## Virial radius is defined. as the radius of a sphere that has a mean enclosed density of

180 times the mean density
3
23%
200 times the mean density
4
31%
180 times the critical density
2
15%
200 times the critical density
4
31%

Total votes: 13

Ilian Iliev
Posts: 8
Joined: August 17 2006
Affiliation: University of Sussex
Contact:

### Virial radius

The mean oversendity is related to the mean density of the universe at the time of formation of the halo. This is of course not very convenient for observations, when usually one does not know the halo formation time. In simulations/theoretical models the halo formation time is also a somewhat fuzzy concept, since halos merge often and continuously infall matter. So, the formation time is often taken to be the time when some given fraction (say, 90%) of the halo mass already has assembled, or the time of the last major merger event.

The Bryan and Norman fits are just the top-hat model results generalized beyond the EdS model.

Generally, there should be a sharp transition between the halo and surrounding infall, where the virialization shock (in the gas) or the last caustic (for the dark matter) is. Identifying this, and which particles belong to the halo and which do not in simulations is not easy, though.

Masahiro Takada
Posts: 7
Joined: February 08 2006
Affiliation: IPMU, U. Tokyo
Contact:

### Virial radius

In fact, the paper by M. White (astro-ph/0207185) is very useful to find how the halo mass function varies with the halo mass definition used, as you might know. The discussion done in Appendix of the paper by Hu & Kravtsov (astro-ph/0203169) is also useful to see. As you have discussed, a halo doesn't have any clear boundary, so there seems no clear solution to answer which halo mass definition is appropriate.

Most interesting result shown in the paper above is Sheth-Tormen halo mass function can well reproduce the simulation results for several cosmological models, with a universal form with single parameters a' and p' in the ST function, *if* the halo mass in the simulation is defined by the overdensity 180 relative to the background mean density (see Figure 5). It is also clearly shown that, if other definitions of halo mass are used, the parameters a' and p' needs to change so that the resulting ST mass function can match the simulation results. From these results, the overdensity 180 relative to the mean background desity seems a good choice for the halo mass definition.