Kavli Affiliate: Pau Amaro Seoane
| First 5 Authors: Pau Amaro Seoane, Josep V. Arnau, Màrius Josep Fullana i Alfonso, ,
| Summary:
The gravitational capture of a small compact object by a supermassive black
hole is one of the most intriguing sources of gravitational waves to be
detected by space-borne observatories. Modeling gravitational waves is a
challenging task. However, various approximations exist that enable us to claim
detection and perform parameter extraction with high accuracy on synthetic
data. The first numerical implementation of relativistic corrections for an
astrophysical system was conducted in a post-Newtonian (PN) framework, and
since then, most comparable programmes have followed a similar approach.
Nevertheless, the PN approach has been developed for two particles in a vacuum.
Here, we present the first results on the impact of cross-terms in the PN
scheme for “monochromatic” sources (meaning that the peak frequency does not
evolve over the observational time), which account for the interplay between
different bodies. We present a conceptual and illustrative study of the
cross-terms on the first PN term in a group of three bodies representing
asymmetric binaries (X-MRIs, E-EMRIs, and X-MRIs with E-EMRIs). We find that
these cross-terms can lead to a complete phase shift of the gravitational wave
by a few times $2pi$ over periods of time of less than one year for the close
binaries. Ignoring the cross-terms in the relativistic semi-Keplerian system
can significantly complicate parameter extraction for monochromatic sources.
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