radio-seti/interstellar-communications/interstellar-communications.ipynb

{
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   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Formulae-from-Cocconi-&amp;-Morrison,-1959\" data-toc-modified-id=\"Formulae-from-Cocconi-&amp;-Morrison,-1959-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Formulae from Cocconi &amp; Morrison, 1959</a></span></li><li><span><a href=\"#This-notebook\" data-toc-modified-id=\"This-notebook-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>This notebook</a></span></li><li><span><a href=\"#Planck's-law-of-blackbody-radiation\" data-toc-modified-id=\"Planck's-law-of-blackbody-radiation-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Planck's law of blackbody radiation</a></span></li><li><span><a href=\"#Rayleigh-Jeans'-law-of-blackbody-radiation\" data-toc-modified-id=\"Rayleigh-Jeans'-law-of-blackbody-radiation-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Rayleigh-Jeans' law of blackbody radiation</a></span></li><li><span><a href=\"#Import-dependencies\" data-toc-modified-id=\"Import-dependencies-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Import dependencies</a></span></li><li><span><a href=\"#Radiation-from-the-Sun\" data-toc-modified-id=\"Radiation-from-the-Sun-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>Radiation from the Sun</a></span><ul class=\"toc-item\"><li><ul class=\"toc-item\"><li><span><a href=\"#Spectral-radiance\" data-toc-modified-id=\"Spectral-radiance-6.0.1\"><span class=\"toc-item-num\">6.0.1&nbsp;&nbsp;</span>Spectral radiance</a></span></li><li><span><a href=\"#Monochromatic-luminosity\" data-toc-modified-id=\"Monochromatic-luminosity-6.0.2\"><span class=\"toc-item-num\">6.0.2&nbsp;&nbsp;</span>Monochromatic luminosity</a></span></li><li><span><a href=\"#Flux\" data-toc-modified-id=\"Flux-6.0.3\"><span class=\"toc-item-num\">6.0.3&nbsp;&nbsp;</span>Flux</a></span></li></ul></li><li><span><a href=\"#Flux-from-galaxy\" data-toc-modified-id=\"Flux-from-galaxy-6.1\"><span class=\"toc-item-num\">6.1&nbsp;&nbsp;</span>Flux from galaxy</a></span></li><li><span><a href=\"#Compare-curves\" data-toc-modified-id=\"Compare-curves-6.2\"><span class=\"toc-item-num\">6.2&nbsp;&nbsp;</span>Compare curves</a></span><ul class=\"toc-item\"><li><span><a href=\"#Spectral-radiance\" data-toc-modified-id=\"Spectral-radiance-6.2.1\"><span class=\"toc-item-num\">6.2.1&nbsp;&nbsp;</span>Spectral radiance</a></span></li></ul></li><li><span><a href=\"#Monochromatic-luminosity\" data-toc-modified-id=\"Monochromatic-luminosity-6.3\"><span class=\"toc-item-num\">6.3&nbsp;&nbsp;</span>Monochromatic luminosity</a></span></li><li><span><a href=\"#Flux\" data-toc-modified-id=\"Flux-6.4\"><span class=\"toc-item-num\">6.4&nbsp;&nbsp;</span>Flux</a></span></li><li><span><a href=\"#Difference-between-Rayleigh-Jeans-and-Cocconi-Morrison\" data-toc-modified-id=\"Difference-between-Rayleigh-Jeans-and-Cocconi-Morrison-6.5\"><span class=\"toc-item-num\">6.5&nbsp;&nbsp;</span>Difference between Rayleigh-Jeans and Cocconi-Morrison</a></span></li><li><span><a href=\"#Varying-star-types\" data-toc-modified-id=\"Varying-star-types-6.6\"><span class=\"toc-item-num\">6.6&nbsp;&nbsp;</span>Varying star types</a></span></li><li><span><a href=\"#Constant-for-different-types-of-stars\" data-toc-modified-id=\"Constant-for-different-types-of-stars-6.7\"><span class=\"toc-item-num\">6.7&nbsp;&nbsp;</span>Constant for different types of stars</a></span></li></ul></li><li><span><a href=\"#Minimum-frequency-for-different-stars\" data-toc-modified-id=\"Minimum-frequency-for-different-stars-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>Minimum frequency for different stars</a></span><ul class=\"toc-item\"><li><span><a href=\"#Minimum-frequencies-detectable-at-Earth's-surface\" data-toc-modified-id=\"Minimum-frequencies-detectable-at-Earth's-surface-7.1\"><span class=\"toc-item-num\">7.1&nbsp;&nbsp;</span>Minimum frequencies detectable at Earth's surface</a></span></li><li><span><a href=\"#10000-m2-detector\" data-toc-modified-id=\"10000-m2-detector-7.2\"><span class=\"toc-item-num\">7.2&nbsp;&nbsp;</span>10000 m2 detector</a></span></li><li><span><a href=\"#1-km2-detector\" data-toc-modified-id=\"1-km2-detector-7.3\"><span class=\"toc-item-num\">7.3&nbsp;&nbsp;</span>1 km2 detector</a></span></li></ul></li><li><span><a href=\"#Individual-stars-of-interest\" data-toc-modified-id=\"Individual-stars-of-interest-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>Individual stars of interest</a></span><ul class=\"toc-item\"><li><span><a href=\"#Tabby's-star\" data-toc-modified-id=\"Tabby's-star-8.1\"><span class=\"toc-item-num\">8.1&nbsp;&nbsp;</span>Tabby's star</a></span></li></ul></li><li><span><a href=\"#Summary\" data-toc-modified-id=\"Summary-9\"><span class=\"toc-item-num\">9&nbsp;&nbsp;</span>Summary</a></span></li></ul></div>"
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   "source": [
    "# Calculating minimum frequency for SETI\n",
    "\n",
    "This notebook accompanies a post I wrote on [my open research site](https://open-research.gemmadanks.com/) with [my notes on one of the first papers on the search for extraterrestrial intelligence (SETI)](https://open-research.gemmadanks.com/research/search-for-interstellar-communications):\n",
    "\n",
    "G. Cocconi and P. Morrison, \"Searching for Interstellar Communications\", *Nature*, vol. 184, pp. 844–846, 1959."
   ]
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   "source": [
    "## Formulae from Cocconi & Morrison, 1959\n",
    "For a star like the quiet sun, Cocconi & Morrison calculated the minimum frequency required for a signal to be detected above background from:\n",
    "\n",
    "$$ f_{min} \\approx 10^4 \\left( { R \\over l_d } \\right) ^{0.4} Hz$$\n",
    "\n",
    "Where $l_d$ is the diameter of the detector's mirror and R is the distance to the star in metres.\n",
    "\n",
    "The authors derived this formula by equating two equations for spectral irradiance ($Wm^{-2}Hz^{-1}$) of:\n",
    "\n",
    "1. The host star at a distance $R$:\n",
    "\n",
    "$$ 10^{-15}f^2/R^2 $$  \n",
    "\n",
    "2. The (isotropic part of the) galactic background:\n",
    "\n",
    "$$ \\left(10^{-12.5}\\over f\\right)\\left(\\lambda\\over l_{d}\\right)^2 $$\n",
    "\n",
    "Substituting $c$ = $3 \\times 10^8$ for $\\lambda$ and solving for $f$ gives:\n",
    "\n",
    "$$ 10^{-15}{f^2 \\over R^2} = \\left(10^{-12.5}\\over f\\right)\\left(3\\times10^8 \\over f.l_{d}\\right)^2 $$\n",
    "\n",
    "$$ {{f^2 \\over R^2}} = {{2.846 \\times 10^{19}}\\over {f^3 \\times {l_{d}}^2}} $$\n",
    "\n",
    "$$ {f^5} = {{2.846 \\times 10^{19}.R^2}\\over {{l_{d}}^2}} $$\n",
    "\n",
    "$$ {f} = { 7777 { \\left( {R} \\over { l_{d} } \\right) }^{2/5}} $$\n",
    "\n",
    "$$ {f} \\approx { 10^4 { \\left( {R} \\over { l_{d} } \\right) }^{0.4}} $$"
   ]
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   "source": [
    "## This notebook\n",
    "\n",
    "I wanted to know what happens to this minimum frequency for stars of other spectral types. This means substituting the luminosity of other stellar classes (different temperature and radii) for $10^{-15}$ in the first equation above.\n",
    "\n",
    "Since Cocconi & Morrison did not say where their formulae above come from, I had to do some investigation which led me to Planck's and subsequently Rayleigh-Jeans' laws of blackbody radiation, which can be used to model the radiation from a star at different frequencies."
   ]
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   "source": [
    "## Planck's law of blackbody radiation\n",
    "\n",
    "Planck's law gives the spectral radiance, $B_f$, (also called specific intensity) of energy emitted per second per unit area, per solid angle from a blackbody as a function of temperature and frequency. It is measured in $Wm^{−2}sr^{−1}Hz^{−1}$ (watts per square metre per steradian per hertz):\n",
    "\n",
    "$$ {B_f\\left(T\\right)} = { {{2hf^3}\\over{c^2}}{{1}\\over{e^{hf\\over\\left(k_BT\\right)} - 1}} }  $$\n",
    "\n",
    "A steradian is a unit of solid angle (one steradian projects onto a sphere an area of $r^2$ and a sphere comprises $4\\pi$ steradians since the surface area of a sphere is $4\\pi r^2$). \n",
    "\n",
    "If we integrate over all solid angles (multiply by $\\pi$) and over the whole surface area of a star (multiply by $4\\pi r^2$) we get the monochromatic luminosity (luminosity per unit wavelength or frequency), $L_f$,  measured in $W {Hz}^{−1}$ for the whole star:\n",
    "\n",
    "$$ {L_f df} = { {{8\\pi^2 r^2 hf^3}\\over{c^2}}{{1}\\over{e^{hf\\over\\left(k_BT\\right)} - 1}} }  $$\n",
    "\n",
    "To get the flux, $F$, ($Wm^{-2}$) passing through a detector at a distance away from the star, $R$, we divide the luminosity by the area of the sphere at $R$ ($4\\pi R^2$):\n",
    "\n",
    "$$ {F_f} = { {{8\\pi^2 r^2 hf^3}\\over{4\\pi R^2c^2}}{{1}\\over{e^{hf\\over\\left(k_BT\\right)} - 1}} }  $$\n",
    "\n",
    "$$ {                    } = { {{2\\pi r^2 hf^3}\\over{R^2c^2}}{{1}\\over{e^{hf\\over\\left(k_BT\\right)} - 1}} }  $$"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Rayleigh-Jeans' law of blackbody radiation\n",
    "\n",
    "For low frequencies, we can also use the simpler Rayleigh-Jeans law:\n",
    "\n",
    "$$ {B_f\\left(T\\right)} = { {{2f^2k_BT}\\over{c^2}} }  $$\n",
    "\n",
    "Integrated over all solid angles and surface area, for a star at a distance R we get the flux, $F_f$:\n",
    "\n",
    "$$ {F_f} = { {{2\\pi r^2f^2k_BT}\\over{R^2c^2}} }  $$\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "# additional imports\n",
    "import statistics\n",
    "from matplotlib import cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from blackbody import (spectral_radiance_planck, spectral_radiance_rayleigh_jeans,\n",
    "                       monochromatic_luminosity_planck, monochromatic_luminosity_rayleigh_jeans, \n",
    "                       flux_from_luminosity)\n",
    "\n",
    "from constants import (BOLTZMANN, LIGHT_SPEED, SUN_TEMP, SUN_RADIUS, AU)\n",
    "\n",
    "from cocconi_morrison import (luminosity_sunlike, flux_sunlike, flux_from_galaxy, frequency_minimum)\n",
    "\n",
    "from utils import light_years_to_metres"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Radiation from the Sun\n",
    "\n",
    "Use a range of frequencies from 1 Hz to 100 billion THz in log-space to compute various metrics of radiation.\n",
    "\n",
    "- Planck's law of blackbody radiation (models the Sun as a blackbody with a surface temperature of 5778 K)\n",
    "- Rayleigh-Jeans law (applies for low frequencies) (models the Sun as a blackbody with a surface temperature of 5778 K)\n",
    "- Formula from Cocconi & Morrison, 1959 (models the quiet Sun, accounting for deviations from a perfect blackbody)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+01, 1.00438494e+01, 1.00878910e+01, ...,\n",
       "       9.91287478e+19, 9.95634209e+19, 1.00000000e+20])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequencies = np.logspace(1, 20, 10000)\n",
    "frequencies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Spectral radiance\n",
    "\n",
    "Energy per second per unit area per solid angle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nicolasgalvarinoguerravaras/Documents/EMJM_MASS/Belgrado_2nd_Semester/Astrobiology/GitHub/techno_signatures/radio-seti/interstellar-communications/blackbody.py:34: RuntimeWarning: overflow encountered in exp\n",
      "  * (1 / (np.exp((PLANCK * frequency) / (BOLTZMANN * temperature))\n"
     ]
    }
   ],
   "source": [
    "# Spectral Radiance, Planck\n",
    "sun_spectral_radiance_planck = [spectral_radiance_planck(freq, SUN_TEMP) for freq in frequencies]\n",
    "\n",
    "# Spectral Radiance, R-J\n",
    "sun_spectral_radiance_rj = [spectral_radiance_rayleigh_jeans(freq, SUN_TEMP) for freq in frequencies]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4131093919289673e-09\n",
      "203.7184332426391\n",
      "144163243416.38754\n"
     ]
    }
   ],
   "source": [
    "print(statistics.mean(sun_spectral_radiance_planck))\n",
    "print(statistics.mean(sun_spectral_radiance_rj))\n",
    "print(statistics.mean(sun_spectral_radiance_rj) / statistics.mean(sun_spectral_radiance_planck))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On average, the Planck radiation is $1.44 \\times 10^{11}$ times more intense than the Rayleigh-Jeans radiation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monochromatic luminosity\n",
    "\n",
    "Total energy emitted at the surface of the Sun per second per Hz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# L from R-J\n",
    "sun_luminosity_rj = [monochromatic_luminosity_rayleigh_jeans(freq, SUN_TEMP, SUN_RADIUS)\n",
    "                       for freq in frequencies]\n",
    "\n",
    "# L from Planck\n",
    "sun_luminosity_planck = [monochromatic_luminosity_planck(freq, SUN_TEMP, SUN_RADIUS)\n",
    "                   for freq in frequencies]\n",
    "\n",
    "# L from Sun-like star\n",
    "sunlike_luminosity = [luminosity_sunlike(freq) for freq in frequencies]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8925488443821397e+21\n",
      "27000979945.62503\n",
      "1.4423343660648783e+24\n"
     ]
    }
   ],
   "source": [
    "# The Sun's emission is closer to RJ than Planck\n",
    "print(statistics.mean(sun_luminosity_rj))\n",
    "print(statistics.mean(sun_luminosity_planck))\n",
    "print(statistics.mean(sunlike_luminosity))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Flux\n",
    "\n",
    "Energy received per second per unit area at Earth distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Flux from Planck\n",
    "sun_flux_planck = [flux_from_luminosity(monochromatic_luminosity_planck(freq, SUN_TEMP, SUN_RADIUS), AU)\n",
    "                   for freq in frequencies]\n",
    "\n",
    "# Flux from R-J\n",
    "sun_flux_rj = [flux_from_luminosity(monochromatic_luminosity_rayleigh_jeans(freq, SUN_TEMP, SUN_RADIUS), AU) \n",
    "               for freq in frequencies]\n",
    "\n",
    "# Flux from R-J for large and hot star\n",
    "large_hot_star_flux_rj = [flux_from_luminosity(monochromatic_luminosity_rayleigh_jeans(freq, SUN_TEMP*2, \n",
    "                                                                                       SUN_RADIUS*100), AU)\n",
    "                          for freq in frequencies]\n",
    "\n",
    "# Flux from R-J for small and cool star\n",
    "small_cool_star_flux_rj = [flux_from_luminosity(monochromatic_luminosity_rayleigh_jeans(freq, SUN_TEMP/2, \n",
    "                                                                                        SUN_RADIUS*0.01), AU)\n",
    "                           for freq in frequencies]\n",
    "\n",
    "# Flux \n",
    "sunlike_flux = [flux_sunlike(freq, AU) for freq in frequencies]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flux from galaxy\n",
    "\n",
    "For different mirrors in the detectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "galactic_flux_100 = [flux_from_galaxy(freq, diameter_mirror=100) for freq in frequencies]\n",
    "galactic_flux_1000 = [flux_from_galaxy(freq, diameter_mirror=1000) for freq in frequencies]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "sun_df = pd.DataFrame({\"sun_spectral_radiance_planck\": sun_spectral_radiance_planck,\n",
    "                       \"sun_spectral_radiance_rj\": sun_spectral_radiance_rj,\n",
    "                       \"sunlike_luminosity\": sunlike_luminosity,\n",
    "                       \"sun_luminosity_rayleigh_jeans\": sun_luminosity_rj,\n",
    "                       \"sun_luminosity_planck\": sun_luminosity_planck,\n",
    "                       \"sun_flux_planck\": sun_flux_planck,\n",
    "                       \"sun_flux_rj\": sun_flux_rj,\n",
    "                       \"large_hot_star_flux_rj\": large_hot_star_flux_rj,\n",
    "                       \"small_cool_star_flux_rj\": small_cool_star_flux_rj,\n",
    "                       \"sunlike_flux\": sunlike_flux,\n",
    "                       \"galactic_flux_100\": galactic_flux_100,\n",
    "                       \"galactic_flux_1000\": galactic_flux_1000})\n",
    "sun_df.index = frequencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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       "      <td>0.000028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.087891</th>\n",
       "      <td>1.808274e-34</td>\n",
       "      <td>1.806238e-34</td>\n",
       "      <td>1.278824e-12</td>\n",
       "      <td>3.451268e-15</td>\n",
       "      <td>3.455158e-15</td>\n",
       "      <td>1.228591e-38</td>\n",
       "      <td>1.227208e-38</td>\n",
       "      <td>2.454415e-34</td>\n",
       "      <td>6.136038e-43</td>\n",
       "      <td>5.714257e-35</td>\n",
       "      <td>0.002768</td>\n",
       "      <td>0.000028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.132126</th>\n",
       "      <td>1.822497e-34</td>\n",
       "      <td>1.822113e-34</td>\n",
       "      <td>1.290063e-12</td>\n",
       "      <td>3.481602e-15</td>\n",
       "      <td>3.482336e-15</td>\n",
       "      <td>1.238255e-38</td>\n",
       "      <td>1.237994e-38</td>\n",
       "      <td>2.475987e-34</td>\n",
       "      <td>6.189969e-43</td>\n",
       "      <td>5.764481e-35</td>\n",
       "      <td>0.002732</td>\n",
       "      <td>0.000027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.176554</th>\n",
       "      <td>1.836884e-34</td>\n",
       "      <td>1.838128e-34</td>\n",
       "      <td>1.301402e-12</td>\n",
       "      <td>3.512202e-15</td>\n",
       "      <td>3.509825e-15</td>\n",
       "      <td>1.248029e-38</td>\n",
       "      <td>1.248875e-38</td>\n",
       "      <td>2.497749e-34</td>\n",
       "      <td>6.244373e-43</td>\n",
       "      <td>5.815145e-35</td>\n",
       "      <td>0.002697</td>\n",
       "      <td>0.000027</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           sun_spectral_radiance_planck  sun_spectral_radiance_rj  \\\n",
       "10.000000                  1.775550e-34              1.774901e-34   \n",
       "10.043849                  1.789440e-34              1.790501e-34   \n",
       "10.087891                  1.808274e-34              1.806238e-34   \n",
       "10.132126                  1.822497e-34              1.822113e-34   \n",
       "10.176554                  1.836884e-34              1.838128e-34   \n",
       "\n",
       "           sunlike_luminosity  sun_luminosity_rayleigh_jeans  \\\n",
       "10.000000        1.256637e-12                   3.391392e-15   \n",
       "10.043849        1.267682e-12                   3.421199e-15   \n",
       "10.087891        1.278824e-12                   3.451268e-15   \n",
       "10.132126        1.290063e-12                   3.481602e-15   \n",
       "10.176554        1.301402e-12                   3.512202e-15   \n",
       "\n",
       "           sun_luminosity_planck  sun_flux_planck   sun_flux_rj  \\\n",
       "10.000000           3.392630e-15     1.206357e-38  1.205917e-38   \n",
       "10.043849           3.419171e-15     1.215794e-38  1.216516e-38   \n",
       "10.087891           3.455158e-15     1.228591e-38  1.227208e-38   \n",
       "10.132126           3.482336e-15     1.238255e-38  1.237994e-38   \n",
       "10.176554           3.509825e-15     1.248029e-38  1.248875e-38   \n",
       "\n",
       "           large_hot_star_flux_rj  small_cool_star_flux_rj  sunlike_flux  \\\n",
       "10.000000            2.411833e-34             6.029583e-43  5.615120e-35   \n",
       "10.043849            2.433031e-34             6.082578e-43  5.664472e-35   \n",
       "10.087891            2.454415e-34             6.136038e-43  5.714257e-35   \n",
       "10.132126            2.475987e-34             6.189969e-43  5.764481e-35   \n",
       "10.176554            2.497749e-34             6.244373e-43  5.815145e-35   \n",
       "\n",
       "           galactic_flux_100  galactic_flux_1000  \n",
       "10.000000           0.002842            0.000028  \n",
       "10.043849           0.002805            0.000028  \n",
       "10.087891           0.002768            0.000028  \n",
       "10.132126           0.002732            0.000027  \n",
       "10.176554           0.002697            0.000027  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sun_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Spectral radiance\n",
    "\n",
    "Rayleigh-Jeans law does not fit at higher frequences, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sun_df[[\"sun_spectral_radiance_planck\", \"sun_spectral_radiance_rj\"]][0:1e20].plot(use_index=True, \n",
    "                                                                                  loglog=True, \n",
    "                                                                                  xlabel='Frequency [Hz]', \n",
    "                                                                                  ylabel=r'Spectral Radiance [$W m^{-2}sr^{-1}Hz^{-1}$]', \n",
    "                                                                                  title='Sun');\n",
    "\n",
    "plt.legend(['Planck', 'Rayleigh-Jeans']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monochromatic luminosity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sun_df[[\"sun_luminosity_planck\", \"sun_luminosity_rayleigh_jeans\"]][0:1e20].plot(use_index=True, \n",
    "                                                                                loglog=True, \n",
    "                                                                                xlabel='Frequency [Hz]', \n",
    "                                                                                ylabel=r'Luminosity [$W {Hz}^{-1}$]', \n",
    "                                                                                title='Sun');\n",
    "\n",
    "plt.legend(['Planck', 'Rayleigh-Jeans']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flux\n",
    "\n",
    "Flux for a star computed using formula from Cocconi & Morrison follows the same slope as Rayleigh-Jeans law but values are higher. \n",
    "\n",
    "The flux for the galactic background radiation has the inverse relationship to frequency. There is a point where the flux from a star equals the flux from galactic background. This gives the minimum frequency for transmission of interstellar communications since any frequency below this will be indistinguishable from the galactic background. The minimum frequency varies according to the temperature and radius of a star. \n",
    "\n",
    "- Hotter and larger stars have lower minimum frequencies (with higher flux)\n",
    "- Smaller and cooler stars have higher minimum frequencies (with lower flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sun_df[[\"sunlike_flux\", \"sun_flux_planck\", \"sun_flux_rj\", \n",
    "        \"large_hot_star_flux_rj\", \"small_cool_star_flux_rj\", \n",
    "        \"galactic_flux_100\", \"galactic_flux_1000\"]][1e-2:1e18].plot(use_index=True, loglog=True, \n",
    "                                                                    xlabel='Frequency [Hz]', \n",
    "                                                                    ylabel=r'Flux [$W {m}^{-2}$]', \n",
    "                                                                    ylim=(1e-28, 1e-10), xlim=(3e4, 3e15), \n",
    "                                                                    title='Flux');\n",
    "\n",
    "plt.legend(['Sun-like', 'Sun, Planck', 'Sun, RJ', \n",
    "            'Large Hot, RJ', 'Small Cool, RJ', \n",
    "            'Gal., 100m mirror', 'Gal., 1000m mirror'],\n",
    "            bbox_to_anchor=(1.0, 1.0),\n",
    "            ncol=1, fancybox=True, shadow=True);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Difference between Rayleigh-Jeans and Cocconi-Morrison\n",
    "\n",
    "The flux is ~370 times higher using Cocconi & Morrison's formula.\n",
    "\n",
    "If using the Rayleigh-Jeans law the formula would be:\n",
    "\n",
    "$$ 2.6987 \\times 10^{-18}f^2/R^2 $$  \n",
    "\n",
    "The Cocconi & Morrison's formula is:\n",
    "\n",
    "$$ 10^{-15}f^2/R^2 $$  \n",
    "\n",
    "In their paper Cocconi & Morrison state their formula is based on the 'quiet Sun', not a blackbody. The Sun deviates from a blackbody at lower frequencies: there is a higher radiance that creates a bulge in the curve at approximately this order of magnitude.\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Varying star types\n",
    "To compute the proportionality factor for minimum frequency for different star types in the formula we use:\n",
    "$$ \\left({c^4 10^{-12.5}}\\over{2\\pi k_B r^2 T}\\right)^{0.2} $$\n",
    "\n",
    "$$ 5\\times 10^8\\over{\\left({r^2 T}\\right)^{0.2}} $$\n",
    "\n",
    "Where r is the radius of the star and T is the temperature of the star. The higher the temperature or the larger the radius, the lower the minimum frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constant_for_flux_calc(solar_radii, temperature):\n",
    "    \"\"\"Constant used to compute flux from Rayleigh-Jeans law given temperature and radius of a star.\n",
    "    \n",
    "    Used to multiply f^2/R^2 (where is frequency and R is distance to a star)\n",
    "    \n",
    "    Args:\n",
    "        solar_radii: radius of star (solar radii)\n",
    "        temperature: temperature of star (Kelvin)\n",
    "    Returns:\n",
    "        Factor used to calculate flux\n",
    "    \"\"\"\n",
    "    return (2 * math.pi * pow(solar_radii * SUN_RADIUS, 2) * BOLTZMANN * temperature) / pow(LIGHT_SPEED, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6987839546541377e-18"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constant_for_flux_calc(1, SUN_TEMP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "370.5372555944942"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constant_cocconi_morrison = 1e-15\n",
    "quiet_sun_factor = constant_cocconi_morrison / constant_for_flux_calc(1, SUN_TEMP)\n",
    "#quiet_sun_factor = 1\n",
    "quiet_sun_factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constant for different types of stars\n",
    "Vary the radius and temperature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.34320220e-23, 9.56766351e-23, 9.79212483e-23, ...,\n",
       "        2.33131132e-21, 2.33355594e-21, 2.33580055e-21],\n",
       "       [1.19560373e-22, 1.22432695e-22, 1.25305016e-22, ...,\n",
       "        2.98326469e-21, 2.98613701e-21, 2.98900933e-21],\n",
       "       [1.52995542e-22, 1.56671111e-22, 1.60346680e-22, ...,\n",
       "        3.81753742e-21, 3.82121299e-21, 3.82488856e-21],\n",
       "       ...,\n",
       "       [2.28229989e-12, 2.33712991e-12, 2.39195994e-12, ...,\n",
       "        5.69478371e-11, 5.70026671e-11, 5.70574972e-11],\n",
       "       [2.92054716e-12, 2.99071046e-12, 3.06087375e-12, ...,\n",
       "        7.28733525e-11, 7.29435158e-11, 7.30136791e-11],\n",
       "       [3.73728088e-12, 3.82706540e-12, 3.91684993e-12, ...,\n",
       "        9.32524529e-11, 9.33422374e-11, 9.34320220e-11]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constant_for_flux_calc(radii[:, None], temperatures)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "radii = np.logspace(-2, np.log10(2000), 100) # log10 solar radii\n",
    "\n",
    "temperatures = np.linspace(2000, 50000, 1000)\n",
    "\n",
    "stellar_constants_np = constant_for_flux_calc(radii[:, None], temperatures) * quiet_sun_factor\n",
    "\n",
    "# index = radii, columns = temperatures\n",
    "stellar_constants = pd.DataFrame(constant_for_flux_calc(radii[:, None], temperatures) * quiet_sun_factor,\n",
    "                                 index = np.around(radii, 2),\n",
    "                                 columns=np.around(temperatures,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2000.0</th>\n",
       "      <th>2048.0</th>\n",
       "      <th>2096.0</th>\n",
       "      <th>2144.0</th>\n",
       "      <th>2192.0</th>\n",
       "      <th>2240.0</th>\n",
       "      <th>2288.0</th>\n",
       "      <th>2336.0</th>\n",
       "      <th>2384.0</th>\n",
       "      <th>2432.0</th>\n",
       "      <th>...</th>\n",
       "      <th>49568.0</th>\n",
       "      <th>49616.0</th>\n",
       "      <th>49664.0</th>\n",
       "      <th>49712.0</th>\n",
       "      <th>49760.0</th>\n",
       "      <th>49808.0</th>\n",
       "      <th>49856.0</th>\n",
       "      <th>49904.0</th>\n",
       "      <th>49952.0</th>\n",
       "      <th>50000.0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>3.462005e-20</td>\n",
       "      <td>3.545176e-20</td>\n",
       "      <td>3.628347e-20</td>\n",
       "      <td>3.711518e-20</td>\n",
       "      <td>3.794690e-20</td>\n",
       "      <td>3.877861e-20</td>\n",
       "      <td>3.961032e-20</td>\n",
       "      <td>4.044203e-20</td>\n",
       "      <td>4.127375e-20</td>\n",
       "      <td>4.210546e-20</td>\n",
       "      <td>...</td>\n",
       "      <td>8.580157e-19</td>\n",
       "      <td>8.588474e-19</td>\n",
       "      <td>8.596791e-19</td>\n",
       "      <td>8.605108e-19</td>\n",
       "      <td>8.613426e-19</td>\n",
       "      <td>8.621743e-19</td>\n",
       "      <td>8.630060e-19</td>\n",
       "      <td>8.638377e-19</td>\n",
       "      <td>8.646694e-19</td>\n",
       "      <td>8.655011e-19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>4.430157e-20</td>\n",
       "      <td>4.536587e-20</td>\n",
       "      <td>4.643018e-20</td>\n",
       "      <td>4.749448e-20</td>\n",
       "      <td>4.855878e-20</td>\n",
       "      <td>4.962308e-20</td>\n",
       "      <td>5.068738e-20</td>\n",
       "      <td>5.175169e-20</td>\n",
       "      <td>5.281599e-20</td>\n",
       "      <td>5.388029e-20</td>\n",
       "      <td>...</td>\n",
       "      <td>1.097961e-18</td>\n",
       "      <td>1.099025e-18</td>\n",
       "      <td>1.100089e-18</td>\n",
       "      <td>1.101154e-18</td>\n",
       "      <td>1.102218e-18</td>\n",
       "      <td>1.103282e-18</td>\n",
       "      <td>1.104346e-18</td>\n",
       "      <td>1.105411e-18</td>\n",
       "      <td>1.106475e-18</td>\n",
       "      <td>1.107539e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>5.669055e-20</td>\n",
       "      <td>5.805248e-20</td>\n",
       "      <td>5.941442e-20</td>\n",
       "      <td>6.077635e-20</td>\n",
       "      <td>6.213829e-20</td>\n",
       "      <td>6.350022e-20</td>\n",
       "      <td>6.486216e-20</td>\n",
       "      <td>6.622409e-20</td>\n",
       "      <td>6.758603e-20</td>\n",
       "      <td>6.894796e-20</td>\n",
       "      <td>...</td>\n",
       "      <td>1.405006e-18</td>\n",
       "      <td>1.406368e-18</td>\n",
       "      <td>1.407730e-18</td>\n",
       "      <td>1.409092e-18</td>\n",
       "      <td>1.410454e-18</td>\n",
       "      <td>1.411816e-18</td>\n",
       "      <td>1.413178e-18</td>\n",
       "      <td>1.414540e-18</td>\n",
       "      <td>1.415902e-18</td>\n",
       "      <td>1.417264e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>7.254411e-20</td>\n",
       "      <td>7.428691e-20</td>\n",
       "      <td>7.602972e-20</td>\n",
       "      <td>7.777252e-20</td>\n",
       "      <td>7.951532e-20</td>\n",
       "      <td>8.125812e-20</td>\n",
       "      <td>8.300092e-20</td>\n",
       "      <td>8.474372e-20</td>\n",
       "      <td>8.648652e-20</td>\n",
       "      <td>8.822933e-20</td>\n",
       "      <td>...</td>\n",
       "      <td>1.797918e-18</td>\n",
       "      <td>1.799660e-18</td>\n",
       "      <td>1.801403e-18</td>\n",
       "      <td>1.803146e-18</td>\n",
       "      <td>1.804889e-18</td>\n",
       "      <td>1.806632e-18</td>\n",
       "      <td>1.808374e-18</td>\n",
       "      <td>1.810117e-18</td>\n",
       "      <td>1.811860e-18</td>\n",
       "      <td>1.813603e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.02</th>\n",
       "      <td>9.283114e-20</td>\n",
       "      <td>9.506132e-20</td>\n",
       "      <td>9.729150e-20</td>\n",
       "      <td>9.952167e-20</td>\n",
       "      <td>1.017519e-19</td>\n",
       "      <td>1.039820e-19</td>\n",
       "      <td>1.062122e-19</td>\n",
       "      <td>1.084424e-19</td>\n",
       "      <td>1.106726e-19</td>\n",
       "      <td>1.129027e-19</td>\n",
       "      <td>...</td>\n",
       "      <td>2.300707e-18</td>\n",
       "      <td>2.302937e-18</td>\n",
       "      <td>2.305167e-18</td>\n",
       "      <td>2.307397e-18</td>\n",
       "      <td>2.309628e-18</td>\n",
       "      <td>2.311858e-18</td>\n",
       "      <td>2.314088e-18</td>\n",
       "      <td>2.316318e-18</td>\n",
       "      <td>2.318548e-18</td>\n",
       "      <td>2.320779e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1221.37</th>\n",
       "      <td>5.164420e-10</td>\n",
       "      <td>5.288490e-10</td>\n",
       "      <td>5.412560e-10</td>\n",
       "      <td>5.536631e-10</td>\n",
       "      <td>5.660701e-10</td>\n",
       "      <td>5.784771e-10</td>\n",
       "      <td>5.908841e-10</td>\n",
       "      <td>6.032911e-10</td>\n",
       "      <td>6.156981e-10</td>\n",
       "      <td>6.281051e-10</td>\n",
       "      <td>...</td>\n",
       "      <td>1.279939e-08</td>\n",
       "      <td>1.281179e-08</td>\n",
       "      <td>1.282420e-08</td>\n",
       "      <td>1.283661e-08</td>\n",
       "      <td>1.284902e-08</td>\n",
       "      <td>1.286142e-08</td>\n",
       "      <td>1.287383e-08</td>\n",
       "      <td>1.288624e-08</td>\n",
       "      <td>1.289864e-08</td>\n",
       "      <td>1.291105e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1381.63</th>\n",
       "      <td>6.608655e-10</td>\n",
       "      <td>6.767421e-10</td>\n",
       "      <td>6.926188e-10</td>\n",
       "      <td>7.084954e-10</td>\n",
       "      <td>7.243721e-10</td>\n",
       "      <td>7.402487e-10</td>\n",
       "      <td>7.561254e-10</td>\n",
       "      <td>7.720020e-10</td>\n",
       "      <td>7.878787e-10</td>\n",
       "      <td>8.037553e-10</td>\n",
       "      <td>...</td>\n",
       "      <td>1.637875e-08</td>\n",
       "      <td>1.639462e-08</td>\n",
       "      <td>1.641050e-08</td>\n",
       "      <td>1.642638e-08</td>\n",
       "      <td>1.644225e-08</td>\n",
       "      <td>1.645813e-08</td>\n",
       "      <td>1.647401e-08</td>\n",
       "      <td>1.648988e-08</td>\n",
       "      <td>1.650576e-08</td>\n",
       "      <td>1.652164e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1562.93</th>\n",
       "      <td>8.456771e-10</td>\n",
       "      <td>8.659937e-10</td>\n",
       "      <td>8.863103e-10</td>\n",
       "      <td>9.066268e-10</td>\n",
       "      <td>9.269434e-10</td>\n",
       "      <td>9.472600e-10</td>\n",
       "      <td>9.675765e-10</td>\n",
       "      <td>9.878931e-10</td>\n",
       "      <td>1.008210e-09</td>\n",
       "      <td>1.028526e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>2.095908e-08</td>\n",
       "      <td>2.097940e-08</td>\n",
       "      <td>2.099971e-08</td>\n",
       "      <td>2.102003e-08</td>\n",
       "      <td>2.104035e-08</td>\n",
       "      <td>2.106066e-08</td>\n",
       "      <td>2.108098e-08</td>\n",
       "      <td>2.110130e-08</td>\n",
       "      <td>2.112161e-08</td>\n",
       "      <td>2.114193e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1768.01</th>\n",
       "      <td>1.082172e-09</td>\n",
       "      <td>1.108170e-09</td>\n",
       "      <td>1.134168e-09</td>\n",
       "      <td>1.160166e-09</td>\n",
       "      <td>1.186164e-09</td>\n",
       "      <td>1.212162e-09</td>\n",
       "      <td>1.238160e-09</td>\n",
       "      <td>1.264158e-09</td>\n",
       "      <td>1.290156e-09</td>\n",
       "      <td>1.316155e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>2.682031e-08</td>\n",
       "      <td>2.684630e-08</td>\n",
       "      <td>2.687230e-08</td>\n",
       "      <td>2.689830e-08</td>\n",
       "      <td>2.692430e-08</td>\n",
       "      <td>2.695030e-08</td>\n",
       "      <td>2.697629e-08</td>\n",
       "      <td>2.700229e-08</td>\n",
       "      <td>2.702829e-08</td>\n",
       "      <td>2.705429e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000.00</th>\n",
       "      <td>1.384802e-09</td>\n",
       "      <td>1.418070e-09</td>\n",
       "      <td>1.451339e-09</td>\n",
       "      <td>1.484607e-09</td>\n",
       "      <td>1.517876e-09</td>\n",
       "      <td>1.551144e-09</td>\n",
       "      <td>1.584413e-09</td>\n",
       "      <td>1.617681e-09</td>\n",
       "      <td>1.650950e-09</td>\n",
       "      <td>1.684218e-09</td>\n",
       "      <td>...</td>\n",
       "      <td>3.432063e-08</td>\n",
       "      <td>3.435390e-08</td>\n",
       "      <td>3.438717e-08</td>\n",
       "      <td>3.442043e-08</td>\n",
       "      <td>3.445370e-08</td>\n",
       "      <td>3.448697e-08</td>\n",
       "      <td>3.452024e-08</td>\n",
       "      <td>3.455351e-08</td>\n",
       "      <td>3.458678e-08</td>\n",
       "      <td>3.462005e-08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 1000 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              2000.0        2048.0        2096.0        2144.0        2192.0   \\\n",
       "0.01     3.462005e-20  3.545176e-20  3.628347e-20  3.711518e-20  3.794690e-20   \n",
       "0.01     4.430157e-20  4.536587e-20  4.643018e-20  4.749448e-20  4.855878e-20   \n",
       "0.01     5.669055e-20  5.805248e-20  5.941442e-20  6.077635e-20  6.213829e-20   \n",
       "0.01     7.254411e-20  7.428691e-20  7.602972e-20  7.777252e-20  7.951532e-20   \n",
       "0.02     9.283114e-20  9.506132e-20  9.729150e-20  9.952167e-20  1.017519e-19   \n",
       "...               ...           ...           ...           ...           ...   \n",
       "1221.37  5.164420e-10  5.288490e-10  5.412560e-10  5.536631e-10  5.660701e-10   \n",
       "1381.63  6.608655e-10  6.767421e-10  6.926188e-10  7.084954e-10  7.243721e-10   \n",
       "1562.93  8.456771e-10  8.659937e-10  8.863103e-10  9.066268e-10  9.269434e-10   \n",
       "1768.01  1.082172e-09  1.108170e-09  1.134168e-09  1.160166e-09  1.186164e-09   \n",
       "2000.00  1.384802e-09  1.418070e-09  1.451339e-09  1.484607e-09  1.517876e-09   \n",
       "\n",
       "              2240.0        2288.0        2336.0        2384.0        2432.0   \\\n",
       "0.01     3.877861e-20  3.961032e-20  4.044203e-20  4.127375e-20  4.210546e-20   \n",
       "0.01     4.962308e-20  5.068738e-20  5.175169e-20  5.281599e-20  5.388029e-20   \n",
       "0.01     6.350022e-20  6.486216e-20  6.622409e-20  6.758603e-20  6.894796e-20   \n",
       "0.01     8.125812e-20  8.300092e-20  8.474372e-20  8.648652e-20  8.822933e-20   \n",
       "0.02     1.039820e-19  1.062122e-19  1.084424e-19  1.106726e-19  1.129027e-19   \n",
       "...               ...           ...           ...           ...           ...   \n",
       "1221.37  5.784771e-10  5.908841e-10  6.032911e-10  6.156981e-10  6.281051e-10   \n",
       "1381.63  7.402487e-10  7.561254e-10  7.720020e-10  7.878787e-10  8.037553e-10   \n",
       "1562.93  9.472600e-10  9.675765e-10  9.878931e-10  1.008210e-09  1.028526e-09   \n",
       "1768.01  1.212162e-09  1.238160e-09  1.264158e-09  1.290156e-09  1.316155e-09   \n",
       "2000.00  1.551144e-09  1.584413e-09  1.617681e-09  1.650950e-09  1.684218e-09   \n",
       "\n",
       "         ...       49568.0       49616.0       49664.0       49712.0  \\\n",
       "0.01     ...  8.580157e-19  8.588474e-19  8.596791e-19  8.605108e-19   \n",
       "0.01     ...  1.097961e-18  1.099025e-18  1.100089e-18  1.101154e-18   \n",
       "0.01     ...  1.405006e-18  1.406368e-18  1.407730e-18  1.409092e-18   \n",
       "0.01     ...  1.797918e-18  1.799660e-18  1.801403e-18  1.803146e-18   \n",
       "0.02     ...  2.300707e-18  2.302937e-18  2.305167e-18  2.307397e-18   \n",
       "...      ...           ...           ...           ...           ...   \n",
       "1221.37  ...  1.279939e-08  1.281179e-08  1.282420e-08  1.283661e-08   \n",
       "1381.63  ...  1.637875e-08  1.639462e-08  1.641050e-08  1.642638e-08   \n",
       "1562.93  ...  2.095908e-08  2.097940e-08  2.099971e-08  2.102003e-08   \n",
       "1768.01  ...  2.682031e-08  2.684630e-08  2.687230e-08  2.689830e-08   \n",
       "2000.00  ...  3.432063e-08  3.435390e-08  3.438717e-08  3.442043e-08   \n",
       "\n",
       "              49760.0       49808.0       49856.0       49904.0       49952.0  \\\n",
       "0.01     8.613426e-19  8.621743e-19  8.630060e-19  8.638377e-19  8.646694e-19   \n",
       "0.01     1.102218e-18  1.103282e-18  1.104346e-18  1.105411e-18  1.106475e-18   \n",
       "0.01     1.410454e-18  1.411816e-18  1.413178e-18  1.414540e-18  1.415902e-18   \n",
       "0.01     1.804889e-18  1.806632e-18  1.808374e-18  1.810117e-18  1.811860e-18   \n",
       "0.02     2.309628e-18  2.311858e-18  2.314088e-18  2.316318e-18  2.318548e-18   \n",
       "...               ...           ...           ...           ...           ...   \n",
       "1221.37  1.284902e-08  1.286142e-08  1.287383e-08  1.288624e-08  1.289864e-08   \n",
       "1381.63  1.644225e-08  1.645813e-08  1.647401e-08  1.648988e-08  1.650576e-08   \n",
       "1562.93  2.104035e-08  2.106066e-08  2.108098e-08  2.110130e-08  2.112161e-08   \n",
       "1768.01  2.692430e-08  2.695030e-08  2.697629e-08  2.700229e-08  2.702829e-08   \n",
       "2000.00  3.445370e-08  3.448697e-08  3.452024e-08  3.455351e-08  3.458678e-08   \n",
       "\n",
       "              50000.0  \n",
       "0.01     8.655011e-19  \n",
       "0.01     1.107539e-18  \n",
       "0.01     1.417264e-18  \n",
       "0.01     1.813603e-18  \n",
       "0.02     2.320779e-18  \n",
       "...               ...  \n",
       "1221.37  1.291105e-08  \n",
       "1381.63  1.652164e-08  \n",
       "1562.93  2.114193e-08  \n",
       "1768.01  2.705429e-08  \n",
       "2000.00  3.462005e-08  \n",
       "\n",
       "[100 rows x 1000 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stellar_constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2000.0</th>\n",
       "      <th>2048.0</th>\n",
       "      <th>2096.0</th>\n",
       "      <th>2144.0</th>\n",
       "      <th>2192.0</th>\n",
       "      <th>2240.0</th>\n",
       "      <th>2288.0</th>\n",
       "      <th>2336.0</th>\n",
       "      <th>2384.0</th>\n",
       "      <th>2432.0</th>\n",
       "      <th>...</th>\n",
       "      <th>49568.0</th>\n",
       "      <th>49616.0</th>\n",
       "      <th>49664.0</th>\n",
       "      <th>49712.0</th>\n",
       "      <th>49760.0</th>\n",
       "      <th>49808.0</th>\n",
       "      <th>49856.0</th>\n",
       "      <th>49904.0</th>\n",
       "      <th>49952.0</th>\n",
       "      <th>50000.0</th>\n",
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       "      <th>2000.00</th>\n",
       "      <td>-8.858612</td>\n",
       "      <td>-8.848302</td>\n",
       "      <td>-8.838231</td>\n",
       "      <td>-8.828388</td>\n",
       "      <td>-8.818764</td>\n",
       "      <td>-8.809348</td>\n",
       "      <td>-8.800132</td>\n",
       "      <td>-8.791107</td>\n",
       "      <td>-8.782266</td>\n",
       "      <td>-8.773602</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.464445</td>\n",
       "      <td>-7.464024</td>\n",
       "      <td>-7.463604</td>\n",
       "      <td>-7.463184</td>\n",
       "      <td>-7.462764</td>\n",
       "      <td>-7.462345</td>\n",
       "      <td>-7.461926</td>\n",
       "      <td>-7.461508</td>\n",
       "      <td>-7.461090</td>\n",
       "      <td>-7.460672</td>\n",
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       "    <tr>\n",
       "      <th>1768.01</th>\n",
       "      <td>-8.965704</td>\n",
       "      <td>-8.955394</td>\n",
       "      <td>-8.945323</td>\n",
       "      <td>-8.935480</td>\n",
       "      <td>-8.925855</td>\n",
       "      <td>-8.916439</td>\n",
       "      <td>-8.907223</td>\n",
       "      <td>-8.898199</td>\n",
       "      <td>-8.889358</td>\n",
       "      <td>-8.880693</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.571536</td>\n",
       "      <td>-7.571116</td>\n",
       "      <td>-7.570695</td>\n",
       "      <td>-7.570275</td>\n",
       "      <td>-7.569856</td>\n",
       "      <td>-7.569436</td>\n",
       "      <td>-7.569018</td>\n",
       "      <td>-7.568599</td>\n",
       "      <td>-7.568181</td>\n",
       "      <td>-7.567764</td>\n",
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       "    <tr>\n",
       "      <th>1562.93</th>\n",
       "      <td>-9.072795</td>\n",
       "      <td>-9.062485</td>\n",
       "      <td>-9.052414</td>\n",
       "      <td>-9.042571</td>\n",
       "      <td>-9.032947</td>\n",
       "      <td>-9.023531</td>\n",
       "      <td>-9.014315</td>\n",
       "      <td>-9.005290</td>\n",
       "      <td>-8.996449</td>\n",
       "      <td>-8.987785</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.678628</td>\n",
       "      <td>-7.678207</td>\n",
       "      <td>-7.677787</td>\n",
       "      <td>-7.677367</td>\n",
       "      <td>-7.676947</td>\n",
       "      <td>-7.676528</td>\n",
       "      <td>-7.676109</td>\n",
       "      <td>-7.675691</td>\n",
       "      <td>-7.675273</td>\n",
       "      <td>-7.674855</td>\n",
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       "    <tr>\n",
       "      <th>1381.63</th>\n",
       "      <td>-9.179887</td>\n",
       "      <td>-9.169577</td>\n",
       "      <td>-9.159506</td>\n",
       "      <td>-9.149663</td>\n",
       "      <td>-9.140038</td>\n",
       "      <td>-9.130622</td>\n",
       "      <td>-9.121406</td>\n",
       "      <td>-9.112382</td>\n",
       "      <td>-9.103541</td>\n",
       "      <td>-9.094876</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.785719</td>\n",
       "      <td>-7.785299</td>\n",
       "      <td>-7.784878</td>\n",
       "      <td>-7.784458</td>\n",
       "      <td>-7.784039</td>\n",
       "      <td>-7.783619</td>\n",
       "      <td>-7.783201</td>\n",
       "      <td>-7.782782</td>\n",
       "      <td>-7.782364</td>\n",
       "      <td>-7.781947</td>\n",
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       "    <tr>\n",
       "      <th>1221.37</th>\n",
       "      <td>-9.286978</td>\n",
       "      <td>-9.276668</td>\n",
       "      <td>-9.266597</td>\n",
       "      <td>-9.256754</td>\n",
       "      <td>-9.247130</td>\n",
       "      <td>-9.237714</td>\n",
       "      <td>-9.228498</td>\n",
       "      <td>-9.219473</td>\n",
       "      <td>-9.210632</td>\n",
       "      <td>-9.201968</td>\n",
       "      <td>...</td>\n",
       "      <td>-7.892811</td>\n",
       "      <td>-7.892390</td>\n",
       "      <td>-7.891970</td>\n",
       "      <td>-7.891550</td>\n",
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       "      <td>-7.889874</td>\n",
       "      <td>-7.889456</td>\n",
       "      <td>-7.889038</td>\n",
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       "      <th>0.02</th>\n",
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       "      <td>-19.021996</td>\n",
       "      <td>-19.011925</td>\n",
       "      <td>-19.002082</td>\n",
       "      <td>-18.992458</td>\n",
       "      <td>-18.983042</td>\n",
       "      <td>-18.973826</td>\n",
       "      <td>-18.964801</td>\n",
       "      <td>-18.955960</td>\n",
       "      <td>-18.947296</td>\n",
       "      <td>...</td>\n",
       "      <td>-17.638139</td>\n",
       "      <td>-17.637718</td>\n",
       "      <td>-17.637298</td>\n",
       "      <td>-17.636878</td>\n",
       "      <td>-17.636458</td>\n",
       "      <td>-17.636039</td>\n",
       "      <td>-17.635620</td>\n",
       "      <td>-17.635202</td>\n",
       "      <td>-17.634784</td>\n",
       "      <td>-17.634366</td>\n",
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       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>-19.139398</td>\n",
       "      <td>-19.129088</td>\n",
       "      <td>-19.119017</td>\n",
       "      <td>-19.109174</td>\n",
       "      <td>-19.099549</td>\n",
       "      <td>-19.090133</td>\n",
       "      <td>-19.080917</td>\n",
       "      <td>-19.071892</td>\n",
       "      <td>-19.063052</td>\n",
       "      <td>-19.054387</td>\n",
       "      <td>...</td>\n",
       "      <td>-17.745230</td>\n",
       "      <td>-17.744809</td>\n",
       "      <td>-17.744389</td>\n",
       "      <td>-17.743969</td>\n",
       "      <td>-17.743550</td>\n",
       "      <td>-17.743130</td>\n",
       "      <td>-17.742712</td>\n",
       "      <td>-17.742293</td>\n",
       "      <td>-17.741875</td>\n",
       "      <td>-17.741458</td>\n",
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       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>-19.246489</td>\n",
       "      <td>-19.236179</td>\n",
       "      <td>-19.226108</td>\n",
       "      <td>-19.216265</td>\n",
       "      <td>-19.206641</td>\n",
       "      <td>-19.197225</td>\n",
       "      <td>-19.188009</td>\n",
       "      <td>-19.178984</td>\n",
       "      <td>-19.170143</td>\n",
       "      <td>-19.161479</td>\n",
       "      <td>...</td>\n",
       "      <td>-17.852322</td>\n",
       "      <td>-17.851901</td>\n",
       "      <td>-17.851481</td>\n",
       "      <td>-17.851061</td>\n",
       "      <td>-17.850641</td>\n",
       "      <td>-17.850222</td>\n",
       "      <td>-17.849803</td>\n",
       "      <td>-17.849385</td>\n",
       "      <td>-17.848967</td>\n",
       "      <td>-17.848549</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>-19.353581</td>\n",
       "      <td>-19.343271</td>\n",
       "      <td>-19.333200</td>\n",
       "      <td>-19.323357</td>\n",
       "      <td>-19.313732</td>\n",
       "      <td>-19.304316</td>\n",
       "      <td>-19.295100</td>\n",
       "      <td>-19.286075</td>\n",
       "      <td>-19.277235</td>\n",
       "      <td>-19.268570</td>\n",
       "      <td>...</td>\n",
       "      <td>-17.959413</td>\n",
       "      <td>-17.958992</td>\n",
       "      <td>-17.958572</td>\n",
       "      <td>-17.958152</td>\n",
       "      <td>-17.957733</td>\n",
       "      <td>-17.957313</td>\n",
       "      <td>-17.956895</td>\n",
       "      <td>-17.956476</td>\n",
       "      <td>-17.956058</td>\n",
       "      <td>-17.955641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>-19.460672</td>\n",
       "      <td>-19.450362</td>\n",
       "      <td>-19.440291</td>\n",
       "      <td>-19.430448</td>\n",
       "      <td>-19.420824</td>\n",
       "      <td>-19.411408</td>\n",
       "      <td>-19.402192</td>\n",
       "      <td>-19.393167</td>\n",
       "      <td>-19.384326</td>\n",
       "      <td>-19.375662</td>\n",
       "      <td>...</td>\n",
       "      <td>-18.066505</td>\n",
       "      <td>-18.066084</td>\n",
       "      <td>-18.065664</td>\n",
       "      <td>-18.065244</td>\n",
       "      <td>-18.064824</td>\n",
       "      <td>-18.064405</td>\n",
       "      <td>-18.063986</td>\n",
       "      <td>-18.063568</td>\n",
       "      <td>-18.063150</td>\n",
       "      <td>-18.062732</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 1000 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           2000.0     2048.0     2096.0     2144.0     2192.0     2240.0   \\\n",
       "2000.00  -8.858612  -8.848302  -8.838231  -8.828388  -8.818764  -8.809348   \n",
       "1768.01  -8.965704  -8.955394  -8.945323  -8.935480  -8.925855  -8.916439   \n",
       "1562.93  -9.072795  -9.062485  -9.052414  -9.042571  -9.032947  -9.023531   \n",
       "1381.63  -9.179887  -9.169577  -9.159506  -9.149663  -9.140038  -9.130622   \n",
       "1221.37  -9.286978  -9.276668  -9.266597  -9.256754  -9.247130  -9.237714   \n",
       "...            ...        ...        ...        ...        ...        ...   \n",
       "0.02    -19.032306 -19.021996 -19.011925 -19.002082 -18.992458 -18.983042   \n",
       "0.01    -19.139398 -19.129088 -19.119017 -19.109174 -19.099549 -19.090133   \n",
       "0.01    -19.246489 -19.236179 -19.226108 -19.216265 -19.206641 -19.197225   \n",
       "0.01    -19.353581 -19.343271 -19.333200 -19.323357 -19.313732 -19.304316   \n",
       "0.01    -19.460672 -19.450362 -19.440291 -19.430448 -19.420824 -19.411408   \n",
       "\n",
       "           2288.0     2336.0     2384.0     2432.0   ...    49568.0  \\\n",
       "2000.00  -8.800132  -8.791107  -8.782266  -8.773602  ...  -7.464445   \n",
       "1768.01  -8.907223  -8.898199  -8.889358  -8.880693  ...  -7.571536   \n",
       "1562.93  -9.014315  -9.005290  -8.996449  -8.987785  ...  -7.678628   \n",
       "1381.63  -9.121406  -9.112382  -9.103541  -9.094876  ...  -7.785719   \n",
       "1221.37  -9.228498  -9.219473  -9.210632  -9.201968  ...  -7.892811   \n",
       "...            ...        ...        ...        ...  ...        ...   \n",
       "0.02    -18.973826 -18.964801 -18.955960 -18.947296  ... -17.638139   \n",
       "0.01    -19.080917 -19.071892 -19.063052 -19.054387  ... -17.745230   \n",
       "0.01    -19.188009 -19.178984 -19.170143 -19.161479  ... -17.852322   \n",
       "0.01    -19.295100 -19.286075 -19.277235 -19.268570  ... -17.959413   \n",
       "0.01    -19.402192 -19.393167 -19.384326 -19.375662  ... -18.066505   \n",
       "\n",
       "           49616.0    49664.0    49712.0    49760.0    49808.0    49856.0  \\\n",
       "2000.00  -7.464024  -7.463604  -7.463184  -7.462764  -7.462345  -7.461926   \n",
       "1768.01  -7.571116  -7.570695  -7.570275  -7.569856  -7.569436  -7.569018   \n",
       "1562.93  -7.678207  -7.677787  -7.677367  -7.676947  -7.676528  -7.676109   \n",
       "1381.63  -7.785299  -7.784878  -7.784458  -7.784039  -7.783619  -7.783201   \n",
       "1221.37  -7.892390  -7.891970  -7.891550  -7.891130  -7.890711  -7.890292   \n",
       "...            ...        ...        ...        ...        ...        ...   \n",
       "0.02    -17.637718 -17.637298 -17.636878 -17.636458 -17.636039 -17.635620   \n",
       "0.01    -17.744809 -17.744389 -17.743969 -17.743550 -17.743130 -17.742712   \n",
       "0.01    -17.851901 -17.851481 -17.851061 -17.850641 -17.850222 -17.849803   \n",
       "0.01    -17.958992 -17.958572 -17.958152 -17.957733 -17.957313 -17.956895   \n",
       "0.01    -18.066084 -18.065664 -18.065244 -18.064824 -18.064405 -18.063986   \n",
       "\n",
       "           49904.0    49952.0    50000.0  \n",
       "2000.00  -7.461508  -7.461090  -7.460672  \n",
       "1768.01  -7.568599  -7.568181  -7.567764  \n",
       "1562.93  -7.675691  -7.675273  -7.674855  \n",
       "1381.63  -7.782782  -7.782364  -7.781947  \n",
       "1221.37  -7.889874  -7.889456  -7.889038  \n",
       "...            ...        ...        ...  \n",
       "0.02    -17.635202 -17.634784 -17.634366  \n",
       "0.01    -17.742293 -17.741875 -17.741458  \n",
       "0.01    -17.849385 -17.848967 -17.848549  \n",
       "0.01    -17.956476 -17.956058 -17.955641  \n",
       "0.01    -18.063568 -18.063150 -18.062732  \n",
       "\n",
       "[100 rows x 1000 columns]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log10(stellar_constants)[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Stellar Prop. Factors')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAABXCAYAAABRAdG4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAfI0lEQVR4nO2de3BV1dn/v/uc5JzkEBKTwyVNgHAJImMtEQOUSw2RVAZbKlCdlksVam2BOmkR3or+RPgVeLXSTCgUC38orSBtZYA40Bk7RlIuE6BBYIqISCDSdAoGk3ANyUnOft4/QnbOPmff78j6zDDk7Nta+9lrfb/rWXvlhCMiAoPBYDAYHsPndgUYDAaDwZCCGRSDwWAwPAkzKAaDwWB4EmZQDAaDwfAkzKAYDAaD4UmYQTEYDAbDkzCDYtzRcByHrVu3Cp8HDhyIVatWuVgjBoNhFcygGLZy69YtLFu2DEOHDkVqairC4TBGjRqFdevWCcf85Cc/wcSJE92rpEZWrFgBjuPAcRx8Ph9yc3Mxc+ZMXLhwwe2qCUycOFGoY+y/w4cPm772qlWrMHDgQPOVZDA0kuR2BRhfbRYsWICqqir87ne/w4gRI3Dt2jUcP34c//73v92umiyRSASBQEBy38CBA3Ho0CHwPI/Tp09j/vz5mDp1Ko4fPw6/36/rWnYxa9YslJWVibaFw2FH66CGG3Fh3IEQg2EjGRkZtH79etn9y5cvJwCif5s3byYiouvXr1NpaSnl5ORQamoqFRQU0I4dO0TnA6AtW7YIn/Py8mjlypXC53feeYdGjx5N6enpFA6H6bHHHqMzZ84I++vq6ggAbd26laZMmUKhUIgWL14sW9chQ4aItm3dupUA0KeffkpVVVUEgPbs2UPjx4+nYDBI69evp0gkQi+88ALl5ORQcnIyDR8+nN55552E+1i7di3NmDGDQqEQfe1rX6OysjLl4EpQVFREzzzzjOS+l156ie677z5KTU2lfv360c9+9jO6cuWK6JijR4/S5MmTqWfPntSjRw8aNWoUHT58mDZv3pzwnJYvX05ERNeuXaOf/vSn1KtXLwoGg/TQQw/R3//+d+GacjGORCK0aNEiys3NpUAgQNnZ2fSDH/xA9z0zvrowg2LYyn333Uff+c53qLGxUXL/9evXadasWTR27Fi6ePEiXbx4kVpaWojneZo4cSIVFRXRgQMH6Ny5c7Rp0yZKTk6myspK4Xw1g3rrrbdo9+7dVFtbS8eOHaOpU6dSfn4+tbW1EVG3eObm5tKWLVvo3LlzdP78ecm6ShnUjh07CACdPHlSMKhhw4bRe++9R+fPn6f6+npasmQJZWVl0bvvvktnzpyh1atXE8dxCfeRmZlJ69atozNnztDatWvJ7/cnGLIaSga1cuVK2r9/P9XV1VFlZSUNGzaMnnrqKWH/xx9/TKFQiH74wx9STU0NffbZZ7Rt2zaqrq6mlpYWeuGFF6hfv37Cc7p+/ToRET3xxBOUl5dH77//Pn3yySdUWlpKycnJdPr0acUYl5WVUW5uLlVVVdGFCxfon//8J5WXl+u6X8ZXG2ZQDFs5ePAgDRgwgHw+Hz3wwAP07LPPUkVFBfE8LxzzzDPPUFFRkei8qqoqCgaDCSP8efPm0eOPPy58VjOoeBobGwkAHTx4kIi6xfPXv/616r3EG9SFCxdo9OjR1L9/f4pEIoJBvf3228IxN2/epEAgQBs2bBBda9q0aVRcXCy6jzlz5oiOmTlzJo0fP161XrEUFRVRUlIS9ejRQ/gXW04sO3fupEAgQNFolIiI5syZQ9/4xjeEz/GsXLmS8vLyRNvOnj1LAOhvf/ubaPuDDz5I8+bNIyL5GJeWllJxcbGoLTAYsbBFEgxbGT9+PM6dO4cDBw7g6aefxhdffIHvf//7+N73vgdS+J7impoaRCIR5ObmIi0tTfi3detWnD17VnP5J06cwPTp0zFo0CD07NkTAwYMAICEhQ2jR4/WdL3z588jLS0NoVAIeXl5ICLs2rULycnJkteqra1FJBLBww8/LLpOUVERTp06Jdo2duxY0efx48fjk08+0VSvWKZPn44TJ04I/95++20AwM6dO/Hwww8jJycHaWlpmD17NiKRCC5dugQA+OijjzBp0iT4fNploat+8ff38MMPJ9xffIznzZuHkydPIj8/H/Pnz8eOHTsQiUR03y/jqwtbJMGwnaSkJIwbNw7jxo3D4sWLsXXrVvzoRz/C/v37UVRUJHkOz/PIyMhATU1Nwj6tL9dbWlrw6KOPYsKECXjrrbeQnZ0NALj//vsThLBHjx6artm/f398+OGH8Pl8yM7ORigUSjhG6locx4k+E1HCtniUDFyJ9PR05Ofni7YdOXIETz75JF588UWsWbMGmZmZOHz4MJ5++mlRLNTqpBWp+4uPS0FBAerq6vDBBx+gqqoKv/jFL7Bs2TIcPnwY6enpltSDcWfDMiiG4wwfPhwA0NDQAKDTcKLRqOiYwsJCXLlyBa2trcjPzxf968qC1Dh9+jQuX76M1atXo7i4GMOHD0dzc7Nh4QeA5ORk5OfnY/DgwZLmFE9+fj6CwSD27dsn2r5//37cf//9om3xS8EPHTokxMosBw8eRK9evbBq1SqMGTMG9957L/7zn/+IjnnooYdQWVkJnuclryH1nLruYf/+/aLtBw4cSLg/KdLS0jB9+nSsW7cOR48exenTpxNixbh7YRkUw1aKioowc+ZMFBYWonfv3qitrcVLL72Ee+65B8XFxQCAQYMGYfv27Th16hT69u2Lnj174pFHHkFJSQlmzJiB3/zmNxgxYgSam5tRXV2NlJQUPPvss6pl5+XlIRgMYv369Vi8eDE+//xzLF261LIsQQuhUAilpaVYtmwZevfujYKCAmzfvh3vvfcePvjgA9Gxe/bswe9//3tMnjwZ77//Pv7617/iL3/5i7D/qaeeAgBhyk4Pw4YNw+XLl/Hmm2+iuLgYBw8exBtvvCE65le/+hXGjBmD2bNnY/HixcjMzMSxY8fQr18/jB07FoMGDcKlS5dw6NAhDB06FKFQCEOGDMGTTz6JhQsXYtOmTcjLy8Mf/vAHfPzxx9i2bZtindasWYOcnBwUFBQgFArhz3/+M/x+P+69917d98f4iuLmCzDGV59XX32VJkyYQL1796ZgMEj9+/en2bNn06lTp4RjGhsbacqUKZSeni5aZt61cmzgwIGUnJxMffv2pcmTJ9OHH34onAuVRRLbt2+n/Px8CgaDVFBQQP/4xz/I7/cLZXS9wD9w4IDqvUit4oula5FEfX29aLvWZebl5eX0+OOPU2pqKmVnZ9Prr78uOqaoqChhMUk8Sqv4Xn75ZerTpw+FQiGaMmUKbdu2jQBQXV2dcMyRI0do0qRJFAqFKC0tjUaPHk1HjhwR7mPmzJmUmZkpWmZ+9epVYZl5IBCQXWYeH+ONGzfSyJEjhSXthYWFVFFRoXh/jLsLjoj9RV0Gw204jsOWLVswZ84ct6vCYHgG9g6KwWAwGJ7E1DuoEydOYPPmzeB5HpMmTcK0adMsqhaDwWAw7nYMGxTP83jzzTfx8ssvIxwO48UXX0RhYSH69etnZf0YjLsCNtPOYCRieIqvtrYW2dnZ6Nu3r/B7LlK/s8JgMBgMhhEMG1RTU5PoG5LD4TCamposqRSDwWAwGIan+KSmJKR+v6SyshKVlZUAgNdee81ocQwGg8G4yzBsUOFwGI2NjcLnxsZGZGZmJhxXUlKCkpIS4fNjz3wMn6/TyLjb3/kVa2zc7X3x3wcmdYzcZ5+EUXIS3y8Wf55UWfH4ZM7Rcq5SmUrH/P+fhbF8U2PCcVL3abbsxHOMJdkGioor1/wv0/6/effgf/941fR1ulB79kax+xeHjcTyhTlp+M3WG7rPsytGajj5y9dK/M+sHvjtX266XY0E9GqF06wt7Sm53bBBDRkyBBcvXkRDQwOysrJQXV2N0tJS1fNSQilCh4ntOF0BjBXE2P3xDTC+I8Tvl+qUch1V7uEpdWwl4dbSRzUZVUxMUlKVv39OrzAY6dBGTcOsaBkVH5+PQzAlWbSNs/gXK+zq+FYYtGoZKgOxlNRk2f1GcMm7ADgTTwDgOCAYlJdVrxipFAbHorZi2KD8fj9+/OMfY/Xq1eB5HsXFxejfv7/qecFQEEC3aEllRlLGFX9M58/iiEq1QUmjkmkkckKq1KjUGr4WcVZrtF1Cq0dcnciuAHMdzu4si+OAlFRtTdwO4bCzw9uedXEcgkG/KxmR2xpuxsw6jd3ab5Bz09i1YGdbNBXJkSNHYuTIkbrOSQl1ZgKx5tL1AOQyJp/M9vhz4o+VO6fzPOn6KQm7YkalZjImsqp4odXTIIyIpJmMxShWtXHR4MakWNghDPZP51lzHZ8PSElN/BP2omNccBK3zQtQ7lM+H4fUFOdTES9nZl0YqaLjXxYbTEmOmbrqet8kbUCxnU0pk4o/r/P4xLL1ZVOSmxXP6T5XfWSvhdj4KAmtXiE1Nr2n+xQA5kXMzOkcxyEY6Ky41dmMXYLghM5oiYWVQuuWeLpRLMcBgUBi3LyaBVk95W01jhtU17y2MJ13uxXFPkD5TAqS27v3x5tWYvny76Gk66s8vSe76/Y1rTEqPWKhVwyMdGIzYm9WrPSc7vMBKTJxsyU7srGzO5GtxBbBcUBK0F71cnvQb0cb8PmA1KBzA0AncNNcXTCoziIFYxKZUfdx4vdQMdsTMinx9SVX8EkEWE5k5QRUqTNpEWzV1X0Ku2NHZbqzJZ0N36gQmst0jJ/bhVRcvCYWdnZ0q8XexwFBmXU5bhiLFzIQLffdaez216WrLK9j9rk5P8UX9MdM8XVuE1bwxdyMUrYU/2DiDULynZOUgMllTUpzzEoZlcrD0JwxSdyflNDqWzSh/Vjh+gYbl9mOY4UYcZy1YmGXGNgtvIafoQ9I0faHiwXcMhGvCDXHdcZAb9zsxMfdKV+hJf0Qnc+gUvxCg5IyIZFJxdVZ8Z2U1HSeRlOSXzAhvV3u2nr2q10/9jpahVZvR3XStKwyHb1lBiVWSlufbdgnAk6Ir3Q/4ZASsOe+XF1ubrNgc5wPwWTpv0iceKytVTGFFzJWwBWD6nrnJDYkOWMSm5L4WvEPWLMhyb5vkt5uxqi0mpDaNfSMyvQKphuZkjWGpXyfHOdDSkBdLOwQCnun8+wfFXOcX1PsrMbtVzFmY+vjOKRoNCgteNnEACsHZ9IrRp2f4gtw3cvK4/4Xv2uS/lnpOKn9SsfJG5J00M1mTdrMSuorpBJHZboWCxjKlIw1PNPTe+ZOv12HzrpbIRb2Te3ZPZI3d76P8yGYpDETgDvTSF4Q7/jn6OP8SEmOulSbTtx6HnrQ+uycz6ACSDAoLcYU2xCMZ05S4i9dT+WsSb4BaJraUz9EVIaa0OozK/2N13CGZbKjmBUgjvMjkMRbbgZ2CYAz03na6s5xfgSTOkyV5WY25ESWKVduwN9tUF41C7fioxfHDSr19ry2cvYkbUaJU3wU91m8X6qDyD0YvdmU0jnCfg2NU9vKIO2jMr0dwvj0nvEGbla4tJbt45KQoiKydgiInZ3fCdHnOIIPQaT4zRmUrjJdFHIrnxeHIIL+dpPX8K55OJ21upBBdRmU2KgAceeTNyllU5J6uNIZloxRyTQO5WXgyg1Kb8aUcD6XJIzK9DRevR3PqPiZ6eBWdUbJ7NigWNhjWpZfUsBnk8kGfB0J29zAbcHWU76PIwR95gxKC17PgKx6Zo4bVOyUi5BFQd2M5I7p/Bw3DyxRrmzmJGtI0tvVRFz1xb2mrCrOhBWEVp9haT5UwKj4me1AVjRwO8TCLmGwW4R1Z9YgBHwRY2W5KJ52mLUeOBCCBuNmNxycX/RiFk0G9fOf/xwpKSnw+Xzw+/147bXXcOPGDZSXl+Py5cvo3bs3Fi1ahLS0NNVrpSR1xEzvxbxnQeI2sSkpm5D0CDo+27Iua1LrCFYYVddxWoRWrygYEUQzImp6dZTB+gbi4ma1EdjZ6Z3IHOQHYjyCvjbry3NzKs+JeIKQzKkblNtZoRxeMzHNGdTy5cuRnp4ufK6oqMADDzyAadOmoaKiAhUVFZgzZ47qdbpevCoZkpxJde7r/llKtBKzD3XjkjtX7XjN+1WnANWvH/C168uWdDY0ox3G7ek9pWtwIAQ47SJry9SenQYm8UdDdSNzCQ6EZIoIPzsNR+4LpbFBHI8A32pDbbwREyXsaCeGp/hqamqwYsUKAEBRURFWrFihzaD8XQaVmB2JMiaZ7CnBsDSYlJwBSJuXwmo5JTG0MGOS2hYvtLaalR7hiznU9Ko9CzqguA2ZFws7RMH26TxL4sgjEL2l4TiX3ktZYc6m65AYZx/xCHSox80+3I+LGnrap2aDWr16NQDg29/+NkpKSnD16lXhL+hmZmbi2rVrkufF/8n3+/OkpwGNzJHbjb1laL92ciAZ/XOzZfc7s7DGxYZvsOikQADZ/fKEz16dVvEi/kAQfQYMsfCKd0fs/cEUhAfeK7nPu+saPFsxbQa1cuVKZGVl4erVq1i1ahVycnI0FxD/J9///Z9LABKn82Szp7gRcSzxo6iE7ErCqWWn92RcXTFrUhkJaFoQoWEk2CtvKJo/P6N6XCc6jd7AaNvM6NXqLEmJjCEP4Nq5k7bWJQEbR/aOTPHcrn/6vSNx/bNj9pcHd997WB3TtGGjcPNMjbGTPZAVKmFn+8t46FHJ7ZoMKisrq/MiGRkYNWoUamtrkZGRgebmZmRmZqK5uVn0fkqJrqkqQeQoxqxiAiAyJpnt8fuk9ovKUjivG2OGpCbaWh6uvPASkqLdU3y6GorORm+4EZrsXFaIVEJbIB5J7S3GLmaDWNhtMFZOe3HEI6lDYXrUhfchXpjWU7tvjufhjzg8xeeFuChgpt2rGlRrayuICKmpqWhtbcW//vUvPPHEEygsLMS+ffswbdo07Nu3D6NGjdJUYHK0LcGQxGaUaFadSBtW7Dly++PLUDqusyjjWZNaY9EixJqF1gHzMSwKJgXMCjGyXCxsEgLbMyMj9SYePgOxc+1FvlcWEBiMm914fYGFHKoGdfXqVfz2t78FAESjUUyYMAEFBQUYMmQIysvLsXfvXvTq1QvPP/+8pgKTo63ijEjCkKQyKgCijqa0r/s6EkYl9aAMGpKiiGrJmLQIB/HahdaJbMnN6T295xMPX7tMFmCx2dgqAE6MkBP6Ew9fxGD2qQGOd3nUb9Pz4ojgi+hcmONl83A5O1M1qL59+2LNmjUJ23v27IlXXnlFd4HJ7Z1CK3ToWNO5bSiizq6QHSUIvFTmJBVgnZmTovhYMLWn2kC7hFZHY9EtmC5kSqZFSm26hQi+No2j2TvsfZTdosbxBC7SCrhhJC4LtqnBBvHg2iw2drfNXA0bn5fj3yTh7+jOoLrfQ8V9jtnW+bPKFJ6GKT7JIFptSKrz09oypsT6SAit3QZkptGZ6VAWNXaOeOvEwi6B8OLUnnAuD65Vx1SVW6biBfGOvXeeB/TEzUaI93Bm1oVKG3XeoCK3ErInccYkbUyqU3rx722kGq5W45K6vpZzulDrNBo7c3ecVIRWbyd1cmrPrHCZESCeB9rarKlHHLZ1fjem86TgeVCrRZmAWybihmnyPKhNYorPC0YqhZenF+GKQd1u9PHZEy+XPclnUgnB1WhKkhmSUgMyMcVn2swA3aMy3eJp8CW6YazorFaKrNXiYWOnd2pUTDwPuuVwJuDyiJ8sGBwQ8eCtiJvXsx+H3k05blBc11RVVyeWMSaRiciZF6BuWvHnKx0HBQEwuSDCVFYVOyqzOVsyLIBmGqwFnVFKXAyLxR2YHVluXMSDb5V52X8XvpfqrIKWwSSBb3HI2L1uYjBv+i4YVGt3Y4vLogDImpGoAxoxJbkGLtfoFDqEohioPRCNjSr2wSoKrQPZkmHxs3kRhJbyqbVVm7BovqY9omDF6F0VPXU3KbSO3I8cLgo38d3Gbmm7s5A74t3UbRw3KGptUTYmObOK25cQZKkOIfEgJDuOgaxJ9SEbXBCReAhpFwudDc+QiBhs3JYIlt7743lEJeJmtXDY2uEdEHqp+hPPo8OmTMBV4bZbnHkeHTe1xc1VE1fBKybmuEF1vUsRAhD7kG5vI4ltAnEPNSGQGjMnyU6i8FAUG5PKw9TUEJXKNjgqc+RdlJFyROfaaFw6xEKojw2iYWtnt0nsiecRvdUm+uwGbmchessnnkf7TXu+zRzonE3xNBY/L8cNim/t/n0eodFLZE+ihhHXORQNLH6/0nEywTT0HkrpPJXyREhdQ0Jo9QipIXEx2NDMCpkVgtR1DSvEwjZBsFl4zT8HHu1aMwGXTMQLo/z4e6coaY6bXbht6lrQ+uycN6iWW93iGlNJyW0xgVab0ovfrydDkhN7xSAqNAItwdfSiPQIrW4hNdCIjQqC2Q5jptyOW62iz1Zjlxg4Ib5KdacoIXLD2kzATeF0cvVje4v83yDzsnl4sW6OG5Qwrx2XRcllTKLFAirTeVpMSjZr0ruIQqo+GsvSc42u69g1mnXDdJwyLIryqiJ7J5lW57WdMS7i1WNndZluYWVMed68sXvRKLrgo87WzT2DksiOxBmTeBWbgCFT0jO9Z8yQ1BqVGbOiqHhUpu891J2RKVnVKWPrblYs7BAKuzu4VWJLUULkpvJfI3ZDSL0g3krPkKI8Wq9p/yvOVuGFuKhhpG06b1C32gSTkTYmuSk++UwqYR5Yo0nJHau83VzWZMSolIRWT8M0Io7uTetZ8S7KerG4U6f0SOez53kebQZjx7uaDbm/qKLtmnOZpx6czn6swHGDar/RtRpNbE5mTSp+v9RnufPkjgVURksOmBWgb1TmxBSfXrGLxax46coeo4TIzYjMPusNwU4BMBNzzWXE9q8oofWqvZmA24JpR0z5DkLbtXb953lgwYcc1O7ec3LcoCJxBtX5s3aTim/URt87yXUOw1N8Ko1dizArZXOxQqtXXPUKgdGOa2b0apVYxdad7yC0NhsXWTtEw+7OzndYc/3O2EmbexduCJdV92cGpfvm23ncuuj8FJ8X4qKGkfbCkZd/W4zBYDAYdy0+JwtbunSpk8V9ZWBxMwaLm3FY7IzB4mYtjhoUg8FgMBhaYQbFYDAYDE/iqEGVlJQ4WdxXBhY3Y7C4GYfFzhgsbtbCFkkwGAwGw5OwKT4Gg8FgeBLHfg/qxIkT2Lx5M3iex6RJkzBt2jSnivY0X375JTZs2IArV66A4ziUlJTgsccew40bN1BeXo7Lly+jd+/eWLRoEdLS0gAAu3btwt69e+Hz+TBv3jwUFBS4exMuwvM8li5diqysLCxdupTFTSM3b97Exo0bUV9fD47jsGDBAuTk5LDYqbBnzx7s3bsXHMehf//+WLhwISKRCIubXZADRKNReu655+jSpUvU3t5OS5Ysofr6eieK9jxNTU107tw5IiJqaWmh0tJSqq+vpy1bttCuXbuIiGjXrl20ZcsWIiKqr6+nJUuWUCQSoS+++IKee+45ikajblXfdXbv3k1r166lV199lYiIxU0j69evp8rKSiIiam9vpxs3brDYqdDY2EgLFy6ktrY2IiIqKyujqqoqFjcbcWSKr7a2FtnZ2ejbty+SkpIwbtw41NTUOFG058nMzMTgwYMBAKmpqcjNzUVTUxNqampQVFQEACgqKhLiVVNTg3HjxiE5ORl9+vRBdnY2amtrXau/mzQ2NuLYsWOYNGmSsI3FTZ2WlhacPn0ajzzyCAAgKSkJPXr0YLHTAM/ziEQiiEajiEQiyMzMZHGzEUem+JqamhAOh4XP4XAYZ8+edaLoO4qGhgbU1dUhPz8fV69eRWZmJoBOE7t27RqAzlgOHTpUOCcrKwtNTU2u1Ndt/vjHP2LOnDm4dav7T5GwuKnT0NCA9PR0vPHGG7hw4QIGDx6MuXPnstipkJWVhalTp2LBggUIBAIYMWIERowYweJmI45kUCSxUJDjOCeKvmNobW1FWVkZ5s6di1AoJHucVCzvRj766CNkZGQI2acaLG7dRKNR1NXV4dFHH8Xrr7+OYDCIiooK2eNZ7Dq5ceMGampqsGHDBmzatAmtra3Yv3+/7PEsbuZxJIMKh8NobGwUPjc2NgojDgbQ0dGBsrIyfOtb38KYMWMAABkZGWhubkZmZiaam5uRnp4OIDGWTU1NyMrKcqXebnLmzBkcPXoUx48fRyQSwa1bt7Bu3ToWNw2Ew2GEw2FhdP/Nb34TFRUVLHYqnDx5En369BHiMmbMGHz22WcsbjbiSAY1ZMgQXLx4EQ0NDejo6EB1dTUKCwudKNrzEBE2btyI3NxcfPe73xW2FxYWYt++fQCAffv2YdSoUcL26upqtLe3o6GhARcvXkR+fr4rdXeTWbNmYePGjdiwYQN++ctf4utf/zpKS0tZ3DRwzz33IBwO47///S+ATuHt168fi50KvXr1wtmzZ9HW1gYiwsmTJ5Gbm8viZiOO/aLusWPH8Kc//Qk8z6O4uBgzZsxwoljP8+mnn+KVV17BgAEDhGnPmTNnYujQoSgvL8eXX36JXr164fnnnxeWru7cuRNVVVXw+XyYO3cuHnzwQTdvwXVOnTqF3bt3Y+nSpbh+/TqLmwY+//xzbNy4ER0dHejTpw8WLlwIImKxU+Hdd99FdXU1/H4/Bg4ciPnz56O1tZXFzSbYN0kwGAwGw5Owb5JgMBgMhidhBsVgMBgMT8IMisFgMBiehBkUg8FgMDwJMygGg8FgeBJmUAwGg8HwJMygGAwGg+FJmEExGAwGw5P8Hwa/32vzp+i5AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 5))\n",
    "\n",
    "cax = ax.imshow(np.log10(stellar_constants), #[::-1], \n",
    "                cmap=cm.coolwarm)\n",
    "ax.set_title('Stellar Prop. Factors')\n",
    "\n",
    "#cbar = fig.colorbar(cax, ticks=[-1, 0, 1])\n",
    "#cbar.ax.set_yticklabels(['< -1', '0', '> 1'])  # vertically oriented colorbar\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 24.0, 'Stellar Radius $[R_{\\\\odot}]$'),\n",
       " Text(42.0, 0.5, 'Temperature [K]')]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 5))\n",
    "ax = sns.heatmap(np.log10(stellar_constants)[::-1])\n",
    "ax.set(xlabel=r'Stellar Radius $[R_{\\odot}]$', ylabel='Temperature [K]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minimum frequency for different stars\n",
    "\n",
    "Varying distances from Earth\n",
    "\n",
    "### Minimum frequencies detectable at Earth's surface\n",
    "The radio window for Earth puts a lower limit of 15 MHz ($1.5 \\times 10^7$) and an upper limit of 1 THz ($1 \\times 10^{12}$) for the frequency that can pass through Earth's atmosphere and reach detectors on the surface.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constant_for_min_frequency(constant_for_flux):\n",
    "    return pow((pow(3e8, 2) * pow(10, -12.5)) / constant_for_flux, 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "min_freq_constants = constant_for_min_frequency(stellar_constants)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 24.0, 'Stellar Radius $[R_{\\\\odot}]$'),\n",
       " Text(42.0, 0.5, 'Temperature [K]')]"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 5))\n",
    "ax = sns.heatmap(np.log10(min_freq_constants)[::-1])\n",
    "ax.set(xlabel=r'Stellar Radius $[R_{\\odot}]$', ylabel='Temperature [K]')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot is inverted from the previous colormap."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 10000 m2 detector\n",
    "\n",
    "Current capabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x360 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diameter_detector = 100\n",
    "freq_min = 7\n",
    "freq_max = 12\n",
    "\n",
    "fig, (ax1, ax2, ax3, ax4, axcb) = plt.subplots(1, 5, gridspec_kw={'width_ratios':[1, 1, 1, 1, 0.08]}, figsize=(5, 5))\n",
    "ax1.get_shared_y_axes().join(ax2, ax3, ax4)\n",
    "\n",
    "axis = [ax1, ax2, ax3, ax4]\n",
    "min_freqs = [10, 100, 1000, 1500]\n",
    "cbar_ax = [None, None, None, axcb]\n",
    "cbar = [False, False, False, True]\n",
    "\n",
    "for i in range(len(min_freqs)):\n",
    "\n",
    "    g = sns.heatmap(np.log10(frequency_minimum(light_years_to_star=min_freqs[i],\n",
    "                                                diameter_detector=diameter_detector,\n",
    "                                                constant=min_freq_constants)).T[::-1],\n",
    "                    ax=axis[i], vmin=freq_min, vmax=freq_max, cbar=cbar[i], cbar_ax=cbar_ax[i], cmap=\"Spectral\")\n",
    "    \n",
    "    g.set_title(str(min_freqs[i]) + ' ly')\n",
    "\n",
    "ax1.set_ylabel('Temperature [Kelvin]')\n",
    "ax1.set_xlabel(r'Solar radii $[R_{\\odot}]$')\n",
    "\n",
    "fig.set_figheight(5)\n",
    "fig.set_figwidth(25)\n",
    "fig.suptitle('100m Mirror', fontsize=20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1 km2 detector\n",
    "Near future capabilities (SKA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x360 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diameter_detector = 1000\n",
    "freq_min = 7\n",
    "freq_max = 12\n",
    "\n",
    "fig, (ax1, ax2, ax3, ax4, axcb) = plt.subplots(1, 5, \n",
    "                                               gridspec_kw={'width_ratios':[1,1,1,1,0.08]})\n",
    "ax1.get_shared_y_axes().join(ax2, ax3, ax4)\n",
    "\n",
    "axis = [ax1, ax2, ax3, ax4]\n",
    "min_freqs = [10, 100, 1000, 1500]\n",
    "cbar_ax = [None, None, None, axcb]\n",
    "cbar = [False, False, False, True]\n",
    "\n",
    "for i in range(len(min_freqs)):\n",
    "\n",
    "    g = sns.heatmap(np.log10(frequency_minimum(light_years_to_star=min_freqs[i],\n",
    "                                                diameter_detector=diameter_detector,\n",
    "                                                constant=min_freq_constants)).T[::-1],\n",
    "                    ax=axis[i], vmin=freq_min, vmax=freq_max, cbar=cbar[i], cbar_ax=cbar_ax[i], cmap=\"Spectral\")\n",
    "    \n",
    "    g.set_title(str(min_freqs[i]) + ' ly')\n",
    "\n",
    "fig.set_figheight(5)\n",
    "fig.set_figwidth(25)\n",
    "fig.suptitle('1000m Mirror', fontsize=20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Individual stars of interest\n",
    "\n",
    "### Tabby's star\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "tabby_distance = 1447\n",
    "tabby_temp = 6750\n",
    "tabby_radius = 1.58"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimum frequency for Tabby's star with 100m diameter detector = 10.65\n"
     ]
    }
   ],
   "source": [
    "tabby_min_freq = np.log10(frequency_minimum(light_years_to_star=tabby_distance,\n",
    "                          diameter_detector=100,\n",
    "                          constant=constant_for_min_frequency(constant_for_flux_calc(tabby_radius, tabby_temp) \n",
    "                                                              * quiet_sun_factor)))\n",
    "\n",
    "print(f\"Minimum frequency for Tabby's star with 100m diameter detector = {round(tabby_min_freq, 2)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.000000e+01    1.556340e-51\n",
       "1.004385e+01    1.570019e-51\n",
       "1.008789e+01    1.583818e-51\n",
       "1.013213e+01    1.597738e-51\n",
       "1.017655e+01    1.611781e-51\n",
       "                    ...     \n",
       "9.826509e+19    1.502806e-13\n",
       "9.869597e+19    1.516014e-13\n",
       "9.912875e+19    1.529339e-13\n",
       "9.956342e+19    1.542780e-13\n",
       "1.000000e+20    1.556340e-13\n",
       "Name: tabby_flux_rj, Length: 10000, dtype: float64"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sun_df[\"tabby_flux_rj\"] = [flux_from_luminosity(monochromatic_luminosity_rayleigh_jeans(freq, tabby_temp, tabby_radius * SUN_RADIUS),\n",
    "                                                light_years_to_metres(tabby_distance)) * quiet_sun_factor\n",
    "                           for freq in frequencies]\n",
    "sun_df[\"tabby_flux_rj\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sun_df[[\"sunlike_flux\", \"sun_flux_planck\", \n",
    "        \"sun_flux_rj\", \"tabby_flux_rj\", \n",
    "        \"galactic_flux_100\", \"galactic_flux_1000\"]][1e-2:1e18].plot(use_index=True, loglog=True, ylim=(1e-45, 1e-10), xlim=(3e4, 3e15), \n",
    "                                                                    xlabel='Frequency [Hz]', \n",
    "                                                                    ylabel=r'Flux [$W {m}^{-2}$]', \n",
    "                                                                    title='Flux');\n",
    "\n",
    "plt.legend(['Sun-like', 'Sun, Planck', 'Sun, RJ', \n",
    "            'Tabby', 'Gal., 100m mirror', 'Gal., 1000m mirror'],\n",
    "            bbox_to_anchor=(1.0, 0.95),\n",
    "            ncol=1, fancybox=True, shadow=True);\n",
    "\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The minimum frequency required for us to detect a message above background radiation is inversely proportional to the radius and temperature of the host star:\n",
    "\n",
    "$${f_{min}} \\propto {{1}\\over{r^{0.4}T^{0.2}}} $$\n",
    "\n",
    "A message sent from a planet orbiting a smaller star will need a higher minimum frequency. \n",
    "\n",
    "The frequency increases further with increasing distance from Earth and decreases with the size of our detector. \n",
    "\n",
    "All minimum frequencies fall within the window that can pass through Earth's atmosphere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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