# What exactly is it that is being magnified 50 times in this gravitational lensing observation?

In the Los Angeles Times news item Scientists get a rare view of a type Ia supernova magnified 50 times what exactly is magnified 50 times?

This supernova is really very far away. Is it somehow imaged by the gravitational lensing and being resolved — the actual supernova itself?

edit: I believe this is it, but it's behind a paywall (will confirm in due course): http://science.sciencemag.org/content/356/6335/291

above: From the Los Angeles Times. Photo credit: Joel Johansson

above: "This schematic image represents how light from a distant galaxy is distorted by the gravitational effects of a nearer foreground galaxy, which acts like a lens and makes the distant source appear distorted, but brighter, forming characteristic rings of light, known as Einstein rings. An analysis of the distortion has revealed that some of the distant star-forming galaxies are as bright as 40 trillion Suns, and have been magnified by the gravitational lens by up to 22 times. (Credit: ALMA ESO/NRAO/NAOJ, L. Calçada (ESO), Y. Hezaveh et al., edited and modified by Joel Johansson)" From the Los Angeles Times.

The magnification refers to the increase in angular extent (expressed as a solid angle) of the background source, but is also the factor by which its total brightness is increased.

The reason for this is that the flux received per unit solid angle is unchanged by gravitational lensing. So if the source area increases by a factor of $M$, then so does the overall brightness.

This increase in total flux observed applies whether the magnified source is resolved by the telescope or not, since that is merely an instrumental issue.

• Is the 'local magnification' (for lack of better words) one-dimensional, so that increase in angular size and increase in solid angle are roughly the same, or do you mean something different than 'angular size' as one might express in arcseconds? – uhoh Apr 27 '17 at 20:00
• So what is really directly observed and reported in this particular case is an unresolved spot that is about 50x brighter than it would be without lensing? – uhoh Apr 27 '17 at 20:02
• @uhoh I mean increase in solid angle. Angular size goes as roughly the square root of solid angle. – Rob Jeffries Apr 27 '17 at 20:03
• Only if magnification is isotropic (again, lacking the correct words for gravitational lensing) – uhoh Apr 27 '17 at 20:04
• @uhoh That is not the case. The magnification is the determinant of a not necessarily isotropic tensor. – Rob Jeffries Apr 27 '17 at 20:07

we estimated the lensing amplification to be $\mu\sim52$.

This refers to the magnification factor. Essentially, it describes the solid angle of the image, as related to the solid angle of the source1: $$\mu\equiv\frac{\theta}{\beta}\frac{d\theta}{d\beta}$$ Here's a diagram of the magnitudes of the angles:

Image courtesy of Wikipedia user Falcorian under the Creative Commons Attribution-Share Alike 3.0 Unported license.

• The formation of the four spots labeled 1 through 4 are an Einstein cross. At this distance aren't all four of these still unresolved point sources? As such, does any one of them have any observationally meaningful solid angle in this particular case? Or is it really brightness of the unresolved spots that's been amplified - thereby allowing the observation of an object that would have otherwise been much dimmer without the lensing? – uhoh Apr 27 '17 at 15:37
• Abstract: This phenomenon was identified because the light from the stellar explosion was magnified more than 50 times by the curvature of space around matter in an intervening galaxy. Light was magnified, not image. It sounds like brightness to me. – uhoh Apr 27 '17 at 16:02
• @uhoh I'm reasonably certain they mean magnification of the image, not brightness. After all, $\mu$ has nothing to do with intensity, and thta's the quantity they're referring to. – HDE 226868 Apr 27 '17 at 17:34
• OK in that case what does magnification of a single, unresolved point mean? What exactly is 50x bigger than it would be without lensing? Are there two objects that appear 50x farther apart than they would appear otherwise? Is $\mu$ actually something that is simply calculated from a model of an assumed mass distribution and distance, and in no way connected to the image other than by inference? I guess I'm holding on to the notion that "magnified" means something is larger (in angular extent) than it would be otherwise, and I'm looking for that thing, or that angle. Thanks for your patience! – uhoh Apr 27 '17 at 19:24
• @uhoh The key is that with this good a resolution - especially for the Keck image - they aren't point sources. The images do show that even with some noise and fuzziness, the objects aren't pointlike. – HDE 226868 Apr 27 '17 at 19:29

It appears to just be a regular photo. It could've been taken by Hubble, and someone just magnified the photo. It doesn't appear to be gravitational lensing. If it was you would be able to see space being bent a bit in the photo, read here

• Do you have any arguments to back up that this is not gravitational lensing? – SE - stop firing the good guys Apr 27 '17 at 13:43
• You can see space being bent. That's the whole point of the fact that there are multiple images in the same photograph. – HDE 226868 Apr 27 '17 at 13:47
• gravitational lensing doesn't necessarily use multiple images. and in the photo presented in the article, its a regular still frame. You can't the effects of gravitational lensing . – bkrumins Apr 27 '17 at 14:21
• also to address the multiple images in one, if I was looking at the right one, they just boxed the area they were looking at and edited the other pictures onto there. – bkrumins Apr 27 '17 at 14:34
• You've drastically misunderstood this whole scientific result and concept. When HDE was talking about multiple images, he wasn't referring to actual .jpeg (or whatever) images, but rather multiple physical manifestations of the same object in multiple places in the sky, often referred to as multiple images. This can only be caused by gravitational lensing. – zephyr Apr 27 '17 at 15:17