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Evidence for an intermediate-mass black hole from a gravitationally lensed gamma-ray burst

Abstract

If gamma-ray bursts are at cosmological distances, they must be gravitationally lensed occasionally1,2. The detection of lensed images with millisecond-to-second time delays provides evidence for intermediate-mass black holes, a population that has been difficult to observe. Several studies have searched for these delays in gamma-ray burst light curves, which would indicate an intervening gravitational lens3,4,5,6. Among the ~104 gamma-ray bursts observed, there have been a handful of claimed lensing detections7, but none have been statistically robust. Here we present a Bayesian analysis identifying gravitational lensing in the light curve of GRB 950830. The inferred lens mass Ml depends on the unknown lens redshift zl, and is given by \((1+z_{\rm{l}})M_{\rm{l}} = 5.{5}_{-0.9}^{+1.7}\times 1{0}^{4}\,M_{\odot}\) (90% credibility), which we interpret as evidence for an intermediate-mass black hole. The most probable configuration, with a lens redshift zl ≈ 1 and a gamma-ray burst redshift zs ≈ 2, yields a present-day number density of about \(2.{3}_{-1.6}^{+4.9}\times 1{0}^{3}\,{\text{Mpc}}^{-3}\) (90% credibility) with a dimensionless energy density \({{{\varOmega }}}_{{\rm{IMBH}}}\approx 4.{6}_{-3.3}^{+9.8}\times 1{0}^{-4}\). The false alarm probability for this detection is ~0.6% with trial factors. While it is possible that GRB 950830 was lensed by a globular cluster, it is unlikely as we infer a cosmic density inconsistent with predictions for globular clusters ΩGC ≈ 8 × 10−6 at 99.8% credibility. If a significant intermediate-mass black hole population exists, it could provide the seeds for the growth of supermassive black holes in the early Universe.

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Fig. 1: The gravitationally lensed γ-ray burst, BATSE trigger 3770—GRB 950830.
Fig. 2: Marginalized posterior distribution of time delays versus magnification ratios for the gravitationally lensed γ-ray burst GRB 950830.
Fig. 3: The redshifted lens mass.

Data availability

The BATSE data catalogue is available from the NASA data archive at https://heasarc.gsfc.nasa.gov/FTP/compton/data/batse/trigger. We use the ‘discsc’, ‘tte’ and ‘tte_list’ datatypes in our search. The data used in our analysis of GRB 950830 can be found at https://heasarc.gsfc.nasa.gov/FTP/compton/data/batse/trigger/03601_03800/03770_burst/tte_bfits_3770.fits.gz and https://heasarc.gsfc.nasa.gov/FTP/compton/data/batse/trigger/03601_03800/03770_burst/tte_list_3770.fits.gz. Source data are provided with this paper.

Code availability

The analysis code PyGRB55 has been written in Python56 by J.P. and is freely available at https://github.com/JamesPaynter/PyGRB under the BSD 3-Clause License. PyGRB is built around Monash University’s Bilby nested sampling wrapper, with additional FITS I/O functionality provided by AstroPy57. The software uses the NumPy58 and SciPy59 computational libraries. Plotting makes use of the Matplotlib60 and corner61 libraries62.

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Acknowledgements

E.T. is supported through Australian Research Council grant no. CE170100004 and no. FT150100281. The analysis software was run on The University of Melbourne’s Spartan HPC system. This research has made use of data provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. J.P. acknowledges S. Wyithe, M. Trenti and A. Melatos for constructive comments in analysing and interpreting the data and results. J.P. also thanks C. Shrader for assistance in understanding the BATSE instrumentation, and J. M. Burgess for constructive feedback on PyGRB and the proper analysis of gamma-ray data.

Author information

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Authors

Contributions

R.W. contributed to the initial planning of the project with later additions from J.P. and E.T. J.P. contributed the data analysis through the pulse-fitting software package PyGRB under the guidance of E.T. The manuscript was drafted by J.P. and E.T. J.P. and R.W. contributed the gravitational lensing calculations while E.T. contributed the Bayesian framework. J.P. and E.T. responded to questions and comments from the referees. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to James Paynter or Rachel Webster.

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The authors declare no competing interests.

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Peer review information Nature Astronomy thanks Zsolt Bagoly, Kevin Hurley, Masamune Oguri and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 The individual pulses that make up channel 1 (red: 20-60 keV) of Figure 2.

a, The solid red lines are the median of 60,000 FRED-X pulses sampled from the posterior distributions. 200 of these curves are sampled and shown in black. b, The same as a) for the sine-Gaussian residual. c, The sum of the medians of the pulses in a and b.

Source data

Extended Data Fig. 2 The individual pulses that make up channel 2 (yellow: 60-110 keV) of Figure 2.

a, The solid yellow lines are the median of ~ 60, 000 FRED-X pulses sampled from the posterior distributions. 200 of these curves are sampled and shown in black. b, The same as a) for the sine-Gaussian residual. c, The sum of the medians of the pulses in a and b.

Source data

Extended Data Fig. 3 The individual pulses that make up channel 2 (green: 110-320 keV) of Figure 2.

a, The solid green lines are the median of ~ 60, 000 FRED-X pulses sampled from the posterior distributions. 200 of these curves are sampled and shown in black. b, The same as a) for the sine-Gaussian residual. c, The sum of the medians of the pulses in a and b.

Source data

Extended Data Fig. 4 The individual pulses that make up channel 2 (blue: 320-2,000 keV) of Figure 2.

a, The solid blue lines are the median of ~ 60,000 FRED-X pulses sampled from the posterior distributions. 200 of these curves are sampled and shown in black. b, The same as a) for the sine-Gaussian residual. c, The sum of the medians of the pulses in a and b.

Source data

Extended Data Fig. 5 The Hardness-Duration plot of BATSE GRBs.

The T90 durations are taken from the BATSE data tables: https://gammaray.nsstc.nasa.gov/batse/grb/catalog/4b/index.html. We calculate the hardness ratios for each of the GRBs with a listed T90. The short γ-ray burst population is shown in purple, and the long GRB population in red. Iso-likelihood contours of a two-component Gaussian mixture model are plotted in grey. The plotted uncertainties in the hardness ratio are defined by 1- σ statistical errors on the number of counts in the numerator and denominator.

Source data

Extended Data Fig. 6 The autocorrelation of the light curve of GRB 950830.

a, The sum of the four energy channels, ~ 20-2,000 keV. b, The autocorrelation function of the summed light curve, where the autocorrelation is defined in equation (6). The black dotted line is a fit to the light curve with a 3rd order Savitzky-Golay smoothing filter with a 101 bin smoothing window. The vertical red dotted line is the point of maximum deviation between the ACF and the Savitzky-Golay smoothing filter at δt= 0.390 seconds. The blue shaded regions delineate regions of 1 − σ, 3 − σ, and 5 − σ away from the Savitzky-Golay fit. The dispersion between the autocorrelation function and the fit, σ2, is defined in equation (7). c, The autocorrelation function for each of the 4 BATSE large area detector broadband energy channels. Each colour indicates a different energy channel, red: 20-60 keV, yellow: 60-110 keV, green: 110-320 keV, blue: 320-2,000 keV. The shaded regions delineate 3-σ deviance from the Savitzky-Golay fits, which are omitted for clarity.

Source data

Extended Data Fig. 7 The autocorrelation of the light curve of GRB 911031.

a, The sum of the four energy channels, 20-2,000 MeV. b, The autocorrelation function of the summed light curve, where the autocorrelation is defined in equation (6). The dotted line is a fit to the light curve with a 3rd order Savitzky-Golay smoothing filter with a 101 bin smoothing window. The blue shaded regions delineate regions of 1 − σ, 3 − σ, and 5 − σ away from the Savitzky-Golay fit. The dispersion between the autocorrelation function and the fit, σ2, is defined in equation (7). c, The light curve for each of the 4 BATSE large area detector broadband energy channels. Each colour indicates a different energy channel, red: 20-60 keV, yellow: 60-110 keV, green: 110-320 keV, blue: 320-2,000 keV. d, The autocorrelation function for each light curve channel. The shaded regions delineate 3 − σ deviance from the Savitzky-Golay fits, which are omitted for clarity.

Source data

Extended Data Fig. 8 The gravitational lens parameter posterior distributions for a model fit to GRB 911031 for each of the 4 BATSE large area detector broadband energy channels.

Each colour indicates a different energy channel, red: 20-60 keV, yellow: 60-110 keV, green: 110-320 keV, blue: 320-2,000 keV. Contours contain 39.3%. 86.4%, and 98.9% of the probability density. The light curve of GRB 911031 is shown in Extended Data Fig. 7.

Source data

Extended Data Fig. 9 Optical depth as a function of source redshift zs.

We estimate the optical depth for mean source redshifts zs=0.1: blue, zs: orange, zs=1.0: green, zs=1.34: black, zs=2.0: red, zs=5.0: purple based on Eq. (38). The median Cmax/Cmin values of 1.5, 2.2, and 2.5 taken as the magnification limit cutoff (Eq.(32)) are shown as solid, dash-dot, and dashed curves respectively. The solid black horizontal line is the estimate lens probability based on seeing one event in 2,679 light curves. The dotted black vertical line is the estimated globular cluster density, Ωgc. The dash-dot vertical black line is the naive estimate for the density Ωlens ~ τ. The calculated lens densities for each redshift are summarized in Extended Data Fig. 10.

Source data

Extended Data Fig. 10 The inferred lens densities Ωl for mean source redshift zs.

A median peak counts ratio \(\tilde{C}=2.5\) from the BATSE \({{\rm{C}}}_{\max }/{{\rm{C}}}_{\min }\) table for 1,024ms integration times is assumed. The peak count ratios are defined through \({\rm{C}}\equiv {{\rm{C}}}_{\max }/{{\rm{C}}}_{\min }\). \({{\rm{C}}}_{\max }\) is the maximum detected counts over a given integration period. \({{\rm{C}}}_{\min }\) is the minimum number of counts that would trigger the second most brightly illuminated detector at that time. Further details are given in the Methods section calculation of optical depths.

Source data

Source Data Fig. 1

Light curve of GRB 950830 with fits.

Source Data Fig. 2

Four overlapping coloured circles and a black circle. Time delay and magnification ratio posteriors for GRB 950830.

Source Data Fig. 3

Coloured probability densities.

Source Data Extended Data Fig. 1

Red lines.

Source Data Extended Data Fig. 2

Yellow lines.

Source Data Extended Data Fig. 3

Green lines.

Source Data Extended Data Fig. 4

Blue lines.

Source Data Extended Data Fig. 5

Hardness duration plot.

Source Data Extended Data Fig. 6

Three-panel autocorrelation of GRB 950830.

Source Data Extended Data Fig. 7

Four-panel autocorrelation of GRB 911031.

Source Data Extended Data Fig. 8

Four colinear coloured circles. Magnification ratio and time delay posterior GRB 911031.

Source Data Extended Data Fig. 9

Lens probability graph.

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Paynter, J., Webster, R. & Thrane, E. Evidence for an intermediate-mass black hole from a gravitationally lensed gamma-ray burst. Nat Astron 5, 560–568 (2021). https://doi.org/10.1038/s41550-021-01307-1

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