[Paper Review] Observability of lensing of gravitational waves from massive black hole binaries with LISA

Mesut Çalışkan, Lingyuan Ji+4 more|arXiv (Cornell University)|Jun 6, 2022

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper investigates the observability of wave-optics effects in gravitational waves from massive black hole binaries lensed by compact objects, using LISA. By performing an information-matrix analysis with analytical waveforms including higher harmonics and spin effects, it demonstrates that LISA can detect lensing signatures for lower-mass lenses and higher impact parameters than previously thought, significantly improving the prospects for single-detection lens parameter estimation via frequency-dependent modulations.

ABSTRACT

The gravitational waves emitted by massive black hole binaries in the LISA band can be lensed. Wave-optics effects in the lensed signal are crucial when the Schwarzschild radius of the lens is smaller than the wavelength of the radiation. These frequency-dependent effects can enable us to infer the lens parameters, possibly with a single detection alone. In this work, we assess the observability of wave-optics effects with LISA by performing an information-matrix analysis using analytical solutions for both point-mass and singular isothermal sphere lenses. We use gravitational-waveform models that include the merger, ringdown, higher harmonics, and aligned spins to study how waveform models and source parameters affect the measurement errors in the lens parameters. We find that previous work underestimated the observability of wave-optics effects and that LISA can detect lensed signals with higher impact parameters and lower lens masses.

Motivation & Objective

• To assess the observability of wave-optics effects in lensed gravitational waves from massive black hole binaries using LISA.
• To determine whether lens parameters—such as mass and impact parameter—can be measured from a single LISA detection using frequency-dependent modulations.
• To evaluate how waveform model complexity (e.g., higher harmonics, spin effects) influences lens parameter measurement accuracy.
• To challenge prior assumptions that wave-optics effects are unobservable for low-mass lenses or high impact parameters.

Proposed method

• Performs an information-matrix analysis to estimate measurement errors in lens parameters from a single LISA detection of a lensed massive black hole binary signal.
• Uses analytical solutions for both point-mass and singular isothermal sphere lens models to compute the lensed gravitational waveform.
• Incorporates realistic gravitational-waveform models that include the full inspiral-merger-ringdown evolution, higher harmonics, and aligned spins.
• Derives analytical expressions for the derivatives of the diffraction integral with respect to lens mass and impact parameter, enabling sensitivity calculations.
• Applies the Fisher information matrix formalism to compute the inverse covariance of lens parameters, quantifying measurement precision.
• Considers both redshifted lens mass and source-plane position as measurable parameters, with a focus on wave-optics-dominated regimes.

Experimental results

Research questions

• RQ1 Can LISA detect wave-optics effects in lensed gravitational waves from massive black hole binaries, even for low-mass lenses?
• RQ2 To what extent do waveform model complexities—such as higher harmonics and spin—improve the measurement of lens parameters?
• RQ3 What is the minimum lens mass and maximum impact parameter for which wave-optics effects remain observable with LISA?
• RQ4 Does the inclusion of frequency-dependent amplitude and phase modulations enable lens parameter estimation from a single detection?
• RQ5 How does the observability of wave-optics effects compare to previous estimates that assumed geometric optics?

Key findings

• LISA can detect wave-optics effects in lensed massive black hole binary signals for lens masses as low as ~10^5 M☉, significantly lower than previous estimates of ~10^6 M☉.
• The observability extends to higher impact parameters than previously believed, enabling detection of lensing by less compact lenses.
• Waveform models that include higher harmonics and spin effects reduce measurement errors in lens parameters, improving the accuracy of single-detection lensing analysis.
• The Fisher information matrix analysis confirms that frequency-dependent modulations from diffraction enable robust lens parameter estimation even without multiple images.
• The study corrects prior underestimations of observability, showing that wave-optics effects are detectable across a broader range of lens masses and geometries than previously thought.