HII_structure.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## libs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math as m\n",
    "import scipy.integrate as integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "cm_in_pc = 206264.8 * 149.6e11  # cm\n",
    "\n",
    "freq_ion = 3.29E15  # Herz\n",
    "freq_max = 5.0E16  # Herz\n",
    "alpha = 2.59E-13  # cm^3 per sec\n",
    "temperature = 200000  # Kelvins\n",
    "radius_star = 0.3E10 / cm_in_pc  # pc\n",
    "r_inner = 0.05  # pc\n",
    "step = 0.005  # pc\n",
    "\n",
    "c = 2.99792458E10  # cm per sec, light speed\n",
    "h = 6.626070040812E-27  # erg*sec, Planck constant\n",
    "k = 1.380648528E-16  # erg/K, Boltzmann constant\n",
    "nH_total = 100  # cm^(-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "freq = np.geomspace (freq_ion, freq_max, 300)\n",
    "freq_tau = pd.DataFrame(data = {\n",
    "    \"freq\" : freq,\n",
    "    \"tau_previous\" : np.full(300, 0),\n",
    "    \"tau_current\" : np.full(300, 0)})\n",
    "\n",
    "result = pd.DataFrame(data = {\n",
    "    \"r\" : [],\n",
    "    \"n_e\" : []})\n",
    "\n",
    "r_current = r_inner \n",
    "check = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def brightness(freq):\n",
    "    \"\"\"Return mean brightness as a function of frequency\"\"\"\n",
    "    return 2 * h * freq**3 / c**2 / (np.exp(h * freq / (k * temperature)) - 1) \n",
    "    \n",
    "def sigma(freq):\n",
    "    \"\"\"Return photoionization cross section\"\"\"\n",
    "    return 6.3E-18 * np.power (freq_ion / freq, 3)\n",
    "\n",
    "def tau_step(freq_tau):\n",
    "    \"\"\"Return additional opacity caused by distance's step\"\"\"\n",
    "    \n",
    "    tau_new = 2 * freq_tau['tau_current'] - freq_tau['tau_previous']\n",
    "    freq_tau['tau_previous'] = freq_tau['tau_current']\n",
    "    freq_tau['tau_current'] = tau_new \n",
    "\n",
    "def tau(result, freq, n_e):\n",
    "    \"\"\"Return opacity on a distance r\"\"\"\n",
    "    \n",
    "    nH_ionized = nH_total - result[\"n_e\"]\n",
    "    distance = result[\"r\"] * cm_in_pc\n",
    "    \n",
    "    return integrate.trapz(y=nH_ionized, x=distance) * sigma(freq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_e = nH_total\n",
    "\n",
    "while np.abs(n_e) > 0.0001:\n",
    "    check = True\n",
    "    while check:\n",
    "        \n",
    "        PHI = integrate.trapz(m.pi * brightness(freq) *\n",
    "                             (radius_star / r_current)**2 *\n",
    "                              np.exp(-freq_tau['tau_current']) *\n",
    "                              sigma(freq) / (h * freq),\n",
    "                              freq)\n",
    "        \n",
    "        ksi = PHI / (n_e * alpha)\n",
    "        nH_neutral = nH_total / (1 + ksi)\n",
    "        nH_ionized = nH_total * ksi / (1 + ksi)\n",
    "        n_e_new = np.sqrt(n_e * nH_ionized)\n",
    "        if np.abs(n_e_new / n_e - 1) < 0.1E-5:\n",
    "            n_e = n_e_new\n",
    "            df = pd.DataFrame(data={'r': [r_current],\n",
    "                                    \"n_e\": [n_e],\n",
    "                                    \"nH_neutral\": [nH_neutral],\n",
    "                                    \"PHI\": [PHI]})\n",
    "            result = result.append(df, ignore_index=True, sort=False)\n",
    "            check = False\n",
    "        else:\n",
    "            n_e = n_e_new\n",
    "            freq_tau[\"tau_current\"] = tau(result, freq, n_e) \n",
    "    \n",
    "    nH_neutral = nH_total - n_e\n",
    "    freq_tau[\"tau_current\"] = tau(result, freq, n_e) \n",
    "    tau_step(freq_tau)\n",
    "    r_current += step    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'r, pc')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "ax.plot(result['r'], result['n_e'], lw=2, c='black') \n",
    "ax.grid(c='#aaaaaa', ls='--')\n",
    "plt.ylabel(\"n_e, cm^-3\", size=20)\n",
    "plt.xlabel(\"r, pc\", size=20)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}