Commit d9e04a2c by Yannick Roehlly

### Add Meiksin intergalactic transmission code [Denis Burgarella]

parent a0c0d1ee
 # -*- coding: utf-8 -*- # Copyright (C) 2012, 2013 Centre de données Astrophysiques de Marseille # Licensed under the CeCILL-v2 licence - see Licence_CeCILL_V2-en.txt # Authors: Denis Burgarella, Yannick Roehlly import math import numpy as np def ig_transmission_meiksin(wavelength, redshift): """Intergalactic transmission (Meiksin, 2006) Compute the intergalactic transmission as described in Meiksin, 2006. Parameters ---------- wavelength : array like of floats The wavelength(s) in nm. redshift : float The redshift. Returns ------- ig_transmission : numpy array of floats The intergalactic transmission at each input wavelength. """ redshift = float(redshift) wavelength = np.array(wavelength, dtype=float) # For redshift below 2, we assume that there is no IGM attenuation. if redshift <= 2.: ig_tranmission = np.ones(len(wavelength)) return ig_tranmission n_transitions_low = 10 n_transitions_max = 31 gamma = 0.2788 # Gamma(0.5,1) i.e., Gamma(2-beta,1) with beta = 1.5 n0 = 0.25 lambda_limit = 91.2 # Lyman limit in nm lambda_n = np.zeros(n_transitions_low) z_n = np.zeros((n_transitions_low, len(wavelength))) for n in range(2, n_transitions_low): lambda_n[n] = lambda_limit / (1. - 1. / float(n*n)) z_n[n, :] = wavelength / lambda_n[n] - 1. # From Table 1 in Meiksin (2006), only n >=3 are relevant. fact has a # length equal to n_transistions_low. fact = np.array([1., 1., 1., 0.348, 0.179, 0.109, 0.0722, 0.0508, 0.0373, 0.0283]) # First, tau_alpha is the mean Lyman alpha transmitted flux, # Here n = 2 => tau_2 = tau_alpha tau_n = np.zeros((n_transitions_max, len(wavelength))) if redshift <= 4: tau_a = 0.00211 * np.power(1. + redshift, 3.7) tau_n[2, :] = 0.00211 * np.power(1. + z_n[2, :], 3.7) elif redshift >= 4: tau_a = 0.00058 * np.power(1. + redshift, 4.5) tau_n[2, :] = 0.00058 * np.power(1. + z_n[2, :], 4.5) # Then, tau_n is the mean optical depth value for transitions # n = 3 - 9 -> 1 for n in range(3, n_transitions_low): if n <= 5: for l, index in enumerate(wavelength): if z_n[n, l] < 3: tau_n[n, l] = (tau_a * fact[n] * np.power(0.25 * (1. + z_n[n, l]), (1. / 3.))) else: tau_n[n, l] = (tau_a * fact[n] * np.power(0.25 * (1. + z_n[n, l]), (1. / 6.))) elif 5 < n <= 9: for l, index in enumerate(wavelength): tau_n[n, l] = (tau_a * fact[n] * np.power(0.25 * (1. + z_n[n, l]), (1. / 3.))) else: for l, index in enumerate(wavelength): tau_n[n, l] = (tau_n[9, l] * 720. / (float(n) * (float(n*n - 1.)))) for n in range(2, n_transitions_low): for l, index in enumerate(wavelength): if z_n[n, l] >= redshift: tau_n[n, l] = 0. z_l = wavelength / lambda_limit - 1. tau_l_igm = np.zeros(len(wavelength)) for l, index in enumerate(wavelength): if z_l[l] >= redshift: tau_l_igm[l] = 0. else: tau_l_igm[l] = (0.805 * np.power(1. + z_l[l], 3) * (1. / (1. + z_l[l]) - 1. / (1. + redshift))) term1 = gamma - np.exp(-1.) term2 = 0. for n in range(n_transitions_max): term2 = term2 + np.power(-1., n) / (math.factorial(n) * float(2*n - 1)) term3 = ((1.+redshift) * np.power(wavelength/lambda_limit, 1.5) - np.power(wavelength/lambda_limit, 2.5)) term4 = np.zeros(len(wavelength)) for n in range(1, n_transitions_max): term4 = (term4 + (2.*np.power(-1., n) / (math.factorial(n) * float((6*n - 5)*(2*n - 1)))) * (np.power(1.+redshift, 2.5-float(3 * n)) * np.power(wavelength/lambda_limit, 3*n) - np.power(wavelength/lambda_limit, 2.5))) tau_l_lls = np.zeros(len(wavelength)) for l, index in enumerate(wavelength): if z_l[l] >= redshift: tau_l_lls[l] = 0. else: tau_l_lls[l] = n0 * ((term1 - term2) * term3[l] - term4[l]) tau_taun = 0. for n in range(n_transitions_max): tau_taun = tau_taun + tau_n[n, :] weight = np.zeros(len(wavelength)) for l, index in enumerate(wavelength): weight[l] = 0.5*(1.+math.erf(0.01*(wavelength[l]-(1+redshift)*60.))) tau = tau_taun + tau_l_igm + tau_l_lls ig_tranmission = np.exp(- tau) * weight return ig_tranmission
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