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Measuring time delays: I. Using a flux time series that is a linear combination of time-shifted light curves
Instrumentation and Methods for Astrophysics · Submitted 26 Jan 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that given a single-band light curve that is a combination of two (or more) time-shifted copies of an original light curve, generated from a red-noise probability distribution, we can test if the total-flux light curve is a composition of time-delayed copies or, alternatively, is consistent with being the original light curve.
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The abstract, sentence by sentence
(Abridged) Several phenomena in astrophysics generate light curves with time delays. Among these are reverberation mapping, and lensed quasars. In some systems, the measurement of the time-delay is complicated by the fact that the delayed components are unresolved and that the light curves are generated from a red-noise process. We derive the likelihood function of the observations given a model of either a combination of time-delayed light curves or a single light curve. This likelihood function is different from the auto-correlation function. We demonstrate that given a single-band light curve that is a combination of two (or more) time-shifted copies of an original light curve, generated from a red-noise probability distribution, we can test if the total-flux light curve is a composition of time-delayed copies or, alternatively, is consistent with being the original light curve. Furthermorew, in some realistic cases, it is possible to measure the time delays and flux ratios between these unresolved components even when the flux ratio is about 1/10. This method is useful for identifying lensed quasars and simultaneously measuring their time delays, and for estimating the reverberation time scales of active galactic nuclei. In a companion paper, we derive a method that uses the center-of-light position (e.g., of a lensed quasar) along with the combined flux. This allow us to identify lensed quasars and supernovae and measure their time delays, with higher fidelity compared to the flux-only method. The astrometry + flux method, however, is not suitable for quasar reverberation mapping. We also comment on the commonly used method of fitting a power-law model to a power spectrum, and present the proper likelihood function for such a fit. We test the new method on simulations and provide Python and MATLAB implementations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | (Abridged) Several phenomena in astrophysics generate light curves with time delays. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | Among these are reverberation mapping, and lensed quasars. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | In some systems, the measurement of the time-delay is complicated by the fact that the delayed components are unresolved and that the light curves are generated from a red-noise process. | background 0.95 | 0.06 | 0.03 | asserted 0.91 |
| s3 | We derive the likelihood function of the observations given a model of either a combination of time-delayed light curves or a single light curve. | contribution 0.54 | 0.97 | 0.12 | asserted 1.00 |
| s4 | This likelihood function is different from the auto-correlation function. | contribution 0.44 | 0.68 | 0.05 | asserted 1.00 |
| s5 | We demonstrate that given a single-band light curve that is a combination of two (or more) time-shifted copies of an original light curve, generated from a red-noise probability distribution, we can test if the total-flux light curve is a composition of time-delayed copies or, alternatively, is consistent with being the original light curve. | contribution 0.50 | 0.90 | 0.68 | asserted 0.95 |
| s6 | Furthermorew, in some realistic cases, it is possible to measure the time delays and flux ratios between these unresolved components even when the flux ratio is about 1/10. | result 0.98 | 0.84 | 0.21 | hedged possibility 0.86 |
| s7 | This method is useful for identifying lensed quasars and simultaneously measuring their time delays, and for estimating the reverberation time scales of active galactic nuclei. | interpretation 0.83 | 0.50 | 0.35 | asserted 0.95 |
| s8 | In a companion paper, we derive a method that uses the center-of-light position (e.g., of a lensed quasar) along with the combined flux. | future work 0.77 | 0.84 | 0.04 | asserted 0.99 |
| s9 | This allow us to identify lensed quasars and supernovae and measure their time delays, with higher fidelity compared to the flux-only method. | contribution 0.39 | 0.59 | 0.10 | asserted 0.98 |
| s10 | The astrometry + flux method, however, is not suitable for quasar reverberation mapping. | limitation 0.98 | 0.56 | 0.05 | asserted 1.00 |
| s11 | We also comment on the commonly used method of fitting a power-law model to a power spectrum, and present the proper likelihood function for such a fit. | contribution 0.90 | 0.84 | 0.03 | asserted 0.91 |
| s12 | We test the new method on simulations and provide Python and MATLAB implementations. | contribution 0.74 | 0.96 | 0.05 | asserted 1.00 |
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The paper
Original abstract
(Abridged) Several phenomena in astrophysics generate light curves with time delays. Among these are reverberation mapping, and lensed quasars. In some systems, the measurement of the time-delay is complicated by the fact that the delayed components are unresolved and that the light curves are generated from a red-noise process. We derive the likelihood function of the observations given a model of either a combination of time-delayed light curves or a single light curve. This likelihood function is different from the auto-correlation function. We demonstrate that given a single-band light curve that is a combination of two (or more) time-shifted copies of an original light curve, generated from a red-noise probability distribution, we can test if the total-flux light curve is a composition of time-delayed copies or, alternatively, is consistent with being the original light curve. Furthermorew, in some realistic cases, it is possible to measure the time delays and flux ratios between these unresolved components even when the flux ratio is about 1/10. This method is useful for identifying lensed quasars and simultaneously measuring their time delays, and for estimating the reverberation time scales of active galactic nuclei. In a companion paper, we derive a method that uses the center-of-light position (e.g., of a lensed quasar) along with the combined flux. This allow us to identify lensed quasars and supernovae and measure their time delays, with higher fidelity compared to the flux-only method. The astrometry + flux method, however, is not suitable for quasar reverberation mapping. We also comment on the commonly used method of fitting a power-law model to a power spectrum, and present the proper likelihood function for such a fit. We test the new method on simulations and provide Python and MATLAB implementations.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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Detection and measurement of sub-pixel motions of sources in astronomical images is required for two major science cases: (i) Detecting motion due to any kind of astrometric noise, or astrophysical motion, that leads to subtraction artifacts seen in image differencing methods, and in turn, leads to false alarms in transient detection; (ii) Measuring astrophysical motion, including proper motion and parallax measurement, detecting astrometric binaries (e.g., [ref] ), astrometric microlensing (e.g., [ref] ; [ref] ; [ref] ; [ref] ; [ref] ), lensed quasars ( [ref] , [ref] ), binary quasars (e.g., [ref] , [ref] ), and studying the black hole in the center of our Galaxy (e.g., [ref] ; [ref] ).
TRANSLIENT: Detecting Transients Resulting from Point Source Motion or Astrometric Errors · Introduction · 0.90
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(While we focus on transients, combined lightcurves from quasars have been studied by, e.g., [ref] .)
Out of One, Many: Distinguishing Time Delays from Lensed Supernovae · Conclusions · 0.95
What it cites · 8 sentences without a confident label
Compares with 1 paper
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Our approach is different than the one outlined by [ref] , [ref] , and [ref] in several respects.
Discovering Strongly-lensed QSOs From Unresolved Light Curves · Introduction · 0.94
Cites as background 2 papers
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Time-delay measurements in these systems may help in recovering the mass of the lensing galaxies (e.g., [ref] , [ref] ); studying the host galaxies of quasars (e.g., [ref] ); probing the galaxy mass evolution (e.g., [ref] ); measuring cosmological parameters (e.g., [ref] , [ref] ); studying the accretion disk around massive black holes (e.g., [ref] , [ref] , [ref] ); and measuring the Hubble constant (e.g., [ref] , [ref] , [ref] , [ref] , [ref] ), although the latter is limited by the knowledge of the mean convergence at the Einstein radius (e.g., [ref] , [ref] ).
Measuring accretion disk sizes of lensed quasars with microlensing time delay in multi-band light curves · Introduction · 0.84
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Time-delay measurements in these systems may help in recovering the mass of the lensing galaxies (e.g., [ref] , [ref] ); studying the host galaxies of quasars (e.g., [ref] ); probing the galaxy mass evolution (e.g., [ref] ); measuring cosmological parameters (e.g., [ref] , [ref] ); studying the accretion disk around massive black holes (e.g., [ref] , [ref] , [ref] ); and measuring the Hubble constant (e.g., [ref] , [ref] , [ref] , [ref] , [ref] ), although the latter is limited by the knowledge of the mean convergence at the Einstein radius (e.g., [ref] , [ref] ).
TDCOSMO V: strategies for precise and accurate measurements of the Hubble constant with strong lensing · Introduction · 0.84
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