@article{TEXTUAL,
      recid = {12127},
      author = {Romero-Shaw, Isobel and Loutrel, Nicholas and Zevin,  Michael},
      title = {Inferring interference: Identifying a perturbing tertiary  with eccentric gravitational wave burst timing},
      journal = {Physical Review D},
      address = {2023-06-08},
      number = {TEXTUAL},
      abstract = {Binary black holes may form and merge dynamically. These  binaries are likely to become bound with high  eccentricities, resulting in a burst of gravitational  radiation at their point of closest approach. When such a  binary is perturbed by a third body, the evolution of the  orbit is affected, and gravitational-wave burst times are  altered. The bursts times therefore encode information  about the tertiary. In order to extract this information,  we require a prescription for the relationship between the  tertiary properties and the gravitational-wave burst times.  In this paper, we demonstrate a toy model for the burst  times of a secular three-body system. We show how Bayesian  inference can be employed to deduce the tertiary properties  when the bursts are detected by next-generation  ground-based gravitational-wave detectors. We study the  bursts from an eccentric binary with a total mass of $60M⊙$  orbiting an $6×10^8M_⊙$ supermassive black hole. When we  assume no knowledge of the eccentric binary, we are unable  to tightly constrain the existence or properties of the  tertiary, and we recover biased posterior probability  distributions for the parameters of the eccentric binary.  However, when the properties of the binary are already well  known - as is likely if the late inspiral and merger are  also detected - we are able to more accurately infer the  mass of the perturber, $m_3$, and its distance from the  binary, R. When we assume measurement precision on the  binary parameters consistent with expectations for  next-generation gravitational-wave detectors, we can be  greater than 90% confident that the binary is perturbed.  When the orbit of the binary around the tertiary is face-on  with respect to the observer, there are large statistical  uncertainties on the recovered tertiary properties ($m_3$,  $R_3$, and orbital phase descriptors $ω_0$ and $V_{3,0]}$)  due to correlations between these parameters in the simple  toy model. However, if the orbit is tilted away from  face-on, these uncertainties can be substantially reduced.  Future models allowing for nonsecular evolution may further  decrease measurement uncertainties by breaking more  correlations between binary and tertiary parameters.},
      url = {http://knowledge.uchicago.edu/record/12127},
}