GitHub_Leptons_DecayingL_VariableDelta_KlenNishina_EnDepRelease.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "import scipy.integrate as integrate\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rc, rcParams\n",
    "import matplotlib.ticker as mticker\n",
    "from scipy import interpolate\n",
    "from scipy.integrate import odeint\n",
    "from scipy.interpolate import griddata\n",
    "from astropy.io import fits\n",
    "from astropy.modeling import models\n",
    "import pylab\n",
    "import sys\n",
    "import time\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "###############\n",
    "# LaTeX block #\n",
    "###############\n",
    "\n",
    "rc('text', usetex=True)\n",
    "rc('font',**{'family':'serif','serif':['Palatino']})\n",
    "rc('xtick', labelsize=18)\n",
    "rc('ytick', labelsize=18)\n",
    "rcParams['legend.numpoints'] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "##################################\n",
    "# define some universal constant #\n",
    "##################################\n",
    "\n",
    "conv_factor_GeV_to_erg = 0.00160218\n",
    "conv_factor_erg_to_GeV = 624.151\n",
    "conv_factor_yr_to_sec = 31.56 * pow(10,6)\n",
    "conv_factor_sec_to_yr = 1. / conv_factor_yr_to_sec\n",
    "conv_factor_pc_to_m = 3.086*pow(10,16)\n",
    "k_boltzmann = 8.617e-14                 # Boltzmann constant, in [GeV K^(-1)]\n",
    "m_p = .939                              # proton mass in GeV/c^2\n",
    "m_e = 0.000510998918                    # electron mass in GeV/c^2\n",
    "D_0_yr = 0.65 * pow(10,24)/conv_factor_sec_to_yr\n",
    "pi = math.pi\n",
    "c = 2.99 * pow(10,8)                    # speed of light in [m sec^(-1)]\n",
    "b_0_yr = 1.4 * pow(10,-16)/conv_factor_sec_to_yr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of energy points is 200\n"
     ]
    }
   ],
   "source": [
    "##################################################################\n",
    "# define the parameters of the specific object I am considering #\n",
    "##################################################################\n",
    "    \n",
    "considered_objects = 3\n",
    "object_name = ['Sample 1','Sample 2','Sample 3'] \n",
    "\n",
    "\n",
    "gamma_inj = 2.4                        # spectral index of the source term Q\n",
    "alpha_dec = [2., 2., 2.]               # decay index for the luminosity of the source\n",
    "tau_dec = [1.e+5, 1.e+5, 1.e+5]        # timescale for the decay of the source-luminosity, in [yr]\n",
    "r_kpc = [0.35, 0.35, 0.35]             # distance of the source in kiloparsec, to be converted in [m] to match the units of the function J_e(E)\n",
    "N_0 = 1.e+39                           # normalization, to compute the energy budget\n",
    "object_age = [1.5e+5, 2.e+5, 2.5e+5]   # age, in [yr]\n",
    "  \n",
    "\n",
    "r = np.zeros(considered_objects)\n",
    "multiplot_color = ['red','blue','green']\n",
    "\n",
    "\n",
    "# In the following lines I define the energy range of interest and its binning, in [GeV]\n",
    "start = 1.0\n",
    "stop = 100000.0\n",
    "steps = 200    # 1000, to make the low-energy wiggles disappear\n",
    "print (\"The number of energy points is\", steps)\n",
    "\n",
    "E_e = np.logspace(np.log10(start), np.log10(stop), num=steps, endpoint=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>Energy loss rate, with Klein-Nishina correction\n",
    "    \n",
    "$$\n",
    "\\begin{align}\n",
    "& b(E) \\equiv \\frac{dE}{dt} = - \\frac{4}{3} \\sigma_T c \\left[ f^{KN}_{i} U_i + U_B \\right] \\, \\left( \\frac{E}{m_e c^2} \\right)^2 \\\\[10 pt]\n",
    "& f^{KN}_{i} = \\frac{ \\frac{45}{64 \\pi^2} \\left( \\frac{m_e c^2}{k_B T_i} \\right)^2 }{ \\frac{45}{64 \\pi^2} \\left( \\frac{m_e c^2}{k_B T_i} \\right)^2 + \\left( \\frac{E}{m_e c^2} \\right)^2 }\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial condition, in [GeV]: 1.000000e+09\n",
      "min(time_ODE): 1.0 , max(time_ODE): 2499999999.9999995\n",
      "\n",
      "time_ODE: [1.00000000e+00 1.00021642e+00 1.00043289e+00 ... 2.49891825e+09\n",
      " 2.49945906e+09 2.50000000e+09]\n",
      "min(ODE_sol_array): 0.0980180813693678 , max(ODE_sol_array): 1000000000.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/matplotlib/font_manager.py:1241: UserWarning: findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n",
      "/usr/local/lib/python3.7/site-packages/matplotlib/font_manager.py:1241: UserWarning: findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Building the Klein-Nishina loss curve ####\n",
    "\n",
    "\n",
    "### Klein-Nishina factor, from Evoli et al. arXiv:2007.01302 (2020) ###\n",
    "#######################################################################\n",
    "ISRF_components = ['IR', 'OPT', 'UV_1', 'UV_2', 'UV_3']\n",
    "T_ISRF = [33.07, 313.32, 3249.3, 6150.4, 23209.0]          # in [K]\n",
    "U_ISRF = [0.25e-9, 0.055e-9, 0.37e-9, 0.23e-9, 0.12e-9]    # energy density of the contributions, in [GeV cm^(-3)]\n",
    "U_B = 0.25e-9                                              # energy density of the magnetic field, in [GeV cm^(-3)]\n",
    "sigma_Thomson = 6.65e-25                                   # in [cm^2]\n",
    "c_cm = 2.99e+10/conv_factor_sec_to_yr                      # speed of light, in [cm yr^(-1)]\n",
    "\n",
    "factor_ratio = ( 45 / (64*np.pi**2) )\n",
    "\n",
    "\n",
    "def loss_rate_KN_ODE(Energy, time):\n",
    "    \n",
    "    f_KN_times_U = 0.\n",
    "    for i in range (len(T_ISRF)):\n",
    "\n",
    "        f_KN_times_U_single = ( (factor_ratio * ( m_e / (k_boltzmann*T_ISRF[i]) )**2) / ( (factor_ratio * ( m_e / (k_boltzmann*T_ISRF[i]) )**2) + (Energy/m_e)**2 ) ) * U_ISRF[i]\n",
    "        f_KN_times_U = f_KN_times_U + f_KN_times_U_single\n",
    "        \n",
    "    dE_dt_KN = - (4/3) * (sigma_Thomson * c_cm) * (f_KN_times_U + U_B) * (Energy/m_e)**2\n",
    "    return dE_dt_KN\n",
    "\n",
    "\n",
    "def loss_rate_KN(Energy):\n",
    "    \n",
    "    f_KN_times_U = 0.\n",
    "    \n",
    "    for i in range (len(T_ISRF)):\n",
    "\n",
    "        f_KN_times_U_single = ( (factor_ratio * ( m_e / (k_boltzmann*T_ISRF[i]) )**2) / ( (factor_ratio * ( m_e / (k_boltzmann*T_ISRF[i]) )**2) + (Energy/m_e)**2 ) ) * U_ISRF[i]\n",
    "        f_KN_times_U = f_KN_times_U + f_KN_times_U_single\n",
    "        \n",
    "    dE_dt_KN = - (4/3) * (sigma_Thomson * c_cm) * (f_KN_times_U + U_B) * (Energy/m_e)**2\n",
    "    return dE_dt_KN\n",
    "#######################################################################\n",
    "\n",
    "\n",
    "max_time = (max(object_age)*1.e+4)      # in [yr]\n",
    "\n",
    "\n",
    "# Initial condition\n",
    "E0 = 1.e+9\n",
    "print (\"Initial condition, in [GeV]:\", \"{:e}\".format(E0))\n",
    "\n",
    "# time points\n",
    "time_ODE = np.logspace(np.log10(1.), np.log10(max_time), num=1.e+5)    # in [sec]\n",
    "print (\"min(time_ODE):\", min(time_ODE), \", max(time_ODE):\", max(time_ODE))\n",
    "print (\"\")\n",
    "print (\"time_ODE:\", time_ODE)\n",
    "\n",
    "\n",
    "\n",
    "# solve ODE\n",
    "ODE_sol = odeint(loss_rate_KN_ODE, E0,time_ODE)\n",
    "#print (ODE_sol[:,0])\n",
    "\n",
    "# interpolate the solution array\n",
    "ODE_sol_func = interpolate.interp1d(time_ODE, ODE_sol[:,0], kind='cubic')\n",
    "\n",
    "# put the function into a numpy array\n",
    "ODE_sol_array = ODE_sol_func(time_ODE)\n",
    "\n",
    "print (\"min(ODE_sol_array):\", min(ODE_sol_array), \", max(ODE_sol_array):\", max(ODE_sol_array))\n",
    "\n",
    "\n",
    "# plot results\n",
    "plt.plot(time_ODE, ODE_sol, label='ODEINT result')\n",
    "plt.plot(time_ODE, ODE_sol_func(time_ODE), label='Interpolated function')\n",
    "plt.plot(time_ODE, ODE_sol_array, label='Array')\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('t [yr]')\n",
    "plt.ylabel('E(t)')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>SNR evolution timescales\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&\\bullet \\hspace{0.5cm} t_{\\mathrm{Sed, kyr}}  =  0.3 E_\\mathrm{SNR,51}^{-1/2} M_{\\mathrm{ej},\\odot} n_{T,1}^{-1/3} \\\\[10 pt]\n",
    "&\\bullet \\hspace{0.5cm} t_{\\mathrm{PDS, kyr}}  =  \\frac{36.1 e^{-1} E_\\mathrm{SNR,51}^{3/14}}{\\xi_n^{5/14} n_{T,1}^{4/7}} \\\\[10 pt]\n",
    "&\\bullet \\hspace{0.5cm} t_{\\mathrm{MCS, kyr}}  =  \\mathrm{min} \\left[ \\frac{61 v_\\mathrm{ej,8}^3}{\\xi_n^{9/14} n_{T,1}^{3/7} E_\\mathrm{SNR,51}^{3/14}}, \\frac{476}{(\\xi_n \\Phi_c)^{9/14}} \\right] t_\\mathrm{PDS, kyr} \\\\[10 pt]  &\\bullet \\hspace{0.5cm} t_{\\mathrm{merge, kyr}} =  153 \\left(\\frac{E_\\mathrm{SNR,51}^{1/14} n_{T,1}^{1/7} \\xi_n^{3/14}}{\\beta C_{06}} \\right)^{10/7} t_\\mathrm{MCS, kyr}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With n_T = 10.0\n",
      "\n",
      "t_Sed: 0.13924766500838337 [kyr] = 1.3924766501{\\times}10^{2} [yr]\n",
      "\n",
      "t_PDS: 3.5627401543017463 [kyr] = 3.5627401543{\\times}10^{3} [yr]\n",
      "\n",
      "t_MCS: 1695.8643134476313 [kyr] = 1.6958643134{\\times}10^{6} [yr]\n",
      "\n",
      "t_merge: 154213.11645933276 [kyr] = 1.5421311646{\\times}10^{8} [yr]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#### Block to compute the SNR evolution-timescales ####\n",
    "\n",
    "\n",
    "## Source parameters ##\n",
    "E_SNR = 1.    # total energy budget of the SNR, in units [10^51 erg]\n",
    "M_ej = 1.     # in units [1 solar masses]\n",
    "n_T = 10.     # in units [1 cm^{-3}]\n",
    "csi_n = 1.    # ambient medium metallicity\n",
    "v_ej = 10.    # in units [10^8 cm/s]\n",
    "phi_c = 1.    # thermal plasma conductivity\n",
    "beta = 2. \n",
    "C_06 = 1.\n",
    "\n",
    "## Timescales, calculated in [kyr] ##\n",
    "t_Sed_kyr = 0.3 * E_SNR**(-1/2) * M_ej * n_T**(-1/3)\n",
    "t_PDS_kyr = ( (36.1/np.exp(1)) * E_SNR**(3/14) ) / (csi_n**(5/14) * n_T**(4/7))\n",
    "t_MCS_kyr = min( (61 * v_ej**3) / ( csi_n**(9/14) * n_T**(3/7) * E_SNR**(3/14) ), 476 / (csi_n * phi_c)**(9/14) ) * t_PDS_kyr\n",
    "t_merge_kyr = 153 * ( ( E_SNR**(1/14) * n_T**(1/7) * csi_n**(3/14) ) / (beta * C_06) )**(10/7) * t_MCS_kyr\n",
    "\n",
    "\n",
    "f = mticker.ScalarFormatter(useMathText=False)\n",
    "f.set_powerlimits((-5,5))\n",
    "\n",
    "\n",
    "print (\"With n_T =\", n_T)\n",
    "print (\"\")\n",
    "print (\"t_Sed:\", t_Sed_kyr, \"[kyr] =\", \"{}\".format(f.format_data( t_Sed_kyr*1000. )), \"[yr]\")\n",
    "print (\"\")\n",
    "print (\"t_PDS:\", t_PDS_kyr, \"[kyr] =\", \"{}\".format(f.format_data( t_PDS_kyr*1000. )), \"[yr]\")\n",
    "print (\"\")\n",
    "print (\"t_MCS:\", t_MCS_kyr, \"[kyr] =\", \"{}\".format(f.format_data( t_MCS_kyr*1000. )), \"[yr]\")\n",
    "print (\"\")\n",
    "print (\"t_merge:\", t_merge_kyr, \"[kyr] =\", \"{}\".format(f.format_data( t_merge_kyr*1000. )), \"[yr]\")\n",
    "print (\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Time arrays ##\n",
    "\n",
    "time_start = t_Sed_kyr\n",
    "time_stop = t_merge_kyr\n",
    "t_range_release = np.logspace(np.log10(time_start), np.log10(time_stop), num=len(E_e))  # in [kyr]\n",
    "\n",
    "\n",
    "t_range_Sed_index = np.argmin(abs(t_Sed_kyr - t_range_release))\n",
    "t_range_PDS_index = np.argmin(abs(t_PDS_kyr - t_range_release))\n",
    "t_range_MCS_index = np.argmin(abs(t_MCS_kyr - t_range_release))\n",
    "t_range_merge_index = np.argmin(abs(t_merge_kyr - t_range_release))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center> Escape-energy time-evolution for Electrons\n",
    "    \n",
    "$$\n",
    "\\begin{align}\n",
    "&\\bullet \\hspace{0.5cm} E_{\\mathrm{esc, Geo, 0}} = E_{\\mathrm{M}} (t_{\\mathrm{Sed}}) \\left( \\frac{t}{t_{\\mathrm{Sed}}} \\right)^{-11/10} \\\\[10pt]\n",
    "&\\bullet \\hspace{0.5cm} E_{\\mathrm{esc, Geo, 1}} = E_{\\mathrm{M}} (t_{\\mathrm{PDS}}) \\left( \\frac{t}{t_{\\mathrm{PDS}}} \\right)^{-11/10} = E_{\\mathrm{esc, Cur}} (t_{\\mathrm{PDS}}) \\left( \\frac{t}{t_{\\mathrm{PDS}}} \\right)^{-11/10}\\\\[10pt]\n",
    "&\\bullet \\hspace{0.5cm} E_{\\mathrm{esc, Geo, 2}} = E_{\\mathrm{M}} (t_{\\mathrm{MCS}}) \\left( \\frac{t}{t_{\\mathrm{MCS}}} \\right)^{-5/4} = E_{\\mathrm{esc, Geo, 1}} (t_{\\mathrm{MCS}}) \\left( \\frac{t}{t_{\\mathrm{MCS}}} \\right)^{-5/4}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E_Sed-PDS for electrons = 2904.6857052944188 [GeV]\n",
      "\n",
      "E_PDS-MCS for electrons = 3.172671475549745 [GeV]\n",
      "\n",
      "E_MCS-merge for electrons = 0.011298280127704704 [GeV]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "### Block to compute the energy vs time evolution, for ELECTRONS ###\n",
    "\n",
    "E_min_escape_el = 1.e+5         # 100 TeV, in [GeV]\n",
    "delta_SedPDS_el = -11/10\n",
    "delta_PDSMCS_el = -11/10\n",
    "delta_MCSMerge_el = -5/4\n",
    "\n",
    "\n",
    "#################\n",
    "## Sedov phase ##\n",
    "#################\n",
    "E_SedPDS_el = E_min_escape_el * (t_range_release[t_range_PDS_index] / t_Sed_kyr)**delta_SedPDS_el\n",
    "print(\"E_Sed-PDS for electrons =\", E_SedPDS_el, \"[GeV]\")   # Escape-energy at the edge between the Sedov phase and the PD stage\n",
    "print (\"\")\n",
    "\n",
    "\n",
    "#################################\n",
    "## Pressure-driven phase (PDS) ##\n",
    "#################################\n",
    "E_PDSMCS_el = E_SedPDS_el * (t_range_release[t_range_MCS_index] / t_PDS_kyr)**delta_PDSMCS_el\n",
    "print (\"E_PDS-MCS for electrons =\", E_PDSMCS_el, \"[GeV]\")  # Escape-energy at the edge between the PD stage and the MC stage\n",
    "print (\"\")\n",
    "\n",
    "\n",
    "#######################################\n",
    "## Momentum-conservation phase (MCS) ##\n",
    "#######################################\n",
    "E_MCSMerge_el = E_PDSMCS_el * (t_range_release[t_range_merge_index] / t_MCS_kyr)**delta_MCSMerge_el\n",
    "print (\"E_MCS-merge for electrons =\", E_MCSMerge_el, \"[GeV]\")  # Escape-energy at the edge between the MC stage and the merge phase\n",
    "print (\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$E_{\\\\mathrm{esc}}$ [GeV]')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Block to compute the array of escape-energies during all the stages, for ELECTRONS ##\n",
    "\n",
    "\n",
    "#################\n",
    "## Sedov phase ##\n",
    "#################\n",
    "E_esc_Sed_phase_el = np.zeros(t_range_PDS_index)\n",
    "E_esc_Sed_phase_el[0] = E_min_escape_el\n",
    "\n",
    "for i in range(1, t_range_PDS_index):\n",
    "    \n",
    "    E_esc_Sed_phase_el[i] = E_esc_Sed_phase_el[i-1] * (t_range_release[t_range_Sed_index + i] / t_range_release[t_range_Sed_index + (i-1)])**delta_SedPDS_el\n",
    "    \n",
    "\n",
    "\n",
    "#################################\n",
    "## Pressure-driven phase (PDS) ##\n",
    "#################################\n",
    "E_esc_PDS_phase_el = np.zeros(t_range_MCS_index - t_range_PDS_index)\n",
    "\n",
    "E_esc_PDS_phase_el[0] = E_esc_Sed_phase_el[-1]\n",
    "for i in range (1, t_range_MCS_index - t_range_PDS_index):\n",
    "    \n",
    "    E_esc_PDS_phase_el[i] = E_esc_PDS_phase_el[i-1] * (t_range_release[t_range_PDS_index + i] / t_range_release[t_range_PDS_index + (i-1)])**delta_PDSMCS_el\n",
    "\n",
    "\n",
    "\n",
    "#######################################\n",
    "## Momentum-conservation phase (MCS) ##\n",
    "#######################################\n",
    "E_esc_MCS_phase_el = np.zeros(t_range_merge_index - t_range_MCS_index + 1)\n",
    "\n",
    "E_esc_MCS_phase_el[0] = E_esc_PDS_phase_el[-1]\n",
    "for i in range (1, t_range_merge_index - t_range_MCS_index):\n",
    "    \n",
    "    E_esc_MCS_phase_el[i] = E_esc_MCS_phase_el[i-1] * (t_range_release[t_range_MCS_index + i] / t_range_release[t_range_MCS_index + (i-1)])**delta_MCSMerge_el\n",
    "\n",
    "\n",
    "\n",
    "# Concatenate the three energy arrays #\n",
    "Escape_energy_vs_time_el = np.concatenate([E_esc_Sed_phase_el, E_esc_PDS_phase_el, E_esc_MCS_phase_el], axis=None)\n",
    "\n",
    "\n",
    "plt.loglog(t_range_release, Escape_energy_vs_time_el)\n",
    "plt.xlabel('t [kyr]')\n",
    "plt.ylabel('$E_{\\mathrm{esc}}$ [GeV]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>Propagated spectrum \n",
    "\n",
    "### $\\bullet$ Equation $\\&$ General Solution:\n",
    "\n",
    "$$\\begin{align}\n",
    "&\\frac{\\partial f(E,t,r)}{\\partial t} = \\frac{D(E)}{r^2} \\frac{\\partial}{\\partial r} r^2 \\frac{\\partial f}{\\partial r} + \\frac{\\partial}{\\partial E} (b(E) f) + Q \\quad \\Rightarrow \\\\[10 pt]\n",
    "&\\Rightarrow \\quad f(r,t,E) = \\frac{Q(E_{\\textrm{t}}) b(E_{\\textrm{t}})}{\\pi^{3/2} b(E) r^3_{\\textrm{diff}}} \\cdot e^{-\\frac{r^2}{r^2_{\\textrm{diff}}}}\n",
    "\\end{align}$$\n",
    "\n",
    "\n",
    "### $\\bullet$ Solution for decaying luminosity:\n",
    "\n",
    "$$\\begin{align}\n",
    "&f(r,t_{\\mathrm{age}},E) = \\int_{t_{\\mathrm{rel}}}^{t_{\\mathrm{age}}} dt' \\frac{S(E_{\\mathrm{t'}}) L(t') }{\\pi^{3/2} r_{\\mathrm{diff}}^3(E,E_{\\mathrm{t'}})} \\cdot \\frac{b(E_{\\mathrm{t'}})}{ b(E)} \\cdot e^{-\\frac{r^2}{r^2_{\\mathrm{diff}}}} \\\\[10 pt]\n",
    "&E_{\\textrm{t}} = \\mathrm{starting \\, energy, \\,given \\, the \\, loss \\, equation} \\\\[10 pt]\n",
    "&r^2_{\\textrm{diff}} (E_{\\textrm{t}},E) \\equiv 4 \\int_{E_{\\textrm{t}}}^{E} \\frac{D(E')}{b(E')} dE' = 4 D_0 E_0 \\int_{E_t/E_0}^{E/E_0} \\frac{\\omega^{\\delta(\\omega)}}{b(\\omega)} \\, d \\omega \\\\[10 pt]\n",
    "&L(t) = \\frac{ L_0 }{ \\left(  1 + \\frac{t}{\\tau_{\\text{d}}}  \\right)^{\\alpha_{\\text{d}}}}\n",
    "\\end{align}$$\n",
    "\n",
    "### $\\bullet$ [Tomassetti, APJ vol. 752, n. 1 (2012)] ###\n",
    "    \n",
    "$$\n",
    "\\begin{align}\n",
    "&\\delta(\\rho) \\approx \\delta_{\\mathrm{high}} + \\frac{\\Delta}{1 + \\frac{\\xi}{1 - \\xi} \\left( \\frac{\\rho}{\\rho_0} \\right)^{\\Delta}} \\\\[10 pt]\n",
    "&\\delta_{\\mathrm{high}} = 1/6, \\qquad \\Delta = 0.55, \\qquad \\rho_0 = 2 \\, \\mathrm{GV}, \\qquad \\xi = 0.1 \\\\[10 pt]\n",
    "&\\rho = \\frac{\\sqrt{E_{k}^2 + 2 m_p E_{k}}}{Z}, \\qquad E_{k} = \\sqrt{(ZR)^2 + m_p^2} - m_p, \\qquad E_{k} \\equiv \\mathrm{kinetic \\; energy \\; per \\; nucleon.} \n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum slope for D(E): 0.17965663594467232\n",
      "Maximum slope for D(E): 0.6659884342071402\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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bDjpz625vOUJvWcZ8r2G8z9tb8SHftt/ea86sr9j3IdN4y1Hm472P+VakKPQ98ZaBzKzZW+VktPdnrFqL/Sy852L3wPq1caO1f/mLtR0d1u67r7XTpo2+CkYgYO1JJ1n7859b+/LLfldem8RydNV9IzhPXOZ6sV6YCIfDI0LU0NCQDYfDNhgMDq+7m2/d28y1jEOh0PCyb5nXaGxszHqsF5y9aw8NDQ2v+esFAS/geed54db7Qek91guEnkLO8XjByLtuMBi0HR0dI36odnd3D4ef3FCT75gXTDNff+4vCfmWwsvU0dGRVZf3nuRqb2/PulYgEBj+RcMLOt5n6P33eEtx5S4DWKjRlgLMVcj31ljvYW9vb8G/UFg79i+JmTLfc6+u3PfcC15j3TI/20I/79bW1uFrZ/6ik1mb9/lmrjNezPvgvReZ/za92sZ7bzIfn7vUW7HvSebn74XdfKF5vFqLva617hfdfL+YoLatX2/tgw9ae+651s6dO3pQlqxtaHDnPfigtevW+V157Ss0OBt3LiqtubnZVtsyYUAxvEmQg4ODk/7n4mQyqVmzZikcDhc1Ia6trU1dXV0aGhpi+/UJquTnXQneSjS1+Hri8biamppqsnaMtGaNG6/8i1+48cejrYIxbZobgnH00dK8edIuu7BMXDkZYwastfnXGM3AqhoASuJt81zNP7hXr16t9vZ2QnMZ1MLnXYxQKKRQKDQ8lr2WxGKxvGuao3YkEtLSpe72m9+49Zbz2Wor6fDDXVD+1KfcVtjwF8EZQNG8zT9KXTZuMsXjccViMTU1NSmRSJRt0uBUVs2f90R0d3drzpw5amtrq5kQGo/H1dfXp4GBAb9LQRE2bpQefdT1Ki9dKv3pT6Of+4EPpHuVDzpI2nzzipWJAhCcARRt/vz5RW28UWldXV0Kh8OEizKp9s+7VIFAQMuXL1dbW5t6e3v9LqcgCxYsUG9vL39FqQH/+pf04IPSnXe6wPyPf4x+blOTC8tHHy194hMMwahmBGcARav0D21vqTJv/eqxrt/Y2CjmbpRXPYe0xsbGEcs+VqtkMqnu7u6a6R2fitasceOU77rLbWv9+uv5z9tsMykUcr3KRx3l1lpGbWByoE+YHAgUJhqNjlgrt62tbcps1gGguq1a5XqU77pLWr5cWr8+/3nvfrcLyccc40IzaypXFyYHAqgLtTZxC0D9e+YZF5TvvNNtcT2aYFA69ljpuOPcihjTp1euRkwOgjMAAMAYNm6UBgZcUL7rLumvfx393MZGF5aPPVb62McYr1xvCM4AAAA51q+Xfv1rF5Tvvlt64YX8502fLh1wgAvKxxwj7bRTRctEhRGcAQAAJL39tvSrX0m33+7GLedMrxi2xRbSYYe5sHzUUdK221a2TviH4AwAAKasN990K2Hcfrt0zz3SG2/kP2/2bLcKxrHHSoceKm25ZWXrRHUgOAMAgCnltddcSO7pcdtdr12b/7wdd0xP7ttvP2kGqWnK41sAAADUvdWr3fCLnh6pt1daty7/eXPnSiecIIXDbmMSJvchE8EZAADUpX/+003uu/12t4vfO+/kP2/XXV1QPuEE6d//nbCM0RGcK8wYM0/SvLlz5/pdCgAAdeeFF6Q77nBh+aGH3FJy+ey+uwvKJ5wg7bJLZWtE7SI4V5i1dqmkpc3NzQv8rgUAgHrw/PNuCEZ3t/SHP4x+3l57pcMyO5ejFARnAABQc1atckH5ttuk3/8+/znGuEl9J5wgHX+89MEPVrZG1J9pfhcAAABQiH/+U7riCumgg6T3v1/6z/8cGZqnT5cOOcSd9+KL0m9/684jNI+up6dHbW1tikQiampqUl9fX8GPa2pqUjwez2qPx+Myxox66+zsnIyXURH0OAMAgKr1yituzPJtt7kJfvnGLE+fLh18sDR/vls+brvtKl9nrerp6dGSJUvU3d0tSerr61NLS4sGBgbU2NiY9zHRaFTxeFzBYHBEaPYEg0FFo9GstmQyqUWLFqm1tbW8L6KCjLXW7xqmpObmZtvf3+93GQAAVJ2hIenOO11Y7uuTNmwYeY4xruf5xBPdMIx3v7viZdaFhoYGxWIxhUKhrLZQKKRYLJb3MfF4XI2NjYrH42pqahoRsuPxuPr7+0cEZK+nub29fRJeycQYYwastc3jnUePMwAA8N2aNdLdd7uw/KtfSevXjzzHG7N84olu3PIOO1S+znoSj8eVSCTU3JydF0Oh0JjDNUbrifYEAoGsIC653uYlS5ZoYGCg9IKrAMEZAAD4Yu1a6d57pZtvdl9H25Rk771dWA6H3dhm5NfV1aXe3t6s0JtMJkecFwwGNTg4qEQiIckF3UyBQGD4WCmCeZYsiUajWrhwYcnPWS2YHAgAACpmwwa3c99pp7ke40jEDcvIDc177CH98IfS//2f9PDDboIfoXlsra2t6u7uVnNzs5LJpLq7u2WtzbrFYrHhYLt69eq8z7PtttuWtS5v6EY4HC7r8/qBHmcAADCprJVWrHA9y7fe6lbHyGf33V3P8vz50pw5la2xnniBOHe4hCTNnz9/eLhEvt7oybBgwQJ1dHRU5FqTjeAMAAAmxf/+rwvLN98sPfts/nPmzpU+8xl3+/CHK1tfvfJWvMgnEAgoEokM//doRnt8sbq6uiTlD/G1iOAMAADK5oUXpCVLXFgebR7Y9ttLJ50knXyy1NzsJv2hPLxe5LEm8Hkh1gvHiUQiKyi/+uqrZQnOyWRS0WhUy5cvn/BzVQuCMwAAmJBkUrr9dheWH3zQDc3ItfXWbiWMk0+WPvlJt/Yyys9b6naPPfYY91xvNY2+vr6speP6+vrKMpFvwYIFCgaD467CUUuYHAgAAIq2fr20dKmb3Lf99tLpp0sPPJAdmjfd1K2x3NPjxjVfe60UChGaJ5O3IUkhPcaBQECtra1Z44+9x2dO5ItGo2poaBjxeG8sdb5Jhn19ferp6amLlTQyEZwBAEBBrHXDL7wVLo4+2oXizBUxjHFbXv/sZy4s336762neYgv/6q4GXV1dampqkjFGLS0to+64l/uYYifwrVixQpIUiURGbHU9a9asEefHYjGFw2G1tLSora1NsVhs3KEViURCbW1tamtrkyS1tbUpGo1m1drW1qZAIFAXK2lkYudAn7BzIACgVrzwgnTTTdINN0h//nP+c5qa3DCME0+U3ve+ytZX7To7O4e3mm5oaFBvb696enoUi8XG3H46Eolo8eLFY07iy9XU1KR4PC7yXXHYORAAAJTszTfd+so33OC2vc6Xw97/fumzn3W3XXetfI21IJlMatGiRVq5cuVwAG5tbVVfX59aWlo0ODg46lJtiUSiqNAspbfDxuQgOAMAAEnSxo3Sb37jwnJPj/TGGyPP2WorN/Ti1FOlgw5ivPJ4urq61NHRMSIAh0IhDQwM6JBDDlEikVB3d3fW8Wg0WvQSbt5uf7lbaKN8CM4AAExxiYR03XXS9ddLf//7yOPGSAcf7MLy8cdL73pXxUusWYODg4pGo3mPNTY2auXKlWpqalJDQ8PwuODu7m4lEonhjUoK5QXnfBP5UB4EZwAApqC1a6U77pCuucathpHPLrtIn/ucG7v8wQ9Wtr56EQgExlzhIhAIDIfrRYsWSUr3RpcyTEMaew3nrq4uhUKhsm1wMtUwOdAnTA4EAFSatVJ/vwvLt9wirVkz8pxtt5U+/WnXu8zmJLUlEomop6dHg4ODowbjlpYW9fb2Vriy6sfkQAAAIEl6+WW3KsY110hPPTXy+LRp0uGHS1/4gjRvnlt/GbXH63GePXv2iGPJZFL9/f3DwzlQGoJzhRlj5kmaN3fuXL9LAQDUsQ0bpPvvd2H5F79wG5bkmjvXheVTT3UrZKA2JRIJRSKR4VCcb71mT7ETDpGNoRo+YagGAGAyJBJu85Hrr3frL+facku3298XviDtvz9DMQCJoRoAAEwZ69e7XuWuLulXv8p/zt57u7A8f760zTaVrQ+oFwRnAABq1MqV0tVXu+EY//jHyOPveY8bhnHaaWxQApQDwRkAgBqyfr10zz1SLOZ6l3NHXBojHXGEtGCBdOSR0iab+FMnUI8IzgAA1IDnnkv3Lq9aNfL4e98rffGL0umnSzvtVPHygCmB4AwAQJV655107/L99+fvXT7sMKmtTTrqKGkGP9WBScU/MQAAqsyqVW6iX1eX9OKLI4/vsIOb6Hf66dKcOZWvD5iqCM4AAFQBa6Xf/166/HLp9ttdb3OuQw91vcvz5jF2GfADwRkAAB+99ZZ0880uMD/xxMjj22+f7l0eZRdlABVCcAYAwAeDg9IVV7jJfsnkyOP77SedfbZ0/PFsgQ1UC4IzAAAVsnGjdN990k9/Ki1bNnKy3xZbSCef7ALzbrv5UyOA0RGcAQCYZEND0rXXuh7mwcGRx4NBF5ZPO02aNavy9QEoDMEZAIBJ8te/Sj/+sXTDDdLatdnHvI1Kzj5bOvxwado0f2oEUDiCMwAAZWSt1NsrXXaZG5aRKxBwk/3OPFOaO7fy9QEoHcEZAIAyWLtWuvFG6Uc/kv7yl5HHP/5x6ZxzpM98Rtpyy8rXB2DiCM4AAEzAqlVu7PJVV0mvvJJ9zBjp6KOlr3xFOvBAdx9A7SI4AwBQgnjc9S7fequ0fn32sa22csMxvvxlhmMA9YTgDABAgax1y8hdcon061+PPL7jji4sf/GLbiwzgPpCcAYAYBzr1km33CL98IfSn/408vg++0jnnisde6w0g5+sQN3inzcAAKN47TWpq8sNyXjhhexj06dLkYgLzHvu6U99ACqL4AwAQI4XX3TrL191lQvPmbbaSlqwwE3422knf+oD4A+CMwAAKX/5ixuOceONIyf8bb+9G7985pns7gdMVQRnAMCU98c/ShddJC1dOvLYhz4knXee9NnPSptvXvnaAFQPgjMAYEqyVnrgAekHP5AefHDk8X32kb72NbcOM9thA5AIzgCAKWbjRumee1wP8yOPjDx+zDEuMO+7b+VrA1DdCM4AgClhwwbpttukRYukp57KPjZ9utsK+/zzpV139ac+ANWP4AwAqGvr1kk33CB1dEjPPpt9bNNN3Q5/7e3SnDn+1AegdhCcAQB1ae1aafFit8vf//t/2ce22ko64wzpq1+V3vc+f+oDUHsIzgCAurJ2rdu05OKLpX/8I/tYIOCWlPvyl6Vtt/WnPgC1i+AMAKgLYwXm7bd3vctnnCFts40/9QGofQTnCjPGzJM0b+7cuX6XAgB1YazA/L73uQl/p58ubbGFP/UBqB+sTFlh1tql1trWmTNn+l0KANS0tWvdttjBoNv+OjM0v+990v/8jzQ4KJ1zDqEZQHnQ4wwAqCnj9TAvXOh6mNnlD0C5EZwBADVh3Tq3SsYPfiCtWpV9jMAMoBIIzgCAqvbOO9KNN0oXXig991z2MQIzgEoiOAMAqtLGjdIdd0jf/Kb09NPZxwjMAPxAcAYAVBVrpfvuk77xDSkezz623XYuMJ95JhP+AFQewRkAUDUeekj6+tel3/0uu32bbaTzznOrZ2y9tT+1AQDBGQDgu4EB18N8333Z7Vts4ZaTa29npz8A/iM4AwB8Mzjoephvuy27fZNNpNZW6YILpPe+15/aACAXwRkAUHEvvyx9//vSlVdK69en26dNk049Vfr2t6Wdd/atPADIi+AMAKiYt96SfvQjt3nJ669nHzvhBOl735M+8hF/agOA8RQcnI0xp09mIbmstVdX8noAgMmzYYN0/fVuabkXX8w+tv/+0iWXSHvt5U9tAFCoYnqcuyT1SlozSbV4ApIOkURwBoAaZ620bJkUjUp/+lP2sY98xPU8z5snGeNPfQBQjGKHakSsta9NSiUpxpiApFcn8xoAgMnX3+9Ww3jwwez2HXaQvvtd6bTTpBkMGARQQ6rxf1lWEn0PAFCjnn9eOv986eabs9vf9S4XpL/6VWmrrfypDQAmopjg3DbZvc2SZK1dY4xpm+zrAADK6803pc5ON1557dp0+4wZbmm5b31L2n57/+oDgIkqODhbaxdPZiF+XQsAMDEbN0o33eR6mXMn/h1/vLRokfShD/lTGwCUUzUO1QAA1IiHH3bbYK9Ykd3e2OiWndvkQkEDAAAgAElEQVR/f3/qAoDJMK3cT2iMObjczwkAqC5//7v0mc9I++6bHZp32EG69lrXRmgGUG/KHpwlMT4ZAOrUG2+4scof/rB0yy3p9s02c1tnP/OM9PnPux0AAaDejDlUwxizTZHPt62kxtLLAQBUo7HGMc+fL3V0sEU2gPo33hjnuKQ5lSgEAFCdHntM+tKX3HjmTE1Nbhzzfvv5UxcAVNp4wfl8SRdL6ivw+baVdPyEKgIAVIWhIekb35Cuusr1OHt22MGtlHHqqQzJADC1jBmcrbU9xphWa+0ZhT6hMeZXEy8LAOCXjRula66RFi6UXnkl3b7JJm7zkm98w21mAgBTTSHL0cWNMbtZax8v8DmTEykIAOCf/n7p7LOlRx/Nbj/0UOknP3GTAgFgqirkj2wxSXsU+oTW2vmllwMA8MMrr7jd/fbcMzs077ijdMcd0n33EZoBYNweZ2vtSkns5AcAdWjDBmnxYumCC6TVq9Ptm24qtbe74RpbbulffQBQTdg5EACmqBUrpDPOkOLx7PYjj3SrZcyd609dAFCtmA8NAFPMmjXSOedIe+2VHZrnzJF+8QvpnnsIzQCQz4SCszFmUbkKAQBMLmulnh5p112lyy939yVp882lCy+U/vxnad48f2sEgGo20R7ncFmqAABMqueec6E4Esne+e+ww1xg/ta3pC228K08AKgJEw3OpixVAAAmxfr10iWXSB/9qHTvven2HXaQbr1VWrZMCgb9qw8AaslEJwfaslQBACi7P/xBamuTnnoq3WaMmxB40UVSIOBfbQBQi1hVAwDqTDIpff3rbqtsm9G98fGPS7GY9B//4V9tAFDLWFUDAOqEN/nvIx+RrrwyHZq33FLq7HS7AhKaAaB09DgDQB1YtcptlX3nndntRx7pVtDYeWdfygKAukKPMwDUMGula65xS8xlhub3vtf1Pi9dSmgGgHKhxxkAatTKlVJrq9TXl93e2uqGZsyc6U9dAFCvCM55GGMCkkKSgpISkvqstcmcc8KS2iQlcx4ekNRtre2qRK0App4NG9zwi69/XXrrrXR7Q4O0eLH0yU/6VxsA1DOCcw5jTKukWJ72iLW2J6MpKBeuk3JhOVNcADAJ/vIX6fTT3VJznmnTpHPPlb77XTcREAAwORjjPFJMUlTSrNQtmmrvTvVEe5KSotbaWdZak3OLCgDKaP166fvfl3bfPTs0f+xj7v4Pf0hoBoDJxs6BGVLBuMda22mtTaZunZK8YRehnIfkDtMAgLIbGJCam6VvflNat861bbKJ9J3vuGN77ulreQAwZUw0ODeVpYrqsihPW2/q6+yMtoCk1ZNfDoCpat066dvflvbaS3ryyXT7nntK8bg7tumm/tUHAFPNhIKztXZNuQqpBqke5nzjk73A3J/THjTGxIwxQ6lbrzGmcZLLBDAFPPWUC8zf/a6bDChJW2whXXqp9PDDbogGAKCyKjLG2RizmzHmdGPMbmV8zkAqtPYWeG6HMWawxJDbJreyRm6oXqjUWGdJfXJDOQYIzwBK9c470qJFUlOT9Pjj6fb99nO9zl/9qjR9un/1AcBUVrbgbIzZORWOj88MyMaYRZIG5CbdDRhjnjHGbD2B64SMMd2ShiS1Knv4RL7zg5JWyq2C0WStnSUpkro/YIzJHbec+/hw6txIzqG4pDnW2qi1tstaG5EL2JLUUeTLAgA9/bS0775umbn1613bZpu5XuZf/1qaO9fX8gBgyitnj/P5cuG4Rakwa4yZI9cbayStkbRY0usqYbm2VGAelNQtaYWkzgIf2i0pYa2NeGsxW2v7lA7C3WNcMygXgpty13G21o5Y2zm1dnNSIycRAsCoNm6ULrvMrZjx6KPp9j33dL3O9DIDQHUoZ3AOSTrfWnumtfaBVFs49dVK2tlae4a1tknSY8aY44t8/tVKL//WKWlwvAekeosblWdd5tSwi7ikQGrt5tzHBuQmBUastYki6uyX2zQFAMY1OCgddJALx2+/7do22UT6wQ+k3/9e2mUXX8sDAGQoZ3CeY629JKetRS4091hrX8toX6T0sIaCWGvjORuQFOLE1Ne+UY577S15ji2X1JZvsmDOes65Zo9xPQCQJFkrXXml9IlPSA89lG7fbTepv98N15jBFlUAUFXKGZxX5mlrTn3NmsBnrX1MbtzwZAulrjdaD7DXa501mS814TCaGtKRz8LUMI4sqbaA0pumAMAIL7wgHXaYdNZZ0ptvurbp06VvfUt65BHp4x/3tz4AQH7l7M/IGu9rjNldLkRa5fTAGmNmapKDc6pXeKyeYSk9pGK4llRoDkqKGGMiSk8+9J4rIjf0o9cY0+KF8tRKGh1yQzvYGAVAXj09UmurNDSUbtt1V+n6690mJwCA6lXO4NxnjLnIWvv11H1vZYmEtfa5nHNDmvxd97wwPNZ1sjYwMcbElJ7YN2Lcc8psa23CGNMjtw13UG5cc6+1Nt+QDwDQa69J//mf0nXXpduMkc47z63VvPnmvpUGAChQOYPzIkkrjTGZwxSscoYtGGN2lgvV1TCBLndVjDYVOPbaWlv0cIzUJMRWSdpxxx2LfTiAGvX730uf/ay0MmNA2447Sj//uXTAAf7VBQAoTtnGOKd2EWyW9IDc0nMr5VbZuEOSjDGHGGOelQvMQU3+BLox13f2Q2q952ZrbfO73/1uv8sBMMnWr5e++U0XjjND8ymnuM1MCM0AUFvKOmc7Nd4373AFa+1ySXOl4THOk80bhjHeOGdp8oeNAJhinnnGBeQVK9JtM2dKV10lnXSSf3UBAEpXkS23c1lr16R6qCdTIWHYC9XVMGwEQB2wVurqcpuZZIbmgw5yvcyEZgCoXb4E50rIXIIu39JxKd5wjv7JrwhAvXv5ZenYY6W2Numtt1zbJptInZ3S8uVuXDMAoHbV+/L63njqoPL3KnvrN/fmOQYABfvVr6RTT5X++c902667Sjfd5DY1AQDUvrrtcU7xdhqMjHJ8j9RXdvoDUJL166Vo1G1okhmazznH7QBIaAaA+lHvwXlR6uv83AOp4RthSZ1sWAKgFImEtN9+biiGZ/vtpWXLpJ/8RNpiC/9qAwCUXy0HZ2/1jmBql8ARUoG4RVLAGNPrnZcKzb2S+kpZj3kijDHzjDFda9ZM9txIAJNpyRI3AfDRR9Nthx0mPfGEdPjh/tUFAJg8ZQ3OxpjTjTHnlfM5c56/1RgzaIwZkustltzKGEOp9u7cx1hr+yQ1pO6uTD22V1LMj53+rLVLrbWtM2dWYkU+AOX25pvS6ae71TFee821zZghXXKJ9Mtfuh5nAEB9MtbasU8wZhtJC+Um0iUl3WqtvXOUc/sl7W6tnV7uQutNc3Oz7e9nMQ+gljz5pHTiidLTT6fbgkHpllukPff0ry4AwMQYYwastc3jnTfmqhqpjUoScr26JtUcSQXkiLX2/3IesloAUGesla68UvrqV6V//Svd/ulPuw1NttnGv9oAAJUz3lCNDkmzJD0mqSn134fKbakdN8Z8YnLLAwB/rV4tnXCCdPbZ6dC85ZbSNde4peYIzQAwdYy3jnNI0lBO13WfpD5jTFhSjzEmbK19InWM1SkA1I2HH3ZjmZ9/Pt328Y+7iYG77OJfXQAAf4zX4xzUKGscW2t7JB0m6XZjzCfLXRgA+MVa6dJLpQMPzA7NX/qS9MgjhGYAmKrG63GOy41vzstamzDGNMv1QF9U1soAwAdDQ9Jpp0l3351umzVLuvZa6Zhj/KsLAOC/8YLzcknnGWN2yjMRUNLwWsnNqQmDo4ZsAKh2/f1SJCI991y6ba+93NCMnXbyrSwAQJUYc6hGanOQxyUljDFXppamG+3cZkkry1xf3WEDFKD6WCv99KfSvvtmh+avfEX67W8JzQAAZ9wNUKy1Tal1mTutta+Nc26LpMXlKq4esQEKUF1ef90tK/elL0nr1rm2bbaRbr9duuwyadNN/a0PAFA9xhuqMcxaW1BvsrX2jELOM8bsZq19vNDrA0C5PfmkG5rxzDPptt13l7q7pYaG0R8HAJiayrrldpFGbI8NAJVyzTVu/HJmaG5rc0vQEZoBAPkU3ONcTsaYOZJm+3FtAFPbW2+5zUyuuy7dttVWUiwmnXyyb2UBAGpA2YOzMWaRpLDcGtAAUDWefVY6/njpqafSbR/9qNTTw9rMAIDxlTU4G2NWSGqUZAo43Zbz2gAwlnvukU45Rcpc0ObUU6UrrnA9zgAAjKdswdkYc4KkptTdHklLJCXK9fwAUIoNG6QLL5S+971022abSZdfLn3xi5Ip5Nd8AABU3h7nPeR6kdustVeX8XkBoCSrV7txy/fdl27bcUe31Fxzs391AQBq02RMDrxtEp4TAIry2GPSCSdIKzMW0gyFpFtukbbbzr+6AAC1q5zL0fWlvs4q5GRjzM5lvHbNYOdAYPJdf720zz7ZoXnhQtfzTGgGAJSqbMHZWtsn6Q5J5xf4kN5yXbuWsHMgMHnWrZPOOkv6/Oelt992bVtvLd15p3TRRdL06b6WBwCocWXdAMVaG5HUYIz54ljnGWNminWcAZTRCy9IBx4oXXllum3XXaUVK6Rjj/WvLgBA/ZiMnQMTkrqMMRtGu0laLSkwCdcGMAX95jdSY6P0xz+m2+bPlx55RPrwh/2rCwBQX8oanI0x/ZIWyK3jPN4NACbEWres3CGHSC+95NqmT5cuvVS69VbpXe/ytz4AQH0p9zrOjam7fZK6Nfo6zg2SrhzlGACM61//cuOZr7km3fae90hLlkgHHeRbWQCAOlbO5eha5NZxjlprfzjOucuNMe1lvDaAKWTVKrd1dubQjD32kO64Q/rAB/yrCwBQ38o5VCOZ+tpV4PkdZbw2gCnikUfc5iWZofnUU6Xf/pbQDACYXOUMzv2prwWt42ytXVzGawOYAq67TjrgAOnFF939adOkyy5z7Ztv7mdlAICpoJzrOPdIekDSGYWcb4z5W7muDaC+vfOO9JWvSKed5tZqlqRZs6T773fthunGAIAKKPc6zi2SmowxxxVw+rblvDaA+vTqq9Jhh0k//nG67WMfk/r73RbaAABUSjlX1Vgg6eLU3R5jTHKM01nDGcC4nnzSbV6SuXX2CSe4oRksNQcAqLRyrqrRp+zxzeONdbZlvHbNMMbMkzRv7ty5fpcCVLWeHulzn5Peeivd9t3vShdc4MY2AwBQacba8uVXY8yzkuKSeuV2BxxNg6RF1trpZbt4jWlubrb9/f3jnwhMMda6gPyd76Tbtt5auvFG6eijfSsLAFDHjDED1trm8c4rZ4+z5Hqdr7LWPj7eicaY1jJfG0CNW7vWTQBcsiTdNneudPfd0q67+lcXAABSEZMDjTHbFHDaWLsF5opN8FoA6siLL7ql5jJDcygkPfoooRkAUB2KGSk4NF6gtdYut9a+VsiTWWsvyddujJkpaaiIugDUuIEBt/Nf5uilL31JWrbMLTsHAEA1KCY4V3KlVFZlBaaI7m5p//3Tm5pMny5dcYX0P/8jzSj3YDIAACag2B9LC4wxayalkrRZmqIrbgBTibXS974nffvb6bZAwAVp1mcGAFSjYoLzckmHTVYhea4FoE6tXSt94QvSrbem2/7t36R77pE+9CH/6gIAYCwFB+fUroAAMCGrVknHHCOtWJFuO+QQ19PMeGYAQDVjGwEAFROPu0mAmaH5rLOYBAgAqA0EZwAVceed0n77SS+84O5Pny5dfrn0059Km2zib20AABSC4AxgUlkrXXqpdMIJbmyz5CYBLlsmnX22v7UBAFAMFnsCMGneecetxxzL2O6ooUG6917pwx/2ry4AAEpBj3OFGWPmGWO61qyZ7FX9AH+99pp01FHZoXm//aQ//pHQDACoTQTnCrPWLrXWts6cOdPvUoBJ8/e/u5B8//3pts98Rurrk7bbzr+6AACYCIIzgLLq75f22kt66ql027e+Jd14o7TZZv7VBQDARDHGGUDZ3HWX61n2JgFusol09dXSqaf6WxcAAOVAjzOACbNW+u//lo4/Ph2aZ82SensJzQCA+kGPM4AJeecd6ZxzpKuuSrexcgYAoB6VJTgbY7aRFJLUIqlZUlBSIOOUpKTVqa/9kn4labm19rVyXB+AP157TTrxROm++9Jt++7rhmwwCRAAUG8mFJyNMQdLisqFZpNqTkgaUDosS9JsuSA9W1Jb6maNMX2SLrbWPjiROgBU3osvSp/6lPTEE+m2k06Srr1W2nxz/+oCAGCylBScjTE7S+qR1Jj6eoakPmvtygIfP0eudzokabkxZkDS6dbaJ8Z+JIBq8Oc/S0ccIT3/fLrtG9+QLrxQmsbMCQBAnSr6R5wx5muS4pL6JM2y1s631i4uNDRLkrV2pbW2y1o7X64X+gFJDxpj/qvYegBU1m9+49Zo9kLz9OnSz34mfe97hGYAQH0rqsfZGHOVpDmS5lhry7L1nbU2KSlqjFkk6TZjzJ7W2hPL8dwAymvJErdKxrp17v673iX19EiHHeZvXQAAVELB/UPGmIslDVprDytXaM5krU1aaw+V1J8K0QCqhLXSpZe6McxeaN5hB9f7TGgGAEwVxfQ4L7HWPjZplaRYay8xxuw+2dcBUJgNG6SvflX6yU/SbbvsIi1bJu28s29lAQBQcQUH50qEZj+uBWB0a9dKp5wi3XFHum2//aS775Zmz/avLgAA/MBUHgB5vfqqFAplh+Zw2O0GSGgGAExFpayqsXP5ywBQTRIJaZ99pIcfTrede66bHMgazQCAqaqUHueEMWaDMeZvxpgVxpjdCnmQMWaOMebg1C6DAKpUf7+0997SM8+4+8ZI//3f7sZycwCAqazUH4OdkpqttXtYax8v8DGrJR0qKZ4K3o+WeO2aZoyZZ4zpWrOm7AuTABP2y19KBx4ovfSSu7/ZZq6X+dxz/a0LAIBqUGpwXjLaknTGmENSvdFZPcvW2jXW2vOttXMlXS2pqcRr1zRr7VJrbevMmTP9LgXIsnixdPTR0ltvufuzZrnxzJGIv3UBAFAtSg3OyTGOrZYUHOfxt5V4XQBlZq30ne9Ira1u6TlJ2mkn6fe/l/bf39fSAACoKkXtHFigpCRZa18b45zVk3BdAEXasEE6+2wpFku3NTZK997rNjgBAABpkxGcCzFWjzWACnj7benkk7OXmzv0ULeF9tZb+1cXAADVqpShGklJgQlelx5nwEdr1khHHJEdmk8+WVq6lNAMAMBoSh3jPL/QZegAVJdVq9zKGb/+dbrt3HOlG26QNt3Ut7IAAKh6pQ7ViEqKGmMkKZG6xSWtkFTIOmvsOwb44Nln3XCMlSvTbRdfLLW3u/WaAQDA6EoNzpk/YhtSt1DWCcb8TekwnZAUt9Y+lzocEOOcgYoaGHDDM15+2d2fPt0tQXfaaf7WBQBArSglOL9qrZ0tScaYmZKa5Zafa8r474DSgTrsPTCjh5rQDFRQX5903HHSG2+4+1tsId12m3TUUf7WBQBALSklOA8PxUhtgrI8dVvstWcE6ka58Oz9t1L3JcmWcG0ARbrtNumUU6T16939WbOke+6R9tnH37oAAKg1pQTncfcRywnUwzIC9aGSzivh2gCKcPnl0pe/7DY5kaT3v1+6/37pox/1ty4AAGpR0cHZWrty/LNGfexwoDbGHFLq8wAYm7XSt74lff/76bZddnGheccd/asLAIBa5tcGKJJEcAYmwTvvSGeeKV19dbptr73cboDbbutfXQAA1DrfgnOq9xlAGa1dK33mM9Jdd6XbjjhC6u6WttrKv7oAAKgHpW6AAqDKvPaaC8mZofmzn5XuvpvQDABAORQcnI0x20xmIX5dC6gHL78sHXyw9JvfpNvOO0+67jppk018KwsAgLpSTI/z1caY4yatkhRjzPHKWNoOwNief1464AC3wYmno0O65BJpGn9TAgCgbAoe42ytnW+M6TfGtFhrz5qMYowxV0lqstbuMRnPD9SbZ56RWlqkv//d3TdGisWkBQv8rQsAgHpUVH+UtbZZ0ruNMX8rZ++zMeZ4Y8yzkmYRmoHCPP64tP/+6dC8ySbSkiWEZgAAJkvRf8i11kYkLZT0M2PMq8aY/zLG7Fbs8xhjdjPGLDLGvCo3NCNqrT2x2OcBpqLf/U468EDppZfc/S23lJYulSLjbk8EAABKVdJydNbaHkk9xph2SWdK6jTGSFJcUr+kpKRXU18lKSBp29TXzO2310haZK29pNQXAEw1y5ZJJ5zglp6TpJkzpV/+ki20AQCYbMZ6e/FO5EmMCUlqkdvUpHGc0+OS+iT1WmuXj3Nu3THGzJM0b+7cuQv+9re/+V0OasySJdIpp7hNTiRp++3dboCf+IS/dQEAUMuMMQOpIcljn1eO4DxKATMlBTOaEmx6ktbc3Gz7+/v9LgM1JBZzOwJ6/2R32knq7ZX+7d/8rQsAgFpXaHCetJ0DUyH5scl6fmAqufhiaeHC9P2PfMSF5ve/37+aAACYaljlFahi1krRaHZobm6WfvtbQjMAAJU2aT3OACZmwwY3NGNxxnZABx3kttDehr01AQCoOIIzUIXWrXOTALu7021HH+0mB26+uX91AQAwlU0oOBtjdpYUlltRY3aqOZG6rbDW3jGR5wemorVr3XJzy5al2z77Wemaa6QZ/KoLAIBvSv4xbIxZJKk9syn1tUmSTZ0zJGmRpMXW2tdKvRYwVbz+ujRvnvSb36TbzjlH+tGPpGnMSAAAwFcl/SjOCM0mdVsjtz5zT+r2WKpttqRLJCWMMaw0C4xhaEhqackOzd/8pvTjHxOaAQCoBkX3OBtj5kiKpu7GJUWstStHOXd3SSdJ+pqkuDEmbK29s9RigXr10kvSoYdKTzyRbuvslL72Nf9qAgAA2Urpxwqnvsastc2jhWZJstY+Zq2NSpol6Q65bbqPK+GaQN164QXpwAOzQ/NPf0poBgCg2pQSnFskDVlrzyz0AdbaNdbaiKSFkq42xmxdwnWBurNypbT//tLTT7v706ZJ110nnXWWr2UBAIA8SgnOs+Um/BXNWtspNwa6e7xzgXr39NMuNK9M/c1mxgzp1lulz33O37oAAEB+pQTnoNzY5lJFJe3JZEFMZU88IR1wgBumIUmbbSbddZcUifhbFwAAGF0pwTkgt05zSay1SUm3STqj1OcAatkjj7gdAF9+2d3faivpl7+UjjzS17IAAMA4SgnO1lr73ASv2yspNMHnAGrOr38thUJSMunuz5wp9fZKBx/sa1kAAKAAfq0Om1B6p0FgSrjvPumII6Q33nD3t9tOevBBae+9/a0LAAAUppTgbIwx25Th2oEyPAdQE+64Qzr6aOntt939977XbXSy++7+1gUAAApXSnBOSppT7kKAenXjjdL8+dL69e7+TjtJDz0k7bqrv3UBAIDiFL1zYErcGCO51TX6JQ16/22tfa2AxwdLvC5QU7q6pDPOkKx19z/0IamvT/rgB/2tCwAAFK/U4GxSX5tSNzt8wJik3BjmfkkD3n/nBGqCM+re5ZdL55yTvv/v/+4mAm6/vX81AQCA0pUanJtSX4OS9pDUmPrvoNz22uMF6j3khnwAdenSS6Xzzkvfb26W7r9fms2UWAAAalYpwTlhrX0s9d+PSbo986AxZneNH6glaaiUgoFqd9FF0gUXpO/vvbe0bJlbeg4AANSuUoLzmNttp0L1aIG6WVKDpBZJu5VwbaBqWStdeKG7eQ44QLrnHmnrrf2rCwAAlEfRwdlae/v4Z+V9nBeoJel8Y8yzpTwPUI2slb7+denii9NtBx8s/eIXbmdAAABQ+0od41wOLT5eGygba6X/+i/pssvSbYcf7tZu3mIL/+oCAADl5Vtwttau9OvaQLls3OhWzrjiinTbvHlSd7e02Wb+1QUAAMrPzx5noKZt3Ci1tUlXX51uO+EE6eabpU039a8uAAAwOQjOQAk2bJC+8AXphhvSbSedJP3859IM/lUBAFCXStlyG5jS1q+XTjklOzSfeqrbWpvQDABA/SI4A0VYt871LN96a7rt9NOla6+Vpk/3ry4AADD5CM4VZoyZZ4zpWrNmjd+loEj/+pcUDrvVMjxnnSXFYtI0/iUBAFD3+HFfYdbapdba1plsI1dT1q6VjjlGWro03XbuudLllxOaAQCYKviRD4zjzTelo46S7r8/3Xb++dKll0rG+FcXAACoLIIzMIbXX5eOOEJ64IF027e/LV10EaEZAICphjUAgFGsWeNC8x/+kG77wQ/c1toAAGDqITgDeSST0mGHSY8+mm774Q/d1toAAGBqIjgDOZJJ6dBDpRUr0m0/+YnbWhsAAExdBGcgw9CQC839/em2K66QzjzTv5oAAEB1IDgDKUNDUkuLNDCQbrvySumMM/yrCQAAVA+CMyBp9WoXmuPxdFssJrW2+lcTAACoLgRnTHmvviqFQtLjj6fbFi92W2kDAAB4CM6Y0l55xYXmJ55w942Rrr5a+sIX/K0LAABUH4IzpqxXXpEOOUR68kl33xjpZz+TTjvN37oAAEB1IjhjSnr5ZRean3rK3TdGuuYa6fOf97UsAABQxQjOmHJeesmF5j/9yd03RrruOunUU30tCwAAVDmCM6aUl16SDj5Y+vOf3f1p06Trr5dOOcXfugAAQPUjOGPK+Oc/XWj+y1/c/WnTpBtukE4+2d+6AABAbSA4Y0r4xz9caP7rX939adOkn/9c+sxn/K0LAADUDoIz6t4//iF98pPS00+7+9OmSTfdJJ10kr91AQCA2jLN7wKAybRqVXZonj5duvlmQjMAACgePc6oWy++6ELzM8+4+9OnS7fcIkUi/tYFAABqE8EZdSlfaL71Vikc9rcuAABQuxiqgbqzapWbCOiF5hkzpCVLCM0AAGBi6HFGXfGWnPvf/3X3Z8yQbrtNOu44f+sCAAC1jx5n1A1vc5PMiYBLlhCaAQBAealJEUIAABtASURBVBCcURdefjl7cxNvTPPxx/tbFwAAqB8EZ9S8V16RDjkkexvtm25iTDMAACgvgjNq2quvSqGQ9NRT7v60adKNN0onnuhvXQAAoP4QnFGzVq+WWlqkJ55w942Rrr9e+vSn/a0LAADUJ4IzatLQkAvNjz3m7hsjXXeddMopvpYFAADqGMEZNSeZlA49VIrH3X1jpJ/9TDr1VH/rAgAA9Y3gjJqyZo102GFSf3+6bfFi6bTT/KsJAABMDQRn1IzXXpMOP1x69NF0W1eX9MUv+lcTAACYOgjOqAmvvy4dcYT0xz+m2668UlqwwL+aAADA1EJwRtV74w3pU5+SHn443Xb55dIZZ/hXUyX09PSora1NkUhETU1N6uvrK/ixyWRS0WhUkUhkuC0ej8sYM+qts7NzMl4GAAB1Y4bfBQBjefNN6cgjpd/9Lt32k59IZ5/tX02V0NPToyVLlqi7u1uS1NfXp5aWFg0MDKixsXHMx3Z1dSkWi2nx4sUjzg0Gg4pGo1ltyWRSixYtUmtra3lfBAAAdcZYa/2uYUpqbm62/Zkz3DDCW2+50PzrX6fbLrtM+spXfCupYhoaGhSLxRQKhbLaQqGQYrHYqI/zQvPAwMCIY/F4XP39/SMCstfT3N7eXqbqAQCoLcaYAWtt83jn0eOMqvTWW9K8edmh+Yc/nBqhOR6PK5FIqLk5+99vKBQac7hGPB5XW1ubBgcH8x4PBAJZQVxyvc1LlizJG7QBAEA2xjij6qxdKx1zjPTAA+m2jg7pv/7Lv5omoqurS5FIRLNmzRq+5Rtj3NDQIElKJBKSXNDNFAgEho/lE41GFQ6HFQwG8x4PBoMjjkWjUS1cuHAiLw8AgCmD4Iyq8vbb0rHHSpkdq4sWSbU8iqC1tVXd3d1qbm5WMplUd3e3rLVZt1gsNhxqV69enfd5tt1221GvkUwm1dfXpz322EPRaHQ4nEciESWTybyP8YZuhMPhib9IAACmAIJzHsaYgDEmbIxpT30NFPCYkDFmwBgz9swtjOrtt6XjjpN+9at02/e/L51/vn81lZMXiHOHS0jS/Pnzh4PzaEF3LN4QjiVLlujEE0/U0NCQYrGYenp6tGCUNfsWLFigjo6Ooq8FAMBUxRjnHMaYVkkjZl8ZYyLW2p5RHhOQ1C0pIKn41AOtWyeFw9J996XbLrxQuuAC/2oqt3g8PuowikAgMLx0XO4QjUyjPd4L5ZkrabS2tqq3t1c9PSO/bbu6uiTlD/EAACA/epxHikmKSpqVunlrd3WP0fPcIanwRXaRZf166cQTpXvvTbd961vuVi+8XuSxlpLzQqwXjnPHM7/66qujBufZs2dLGhm699hjj7y1RKNRLV68uMDqAQCARHDOkgrGPdbaTmttMnXrlNSVOmVE91xqaEZS0uiztjCqd96RTj5ZuuuudNvXvy595zu+lTQpvKUH8wXZXN5qGrkraPT19amtrS3vY7xAni9s54b1BQsWKBgMjrseNAAAyEZwHmlRnrbe1NfZeY4ttNZG87RjHBs2SJ//vJTa40OSdN55blyzMb6VNSni8bik0YdaZAoEAmptbc0af+w9PnMiXzQaHV6JIxgMKhwOZz0mmUyqp6cnq2e5r69PPT09rKQBAEAJajY4pybwxYwxvQWe22GMGTTGDKVuvbkT+VI9zPE8T+EF5qwdS1LjoZeU/CKmsI0bpQULpJtuSrd9+ctSZ2dlQ3NXV5eamppkjFFLS8twQB3vMcVO4FuxYoUkKRKJjFiGbtasWSPOj8ViCofDamlpUVtbm2KxmJYvXz7mNbq7u9XY2KhIJKJoNKpoNDrc5mlra1MgEGAlDQAASlBzOwcaY0KS2iR5P/nj1tqmMc4PShqQG4O8wFqbTD1HTFJQUou1dszxycaYAUmrrbUtGW0BSYuttZHU/Q5J7ZIarLXjDtuYyjsHWiuddZZ01VXptrY26corKxuaOzs7h7eabmhoGJ5IF4vFxtx+OhKJaPHixWNO4svV1NSkeDyuWvv3BgDAVFB3OwdmhN3ZcsMpEnJBdTzdkhJewJUka22fMSYiF6i75SYBjnbdsFzAPiTnUIfSEwdRIGvd7n+Zofm006QrrqhsaE4mk1q0aJFWrlw5HIBbW1vV19enlpYWDQ4OjrpUWyKRKCo0S26oBWOKAfz/9u4vRJKr7OP473FjjBrc3t33NYghIT1oQNSLnlVQb4LOGAzGf9lJ/BNQCZkBRVCUNCtEEYVhVpEoiM4sQcSArjOiJho13euFeCM7M+iFeuPMEm9ykZdML8GgxuS8F+fUdG9P/6n+U1V9ur8faGarprrmzD5d00+fes45AOIWU6nGM5KqzrkTYcBe53WFW4Skt6IO08uFkoxdSaVQctHp+WX5BHneOddo2V+R1EjTs4wm56RqVfr2t5v77r1XOn9eeknOr8SNjQ2tra0dSYAXFha0s7NzuNpfu2q1OvAUbsmAvfYltAEAQFyi6XFuSXQHcU/42q0Uoy6fWC+qOXOGpMNSjJqkpQ4J8nlJFTPr1OO9Z77rdL5LvfTM+tKXpK9/vbm9tCR9//vSsWP5t2Vvb0/VaucbBpVKRZcvX9b8/Lzm5uYO64I3Nze1v7+vnZ2dgX5WkjgnA/kAAECcokmch7QgST16hpNe60730C9KWumS/N6vozNsJHXXS2J6uiO+9jX/SHzgA35g4DUFvQJLpVLPGS5KpdJhcr266idaSXqjhynTkHrP4byxsaGFhYVUs24AAIBiTG3iHHqM+2U4SXJ7VbYSZuqodhs02CmZNrNk4OAuJRxXO3dOevDB5vYdd0g//rH00pcW16a0S02vra2NvCx1MqNGr6R4c3Oz54BEAABQvKlNnNVMhnvNG/ZM+46QNJclLYUBhEnPcpKEL7XWO7cotX2FpIce8nXNicVF6ac/lV72suLalLekxzlZ3a9Vo9HQ9vb2kYVLAADA5JnmxDmNqxJgM1tXc3XAbt1/J1ufF6ahq7Q8b9PM6pLW2nuewyDEZUm66aabRm78pPvud6XPfa65fdttfoXA664rrEm52t/f19LS0mFS3Gm+5sSgAw4BAED+pjlx7rTKX0/OuRX5WuVBnpN6Sjrn3IbCIMTTp09P9YS+Dz/s52pOvOMd0mOPSa94RXFtylu5XB54ICEAAJhcMU1HN6ikDCNN6cRgy8Chpx/+0K8KmHjrW6XHH5euv764NgEAAIxqmhPnNMlwklRTYDomFy5In/iEn7NZkioV6Te/kV71qkKbBQAAMLKpTZxb64vDQiadJOUcs7n29Zj97GfSxz4mvfii337zm6UnnpB6lPYCAABEY2oT56DjdHMtkol1azm0Zar98pfSPfdIL7zgt9/wBqlWk06dKrZdAAAA4zLtifNW+Hp07WTvLeFrt5UFkcITT0h33SU9/7zfft3rpHpdevWri20XAADAOE174rwavt7d/o1QvnFG0rku8zIjhd/9Tnr/+6X//Mdvl8t+32teU2y7AAAAxi3mxDlZqa8cVgk8IiTEi5JKZlZLjgtJc01SfZDp5MbBzO40s40rV67k+WMz8Yc/SHfeKf3rX377ppt80nzjjcW2CwAAIAtRJc5mtmxme2Z2IN9bLPmZMQ7C/s3254Rls+fC5uXw3JqkdefcYvvxWXPOPeacWz5+/HjeP3qsLl3yS2c/95zffu1rfdJ8883FtgsAACArUS2A0rqAyIDP21ezhxoj+vOfpdtvl5591m/fcIN08aI0N9f7eQAAADGLqscZxfvb36TFRengwG+fOuUHAt56a7HtAgAAyBqJM1Lb25Pe9S7p6af99vHjfkaNN76x2HYBAADkgcQZqfzjHz5pfuopv/3KV0q//rVfGRAAAGAWkDijr6ee8knzk0/67euu8wuevO1txbYLAAAgTyTO6Onpp6WFBenvf/fb114r/fzn0m23FdosAACA3JE4o6uDA+nd75b++le/feyY9JOf+Bk1AAAAZg2Jc85iWQDl2Wel97xH+tOf/LaZ9MgjfpVAAACAWUTinLMYFkB57jnpve+V/vjH5r6HH5Y+/OHi2gQAAFA0Emdc5d//lj74Qen3v2/u+853pE9+srg2AQAATAISZxx6/nnp7rv93MyJb3xD+tSnimsTAADApCBxhiTphReke++VHn20ue8rX5E+//ni2gQAADBJSJyhF1+U7rvPz5iRqFalBx8srk0AAACThsR5xjknffrT0g9+0Nz3mc9Iq6t+Jg0AAAB4JM4zzDnpC1+Qvve95r777pMeeoikGQAAoB2J8wz78pelb36zuf3Rj0rr69JLeFUAAAAcQYo0o1ZXpa9+tbn9oQ/5co1jx4prEwAAwCQjcc7ZJKwc+K1vSV/8YnP7jjukH/1IuuaawpoEAAAw8Uicc1b0yoHnz0uf/Wxz+53vlLa2pGuvLaQ5AAAA0SBxniGPPCKtrDS33/526Re/kF7+8uLaBAAAEAsS5xmxtSV9/ON+Jg1Jmp+XHn9cuv76YtsFAAAQCxLnGfCrX0kf+Yhf6ESS3vQm6be/lQqqFgEAAIgSifOUu3hRuusu6b//9du33irVatKpU8W2CwAAIDYkzlPun/9slmfccotUr0s33FBsmwAAAGJE4jzl3vc+6dFHpde/3vc+33hj0S0CAACIEzP3zoDbb5f+8hfmaQYAABgFPc4zgqQZAABgNCTOAAAAQAokzgAAAEAKJM45M7M7zWzjypUrRTcFAAAAAyBxzplz7jHn3PJxVh8BAACICokzAAAAkAKJMwAAAJACiTMAAACQAokzAAAAkAKJMwAAAJACiTMAAACQAokzAAAAkAKJMwAAAJACiTMAAACQgjnnim7DTDKzpyU92bLruKRu63AP+r1O+/5H0v8N2Mws9Ppd8jxf2uelOa7fMd2+P8j+aYxf1rFLe2zW1540GfGL7dpLcyzXXr7nmuRrr9v+SYjfNF57/Y6JMW+52Tn3v32Pcs7xmICHpI1xfa/Lvu2if8d+v0ue50v7vDTH9Tum2/cH2T+N8cs6duOI3ziuvUmJX2zXXppjufbijV2/Y4b53qTGbxqvvXHHb1Jj1+lBqcbkeGyM3+t1fNHG3bZhz5f2eWmO63dMt+8Pun8SjLNtWccu7bFce/meb5zx49rL91yTfO2l/ZlFmMZrr98x0/S38yqUaswIM9t2zp0uuh0YDvGLG/GLF7GLG/GL16TGjh7n2bFRdAMwEuIXN+IXL2IXN+IXr4mMHT3OAAAAQAr0OAMAAAApXFN0AzA5zKwkaU3SSUkVSfuSVpxz+4U2DJgB4fpbkFSWv/bqzrlGsa1CGmb2gKR71Py7uSVplfgB2TGzM5JWJLVfZyVJm865TEo9SJwh6fBNe0fSknNuN+zblLRjZrfwBhCP5E3cOTdfdFuQjpktS1rvsH/JObdVQJOQkpmtS7pbvh5zXdKSpAfkk+jFApuGIZjZgnwH0v3JeyEmVlm+s6Ehnyy3yix21DhDkmRma5LKzrmlln0lSQeSqs65c4U1Dn2ZWUX+k/dy2NVwzp0osEkYgJk5SVU1B8Msy795S9IJPrhOLjPbaf+QamY78okzsYtIeM+7LJ+EzXG3dbKFDodS3vkJNc5ILEuqte4If/D35RMyTLYkyZpThp+0MX7hzXrLOXfOOdcIj3NqJtELBTYP/R25UyDpQu6twDisSaoX3QgMJPcPpiTOkJmV5T9hd/p0vSt/OwQTzDm36JxL6tGfKbo9GNhqh33JB9mTeTYEg+lSRzkn/2GI3uZIhLt2SWcR4lBSAe93JM6QeifGJGFAhkIPc6e7BEnCvJ1nezCaUCN7WtL9RbcFAznrnKsW3QgMrGxm62Z2EB618CEoMyTOkTGzUniR1FIeu2Zme31eVElRfackuZGca8SmQ5nFDznJOX4r8jNrUHozBlnHzsw2Q21zTf5vKSU2Y5Rl/EKtLOU1Gcn42jsrn6dU5ctsFuQnNcjsfZLEORJmthBmuTiQr0fuefs2lF9clu9Nng8DxZbC9k7oFUn0vRXMLcfRZBw/ZCzv+IVplsrhORhBjrFbD4ME58L2ZpjhBiPIOn6hU2iR2WvGL4drb1fSLc65qnNuI0xukIzJWlNGSJwnXHjh7UnalHRJUtrRo5uS9p1zS0nS65yrq/lGvNlybNLT3OlFXVIBxffTIqf4ISNFxC+8eazJv3Fw7Q0p79iFYxTGGSTHnh2y+TMvx/ityfdWYkzyip1z7shc92HMQUMZ3vEhcZ58z8hPB3cijLTf6/eE0FtVUYfR3uG2766kUrg9JTUHQ3Qqxzgp6pxHkUf8kJ1c4xd6v2ry86kzSGk0hV17LTMSUeI2vMzjlwwI5Fobu6Lf97aV4SBPEucJ55zbHeIW0j3ha7dpdZL9yeT8+23brcryq2BhCDnFDxkpIH4X5VfrpK55RHnELrzZ90Ich5TTtXde0gNm5pKH/OI1krQX9jGmZEA5XXu9PpSe7HGekbFy4HRakA5vGXaSfPqrhOMaZrYrPxK8XUWMDs/bQPHDxBkqfmHgTDW55Y9CDBq7spkttMcslNuUJbF6Z74Gjd/9OlqiuCLpjHx5ANPT5WfQ2J01s/X24605vW5m5TckzlMmfArrd3sweaG1TkNXlVQzs+VkXlLzqwlu0PuVnxHihwkwbPxC0lyWtGRmS2q+mSfnOqz5QzaGjF1d0kXzS6PXw3nK8rebF/nbmZ9h4tcpPmaW9EbvUsKRjyGvvXX5nGUxiVO4O7CmjP9ekjhPn+RF1etFc6Rm2TlXN7N5SWvhjbsh6RLzWuZuqPi1OSlqK4sycPzMbF3NgSzd6vdO9jknRjdw7Jxzu2ZWl59BQ2rWVvJBJ3/j+NspNf928jc0P8Nce/tmtiV/7ZXlr72acy7zEkYS59nU8cUZPn1TNzv5jsQvfGJfk/8DVAn7duT/mFR5E58o7aPAV8Sy9rE4ch2FKbAQh65/B8Md1oqaH2I3w4eiNXqeJ0Kna6+Qjj0S5+nD8rxxGyp+ITEm+Soe11+8iF3cRoofd1cLFdW1x6wa0ye5nZHmNhO9kJOH+MWN+MWL2MWN+MUrqtiROE+fNC+q5MXJ7afJQ/ziRvziReziRvziFVXsSJynTGstViiY7yS5LbKdfYswCOIXN+IXL2IXN+IXr9hiR+I8nfpNV5bMg1jLoS0YHPGLG/GLF7GLG/GLVzSxI3GeTsmKPd1Ge78lfGWhhclE/OJG/OJF7OJG/OIVTexInKfTavh6d/s3wm2QM5LOMUXZxCJ+cSN+8SJ2cSN+8YomdiTO8UnmWS53W6s9vLAWJZXMrJYcF158NUl1pt4pDPGLG/GLF7GLG/GL11TFjsQ5Ama2bGZ7ZnYg/6lL8iNMD8L+zfbnhOVf58Lm5fDcmqT1PFbWQRPxixvxixexixvxi9c0x86cc0W3AQAAAJh49DgDAAAAKZA4AwAAACmQOAMAAAApkDgDAAAAKZA4AwAAACmQOAMAAAApkDgDAAAAKZA4AwAAACmQOAMAAAApkDgDAAAAKZA4AwAAAClcU3QDAADZM7NSp/3OuUbebcnLLP7OALJFjzMAFMzMzpjZnpkddHi4Ho+dAX7MjqSDlseOpLWUbVs3s5229hyEfZtmtmxm5eF++6t+1maX/4M9M1vo8pxah/+v5P/lfIffe3PUdgKYXeacK7oNAAAd9pBellSStC9pSVJr72hJ0klJFUlnJdWdc0spz12TtBDOO9+v19XM1iQth80NSZfCcxst7ViUdEZSkjRXnXPn0rSnx89t/T+QpBNpeojNbDO0ZcU5t9HjnFtp/88AoB2lGgAwIZxzDTPbl0+MG8653S6H1s1Mkk4N8WN2eyWiZlaR75UtyyfM1R7H1yVVzWxZ0rqkbu1NLfwfrKrZG74gaSvFU8uS9tuT5pZzbodzPTNqGwHMLko1AGA2JMlv18QxlFtclE9Cl5xzK2l6e0Oyui9pexwNlU/YEyv9Dg49yhWlKD0BgFGQOANAnLbke3nHqSZfzlB3zqXp5b3KuAbdhfMkP3+h2yC/FsvheUd6mwFgnEicASBCzrl959z+uM5nZg+oWavct5e3Q3vmxtWWoPVDwXLXo7wVXd1L3Umj7SsADIzEGQAiE5LccTsbvu6OMyFPhNk5ai2zh9RCbXRHzrm6fPmH1CORD7NtlEWZBoAckDgDQHwG7hHuJdQ2J+UQ46pTPjy3me3Jt7kaeqZvke/5XQ+zfXST9DqXw6DFTlaUUbIPAO1InAFgMpVC0tn+yKK3uTUp3RvXSUNCvic/Q8hiMkuIc64RpoRryNcwd+t5bi2/ONvlmDOSVsfVZgDohcQZACZTknS2P7IoSTiZwTml5mIj3QYxJolxxx70tkGCZ9q/HxLuxjADGQFgGCTOADCZdp1z1vqQdEJ+UZRxa52ibiyD/FqmiJOatcrtkt7tbmUYUktvcoee6TSDAgFgbFgABQAikfTAhlX9xqk1se27dHZIitfUeYaKWhjY13qeWliwpdPxu+qeWMs5txsWhSmrJVEOZSAVZfNBAgA6InEGgPiMtTQhJKfJ5kKK4xtmti6fzC6qOV3clpqDC1vLP+Z7rIKYxpp8uUfFzMphIOCK/HzTDAoEkBtKNQAgMs65aganPSx5SDMA0Tm365zbcs611idfalkEZaBe7D5+0vLv5OctiynoAOSMxBkAImVmlRSr6qXVmoSeHfK8h6UYbT3Bi0O3SkcGCS6b2Zmwvz7KeQFgUCTOABCv8xq9N1fSYaKb1AuXJF0cQ1KeJLbLoSZ5FMkgwZL8782gQAC5I3EGgHhVNMYlpMO0bkkpREXSTliZr6s+yXVrL/ZOp+Q59Jr3W1JboUY66cUuqfsUdwCQGQYHAsBkSZLLUlgtrz0xLskPvFuSjpREjMw5t2FmdfnEdEF+RoxdSRd09QwYZTVnulBo537buepmthLOVZK0Z2Yb8tPQnZJPzk9Lmk/ZvC1JD4iVAgEUhMQZAAoWem13dHXZRTnsy11IShdDD/EZ+RrlFTXbty+fKG/LJ8VdZ7doScSr8on4cstzN51zg9Q/X5BPnC8M/EsBwBiQOANAwcLgt7EsPDJOIRk+Fx6jnqfj6oADnmdXkvU9sLNS21cAGBg1zgAAAEAKJM4AMFtO9j8EANAJiTMAzIakRGEs09dF6HT4ygcHAEMjcQaA2ZAkzBUzOzCzHTOb6pX3zGw9/J4HosYZwBiYc67oNgAAMhZmyGhPGhvTPK3bLP7OALJF4gwAAACkQKkGAAAAkAKJMwAAAJACiTMAAACQAokzAAAAkAKJMwAAAJACiTMAAACQAokzAAAAkML/Azoi0LA52e4gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 792x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Building the diffusion coefficient from Tomassetti THMb ###\n",
    "\n",
    "rigidity_array_D = np.sqrt(E_e**2 + 2*m_p * E_e)\n",
    "\n",
    "\n",
    "### Parameters to implement the variable slope from Tomassetti ###\n",
    "##################################################################\n",
    "ref_rigidity_tomassetti = 2.     # in [GV]\n",
    "delta_HIGH_tomassetti = 1./6.\n",
    "Delta_tomassetti = 0.55\n",
    "csi_tomassetti = 0.1\n",
    "ref_E_0 = 1.                     # in [GeV]: D(E) = D_0 (E/E_0)^delta\n",
    "\n",
    "ref_energy_tomassetti = np.sqrt(ref_rigidity_tomassetti**2 + m_p**2) - m_p   # in [GeV]\n",
    "\n",
    "\n",
    "delta_tomassetti_variable = delta_HIGH_tomassetti + Delta_tomassetti / ( 1 + ( csi_tomassetti/(1-csi_tomassetti) ) * pow( rigidity_array_D[:len(E_e)-1] / ref_rigidity_tomassetti, Delta_tomassetti) )                \n",
    "print (\"Minimum slope for D(E):\", min(delta_tomassetti_variable))\n",
    "print (\"Maximum slope for D(E):\", max(delta_tomassetti_variable))\n",
    "print (\"\")\n",
    "\n",
    "\n",
    "D_0_low = D_0_yr/conv_factor_yr_to_sec * (min(E_e) / ref_E_0)**(max(delta_tomassetti_variable))\n",
    "\n",
    "\n",
    "D_next = np.zeros(len(E_e))\n",
    "for iD in range(len(E_e)):\n",
    "    if iD == 0:\n",
    "        D_next[iD] = D_0_low\n",
    "    else:\n",
    "        D_next[iD] = D_next[iD-1] * (E_e[iD] / E_e[iD-1])**delta_tomassetti_variable[iD-1]\n",
    "\n",
    "    \n",
    "D_next_function = interpolate.interp1d(E_e, D_next, kind='cubic', bounds_error=False)\n",
    "\n",
    "##################################################################\n",
    "\n",
    "\n",
    "plt.figure(figsize=(11,7))\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.tick_params(axis='both', which='major', labelsize=26)\n",
    "ax.tick_params(axis='both', which='minor', labelsize=26)\n",
    "ax.xaxis.set_tick_params(pad=7)\n",
    "ax.xaxis.labelpad = 7\n",
    "\n",
    "\n",
    "\n",
    "plt.loglog(E_e, D_next_function(E_e), lw=3, label='Tomassetti, ApJ vol. 752, n. 1 (2012)', color='blue')\n",
    "plt.text(4, 1.e+24, '$\\sim E^{0.67}$', fontsize=23)\n",
    "plt.text(2.e+4, 3.e+25, '$\\sim E^{0.17}$', fontsize=23)\n",
    "plt.legend(frameon=False, fontsize = 21)\n",
    "plt.xlabel('E [GeV]', fontsize=27)\n",
    "plt.ylabel('$D(E) \\, \\mathrm{[m^2 \\, s^{-1}]}$', fontsize=27)\n",
    "\n",
    "\n",
    "plt.savefig('Diffusion_coefficient_Tomassetti.pdf',format='pdf',bbox_inches='tight', dpi=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I am examining the object Sample 1\n",
      "I am examining the object Sample 2\n",
      "I am examining the object Sample 3\n",
      "287.380045 seconds\n"
     ]
    }
   ],
   "source": [
    "#############################\n",
    "# Calculating the integrand #\n",
    "#############################\n",
    "\n",
    "\n",
    "start = time.process_time()\n",
    "\n",
    "\n",
    "steps_t_integral = 1000   # 40000, to make the high-energy wiggles disappear\n",
    "int_var_length = 100\n",
    "\n",
    "result_integrand_matrix = np.zeros( (  considered_objects,len(E_e),steps_t_integral  ) )\n",
    "t_integral = np.zeros( (considered_objects, steps_t_integral) )\n",
    "\n",
    "for i in range(considered_objects):\n",
    "\n",
    "    print (\"I am examining the object\",object_name[i])\n",
    "    r[i] = r_kpc[i]*1000*conv_factor_pc_to_m    # distance of the object, in [m]\n",
    "\n",
    "    \n",
    "\n",
    "#######################################################################################################\n",
    "# given the parameters found for the specfic object, I now define the functions plotting the spectrum #\n",
    "#######################################################################################################\n",
    "\n",
    "    start_time = 1.\n",
    "    stop_time = object_age[i]\n",
    "    t_integral[i] = np.logspace(np.log10(start_time), np.log10(stop_time), num=steps_t_integral, endpoint=True)  # time-step, in [yr]\n",
    "\n",
    "\n",
    "###### Section dedicated to the calculation of the integral giving the spectrum #######\n",
    "\n",
    "\n",
    "## The following matrix keeps track of the different instants of life (along the columns) of the particles of a certain measured energy (in the rows) ##\n",
    "    E_t_prime_matrix = np.zeros( (  len(E_e),len(t_integral[i])  ) )\n",
    "    numerator_no_loss_matrix = np.zeros( (  len(E_e),len(t_integral[i])  ) )\n",
    "    loss_ratio_matrix = np.zeros( (  len(E_e),len(t_integral[i])  ) )\n",
    "    exponential_factor_matrix = np.zeros( (  len(E_e),len(t_integral[i])  ) )\n",
    "    denominator_matrix = np.zeros( (  len(E_e),len(t_integral[i])  ) )\n",
    "    \n",
    "    \n",
    "    ## Calculation of the diffusive distance with variable delta ##\n",
    "    ###############################################################\n",
    "    integrand = np.zeros( (len(E_e), len(t_integral[i]), int_var_length) )\n",
    "    r_diff_square_variable = np.zeros( (len(E_e), len(t_integral[i])) )\n",
    "    \n",
    "    \n",
    "    for ie in range(len(E_e)):\n",
    "        \n",
    "        index_current_energy = np.argmin(abs(E_e[ie] - ODE_sol_array))\n",
    "        \n",
    "        for it in range(len(t_integral[i])):\n",
    "            \n",
    "            \n",
    "            current_t = time_ODE[index_current_energy]\n",
    "            delta_t = abs(object_age[i] - t_integral[i][it])\n",
    "            target_t = current_t - delta_t\n",
    "            target_t_index = np.argmin(abs(target_t - time_ODE))\n",
    "            \n",
    "\n",
    "            if (1 - b_0_yr * (object_age[i] - t_integral[i][it]) * ODE_sol_array[index_current_energy] > 0.):\n",
    "                \n",
    "                E_t_prime_matrix[ie][it] = ODE_sol_array[target_t_index]\n",
    "                integration_variable = np.zeros(int_var_length)\n",
    "                min_integration_variable = E_t_prime_matrix[ie][it] / ref_E_0\n",
    "                integration_variable = np.logspace(np.log10(min_integration_variable), np.log10(ODE_sol_array[index_current_energy]/ref_E_0), num=int_var_length)\n",
    "                \n",
    "                integrand[ie][it] = (D_next_function(integration_variable)/conv_factor_sec_to_yr) / loss_rate_KN(integration_variable * ref_E_0)\n",
    "                r_diff_square_variable[ie][it] = 4 * integrate.trapz(integrand[ie][it], integration_variable)\n",
    "                \n",
    "                #integrand[ie][it] = diffusione(integration_variable) / loss_rate_KN(integration_variable * ref_E_0)\n",
    "                #r_diff_square_variable[ie][it] = (4 * D_0_yr_SBPL * ref_E_0) * integrate.trapz(integrand[ie][it], integration_variable)\n",
    "    ###############################################################\n",
    "    \n",
    "\n",
    "    for e in range(len(E_e)):\n",
    "\n",
    "        index_current_energy = np.argmin(abs(E_e[e] - ODE_sol_array))\n",
    "        \n",
    "        ## When this energy is released\n",
    "        t_rel_E = t_range_release[np.argmin(abs(ODE_sol_array[index_current_energy] - Escape_energy_vs_time_el))]\n",
    "\n",
    "        for t in range(len(t_integral[i])):\n",
    "\n",
    "            \n",
    "            current_t = time_ODE[index_current_energy]\n",
    "            delta_t = abs(object_age[i] - t_integral[i][t])\n",
    "            target_t = current_t - delta_t\n",
    "            target_t_index = np.argmin(abs(target_t - time_ODE))\n",
    "\n",
    "\n",
    "            if (1 - b_0_yr * ( object_age[i] - t_integral[i][t] ) * ODE_sol_array[index_current_energy]) > 0.:\n",
    "\n",
    "                E_t_prime_matrix[e][t] = ODE_sol_array[target_t_index]\n",
    "\n",
    "                if E_t_prime_matrix[e][t] != 0.:\n",
    "\n",
    "                    if r_diff_square_variable[e][t] != 0.:\n",
    "                        \n",
    "                        numerator_no_loss_matrix[e][t] = N_0 * pow( E_t_prime_matrix[e][t] , -gamma_inj ) * ( 1 / pow( 1 + t_integral[i][t]/(tau_dec[i]) , alpha_dec[i]) )\n",
    "                        loss_ratio_matrix[e][t] = loss_rate_KN(E_t_prime_matrix[e][t] * ref_E_0) / loss_rate_KN(ODE_sol_array[index_current_energy] * ref_E_0)\n",
    "                        exponential_factor_matrix[e][t] = np.exp( - pow( r[i], 2) / r_diff_square_variable[e][t] )\n",
    "                        denominator_matrix[e][t] = pow( pi * r_diff_square_variable[e][t] , 3/2 )\n",
    "\n",
    "                        if (t_integral[i][t] >= t_rel_E*1.e+3):\n",
    "                            result_integrand_matrix[i][e][t] = (tau_dec[i]) * (c/(4*pi)) * (numerator_no_loss_matrix[e][t] * loss_ratio_matrix[e][t] * exponential_factor_matrix[e][t]) / denominator_matrix[e][t]  \n",
    "\n",
    "                            \n",
    "print (time.process_time() - start, \"seconds\")  \n",
    "\n",
    "## Now I have an integrand matrix that contains the current energy-values in the rows and the different release-times in the columns ##\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/matplotlib/font_manager.py:1241: UserWarning: findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(13,9))\n",
    "\n",
    "\n",
    "J_e = np.zeros( (considered_objects,len(E_e)) )  \n",
    "\n",
    "for i in range(considered_objects):\n",
    "    for e in range(len(E_e)):\n",
    "        J_e[i][e] = integrate.trapz(result_integrand_matrix[i][e], t_integral[i]/(tau_dec[i]))\n",
    "\n",
    "\n",
    "\n",
    "f = mticker.ScalarFormatter(useMathText=True)\n",
    "f.set_powerlimits((-5,5))\n",
    "object_age_latex = []\n",
    "for i in range(considered_objects):\n",
    "    object_age_latex.append(\"${}$\".format(f.format_data(object_age[i])))\n",
    "    \n",
    "\n",
    "legend_label = []\n",
    "for i in range(considered_objects):\n",
    "    legend_label.append( '$t_{\\mathrm{age}} = \\,$' + str(object_age_latex[i]) + '$\\, \\mathrm{yr}, \\, d = \\,$' + str(int(r_kpc[i]*1000)) + '$\\, \\mathrm{pc}$')\n",
    "\n",
    "        \n",
    "for i in range(considered_objects):\n",
    "    plt.plot(E_e, J_e[i]*(E_e**3)*conv_factor_yr_to_sec, lw=2, color=multiplot_color[i], label=legend_label[i])\n",
    "        \n",
    "plt.plot(E_e, J_e[1]*(E_e**3)*conv_factor_yr_to_sec, lw=3.5, color='blue')   # mark the second curve\n",
    "\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.tick_params(axis='both', which='major', labelsize=27)\n",
    "ax.tick_params(axis='both', which='minor', labelsize=27)\n",
    "ax.xaxis.set_tick_params(pad=7)\n",
    "ax.xaxis.labelpad = 7\n",
    "\n",
    "\n",
    "\n",
    "### Plot cosmetics ###\n",
    "leg = plt.legend(fontsize = 20, frameon=True, framealpha=0.9, facecolor='white', edgecolor='white', loc='best')\n",
    "\n",
    "\n",
    "plt.axis([1.e1,3.e4, 1.e0,3.e2],interpolation='none')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'$E_{k} \\, [\\mathrm{GeV}]$',fontsize=27)\n",
    "plt.ylabel(r'$E^{3} \\cdot \\Phi_{e^{\\pm}}(E) \\, [\\mathrm{GeV}^2 \\, \\mathrm{m}^{-2} \\, \\mathrm{s}^{-1} \\, \\mathrm{sr}^{-1}]$',fontsize=27)\n",
    "\n",
    "\n",
    "plt.savefig('Electrons_DifferentAges_VariableDelta_KN_EnDepRelease.pdf',format='pdf',bbox_inches='tight', dpi=200)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center>Total energy budget of the source\n",
    "    \n",
    "$$\n",
    "\\begin{align}\n",
    "E_{\\mathrm{tot}} &= \\int d^3 \\vec{r} \\int^{t_{\\mathrm{age}}}_{t_{\\mathrm{rel}}} dt \\int_0^{+ \\infty} dE \\, E \\cdot Q(E, \\vec{r}, t), \\qquad \\qquad \\qquad Q(E, \\vec{r}, t) = S_0 \\left( \\frac{E}{E_0} \\right)^{-\\Gamma_{\\mathrm{inj}}} \\, \\delta(\\vec{r}) \\, L(t) \\\\[10 pt]\n",
    "&= L_0 \\, E_0^2 \\, S_0 \\cdot \\tau_{\\mathrm{d}} \\int^{+ \\infty}_{0} d\\omega \\cdot \\omega^{-\\Gamma_{\\mathrm{inj}} + 1 }  \\int^{t_{\\mathrm{age}}}_{t_{\\mathrm{rel}}(\\omega)} dz \\, \\frac{1}{\\left( 1 + z \\right)^{\\alpha}} \\\\[10 pt]\n",
    "&= N_0 \\cdot \\tau_{\\mathrm{d}} \\int^{+ \\infty}_{0} d\\omega \\cdot \\omega^{-\\Gamma_{\\mathrm{inj}} + 1 } \\int^{t_{\\mathrm{age}}}_{t_{\\mathrm{rel}}(\\omega)} dz \\, \\frac{1}{\\left( 1 + z \\right)^{\\alpha}}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Energy budget in electrons of object 0 = 8.357229523844477e+47 [erg]\n",
      "Energy budget in electrons of object 1 = 1.0149253786212213e+48 [erg]\n",
      "Energy budget in electrons of object 2 = 1.1587921642888901e+48 [erg]\n"
     ]
    }
   ],
   "source": [
    "def f_time(z, alpha_var):\n",
    "    return pow(1 + z, -alpha_var)\n",
    "\n",
    "\n",
    "\n",
    "integration_var_omega = np.logspace(np.log10(1./ref_E_0), np.log10(max(E_e)/ref_E_0), num=len(E_e))\n",
    "integrand_temp = np.zeros( (considered_objects,len(E_e)) )\n",
    "integrand_omega = np.zeros( (considered_objects,len(E_e)) )\n",
    "t_rel_E_omega = np.zeros(len(E_e))\n",
    "\n",
    "\n",
    "for ic in range(considered_objects):\n",
    "\n",
    "    for ie in range(len(E_e)):\n",
    "\n",
    "        integrand_temp[ic][ie] = integration_var_omega[ie]**(-gamma_inj + 1)\n",
    "        \n",
    "        ## When this energy is released\n",
    "        t_rel_E_omega[ie] = t_range_release[np.argmin(abs(E_e[ie] - Escape_energy_vs_time_el))]*1.e+3\n",
    "\n",
    "        integral_time, error_time = integrate.quad(f_time, t_rel_E_omega[ie]/tau_dec[ic], object_age[ic]/tau_dec[ic], args=alpha_dec[ic])\n",
    "\n",
    "        if (t_rel_E_omega[ie]/tau_dec[ic] < object_age[ic]/tau_dec[ic]):\n",
    "            integrand_omega[ic][ie] = integrand_temp[ic][ie] * integral_time\n",
    "            \n",
    "\n",
    "            \n",
    "Energy_budget_EnDepRelease = np.zeros(considered_objects)         \n",
    "for ic in range(considered_objects):\n",
    "    \n",
    "    Energy_budget_EnDepRelease[ic] = N_0 * tau_dec[ic]*conv_factor_yr_to_sec * integrate.trapz(integrand_omega[ic], integration_var_omega)\n",
    "    print ('Energy budget in electrons of object', ic, '=', Energy_budget_EnDepRelease[ic]*conv_factor_GeV_to_erg, '[erg]')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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