{
 "metadata": {
  "name": "",
  "signature": "sha256:f4262e7b7b1ea443ce55e9fcdd38ecb39c519bd6fcdb6000543640860c1845ce"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "La radiaci\u00f3n del cuerpo negro y el fondo c\u00f3smico de microondas (CMB) en Python: parte I"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Autor: [Eduardo Mart\u00edn Calleja](http://balbuceosastropy.blogspot.com.es/)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Este post es el primero de una serie de dos en el cual examinaremos con ayuda del lenguaje Python las caracter\u00edsticas de la radiaci\u00f3n de un cuerpo negro en general y, en un segundo post, aplicaremos lo visto al caso particular del espectro de radiaci\u00f3n t\u00e9rmica del fondo c\u00f3smico de microondas (CMB).\n",
      "\n",
      "El estudio de las propiedades de los objetos celestes, como su color o luminosidad, necesita del concepto de cuerpo emisor ideal de radiaci\u00f3n conocido como \"cuerpo negro\". Las estrellas radian energ\u00eda que depende de su temperatura y de la longitud de onda de la radiaci\u00f3n, y la ley de emisi\u00f3n de un cuerpo negro pude considerarse como una primera aproximaci\u00f3n de las caracter\u00edsticas de esta radiaci\u00f3n. Por este motivo mostrar\u00e9 en este post como construir en Python las curvas de radiaci\u00f3n caracter\u00edsticas de un cuerpo negro a diferentes temperaturas, lo que constituir\u00e1 adem\u00e1s un buen ejercicio para practicar con el uso de unidades f\u00edsicas con el m\u00f3dulo *quantities*, que fue el objeto del [post anterior](http://balbuceosastropy.blogspot.com.es/2013/09/trabajando-con-unidades-y-constantes.html)\n",
      "\n",
      "Como de costumbre, esta entrada est\u00e1 escrita \u00edntegramente utilizando el Notebook de IPhython"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Importaciones y referencias"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Puede consultarse el siguiente art\u00edculo en Wikipedia. Personalmente recomiendo la versi\u00f3n inglesa del mismo: [Planck's law](http://en.wikipedia.org/wiki/Planck%27s_law)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "from __future__ import division\n",
      "\n",
      "import quantities as pq\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "# Generar un cuadro con versiones de las librer\u00edas utilizadas en este notebook\n",
      "#https://github.com/jrjohansson/version_information\n",
      "%load_ext version_information\n",
      "%version_information numpy, matplotlib, quantities"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]</td></tr><tr><td>IPython</td><td>2.3.1</td></tr><tr><td>OS</td><td>Linux 3.13.0 44 generic x86_64 with debian jessie sid</td></tr><tr><td>numpy</td><td>1.9.1</td></tr><tr><td>matplotlib</td><td>1.4.2</td></tr><tr><td>quantities</td><td>0.10.1</td></tr><tr><td colspan='2'>Thu Jan 22 20:25:59 2015 CET</td></tr></table>"
       ],
       "json": [
        "{\"Software versions\": [{\"version\": \"2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\", \"module\": \"Python\"}, {\"version\": \"2.3.1\", \"module\": \"IPython\"}, {\"version\": \"Linux 3.13.0 44 generic x86_64 with debian jessie sid\", \"module\": \"OS\"}, {\"version\": \"1.9.1\", \"module\": \"numpy\"}, {\"version\": \"1.4.2\", \"module\": \"matplotlib\"}, {\"version\": \"0.10.1\", \"module\": \"quantities\"}]}"
       ],
       "latex": [
        "\\begin{tabular}{|l|l|}\\hline\n",
        "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
        "Python & 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n",
        "IPython & 2.3.1 \\\\ \\hline\n",
        "OS & Linux 3.13.0 44 generic x86\\_64 with debian jessie sid \\\\ \\hline\n",
        "numpy & 1.9.1 \\\\ \\hline\n",
        "matplotlib & 1.4.2 \\\\ \\hline\n",
        "quantities & 0.10.1 \\\\ \\hline\n",
        "\\hline \\multicolumn{2}{|l|}{Thu Jan 22 20:25:59 2015 CET} \\\\ \\hline\n",
        "\\end{tabular}\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "Software versions\n",
        "Python 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n",
        "IPython 2.3.1\n",
        "OS Linux 3.13.0 44 generic x86_64 with debian jessie sid\n",
        "numpy 1.9.1\n",
        "matplotlib 1.4.2\n",
        "quantities 0.10.1\n",
        "Thu Jan 22 20:25:59 2015 CET"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Radiaci\u00f3n del cuerpo negro"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La ecuaci\u00f3n de Plank representa la intensidad de la radiaci\u00f3n de un cuerpo negro en funci\u00f3n de la longitud de onda. Existe una curva para cada temperatura del cuerpo negro. Su forma es conocida como Ley de Plank:\n",
      "\n",
      "$$ B_\\lambda(T) = \\frac{2hc^2}{\\lambda^5} \\frac{1}{e^\\frac{hc}{\\lambda k_B T} -1}$$\n",
      "\n",
      "\n",
      "$B$ Es la **radiancia espectral**, definida como la potencia emitida por un \u00e1rea unidad del cuerpo negro en un \u00e1ngulo s\u00f3lido unitario normal al \u00e1rea, por unidad de longitud de onda. Se emplea normalmente la letra *B* en lugar de la letra *I* con la que se designan gen\u00e9ricamente las intensidades, para subrayar que nos estamos refiriendo espec\u00edficamente a un cuerpo negro (\"*blackbody*\").  Sus unidades, suponiendo que medimos las longitudes de onda en namometros, ser\u00e1n: $W m^{\u207b2} nm^{-1} sr^{\u207b1}$, siendo $sr$ la unidad de \u00e1ngulo s\u00f3lido \"estereorradian\".\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La f\u00f3rmula anterior utiliza las constantes siguientes:\n",
      "\n",
      "- $k_B$ la constante de Boltzmann\n",
      "\n",
      "- $h$ la constante de Plank\n",
      "\n",
      "las cuales, en el paquete  de Python *quantities* se definen como:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print repr(pq.constants.Planck_constant)\n",
      "print repr(pq.constants.Boltzmann_constant)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "UnitConstant('Planck_constant', 6.62606896e-34 * s*J, 'h')\n",
        "UnitConstant('Boltzmann_constant', 1.3806504e-23 * J/K, 'k')\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vamos a definir una funci\u00f3n que permitir\u00e1 calcular la radiancia espectral seg\u00fan la anterior f\u00f3rmula de Plank"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def B(wl,T):\n",
      "    '''wl es un array de longitudes de onda con unidades de longitud\n",
      "    T es una temperatura expresada en Kelvin\n",
      "    el resultado es un array de r.e. con unidades W/(m**2 * nm * sr)\n",
      "    '''\n",
      "    I = 2 * pq.constants.h * (pq.c)**2 / wl**5 *  \\\n",
      "        1 / (np.exp((pq.constants.h*pq.c \\\n",
      "        / (wl*pq.constants.k*T)).simplified)-1)\n",
      "    return I.rescale(pq.watt/(pq.m**2 * pq.nm *pq.sr))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Comprobaremos el correcto funcionamiento de la funci\u00f3n con un ejemplo:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B( 5000 *pq.angstrom, 5780 *pq.K)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array(26421.6296096971) * W/(m**2*nm*sr)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A continuaci\u00f3n aplicaremos esta funci\u00f3n para obtener las curvas de radiaci\u00f3n del cuerpo negro para cuatro temperaturas"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "T1 = 4000 * pq.Kelvin\n",
      "T2 = 5000 * pq.Kelvin\n",
      "T3 = 6000 * pq.Kelvin\n",
      "T4 = 7000 * pq.Kelvin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Representaremos las curvas con la funci\u00f3n *plot()* del paquete Matplotlib"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wl = np.arange(10,2000,10) * pq.nm    # array de longitudes de onda en nanometros\n",
      "\n",
      "fig, ax = plt.subplots(figsize=(12, 8))\n",
      "ax.plot(wl, B(wl,T4), label='7000K')\n",
      "ax.plot(wl, B(wl,T3), label='6000K')\n",
      "ax.plot(wl, B(wl,T2), label='5000K')\n",
      "ax.plot(wl, B(wl,T1), label='4000K')\n",
      "ax.legend()\n",
      "ax.set_title(u'Radiaci\u00f3n del cuerpo negro')\n",
      "ax.title.set_fontsize(20)\n",
      "ax.set_xlabel('Longitud de onda en nm')\n",
      "ax.xaxis.label.set_fontsize(15)\n",
      "ax.set_ylabel('Radianza espectral $(W m^{-2}nm^{-1}sr^{-1})$')\n",
      "ax.yaxis.label.set_fontsize(15)\n",
      "ax.axvspan(0,400,facecolor = 'violet',alpha = 0.6)\n",
      "ax.axvspan(400,700, facecolor='yellow', alpha = 0.5)\n",
      "ax.axvspan(700,2000, facecolor ='red', alpha = 0.3)\n",
      "ax.text(150,6e4, 'UV', fontsize=30, color = 'b')\n",
      "ax.text(1200,6e4, 'IR', fontsize=30, color = 'r')\n",
      "ax.text(420,6e4, 'VISIBLE', fontsize=20, color = 'green');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvYAAAIDCAYAAABvvlqKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwN7MzMzMbADwwN7MzMzMbAD4Lzn9X325m4NyAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd07d15fc90>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "En la anterior figura se aprecia muy bien como, conforme se eleva la temperatura del cuerpo negro, el m\u00e1ximo de la intensidad emitida va correspondiendo a longitudes de onda cada vez m\u00e1s cortas, es decir, frecuencias m\u00e1s elevadas, o fotones m\u00e1s energ\u00e9ticos, entrando este m\u00e1ximo, a partir de los 7000K, en la regi\u00f3n del ultravioleta. Este hecho se expresa matem\u00e1ticamente mediante la ley de Wien."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ley de Wien"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La longitud de onda m\u00e1xima $\\lambda_{max} $   a la que emite un cuerpo negro viene dada por:\n",
      "\n",
      "$$ \\lambda_{max} = \\frac{b}{T} $$\n",
      "\n",
      "Siendo $b$ la constante de Wien, cuyo valor viene dado por:\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print repr(pq.constants.b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "UnitConstant('Wien_wavelength_displacement_law_constant', 0.0028977685 * m*K, 'b')\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Veamos algunos ejemplos:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La estrella Betelgeuse, en la constelaci\u00f3n de Orion, tiene una temperatura superficial de 3600K. Si la consideramos en primera aproximaci\u00f3n como un cuerpo negro, \u00bfen qu\u00e9 longitud de onda presentar\u00e1 su espectro el m\u00e1ximo de radiaci\u00f3n?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l_max = pq.constants.b/(3600 * pq.K)\n",
      "print '%d Angstrom' %l_max.rescale(pq.angstrom)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "8049 Angstrom\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Es decir, la radiaci\u00f3n de Betelgeuse alcanzar\u00e1 su m\u00e1ximo en la regi\u00f3n del infrarojo cercano."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La ley de Wien tambi\u00e9n se puede utilizar para estimar la temperatura de una estrella a partir de su espectro (siempre con la aproximaci\u00f3n de suponer un modelo de radiaci\u00f3n de cuerpo negro):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Supongamos que la radiaci\u00f3n de una estrella tiene su intensidad m\u00e1xima en los 400 nm\n",
      "\n",
      "lmax  = 400 * pq.nm\n",
      "\n",
      "T = pq.constants.b / lmax\n",
      "\n",
      "print \"Su temperatura efectiva ser\u00e1: %d K\" %T.simplified"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Su temperatura efectiva ser\u00e1: 7244 K\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ley de Stefan\u2013Boltzmann"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La ley de Stefan-Boltzmann es otra consecuencia importante de la ley de radiaci\u00f3n de Plank. Indica que el valor de la energ\u00eda total radiada por unidad de superficie y unidad de tiempo en todas las longitudes de onda, es proporcional a la cuarta potencia de la temperatura.\n",
      "\n",
      "A la energ\u00eda total radiada por unidad de superficie de un cuerpo negro en una unidad de tiempo, en todas las longitudes de onda se la conoce como **potencia emisiva**, y viene dada por:\n",
      "\n",
      "$$ E = \\sigma T^4 $$\n",
      "\n",
      "E se mide en $W/m^2$\n",
      "\n",
      "$\\sigma$ es la llamada constante de Stefan-Boltzmann, y su valor es:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print pq.constants.sigma, '=', pq.constants.sigma.simplified"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 sigma (Stefan_Boltzmann_constant) = 5.6704e-08 kg/(s**3*K**4)\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Un concepto relacionado es el de la **luminosidad intr\u00ednseca** de una estrella, L, definida como la energ\u00eda total radiada por la estrella en una unidad de tiempo. Si el radio de la estrella es R y la temperatura de su superficie es T, se cumplir\u00e1 que:\n",
      "\n",
      "$$L = 4 \\pi R^2 E = 4 \\pi R^2 \\sigma T^4 $$\n",
      "\n",
      "La f\u00f3rmula anterior se podr\u00eda en principio utilizar para calcular la temperatura de la estrella conocida su luminosidad. Sin embargo las estrellas no son cuerpos negros perfectos, aunque unas se aproximan m\u00e1s que otras. Por esta raz\u00f3n se utiliza el concepto de **temperatura efectiva**, que es la temperatura que tendr\u00eda un cuerpo negro cuya luminosidad fuera la de la estrella. Esta temperatura efectiva puede considerarse como una aproximaci\u00f3n de la temperatura real de la superficie de la estrella. veamos un ejemplo:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "La luminosidad del Sol es: 3.839 x 10\u00b2\u2076 W. \u00bfCual ser\u00e1 su temperatura efectiva?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Necesitaremos el valor del radio del Sol:\n",
      "sun_radius = 695000000.0 * pq.m\n",
      "\n",
      "l_sun = 3.839e26 * pq.watt\n",
      "\n",
      "temp_sun = (l_sun/(4 * np.pi * sun_radius**2 * pq.constants.sigma))**(1./4)\n",
      "print temp_sun.simplified"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5779.04712292 K\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Bueno, de momento paramos en este punto para no hacer la entrada demasiado larga. En mi siguiente post aplicar\u00e9 lo anterior al estudio con ayuda del lenguaje Python del espectro de radiaci\u00f3n del fondo c\u00f3smico de microondas (CMB)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}