[Paper Review] Reinterpreting Low Frequency LIGO/Virgo Events as Magnified Stellar-Mass Black Holes at Cosmological Distances

Tom Broadhurst, J. M. Diego+1 more|arXiv (Cornell University)|Feb 14, 2018

Pulsars and Gravitational Waves Research34 references28 citations

TL;DR

This paper proposes that the four highest-mass LIGO/Virgo binary black hole (BBH) events—previously interpreted as 20–35M⊙ mergers at low redshift—are instead lensed, magnified signals from stellar-mass black holes (5–15M⊙) at cosmological distances (z ≈ 1–2.5). Gravitational lensing by intervening galaxies amplifies the wave strain by √µ, causing the detectors to misestimate distance (underestimating by √µ) and overestimate mass (by factor of 1+z), reconciling high inferred masses with stellar-origin black hole populations.

ABSTRACT

Gravitational waves can be focussed by the gravity of an intervening galaxy, just like light, thereby magnifying binary merging events in the far Universe. High magnification by galaxies is found to be responsible for the brightest sources detected in sky surveys, but the low angular resolution of LIGO/Virgo is insufficient to check this lensing possibility directly. Here we find that the first six binary black hole (BBH) merging events reported by LIGO/Virgo show clear evidence for lensing in the plane of observed mass and source distance. The four lowest frequency events follow an apparent locus in this plane, which we can reproduce by galaxy lensing, where the higher the magnification, the generally more distant the source so the wave train is stretched more by the Universal expansion, by factors of 2-4. This revises the reported BBH distances upwards by an order of magnitude, equal to the square root of the magnification. Furthermore, the reported black hole masses must be decreased by 2-4 to counter the larger stretch factor, since the orbital frequency is used to derive the black hole masses. This lowers the masses to 5-15 solar masses, well below the puzzlingly high values of 20-35 solar masses otherwise estimated, with the attraction of finding agreement in mass with black holes orbiting stars in our own Galaxy, thereby implying a stellar origin for the low frequency events in the far Universe. We also show that the other two BBH events of higher frequency detected by LIGO/VIRGO, lie well below the lensing locus, consistent with being nearby and unlensed. If this apparent division between local and distant lensed events is reinforced by new detections then the spins and masses of stellar black holes can be compared over a timespan of 10 billion years by LIGO/Virgo.

Motivation & Objective

• To resolve the discrepancy between the high inferred masses (20–35M⊙) of LIGO/Virgo's first BBH events and the expected 5–15M⊙ masses from stellar evolution.
• To test whether gravitational lensing by intervening galaxies could explain the observed mass-distance correlation in the LIGO/Virgo data.
• To assess whether lensing can reconcile the high inferred masses with known stellar-mass black hole populations in the Milky Way.
• To evaluate the consistency of lensing with the observed distribution of chirp masses and inferred distances, particularly the clustering of high-mass events along a distinct locus.

Proposed method

• Uses the observed chirp mass and inferred luminosity distance of the six LIGO/Virgo BBH events to test for a correlation consistent with lensing.
• Applies the lensing magnification relation h(t) ∝ √µ, where µ is the magnification factor, to correct for overestimated strain and thus underestimate of true distance.
• Reconstructs the true source redshift z and intrinsic chirp mass by scaling inferred distance by √µ and inferred mass by (1+z), reversing the lensing bias.
• Simulates BBH event populations using log-normal and Gaussian mass functions consistent with galactic black holes, combined with star formation rate (SFR) evolution models to predict detectable events.
• Models lensing optical depth using the µ−2 law for fold caustics, with magnification µ > 80 being common for compact sources near caustics.
• Compares simulated lensed and unlensed event distributions in the chirp mass–distance plane against the observed data, using Monte Carlo simulations with uncertainty in geometric factor Θ.

Experimental results

Research questions

• RQ1 Can gravitational lensing by intervening galaxies explain the apparent clustering of high-mass LIGO/Virgo BBH events along a specific locus in the chirp mass–distance plane?
• RQ2 To what extent does lensing account for the overestimation of black hole masses (20–35M⊙) and underestimation of distances in the LIGO/Virgo data?
• RQ3 Does the observed distribution of BBH events favor a stellar-mass origin (5–15M⊙) at high redshift (z ≈ 1–2.5) when lensing is considered, rather than primordial or massive binary progenitors?
• RQ4 How does the inclusion of lensing affect the inferred intrinsic mass function and event rate evolution of BBHs?

Key findings

• The four highest-mass LIGO/Virgo BBH events (chirp mass 20–35M⊙) are best explained as lensed, distant sources at redshift z ≈ 1–2.5, with magnification µ ≈ 2–4, rather than nearby, high-mass mergers.
• Lensing reduces the inferred distance by a factor of √µ ≈ 1.4–2, revising the true luminosity distance upward by an order of magnitude.
• The intrinsic black hole masses are reduced from 20–35M⊙ to 5–15M⊙, bringing them into agreement with stellar-mass black holes observed in the Milky Way.
• The two lower-mass events (chirp mass 8–9M⊙) lie below the lensing locus and are consistent with being nearby and unlensed, supporting a bimodal distribution of local vs. distant events.
• The model with a log-normal mass function (5–15M⊙) and enhanced SFR at z ≈ 2 produces a distribution of lensed events that matches the observed data, including the high-mass tail.
• The probability of high magnification (µ > 80) is consistent with the µ−2 law for fold caustics, and such magnifications are plausible for compact, high-redshift sources near lensing caustics.