<p>The magnification refers to the increase in angular extent (expressed as a <a href="https://en.m.wikipedia.org/wiki/Solid_angle" rel="nofollow noreferrer">solid angle</a>) of the background source, but is also the factor by which its total brightness is increased.</p>

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

<p>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.</p>

CC BY-SA 3.0
2017-04-27T20:00:37.917Z
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
CC BY-SA 3.0
2017-04-27T20:02:53.460Z
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
CC BY-SA 3.0
2017-04-27T20:03:01.897Z
@uhoh I mean increase in solid angle. Angular size goes as roughly the square root of solid angle.
ProfRob
CC BY-SA 3.0
2017-04-27T20:04:35.980Z
Only if magnification is isotropic (again, lacking the correct words for gravitational lensing)
uhoh
CC BY-SA 3.0
2017-04-27T20:07:34.513Z
@uhoh That is not the case. The magnification is the determinant of a not necessarily isotropic tensor.
ProfRob
CC BY-SA 3.0
2017-04-27T20:18:20.850Z
Got it, thanks. Adjustment in text noted, thanks. Great answer, thanks! ;)
uhoh
CC BY-SA 4.0
2024-02-11T21:40:00.217Z
It is still an unresolved spot, supernovas are extremely bright but not that big and the distance of billions of light-years is gigantic. Gravitational lenses are not good at making resolved images because they are highly distorted. But such distortion does not matter if the goal is just to brighten an unresolved spot.
Kevin Kostlan
CC BY-SA 3.0
2017-04-27T19:57:15.170Z
2017-04-27T20:04:49.723Z
2017-04-27T20:04:49.723Z
ProfRob
<p>Reading through <a href="http://science.sciencemag.org/content/sci/356/6335/291.full.pdf" rel="nofollow noreferrer">the full article</a>, I see that the authors write</p>

<blockquote>
  <p>we estimated the lensing amplification to be $\mu\sim52$.</p>
</blockquote>

<p>This refers to the <a href="https://en.wikipedia.org/wiki/Gravitational_lensing_formalism#Magnification" rel="nofollow noreferrer"><em>magnification factor</em></a>. Essentially, it describes the solid angle of the image, as related to the solid angle of the source<sup><a href="http://www.pa.msu.edu/~abdo/GravitationalLensing.pdf" rel="nofollow noreferrer">1</a></sup>:
$$\mu\equiv\frac{\theta}{\beta}\frac{d\theta}{d\beta}$$
<a href="https://en.wikipedia.org/wiki/File:Gravitational-lensing-angles.png" rel="nofollow noreferrer">Here's</a> a diagram of the magnitudes of the angles:</p>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/e/e4/Gravitational-lensing-angles.png" alt="">
<br>
<sup>Image courtesy of Wikipedia user Falcorian under <a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en" rel="nofollow noreferrer">the Creative Commons Attribution-Share Alike 3.0 Unported license</a>.</sup></p>

CC BY-SA 3.0
2017-04-27T15:37:12.283Z
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
CC BY-SA 3.0
2017-04-27T16:02:33.333Z
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
CC BY-SA 3.0
2017-04-27T17:34:27.990Z
@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
CC BY-SA 3.0
2017-04-27T19:24:02.047Z
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
CC BY-SA 3.0
2017-04-27T19:29:06.310Z
@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
CC BY-SA 3.0
2017-04-27T19:56:33.330Z
OK I'll try to follow that up, and get the paper soon. The image in my question (from the LATimes) is heavily saturated so things that are brighter can also appear bigger in that image artifactually (is that a word?) At 4.4 billion light years, an apparent angle of 0.1 arcsec (just for example) corresponds to an inferred size of ~2000 ly. Divide by 50x, that gives 40 ly. Is that the right 'approximate ballpark' for the size of the light emission from a supernova event like this?
uhoh
CC BY-SA 4.0
2019-01-25T03:33:06.000Z
[Cases of gravitational lensing resulting in a recognizable image of an extended object?](https://astronomy.stackexchange.com/q/29315/7982)
uhoh
CC BY-SA 3.0
2017-04-27T13:44:33.733Z
2017-04-27T13:44:33.733Z
HDE 226868
<p>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, <a href="https://en.wikipedia.org/wiki/Gravitational_lens" rel="nofollow noreferrer">read here</a></p>

CC BY-SA 3.0
2017-04-27T13:43:42.963Z
Do you have any arguments to back up that this is not gravitational lensing?
SE - stop firing the good guys
CC BY-SA 3.0
2017-04-27T13:47:15.333Z
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
CC BY-SA 3.0
2017-04-27T14:21:45.083Z
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
CC BY-SA 3.0
2017-04-27T14:34:47.987Z
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
CC BY-SA 3.0
2017-04-27T15:12:39.317Z
Both the paper and the article state that multiple images were observed, as you can see in the pictures given in the question.
HDE 226868
CC BY-SA 3.0
2017-04-27T15:17:31.137Z
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
CC BY-SA 3.0
2017-04-27T13:24:50.833Z
2017-04-27T13:24:50.833Z
bkrumins
<p>In the Los Angeles Times news item <a href="http://www.latimes.com/science/sciencenow/la-sci-sn-supernova-gravitational-lensing-20170420-story.html" rel="nofollow noreferrer">Scientists get a rare view of a type Ia supernova magnified 50 times</a> <em>what exactly is magnified 50 times?</em> </p>

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

<p><strong>edit:</strong> I believe this is it, but it's behind a paywall (will confirm in due course): <a href="http://science.sciencemag.org/content/356/6335/291" rel="nofollow noreferrer">http://science.sciencemag.org/content/356/6335/291</a></p>

<hr>

<p><a href="https://i.sstatic.net/FfdWV.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FfdWV.jpg" alt="enter image description here"></a></p>

<p><strong>above:</strong> From the <a href="http://www.latimes.com/science/sciencenow/la-sci-sn-supernova-gravitational-lensing-20170420-story.html" rel="nofollow noreferrer">Los Angeles Times</a>. Photo credit: Joel Johansson</p>

<p><a href="https://i.sstatic.net/PSXKk.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/PSXKk.jpg" alt="enter image description here"></a></p>

<p><strong>above:</strong> "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 <a href="http://www.latimes.com/science/sciencenow/la-sci-sn-supernova-gravitational-lensing-20170420-story.html" rel="nofollow noreferrer">Los Angeles Times</a>.</p>

<supernova><gravitational-lensing>
What exactly is it that is being magnified 50 times in this gravitational lensing observation?
uhoh
# What exactly is it that is being magnified 50 times in this gravitational lensing observation?

(Asked by: username_0 on 2017-04-27)

In the Los Angeles Times news item [Scientists get a rare view of a type Ia supernova magnified 50 times](http://www.latimes.com/science/sciencenow/la-sci-sn-supernova-gravitational-lensing-20170420-story.html) *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>

---

[![enter image description here](https://i.sstatic.net/FfdWV.jpg)](https://i.sstatic.net/FfdWV.jpg)

**above:** From the [Los Angeles Times](http://www.latimes.com/science/sciencenow/la-sci-sn-supernova-gravitational-lensing-20170420-story.html). Photo credit: Joel Johansson

[![enter image description here](https://i.sstatic.net/PSXKk.jpg)](https://i.sstatic.net/PSXKk.jpg)

**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](http://www.latimes.com/science/sciencenow/la-sci-sn-supernova-gravitational-lensing-20170420-story.html).

**Tags:** supernova, gravitational-lensing

---

## 3 answers

### Answer by username_1 on 2017-04-27. Score: 3 | Accepted answer

The magnification refers to the increase in angular extent (expressed as a [solid angle](https://en.m.wikipedia.org/wiki/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.

> **Comments:**
> **username_0**: 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?  
> **username_0**: 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?  
> **username_1**: @uhoh I mean increase in solid angle. Angular size goes as roughly the square root of solid angle.  
> **username_0**: Only if magnification is isotropic (again, lacking the correct words for gravitational lensing)  
> **username_1**: @uhoh That is not the case. The magnification is the determinant of a not necessarily isotropic tensor.  
> **username_0**: Got it, thanks. Adjustment in text noted, thanks. Great answer, thanks! ;)  
> **username_2**: It is still an unresolved spot, supernovas are extremely bright but not that big and the distance of billions of light-years is gigantic. Gravitational lenses are not good at making resolved images because they are highly distorted. But such distortion does not matter if the goal is just to brighten an unresolved spot.  

---

### Answer by username_3 on 2017-04-27. Score: 3

Reading through [the full article](http://science.sciencemag.org/content/sci/356/6335/291.full.pdf), I see that the authors write

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

This refers to the [*magnification factor*](https://en.wikipedia.org/wiki/Gravitational_lensing_formalism#Magnification). Essentially, it describes the solid angle of the image, as related to the solid angle of the source[1](http://www.pa.msu.edu/~abdo/GravitationalLensing.pdf):
$$\mu\equiv\frac{\theta}{\beta}\frac{d\theta}{d\beta}$$
[Here's](https://en.wikipedia.org/wiki/File:Gravitational-lensing-angles.png) a diagram of the magnitudes of the angles:

![](https://upload.wikimedia.org/wikipedia/commons/e/e4/Gravitational-lensing-angles.png)
  
Image courtesy of Wikipedia user Falcorian under [the Creative Commons Attribution-Share Alike 3.0 Unported license](https://creativecommons.org/licenses/by-sa/3.0/deed.en).

> **Comments:**
> **username_0**: 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?  
> **username_0**: 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.  
> **username_3**: @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.  
> **username_0**: 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!  
> **username_3**: @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.  
> **username_0**: OK I'll try to follow that up, and get the paper soon. The image in my question (from the LATimes) is heavily saturated so things that are brighter can also appear bigger in that image artifactually (is that a word?) At 4.4 billion light years, an apparent angle of 0.1 arcsec (just for example) corresponds to an inferred size of ~2000 ly. Divide by 50x, that gives 40 ly. Is that the right 'approximate ballpark' for the size of the light emission from a supernova event like this?  
> **username_0**: [Cases of gravitational lensing resulting in a recognizable image of an extended object?](https://astronomy.stackexchange.com/q/29315/7982)  

---

### Answer by username_4 on 2017-04-27. Score: -3

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](https://en.wikipedia.org/wiki/Gravitational_lens)

> **Comments:**
> **username_5**: Do you have any arguments to back up that this is not gravitational lensing?  
> **username_3**: You *can* see space being bent. That's the whole point of the fact that there are multiple images in the same photograph.  
> **username_4**: 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 .  
> **username_4**: 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.  
> **username_3**: Both the paper and the article state that multiple images were observed, as you can see in the pictures given in the question.  
> **username_6**: 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.  

---

