Extreme Love in the SPA: constraining the tidal deformability of supermassive objects with extreme mass ratio inspirals and semi-analytical, frequency-domain waveforms

TL;DR

This paper explores how future LISA observations of extreme mass ratio inspirals can precisely measure the tidal Love number of supermassive objects, testing deviations from classical black hole predictions in General Relativity.

Contribution

It introduces a semi-analytical, frequency-domain waveform model for EMRIs that enables fast and accurate Fisher matrix analyses to constrain the tidal Love number.

Findings

LISA can constrain the tidal Love number of supermassive objects by several orders of magnitude more than current detectors.

The semi-analytical waveform approach accelerates high-precision parameter estimation.

Constraints are significantly tighter for higher spin values of the central object.

Abstract

We estimate the accuracy in the measurement of the tidal Love number of a supermassive compact object through the detection of an extreme mass ratio inspiral~(EMRI) by the future LISA mission. A nonzero Love number would be a smoking gun for departures from the classical black hole prediction of General Relativity. We find that an EMRI detection by LISA could set constraints on the tidal Love number of a spinning central object with dimensionless spin $\hat a=0.9$ ($\hat a=0.99$) which are approximately four (six) orders of magnitude more stringent than what achievable with current ground-based detectors for stellar-mass binaries. Our approach is based on the stationary phase approximation to obtain approximate but accurate semi-analytical EMRI waveforms in the frequency-domain, which greatly speeds up high-precision Fisher-information matrix computations. This approach can be easily extended to several other tests of gravity with EMRIs and to efficiently account for multiple deviations in the waveform at the same time.