How Gravitational Lensing Shows Us Dark Matter!

"You may hate gravity, but gravity doesn't care." -Clayton Christensen

What's the deal with gravity, dark matter, and this whole "lensing" business anyway? You've probably heard that energy -- most commonly mass -- bends light. And perhaps you've seen an image or two like this one to illustrate that.

Image credit: ESA, NASA, J.-P. Kneib and Richard Ellis.

Above is the great galaxy cluster Abell Cluster 2218. But those giant, stretched arcs you see? Those are actually background galaxies that get distorted and magnified by the giant cluster.

As the light leaves its source, the mighty gravity of the massive cluster bends that light, creating the multiple, swooping images you see above.

This is called strong gravitational lensing, and it's one of the most spectacular sights in the Universe. But, unfortunately, it's ultra-rare that we get such a fortuitous alignment between a foreground mass and a background galaxy. How, then, are we supposed to measure where the matter is (and how much matter there is) if we get a galaxy cluster without those strong features.

Like, say, this guy.

Image credit: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.

It turns out that almost every cluster has no arcs, multiple images, or Einstein rings to help us out. So how do we map the dark matter?

We turn to the much less visually spectacular (but much more cosmically powerful) weak gravitational lensing.

What the hell is that? Let's dive on in.

Image credit: ESA's Euclid.

Above is what part of the Universe might look like. There might be some regions with lots of mass in it, where the matter has started to cluster together on large scales. There are others with dearths of matter, where we have great voids in the Universe. As a result, when light from objects behind these masses makes its way towards us, it doesn't get bent in a spectacular fashion, but it gets sheared.

What does that mean? Let's show you. Take a look at what some circular light sources would look like if there were no mass in between us -- looking out -- and those light sources.

Image credit: Smoot lensing subgroup, as is the image below.

But now, what if we took those same light sources, and in between us and them, we put some typical-to-the-Universe sources of mass? Now remember, we're not allowing any strong effects: no magnification, no multiple images, no rings, no great distorted arcs. What would it look like now?

Why, these light sources get distorted: stretched into elliptical shapes, due to the masses in between us and them!

"Great," you must be thinking, "all we have to do is measure how elliptical galaxies are, and we can figure out the masses in between us and them!"

Not so fast. The problem is, real galaxies come in different shapes. As we astrophysicists are creative name-givers, we call this effect "shape noise." (No, seriously, we name things like kindergarteners.) So when we look out at the Universe, what we see is a combination of this shape noise and the weak gravitational lensing effects of the intervening mass.

Image credit: TallJimbo.

So what can we do? Well, we have to measure many background galaxies, to average out the effect of shape noise. How do we do this? Let's take a look at a cropped (but un-edited) version of one of the most famous pictures of the Universe: the Hubble Deep Field!

Image credit: R. Williams (STScI), the Hubble Deep Field Team and NASA.

As you can well imagine, the largest galaxies in that picture are, by-and-large, the closest galaxies to us. So, if we understand dark matter (and we think we do), the blue lines show us how we expect the background galaxies to be distorted.

Image credit: Mike Hudson. is his research page.

That's the effect of weak lensing: a shear in how the background galaxies appear.

Well, we can work the other way, too! Observe the distortion of the background galaxies, account for the shape noise, and re-create a map of the total matter -- both luminous and dark -- based on what we know about weak lensing. So what do we get, looking at that arc-free cluster back up top? (The third image in this article.)

Image credit: Douglas Clowe et al.

Well, we can recreate the distribution of matter, most of which is not accounted for by atoms! In fact, if we show those results from weak lensing in blue, and overlay the Chandra X-Ray observatory data in pink, you may recognize this as one of the most famous images ever...

Image credit: X-ray: NASA/CXC/CfA/M.Markevitch et al.; Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/ D.Clowe et al.; Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.

The Bullet Cluster! You can not only measure the amount of total matter, with weak lensing, but you can compare it with where the hot gas is in the X-ray. This combination is a big part of how we know dark matter doesn't collide with either itself or with normal, atomic matter.

So if you want to know how much mass is in a cluster, and where that mass is, all you need to do is measure all the background sources of light coming from behind that cluster, and as long as you've got enough of them, weak gravitational lensing takes care of the rest!

And that's how weak gravitational lensing shows us where dark matter is!

More like this

Hello Nathan,
you said: « dark matter doesn't collide with either itself or with normal, atomic matter. »
But why is it called matter then? In fact, does it has any other known property than its mass?

I have an unrelated question that may look silly but that nobody could explain to me. Wikipedia says that the universe's mass has a Schwarzschild radius of approximately 10 billion light years[1], and even if this number is wrong, it led me to wonder the following:

The expanding universe at some moment, because of the sheer density of its own mass, was inside its Schwarzschild radius. How could it become bigger? Mass remained the same...


Mind blown. Cool post Nathan :P

@1: I believe the answer is inflation followed by the big bang.

My guess is that when the mass of the universe was contained in a singularity, there was no schwarzschild radius because space didn't exist. There was no space (or time for that matter) for a schwarzschild radius to be present in.

By Stinky McStinkface (not verified) on 20 Apr 2011 #permalink

Pronoein, I am not an astronomer, but I think it is called matter *solely* because it has mass, because isn't that the only thing that really makes matter unique... I guess it just floats around being bored and solitary and dark and stuff. Like some sort of teen emo poet.

@Pronoein & @crd2: Just a BTW, the man's name is Ethan, not Nathan. ;)

@Stinky: While I don't have too much trouble with the idea that the universe might once have been within its own R_Schwarzschild, but have expanded beyond that, I would think that there was certainly time between the initial inflation & Big Bang, and when it grew beyond R_Schwarzschild. But IANAPA/P/C (I Am Not A Professional Astronomer/Physicist/Cosmologist).

By Randy Owens (not verified) on 20 Apr 2011 #permalink

Caminin avlusu hınca hınç doluydu. Belli ki cenazenin yakınları onu son yolculuÄuna uÄurlamak, dostları da son görevlerini ifa etmek için oradaydılar.Sahte gözyaÅı dökenler,kara gözlüklerin ardında cenazeye gelenleri inceleyenler,aÄlamamasını kara gözlüklerle örtmeye çalıÅanlar,bedenen orada ama ruhen çok uzaktaki olanlar,âYahu tam da ölecek zamanı buldu.Bugün de çok önemli iÅlerim vardı.Ãabuk bitse de gitsemâ diyenler... Kimler yoktu ki...

This was a great one - loved the ending Easter eggs!

@ Pronoein: It is called matter because it behaves like particles (say, in the Bullet Cluster, but also LCDM cosmology). It is a matter [sic!] of convenience, not an absolute thing.

@ Pronoein: I'm not into general relativity, but as far as I understand a Schwarzschild radius is derived from a GR solution _outside_ a body. So this physics would be misapplied on a scenario where the universe originated like that.

If you go to the Planck scale, quantum effects wash out such concerns: "Because the Schwarzschild radius of a black hole is roughly equal to the Compton wavelength at the Planck scale, a photon with sufficient energy to probe this realm would yield no information whatsoever. Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole (a.k.a Planck particle), thus completely distorting that region of space, and swallowing the photon."

Goes on to explain that perhaps quantum gravity could explain what actually happens. It isn't called a singularity for no reason!

OTOH standard cosmology stops with the end of inflation so it doesn't need to be like those scenarios. For example, if eternal inflation is valid you would have to consider other types of singularities I think, as in how semiclassical worldlines stops branching (say, by particles decaying).

As I understand it there is a conjecture that branching will end _latest_ at the Planck scale* - so that tapering off can happen more "smoothly" for all I know. Big Smooch instead of Big Bang!?**

[* Because you run redshift backwards looking back in time, getting ever increasing particle energy from blueshift.]

** I think there is a lot of leeway to avoid singularities in modern physics, as opposed to when they were a big deal, even sought out, yesteryears.

By Torbjörn Lars… (not verified) on 21 Apr 2011 #permalink

@ Pronoein:

Ahh, you helped me realize an analogy, perhaps an abstraction, on looking at singularities.

I was going to throw in that the finishing note in the previous comment shouldn't be taken to mean that it isn't useful to look at singularities, it is. But then why are they useful (especially if the resulting physics is to resolve them)?

This happens in biology too! There you have "singularities" in the form of "chicken and egg" systems, where like the proverbial paradox you see a chicken lay an egg and an egg become a chicken so wonder how the coupled system evolved in the first place. The resolution takes you to a prediction of a previous decoupled system through a bottleneck of possible pathways!

What I mean is that the proverbial "paradox" predicts generally that populations evolves (which is a narrowing of pathways already there), but also more specifically that previous eggs were simpler as life started out simple. (Birds (dinosaurs): eggs - reptiles - amphibians - fishes - ... - sponges: oova - ... - slime molds: asexual spores; at which point it simply becomes a feature of multicellularity. I gloss over the problem of origin of sexuality, of course.)

Another chicken and egg illustration is DNA - proteins, where DNA codes the proteins that makes up the cell machinery that decodes DNA. And the resolution is the RNA last common ancestor from messenger RNA, transcript RNA and the preserved RNA core in the ribosome protein factory.

Pulling the abstraction back to physics, singularities are useful because they provide a lot of easier to achieve information on several areas of physics if you can study them. (I would think professional theorists would have another view; certainly more nuanced at least.)

By Torbjörn Lars… (not verified) on 21 Apr 2011 #permalink

Gravitational lensing is a particularly important effect. It offers excellent evidence to differentiate between competing theories. But theorist still argue.

SciLogs, quotes Analyzing the Bullet Cluster, Brownstein and Moffat (2007)
---"Using Modified Gravity (MOG) theory, the ânormalâ matter in the Bullet Cluster is enough to account for the observed gravitational lensing effect."

My problem is that dark matter and MOG seem equally reasonable hypothesies. As well, I wish Cooperstock's general relativity work would be expanded to lensing.

I may be particularly gullible; but as well, theorists seem so involved in their own incredibly diffcult calculations that they ignore alternatives.

Considering these lensing alternative:
---Dark matter hypothesis seems to be a general relativistic bending of light due to the Newtonian gravitation of the galaxtic matter and the hypothesized dark matter.
---A MOG hypothesis seems to be a general relativistic bending of light due to the Modified Newtonian gravitation of galactic matter only.
---A general relativitic hypothesis would reguire a general relativistic bending of light due to the general relativistic gravitation of galactic matter only.

Now, above you drew a 2 X 2 matrix (model distribution of galaxies).
(with shape noise, without shape noise)
_________ by X
(Unlensed, lensed) but lensed is due to a Newtonian gravity of the galactic arrangement.

Has anyone build a 2 X 4 matrix (model of galaxies??
(with shape noise, without shape noise)
_________ by X
(unlens, lens Newt, lensed Mog, lensed GR)
p.s. I assume unlens = unlens Newt = unlens MOG = unlens GR

Because, unless a suitable dark matter particle is found (and it might not be found soon, even if it exists), I don't think any of these theorists will give up their theory.

A simple toy model galaxy arrangement etc for lensing is needed. It must be simple enough for alternative theories to calculate (with an appropriate supercomputer). Then, maybe these theorists would respect if not convince one or the other.

Especially if a suitable dark matter particle is not found; there needs to be some simple toy models against which the alternative theories can be compared and evaluated.

Either MOG can account for some portion or not of gravitational lensing (also galactic rotation discrepancy). Ditto GR.

As well, does MOG deviated from only Newtonian gravity or general relativity also. I've never found hand waving answers to these questions, i.e. not based on calculation.

Further, it seems that even the amount and distribution of baryonic matter is differently assumed in each of these theories. I sure all of these assumptions are well argued; but unless the different theories are applied to the same simple toy model galaxy or galaxy configuration no comparitive insight can be gained.

Show me the simple toy model comparison between these different theories. I am not convinced that any comparison has been done. Neither for lensing or galactic rotation.

Without such comparison, I am left with the feeling that theorists are no different than Cartographers propounding on the merits of their favorite universe projection. The Dark matter projection, the Modified gravity projection, the General relativity projection. they are all correct from their point of view.

Yes, I am the frustrated twelve year old; please try again to convince me that you grownup theorists know what you talk about.

What keeps dark matter from clumping under its own gravity like normal matter does? Is there a limit to the amount of dark matter you can fit in a given volume?

@ Randy O: I know his name is Ethan, I was only teasing.

@ OKThen: I think your forgetting how much other evidence supports dark matter vs MOG. I know you've been following SWAB for a while so I'm sure you've read about all the other evidence that is out there in support of dark matter. MOG falls short in a big way when compared to DM. Not to say that MOG isn't intriguing, just that it lacks a multitude of supporting evidence.

@Pronoein: Mass isn't responsible for the fact that matter collide with each other.
There's two main causes for that. Electromagnetic force for charged particles and the exclusion principle for uncharged particles.
Mass is responsible for the particles inertia.

@The Bobs: What keeps dark matter form clumping under its own gravity is the absence of particles collisions (or, in other words, friction)

A particle under the influence of a gravity force converts its potential energy in kinetic energy.
If there's no friction, this particle will never rest in the center of gravity because all potential energy will be converted in kinetic one and vice versa (it's a conservative system)
But, if there's friction, the particle will loose part of its kinetic energy in heat (non-conservative system) and will condense in the gravity center.

By ChicoPinto (not verified) on 21 Apr 2011 #permalink


I'm not excited about MOG; but it's there and a possibility.

Yeah, I've been reading SWAB. I hear the arguements for cold dark matter; but I remain unconvinced. Also, I'm biased against a suitable particle being found; but I'd really be excited if an appropriate particle was found.

I like Cooperstock's General Relativity work; but if the GR experts don't improve their calculations to the point of acceptance for gravitational rotation by mainstream experts; and then maybe expand their work to lensing. Well a non-expert like me can only wait. But I'm biased towards general relativity solving part of the dark matter mystery..

There are a number of big assumptions (in the big bang theory and dark matter theory) that I don't accept as fundamentally true; but that I accept as pragmatically correct for calculation purposes. No need to list my doubted assumptions.

So I view the dark matter hypothesis as pragmatically correct for calculation purposes. Ditto MOG. But like Hooke's law, I don't expect any fundamental insight from either.

I do expect fundamental insight someday from new theories of quantum gravity, extra dimensions and a quantum theory of time. But those are my biases based on my interpretation of speculative work. So I listen, try to hone my understanding, but must await the difficult work by experts.

But this is key. I try not to hold onto an ideas once it is clearly contradicted by the evidence. The problem is there is not enough evidence to clearly rule out a great many speculative ideas. So if we can't falsify MOG or dark matter; my question is can we do a more insightful comparison.

Here's an example of what I mean as a more insightful comparison. It's on the web site BigThink and it's comparing electric versus gasoline cars.
Well this comparison really opened my eyes.

Similarly I'd like to have my eyes opened about the dark matter observations.

Regarding the neutrino as dark matter,
It will be interesting to see if KATRIN (2012)is able to rule out a totally collision less CDM-dominated Universe.

To quote Yannick Mellier from an excerpt in book Particle Dark Matter - Betrone

â Since one historical validation of Einsteinian gravitation results from gravitational deflection of light behind the sun in 1919 it would be ironic if the gravitational effect were eventually to kill it almost 100 years later.â

In general,
Once we have the James Webb Telescope up, and I do mean *up* and running (2014/15)we will be able to make use of strong and weak lensing to a higher degree, who knows maybe the data retrieved will help better utilize HST data and the info coupled could draw this *matter* to a closer view.

There are several Events that will transpire in the coming years, the two above and LSST, Large Synoptic Survey Telescope is in the D & D stage. (design and development) and will acquire
First light four years from construction start date JDEM Joint Dark Energy (2020)â¦should offer a unique view.

By Sphere Coupler (not verified) on 21 Apr 2011 #permalink

"But, if there's friction, the particle will loose part of its kinetic energy in heat (non-conservative system) and will condense in the gravity center."

And by heating up become visible.

Since this is supposed to be DARK matter, it rather removes itself from the pool.

What keeps dark matter from clumping under its own gravity like normal matter does?

Because only gravity can slow it down. And that takes a very long time indeed. The two parts of the Bullet Cluster will pass through each other a few more times before merging.

By David MarjanoviÄ (not verified) on 04 May 2011 #permalink

"Because only gravity can slow it down."

It may be just a language problem, but gravity can't slow it down, only inelastic collisions can do so. Gravity causes collapse, but absent inelastic collisions, they'll keep moving.

If your cloud of matter is very widely spread, then it will take a VERY LONG time to collapse and that's another reason why maybe the cloud hasn't collapsed (and when it HAS collapsed, stops being Dark Matter and becomes acknowledged Matter like what we see in the galaxy - a theory, not saying that's true).

What we need is some sound hypothesis which will allow us to make a model of the density variance of dark matter. It may be quite diffuse or clumpy. That is what we need to find out.

@WOW said: It may be just a language problem, but gravity can't slow it down, only inelastic collisions can do so. Gravity causes collapse, but absent inelastic collisions, they'll keep moving.

Arent't there inelastic collisions when they merge? I think there is. The "collisions" occur between the atoms IN the objects composing each merging group; and the collisions, due to friction, produce thermal energy. This energy is sourced from the kinetic energy of the moving object. See further example here.

I compare the processes which occur in objects subjected to the changing gravitational stress of Jupiter's nearness (its moons being the objects). This effect is conventionally offered as explaining vulcanism, fluid water, etc on different moons.
Thus in the merger process, energy will be converted from kinetic to thermal form causing loss of momentum.

There is one "aber", and that is the distance between objects in the merging clusters/galaxies can be so large as to make gravitational effects effectively meaningless. So my point would be moot.

PS Has anyone ever postulated that the flexing of spacetime may consume energy from (???) due to gravitational interaction. The idea just occured to me.

By idealist707 (not verified) on 17 Jun 2011 #permalink

Update some concepts:

On Light And Dark Mass And Energy

Most probably wrong common statements :

1) â â¦could help solve mysteries such as the nature of the dark energy that is accelerating the expansion of the universe.â
2) â Light has no resting mass, just energy. Gravity is a bend in space, therefore Gravity does not pull at light but the light 'bends' with space.

Most probably right :

1) The present universe expansion is an accelerating separation of galaxy clusters, fueled by singularityâs mass reconverting to energy since Big Bang. In the present universe nearly all mass formats are destined to reconvert to energy. The attempts to postpone this reconversion are termed evolution/natural selection. The accelerating pace of expansion is Newtonian.

2) Light has mass. Every object and every process in the universe is a progeny, consequence, derivative of singularity, energy-mass superposition, dualism. Gravity is NOT âa bend in spaceâ. It is the propensity to natural-selection, to delay reconversion to energy, to maintain the energy in mass format. Light bends by gravity when gravityâs pull does not suffice to overcome lightâs momentum. However, lightâs momentum is no match for black-holeâs gravityâ¦

Dov Henis (comments from 22nd century)

See the book Einsteins' Lens by Gates. It cover GL very, very well.

By wayne Watson (not verified) on 22 Mar 2013 #permalink

Make that Einstein''s Telescope

By wayne Watson (not verified) on 22 Mar 2013 #permalink

The book talks about caustics and critical curves. The author does not fully explain these, but apparently of some value. One seems to be a multiplication effect. The common use of caustic seems to be they are like bundles of rays. Why are they important at all?

By wayne Watson (not verified) on 25 Mar 2013 #permalink

google it.
"caustics physics". pretty easy explanations.
Critical curves are harder to get.

Don't confuse the effects of gravitational lensing with astronomical and atmospheric refraction.

Thanks for the very clear explanation, I really enjoyed the read. I once did this type of analysis in a kaggle competition and it was a lot of fun.

The only thing that puzzles me is: how do you know that its not just ordinary cold gas / matter instead of dark matter? Eg 100 hydrogen atoms/m3.. Can that be excluded with observations techniques or is it an assumption that there is no cold gas?

@Thijs #27: You may want to read some of Ethan's more recent postings; he covers the many lines of evidence for dark matter in great detail.

1) We can exclude ordinary matter as gas or dust observationally because, in order to have the necessary mass, it would have to be dense enough to show clear spectral absorption lines. Since we don't see it, it's not there.

2) We can exclude ordinary matter computationally, using data from the cosmic microwave background to constrain the maximum amount of baryonic matter which could have been formed during nucleosynthesis.

3) We can exclude ordinary matter via gravitational lensing observations as described in this posting. From the X-ray features, we know that ordinary matter (hot gas) follows the visible luminous mass distribution. Since we observe a different mass distribution from lensing (in many clusters, not just the Bullet Cluster), that different mass must not be ordinary matter.

By Michael Kelsey (not verified) on 17 Nov 2014 #permalink