Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

TLDR

Newly formed black holes emit characteristic ringdown waves in discrete quasinormal mode frequencies. The study aims to enable LISA to detect these ringdown waves from supermassive black holes and to develop a multimode formalism for detecting the signals, estimating black‑hole parameters, and testing the no‑hair theorem. The authors construct a multimode formalism applicable to any interferometric detector, apply it to LISA using its sensitivity models to compute expected SNR, parameter‑estimation accuracy, and mode resolvability, and examine how uncertainties in spin and mode energy affect spectroscopy. Their results indicate that LISA can achieve sufficient SNR to resolve multiple ringdown modes, allowing precise black‑hole parameter estimation, though uncertainties in spin and emitted energy limit the ultimate precision of black‑hole spectroscopy.

Abstract

Newly formed black holes are expected to emit characteristic radiation in the form of quasinormal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multimode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black-hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black-hole spin and the energy emitted in each mode, will affect our ability to do black-hole spectroscopy.