hr.ipynb

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    "<div class=\"alert alert-block alert-success\" markdown=\"1\">\n",
    "\n",
    "<h1> Chapter 3: The Rise and Fall of a Superstar </h1>\n",
    "\n",
    "<img src=\"./visual_arts/real_time_stellar_evolution.gif\" width=\"80%\">\n",
    "\n",
    "<p style='text-align: justify;'>\n",
    "\n",
    "Impressive! Just by finding the wavelength at the peak of the Planck spectrum, I was able to tell the exact temperature of stars millions of light years away. In this particular case with the three stars, I got the values 5780 K, 6330 K, 3780 K. Wien's displacement law is indeed very powerful.\n",
    "\n",
    "But how was this helping me to find my friend?\n",
    "\n",
    "HAL immediately responded to my question: 'Lani, don't you know that the emitted light of stars provide a lot of information on the properties of stars?'\n",
    "\n",
    "HAL explained that the total energy emitted by a star, or <b><i>Luminosity</b></i>, is proportional to some power of its temperature and of its radius. This relation is determined by the Stefan-Boltzmann law and the surface area of a star!\n",
    "\n",
    "<p> <a href=\"#science_box\">\n",
    "(For more scientific and detailed background click here)</a>.</p>\n",
    "\n",
    "The Stefan-Boltzmann law is a direct consequence of the Planck spectrum, which results from the quantum nature of the smallest particles in the Universe. How could the smallest particles affect the largest things like the stars in this galaxy? \n",
    "\n",
    "This was amazing. The laws of black-body radiation allow us to measure the sizes of stars, just by observing their emitted light.\n",
    "\n",
    "HAL responded again:'Yes Lani, but we need to determine the current evolutionary state of the three detected objects.' \n",
    "\n",
    "It explained that during their lives, stars change their temperatures and sizes. HAL displayed a diagram on my screen showing simulations of stars when changing their temperatures and sizes. Astronomers have identified a particular pattern in the relation between the total emitted flux of light, called luminosity, and the temperature of a star. This relation is visualized in the so-called Hertzsprung-Russell diagram. \n",
    "\n",
    "HAL continued: 'The Hertzsprung-Russell diagram tells us if a star is a small hot <b><i>white dwarf</b></i> or a cool large <b><i>red giant</b></i>...Or... a <b><i>main sequence star</b></i>, just as the one you are searching for.' \n",
    "\n",
    "HAL suggested to put the measured temperatures of the three objects on the x-axis of the diagram. HAL would then use \n",
    "the Stefan-Boltzmann law to calculate the total emitted luminosities of these stars.\n",
    "\n",
    "Together we would be able to find the 'Sun', a main sequence star in the Milky Way.\n",
    "\n",
    "</p>\n",
    "\n",
    "\n",
    "<h1> It's your turn now! </h1>\n",
    "\n",
    "<p>\n",
    "You have computed the temperature of three stars in the previous Chapter. Provide these in the correct boxes below and the program will enter the luminosity for each star and plot the data points on the Hertzsprung-Russell diagram.\n",
    "\n",
    "Then find the main sequence star. Remember there are small hot white dwarfs, cool large red giants and then there are main sequence stars.\n",
    "</p>\n",
    "\n",
    "<br>\n",
    "\n",
    "<p>Once you are done, go to <a href=\"Interlude.ipynb\">\n",
    "[Chapter 4]</a>.</p>\n",
    "\n",
    "\n",
    "<h1> Bakgrund </h1>\n",
    "<p>\n",
    "Hertzsprung-Russell diagram är ett diagram som skapades utifrån observerade stjärnor och deras egenskaper (ljusstyrka, radie och massa). Den visar ett mönster som stjärnor faller in i när en placerar dem i en graf som visar luminositet (ett mått på hur ljusstarkt något är) mot temperaturen av objektet (som vi tidigare har visat är starkt kopplat till vilken färg stjärnan har, eller hur?)\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "Igen, precis som med svartkroppsstrålning, så är relationen (vilket vi kallar Stefan-Boltzmanns lag) mellan luminositeten, temperaturen och radien av stjärnan baserat på kvantmekaniska processer. Det är alltså väldigt komplicerade fenomen som ligger bakom denna ekvation - kan vara svårt att tro!\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "Tillbaka till HR-diagrammet, som ni kan se så kan stjärnorna organiseras in i tre olika regioner. Notera att stjärnorna INTE tillbringar hela sin “livstid” i en region, utan rör sig mellan regionerna:\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "<b>Huvudserien (main sequence)</b> - här tillbringar stjärnorna största delen av sin livstid. Det som kännetecknar dessa stjärnor är att de omvandlar väte till helium i sina kärnor (via fusion).\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "<b>Jättar och superjättar (Giants/Supergiants)</b> - de stjärnor som, efter att ha förvandlat all sin väte till helium i kärnan, fortsätter att ha energi för att lysa, faller in i jätte- eller superjättekategorin. Dessa stjärnor lever på sluttampen av sin livstid.\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "<b>Vita dvärgar (white dwarfs)</b> - dessa svagt lysande stjärnor är de stjärnor som inte har tillräckligt med energi för att byggas upp till bli jättar, utan istället svalnar av och till sist slutar lysa överhuvudtaget.\n",
    "</p>\n",
    "<h1> Instruktioner </h1>\n",
    "<p>\n",
    "Din uppgift att är bestämma var på HR-diagrammet stjärnorna från förra kapitlet hör hemma.\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "Temperaturen har du räknat ut i förra kapitlet och luminositeten (ljusstyrkan) inkluderas automatiskt när du skriver in temperatur-värdena.\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "Var på diagrammet platsar stjärnorna? I vilka grupper skulle du dela in dem i?\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "BONUS: Kan du även uppskatta vilken radie stjärnorna har?\n",
    "</p>\n",
    "\n",
    "<p><a href=\"Interlude.ipynb\">\n",
    "[Chapter 4]</a>.</p>\n",
    "\n",
    "</div>"
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     "text": [
      "Enter the value of the temperature of the first star (Kelvin)\n"
     ]
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      "Enter the value of the temperature of the second star (Kelvin)\n"
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      "Enter the value of the temperature of the third star (Kelvin)\n"
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    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from src.support import *\n",
    "\n",
    "plt.style.use('seaborn-ticks')\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "L1,L2,L3=get_object_luminosities()\n",
    "\n",
    "T=np.array([5700,6300,3700])\n",
    "L=np.array([L1,L2,L3])\n",
    "\n",
    "\n",
    "\n",
    "#Temperature input\n",
    "from IPython.display import display\n",
    "from ipywidgets import widgets\n",
    "import numpy as np\n",
    "from IPython.display import clear_output\n",
    "\n",
    "print('Enter the value of the temperature of the first star (Kelvin)')\n",
    "star1 = widgets.FloatText()\n",
    "display(star1)\n",
    "\n",
    "print('Enter the value of the temperature of the second star (Kelvin)')\n",
    "star2 = widgets.FloatText()\n",
    "display(star2)\n",
    "\n",
    "print('Enter the value of the temperature of the third star (Kelvin)')\n",
    "star3 = widgets.FloatText()\n",
    "display(star3)\n",
    "\n",
    "button = widgets.Button(description=\"Plot stars\")\n",
    "display(button)\n",
    "\n",
    "\n",
    "def on_button_clicked(b):\n",
    "    T = np.array([star1.value,star2.value,star3.value])\n",
    "    plot_HR(Ls=L,Ts=T)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "button.on_click(on_button_clicked)"
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    "<div class=\"alert alert-block alert-success\">\n",
    "\n",
    "\n",
    "<p>Now go to <a href=\"Interlude.ipynb\">\n",
    "[Chapter 4]</a>.</p>\n",
    "\n",
    "</div>"
   ]
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    "<div class=\"alert alert-block alert-danger\" markdown=\"1\">\n",
    "\n",
    "<h1> Summary: What have we learned? </h1>\n",
    "<p>\n",
    "- The luminosity of a star is determined by the star's temperature and radius.\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "- The physics relation between luminosity, temperature and radius is called Stefan-Boltzmann law. As for the black-body radiation, the Stefan-Boltzmann law is also rooted in quantum physics. Indeed, you can derive the Stefan-Boltzmann law by integrating the Planck spectrum over frequency.\n",
    "</p>\n",
    "\n",
    "<p>\n",
    "- When plotted on a graph with temperature and luminosity on the axes, stars occupy only certain regions of the graph. \n",
    "</p>\n",
    "\n",
    "<p>\n",
    "- This graph is called the Hertzsprung-Russell diagram, and it is a fundamental tool in astrophysics. \n",
    "</p>\n",
    "\n",
    "<p>\n",
    "- The position occupied by a star in the HR diagram depends on the evolutionary stage of the star. In fact, during their evolution, the temperature and radius of a star do change. As a result, stars move around the different regions of the HR diagram during their evolution.\n",
    "</p>\n",
    "\n",
    "<p><a href=\"Interlude.ipynb\">\n",
    "[Chapter 4]</a>.</p>\n",
    "</div>\n",
    "\n",
    "<a name=\"science_box\"></a>\n",
    "<div class=\"alert alert-block alert-info\" markdown=\"1\">\n",
    "\n",
    "\n",
    "<h1> If you want to learn more: Stefan-Boltzmann law</h1>\n",
    "<p style='text-align: justify;'>\n",
    "The Stefan-Boltzmann law is a relation between the power (energy per time unit) emitted by a black body and the temperature of the black body. If we apply it to the emission of stars, it states that the star luminosity is directly proportional to the fourth power of the surface temperature of the star. The value of the proportionality constant depends on other fundamental constants in nature, such as the Boltzmann constant k*, the Planck constant *h, and the speed of light c. To learn more about the Stefan-Boltzmann law, see the material available on the ESA webpage\n",
    "</p>\n",
    "\n",
    "\\begin{align}\n",
    "B_{\\lambda}(T) & = \\frac{2\\,h\\,c^2}{\\lambda^5(\\mathrm{e}^{\\frac{hc}{2\\lambda\\, k_B\\, T}}-1)}\n",
    "\\end{align}\n",
    "\n",
    "<p style='text-align: justify;'>\n",
    "The law giving the total energy flux or power per unit surface area emitted from a black body at temperature T can be computed by solving the following integral:\n",
    "</p>\n",
    "\\begin{align}\n",
    "F(T) & = \\pi \\int_0^{\\infty} \\mathrm{d}\\lambda \\, B_{\\lambda}(T) \\\\\n",
    "& = \\sigma_{\\mathrm{SB}}\\, T^4 \\, ,\n",
    "\\end{align}\n",
    "\n",
    "<p style='text-align: justify;'>\n",
    "where the Stefan-Boltzmann constant has a value of $\\sigma_{\\mathrm{SB}}= 5.67\\times 10^{-8} \\,[\\mathrm{W}\\mathrm{m}^{-2}\\mathrm{K}^{-4}]$ (for a detailed derivation of the Stefan-Boltzmann law see <a href= \"http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan2.html\">\n",
    "here</a>).\n",
    "</p>\n",
    "\n",
    "<p style='text-align: justify;'>\n",
    "The total emitted power $L_{\\star}$ of a spherical star of temperature $T_{\\star}$ and radius radius $R_{\\star}$ can therefore optained by simply multiplying the Stefan-Boltzmann law with the stars surface area $A_{\\star}= 4 \\pi \\, R^2_{\\star}$:\n",
    "</p>\n",
    "<font color='red'>\n",
    "\\begin{align}\n",
    "L_{\\star} & = 4 \\pi \\, R^2_{\\star} \\, \\sigma_{\\mathrm{SB}} \\, T^4_{\\star} \\\\\n",
    "\\end{align}</font>\n",
    "\n",
    "<p style='text-align: justify;'>\n",
    "This remarkably simple equation has pronounced consequences for astronomical observations. It establishes an immediate relation between the observable total emmited power $L_{\\star}$ and temperature $T_{\\star}$ of a star with its size $R_{\\star}$. \n",
    "</p>\n",
    "\n",
    "Astronomers can use this law of stellar radiation to study the properties and the evolution of stars in the galaxy.\n",
    "\n",
    "<h2> The Hertzsprung-Russell diagram and the evolution of stars</h2>\n",
    "<p style='text-align: justify;'>\n",
    "The Hertzsprung-Russell diagram (HR diagram) is one of the most important tools in the study of stellar evolution. Developed independently in the early 1900s by Ejnar Hertzsprung and Henry Norris Russell, it plots the temperature of stars against their luminosity. This is the theoretical HR diagram but scientists also refer to more observational properties of the stars. In particular, they can plot the colour of stars (or spectral type) against their absolute magnitude. In this case, we talk of the observational HR diagram, also known as a colour-magnitude diagram. Depending on its initial mass, every star goes through specific evolutionary stages dictated by its internal structure and how it produces energy. Each of these stages corresponds to a change in the temperature and luminosity of the star, which can be seen to move to different regions on the HR diagram as it evolves. This reveals the true power of the HR diagram – astronomers can deduce a star's internal structure and evolutionary stage simply by determining its position in the diagram.\n",
    "</p>\n",
    "\n",
    "<img src=\"./visual_arts/Hertzsprung-Russel_StarData.png\" width=\"60%\">\n",
    "\n",
    "From the figure, we can identify 3 main regions (or evolutionary stages) of the HR diagram:\n",
    "\n",
    "\n",
    "<ol>\n",
    "<li> <p>The main sequence stretching from the upper left (hot, luminous stars) to the bottom right (cool, faint stars) dominates the HR diagram. It is here that stars spend about 90% of their lives burning hydrogen into helium in their cores. Main sequence stars have a luminosity class labelled V.</p></li>\n",
    "<li> <p>Red giant and supergiant stars (luminosity classes I through III) occupy the regions above the main sequence. They have low surface temperatures and high luminosities. According to the Stefan-Boltzmann law that we have discovered above, means giant and supergiant stars also have large radii. Stars enter this evolutionary stage once they have exhausted the hydrogen fuel in their cores and have started to burn helium and other heavier elements.</p></li>\n",
    "<li> <p>White dwarf stars (luminosity class D) are the final evolutionary stage of low to intermediate mass stars, and are found in the bottom left of the HR diagram. These stars are very hot but have low luminosities due to their small size.</p></li>\n",
    "</ol>\n",
    "\n",
    "\n",
    "<p style='text-align: justify;'>\n",
    "The Sun is found on the main sequence with a solar luminosity of 1 and a temperature of around 5,400 Kelvin.\n",
    "Astronomers generally use the HR diagram to either summarise the evolution of stars, or to investigate the properties of a collection of stars. In particular, by plotting a HR diagram for either a globular or open cluster of stars, astronomers can estimate the age of the cluster from where stars appear to turnoff the main sequence (see the entry on main sequence for how this works).</p>\n",
    "\n",
    "<p><a href=\"Interlude.ipynb\">\n",
    "[Chapter 4]</a>.</p>\n",
    "\n",
    "<a href=\"http://astronomy.swin.edu.au/cosmos/h/hertzsprung-russell+diagram\">\n",
    "Text adapted from Swinburne University of Technology</a>\n",
    "</p>\n",
    "\n",
    "See also ESA resources <a href=\"http://sci.esa.int/education/35774-stellar-radiation-stellar-types/?fbodylongid=1703\">\n",
    "here</a> and <a href=\"https://www.cosmos.esa.int/web/cesar/the-hertzsprung-russell-diagram!\">\n",
    "here</a>.\n",
    "\n",
    "More background and motivation of HR diagrams can be found <a href=\"https://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_hrintro.html\">\n",
    "here</a>.\n",
    "\n",
    "\n",
    "<h2> Literature </h2>\n",
    "\n",
    "<ol>\n",
    "<li> <p>Some information on Stefan Boltzmann law in astronomy <a href=\"https://www.teachastronomy.com/textbook/Properties-of-Stars/Stefan-Boltzmann-Law/\">\n",
    "https://www.teachastronomy.com/textbook/Properties-of-Stars/Stefan-Boltzmann-Law/</a>.</p></li>\n",
    "<li> <p>Introduction to astronomy <a href=\"http://web.phys.ntnu.no/~mika/skript_astro.pdf\">\n",
    "http://web.phys.ntnu.no/~mika/skript_astro.pdf</a>.</p></li>     \n",
    "</ol>\n",
    "\n",
    "</div>"
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