cleaning and implementing Halos.jl

.github/workflows/CI.yml

@@ -23,7 +23,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.5'
+          - '1.8'
           - '1.9'
           - 'nightly'
         os:

src/Background.jl

@@ -104,8 +104,8 @@ function FLRW(h::Real, Ω_χ0::Real, Ω_b0::Real, Ω_k0::Real=0; T0_CMB_K::Real
         z_eq_mr = EdS ? NaN : exp(Roots.find_zero( y -> Ω_r(exp(y), Ω_m0, Ω_r0, Ω_Λ0, Ω_k0) - Ω_m(exp(y), Ω_m0, Ω_r0, Ω_Λ0, Ω_k0), (-10, 10), Roots.Bisection())) 
         z_eq_Λm = exp(Roots.find_zero( y -> Ω_Λ(exp(y), Ω_m0, Ω_r0, Ω_Λ0, Ω_k0) - Ω_m(exp(y), Ω_m0, Ω_r0, Ω_Λ0, Ω_k0), (-10, 10), Roots.Bisection())) 
     catch e
-        println("Impossible to definez z_eq_mr and/or z_eq_Λm for this cosmology")
-        println("Error: ", e)
+        Throw(e("Impossible to definez z_eq_mr and/or z_eq_Λm for this cosmology"))
+
     end
 
     k_eq_mr =  EdS ? NaN : Ω_r0 / Ω_m0 * (100. * h * sqrt(Ω_m0 * (1+z_eq_mr)^3 + Ω_r0 * (1+z_eq_mr)^4 + Ω_Λ0 + Ω_k0 * (1+z_eq_mr)^2) * KM_TO_MPC / C_LIGHT) 

src/CosmoTools.jl

@@ -2,6 +2,10 @@ module CosmoTools
 
 import QuadGK, Roots
 
+include("Background.jl")
+include("TransferFunction.jl")
+include("PowerSpectrum.jl")
 include("MassFunction.jl")
+include("Halos.jl")
 
 end

src/Halos.jl

@@ -0,0 +1,195 @@
+##################################################################################
+# This file is part of CosmoTools.
+#
+# Copyright (c) 2023, Gaétan Facchinetti
+#
+# Cosmojuly is free software: you can redistribute it and/or modify it 
+# under the terms of the GNU General Public License as published by 
+# the Free Software Foundation, either version 3 of the License, or any 
+# later version. 21cmCAST is distributed in the hope that it will be useful, 
+# but WITHOUT ANY WARRANTY; without even the implied warranty of 
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 
+# See the GNU General Public License for more details.
+#
+# You should have received a copy of the GNU 
+# General Public License along with 21cmCAST. 
+# If not, see <https://www.gnu.org/licenses/>.
+#
+##################################################################################
+
+
+export Halo, nfwProfile, αβγProfile, HaloProfile, coreProfile, plummerProfile
+export halo_from_ρs_and_rs, halo_from_mΔ_and_cΔ
+export mΔ_from_ρs_and_rs, mΔ, rΔ_from_ρs_and_rs, rΔ, ρ_halo, μ_halo, m_halo
+export velocity_dispersion, gravitational_potential, escape_velocity
+
+abstract type HaloProfile{T<:Real} end
+
+################################################
+# Dimensionless Halo
+
+struct αβγProfile{T<:Real} <: HaloProfile{T}
+    α::T
+    β::T
+    γ::T
+end
+
+# definition of length and iterator on our struct
+# allows to use f.(x, y) where y is of type HaloProfile
+Base.length(::HaloProfile) = 1
+Base.iterate(iter::HaloProfile) = (iter, nothing)
+Base.iterate(::HaloProfile, state::Nothing) = nothing
+
+# constructor method of αβγProfile
+αβγProfile(α::Real, β::Real, γ::Real) = αβγProfile(promote(α, β, γ)...)
+
+## definition of densities and mass profiles
+const nfwProfile::αβγProfile = αβγProfile(1, 3, 1)
+const coreProfile::αβγProfile = αβγProfile(1, 3, 0)
+const plummerProfile::αβγProfile = αβγProfile(2, 5, 0)
+
+# Density profile and mass
+ρ_halo(x::Real, p::αβγProfile = nfwProfile) = x^(-p.γ) * (1+x^p.α)^(-(p.β - p.γ)/p.α)
+μ_halo(x::Real, p::αβγProfile = nfwProfile) = HypergeometricFunctions._₂F₁((3 - p.γ)/p.α, (p.β - p.γ)/p.α, (3 + p.α - p.γ)/p.α, -x^p.α) * x^(3-p.γ) / (3-p.γ)
+
+function gravitational_potential(x::Real, xt::Real, p::αβγProfile = nfwProfile) 
+    (p == nfwProfile) && return (log(1+x)/x -log(1+xt)/xt)
+    return - quadgk(xp -> μ_halo(xp, p) / xp^2, x, xt, rtol=1e-3)[1] 
+end
+
+# s- and p-wave luminosity of the halo
+λ0_halo(x::Real, p::αβγProfile = nfwProfile) = HypergeometricFunctions._₂F₁((3 - 2*p.γ)/p.α, 2*(p.β - p.γ)/p.α, (3 + p.α - 2*p.γ)/p.α, -x^p.α) * x^(3-2*p.γ) / (3-2*p.γ)
+λ1_halo(x::Real, p::αβγProfile = nfwProfile) = 1.0 # TO DO
+
+################################################
+#
+# Dimensionfull Halo
+
+# Whenever possible do all the computation using the dimensionless profile
+# Otherwise unit conversion slightly slow down the code
+
+## Definition of relationships between concentration, mass, scale density and scale radius
+function cΔ_from_ρs(ρs::Real, hp::HaloProfile = nfwProfile, Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0)
+    g(c::Real) = c^3 / μ(c, hp) - 3 * ρs / Δ / ρ_ref
+    Roots.find_zero(g, (1e-10, 1e+10), Bisection()) 
+end
+
+mΔ_from_ρs_and_rs(ρs::Real, rs::Real, hp::HaloProfile = nfwProfile, Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0) = 4 * pi * ρs * rs^3 * μ_halo(cΔ_from_ρs(ρs, hp, Δ, ρ_ref), hp)
+ρs_from_cΔ(cΔ::Real, hp::HaloProfile = nfwProfile , Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0) = Δ * ρ_ref  / 3 * cΔ^3 / μ_halo(cΔ, hp) 
+rs_from_cΔ_and_mΔ(cΔ::Real, mΔ::Real, Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0) =  (3 * mΔ / (4 * pi * Δ * ρ_ref))^(1 // 3) / cΔ 
+rΔ_from_ρs_and_rs(ρs::Real, rs::Real, hp::HaloProfile = nfwProfile, Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0) = (3 * mΔ_from_ρs_and_rs(ρs, rs, hp, Δ, ρ_ref) / (4*π*Δ*ρ_ref))^(1//3)
+
+struct Halo{T<:Real}
+    hp::HaloProfile
+    ρs::T
+    rs::T
+end
+
+Base.length(::Halo) = 1
+Base.iterate(iter::Halo) = (iter, nothing)
+Base.iterate(::Halo, state::Nothing) = nothing
+
+
+halo_from_ρs_and_rs(hp::HaloProfile, ρs::Real, rs::Real) = Halo(hp, promote(ρs, rs)...)
+
+function halo_from_mΔ_and_cΔ(hp::HaloProfile, mΔ::Real, cΔ::Real;  Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0)
+    ρs = ρs_from_cΔ(cΔ, hp, Δ, ρ_ref)
+    rs = rs_from_cΔ_and_mΔ(cΔ, mΔ, Δ, ρ_ref)
+    return Halo(hp, promote(ρs, rs)...)
+end
+
+ρ_halo(r::Real, h::Halo{<:Real}) = h.ρs * ρ_halo(r/h.rs, h.hp)
+m_halo(r::Real, h::Halo{<:Real}) = 4.0 * π * h.ρs * h.rs^3 * μ_halo(r/h.rs, h.hp)
+mΔ(h::Halo{<:Real}, Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0) = mΔ_from_ρs_and_rs(h.ρs, h.rs, h.hp, Δ, ρ_ref)
+rΔ(h::Halo{<:Real}, Δ::Real = 200, ρ_ref::Real = planck18_bkg.ρ_c0) = rΔ_from_ρs_and_rs(h.ρs, h.rs, h.hp, Δ, ρ_ref)
+
+ρs(h::Halo) = h.ρs * ρ_0
+rs(h::Halo) = h.rs * r_0
+
+################################################
+# Velocity of the particles inside the halo
+
+""" 1D Jeans velocity dispersion in (Mpc / s) """
+velocity_dispersion(r::Real, rt::Real, h::Halo) = sqrt(G_NEWTON / ρ_halo(r, h) *  quadgk(rp -> ρ_halo(rp, h) * m_halo(rp, h)/rp^2, r, rt, rtol=1e-5)[1])
+
+""" 1D Jeans velocity dispersion in (km / s) """
+velocity_dispersion_kms(r::Real, rt::Real, h::Halo) = velocity_dispersion(r, rt, h) * MPC_TO_KM
+
+""" gravitational potential in (Mpc / s)^2 """
+gravitational_potential(r::Real, rt::Real, h::Halo) = - 4 * π * h.ρs * h.rs^2 * G_NEWTON * gravitational_potential(r/h.rs, rt/h.rs, h.hp) 
+
+""" gravitational potential in (km / s)^2 """
+gravitational_potential_kms(r::Real, rt::Real, h::Halo) = gravitational_potential(r, rt, h) * MPC_TO_KM
+
+""" escape velocity in (Mpc / s) """
+escape_velocity(r::Real, rt::Real, h::Halo) = sqrt(2*abs(gravitational_potential(r, rt, h)))
+
+""" escape velocity in (km / s) """
+escape_velocity_kms(r::Real, rt::Real, h::Halo) = sqrt(2*abs(gravitational_potential_kms(r, rt, h))) * MPC_TO_KM
+
+""" circular velocity in (Mpc / s)"""
+circular_velocity(r::Real, h::Halo) = sqrt(G_NEWTON * m(r, h) / r)
+
+""" circular velocity in (km / s)"""
+circular_velocity_kms(r::Real, h::Halo) = sqrt(G_NEWTON * m(r, h) / r) * MPC_TO_KM
+
+
+
+
+#######################################
+# Relation between concentration and mass
+# Considering relations derived in the litterature
+
+export MassConcentrationModel, SCP12, MDvdB08, median_concentration, PKCBRP12
+
+abstract type MassConcentrationModel end
+abstract type SCP12 <: MassConcentrationModel end
+abstract type MDvdB08 <: MassConcentrationModel end
+abstract type PKCBRP12 <: MassConcentrationModel end
+
+function median_concentration(m200::Real, z::Real, cosmo::Cosmology, ::Type{SCP12})
+
+    (z != 0) && Throw(ArgumentError("The mass-concentration model SCP12 is not defined for z > 0"))
+
+    cn::Vector = [37.5153, -1.5093, 1.636e-2, 3.66e-4, -2.89237e-5, 5.32e-7]
+    m200_min = (m200 > 7.24e-10) ? m200 : 7.24e-10
+
+    return sum(cn .* log(m200_min * cosmo.bkg.h).^(0:5))
+end
+
+
+function median_concentration(m200::Real, z::Real, cosmo::Cosmology, ::Type{MDvdB08})
+
+    # parameters of the model
+    K200 = 3.6
+    F = 0.01
+
+    zc = 10^Roots.find_zero(logz -> σ_mps_M(F * m200, TopHatWindow, cosmology = cosmo) * growth_factor_Carroll(10^(logz), cosmo.bkg) / growth_factor_Carroll(0.0, cosmo.bkg) - 1.686, (-6, 10), Roots.Bisection())
+    return K200 * (ρ_critical(zc, cosmo.bkg)/ ρ_critical(z, cosmo.bkg))^(1/3)
+end
+
+
+function median_concentration(m200::Real, z::Real, cosmo::Cosmology, ::Type{PKCBRP12})
+
+    x = (cosmo.bkg.Ω_Λ0 / cosmo.bkg.Ω_m0)^(1/3)/(1+z)
+
+    func_C(sigp::Real) = 2.881*( (sigp/1.257)^1.022 +1  )*exp(0.060/sigp^2)
+    func_cmin(x::Real) = 3.681 + (5.033 - 3.681)*(atan(6.948 * (x - 0.424))/π + 0.5)
+    func_sigm1min(x::Real) = 1.047 + (1.646 - 1.047)*(atan(7.386 * (x - 0.526))/π + 0.5)
+
+    func_B0(x::Real) = func_cmin(x)/func_cmin(1.393)
+    func_B1(x::Real) = func_sigm1min(x) / func_sigm1min(1.393)
+
+    norm_D = growth_factor_Carroll(z, cosmo.bkg) /  growth_factor_Carroll(0, cosmo.bkg) 
+    sigp   = func_B1(x) * σ_mps_M(m200, TopHatWindow, cosmology = cosmo) * norm_D
+
+
+    return func_B0(x) * func_C(sigp)
+end
+
+
+median_concentration(m200::Real, ::Type{T} = SCP12; z::Real = 0, cosmo::Cosmology=planck18) where {T <: MassConcentrationModel} = median_concentration(m200, z, cosmo, T)
+
+#######################################
+
+

src/MassFunction.jl

@@ -1,6 +1,4 @@
 
-include("PowerSpectrum.jl")
-
 export dn_dM, MassFunctionType, PressSchechter, SethTormen
 
 

src/PowerSpectrum.jl

@@ -1,6 +1,3 @@
-
-include("TransferFunction.jl")
-
 export Cosmology, planck18, curvature_power_spectrum, matter_power_spectrum, power_spectrum_ΛCDM
 export window_function, Window, TopHatWindow, SharpKWindow, GaussianWindow, radius_from_mass, mass_from_radius, dradius_dmass
 export σ2_mps, dσ2_mps_dR, σ_mps, dσ_mps_dR, σ2_mps_M, dσ2_mps_dM, σ_mps_M, dσ_mps_dM

src/TransferFunction.jl

@@ -8,7 +8,7 @@
 #
 ########################################################
 
-include("Background.jl")
+
 
 export transfer_function, TrivialTF, EH98, TransferFunctionModel, EH98_planck18