Science with the space-based interferometer LISA. V. Extreme mass-ratio inspirals

TLDR

LISA will observe extreme‑mass‑ratio inspirals—systems of a massive black hole and a stellar‑mass compact object—that complete ~10⁴–10⁵ cycles in band, enabling exquisitely precise parameter measurements. This study quantifies how astrophysical uncertainties affect predicted EMRI detection rates and evaluates the precision with which LISA can recover source parameters. The authors model LISA’s sensitivity to EMRIs to assess the statistical errors in intrinsic parameters, luminosity distance, sky localization, and tests of the Kerr metric. Astrophysical assumptions lead to a three‑order‑of‑magnitude spread in predicted EMRI rates, yet LISA should detect at least a few per year and up to thousands under optimistic models; parameter estimation will achieve fractional errors of 10⁻⁶–10⁻⁴ for masses, spin, and eccentricity, ~10 % for luminosity distance, a few‑square‑degree sky localization, and percent‑level tests of the Kerr multipolar structure.

Abstract

The space-based Laser Interferometer Space Antenna (LISA) will be able to observe the gravitational-wave signals from systems comprised of a massive black hole and a stellar-mass compact object. These systems are known as extreme-mass-ratio inspirals (EMRIs) and are expected to complete $\sim 10^4$-$10^5$ cycles in band, thus allowing exquisite measurements of their parameters. In this work, we attempt to quantify the astrophysical uncertainties affecting the predictions for the number of EMRIs detectable by LISA, and find that competing astrophysical assumptions produce a variance of about three orders of magnitude in the expected intrinsic EMRI rate. However, we find that irrespective of the astrophysical model, at least a few EMRIs per year should be detectable by the LISA mission, with up to a few thousands per year under the most optimistic astrophysical assumptions. We also investigate the precision with which LISA will be able to extract the parameters of these sources. We find that typical fractional statistical errors with which the intrinsic parameters (redshifted masses, massive black hole spin and orbital eccentricity) can be recovered are $\sim 10^{-6}$-$10^{-4}$. Luminosity distance (which is required to infer true masses) is inferred to about $10\%$ precision and sky position is localized to a few square degrees, while tests of the multipolar structure of the Kerr metric can be performed to percent-level precision or better.