Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly spinning black holes

Observations of gravitational-wave signals emitted by compact binary inspirals provide unique insights into their properties, but their analysis requires accurate and efficient waveform models. Intermediate- and extreme-mass-ratio inspirals (I/EMRIs), with mass ratios <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>q</a:mi> <a:mo>≳</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>2</a:mn> </a:msup> </a:math> , are promising sources for future detectors such as the Laser Interferometer Space Antenna (LISA). Modeling waveforms for these asymmetric-mass binaries is challenging, entailing the tracking of many harmonic modes over thousands to millions of cycles. The FastEMRIWaveforms () modeling framework addresses this need, leveraging precomputation of mode data and interpolation to rapidly compute adiabatic waveforms for eccentric inspirals into zero-spin black holes. In this work, we extend to model eccentric equatorial inspirals into black holes with spin magnitudes <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo stretchy="false">|</c:mo> <c:mi>a</c:mi> <c:mo stretchy="false">|</c:mo> <c:mo>≤</c:mo> <c:mn>0.999</c:mn> </c:math> . Our model supports eccentricities <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>e</g:mi> <g:mo>≤</g:mo> <g:mn>0.9</g:mn> </g:math> and semilatus recta <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>p</i:mi> <i:mo>≤</i:mo> <i:mn>200</i:mn> </i:math> , enabling the generation of long-duration IMRI waveforms, and produces waveforms in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo>∼</k:mo> <k:mn>100</k:mn> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>ms</k:mi> </k:math> with hardware acceleration. Characterizing systematic errors, we estimate that our model attains mismatches of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mo>∼</m:mo> <m:msup> <m:mn>10</m:mn> <m:mrow> <m:mo>−</m:mo> <m:mn>5</m:mn> </m:mrow> </m:msup> </m:math> (for LISA sensitivity) with respect to error-free adiabatic waveforms over the majority of the parameter space. We find that kludge models can introduce errors in signal-to-noise ratios (SNRs) as great as <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:msubsup> <o:mrow> <o:mtext> </o:mtext> </o:mrow> <o:mrow> <o:mo>−</o:mo> <o:mn>40</o:mn> <o:mo>%</o:mo> </o:mrow> <o:mrow> <o:mo>+</o:mo> <o:mn>60</o:mn> <o:mo>%</o:mo> </o:mrow> </o:msubsup> </o:mrow> </o:math> and induce marginal biases of up to <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mo>∼</q:mo> <q:mn>1</q:mn> <q:mi>σ</q:mi> </q:math> in parameter estimation. We show that LISA’s horizon redshift for I/EMRI signals varies significantly with <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>a</s:mi> </s:math> , reaching a redshift of 3 (15) for EMRIs (IMRIs) with only minor <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mo stretchy="false">(</u:mo> <u:mo>∼</u:mo> <u:mn>10</u:mn> <u:mo>%</u:mo> <u:mo stretchy="false">)</u:mo> </u:math> dependence on <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>e</y:mi> </y:math> for an SNR threshold of 20. For signals with <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>SNR</ab:mi> <ab:mo>∼</ab:mo> <ab:mn>50</ab:mn> </ab:math> , spin and eccentricity at plunge are measured with uncertainties of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>δ</cb:mi> <cb:mi>a</cb:mi> <cb:mo>∼</cb:mo> <cb:msup> <cb:mn>10</cb:mn> <cb:mrow> <cb:mo>−</cb:mo> <cb:mn>7</cb:mn> </cb:mrow> </cb:msup> </cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>δ</eb:mi> <eb:msub> <eb:mi>e</eb:mi> <eb:mi mathvariant="normal">f</eb:mi> </eb:msub> <eb:mo>∼</eb:mo> <eb:msup> <eb:mn>10</eb:mn> <eb:mrow> <eb:mo>−</eb:mo> <eb:mn>5</eb:mn> </eb:mrow> </eb:msup> </eb:math> . This work advances the state of the art in waveform generation for asymmetric-mass binaries, providing open-source tools for the investigation of I/EMRI astrophysics and data analysis.