halo circular velocity

[ntessore]

Description

We require a model that assigns a circular velocity to halos of a given mass, @itrharrison has proposed the following model:

Inputs

• halo virial mass
• halo mean overdensity
• halo redshift
• cosmology

Outputs

• halo virial velocity

In addition, the halo virial radius could be obtained from the same model.

References

https://arxiv.org/abs/1403.1873

[itrharrison]

The above screenshot is a footnote in https://arxiv.org/abs/1403.1873

[rrjbca]

Can you update the issue name, description and references to give more detail about the specific model you want to implement. Additionally, are we assuming that our existing halo mass functions e.g. Sheth-Tormen can be used to sample virial masses? And do we have/need a way to calculate the "halo mean overdensity"?

[ntessore]

There's a number Δ_c(z) such that a region of space will start to collapse on itself if its mean overdensity is Δ_c(z) times the critical density ρ_c(z) of the universe. The collapse results in a virialised halo. The Press-Schechter formalism estimates how often the random matter field will exceed the Δ_c(z) ρ_c(z) density. So, if we assume that everything happens instantly, the mass functions do tell us the number of virialised halos at a given mass. In de Sitter space Δ_c ≈ 178 ≈ 180 but that might change a little in LCDM?

Comparisons with simulations often use a different definition of the spherical collapse with corresponding overdensities Δ = 200 (and Δ = 500 sometimes). There is a good overview on this by White (2000). So it really depends on where the model is coming from, and how sensitive it is to these details, but I think it should be fine for our purposes.