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#### Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory

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2209.03390.pdf

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PhysRevD.106.124040.pdf

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##### Citation

Ramos Buades, A., van de Meent, M., Pfeiffer, H. P., Rüter, H. R., Scheel, M. A., Boyle, M., et al. (2022).
Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory.*
Physical Review D,* *106*(12): 124040. doi:10.1103/PhysRevD.106.124040.

Cite as: https://hdl.handle.net/21.11116/0000-000C-3E32-7

##### 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.

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.