, we should be able to determine the CO and IMBH masses, and the IMBH spin magnitude to fractional accuracies of 0.001, 0.0003, and 0.001, respectively. We also expect to determine the location of the source in the sky and the luminosity distance to within 0.003 steradians, and 10%, respectively. We also assess how the precision of parameter determination depends on the network configuration.