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Authors: E A Huerta, Jonathan R Gair

Date: 22 Dec 2008

Abstract: We present an improved numerical kludge waveform model for circular, equatorial extreme-mass-ratio inspirals (EMRIs). The model is based on true Kerr geodesics, augmented by appropriate conservative and radiative self--force corrections from perturbative. We present a Monte Carlo analysis of parameter estimation errors from 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 events, namely black holes, neutron stars or white dwarfs inspiralling 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 ~0.0003 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 is not necessary to go beyond first order to obtain accurate parameter-error estimates.

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