How do you calculate the virial radius

Romain Paviot
  • 8 Mar '18

Hello ! I have some problem in understanding how you calculate your virial Radius. I'm currently working with Illustris 3 at redshift 0. I retrieve the virial mass (Tophat200) and i calculate the virial radius with the following code :

Mvir = 4/3piRvir*3 deltac * pc with deltac calculated with the formula from Bryan and Norman (1998)).

def param(z): Om = WMAP9.Om(z) E = WMAP9.efunc(z) rhoc = WMAP9.critical_density(z) deltac = 18pi**2+82(1-Om)-(39(1-Om)*2) return rhoc,deltac

def radius(M,rhoc,deltac): radius = (M/(deltacrhoc(4/3)pi))*(1./3) return radius

for i in range(M.size): Rvir[i]=radius(M[i],rhoc,deltac).value/(1e18*1e6)

For example for M(TOPHAT200) = 3.63 * 1e14 solar mass i found a virial radius of approx 4.5 Mpc for the same halo however, R(TOPHAT200) = 1310 ckpc/h = 1.8 Mpc at z = 0

Even if it not a fiducial cosmology it shouldn't lead to such difference right ? so i was wondering where i was wrong in my calculation

And a last question : The actual total mass is always greater than the tophat mass. Does it means that our actual mean density is greater than deltac ? So does it mean so the group is already virialized since a given time t ?

Have a great day and thanks you for reading this !! Cordially, Romain

Romain Paviot
  • 12 Mar '18

my bad i have managed to calculate it afterward

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