Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Across the Universe: GW231123 as a magnified and diffracted black hole merger

Srashti Goyal, Hector Villarrubia-Rojo, Miguel Zumalacarregui

TL;DR

GW231123 presents an apparent anomaly in BBH mass estimates, prompting a lensing hypothesis that includes wave-optics diffraction by a microlens embedded in an external macro-potential. The authors develop an embedded point-lens model, perform Bayesian model comparison across unlensed, isolated-PL, and embedded-PL hypotheses, and find false-alarm probabilities $\text{FAP}<1\%$ with Bayes factors favoring lensing, particularly for NRSur-based waveforms. The embedded lensing scenario yields more typical source masses and higher redshift, constraining the microlens to $M_L(1+z_L)\sim300$–$1500\,M_\odot$ and predicting a substantial chance of a second macroimage with a few days delay. They also derive constraints on the microlens population as potential dark-matter compact objects, noting mild tension with other limits and illustrating how GW diffraction can probe lensing across scales from stars to galaxies. Overall, the work demonstrates how incorporating wave-optics lensing and a macrolens context can reconcile GW231123 with the BBH population and motivates further lensing tests via additional images and more sophisticated lens models.

Abstract

GW231123 appears as the most massive binary black hole (BBH) ever observed by the LIGO interferometers with total mass $190-265 M_\odot$. A high observed mass can be explained by the combination of cosmological redshift and gravitational magnification if the source is aligned with a gravitational lens, such as a galaxy. Small-scale objects such as stars and remnants diffract the signal, distorting the wavefront and providing additional lensing signatures. Here we present an analysis of GW231123 combining for the first time the effects of diffraction by a small-scale lens and gravitational magnification by an external potential, modelled as an embedded point-mass lens (PL), finding an intriguing case for the lensing hypothesis. Lensing is favoured by the data, with a false alarm probability of the observed Bayes factors bounded below $<1\%$, or $\sim 2.6 σ$ confidence level. Including lensing lowers the total source mass of GW231123 to $100-180 M_\odot$, closer to BBHs reported so far, and also removes discrepancies between different waveform approximants and the need for high component spins. We reconstruct all source and lens properties, including the microlens mass $190-850 M_\odot$, its offset, the magnitude of the external gravitational potential and its orientation. The embedded PL analysis leads to a lighter microlens compared to the isolated PL. Within our assumptions, the reconstruction is complete up to an ambiguity between the distance and projected density (mass-sheet degeneracy). Assuming a single galaxy as the macroscopic lens allows us to infer the total amplification of the signal, placing the event at redshift $0.7-2$, and predict the probability $~55\%$ of forming an additional detectable image due to strong lensing by the macrolens. We discuss the implications of our findings on the source and nature of the microlens, including a possible dark matter origin.

Across the Universe: GW231123 as a magnified and diffracted black hole merger

TL;DR

GW231123 presents an apparent anomaly in BBH mass estimates, prompting a lensing hypothesis that includes wave-optics diffraction by a microlens embedded in an external macro-potential. The authors develop an embedded point-lens model, perform Bayesian model comparison across unlensed, isolated-PL, and embedded-PL hypotheses, and find false-alarm probabilities with Bayes factors favoring lensing, particularly for NRSur-based waveforms. The embedded lensing scenario yields more typical source masses and higher redshift, constraining the microlens to – and predicting a substantial chance of a second macroimage with a few days delay. They also derive constraints on the microlens population as potential dark-matter compact objects, noting mild tension with other limits and illustrating how GW diffraction can probe lensing across scales from stars to galaxies. Overall, the work demonstrates how incorporating wave-optics lensing and a macrolens context can reconcile GW231123 with the BBH population and motivates further lensing tests via additional images and more sophisticated lens models.

Abstract

GW231123 appears as the most massive binary black hole (BBH) ever observed by the LIGO interferometers with total mass . A high observed mass can be explained by the combination of cosmological redshift and gravitational magnification if the source is aligned with a gravitational lens, such as a galaxy. Small-scale objects such as stars and remnants diffract the signal, distorting the wavefront and providing additional lensing signatures. Here we present an analysis of GW231123 combining for the first time the effects of diffraction by a small-scale lens and gravitational magnification by an external potential, modelled as an embedded point-mass lens (PL), finding an intriguing case for the lensing hypothesis. Lensing is favoured by the data, with a false alarm probability of the observed Bayes factors bounded below , or confidence level. Including lensing lowers the total source mass of GW231123 to , closer to BBHs reported so far, and also removes discrepancies between different waveform approximants and the need for high component spins. We reconstruct all source and lens properties, including the microlens mass , its offset, the magnitude of the external gravitational potential and its orientation. The embedded PL analysis leads to a lighter microlens compared to the isolated PL. Within our assumptions, the reconstruction is complete up to an ambiguity between the distance and projected density (mass-sheet degeneracy). Assuming a single galaxy as the macroscopic lens allows us to infer the total amplification of the signal, placing the event at redshift , and predict the probability of forming an additional detectable image due to strong lensing by the macrolens. We discuss the implications of our findings on the source and nature of the microlens, including a possible dark matter origin.

Paper Structure

This paper contains 12 sections, 15 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Diffraction by a point mass embedded in an external potential
  3. Bayesian Inference
  4. Source and Lens Properties
  5. Source properties and waveform systematics
  6. Microlens properties
  7. Additional macroimages
  8. Conclusions and prospects
  9. Microlensing diffraction analysis
  10. Source properties
  11. Microlens mass and radius
  12. Microlens as dark matter

Figures (9)

  • Figure 1: Diffracted and magnified GWs. Top left: A small-scale point-lens in an external potential diffracts the signal. The external potential produces additional images and extends the Einstein ring (color shows the micro-magnification). This represents the local region near a macroimage produced by a galaxy, shown in the right panel. The offset between the lens and source ($y_{\rm macro}$) determines whether additional images (dashed line) form. In contrast, the isolated point lens (bottom left panel) only produces two images and does not capture effects from the macroscopic potential.
  • Figure 2: False alarm probability of observing Bayes Factors from GW231123-like unlensed signals. The curves are generated by analysing a hundred unlensed NRsur signals injected into Gaussian noise with lensed and unlensed hypotheses. The shaded region shows the Poisson error. Horizontal lines show the corresponding confidence levels. The GW231123 Bayes factor lies outside the distribution, with FAP $<1\%$ and significance $\gtrsim 2.6 \sigma$.
  • Figure 3: 1D marginalised posterior distributions of $(i)$ detector frame chirp mass $\mathcal{M}_c^{\rm det}$, mass ratio $q$ and projected spin components $\chi_1$ and $\chi_2$ (perpendicular to the binary orbital plane) under unlensed and lensed hypotheses with different waveforms. The posteriors are in agreement for all the waveform models after incorporating lensing by an isolated or embedded point mass. $(ii)$ luminosity distance of the source $d_L$, and parameters of the point mass lens (redshifted lens mass $M_L(1+z_L)$, impact parameter $y$) without and with external potential (assuming $\kappa = \gamma$). The posteriors under both lensing hypotheses are consistent among the three waveforms.
  • Figure 4: GW231123 total source-frame mass $M^{\rm src}_{\rm tot}$ versus redshift $z$, as a lensed black hole merger. Contours indicate 68, 95, and 99% credible regions for different waveform and lensing models: unlensed (gray filled; Phenom and NRSur), diffracted (blue unfilled; NRSur), and magnified+diffracted by a singular isothermal macrolens (red filled; NRSur). Circles indicate median values of GWTC-4 events gwtc4catalog. The black curve marks the approximate detector horizon for O4. Unlike the unlensed interpretation, which requires unusually high masses relative to the GWTC-4 population gwtc4pop, lensing analyses harmonize the event with the broader distribution of binary black holes.
  • Figure S1: Different microlensing regions inferred from the Embedded PL (NRSur) analysis, showing the multi-modality in the posteriors, related to the properties of the microimages. We identified a very subdominant mode with 4 images (black, $4\%$ of samples) and three main modes with 2 images, which can be classified in terms of the time delay between them $\Delta t_{01}$: $\sim 22$ ms (red, $43\%$), $\sim 44$ ms (blue, $38\%$) and $\sim 66$ ms (green, $15\%$). The best fit is provided by the mode at $\sim 44$ ms (blue), see Fig. \ref{['fig:time_bestfit']} for the best fitting results for each of the modes.
  • ...and 4 more figures