From d16b2b06442c875c4e612516d7f02c5ccf343b72 Mon Sep 17 00:00:00 2001 From: Aaron LI Date: Mon, 25 Feb 2019 00:01:51 +0800 Subject: Add utils/virial module Implement the M500 to M200 conversion. --- fg21sim/utils/virial.py | 71 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 fg21sim/utils/virial.py diff --git a/fg21sim/utils/virial.py b/fg21sim/utils/virial.py new file mode 100644 index 0000000..2e81ab4 --- /dev/null +++ b/fg21sim/utils/virial.py @@ -0,0 +1,71 @@ +# Copyright (c) 2019 Weitian LI +# 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) -- cgit v1.2.2