Testing eccentric corrections to the radiation-reaction force in the test-mass limit of effective-one-body models

In this work, we test an effective-one-body radiation-reaction force for eccentric planar orbits of a test mass in a Kerr background, which contains third-order post-Newtonian (PN) nonspinning and second-order PN spin contributions. We compare the analytical fluxes connected to two different resummations of this force, truncated at different PN orders in the eccentric sector, with the numerical fluxes computed through the use of frequency- and time-domain Teukolsky-equation codes. We find that the different PN truncations of the radiation-reaction force show the expected scaling in the weak gravitational-field regime, and we observe a fractional difference with the numerical fluxes that is <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo>&lt;</a:mo><a:mn>5</a:mn><a:mo>%</a:mo></a:math>, for orbits characterized by eccentricity <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>0</c:mn><c:mo>≤</c:mo><c:mi>e</c:mi><c:mo>≤</c:mo><c:mn>0.7</c:mn></c:math>, central black-hole spin <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mo>−</e:mo><e:mn>0.99</e:mn><e:mi>M</e:mi><e:mo>≤</e:mo><e:mi>a</e:mi><e:mo>≤</e:mo><e:mn>0.99</e:mn><e:mi>M</e:mi></e:math> and fixed orbital-averaged quantity <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>x</g:mi><g:mo>=</g:mo><g:mo stretchy="false">⟨</g:mo><g:mi>M</g:mi><g:mi mathvariant="normal">Ω</g:mi><g:msup><g:mo stretchy="false">⟩</g:mo><g:mrow><g:mn>2</g:mn><g:mo>/</g:mo><g:mn>3</g:mn></g:mrow></g:msup><g:mo>=</g:mo><g:mn>0.06</g:mn></g:math>, corresponding to the mildly strong-field regime with semilatera recta <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mn>9</l:mn><l:mi>M</l:mi><l:mo>&lt;</l:mo><l:mi>p</l:mi><l:mo>&lt;</l:mo><l:mn>17</l:mn><l:mi>M</l:mi></l:math>. Our analysis provides useful information for the development of spin-aligned eccentric models in the comparable-mass case.