# Pairwise velocity dispersion in Cosmological simulations

1. Nov 10, 2014

### sketos

There are numerous publications about pairwise velocity dispersion ( PVD ) of galaxies in real redshift surveys. It is customary to use an exponential form for the distribution of pairwise velocities and then model the redshift space distortions in the 2PCF to retrieve the PVD.

Now if i have a cosmological simulation i know exactly the position and the velocity of every particle (x,y,z) (u_x,u_y,u_z). I want to compute the PVD from cosmological simulations.

If i take u_{12}(r)=u_1(x)-u_2(x+r) and then σ_{12}=<u_{12}^2-<u_{12}>^2> i can have the σ_{12}(r).

My question is how can i retrieve σ_{12}(r_p), (i.e. in terms of the perpendicular distance)????

2. Nov 10, 2014

### Chalnoth

There are probably libraries you could use to help, but if you just want a general algorithm, you could try this:

1. First, compute each individual component of $\sigma(r)_{12}$. You'd get one term for each selection of two galaxies in the sample. Each of these samples will have an associated distance, the distance between the two galaxies.
2. Select a method to place the galaxies into bins. One simple method would be to use bins in radial distance. For each bin in radial distance, average the velocity dispersion components that fall within it. This is similar to constructing a histogram (though the way samples are combined is different).

3. Nov 11, 2014

### sketos

Thank you for your reply , but this was my first thought too. But by doing so, you end up computing the σ12(r) associated with the galaxy pair distance r. I need to compute it in terms of the perpendicular distance r_p ( as it's usually done in real redshift surveys).

Is there any difference at all??

4. Nov 11, 2014

### Chalnoth

Ahh, I see what you mean. I don't think it'd be very different. It's just that your selection of bins is defined by $r_p$ instead. You do have to select an origin, however.

Are you also going to be using a definition of velocity that is based on observations? Velocity dispersion is usually inferred from redshift, for example...

5. Nov 11, 2014

### Chronos

I remember not so many years ago what it was announced a preferred 'tilt' in galaxies across the local universe had been discovered. Not long before that, it was announced that redshift was 'quantized'. A little creative binning can yield 'incredible' conclusions. While statistics is a marvelous and powerful tool to explore the universe, assumptions must always be viewed with extreme suspicion. Patterns in noisy data are all too often little more than dragons in the clouds.

6. Nov 11, 2014

### sketos

i have a mock catalogue so i think the way the data are constructed it assumes that there is an observer. So i have data points which correspond to (xi,yi,zi) and (uxi,uyi,uzi).

so i guess i need to find how r is related to rp.

7. Nov 11, 2014

### Chalnoth

I'm not completely certain, but if the name is any indication, it's the component of $r$ which is perpendicular to the line-of-sight direction. Said another way, it's the $r$ inferred from the angular separation of the galaxies as viewed by a particular observer. It's probably best to place the observer in the center of the data set.

You should verify, of course, because as I said, I'm not certain.