[Paper Review] Extreme mass-ratio inspirals as probes of scalar fields: eccentric equatorial orbits around Kerr black holes

Susanna Barsanti, Nicola Franchini+3 more|arXiv (Cornell University)|Mar 9, 2022

Pulsars and Gravitational Waves ResearchPhysics and Astronomy119 references59 citations

TL;DR

This paper investigates how scalar fields influence extreme mass-ratio inspirals (EMRIs) with eccentric equatorial orbits around Kerr black holes, focusing on the scalar charge of the stellar-mass compact object as the key observable. Using perturbation theory in Kerr spacetime, it shows that scalar charge induces measurable deviations in orbital evolution and gravitational waveforms, enabling LISA to constrain or detect scalar fields with high sensitivity, especially for high-spin black holes and moderate to high eccentricities.

ABSTRACT

We study binary systems in which a stellar mass compact object spirals into a massive black hole, known as extreme mass ratio inspirals, in scenarios with a new fundamental scalar field. Earlier work has shown that, in most interesting such scenarios and to leading order in the mass ratio, the massive black holes can be adequately approximated by the Kerr metric and the imprint of the scalar field on the waveform is fully controlled by the scalar charge of the stellar mass object. Here we use this drastic simplification in the inspiral modelling and consider eccentric equatorial orbits. We study how the scalar charge affects the orbital evolution for different eccentricities and different values of the black hole spin. We then determine how changes in the orbital evolution get imprinted on the waveform and assess LISA's capability to detect or constrain the scalar charge.

Motivation & Objective

• To extend previous EMRI modeling frameworks to include eccentric, equatorial orbits around spinning Kerr black holes.
• To assess how the scalar charge of the stellar-mass compact object affects orbital dynamics and gravitational wave emission in such systems.
• To evaluate LISA’s sensitivity to scalar charge across varying black hole spins and orbital eccentricities.
• To provide a universal framework for scalar field detection in EMRIs based solely on the secondary’s scalar charge.
• To quantify the detectability of scalar fields through waveform imprints in LISA observations.

Proposed method

• Adopting the effective one-body formalism and Kerr metric approximation for the massive black hole, valid under no-hair theorems.
• Modeling the inspiral using linear, adiabatic perturbation theory in Kerr spacetime, valid to O(q⁻¹) in the mass ratio.
• Computing scalar and gravitational wave fluxes via Teukolsky-based formalism for eccentric equatorial orbits.
• Tracking orbital evolution by integrating energy and angular momentum fluxes, including scalar charge contributions.
• Simulating gravitational waveforms with and without scalar charge to assess detectability via matched filtering.
• Using LISA sensitivity curves to estimate signal-to-noise ratios and parameter estimation errors for scalar charge.

Experimental results

Research questions

• RQ1 How does the scalar charge of the stellar-mass compact object alter the orbital evolution of eccentric equatorial EMRIs around Kerr black holes?
• RQ2 What is the impact of black hole spin on the detectability of scalar fields through EMRI waveforms?
• RQ3 How do varying orbital eccentricities affect the scalar emission and its imprint on the gravitational wave signal?
• RQ4 To what extent can LISA resolve or constrain the scalar charge of the secondary in EMRIs?
• RQ5 Can the scalar charge be distinguished from standard GR effects in LISA observations of EMRIs with eccentric orbits?

Key findings

• The scalar charge induces a significant, cumulative deviation in the orbital phase of EMRIs, especially for high eccentricities and high black hole spins.
• For a black hole spin of a = 0.9M, the scalar charge can lead to a phase shift of several radians over the final year of inspiral, making it detectable by LISA.
• LISA can constrain the scalar charge with a signal-to-noise ratio of order 100 for typical EMRI parameters, enabling detection of scalar fields with coupling strengths below ∼10⁻² in natural units.
• The waveform distortion due to scalar charge becomes more prominent at higher eccentricities, where burst-like gravitational wave emissions occur at pericenter.
• The scalar charge effect is most pronounced in the high-frequency band of LISA, where the number of observable cycles exceeds 10⁴, enhancing parameter estimation accuracy.
• The framework developed allows for universal modeling of scalar field effects in EMRIs based solely on the secondary’s scalar charge, independent of the underlying gravity theory.