Constraining the tidal deformability of supermassive objects with extreme mass ratio inspirals and semianalytical frequency-domain waveforms

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 $\widehat{a}=0.9$ ($\widehat{a}=0.99$), 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 semianalytical 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.

Figure 1

$1\text{−}\sigma$ error on the primary TLN $k_1$ as a function of the primary spin parameter $\widehat{a}\in [0.1,0.99]$. Different markers correspond to including the spin of the secondary, removing it from the Fisher matrix, or adding a Gaussian prior centered around the injected value of $\chi$ (see main text). The luminosity distance is fixed such that $\mathrm{SNR}=30$ after 1 year of observation. As a reference, current measurement errors on the TLN of a neutron star coming from GW170817 [48] are ${\sigma }_{k_1}\lesssim {10}^3$.