Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals (1703.09722v2)

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.

• The paper demonstrates LISA’s capability to detect EMRIs with rates varying by up to three orders of magnitude based on astrophysical models.
• The paper shows that EMRI signal parameter precision can reach levels from 10⁻⁶ to 10⁻⁴, enabling detailed tests of black hole metrics.
• The paper highlights how EMRI observations inform the mass distribution of black holes and provide cosmological constraints such as the Hubble constant.

Overview of the Paper: Science with the Space-based Interferometer LISA. V. Extreme Mass-Ratio Inspirals

This paper explores the scientific potential of the Laser Interferometer Space Antenna (LISA) with a focus on extreme-mass-ratio inspirals (EMRIs), which involve a stellar-mass compact object orbiting a much more massive black hole. LISA is anticipated to detect the gravitational-wave signals emitted by such systems, providing a unique opportunity to extract detailed astrophysical information and enhance our understanding of massive black holes and their environments.

Key Contributions and Findings

1. EMRI Detection Potential: The paper thoroughly assesses the ability of LISA to detect EMRIs. It finds that, depending on the underlying astrophysical model, the intrinsic EMRI detection rate by LISA could vary up to three orders of magnitude. This significant variation underscores the uncertainties affecting astrophysical predictions related to EMRIs. Nonetheless, the paper predicts at least a few detections per year, with optimistic scenarios suggesting thousands.
2. Parameter Estimation Precision: EMRI signals can be used to measure intrinsic parameters such as the redshifted masses and spins of black holes with remarkable accuracy. The expected precision ranges from $10^{-6}$ to $10^{-4}$ for intrinsic parameters. Such precision facilitates tests of the Kerr metric's multipolar structure to percent-level accuracy.
3. Astrophysical Implications: Detecting EMRIs can reveal insights into the mass distribution of massive black holes and the dynamical structures at galactic centers. The paper finds that most detectable EMRIs with LISA will come from black holes with masses between $10^5 M_\odot$ and $10^6 M_\odot$, at redshifts between $0.5$ and $2$.
4. Technical Analysis: The paper employs analytical kludge (AK) waveform models as stand-ins for more computationally intensive models like those derived from black hole perturbation theory. It evaluates two variants, AKS and AKK, which provide bounds for the expected EMRI signal-to-noise ratios and allow predictions of detection rates and parameter precisions.
5. Impacts on Cosmology and Fundamental Physics: Beyond the astrophysical implications, the paper discusses the potential to utilize EMRIs as cosmological probes and for testing fundamental theories of gravity. For instance, it assesses how well LISA measurements can constrain the Hubble constant.

Conclusion and Future Directions

The paper provides a comprehensive overview of LISA's capabilities for observing EMRIs, highlighting the instrument's pivotal role in advancing gravitational-wave astronomy and our understanding of black holes. Despite uncertainties in astrophysical modeling, LISA's observations promise robust scientific contributions, with implications spanning astrophysics, cosmology, and fundamental physics. Future research may focus on refining waveform models, reducing astrophysical uncertainties, and integrating EMRI observations with those from other astrophysical phenomena to bolster the scientific yield of LISA's mission.