@RobJeffries' answer to the question Does gravitational lensing provide time evolution information? points out that there can be a substantial different in arrival times of light from a given source seen in different images from a gravitational lens.

The linked paper there shows "$\Delta t$" values of the order of 30 days, but it is hard for me to understand what the actual observable is.

What I'm asking for here is (ideally) if there is a well defined event that a lay person could understand, something blinking or disappearing or brightening substantially that has already been seen in one image produced by a gravitational lens that has not yet been seen in one of the other images, and is expected to be seen in the (presumably near) future.

If something like this does not exist, a substitute could be a case where this has happened, and the second sighting of the same event was predicted, waited for, and observed on time.

I have no idea if this happens all the time, or has never happened yet.

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    $\begingroup$ FWIW, this kind of thing is a bit easier in radio astronomy. I've been looking for a good relevant article, but without success, but I've only been looking for stuff on HTML pages, not PDF links. I read about it years ago, with the astronomer comparing tapes of radio data, with a time delay of several months, but I can't remember where I read it. $\endgroup$
    – PM 2Ring
    Apr 5, 2019 at 10:59
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    $\begingroup$ I think the observable here is that you cross-correlate time-series observations, usually at radio wavelengths, to determine the delay. The "events" are just the general variability of the background quasar/AGN. I think there is an example where a type Ia supernova was seen in >1 image at different times. $\endgroup$
    – ProfRob
    Apr 5, 2019 at 11:09
  • $\begingroup$ @PM2Ring re the typo, next time feel free to just make an edit. It's pretty common in the more civil SE sties for people to edit each other's posts I think. As for radio, I'm not so interested in time correlations as I am "...a well defined event that a lay person could understand, something blinking or disappearing or brightening substantially..." $\endgroup$
    – uhoh
    Apr 5, 2019 at 11:17
  • $\begingroup$ @RobJeffries ditto re "event". So a supernova would exactly fit the bill! $\endgroup$
    – uhoh
    Apr 5, 2019 at 11:21
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    $\begingroup$ Optical observations may be easier for a lay person to relate to, but radio gives you a much more useful fingerprint / barcode. Bear in mind that the different paths mean that the signals experience different filtering & distortions, and the source isn't a point, so the images aren't of exactly the same thing, so it can be quite hard to even verify that they actually come from the same source. $\endgroup$
    – PM 2Ring
    Apr 5, 2019 at 11:48

1 Answer 1


What you do is cross-correlate the observational datasets for the multiple sources and look for the "lag" that maximises the cross-correlation function. Generally speaking, the "events" are not really individual flares or dips, but the summation of all the time variability that is seen.

The variability in question usually comes about from the central portions of the "central engine" of a quasar or active galactic nucleus. For a supermassive black hole at the centre of a quasar, the innermost stable circular orbit is at 3 times the Schwarzschild radius ($= 6GM_{\rm BH}/c^2$). This basically defines the inner edge of any accretion disk and if we divide this by $c$ then we get a a timescale for the most rapid variations in luminosity output. So this is very nearly the same formula as presented in the linked question $$\tau \sim 3\times 10^{-5} \left(\frac{M_{\rm BH}}{M_{\odot}}\right)\ {\rm sec}\, ,$$ except that the supermassive black holes are much less massive than entire foreground lensing galaxies (usually). This the timescale of variation is much shorter than the potential delay time due to gravitational lensing. It is this difference in timescales that means there is plenty of "structure" within the light curves that can be locked onto by the cross-correlation.

There is a notable example however of a type Ia supernova being seen in a multiply lensed image (Goobar et al. (2017), but the predicted delay in the light curves was $<35$ hours and the light curves are not good enough to measure this. This technique is an active area of research and a major bit of science that is exprected to be achieved by the Large Synoptic Survey Telescope (Huber et al. 2019).

Finally, the thing you are really looking for has happened in terms of SN "Refsdal". This was a type II supernova seen to "go off" in a multiply imaged galaxy, seen through/around a galaxy cluster. A prediction was made, based on a model for the cluster gravitational potential, that another image ought to appear within a year or two. This further image was then detected by Kelly et al. (2016) in a paper entitled "Deja vu all over again".

From Kelly et al. (2016) ("Deja vu all over again"). See "SX" in the third panel:

MACS J1149.5+2223 galaxy-cluster field taken with HST

Figure 1. Coadded WFC3-IR F125W and F160W exposures of the MACS J1149.5+2223 galaxy-cluster field taken with HST. The top panel shows images acquired in 2011 before the SN appeared in S1–S4 or SX. The middle panel displays images taken on 2015 April 20 when the four images forming the Einstein cross are close to maximum brightness, but no flux is evident at the position of SX. The bottom panel shows images taken on 2015 December 11 which reveal the new image SX of SN Refsdal. Images S1–S3 in the Einstein cross configuration remain visible in the 2015 December 11 coadded image (see Kelly et al. 2015a and Rodney et al. 2015b for analysis of the SN light curve).

Kelly, P. L., Brammer, G., Selsing, J., et al. 2015a, ApJ, submitted (arXiv:1512.09093)

Rodney, S. A., Strolger, L.-G., Kelly, P. L., et al. 2015b, ApJ, in press (arXiv:1512.05734)

  • $\begingroup$ I've added Figure 1 from "Deja vu all over again". I hope you don't mind, it's just so cool! $\endgroup$
    – uhoh
    Apr 5, 2019 at 11:55
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    $\begingroup$ Named after the gravitational lensing pioneer Sjur Refsdal. $\endgroup$
    – PM 2Ring
    Apr 5, 2019 at 11:59

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