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Abstract

Extreme-mass-ratio inspirals are one of the most exciting and promising
target sources for space-based interferometers (such as LISA, TianQin). The
observation of their emitted gravitational waves will offer stringent tests on
general theory of relativity, and provide a wealth of information about the
dense environment in galactic centers. To unlock such potential, it is
necessary to correctly characterize EMRI signals. However, resonances are a
phenomena that occurs in EMRI systems and can impact parameter inference, and
therefore the science outcome, if not properly modeled. Here, we explore how to
model resonances and develop an efficient implementation. Our previous work has
demonstrated that tidal resonances induced by the tidal field of a nearby
astrophysical object alters the orbital evolution, leading to a significant
dephasing across observable parameter space. Here, we extensively explore a
more generic model for the tidal perturber with additional resonance
combinations, to study the dependence of resonance strength on the intrinsic
orbital and tidal parameters. To analyze the resonant signals, accurate
templates that correctly incorporate the effects of the tidal field are
required. The evolution through resonances is obtained using a step function,
whose amplitude is calculated using an analytic interpolation of the resonance
jumps. We benchmark this procedure by comparing our approximate method to a
numerical evolution. We find that there is no significant error caused by this
simplified prescription, as far as the astronomically reasonable range in the
parameter space is concerned. Further, we use Fisher matrices to study both the
measurement precision of parameters and the systematic bias due to inaccurate
modeling. Modeling of self-force resonances can also be carried out using the
implementation presented in this study, which will be crucial for EMRI waveform
modeling.