# Problem interpreting Mpc/h in maps of DM

1. Nov 4, 2012

### BillSaltLake

Problem interpreting Mpc/h in "maps" of DM

In charts of ρ distribution, such as the z = 0 image
http://www.mpa-garching.mpg.de/galform/virgo/millennium/seqF_063a_half.jpg

(taken from http://www.mpa-garching.mpg.de/galform/virgo/millennium/ ),
the distance scale is usually expressed in units of Mpc/h. In this image, there is a scale of 31.25 Mpc/h, although I think this is a misnomer-- it should be written [31.25/h] Mpc, because h is decreasing. At present, that scale then represents 31.25/0.71= 44 Mpc. Does that seem correct?
There may be another problem; I expect the distances to scale with the scale factor "a", not with h ($\propto$ $\dot{a}$/a). For example, from 1 Gyr to the present, h has changed by ratio ~9, whereas a has changed by ratio ~6.5, and I would think that the scale in the t = 1 Gyr image
http://www.mpa-garching.mpg.de/galform/virgo/millennium/seqF_019a_half.jpg
should represent 1/6.5 (not 1/9) of the scale in the z = 0 image. Does this seem correct?

2. Nov 5, 2012

### Jorrie

Re: Problem interpreting Mpc/h in "maps" of DM

Mpc/h and [31.25/h] Mpc are basically the same thing. This is comoving distance, which does not change with the evolution of h (or a), because it is present proper distance. I think the h is there to cater for the uncertainty in h, which may soon be revised upwards to around 0.74, yet they do not have to alter the scale of their simulation.

3. Nov 5, 2012

### BillSaltLake

Re: Problem interpreting Mpc/h in "maps" of DM

Note that h ($\propto$ H) and a have different time evolution. Therefore a parameter that scales with h does not scale with a, and comoving distance scales with a. I think that the scale in the image should read "44/(1+z) Mpc", noting that 1/(1+z) $\propto$ a.

4. Nov 5, 2012

### Jorrie

Re: Problem interpreting Mpc/h in "maps" of DM

The picture is for z=0 (today), so it could have read either 44 Mpc (h=0.71), or 31.25 Mpc/h. The latter value remains constant when h (= H0/100) is refined by observation. Cosmologists use this so that their reports do not have to be updated as better values of H0 become accepted. AFAIK, h refers only to H0 and hence does not evolve with a. The parameter evolving with a is usually referred to as H(t).

BTW, although not applicable here, I thought it is proper distance that scales with a and comoving distance is constant for a given galaxy.

Last edited: Nov 6, 2012