Velocity dispersion - confused.

[Tomer]

Hey guys,

stupid question probably, but I somehow don't get it.
I'm just reading an article about dark matter in elliptical galaxies. They mention at a certain point that while for the detection of DM in spiral galaxies we measure the rotational velocity of its stars around the center, for the detection of DM in elliptical galaxies we measure the velocity dispersion. They then write: "this gives us an estimate of how fast the stars move as a function of the distance from the center".
What I don't get is:
1. How do we get this estimate? As I understand dispersion - I could have a dispersion of 400 km/s but still have an average of 0. Or I could have a dispersion of 10 Km/s with an average of 1000 km/s. How are the average and the dispersion connected?
2. Why do we talk of the dispersion and not of the mean velocity then?

Thanks a lot - this is really important!

Tomer.

 

[Bobbywhy]

Tomer, You may find some answers here, where I have excerpted a few sentences from a longer article:

“The observations of stellar velocity dispersion, interpreted in terms of Jeans' equation or of the Virial theorem, can provide the total mass for R < Re, or even at larger distances. … This formula gives a first approximate mass. In practice however, much more sophisticated models than this one are used to interpret the velocity dispersions. … As in the case of spirals with their rotation curve, a flat or slowly increasing velocity dispersion, (r), may indicate dark halos dominating the dynamics (Saglia et al. 1993) but there is a surprisingly large variety of -profiles, some of which decrease outwards relatively fast. Therefore, Saglia et al. did not find any compelling evidence of dark matter out to 1-2 Re. Carollo et al. (1995) observed flat or gently declining velocity dispersion profiles in four elliptical galaxies, concluding that massive dark halos must be present in three of the four galaxies, although no clear conclusion was obtained for the fourth. Bertin et al. (1994) found that in a sample of 6 galaxies, three of them were not suitable for reliable modelling, two of them presented no evidence for dark matter and one (NGC 7796) appeared to have a distinct dark halo. But the conclusion that some galaxies have a dark halo while others do not is problematic for understanding what an elliptical galaxy is.
http://ned.ipac.caltech.edu/level5/March01/Battaner/node11.html

Secondly, this Nature article, plus references therein, appears to address your questions:

“Lost and found dark matter in elliptical galaxies”
http://www.nature.com/nature/journal/v437/n7059/abs/nature03970.html

 

[Tomer]

Hi Bobby, thanks for replying. However, I've read the first article you posted already and couldln't find an answer to my question there. I do not understand why my article stated that dispersion implies something about the average velocity - is this even true? I can accept the fact that it implies something about the mass.

Even more importantly - why don't we speak of velocities themselves? Is it really easier to deduce the mass from a given dispersion function than of an average velocity function?

 

[Parlyne]

The average will tell you about the motion of the galaxy with respect to us. The dispersion will tell you about the motion of the individual stars with respect to the galaxy.

 

[pmacias]

Hi Tomer,

No question is ever stupid when it comes to science! It's always better to ask and clarify any confusion rather than assume and potentially misunderstand something.

To answer your questions:
1. Velocity dispersion is a measure of how spread out the velocities of stars are in a galaxy. It is calculated by taking the square root of the variance of the velocities. So, in your example, a dispersion of 400 km/s would mean that the velocities of stars vary by an average of 20 km/s (sqrt(400) = 20). Similarly, a dispersion of 10 km/s would mean that the velocities of stars vary by an average of 3.16 km/s (sqrt(10) = 3.16). The average velocity is not considered in this calculation, only the variation of velocities.

2. We talk about dispersion because it gives us a better understanding of the dynamics of the galaxy. In spiral galaxies, the rotation of stars around the center is primarily affected by the gravitational pull of the matter within the galaxy, including dark matter. However, in elliptical galaxies, the motion of stars is more random and not necessarily affected by the gravitational pull of the matter within the galaxy. By measuring the dispersion of velocities, we can get a better estimate of the total mass of the galaxy, including the presence of dark matter, rather than just looking at the average velocity.

I hope this helps clarify things for you. Keep asking questions and keep exploring the wonders of the universe!