What is the correlation between dark matter and Einstein Rings?

Question

I have once heard a TED Talk about Dark Matter, Einstein Rings and gravitation lenses. http://ed.ted.com/lessons/patricia-burchat-sheds-light-on-dark-matter

I don't think I understood the talk well. Thus I have three questions: It was said that the stars of a galaxy revolve around their center. It was also said, that one could expect stars to move more slowly the farther they are away from their center. However I have two different view points on this: First I remember Merry-go-rounds in which the out parts move faster than the inner parts, I think this view point is not applicable, because the parts are moved mechanically and their movement are fixed circles etc. Secondly I remember Kerbal's Space Program which emulates our solar system to some degree and the movement of objects in it. I don't think that stars, solar systems etc. move in a circle around the center of galaxy, maybe in a ellipse or if you are closer to the center in some other weird way. There are some effects of gravitation working, I don't know which, but well I guess there the path of the objects wouldn't be an ellipse anymore. However I can be clearly seen in KSP that objects slow down, if they move away from the center and then are pulled back and accelerated, if they have passed the turning point and this repeats again and again. However it was said in the TED talk that all objects move at the same speed... and I kinda find that hard to believe, because this would shatter my second view point. So I guess either statement in the talk is wrong or I just misunderstood it.

2th question: Dark matter was shown to surround galaxies in the form of a sphere. Why the hell, should it be a sphere!? I try to imagine a scenario after Big bang, when dark matter had the chance to form "planets" , round objects. The only thing I could imagine is, that those sphere are in facts planets of dark matter and they belong to a solar system of dark matters objects and a galaxy of dark matter objects etc. etc. So intriguing that looks, the less likely I hold it.

3th Question, I would also think, that giant bubbles of dark matter distort Einstein Rings, however it seems that they can be completely explained with the standard viewpoint of gravitation etc.
I didn't find that talk too informative or intuitive, however interesting and I would like to understand the things better, so if someone has information on those topics or source he/she can provide, I would be very happy, if that persons shares them.

Answer 1

First question

Comparing a galaxy (or solar systems) to a merry-go-round is not a good comparison. Acceleration in a merry-go-round is proportional to the distance from the center of the merry-go-round, but acceleration in a central mass system is inversely proportional to the distance from the center. Single star solar systems are very close to central mass systems. For example, Pluto's orbital velocity is an order of magnitude smaller than that of Mercury. Galaxies are not quite central mass systems, but the visual appearance is much, much closer to that of a central mass system than that of a merry-go-round.

Looking at luminosity would determine the distribution of mass in a galaxy if almost all of the mass in a galaxy was concentrated in the stars that comprise the galaxy. This mass distribution would in turn would dictate how velocities vary with distance from the center of the galaxy.

This is not the velocity profile that astronomers see. It's not even close. This is the galactic rotation problem. This is a very profound problem. There are very few ways to get out of this conundrum.

One possibility is that there's a lot of ordinary matter that we can't see, and that this invisible ordinary matter is distributed rather differently than the stars. This is the baryonic dark matter hypothesis. There are two problems with this route. One problem is that all the forms of invisible ordinary matter scientists can think of (e.g., interstellar gas, brown dwarfs, rogue planets), should be closely correlated with star density.The other problem is that this doesn't jibe with big bang cosmology. Invoking baryonic dark matter to solve the galactic rotation problem adds more problems than it solves.

A second possibility is that our model of gravitation is fundamentally flawed. Most scientists don't want to go down this pathway. A few do. Modified theories of gravitation are non-mainstream (but definitely not crackpot) physics. There are a number of problems with these modified theories of gravitation (e.g., the Bullet Galaxy). However, the proponents of modified gravity theories are very happy to point out that there are also problems with the other alternatives.

The mainstream hypothesis is that some form of non-baryonic dark matter exists and overwhelms the baryonic matter with which we are familiar. "Dark matter" simply means matter that cannot be seen. We can't see baryonic dark matter such as brown dwarfs and rogue planets in a distant galaxy. Non-baryonic dark matter is not only stuff that we cannot see, but also stuff that operates by hitherto unknown laws of physics.

Second question

Most hypotheses regarding non-baryonic dark matter assume that it interacts via gravitation only. Dark matter will naturally have a spherical mass distribution if that is the case. Moreover, as scientists haven't the foggiest idea what dark matter is, it's best to make the simplest assumptions possible about it. That simplest assumption is an unknown spherical distribution of mass that resolves the galactic rotation problem. It's the canonical spherical cow assumption. Anything beyond that spherical cow assumption invokes even more unknown physics.

Third question

An extremely massive point mass that is much, much larger than the largest supermassive black hole ever framed of would result in an extremely sharp Einstein ring. Astronomers don't see that. That's consistent with the fact that the supermassive black holes at the centers of galaxies are but a tiny fraction of the total mass of the galaxy. A lumpy mass distribution (e.g., a spiral galaxy whose mass is ruled by visible baryonic matter) would result in a rather distorted Einstein ring. Astronomers don't see that, either. A spherical mass distribution will give a nice clean Einstein ring. That's the kind of Einstein rings that astronomers do see.

By asking this third question, you have missed one of the key points of the cited TED talk. If Einstein's theory of gravitation is correct, the Einstein rings astronomers see are a measure of the total amount of mass in the intervening galaxy that creates the rings. This observed deflection is inconsistent with the mass implied by the intervening galaxy's luminosity. Einstein rings form yet another piece of evidence for the existence of non-baryonic dark matter.