Looking for some help with gravitational lensing and dark matter

[jmandell]

Greetings to all,

A little information yo provide context to my question. I'm 16, and a junior in high school and I'm attending an astronomy camp on kitts peak doing research projects with the large telescopes.

While researching possible projects on that particularly interested me was determining the amount of dark matter in galaxy clusters through gravitational lensing.

My plan was to image a cluster and the determine the mass by the amount lensing of background galaxies. That would find the total mass of the cluster, dark matter and all.

Then the mass of the luminous matter would be derived and subtracted from the mass of the cluster on the whole., thus leaving the amount of dark matter.


Based on my research I believe this is right, but then again I might be totally off the mark. Does this sound right to you guys?

If so, I'm having a little trouble finding all the calculations - any suggestion?



Thanks,
Justin

 

[Chronos]

Estimating the amount of matter [baryonic] in galactic clusters is difficult. It is usually based on luminosity - which is assumed to originate from ordinary stars. The error bars are fairly large.

 

[Bobbywhy]

Welcome to Physics Forums!

You are really fortunate to have such an opportunity to observe the sky from Kitt Peak. Not to mention the chance to interact with the astronomers, engineers, and scientists there!
As for your question, others have already asked the same. Here is a recent paper:

“Masses of galaxy clusters from gravitational lensing
Authors: Henk Hoekstra, Matthias Bartelmann, Haakon Dahle, Holger Israel, Marceau Limousin, Massimo Meneghetti
(Submitted on 13 Mar 2013)
Abstract: Despite consistent progress in numerical simulations, the observable properties of galaxy clusters are difficult to predict ab initio. It is therefore important to compare both theoretical and observational results to a direct measure of the cluster mass. This can be done by measuring the gravitational lensing effects caused by the bending of light by the cluster mass distribution. In this review we discuss how this phenomenon can be used to determine cluster masses and study the mass distribution itself. As sample sizes increase, the accuracy of the weak lensing mass estimates needs to improve accordingly. We discuss the main practical aspects of these measurements. We review a number of applications and highlight some recent results.
http://arxiv.org/abs/1303.3274

 

[jmandell]

Welcome to Physics Forums!

You are really fortunate to have such an opportunity to observe the sky from Kitt Peak. Not to mention the chance to interact with the astronomers, engineers, and scientists there!
As for your question, others have already asked the same. Here is a recent paper:

“Masses of galaxy clusters from gravitational lensing
Authors: Henk Hoekstra, Matthias Bartelmann, Haakon Dahle, Holger Israel, Marceau Limousin, Massimo Meneghetti
(Submitted on 13 Mar 2013)
Abstract: Despite consistent progress in numerical simulations, the observable properties of galaxy clusters are difficult to predict ab initio. It is therefore important to compare both theoretical and observational results to a direct measure of the cluster mass. This can be done by measuring the gravitational lensing effects caused by the bending of light by the cluster mass distribution. In this review we discuss how this phenomenon can be used to determine cluster masses and study the mass distribution itself. As sample sizes increase, the accuracy of the weak lensing mass estimates needs to improve accordingly. We discuss the main practical aspects of these measurements. We review a number of applications and highlight some recent results.
http://arxiv.org/abs/1303.3274

Thanks for the welcome! I am really looking forward for the camp.

As for the paper, that was one that was on my list to read (along with like 5 others)

 

[marcus]

Well since that is on your list, let's look at at this. Let's look at Figure 11 on page 32. It looks like you divide the field up into squares and you determine the preferred direction of the background ellipses. Background galaxy outlines are either perfect circle or roughly elliptical with the major axis pointing in some direction. The direction might be random (no weak lensing distortion) or it might have some "majority" preferred direction.

If there is no preferred direction in that square then you just put a dot in the middle and move on to the next square.
If there is some preferred direction then you put a little line segment centered at the midpoint of the square. The length of the segment depends on the PERCENTAGE of the galaxies that have their major axis aligned more or less in the preferred direction. You use some statistical measure of the amount of alignment in the preferred direction and that determines the length of the little mark you make in each square.

Look at Figure 11. they had a square field containing the foreground cluster and a lot of background galaxies. They divided this square field into 144 little squares.

In the middle of each little square they put a little (dot) or line segment.

This segment shows two things: the DIRECTION of the alignment of whatever ellipses are in background, and also the AMOUNT OF ALIGNMENT.

It seems to me that a summer project that produces a Figure 11 is already a good project. But FROM THAT. I Think you can find some way to draw rough contour lines of mass concentration and also you may be able to estimate the total mass that is distorting the background.

the idea is that IN THE ABSENCE OF A FOREGROUND DISTORTING MASS on average galaxies should be either circular or if elliptical silhouette the axis should be pointed at random because the galaxies are tilted randomly. BUT IF there is a foreground mass then the WEAKLENSING DISTORTION is what stretches the silhouettes of background galaxies out in kind of circles around the concentration of mass, as you can see in Figure 11.

I am totally not an expert and I am not recommending you do this project but I am willing to talk about it since you already have a good paper that you plan to read. So as a non expert I will talk about it with you. I think it is interesting.
The math is probably hard to do a complete mass estimate job and the statistics of the alignment measure probably would use a fairly sophisticated computer program. So that is more than a summer project, maybe. But the topic itself is extremely interesting and you might be able to get a PARTIAL result, like the Figure 11 picture.

Weak lensing is a beautiful way to observe the density contours of DM clouds.

Personally if I was doing a first project of this sort I would not do 144 little squares. I would only do 16 or 36 or 64, and get a cruder picture. It's sophisticated stuff. Fewer squares (i.e. lower resolution) should be enough.

 

[jmandell]

Well since that is on your list, let's look at at this. Let's look at Figure 11 on page 32. It looks like you divide the field up into squares and you determine the preferred direction of the background ellipses. Background galaxy outlines are either perfect circle or roughly elliptical with the major axis pointing in some direction. The direction might be random (no weak lensing distortion) or it might have some "majority" preferred direction.

If there is no preferred direction in that square then you just put a dot in the middle and move on to the next square.
If there is some preferred direction then you put a little line segment centered at the midpoint of the square. The length of the segment depends on the PERCENTAGE of the galaxies that have their major axis aligned more or less in the preferred direction. You use some statistical measure of the amount of alignment in the preferred direction and that determines the length of the little mark you make in each square.

Look at Figure 11. they had a square field containing the foreground cluster and a lot of background galaxies. They divided this square field into 144 little squares.

In the middle of each little square they put a little (dot) or line segment.

This segment shows two things: the DIRECTION of the alignment of whatever ellipses are in background, and also the AMOUNT OF ALIGNMENT.

It seems to me that a summer project that produces a Figure 11 is already a good project. But FROM THAT. I Think you can find some way to draw rough contour lines of mass concentration and also you may be able to estimate the total mass that is distorting the background.

the idea is that IN THE ABSENCE OF A FOREGROUND DISTORTING MASS on average galaxies should be either circular or if elliptical silhouette the axis should be pointed at random because the galaxies are tilted randomly. BUT IF there is a foreground mass then the WEAKLENSING DISTORTION is what stretches the silhouettes of background galaxies out in kind of circles around the concentration of mass, as you can see in Figure 11.

I am totally not an expert and I am not recommending you do this project but I am willing to talk about it since you already have a good paper that you plan to read. So as a non expert I will talk about it with you. I think it is interesting.
The math is probably hard to do a complete mass estimate job and the statistics of the alignment measure probably would use a fairly sophisticated computer program. So that is more than a summer project, maybe. But the topic itself is extremely interesting and you might be able to get a PARTIAL result, like the Figure 11 picture.

Weak lensing is a beautiful way to observe the density contours of DM clouds.

Personally if I was doing a first project of this sort I would not do 144 little squares. I would only do 16 or 36 or 64, and get a cruder picture. It's sophisticated stuff. Fewer squares (i.e. lower resolution) should be enough.

Thanks for the explanation. The more I read the more it looks like this is going to be hard in the short amount of time, but we are allowed to take our data and work on it later and use it for science fairs, competitions, etc. I think that's what I'm going to do if we still that've scope time available after the other students make their proposals.