B How to measure the amount of gravitational lensing?

[exmarine]

I am reading papers about dark matter and MOND. As they often mention this effect, I wonder how they know / measure / quantify how much gravitational lensing a particular galaxy causes?

Thanks.

 

[phinds]

It's not measured, it's observed. Google "Einstein Rings".

 

[Vanadium 50]

Much the same way as with a glass lens - you trace the rays. It's in some ways easier with gravity because you can get multiple images.

 

[sunrah]

There are two different image distortions involved in gravitational lensing, shear and convergence. Basically shear describes elliptification of the source and convergence its magnification (positive or negative). It is possible to quantify both (although shear is vector-like, so depends on coordinates) - anyway I guess they mean convergence. If you're interested in lensing I recommend reading "Introduction to gravitational lensing" by Massimo Meneghetti http://www.ita.uni-heidelberg.de/~massimo/sub/Lectures/gl_all.pdf it is the best introduction I'v found. (PS I am not Massimo Meneghetti.)

 

[exmarine]

I suppose they “measure” it if it is used – along with velocity profiles – to calculate the amount of missing dark matter. And I don’t suppose there is an Einstein ring or cross around every galaxy.

And how would one trace the rays when we can’t know precisely where the objects behind the galaxies are located?

Ah, thanks for the link! Will read it.

 

[sunrah]

Well there are two different types of lensing; strong and weak. Strong depends on the alignment of the lens object (a galaxy for example), it is very sensitive to the position of the lens with respect to us. That's where you might see an Einstein ring or cross and can tell you something about the distribution of dark matter around your lensing galaxy.

And I don’t suppose there is an Einstein ring or cross around every galaxy.

Exactly, it depends on alignment between source, lens and us. All the photos of lensing you've seen are examples of strong lensing though. Weak lensing is much more interesting. It doesn't produce dramatic images, but tells us a lot about the evolution of our universe, particular the distribution of dark matter at different times.

And how would one trace the rays when we can’t know precisely where the objects behind the galaxies are located?

Spectrographs can give redshift data, allowing us to calculate distances. At the end of the day there is always an error in our measurements, meaning that everything is a bit of an educated (or informed) guess.

 

[Drakkith]

It's not measured, it's observed. Google "Einstein Rings".

I dunno. Seems like you can easily do a measurement from your observations.

 

[phinds]

I dunno. Seems like you can easily do a measurement from your observations.

Yeah I was really thinking more of "calculate" than measure, as in "calculate in advance" meaning BEFORE you observe.

 

[exmarine]

On page 7 of the document linked in post #4 (page 13 of the pdf), Meneghetti gives the metric for very small potential in nearly flat / Minkowski space. Ok, if I put a very small potential in the Schwarzschild metric, it should approach Minkowski. And if I then transform it from spherical to Cartesian coordinates I don’t get his results. I get a whole bunch of sines and cosines, and off-diagonal terms as one would expect. Then there is no direction I select (set of angles) that gives his exact diagonal matrix terms. For example, I can get his term for the xx term, but then the yy and zz terms are each 1 instead of his terms. Another direction gives me his term for yy, but then xx and zz diagonal terms are each 1, etc. It seems like there should be spherical symmetry, but I cannot get all 3 terms to equal his at once. Any idea what he is doing there? Thanks.

 

[Chronos]

A reasonably good explanation of the process is discusse here; https://arxiv.org/abs/1303.3274, Masses of galaxy clusters from gravitational lensing.