coshalo {celestial}

Virial halo conversion functions

Description

All 6 Virial parameter conversion functions. Each can map precisely to the other as a one paramter function.

Usage

coshaloMvirToSigma(Mvir=1e+12, z=0, H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, Rho='crit', Dist='Co', DeltaVir=200, Munit=1, Lunit=1e6, Vunit=1e3, Dim=3, ref)
coshaloSigmaToMvir(Sigma=230, z=0, H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, Rho='crit', Dist='Co', DeltaVir=200, Munit=1, Lunit=1e6, Vunit=1e3, Dim=3, ref)
coshaloMvirToRvir(Mvir=1e12, z=0, H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, Rho='crit', Dist='Co', DeltaVir=200, Munit=1, Lunit=1e6, Vunit=1e3, Dim=3, ref)
coshaloRvirToMvir(Rvir=162.635, z=0, H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, Rho='crit', Dist='Co', DeltaVir=200, Munit=1, Lunit=1e6, Vunit=1e3, Dim=3, ref)
coshaloSigmaToRvir(Sigma=230, z=0, H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, Rho='crit', Dist='Co', DeltaVir=200, Munit=1, Lunit=1e6, Vunit=1e3, Dim=3, ref)
coshaloRvirToSigma(Rvir=162.635, z=0, H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, Rho='crit', Dist='Co', DeltaVir=200, Munit=1, Lunit=1e6, Vunit=1e3, Dim=3, ref)
coshaloSigmaToTvir(Sigma=230, Vunit=1e3, Tunit='K', Type='halo', Dim=3) 

Arguments

Mvir

Mass within virial radius in units of 'Munit'.

Sigma

Velocity dispersion (3D) within virial radius in units of 'Vunit'. For coshaloSigmaToTvir the Sigma input should be the virial Sigma which can be found by setting DeltaVir='get' in the the other coshalo functions.

Rvir

Virial radius (3D) in units of 'Lunit'.

z

Cosmological redshift, where z must be > -1 (can be a vector).

H0

Hubble constant as defined at z=0 (default is H0=100 (km/s)/Mpc).

OmegaM

Omega Matter (default is 0.3).

OmegaL

Omega Lambda (default is for a flat Universe with OmegaL = 1-OmegaM = 0.7).

OmegaR

Omega Radiation (default is 0, but OmegaM/3400 is typical).

Rho

Set whether the critical energy density is used (crit) or the mean mass density (mean).

Dist

Determines the distance type, i.e. whether the Rho critical energy or mean mass densities are calculated with respect to angular / physical distances (Ang) or with respect to comoving distances (Co). In effect this means Rvir values are either angular / physical (Ang) or comoving (Co). It does not affect Mvir <-> Sigma conversions, but does affect Mvir <-> Rvir and Rvir <-> Sigma.

DeltaVir

Desired overdensity of the halo with respect to Rho. If set to 'get' it will estimate the required DeltaVir for a virial collapse using the cosgrowDeltaVir function.

Munit

Base mass unit in multiples of Msun.

Lunit

Base length unit in multiples of parsecs.

Vunit

Base velocity unit in multiples of m/s.

Type

Specify the 'halo' or 'gas' temperature to be computed.

Tunit

Specify the output temperature to be Kelvin ('K'), 'eV' or 'keV'.

Dim

The dimensional type for the halo (either the 2 or 3). 3 (default) means quantities are intrinsic 3D values. 2 means quantities are for projected systems (i.e. radius and velocity dispersion are compressed). From comparisons to simulations (so NFW, c~5 halos) Rvir[proj]=Rvir[3D]/1.37 and Sigma[proj]=Sigma[3D]/sqrt(3). The former has dependence on the halo profile (so is approximate), whereas the latter is a dimensionality argument that should hold for any virialised system. Note that for projected systems Sigma is measured along one dimension: the line-of-site.

ref

The name of a reference cosmology to use, one of 137 / 737 / Planck / Planck13 / Planck15 / Planck18 / WMAP / WMAP9 / WMAP7 / WMAP5 / WMAP3 / WMAP1 / Millennium / GiggleZ. Planck = Planck18 and WMAP = WMAP9. The usage is case insensitive, so wmap9 is an allowed input. See cosref for details. This overrides any other settings for H0/ OmegaM and OmegaL.

Details

These functions allow for various analytic conversions between the 3 major properties related to virial radius: the mass, velocity dispresion and size. The default properties calculate properties for 1e12 Msun halos and assume masses in Msun, velocities in km/s and distances in Kpc.

Value

coshaloMvirToSigma

Outputs approximate velocity dispersion (in units of Vunit) given mass (this is exactly the escape velocity at Rvir).

coshaloSigmaToMvir

Outputs mass (in units of Munit) given velocity dispersion.

coshaloMvirToRvir

Outputs radius (in units of Lunit) given mass.

coshaloRvirToMvir

Outputs mass (in units of Munit) given radius.

coshaloSigmaToRvir

Outputs radius (in units of Lunit) given velocity dispersion.

coshaloRvirToSigma

Outputs approximate velocity dispersion (in units of Vunit) given radius (this is exactly the escape velocity at Rvir).

coshaloSigmaToTvir

Output temperture (in units of Tunit) given velocity dispersion. Based on Eqns. 3/7/8/9 of Bryan & Norman (1998).

Author(s)

Aaron Robotham, Chris Power

References

coshaloSigmaToTvir based on the equations in:

Bryan & Norman, 1998, ApJ, 495, 80

See Also

cosvol, cosmap, cosdist, cosgrow, cosNFW

Examples

coshaloMvirToSigma(1e13) # Velocity in km/s
coshaloMvirToSigma(1e13, Vunit=1) # Velocity in m/s
coshaloSigmaToMvir(coshaloMvirToSigma(1e13, Vunit=1),Vunit=1)
coshaloMvirToRvir(1e13) #Radius in kpc
coshaloSigmaToRvir(coshaloMvirToSigma(1e13, Vunit=1),Vunit=1)

#Some sanity checks

rho_crit200=cosgrowRhoCrit(z=0)*200 #200 times rho critical at z=0
rho_mean200=cosgrowRhoMean(z=0)*200 #200 times rho mean at z=0
#For a 10^12 Msun/h halo, the radius in Mpc/h where the contained density equals rho_crit*200
rad_crit200=(1e12/rho_crit200*3/4/pi)^(1/3)
coshaloMvirToRvir(1e12,Lunit=1e6)-rad_crit200 # ~0 as expected
#For a 10^12 Msun/h halo, the radius in Mpc/h where the contained density equals rho_crit*200
rad_mean200=(1e12/rho_mean200*3/4/pi)^(1/3) # ~0 as expected
coshaloMvirToRvir(1e12,Lunit=1e6,Rho='mean')-rad_mean200