### Conversion from comoving to physical coordinates

Justo Antonio Gonzalez Villalba
• 1
• 21 Jun '22

Hi Dylan,

I am not clear about the conversion from comoving coordinates to physical coordinates:

-In the data specification some magnitudes appear with the hubble factor (h=0.67) in the units. For example, the units of Masses are 1e10Msun / h. In this case should I multiply by the hubble parameter (h=0.67) to cancel it in the denominator in the units, and recover physical units (1e10Msun), or is it the other way around, and I should divide by the hubble parameter?

-Same question for the scale factor. For example, the units of Potential are (km/s)^2/a. In this case should I multiply or divide by the scale factor to recover (km/s)^2.

-Finally, some fields appear with comoving kiloparsec, for example Coordinates have as units ckpc/h. In this case, and assuming that the h factor is cancelled out correctly, what remains is physical kpc, or is it necessary a further transformation from ckpc to kpc?

Thanks a lot for your help!

Dylan Nelson
• 21 Jun '22

Hi Justo,

Yes this can be confusing, and in general it's good to double-check with any existing numbers to make sure you're going in the right direction. Lengths/coordinates are an easy one, since TNG100 is 75 cMpc/h ~ 110 cMpc.

In all cases, `ckpc/h` means you need to both (i) remove the little h factor, and (ii) also then convert from comoving to physical. (By multiplying by the scalefactor). You can see some other examples e.g. in the table on the Data Background page.

Justo Antonio Gonzalez Villalba
• 2
• 21 Jun '22

Thanks for the pointer!

Could you confirm if the following examples are correct? (assuming h=0.67 and a =0.8 (z = 0.25) )

-'Masses' is stored as 67 1e10Msun / h, so the physical mass would be 67/h = 67/0.67 = 100 1e10Msun

-'Potential' is stored as 8 (km/s)^2/a, so the physical potential would be 8/a = 8/0.8 = 10 (km/s)^2

-'Coordinates' is stored as 6.7 ckpc/h, so the comoving coordinates would be 6.7/h = 6.7/6.7 = 1 ckpc, and the phsicial coordinates 1*a = 0.8 kpc

Dylan Nelson
• 21 Jun '22

Yes it seems ok to me, except a typo (?) with `6.7/h = 6.7/6.7`.

Justo Antonio Gonzalez Villalba
• 22 Jun '22

Yep,there was a typo in the last line, it should read:

-'Coordinates' is stored as 6.7 ckpc/h, so the comoving coordinates would be 6.7/h = 6.7/0.67 = 10 ckpc, and the physical coordinates 10*a = 8 kpc

Thanks again for all clarifications!

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