I have two questions regarding peculiar velocities. In the data specifications, considering particles (dm in particular), you describe the field velocities as follows: "Spatial velocity. Multiply this value by √a to obtain peculiar velocity." . Also, when considering groups, under the field GroupVel you write: "... The peculiar velocity is obtained by multiplying this value by 1/a.". What is the difference between those two fields that forces us to get peculiar velocities by multiplying the first with sqrt(a) and the second by dividing a? Since they are both velocities shouldn't we multiply with the same constant (assuming that we are not at z = 0).
The second question is a more generic one. We use the term peculiar velocities in order to distinguish between a velocity component owning to the expansion and a component owning to the dirty gravitational games played by the particles right? Since you multiply/divide by a factor of alpha I understand that you somehow want to "correct" for the expansion and thus peculiar in this case means "real" velocity. When I do the math in order to get there though, I find that the transformation needed in order to "correct" for the expansion is given by the following formula: V_real = alpha V_co + H(z) X_real, where x the spacial coordinate. What am I getting wrong here? Should I multiply/divide as you suggest or use the latter formula?
Thank you in advance, and I hope that this message finds you in good health :)
(1) Due to unfortunate historical reasons, the factors of the scalefactor a required for different fields, are different. So yes you need to multiple by sqrt(a) in one case and 1/a in the other case.
(2) The quote should probably say "proper" or "physical", not "peculiar". After converting a velocity to physical km/s units, you are right the Hubble expansion is still missing. If you want to include this (depends on the situation), you must add in the term which includes H(z).