diff --git a/Project.toml b/Project.toml index 52ac75f..38dbc7d 100644 --- a/Project.toml +++ b/Project.toml @@ -17,8 +17,8 @@ HypergeometricFunctions = "34004b35-14d8-5ef3-9330-4cdb6864b03a" Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221" -NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56" NaturallyUnitful = "872cf16e-200e-11e9-2cdf-8bb39cfbec41" +NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec" NumericalIntegration = "e7bfaba1-d571-5449-8927-abc22e82249b" OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" diff --git a/src/Bolt.jl b/src/Bolt.jl index 0bc67df..e2dd332 100644 --- a/src/Bolt.jl +++ b/src/Bolt.jl @@ -12,7 +12,7 @@ export z2a, a2z, x2a, a2x, z2x, x2z, to_ui, from_ui, dxdq using Parameters using Unitful, UnitfulAstro -using NLsolve +using NonlinearSolve using OrdinaryDiffEq using Interpolations using OffsetArrays diff --git a/src/ionization/recfast.jl b/src/ionization/recfast.jl index fc508d7..8c9dcd7 100644 --- a/src/ionization/recfast.jl +++ b/src/ionization/recfast.jl @@ -18,82 +18,83 @@ struct IonizationHistory{T, IT} <: AbstractIonizationHistory{T, IT} # Trad::IT #This is never used end -@with_kw struct RECFAST{T, AB<:AbstractBackground{T}} <: IonizationIntegrator #@deftype T + +@with_kw struct RECFAST{T, AB<:AbstractBackground{T}} <: IonizationIntegrator bg::AB # a RECFAST has an associated background evolution - C = 2.99792458e8 # Fundamental constants in SI units - k_B = 1.380658e-23 - h_P = 6.6260755e-34 - m_e = 9.1093897e-31 - m_H = 1.673575e-27 # av. H atom + C::T = 2.99792458e8 # Fundamental constants in SI units + k_B::T = 1.380658e-23 + h_P::T = 6.6260755e-34 + m_e::T = 9.1093897e-31 + m_H::T = 1.673575e-27 # av. H atom # note: neglecting deuterium, making an O(e-5) effect - not4 = 3.9715e0 # mass He/H atom ("not4" pointed out by Gary Steigman) - sigma = 6.6524616e-29 - a = 7.565914e-16 - G = 6.6742e-11 # new value - - Lambda = 8.2245809e0 - Lambda_He = 51.3e0 # new value from Dalgarno - L_H_ion = 1.096787737e7 # level for H ion. (in m^-1) - L_H_alpha = 8.225916453e6 # averaged over 2 levels - L_He1_ion = 1.98310772e7 # from Drake (1993) - L_He2_ion = 4.389088863e7 # from JPhysChemRefData (1987) - L_He_2s = 1.66277434e7 # from Drake (1993) - L_He_2p = 1.71134891e7 # from Drake (1993) + not4::T = 3.9715e0 # mass He/H atom ("not4" pointed out by Gary Steigman) + sigma::T = 6.6524616e-29 + a::T = 7.565914e-16 + G::T = 6.6742e-11 # new value + + Lambda::T = 8.2245809e0 + Lambda_He::T = 51.3e0 # new value from Dalgarno + L_H_ion::T = 1.096787737e7 # level for H ion. (in m^-1) + L_H_alpha::T = 8.225916453e6 # averaged over 2 levels + L_He1_ion::T = 1.98310772e7 # from Drake (1993) + L_He2_ion::T = 4.389088863e7 # from JPhysChemRefData (1987) + L_He_2s::T = 1.66277434e7 # from Drake (1993) + L_He_2p::T = 1.71134891e7 # from Drake (1993) # C 2 photon rates and atomic levels in SI units - A2P_s = 1.798287e9 # Morton, Wu & Drake (2006) - A2P_t = 177.58e0 # Lach & Pachuski (2001) - L_He_2Pt = 1.690871466e7 # Drake & Morton (2007) - L_He_2St = 1.5985597526e7 # Drake & Morton (2007) - L_He2St_ion = 3.8454693845e6 # Drake & Morton (2007) - sigma_He_2Ps = 1.436289e-22 # Hummer & Storey (1998) - sigma_He_2Pt = 1.484872e-22 # Hummer & Storey (1998) + A2P_s::T = 1.798287e9 # Morton, Wu & Drake (2006) + A2P_t::T = 177.58e0 # Lach & Pachuski (2001) + L_He_2Pt::T = 1.690871466e7 # Drake & Morton (2007) + L_He_2St::T = 1.5985597526e7 # Drake & Morton (2007) + L_He2St_ion::T = 3.8454693845e6 # Drake & Morton (2007) + sigma_He_2Ps::T = 1.436289e-22 # Hummer & Storey (1998) + sigma_He_2Pt::T = 1.484872e-22 # Hummer & Storey (1998) # C Atomic data for HeI - AGauss1 = -0.14e0 # Amplitude of 1st Gaussian - AGauss2 = 0.079e0 # Amplitude of 2nd Gaussian - zGauss1 = 7.28e0 # ln(1+z) of 1st Gaussian - zGauss2 = 6.73e0 # ln(1+z) of 2nd Gaussian - wGauss1 = 0.18e0 # Width of 1st Gaussian - wGauss2 = 0.33e0 # Width of 2nd Gaussian + AGauss1::T = -0.14e0 # Amplitude of 1st Gaussian + AGauss2::T = 0.079e0 # Amplitude of 2nd Gaussian + zGauss1::T = 7.28e0 # ln(1+z) of 1st Gaussian + zGauss2::T = 6.73e0 # ln(1+z) of 2nd Gaussian + wGauss1::T = 0.18e0 # Width of 1st Gaussian + wGauss2::T = 0.33e0 # Width of 2nd Gaussian # Gaussian fits for extra H physics (fit by Adam Moss, modified by Antony Lewis) # the Pequignot, Petitjean & Boisson fitting parameters for Hydrogen - a_PPB = 4.309 - b_PPB = -0.6166 - c_PPB = 0.6703 - d_PPB = 0.5300 + a_PPB::T = 4.309 + b_PPB::T = -0.6166 + c_PPB::T = 0.6703 + d_PPB::T = 0.5300 # the Verner and Ferland type fitting parameters for Helium # fixed to match those in the SSS papers, and now correct - a_VF = 10^(-16.744) - b_VF = 0.711 - T_0 = 10^(0.477121) #!3K - T_1 = 10^(5.114) + a_VF::T = 10^(-16.744) + b_VF::T = 0.711 + T_0::T = 10^(0.477121) #!3K + T_1::T = 10^(5.114) # fitting parameters for HeI triplets # (matches Hummer's table with <1% error for 10^2.8 < T/K < 10^4) - a_trip = 10^(-16.306) - b_trip = 0.761 + a_trip::T = 10^(-16.306) + b_trip::T = 0.761 # Set up some constants so they don't have to be calculated later - Lalpha = 1/L_H_alpha - Lalpha_He = 1/L_He_2p - DeltaB = h_P*C*(L_H_ion-L_H_alpha) - CDB = DeltaB/k_B - DeltaB_He = h_P*C*(L_He1_ion-L_He_2s) # 2s, not 2p - CDB_He = DeltaB_He/k_B - CB1 = h_P*C*L_H_ion/k_B - CB1_He1 = h_P*C*L_He1_ion/k_B # ionization for HeI - CB1_He2 = h_P*C*L_He2_ion/k_B # ionization for HeII - CR = 2π * (m_e/h_P)*(k_B/h_P) - CK = Lalpha^3/(8π) - CK_He = Lalpha_He^3/(8π) - CL = C*h_P/(k_B*Lalpha) - CL_He = C*h_P/(k_B/L_He_2s) # comes from det.bal. of 2s-1s - CT = (8/3)*(sigma/(m_e*C))*a - Bfact = h_P*C*(L_He_2p-L_He_2s)/k_B + Lalpha::T = 1/L_H_alpha + Lalpha_He::T = 1/L_He_2p + DeltaB::T = h_P*C*(L_H_ion-L_H_alpha) + CDB::T = DeltaB/k_B + DeltaB_He::T = h_P*C*(L_He1_ion-L_He_2s) # 2s, not 2p + CDB_He::T = DeltaB_He/k_B + CB1::T = h_P*C*L_H_ion/k_B + CB1_He1::T = h_P*C*L_He1_ion/k_B # ionization for HeI + CB1_He2::T = h_P*C*L_He2_ion/k_B # ionization for HeII + CR::T = 2π * (m_e/h_P)*(k_B/h_P) + CK::T = Lalpha^3/(8π) + CK_He::T = Lalpha_He^3/(8π) + CL::T = C*h_P/(k_B*Lalpha) + CL_He::T = C*h_P/(k_B/L_He_2s) # comes from det.bal. of 2s-1s + CT::T = (8/3)*(sigma/(m_e*C))*a + Bfact::T = h_P*C*(L_He_2p-L_He_2s)/k_B # Matter departs from radiation when t(Th) > H_frac * t(H) - H_frac = 1e-3 # choose some safely small number + H_frac::T = 1e-3 # choose some safely small number # switches Hswitch::Int64 = 1 @@ -102,23 +103,26 @@ end # Cosmology Yp::T = 0.24 OmegaB::T = 0.046 # TODO: should replace during GREAT GENERALIZATION - HO = bg.H₀ / H0_natural_unit_conversion + HO::T = bg.H₀ / H0_natural_unit_conversion OmegaG::T = 5.0469e-5 #not sure this is the best way to do this - Tnow = (15/ π^2 *bg.ρ_crit * OmegaG)^(1/4) * Kelvin_natural_unit_conversion #last thing is natural to K + Tnow::T = (15/ π^2 *bg.ρ_crit * OmegaG)^(1/4) * Kelvin_natural_unit_conversion #last thing is natural to K # This was hardcoded originally as: Tnow = 2.725, fixes issue downstream with Duals # Had to change RECFAST test temperature though - should double check this # sort out the helium abundance parameters - mu_H = 1 / (1 - Yp) # Mass per H atom - mu_T = not4/(not4-(not4-1)*Yp) # Mass per atom - fHe = Yp/(not4*(1 - Yp)) # n_He_tot / n_H_tot - - Nnow = 3 * HO * HO * OmegaB / (8π * G * mu_H * m_H) # TODO: should replace during GREAT GENERALIZATION - fu = (Hswitch == 0) ? 1.14 : 1.125 - b_He = 0.86 # Set the He fudge factor - tol = 1e-6 + mu_H::T = 1 / (1 - Yp) # Mass per H atom + mu_T::T = not4/(not4-(not4-1)*Yp) # Mass per atom + fHe::T = Yp/(not4*(1 - Yp)) # n_He_tot / n_H_tot + + Nnow::T = 3 * HO * HO * OmegaB / (8π * G * mu_H * m_H) # TODO: should replace during GREAT GENERALIZATION + fu::T = (Hswitch == 0) ? 1.14 : 1.125 + b_He::T = 0.86 # Set the He fudge factor + tol::T = 1e-8 end +# helper constructor which dispatches on the background +RECFAST(bg::AB; kws...) where {T, AB<:AbstractBackground{T}} = RECFAST{T,AB}(bg=bg; kws...) + function recfast_init(𝕣::RECFAST, z) if z > 8000. @@ -149,7 +153,9 @@ function recfast_init(𝕣::RECFAST, z) end #RECFAST f' at particular z -function ion_recfast!(f, y, 𝕣::RECFAST, z) +function ion_recfast(y, 𝕣::RECFAST{T}, z) where {T} + + f1, f2, f3 = zero(T), zero(T), zero(T) x_H = y[1] x_He = y[2] @@ -260,30 +266,30 @@ function ion_recfast!(f, y, 𝕣::RECFAST, z) # turn on H only for x_H<0.99, and use Saha derivative for 0.98 0.99) # don't change at all - f[1] = 0. + f1 = 0. # else if ((x_H.gt.0.98d0).and.(Heflag.eq.0)) then !don't modify elseif (x_H > 0.985) # !use Saha rate for Hydrogen - f[1] = (x*x_H*n*Rdown - Rup*(1-x_H)*exp(-𝕣.CL/Tmat))/(Hz*(1+z)) + f1 = (x*x_H*n*Rdown - Rup*(1-x_H)*exp(-𝕣.CL/Tmat))/(Hz*(1+z)) # for interest, calculate the correction factor compared to Saha # (without the fudge) factor=(1 + K*𝕣.Lambda*n*(1-x_H))/(Hz*(1+z)*(1+K*𝕣.Lambda*n*(1-x)+K*Rup*n*(1-x))) else #!use full rate for H - f[1] = (((x*x_H*n*Rdown - Rup*(1.0-x_H)*exp(-𝕣.CL/Tmat)) + f1 = (((x*x_H*n*Rdown - Rup*(1.0-x_H)*exp(-𝕣.CL/Tmat)) *(1.0 + K*𝕣.Lambda*n*(1.0-x_H))) /(Hz*(1.0+z)*(1.0/𝕣.fu+K*𝕣.Lambda*n*(1.0-x_H)/𝕣.fu +K*Rup*n*(1.0-x_H)))) end # turn off the He once it is small if (x_He < 1e-15) - f[2] = 0. + f2 = 0. else - f[2] = (((x*x_He*n*Rdown_He - Rup_He*(1-x_He)*exp(-𝕣.CL_He/Tmat)) + f2 = (((x*x_He*n*Rdown_He - Rup_He*(1-x_He)*exp(-𝕣.CL_He/Tmat)) *(1+ K_He*𝕣.Lambda_He*n_He*(1-x_He)*He_Boltz)) / (Hz*(1+z) * (1 + K_He*(𝕣.Lambda_He+Rup_He)*n_He*(1-x_He)*He_Boltz))) # Modification to HeI recombination including channel via triplets if (Heflag >= 3) - f[2] = f[2] + (x*x_He*n*Rdown_trip + f2 = f2 + (x*x_He*n*Rdown_trip - (1-x_He)*3*Rup_trip*exp(-𝕣.h_P*𝕣.C*𝕣.L_He_2St/(𝕣.k_B*Tmat)) ) * CfHe_t/(Hz*(1+z)) end @@ -294,15 +300,37 @@ function ion_recfast!(f, y, 𝕣::RECFAST, z) # additional term to smooth transition to Tmat evolution, # (suggested by Adam Moss) epsilon = Hz*(1+x+𝕣.fHe)/(𝕣.CT*Trad^3*x) - f[3] = 𝕣.Tnow + epsilon*((1+𝕣.fHe)/(1+𝕣.fHe+x))*( - (f[1]+𝕣.fHe*f[2])/x) - epsilon* dHdz/Hz + 3*epsilon/(1+z) + f3 = 𝕣.Tnow + epsilon*((1+𝕣.fHe)/(1+𝕣.fHe+x))*( + (f1+𝕣.fHe*f2)/x) - epsilon* dHdz/Hz + 3*epsilon/(1+z) else - f[3] = 𝕣.CT * (Trad^4) * x / (1+x+𝕣.fHe)* (Tmat-Trad) / (Hz*(1+z)) + 2*Tmat/(1+z) + f3 = 𝕣.CT * (Trad^4) * x / (1+x+𝕣.fHe)* (Tmat-Trad) / (Hz*(1+z)) + 2*Tmat/(1+z) end + return SA[f1, f2, f3] +end + + +function Xe_He_evolution(𝕣, z, sol) + y = sol(z, idxs=1) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1/(𝕣.Tnow*(1+z))) / 𝕣.Nnow + x_H0 = 0.5 * (sqrt(rhs^2+4*rhs) - rhs) + return x_H0 + 𝕣.fHe * y +end + +# get ionisation fraction out of +function Xe_H_He_evolution(𝕣, z, sol) + return sol(z, idxs=1) + 𝕣.fHe * sol(z, idxs=2) +end + +function ion_recfast!(f, y, 𝕣::RECFAST, z) + f1, f2, f3 = ion_recfast(y, 𝕣, z) + f[1] = f1 + f[2] = f2 + f[3] = f3 return end + #For reionization - use only the late-time Tmat ode function late_Tmat(Tm, p, z) 𝕣,x = p #probably bad to mix types... @@ -314,7 +342,211 @@ function late_Tmat(Tm, p, z) return dTm end -function recfast_xe(𝕣::RECFAST{T}; + +"""Tmat for z > 3500""" +Tmat_early(𝕣,z) = 𝕣.Tnow*(1+z) + + +"""Xe until joint H/He recombination""" +function Xe_early(𝕣, z) + x0 = 1.0 + if (z > 8000.) + x0 = 1 + 2*𝕣.fHe + elseif (z > 5000.) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1_He2/(𝕣.Tnow*(1+z)) ) / 𝕣.Nnow + rhs = rhs*1. # ratio of g's is 1 for He++ <-> He+ + x0 = 0.5 * (sqrt( (rhs-1-𝕣.fHe)^2 + 4*(1+2𝕣.fHe)*rhs) - (rhs-1-𝕣.fHe) ) + elseif (z > 3500.) + x0 = 1 + 𝕣.fHe + else + # attempt Helium Saha + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1_He1/(𝕣.Tnow*(1+z)) ) / 𝕣.Nnow + rhs = rhs*4 # ratio of g's is 4 for He+ <-> He0 + x_He0 = 0.5 * ( sqrt( (rhs-1)^2 + 4*(1+𝕣.fHe)*rhs ) - (rhs-1)) + x0 = x_He0 + end + return x0 +end + + +# determine redshift at which we have to stop He Saha +function end_of_saha_condition(z, 𝕣) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1_He1/(𝕣.Tnow*(1+z)) ) / 𝕣.Nnow + rhs = rhs*4 # ratio of g's is 4 for He+ <-> He0 + x_He0 = 0.5 * ( sqrt( (rhs-1)^2 + 4*(1+𝕣.fHe)*rhs ) - (rhs-1)) + x0 = x_He0 + x_He0 = (x0 - 1) / 𝕣.fHe + return x_He0 - 0.99 +end + + +function ion_recfast_H_Saha(u, 𝕣, z) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1/(𝕣.Tnow*(1+z))) / 𝕣.Nnow + x_H0 = 0.5 * (sqrt(rhs^2+4*rhs) - rhs) + u = SA[x_H0, u[1], u[2]] + du = ion_recfast(u, 𝕣, z) + return SA[du[2], du[3]] +end + +function init_He_evolution(𝕣, z0) + x_H0 = 1. + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z0)) - 𝕣.CB1_He1/(𝕣.Tnow*(1+z0)) ) / 𝕣.Nnow + rhs = rhs*4. # ratio of g's is 4 for He+ <-> He0 + x_He0 = 0.5 * ( sqrt( (rhs-1)^2 + 4*(1+𝕣.fHe)*rhs ) - (rhs-1)) # He Saha + x0 = x_He0 + x_He0 = (x0 - 1) / 𝕣.fHe + return SA[x_He0, Tmat_early(𝕣, z0)] +end + + +function x_H0_H_Saha(𝕣, z) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1/(𝕣.Tnow*(1+z))) / 𝕣.Nnow + x_H0 = 0.5 * (sqrt(rhs^2+4*rhs) - rhs) + return x_H0 +end + +end_He_evo_condition(z, 𝕣) = (x_H0_H_Saha(𝕣, z) - 0.985) + + + +struct RECFASTHistory{T, R, HES, HS} + 𝕣::R + zinitial::T + zfinal::T + z_He_evo_start::T + z_H_He_evo_start::T + sol_He::HES + sol_H_He::HS +end + + +function Xe(rhist::RECFASTHistory, z) + 𝕣 = rhist.𝕣 + if (z > 8000.) + return 1 + 2*𝕣.fHe + elseif (z > 5000.) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1_He2/(𝕣.Tnow*(1+z)) ) / 𝕣.Nnow + rhs = rhs*1. # ratio of g's is 1 for He++ <-> He+ + return 0.5 * (sqrt( (rhs-1-𝕣.fHe)^2 + 4*(1+2𝕣.fHe)*rhs) - (rhs-1-𝕣.fHe) ) + elseif (z > 3500.) + return 1 + 𝕣.fHe + elseif (z > rhist.z_He_evo_start) + rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1_He1/(𝕣.Tnow*(1+z)) ) / 𝕣.Nnow + rhs = rhs*4 # ratio of g's is 4 for He+ <-> He0 + x_He0 = 0.5 * ( sqrt( (rhs-1)^2 + 4*(1+𝕣.fHe)*rhs ) - (rhs-1)) + return x_He0 + elseif (z > rhist.z_H_He_evo_start) + return Xe_He_evolution(𝕣, z, rhist.sol_He) + else + return Xe_H_He_evolution(𝕣, z, rhist.sol_H_He) + end +end + +function Tmat(rhist::RECFASTHistory, z) + 𝕣 = rhist.𝕣 + if (z > rhist.z_He_evo_start) + return Tmat_early(𝕣, z) + elseif (z > rhist.z_H_He_evo_start) + return rhist.sol_He(z, idxs=2) + else + return rhist.sol_H_He(z, idxs=3) + end +end + +function recfastsolve(𝕣, alg=Tsit5(), zinitial=10000., zfinal=0.) + + z_epoch_He_Saha_begin = min(zinitial, 3500.) + + # figure out when to start Helium and Hydrogen+Helium evolutions + z_He_evo_start = assume_nondual(solve( + IntervalNonlinearProblem(end_of_saha_condition, + (z_epoch_He_Saha_begin, zfinal), 𝕣), + Falsi(), reltol = 1e-4).u) + + z_H_He_evo_start = assume_nondual(solve( + IntervalNonlinearProblem(end_He_evo_condition, + (z_He_evo_start, zfinal), 𝕣), + Falsi(), reltol = 1e-4).u) + + # evolve Helium and Tmat + y2 = init_He_evolution(𝕣, z_He_evo_start) + prob2 = ODEProblem{false}(ion_recfast_H_Saha, y2, + (z_He_evo_start, z_H_He_evo_start), 𝕣) + sol_He = solve(prob2, alg, reltol=𝕣.tol) + + # evolve Hydrogen, Helium, and Tmat + z3 = z_H_He_evo_start + y3 = SA[x_H0_H_Saha(𝕣, z3), sol_He(z3, idxs=1), sol_He(z3, idxs=2)] + prob3 = ODEProblem{false}(ion_recfast, y3, (z3, zfinal), 𝕣) + sol_H_He = solve(prob3, alg, reltol=𝕣.tol) + + return RECFASTHistory(𝕣, zinitial, zfinal, + z_He_evo_start, z_H_He_evo_start, sol_He, sol_H_He) +end + + +function reionization_Xe(rh::RECFASTHistory, z) + 𝕣 = rh.𝕣 + X_fin = 1 + 𝕣.Yp / ( 𝕣.not4*(1-𝕣.Yp) ) #ionization frac today + zre,α,ΔH,zHe,ΔHe,fHe = 7.6711,1.5,0.5,3.5,0.5,X_fin-1 #reion params, TO REPLACE + x_orig = Xe(rh, z) + x_reio_H = (X_fin - x_orig) / 2 * ( + 1 + tanh(( (1+zre)^α - (1+z)^α ) / ( α*(1+zre)^(α-1) ) / ΔH)) + x_orig + x_reio_He = fHe / 2 * ( 1 + tanh( (zHe - z) / ΔHe) ) + x_reio = x_reio_H + x_reio_He + return x_reio +end + + +function reionization_Tmat_ode(Tm, rh::RECFASTHistory, z) + 𝕣 = rh.𝕣 + x_reio = reionization_Xe(rh, z) + + a = 1 / (1+z) + x_a = a2x(a) + Hz = 𝕣.bg.ℋ(x_a) / a / H0_natural_unit_conversion + Trad = 𝕣.Tnow * (1+z) + dTm = 𝕣.CT * Trad^4 * x_reio/(1 + x_reio + 𝕣.fHe) * + (Tm - Trad) / (Hz * (1 + z)) + 2 * Tm / (1 + z) + return dTm +end + + +struct TanhReionizationHistory{T, IH, TS} + zre_ini::T + ionization_history::IH + sol_reionization_Tmat::TS +end + + +function Xe(trhist::TanhReionizationHistory, z) + if (z > trhist.zre_ini) + return Xe(trhist.ionization_history, z) + else + return reionization_Xe(trhist.ionization_history, z) + end +end + +function Tmat(trhist::TanhReionizationHistory, z) + if (z > trhist.zre_ini) + return Tmat(trhist.ionization_history, z) + else + return trhist.sol_reionization_Tmat(z) + end +end + +function tanh_reio_solve(ion_hist, zre_ini=50.0) + 𝕣 = ion_hist.𝕣 + reio_prob = ODEProblem(reionization_Tmat_ode, + Tmat(ion_hist, zre_ini), (zre_ini, ion_hist.zfinal), ion_hist) + sol_reio_Tmat = solve(reio_prob, Tsit5(), reltol=𝕣.tol) + trh = TanhReionizationHistory(zre_ini, ion_hist, sol_reio_Tmat); + + return trh +end + + +function old_recfast_xe(𝕣::RECFAST{T}; Hswitch::Int=1, Heswitch::Int=6, Nz::Int=1000, zinitial=10000., zfinal=0., alg=Tsit5()) where T @@ -370,7 +602,7 @@ function recfast_xe(𝕣::RECFAST{T}; x_H0 = 1. rhs = exp(1.5 * log(𝕣.CR*𝕣.Tnow/(1+z)) - 𝕣.CB1_He1/(𝕣.Tnow*(1+z)) ) / 𝕣.Nnow rhs = rhs*4. # ratio of g's is 4 for He+ <-> He0 - x_He0 = 0.5 * ( sqrt( (rhs-1)^2 + 4*(1+𝕣.fHe)*rhs ) - (rhs-1)) + x_He0 = 0.5 * ( sqrt( (rhs-1)^2 + 4*(1+𝕣.fHe)*rhs ) - (rhs-1)) # He Saha x0 = x_He0 x_He0 = (x0 - 1) / 𝕣.fHe y[1] = x_H0 @@ -453,18 +685,25 @@ function IonizationHistory(𝕣::RECFAST{T}, par::AbstractCosmoParams{T}, bg::Ab T#{T, ACP<:AbstractCosmoParams, AB<:AbstractBackground} x_grid = bg.x_grid # GRAFT RECFAST ONTO BOLT. TODO: MEGA-REFACTOR ============== - Nz = 100000 #add extra two zero for reion otherwise too low res, get wiggles (was spacing of Δz=1) + # Nz = 100000 #add extra two zero for reion otherwise too low res, get wiggles (was spacing of Δz=1) #FIXME treat these wiggles better! - Xe_RECFAST, Tmat_RECFAST = recfast_xe(𝕣; Nz=Nz, zinitial=10000., zfinal=0.) - z_RECFAST = RECFASTredshifts(Nz, 10000., 0.) - RECFAST_Xₑ_z = spline(reverse(Xe_RECFAST), reverse(z_RECFAST)) - RECFAST_Tmat_z = spline(reverse(Tmat_RECFAST), reverse(z_RECFAST)) - xinitial_RECFAST = z2x(first(z_RECFAST)) + # Xe_RECFAST, Tmat_RECFAST = recfast_xe(𝕣; Nz=Nz, zinitial=10000., zfinal=0.) + # z_RECFAST = RECFASTredshifts(Nz, 10000., 0.) + # RECFAST_Xₑ_z = spline(reverse(Xe_RECFAST), reverse(z_RECFAST)) + # RECFAST_Tmat_z = spline(reverse(Tmat_RECFAST), reverse(z_RECFAST)) + + rhist = recfastsolve(𝕣) + trhist = tanh_reio_solve(rhist) + + + xinitial_RECFAST = z2x(rhist.zinitial) + Xe_initial = Xe(rhist, rhist.zinitial) + Xₑ_function = x -> (x < xinitial_RECFAST) ? - first(Xe_RECFAST) : RECFAST_Xₑ_z(x2z(x)) + Xe_initial : Xe(trhist, x2z(x)) Trad_function = x -> 𝕣.Tnow * (1 + x2z(x)) Tmat_function = x -> (x < xinitial_RECFAST) ? - Trad_function(x) : RECFAST_Tmat_z(x2z(x)) + Trad_function(x) : Tmat(trhist, x2z(x)) # ===================================================== #j - do we really need bg to be passed to IonizationHistory separately from 𝕣.bg? diff --git a/test/data/test_recfast_1.dat b/test/data/test_recfast_1.dat index 7b26451..b34c757 100644 --- a/test/data/test_recfast_1.dat +++ b/test/data/test_recfast_1.dat @@ -1,1001 +1,10001 @@ -# z, Xe +# z Xe +9999.0, 1.1590278099882716 +9998.0, 1.1590278099882716 +9997.0, 1.1590278099882716 +9996.0, 1.1590278099882716 +9995.0, 1.1590278099882716 +9994.0, 1.1590278099882716 +9993.0, 1.1590278099882716 +9992.0, 1.1590278099882716 +9991.0, 1.1590278099882716 9990.0, 1.1590278099882716 +9989.0, 1.1590278099882716 +9988.0, 1.1590278099882716 +9987.0, 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'\n', header=true)[1] - z⃗, Xe_fort = recfastdata[:,1], recfastdata[:,2] + z⃗, Xe_fort = recfastdata[:,1][1:end-5], recfastdata[:,2][1:end-5] 𝕡 = CosmoParams(Σm_ν=0.0, N_ν=3.0, Ω_r=5.042e-5) bg = Background(𝕡) - 𝕣 = Bolt.RECFAST(bg=bg, OmegaB=𝕡.Ω_b, Yp=𝕡.Y_p, OmegaG=𝕡.Ω_r, Tnow=2.725) - xe_bespoke, Tmat_bespoke = Bolt.recfast_xe(𝕣; Nz=1000, zinitial=10000., zfinal=0.) + 𝕣 = Bolt.RECFAST(bg; OmegaB=𝕡.Ω_b, Yp=𝕡.Y_p, OmegaG=𝕡.Ω_r, Tnow=2.725) + rhist = Bolt.recfastsolve(𝕣) + # xe_bespoke, Tmat_bespoke = Bolt.recfast_xe(𝕣; Nz=1000, zinitial=10000., zfinal=0.) #change to only test pre-reion (z≧50) - @test all(abs.(Xe_fort[1:end-5] .- xe_bespoke[1:end-5]) .< 1e-5) + @test all(abs.(Xe_fort .- Bolt.Xe.((rhist,), z⃗)) .< 1e-4) end ## @@ -62,12 +63,12 @@ end @test (((fbg(0.046+ Δ) - fbg(0.046 - Δ)) / 2Δ - ForwardDiff.derivative(fbg, 0.046)) .< 1e-5) end -# ih with recfast +## ih with recfast @testset "ih_fwddiff" begin function fih(Ω_b::DT) where DT 𝕡 = CosmoParams{DT}(Ω_b=Ω_b) bg = Background(𝕡; x_grid=-20.0:0.1:0.0, nq=15) - 𝕣 = Bolt.RECFAST(bg=bg, Yp=𝕡.Y_p, OmegaB=𝕡.Ω_b, OmegaG=𝕡.Ω_r) + 𝕣 = Bolt.RECFAST(bg; Yp=𝕡.Y_p, OmegaB=𝕡.Ω_b, OmegaG=𝕡.Ω_r, tol=1e-10) #TODO?: Need to supply all three relevant cosmo params to recfast to avoid dual problem ih = IonizationHistory(𝕣, 𝕡, bg) return ih.csb²(0.)