Prospects for observing extreme-mass-ratio inspirals with LISA (1704.00009v1)

Abstract: One of the key astrophysical sources for the Laser Interferometer Space Antenna (LISA) are the inspirals of stellar-origin compact objects into massive black holes in the centres of galaxies. These extreme-mass-ratio inspirals (EMRIs) have great potential for astrophysics, cosmology and fundamental physics. In this paper we describe the likely numbers and properties of EMRI events that LISA will observe. We present the first results computed for the 2.5 Gm interferometer that was the new baseline mission submitted in January 2017 in response to the ESA L3 mission call. In addition, we attempt to quantify the astrophysical uncertainties in EMRI event rate estimates by considering a range of different models for the astrophysical population. We present both likely event rates and estimates for the precision with which the parameters of the observed sources could be measured. We finish by discussing the implications of these results for science using EMRIs.

Prospects for Observing Extreme-Mass-Ratio Inspirals with LISA

The paper explores the potential for the Laser Interferometer Space Antenna (LISA) to detect extreme-mass-ratio inspirals (EMRIs), a promising source of gravitational waves (GWs) from the inspiral of stellar-origin compact objects into massive black holes (MBHs). The authors meticulously analyze the number and properties of EMRI events that LISA might observe and attempt to quantify the associated astrophysical uncertainties.

Estimation of EMRI Event Rates

The authors commence by discussing the key parameters involved in estimating EMRI event rates: MBH mass and spin distributions, the intrinsic rate of EMRI occurrences, and the characteristics of the inspiralling compact objects. They employ multiple astrophysical models to cover plausible population variations, ranging from conservative to optimistic in terms of both physical parameters and rate estimates. The primary computational tool for EMRI gravitational waveforms used is the approximate Analytic Kludge (AK) model, which captures key waveform features for signal-to-noise ratio (SNR) and parameter-estimation precision calculations.

Two conditions—Schwarzschild and Kerr plunge—are employed to predict the number of observable events with LISA. They find that LISA is likely to detect several hundred EMRI events over two years, which suggests robustness to model assumptions. Notably, event rates vary by an order of magnitude depending on the model and range from nearly zero in a pessimistic case to several thousand in more favorable scenarios.

Detector Sensitivity and Configuration

The analysis includes different LISA configurations, showing a marked difference in detectable events depending on the arm length and link configuration of the detector—spanning a decrease by a factor of ten in lower configurations to an increase by a factor of three with a longer arm length. The authors utilize a noise model involving several parameters to determine SNR thresholds critical for detection, estimating $\rho_{\text{thresh}}$ values of 20 and 30 for confident detections.

Implications for Science and Parameter Estimation

Parameter estimation using the Fisher matrix suggests LISA will achieve high precision for intrinsic and extrinsic EMRI parameters, irrespective of the underlying astrophysical model. Redshifted masses, MBH spins, and orbital characteristics are expected to be measurable with sub-percent accuracy, whereas sky positioning may be refined to a few square degrees. Such precision opens avenues for probing both astrophysical and cosmological questions.

Astrophysical Implications: The potential to measure the MBH mass function down to unprecedented precision offers crucial insights into galaxy evolution and MBH growth dynamics. The mass function measurement's accuracy, influenced by the number of observations, is expected to refine constraints on MBH population characteristics significantly.

Cosmological Significance: Utilizing EMRIs as standard sirens, the paper discusses prospects for constraining the Hubble constant. EMRI detections will provide a unique probe independent from traditional electromagnetic methods. While the baseline LISA configuration might moderate capabilities compared to longer baselines, statistical methods leveraging sky position will nonetheless enable valuable cosmological insights.

Fundamental Physics and General Relativity Tests: EMRIs will facilitate rigorous exploration of the Kerr metric in general relativity, potentially identifying deviations in space-time structure indicative of alternative gravitational theories. The sensitivity to quadrupole moment deviations is profound, resolving discrepancies at the percent level or less.

Conclusions

The findings lay a solid foundation for anticipating LISA's role in the field of GW astronomy. The exploration of EMRI detectability emphasizes the substantial impact even in the face of astrophysical uncertainties. Close integration with theoretical predictions and observation models is pivotal for deciphering insights from potential detections. LISA's promise of hundreds of observable EMRI events accentuates the vast scientific promise for uncharted investigations into the universe's structure and foundational physics principles.