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Abstract

The modelling of unequal mass binary black hole systems is of high importance
to detect and estimate parameters from these systems. Numerical relativity (NR)
is well suited to study systems with comparable component masses, $m_1\sim
m_2$, whereas small mass ratio (SMR) perturbation theory applies to binaries
where $q=m_2/m_1<< 1$. This work investigates the applicability for NR and SMR
as a function of mass ratio for eccentric non-spinning binary black holes. We
produce $52$ NR simulations with mass ratios between $1:10$ and $1:1$ and
initial eccentricities up to $0.7$. From these we extract quantities like
gravitational wave energy and angular momentum fluxes and periastron advance,
and assess their accuracy. To facilitate comparison, we develop tools to map
between NR and SMR inspiral evolutions of eccentric binary black holes. We
derive post-Newtonian accurate relations between different definitions of
eccentricity. Based on these analyses, we introduce a new definition of
eccentricity based on the (2,2)-mode of the gravitational radiation, which
reduces to the Newtonian definition of eccentricity in the Newtonian limit.
From the comparison between NR simulations and SMR results, we quantify the
unknown next-to-leading order SMR contributions to the gravitational energy and
angular momentum fluxes, and periastron advance. We show that in the comparable
mass regime these contributions are subdominant and higher order SMR
contributions are negligible.