{ "metadata": { "name": "", "signature": "sha256:202f95a5a6855adc375fa658e660be4751127a9934f82bfce4b58fd533bbea67" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "The Blackbody Radiation and the Cosmic Microwave Background (CMB) in Python: part I" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Autor: [Eduardo Mart\u00edn Calleja](http://balbuceosastropy.blogspot.com.es/)\n", "\n", "This post is the first in a series of two in which we will examine, with the help of the Python language, the features of the blackbody radiation. In a second part, we will apply it to the particular case of the spectrum of the cosmic microwave background (CMB).\n", "\n", "The study of the properties of celestial bodies, such as its color or luminosity, needs the concept of an ideal radiation emitter known as a \"blackbody\". The stars radiate energy that depends on its temperature and the length of the radiation wavelength, and the blackbody emission law can be considered as a first approximation of the characteristics of this radiation. For this reason I will show in this post how to build with Python the curves of radiation of a blackbody at different temperatures, which will also constitute a good exercise to practice with the use of physical units with the \"quantities\" Python package, which was the subject of a [previous post](http://balbuceosastropy.blogspot.com.es/2013/09/how-to-work-with-physical-units-in.html).\n", "\n", "As usual, this entry has been written entirely using the amazing IPython Notebook." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Imports and references" ] }, { "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", "# This IPython magic generates a table with version information\n", "# https://github.com/jrjohansson/version_information\n", "%load_ext version_information\n", "%version_information numpy, matplotlib, quantities" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
Python2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]
IPython2.3.1
OSLinux 3.13.0 45 generic x86_64 with debian jessie sid
numpy1.9.1
matplotlib1.4.2
quantities0.10.1
Sat Feb 21 00:33:52 2015 CET
" ], "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 45 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 45 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|}{Sat Feb 21 00:33:52 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 45 generic x86_64 with debian jessie sid\n", "numpy 1.9.1\n", "matplotlib 1.4.2\n", "quantities 0.10.1\n", "Sat Feb 21 00:33:52 2015 CET" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can check out the [Planck's law](http://en.wikipedia.org/wiki/Planck%27s_law) in the wikipedia" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Blackbody Radiation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Plank equation represents the intensity of the radiation from a blackbody as a function of the wavelength. There is a curve for each blackbody temperature. Its form is:\n", "\n", "$$ B_\\lambda(T) = \\frac{2hc^2}{\\lambda^5} \\frac{1}{e^\\frac{hc}{\\lambda k_B T} -1}$$\n", "\n", "$B$ is the **spectral radiance**, defined as the power emitted per unit area within a unit solid angle normal to the area, per unit of wavelength. The letter *B* is commonly used instead of the letter *I* with generically designates intensities, to emphasize that we are specifically referring to a \"blackbody\". Its units, assuming that we measure the wavelengths in namometers, will be: $W m ^ {\u207b2} nm ^ {-1} sr ^ {\u207b1} $, $sr$ being the unit of solid angle \"steradian\".\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The formula above uses the following constants:\n", "\n", "- $k_B$ is the Boltzmann constant \n", "\n", "- $h$ is the Plank constant\n", "\n", "which, in the Python package *quantities* are defined as:" ] }, { "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": [ "Let's define a function that will calculate the spectral radiance according to the previous Plank law:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def B(wl,T):\n", " '''wl is an array of wavelengths with units of length\n", " T is a temperature in Kelvin\n", " the result is an array of s.r. with units 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": [ "We will check the correct operation of the function with an example:" ] }, { "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(26421.629609697076) * W/(m**2*nm*sr)" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will then use this function to plot the blackbody radiation curves for four temperatures:" ] }, { "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": [ "We will draw the curves with the Python Matplotlib *plot()* function" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wl = np.arange(10,2000,10) * pq.nm\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('Blackbody radiation')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('wavelength in nm')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('spectral radiance $(W m^{-2}nm^{-1}sr^{-1})$')\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": 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mVuF/fz3GBecWbLDQVVdtoHPnffTtO5Ljxyvx8MNfF3GUIiIiIqepx14ki137jZv/UpXp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\nyzmm7xdVJZje+BvmFc/in76A5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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous figure shows crearly that, as the blackbody temperature rises, the maximum of the emitted intensity will correspond to wavelengths increasingly shorter, i.e., higher frequencies, most energetic photons, entering this maximum, starting from 7000K, in the ultraviolet region. This fact is expressed mathematically by the Wien law." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Wien law" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The maximum wavelength $\\lambda_{max} $ which emits a black body is given by:\n", "\n", "$$ \\lambda_{max} = \\frac{b}{T} $$\n", "\n", "Being $b$ the Wien constant, whose value is given by:\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": [ "Here are some examples:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The star Betelgeuse, in the constellation of Orion, has a surface temperature of 3600K. If we consider it in a first approximation as a blackbody, at what wavelength present its spectrum a maximum of radiation?" ] }, { "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": [ "I.e., the radiation of Betelgeuse will reach its peak in the infrared region" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Wien law can also be used to estimate the temperature of a star from its spectrum (always with the approach of assuming a model of black body radiation):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Suppose that the radiation from a star has its maximum intensity at 400 nm\n", "\n", "lmax = 400 * pq.nm\n", "\n", "T = pq.constants.b / lmax\n", "\n", "print \"Its effective temperature will be: %d K\" %T.simplified" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Its effective temperature will be: 7244 K\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Stefan\u2013Boltzmann law" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Stefan-Boltzmann law is another important consequence of the Plank's radiation law. It indicates that the value of the total energy radiated per unit area and unit of time in all wavelengths, is proportional to the fourth power of the temperature.\n", "\n", "The total energy radiated by a blackbody per unit area and unit time in all wavelengths is known as **emissive power**, and it is given by:\n", "\n", "$$ E = \\sigma T^4 $$\n", "\t \t\n", "E is measured in $W/m^2$\n", "\n", "$\\sigma$ is called the Stefan-Boltzmann constant, and its value is:" ] }, { "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": [ "A related concept is that of the **intrinsic brightness** of a star, L, defined as the total energy radiated by the star in a unit of time. If the radius of the star is R and its surface temperature is T, it will be given by:\n", "\n", "$$L = 4 \\pi R^2 E = 4 \\pi R^2 \\sigma T^4 $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above formula could be in principle used to calculate the temperature of the star once known its brightness. However stars are not perfect blackbodies, although some approach more than others. For this reason it is used the concept of **effective temperature**, which is the temperature that would have a blackbody whose brightness was the same as the star. This effective temperature can be considered an approximation of the actual temperature of the surface of the star. Here is an example:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The brightness of the Sun is: $3.839 \\times 10 ^ {26} W$. What will be its effective temperature?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# We will need the value of the radius of the Sun:\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": [ "Well, we wll stop now at this point to make the entry not too long. In my next post I will apply the above to study the radiation spectrum of the cosmic microwave background (CMB) with the help of the Python language." ] } ], "metadata": {} } ] }