Trouble understanding speed-dispersion in (elliptical) galaxies

Question

I'm learning about LOSVDs (Line Of Sight Velocity Distributions) and I'm having a bit of trouble understanding the used terms.

As I understand, the LOSVD of a given (elliptical) galaxy is the density distribution of the LOS-velocities. The full LOSVD is difficult to find and it's easier to find 2 parameters of the distribution: $\bar v_{_{LOS}}$ and $\sigma_{_{LOS}}$ by fitting a (Gaussian) model to the spectrum of the galaxy.

I have a limited understanding of statistics, so I'm having trouble intuitively understanding what these 2 parameters mean later on.

I think that $\bar v_{_{LOS}}$ is simply the average value of the LOS-velocity for the whole galaxy while $\sigma_{_{LOS}}$ is the equivalent of a standard deviation.

Now later on in my coursebook, there's an explanation of how to get a LOSVDs for every point (/pixel) in the (projection onto the celestial sphere of the) galaxy by using 3D spectrography.
From this we can get a 3D dynamic model from our 2D kinematic model. In this newly found 3D distribution there's also 3 Sigmas, one for every dimension.

But here comes the part I don't understand:
The book is looking at the movement of stars in a spiral galaxy, the Milky way in particular.

We're trying to find a correlation between the age of MS-stars and their dispersion and so there's a dataset of a few stars in the neighbourhood of the sun with their dispersion in every dimension.

What is the meaning of dispersion in this context? How can a single object have a dispersion if it's a parameter of a density distribution?

Answer 1

The total light of a galaxy is the sum of perhaps billions of stars, each with their own line of sight velocity. You can characterise this distribution with a mean and a standard deviation (dispersion), and this will be reflected in the absorption line profiles of that galaxy.

Equally you might choose to measure this distribution as a function of position in a galaxy, if you are able to spatially resolve different regions. For instance one could put a spectrograph slit across a galaxy and get the velocity dispersion as a function of position along the slit.

When you are talking about nearby stars, you can measure the 3D velocities individually, providing you can measure the radial velocity, proper motion and distance of each star. You can then find the mean and standard deviation for this group of measurements in each velocity coordinate.