Gravitational waves and gravitational lensing are two predictions of general relativity. Gravitational waves are produced whenever masses accelerate. Gravitational lensing is produced by anything with mass. Gravitational lensing can magnify images, making it easier to spot far away things. In theory, gravitational waves can be lensed too. In this paper, we looked for evidence that GW170814 might have been lensed. (We didn’t find any, but this was my first foray into traditional astronomy).
The lensing of gravitational waves
Strong gravitational lensing magnifies a signal. A gravitational wave which has been lensed would therefore have a larger amplitude than if it had not been lensed. We infer the distance to the source of a gravitational wave from the amplitude. If we didn’t know a signal was lensed, we’d therefore think the source is much closer than it really is.
The shape of the gravitational wave encodes the properties of the source. This information is what lets us infer parameters. The example signal is GW150914 (which is fairly similar to GW170814). I made this explainer with Ban Farr and Nutsinee Kijbunchoo for the LIGO Magazine.
Mismeasuring the distance to a gravitational wave has important consequences for understanding their sources. As the gravitational wave travels across the expanding Universe, it gets stretched (redshifted) so by the time it arrives at our detectors it has a longer wavelength (and shorter frequency). If we assume that a signal came from a closer source, we’ll underestimate the amount of stretching the signal has undergone, and won’t fully correct for it. This means we’ll overestimate the masses when we infer them from the signal.
This possibility got a few people thinking when we announced our first detection, as GW150914 was heavier than previously observed black holes. Could we be seeing lensed gravitational waves?
Such strongly lensed gravitational waves should be multiply imaged. We should be able to see multiple copies of the same signal which have taken different paths from the source and then are bent by the gravity of the lens to reach us at different times. The delay time between images depends on the mass of the lens, with bigger lensing having longer delays. For galaxy clusters, it can be years.
The idea
Some of my former Birmingham colleagues who study gravitational lensing, were thinking about the possibility of having multiply imaged gravitational waves. I pointed out how difficult these would be to identify. They would come from the same part of the sky, and would have the same source parameters. However, since our uncertainties are so large for gravitational wave observations, I thought it would be tough to convince yourself that you’d seen the same signal twice [bonus note]. Lensing is expected to be rare [bonus note], so would you put your money on two signals (possibly years apart) being the same, or there just happening to be two similar systems somewhere in this huge patch of the sky?
However, if there were an optical counterpart to the merger, it would be much easier to tell that it was lensed. Since we know the location of galaxy clusters which could strongly lens a signal, we can target searches looking for counterparts at these clusters. The odds of finding anything are slim, but since this doesn’t take too much telescope time to look it’s still a gamble worth taking, as the potential pay-off would be huge.
Somehow [bonus note], I got involved in observing proposals to look for strongly lensed. We got everything in place for the last month of O2. It was just one month, so I wasn’t anticipating there being that much to do. I was very wrong.
GW170814
For GW170814 there were a couple of galaxy clusters which could serve as being strong gravitational lenses. Abell 3084 started off as the more probably, but as the sky localization for GW170814 was refined, SMACS J0304.3−4401 looked like the better bet.
Sky localization for GW170814 and the galaxy clusters Abell 3084 (filled circle), and SMACS J0304.3−4401 (open). The left plot shows the low-latency Bayestar localization (LIGO only dotted, LIGO and Virgo solid), and the right shows the refined LALInference sky maps (solid from GCN 21493, which we used for our observations, and dotted from GWTC-1). The dashed lines shows the Galactic plane. Figure 1 of Smith et al. (2019).
We observed both galaxy clusters using the Gemini Multi-Object Spectrographs (GMOS) on Gemini South and the Multi Unit Spectroscopic Explorer (MUSE) on the Very Large Telescope, both in Chile. You’ll never guess what we found…
That’s right, absolutely nothing! [bonus note] That’s not actually too surprising. GW170814‘s source was identified as a binary black hole—assuming no lensing, its source binary had masses around 25 and 30 solar masses. We don’t expect significant electromagnetic emission from a binary black hole merger (which would make it a big discovery if found, but that is a long shot). If there source were lensed, we would have overestimated the source masses, but to get the source into the neutron star mass range would take a ridiculous amount of lensing. However, the important point is that we have demonstrated that such a search for strong lensed images is possible!
The future
In O3 [bonus notebonus note], the team has been targeting lower mass systems, where a neutron star may get mislabelled as a black hole by mistake due to a moderate amount of lensing. A false identification here could confuse our understanding of the minimum mass of a black hole, and also mean that we miss all sorts of lovely multimessenger observations, so this seems like a good plan to me.
arXiv: 1805.07370 [astro-ph.HE]
Journal: Monthly Notices of the Royal Astronomical Society; 485(4):5180–5191; 2019
Conference proceedings: 1803.07851 [astro-ph.HE] (from when work was still in-progress)
Future research: Are Double Stuf Oreos just gravitationally lensed regular Oreos?
Bonus notes
Statistical analysis
It is possible to do a statistical analysis to calculate the probability of two signals being lensed images of each. The best attempt I’ve seen at this is Hannuksela et al. (2019). They do a nice study considering lensing by galaxies (and find nothing conclusive).
Biasing merger rates
If we included lensed events in our calculations of the merger rate density (the rate of mergers per unit volume of space), without correcting for them being lensed, we would overestimate the merger rate density. We’d assume that all our mergers came from a smaller volume of space than they actually did, as we wouldn’t know that the lensed events are being seen from further away. As long as the fraction of lensed events is small, this shouldn’t be a big problem, so we’re probably safe not to worry about it.
Slippery slope
What actually happened was my then boss, Alberto Vecchio, asked me to do some calculations based upon the sky maps for our detections in O1 as they’d only take me 5 minutes. Obviously, there were then more calculations, advice about gravitational wave alerts, feedback on observing proposals… and eventually I thought that if I’d put in this much time I might as well get a paper to show for it.
It was interesting to see how electromagnetic observing works, but I’m not sure I’d do it again.
Upper limits
Following tradition, when we don’t make a detection, we can set an upper limit on what could be there. In this case, we conclude that there is nothing to see down to an i-band magnitude of 25. This is pretty faint, about 40 million times fainter than something you could see with the naked eye (translating to visibly light). We can set such a good upper limit (compared to other follow-up efforts) as we only needed to point the telescopes at a small patch of sky around the galaxy clusters, and so we could leave them staring for a relatively long time.
O3 lensing hype
In O3, two gravitational wave candidates (S190828j and S190828l) were found just 21 minutes apart—this, for reasons I don’t entirely understand, led to much speculation that they were multiple images of a gravitationally lensed source. For a comprehensive debunking, follow this Twitter thread.
Christopher Berry 