{ "metadata": { "name": "", "signature": "sha256:af4a12299dad57177887710e759adafbeaf8194f0227967b7eaf543a32c3cae5" }, "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 II" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Autor: [Eduardo Mart\u00edn Calleja](http://balbuceosastropy.blogspot.com.es/)\n", "\n", "In this post, continuation of [this one](http://balbuceosastropy.blogspot.com.es/2013/10/the-blackbody-radiation-and-cosmic.html), I will examine, using code written in Python, the graphical representation of the thermal radiation from a blackbody at a temperature of 2.725 K. Then I will include in this graph the results of the measurements of the spectrum of the cosmic microwave background (CMB) radiation by the FIRAS device of the Cosmic Background Explorer satellite [COBE](http://lambda.gsfc.nasa.gov/product/cobe/), to check the exquisite accuracy of the adjustment of the actual data to the spectrum of a black body at the temperature indicated.\n", "\n", "One of the main difficulties when it comes to plot the radiation curves is, IMHO, the diversity of physical units in which these can be expressed. This is why in this post I will examine in some detail, and with the help of the Python package \"quantities\", the most common alternatives in terms of physical units for the presentation of the results." ] }, { "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", "import pandas as pd\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, pandas" ], "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
pandas0.15.2
Sat Feb 21 11:11:30 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\"}, {\"version\": \"0.15.2\", \"module\": \"pandas\"}]}" ], "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", "pandas & 0.15.2 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Sat Feb 21 11:11:30 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", "pandas 0.15.2\n", "Sat Feb 21 11:11:30 2015 CET" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this entry we will use the same function defined in the [previous post](http://balbuceosastropy.blogspot.com.es/2013/10/the-blackbody-radiation-and-cosmic.html) to calculate the spectral radiance according to the Plank's 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": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Blackbody radiation at T = 2.725K" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Case 1. Units: $\\lambda$ in mm and B in $W m^{-2} mm^{-1} sr^{-1}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As already said, the cosmic microwave background is a perfect example of radiation from a blackbody at a temperature of 2.725 K. Let's graph the spectral radiance curve that corresponds to this temperature. In the first place, and to get an idea of the range of magnitudes in which we move, we will compute the wavelength in which it reaches its maximum, for what we will use Wien's law:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "TCMB = 2.725 *pq.K\n", "lmax = pq.constants.b / TCMB\n", "print lmax.simplified" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0010634012844 m\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "I.e., the photons of the CMB have a wavelength of approximately one millimeter. With this information we can assign a range of values to the wavelengths for the calculation of the curve of the spectral radiance, and set the right units for B:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wl = np.arange(0.1,10,0.1) * pq.mm\n", "I = B(wl,TCMB).rescale(pq.watt/(pq.m**2 * pq.mm * pq.sr))\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wl, I*1e7)\n", "ax.set_title('Blackbody spectrum at T = 2.725 K \\\n", "\\n (wavelength in mm)')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Wavelength in mm')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Spectral Radiance ($10^{-7} W m^{-2} mm^{-1} sr^{-1}$)')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Il/oubuq/eKnv2osSMxEREZGMUI2ZiIiISIOoxkxEREQkUkrMpKlUKxEv9V3c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\nTIsTi4hUt9TXmCXJJ59Anz5xRyFpsuGG8Pjj4UGAiy+OOxo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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Case 2. Units: $\\nu$ in GHz and B in $W m^{-2} GHz^{-1} sr^{-1}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quite often you will find graphics with B expressed as a function of the frequency $\\nu$ measured in $Hz$ rather than depending on wavelength $\\lambda$ as we have been doing so far. In that case, Plank's law is written as:\n", "\n", "$$B_\\nu(T) = \\frac{2 h \\nu^3}{c^2} \\frac{1}{e^{\\frac{h \\nu}{k_B T}}-1}$$\n", "\n", "Where $\\nu$ es the radiation frequency, measured in $Hz$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we write the function to calculate B in accordance with the formula above:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def B_f(wf,T):\n", " '''wf is an array of frequencies with units in GHz\n", " T is a temperature in Kelvin.\n", " It returns an array of spectral radiances \n", " with units W/(m**2 x GHz x sr)\n", " '''\n", " wf = wf.rescale(pq.hertz)\n", " I = 2 * pq.constants.h * wf**3 / pq.c**2 * 1 \\\n", " / (np.exp((pq.constants.h*wf \\\n", " / (pq.constants.k*T)).simplified)-1)\n", " return I.rescale(pq.watt/(pq.m**2 * pq.gigahertz *pq.sr))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's test the function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "B_f(10**13*pq.hertz, 7000*pq.K)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "array(0.20777704540401157) * W/(m**2*sr*GHz)" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we plot the graph:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wf = np.arange(0.1,1000,1)* pq.gigahertz\n", "I = B_f(wf,TCMB)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wf, I*10**9) # Scale the units\n", "ax.set_title('Blackbody spectrum at T = 2.725K \\\n", " \\n (Frequencies en GHz)')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel(r'Frequence $ \\nu \\; (GHz)$')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Spectral Radiance $(10^{-9} W m^{-2} GHz^{-1} sr^{-1})$')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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/DJzcmZmZmbUUT8uamZmZ5czTsmZmZmZWlZM7a0quGyk2919xue+Kzf1n4OTO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\nu+ce+MlPQvuF1CxNuZP6U/4EVNytYcoUFXci5WiLLcIMFuPHw3HHwdd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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Case 3. Units: $\\nu$ in $cm^{-1}$ and B in $W / (m^{2} \\: cm^{-1} sr)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fact is that the preferred unit of frequency when it comes to represent the CMB spectrum is the \"wave number k\", which gives the number of wavelengths per distance unit. It is normally expressed in \"cycles / cm\", or just $cm ^ {-1} $ as the number of cycles is a magnitude without dimension. We will then see now how to make conversions from GHz to cycles/ cm" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Conversion of 160 GHz to cm**(-1)\n", "\n", "frec = 160 * pq.gigahertz\n", "wl = pq.c / frec\n", "print 'wavelength in cm = ', wl.rescale(pq.cm)\n", "k = 1/( wl.rescale(pq.cm))\n", "print 'wavenumber in cycles per cm = ', k" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "wavelength in cm = 0.18737028625 cm\n", "wavenumber in cycles per cm = 5.33702552317 1/cm\n" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# The conversion can be made easier\n", "# just by dividing by the speed of light.\n", "fec_in_wave_number = (frec/pq.c).rescale(1/pq.cm)\n", "print fec_in_wave_number" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "5.33702552317 1/cm\n" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a curiosity, the frequency unit 1/cm is called, in the cgs system of units, a \"kayser\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The formula of Plank's law changes when the frequency is entered in cycles per unit length (k). Its form in this case is the following:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$B_k(T) = 2 h c^2 k^3 \\frac{1}{e^{\\frac{h c k}{k_B T}}-1}$$\n", "\n", "Note: we should not confuse the wavenumber unit (cycles per length unit) with the angular wavenumber, which is usually also represented with the $k$ symbol but whose value is 2 $ \\pi$ times the spacial wavenumber.\n", "\n", "We will then define a function to calculate the spectral radiance according to the above formula." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def B_k(wk,T):\n", " '''wk is an array of frequencies with units in cm^(-1)\n", " T is a temperature in Kelvin.\n", " It returns an array of spectral radiances \n", " with units W/(m**2 x cm**(-1) x sr)\n", " '''\n", " wk = wk.rescale(1/pq.m)\n", " I = 2 * pq.constants.h * pq.c**2 * wk**3 * 1 \\\n", " / (np.exp((pq.constants.h*pq.c*wk \\\n", " / (pq.constants.k*T)).simplified)-1)\n", " return I.rescale(pq.watt/(pq.m**2 * pq.cm**(-1)*pq.sr))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A first test:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f = 5.35 * pq.cm**(-1)\n", "B_k(f, TCMB)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "array(1.1502029877502701e-07) * cm*W/(m**2*sr)" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now, let's plot the graph in the new units:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wk = np.arange(0.1,20,0.1) / pq.cm\n", "I = B_k(wk,TCMB)\n", "I = I*10**7 # We express the units in multiples of 10^(-7)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wk, I)\n", "ax.set_title('Blackbody spectrum at T = 2.725K \\\n", " \\n (Frequencies in $cm^{-1}$)')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frequency (cycles / cm )')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Spectral Radiance $(10^{-7}W m^{-2} (cm^{-1})^{-1}sr^{-1})$')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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XEX6v75jZQ4T60C0ISdzjhHae7nngwOg9eyfaZlRUYF/WotKBRwl/g08C+0R1hKnc3dOv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\ntJcOHcJCwqNGhf/mbLEF3HsvLF+e+/iktCmRy4ASORERKYRtt4VnnoG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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Case 4. Units: $\\nu$ in $cm^{-1}$ and B in $MJy / sr$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is yet another unit of measurement for frequencies, the **Jansky**, which is the one used with the data that we can download from the COBE, and is defined as:\n", "\n", "$$ 1 Jy = 10^{-26} \\frac{W}{m^2 Hz} $$\n", "\n", "A multiple is the Megajansky = 10**6 janskys\n", " \t\n", "Its use is particularly widespread in radio astronomy. To be able to work easily in Python with these units, we will define the Jansky unit through the package *quantities* [check out this post](http://balbuceosastropy.blogspot.com.es/2013/09/how-to-work-with-physical-units-in.html):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Jy = pq.UnitQuantity('jansky', 1e-26*pq.watt/(pq.m**2*pq.hertz), symbol = 'Jy')\n", "MJy = pq.UnitQuantity('megajansky', 10**6 * Jy, symbol = 'MJy')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "An example follows of conversion of a spectral radiance to this units:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "I = 3.34 * 10**(-18) * pq.W * pq.m**(-2) * pq.hertz**(-1) * pq.sr**(-1)\n", "I.rescale(MJy)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "array(333.99999999999994) * MJy" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next plot we'll set the x-coordinate units to cycles/cm, and the y-coordinate to spectral radiance in $MJy*sr^{-1}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "wf = np.arange(0.1,1000,1)* pq.gigahertz\n", "I = B_f(wf,TCMB)\n", "I = I.rescale(MJy*pq.sr**(-1)) # conversion to MJy * sr**(-1)\n", "wk = (wf/pq.c).rescale(1/pq.cm) # convert freq. to 1/cm\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wk, I)\n", "ax.set_title('Blackbody spectrum at T = 2.725K \\\n", " \\n spectral radiance in MJy / sr')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frequency (cycles/cm)')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Spectral radiance ($MJy \\, sr^{-1}$)')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Rf4Dp7j7CwmWQricMEbUBB2Xm6zGzUwgTdC4CTio0H5ZIpZnZSOAKYKS7X5Vy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\n8Sl3pVH+kqVCLod7eCyXeuREqt8GG4Qrc5Mnh6lJlixJOyIRkeSpRy7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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "CMB spectrum with data from COBE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once explored the various types of units in which the graph of the spectrum of the cosmic microwave background can be represented, we will use the latter format, since it is precisely in these units that the COBE satellite data are provided.\n", "\n", "It only remains for us to download the spectrum of the CMB data obtained with the COBE FIRAS instrument, which are available publicly in [FIRAS CMB Monopole Spectrum](http://lambda.gsfc.nasa.gov/product/cobe/firas_monopole_get.cfm). In order to read and manipulate the file with ease, we will use the Pandas Python package.\n", "\n", "The first step will be downloading the file from the indicated address. It is the file \"firas_monopole_spec_v1.txt\". If you open it with a text editor, you will see that the columns are delimited by spaces, and that the first 18 rows are comments and must be skipped, although you need to read them since they describe the units used and the meaning of each column of data.\n", "\n", "In this case I've downloaded the file in the directory \"../datos\". Now I will create a Pandas dataframe with all the 5 columns of data. As a separator between columns I use a regular expression which means \"any number of spaces\" " ] }, { "cell_type": "code", "collapsed": false, "input": [ "df = pd.read_table('../datos/firas_monopole_spec_v1.txt', \n", " skiprows=18, sep='\\s+', header=None, \n", " names =['freq', 'I', 'residual', 'uncert', 'poles'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's show the ten first lines of the table:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "df[0:10]" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
freqIresidualuncertpoles
0 2.27 200.723 5 14 4
1 2.72 249.508 9 19 3
2 3.18 293.024 15 25 -1
3 3.63 327.770 4 23 -1
4 4.08 354.081 19 22 3
5 4.54 372.079-30 21 6
6 4.99 381.493-30 18 8
7 5.45 383.478-10 18 8
8 5.90 378.901 32 16 10
9 6.35 368.833 4 14 10
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ " freq I residual uncert poles\n", "0 2.27 200.723 5 14 4\n", "1 2.72 249.508 9 19 3\n", "2 3.18 293.024 15 25 -1\n", "3 3.63 327.770 4 23 -1\n", "4 4.08 354.081 19 22 3\n", "5 4.54 372.079 -30 21 6\n", "6 4.99 381.493 -30 18 8\n", "7 5.45 383.478 -10 18 8\n", "8 5.90 378.901 32 16 10\n", "9 6.35 368.833 4 14 10" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we will use the first two columns of the dataframe to superimpose these points of the meassured CMB spectrum to the blackbody curve at a temperature of 2.725 K. In the resulting graph, you will see that the measured CMB data fits perfectly to the theoretical spectrum, so we can conclude that the cosmic microwave background radiation follows a perfect blackbody emission pattern." ] }, { "cell_type": "code", "collapsed": false, "input": [ "wf = np.arange(0.1,1000,1)* pq.gigahertz\n", "I = B_f(wf,TCMB)\n", "I = I.rescale(MJy*pq.sr**(-1)) # conversion to MJy * sr**(-1)\n", "wk = (wf/pq.c).rescale(1/pq.cm) # convert freq. to 1/cm\n", "\n", "fig, ax = plt.subplots(figsize=(10, 8))\n", "ax.plot(wk, I)\n", "ax.set_title('Blackbody spectrum at T = 2.725K \\\n", "\\n with data from the COBE satellite')\n", "ax.title.set_fontsize(20)\n", "ax.set_xlabel('Frequency (cycles/cm)')\n", "ax.xaxis.label.set_fontsize(15)\n", "ax.set_ylabel('Spectral Radiance ($MJy \\, sr^{-1}$)')\n", "ax.yaxis.label.set_fontsize(15)\n", "ax.set_xlim(0,25)\n", "ax.set_ylim(0,400)\n", "\n", "ax.scatter(df['freq'], df['I'],c='red', s= 50)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ZV65VIvIorn/oEbgkbibuPE/0DHCWf8+q/DrzfAf7UPNdBx7HfQb/A5zq+xHGU1VNvGPD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