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# Copyright (c) 2019 Weitian LI <wt@liwt.net>
# MIT License
"""
Virial radius/mass utilities.
.. [duffy2008]
Duffy et al. 2008, MNRAS, 390, L64
http://adsabs.harvard.edu/abs/2008MNRAS.390L..64D
.. [ettori2009]
Ettori & Balestra 2009, A&A, 496, 343
http://adsabs.harvard.edu/abs/2009A%26A...496..343
.. [lokas2001]
Łokas & Mamon 2001, MNRAS, 321, 155
http://adsabs.harvard.edu/abs/2001MNRAS.321..155L
"""
import logging
import numpy as np
from ..share import COSMO
logger = logging.getLogger(__name__)
def concentration(mass, z=0):
"""
Calculate the NFW concentration parameter (c = r_vir / r_s) from the
mass-concentration relation: c = A [M/M_pivot]^B (1+z)^C
Reference: [duffy2008],Tab.1
"""
A, B, C = 5.71, -0.084, -0.47 # for M200
M_pivot = 2e12 / COSMO.h # [Msun]
return A * (mass/M_pivot) ** B + (1+z) ** C
def mass_fraction_nfw(s, c):
"""
Calculate the mass fraction (of virial mass) within the scaled radius
``s = r / r_vir``.
Reference: [lokas2001]
Parameters
----------
s : float
The radius scaled by the virial radius, i.e., s = r / r_vir.
c : float
The concentration parameter, i.e., c = r_vir / r_s.
"""
nom = np.log(1 + c*s) - c*s / (1 + c*s)
denom = np.log(1 + c) - c / (1 + c)
return nom / denom
def M200(M500, z=0):
"""
Estimate the M200 from the M500.
"""
# r500 ~= 0.65 r200; Ref.[ettori2009],Sec.2
s = 0.65
# Begin with 'M200 = 1.5*M500'
c = concentration(M500*1.5, z)
mass = M500 / mass_fraction_nfw(s, c)
# Again with the updated mass
c = concentration(mass, z)
return M500 / mass_fraction_nfw(s, c)
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