Discovering Love numbers through resonance excitation during extreme mass ratio inspirals

Abstract

General Relativity predicts that black holes (BHs) do not possess an internal structure and consequently cannot be excited. This leads to a specific prediction about the waveform of gravitational waves (GWs) which they emit during a binary BH inspiral and to the vanishing of their Love numbers. However, if astrophysical BHs do possess an internal structure, their Love numbers would no longer vanish, and they could be excited during an inspiral by the transfer of orbital energy. This would affect the orbital period and lead to an observable imprint on the emitted GWs waveform. The effect is enhanced if one of the binary companions is resonantly excited. We discuss the conditions for resonant excitation of a hypothetical internal structure of BHs and calculate the phase change of the GWs waveform that is induced due to such resonant excitation during intermediate- and extreme-mass-ratio inspirals. We then relate the phase change to the electric quadrupolar Love number of the larger companion, which is resonantly excited by its smaller companion. We discuss the statistical error on measuring the Love number by LISA and show that, because of this phase change, the statistical error is small even for values of the Love number as small as 10−4 for moderate values of the spin parameter. Our results indicate that, for extreme-mass-ratio inspirals with moderate spin parameter, the Love number could be detected by LISA with an accuracy which is higher by up to two orders of magnitude than what can be achieved via tidal deformation effects. Thus, our results indicate that resonant excitation of the central BH during an extreme- or intermediate-mass-ratio inspirals is the most promising effect for putting bounds on, or detecting, non-vanishing tidal Love numbers of BHs.