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

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 ∼ 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 ∼ 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.

Location of the last stable orbit in Kerr spacetime

“…For the extremal limit a = 1 there is no major simplification. But at the endpoints e = 0 and e = 1 there is, respectively, S pol (a = 1, e = 0) = (−1 + p) 2…”

“…The ISCO delineates one edge of a more general structure called the 'separatrix' that divides the stable region of the parameter space from the unstable/plunging region. This separatrix is particularly important for the physics of extreme mass-ratio inspirals (EMRIs) [2], key sources for the future space-based gravitational wave detector LISA. The event rate of these binaries is strongly influenced by the location of the separatrix, with highly spinning massive black holes more likely to capture stellar mass compact objects on prograde orbits [3].…”

Growth of resonances and chaos for a spinning test particle in the Schwarzschild background

“…The Laser Interferometric Space Antenna (LISA) mission, the first dedicated space-based gravitational wave detector, is expected to be launched in 2034 [4]. Unlike ground-based detectors, the sensitivity of LISA will lie in the range from 10 −4 Hz to 10 −2 Hz, allowing for observation of many different types of sources such as supermassive black hole mergers [5] or stellar mass compact binaries long before merger [6].…”

Gaussian processes for the interpolation and marginalization of waveform error in extreme-mass-ratio-inspiral parameter estimation

“…The waveform difference at each parameter point is also taken to be perfectly correlated across all frequency bins, which gives the particular normalizing factor in (11). Finally, the inner product for waveform differences in (15) is chosen to be proportional to the noise-weighted one in (2). These assumptions simplify the GPR calculations, but are also conservative in the sense that they generally yield less informative likelihoods; a more detailed justification is provided in [17].…”