color_astro.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Colour in Astronomy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Apparent Magnitudes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1: Obtain the apparent BVR magnitudes for your programme stars."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution:\n",
    "\n",
    "The first step is to obtain instrumental and absolute BVR magnitudes. This is\n",
    "accomplished by observing at least one standard star with known magnitudes on the\n",
    "standard system along with your night’s data and using it to determine the\n",
    "transformation equations. Often the standard star is not in your science images, so\n",
    "you have to take a set of calibration images that measure the standard star in your\n",
    "instrumental system. This usually requires calibration of the differing atmospheric\n",
    "transmission between the observations of the standard and science images, which\n",
    "changes with zenith angle and sky conditions.\n",
    "\n",
    "Let’s assume that the programme and the secondary stars have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Target ins</th>\n",
       "      <th>Standard ins</th>\n",
       "      <th>Standard</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B-band</th>\n",
       "      <td>20.41</td>\n",
       "      <td>19.86</td>\n",
       "      <td>16.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V-band</th>\n",
       "      <td>18.79</td>\n",
       "      <td>18.37</td>\n",
       "      <td>14.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R-band</th>\n",
       "      <td>17.56</td>\n",
       "      <td>17.33</td>\n",
       "      <td>13.72</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Target ins  Standard ins  Standard\n",
       "B-band       20.41         19.86     16.14\n",
       "V-band       18.79         18.37     14.64\n",
       "R-band       17.56         17.33     13.72"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.Series\n",
    "item1=pd.Series({ 'Target ins':20.41,\n",
    "                  'Standard ins':19.86,\n",
    "                  'Standard':16.14})\n",
    "item2=pd.Series({ 'Target ins':18.79,\n",
    "                  'Standard ins':18.37,\n",
    "                  'Standard':14.64})\n",
    "item3=pd.Series({ 'Target ins':17.56,\n",
    "                  'Standard ins':17.33,\n",
    "                  'Standard':13.72})\n",
    "df = pd.DataFrame([item1, item2, item3], index=['B-band', 'V-band', 'R-band'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### First calculate the transformation constant C, \n",
    "      Secondary Standard: C = m_std – m_ins.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Target ins</th>\n",
       "      <th>Standard ins</th>\n",
       "      <th>Standard</th>\n",
       "      <th>Secondary Standard (C)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B-band</th>\n",
       "      <td>20.41</td>\n",
       "      <td>19.86</td>\n",
       "      <td>16.14</td>\n",
       "      <td>-3.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V-band</th>\n",
       "      <td>18.79</td>\n",
       "      <td>18.37</td>\n",
       "      <td>14.64</td>\n",
       "      <td>-3.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R-band</th>\n",
       "      <td>17.56</td>\n",
       "      <td>17.33</td>\n",
       "      <td>13.72</td>\n",
       "      <td>-3.61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Target ins  Standard ins  Standard  Secondary Standard (C)\n",
       "B-band       20.41         19.86     16.14                   -3.72\n",
       "V-band       18.79         18.37     14.64                   -3.73\n",
       "R-band       17.56         17.33     13.72                   -3.61"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Stnd=df['Standard']\n",
    "Stnd_ins=df['Standard ins']\n",
    "df['Secondary Standard (C)']=Stnd-Stnd_ins\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Now, \n",
    "     Use C with Target_ins : m_std = C + m_ins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Target ins</th>\n",
       "      <th>Standard ins</th>\n",
       "      <th>Standard</th>\n",
       "      <th>Secondary Standard (C)</th>\n",
       "      <th>Target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B-band</th>\n",
       "      <td>20.41</td>\n",
       "      <td>19.86</td>\n",
       "      <td>16.14</td>\n",
       "      <td>-3.72</td>\n",
       "      <td>16.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>V-band</th>\n",
       "      <td>18.79</td>\n",
       "      <td>18.37</td>\n",
       "      <td>14.64</td>\n",
       "      <td>-3.73</td>\n",
       "      <td>15.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>R-band</th>\n",
       "      <td>17.56</td>\n",
       "      <td>17.33</td>\n",
       "      <td>13.72</td>\n",
       "      <td>-3.61</td>\n",
       "      <td>13.95</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Target ins  Standard ins  Standard  Secondary Standard (C)  Target\n",
       "B-band       20.41         19.86     16.14                   -3.72   16.69\n",
       "V-band       18.79         18.37     14.64                   -3.73   15.06\n",
       "R-band       17.56         17.33     13.72                   -3.61   13.95"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C=df['Secondary Standard (C)']\n",
    "T=df['Target ins']\n",
    "df['Target']= T+C\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Hence, B-V is :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B-V =  1.62\n"
     ]
    }
   ],
   "source": [
    "m=T['B-band']-T['V-band']\n",
    "print('B-V = ',round(m,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Colour of a star"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2: Spica and Antares are two well-known stars with colour indices (B-V)=-0.13 and (B-V)=+1.83. How many times more blue light (B band) do these objectsemit, as compared to its green light (V band)?Are your objects bluer or redder than the star Vega, which has B-V=0?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution:\n",
    "\n",
    "Colour is defined as the difference between the magnitude of a star in one filter and\n",
    "the magnitude of the same star in a different filter.\n",
    "The physical property that magnitude actually measures is radiant flux - the amount\n",
    "of light that arrives in a given area on Earth in a given time. Remember that\n",
    "magnitude is a logarithmic quantity; a magnitude m=4 star emits 2.51 times as much\n",
    "light as a magnitude m=5 star. This allows us to define colour in terms of the\n",
    "amount of light given off by a star. Colour is a difference in magnitudes; B-V is the\n",
    "difference between a star's blue magnitude and the same star's green magnitude.\n",
    "Since magnitude is defined as\n",
    "\n",
    "m = -2.5 log(Fx/Fvega)\n",
    "\n",
    "where Fx is the observed flux in the band x, and Fvega is the flux of the star Vega. The\n",
    "star Vega, in the constellation of Lyra is used as a reference in the magnitude\n",
    "system. Vega has the arbitrary definition of zero magnitude at all wavelengths\n",
    "\n",
    "U=B=V=R=I=0\n",
    "\n",
    "This does not mean that Vega show the same brightness through all filters. It is an\n",
    "arbitrary decision taken by the astronomers who have agreed on taking Vega as the\n",
    "zero point for the magnitude scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Spica is the brightest star in the constellation of Virgo and one of the brightest stars in the night-time sky. Spica is believed to be the star that provided Hipparchus with the data which enabled him to discover the precession of equinoxes. It has a colour of B-V=-0.13. Antares, the brightest star in Scorpius, has B-V=1.83. In terms of radiant flux a colour index can be expressed as B-V = -2.5 log (Fblue) + 2,5 log (Fgreen), which is equal to -2,5log(Fblue/Fgreen).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spica emit 1.13 times more blue light (B band) as compared to its green light (V band)\n",
      "Antares emit 0.19 times more blue light (B band) as compared to its green light (V band)\n"
     ]
    }
   ],
   "source": [
    "spica=-0.13\n",
    "antares=1.83\n",
    "s=spica/-2.5\n",
    "a=antares/-2.5\n",
    "x1=10**s\n",
    "x2=10**a\n",
    "print(\"Spica emit\",round(x1,2),\"times more blue light (B band) as compared to its green light (V band)\")\n",
    "print(\"Antares emit\",round(x2,2),\"times more blue light (B band) as compared to its green light (V band)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### By definition for Vega , (Fblue/Fgreen) = 1\n",
    "      For Spica , (Fblue/Fgreen) > 1\n",
    "      For Antares , (Fblue/Fgreen) < 1\n",
    "      Therefore, since Spica emits more blue light than Vega it will appear bluer than\n",
    "      Vega. Antares, on the other hand, will appear redder than Vega."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Since Spica emits more blue light than Vega it will appear bluer than Vega.\n",
      "Since Antares emits less blue light than Vega it will appear redder than Vega.\n"
     ]
    }
   ],
   "source": [
    "x3=1\n",
    "if(x1>x3):\n",
    "    print('\\nSince Spica emits more blue light than Vega it will appear bluer than Vega.')\n",
    "else:\n",
    "    print('Since Spica emits less blue light than Vega it will appear redder than Vega.')\n",
    "if(x2>x3):\n",
    "    print('Since Antares emits more blue light than Vega it will appear bluer than Vega.')\n",
    "else:\n",
    "    print('Since Antares emits less blue light than Vega it will appear redder than Vega.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Colour and Temperature\n",
    "\n",
    "The colour of a star is primarily a function of its effective temperature.A star approximates the behaviour of a black body radiator. As a\n",
    "blackbody gets hotter, its colour changes. If we heat a solid bar, it would\n",
    "first emit radiation in the infrared region. Further heating would see it glow a dull\n",
    "reddish colour. With more heating it could eventually glow orange, yellow, white\n",
    "and eventually blue-hot. Ultimately if it were hot enough a black body emits most of\n",
    "its energy in the ultraviolet region.\n",
    "The colour that we see is usually an additive combination of the emissions from each\n",
    "wavelength. Hot stars appear blue because most energy is emitted in the bluer parts\n",
    "of the spectrum. There is little emission in the blue parts of the spectrum for cool\n",
    "stars - they appear red."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3: Create a programme that obtains the blackbody energy distribution curve for a given         temperature. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution:\n",
    "\n",
    "For, a range of wavelengths (100-30000 Å) we calculate the radiated power of a black\n",
    "body using the Power Density Planck law\n",
    "F( λ )=((2π(cxc))xh)/(λ^5)/((e^(hc/λkT) −1)), \n",
    "h = 6.626 x 10-34 joule s\n",
    "k = 1.381 x 10-23 joule/K\n",
    "c = 2.998 x 108 m/sec\n",
    "λ should be in meters. F(λ) is in units of watts/m3\n",
    "Let us look at two different stars, one with an effective temperature of 12,500 K and\n",
    "the other of 5,000 K. Each of these will produce a spectrum that approximates a\n",
    "black body curve. The diagram below shows these two curves on a normalized\n",
    "intensity plot, that is, we have divided each value of the flux by the maximum value\n",
    "of the flux (if we used a true intensity scale the plot for the 5,000 K star would be\n",
    "dwarfed by that for the hotter star). We can see that in the visible part of the\n",
    "spectrum the curve is sloping down to the right for the 12,500 K star whilst it slopes\n",
    "up for the cooler star. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def energy(l,t):     ## function to calculate radiated power of black body using Planck's law.\n",
    "    l=l*(10**(-10))\n",
    "    h = 6.626*(10**(-34))\n",
    "    k = 1.381*(10**(-23))\n",
    "    c = 2.998*(10**8)\n",
    "    a=(h*c)/(l*k*t)\n",
    "    m=np.exp(a)\n",
    "    f=(2*3.14*(c**2)*h)/((l**5)*(m-1))\n",
    "    return f\n",
    "x = np.arange(100,30000,50)\n",
    "ya1 = energy(x,5000)  ## flux for range of wavelengths at 5000K\n",
    "y1 = ya1/np.max(ya1)  ## normalised flux for range of wavelengths at 5000K\n",
    "ya2 = energy(x,12500) ## flux for range of wavelengths at 12500K\n",
    "y2 = ya2/np.max(ya2)  ## normalised flux for range of wavelengths at 12500K\n",
    "plt.xlabel('Wavelength (Angstrom)')\n",
    "plt.ylabel('Normalised flux')\n",
    "plt.title(\"Comparison of B-V color for 'hot' and 'cold' star.\")\n",
    "plt.plot(x, y1,color='red',label='5000 K')\n",
    "plt.plot(x, y2,color='blue',label='12500 K')\n",
    "plt.legend()\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The blue curve represents the 12,500 K star and red curve is 5000 K star."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1= energy(4400,5000)/(np.max(ya1)) ## reresents energy at B-band for 5000K.\n",
    "p2=energy(4400,12500)/(np.max(ya2)) ## reresents energy at B-band for 12500K.\n",
    "p3= energy(5500,5000)/(np.max(ya1)) ## reresents energy at V-band for 5000K.\n",
    "p4=energy(5500,12500)/(np.max(ya2)) ## reresents energy at V-band for 12500K.\n",
    "x2= [4400,4400]\n",
    "y_r1= [0,p1] \n",
    "y_b1= [0,p2]\n",
    "y_rf1= [p1,p1] ## Normalised flux for B-band for 5000K. \n",
    "y_bf1= [p2,p2] ## Normalised flux for B-band for 12500K. \n",
    "x3= [0,4400]\n",
    "x4=[5500,5500]\n",
    "y_r2= [0,p3]\n",
    "y_b2= [0,p4]\n",
    "y_rf2= [p3,p3] ## Normalised flux for V-band for 5000K. \n",
    "y_bf2= [p4,p4] ## Normalised flux for V-band for 12500K. \n",
    "x5=[0,5500]\n",
    "plt.xlabel('Wavelength (Angstrom)')\n",
    "plt.ylabel('Normalised flux')\n",
    "plt.title(\"Comparison of B-V color for 'hot' and 'cold' star.\")\n",
    "plt.plot(x, y1,color='red',label='5000 K')\n",
    "plt.plot(x, y2,color='blue',label='12500 K')\n",
    "plt.plot(x2, y_r1,linewidth=1,color='black',linestyle='--',label='B_5000 K')\n",
    "plt.plot(x3, y_rf1,linewidth=1,color='black',linestyle='--',)\n",
    "plt.plot(x2, y_b1,linewidth=1,color='black',label='B_12500 K')\n",
    "plt.plot(x3, y_bf1,linewidth=1,color='black')\n",
    "plt.plot(x4, y_r2,linewidth=1,color='brown',linestyle='--',label='V_5000 K')\n",
    "plt.plot(x5, y_rf2,linewidth=1,color='brown',linestyle='--',)\n",
    "plt.plot(x4, y_b2,linewidth=1,color='brown',label='V_12500 K')\n",
    "plt.plot(x5, y_bf2,linewidth=1,color='brown')\n",
    "plt.legend()\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Blue curve emits more energy in the B waveband than in the V waveband. This means that it is brighter in B than in V, therefore its apparent magnitude B will be lower than apparent magnitude V. The colour Index is\n",
    "B – V, so for this star it will be < 0, that is, negative. The red curve represents the\n",
    "5000 K star. For this B-V is positive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 4: Create several blackbody energy distribution curves for 9 different temperatures ranging from 3000K to 20000K (do not forget the curve that corresponds to T=9790 K, Vega’s effective temperature). Taking into account the effective wavelengths for the various filters given bellow, annotate the flux values for each filter and each curve and create a (B-V)-temperature plot. What do you observe? Which end of the line in your graph corresponds to hotter stars? Which corresponds to cooler stars? How do you know? Calculate the temperature of Spica and Antares and compare the values that you get with those found in precise measurements. Why are your values of the temperature lower than the real ones? In other words, why are they redder than they should be?\n",
    "\n",
    "In terms of flux,\n",
    "\n",
    "B-V = (-2.5)*(np.log10((Fb x Fv_vega)/(Fv x Fb_vega)))\n",
    "\n",
    "If we calculate the B-V colour index for each curve and represent the blackbody\n",
    "temperature as a function of the colour you should get a plot like this:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def energy(l,t):        ## function to calculate radiated power of black body using Planck's law.\n",
    "    l=l*(10**(-10))\n",
    "    h = 6.626*(10**(-34))\n",
    "    k = 1.381*(10**(-23))\n",
    "    c = 2.998*(10**8)\n",
    "    a=(h*c)/(l*k*t)\n",
    "    m=np.exp(a)\n",
    "    f=(2*3.14*(c**2)*h)/((l**5)*(m-1))\n",
    "    return f\n",
    "x=np.arange(2500,22500,2500)\n",
    "Fb=energy(4400,x)\n",
    "Fv=energy(5500,x)\n",
    "Fv_vega=energy(5500,9790)   ## flux for B-band at Vega’s effective temperature.\n",
    "Fb_vega=energy(4400,9790)   ## flux for V-band at Vega’s effective temperature.\n",
    "e=(Fb*Fv_vega)/(Fv*Fb_vega)\n",
    "b= (-2.5)*(np.log10(e))\n",
    "plt.plot(b,x,marker='o', color='red',linewidth=0.5,markerfacecolor='blue', markersize=5)\n",
    "plt.xlabel(\"B-V\")\n",
    "plt.ylabel(\"Temperature(K)\")\n",
    "plt.title(\"Relationship between color and temperatures from black body curves\")\n",
    "plt.ylim(0,22500)\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that as the B-V of stars increases, more its temperature decreases and more cooler it becomes.\n",
    "The left side of graph represents the hotter stars, which have actually low B-V, \n",
    "and the right side represents the hotter stars, which have high B-V,  Since we saw that the above graph of relationship between color and temperatures from black body curves comes out to be inversely proportional."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spica has (B-V)=-0.13 and Antares (B-V)=1.83.We can deduce approximately the temperatures: 3000 K for Antares and 12300 K for Spica. The real temperatures of Antares and Spica are 3400 K and 18000 K, respectively.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main reason for the discrepancy in the temperature is that only the peak wavelength has been used to derive the B and V magnitudes, without taking into account the transmission curves of each filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another reason why we obtain lower temperatures is that the Interstellar space is\n",
    "not a perfect vacuum. The interstellar medium (ISM) comprises cold neutral gas (H I\n",
    "at ≈ 70 K), warm neutral gas (H I at 6,000 K) and hot ionised plasma (H II at 106\n",
    "K)\n",
    "primarily located in the plane of the galaxy in the spiral arms. Cosmic dust is made\n",
    "up of small grains of silicates, iron, carbon, frozen water and ammonia ice 0.1 to 0.01\n",
    "microns (μm) in size. Although this cosmic dust only makes up 1% of the mass of the\n",
    "ISM, it absorbs and scatters light from stars. This means that light from a distant star\n",
    "is reduced in intensity so that the star appears dimmer than it would be if there was\n",
    "no intervening material."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5: Using the blackbody curves obtained in the previous exercise, annotate the wavelength at which the flux is maximum. What do you observe? Create a plot of temperature as a function of the λpeak using a logaritmic scale. What do you observe? Fit a function (straight line) to the data and calculate Wien’s constant. The Sun has a peak wavelength of thermal radiation of 5300 Å. What is the Sun's average temperature? And for the Polar star which has λpeak=3500 Å."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def energy(l,t):\n",
    "    l=l*(10**(-10))\n",
    "    h = 6.626*(10**(-34))\n",
    "    k = 1.381*(10**(-23))\n",
    "    c = 2.998*(10**8)\n",
    "    a=(h*c)/(l*k*t)\n",
    "    m=np.exp(a)\n",
    "    f=(2*3.14*(c**2)*h)/((l**5)*(m-1))\n",
    "    return f\n",
    "x = np.arange(100,30000,50)\n",
    "\n",
    "t = range(2500,22500,2500)\n",
    "\n",
    "for i in t:\n",
    "    y=energy(x,i)\n",
    "    plt.plot(x, y,label=i)\n",
    "plt.xscale('log')\n",
    "plt.ylim([10**11,10**17])\n",
    "plt.yscale('log')\n",
    "plt.ylabel(\"Flux(watts/(m^3)\")\n",
    "plt.xlabel(\"Wavelength(Å)\")\n",
    "plt.title(\"Blackbody curves for thermal bodies at different temperatures.\")\n",
    "plt.legend()\n",
    "plt.show()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thermal radiation is emitted by stars. The curves show that\n",
    "hotter stars give off more thermal radiation. The curves also show that the peak\n",
    "wavelength of the thermal radiation moves to shorter wavelengths as the\n",
    "temperature increases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Temperature and Peak Wavelength (Wien’s law): \n",
    "Wien's Law tells us that objects of different temperature emit spectra that peak at different wavelengths."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hotter objects emit most of their radiation at shorter wavelengthsamd  hence\n",
    "they will appear to be bluer.Cooler objects emit most of their radiation at longer wavelengths and hence\n",
    "they will appear to be redder.\n",
    "Furthermore, at any wavelength, a hotter object radiates more (is more luminous)\n",
    "than a cooler one. We can understand this by the size of the area that encloses each\n",
    "curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def energy(l,t):\n",
    "    l=l*(10**(-10))\n",
    "    h = 6.626*(10**(-34))\n",
    "    k = 1.381*(10**(-23))\n",
    "    c = 2.998*(10**8)\n",
    "    a=(h*c)/(l*k*t)\n",
    "    m=np.exp(a)\n",
    "    f=(2*3.14*(c**2)*h)/((l**5)*(m-1))\n",
    "    return f\n",
    "x = np.arange(100,30000,50)\n",
    "\n",
    "t = range(2500,22500,2500)\n",
    "k=[]\n",
    "for i in t:\n",
    "    y=energy(x,i)\n",
    "    ya=np.max(y)\n",
    "    for j in x:\n",
    "        yt=energy(j,i)\n",
    "        if yt==ya:\n",
    "            k.append(j)\n",
    "tl=np.log10(t)\n",
    "xp=np.log10(k)\n",
    "plt.plot(xp,tl,color='red',marker='o',linewidth=0.5,markerfacecolor='blue', markersize=5)\n",
    "plt.xlabel(\"log(λpeak)Å\")\n",
    "plt.ylabel(\"log(T)K\")\n",
    "plt.title(\"Temperature as a function of peak wavelength\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best-fit is\n",
    "\n",
    "Log(T K) = 7.4574 - 0.9986 log ( λpeak (Å))\n",
    "\n",
    "\n",
    "thus,\n",
    "λpeak T = 107.4574 = 28668171.9 Å K\n",
    "\n",
    "\n",
    "The Wien’s constant in units of the International System that we find from our data\n",
    "is\n",
    "2.867 x (10^(-3))m K  which can be compared with the carefully measured relationship between\n",
    "temperature and peak wavelength of thermal radiation.\n",
    "\n",
    "λpeak T = 2.897 x (10^(-3)) m K,\n",
    "where λpeak is measured in meters and T is measured in Kelvin.\n"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "..The Sun's peak wavelength is 5300 Angstroms.\n",
    "\n",
    "    Convert this length to meters:\n",
    "    1 meter = 1010 Angstroms\n",
    "    5300 Angstroms (1 m/ 1010 Angstroms) = 5.3 x (10^(-7)) m.\n",
    "    Insert this length into the peak wavelength equation:\n",
    "    λpeak T = 2.897 x (10^(-3)) m K.\n",
    "    to get T : (5.3 x (10^(-7)) m) T = 2.897 x (10^(-3)) m K.\n",
    "    Now, solve for T: \n",
    "    T = (2.897 x (10^(-3)) m K) / (5.3 x (10^(-7)) m) = 5460 K\n",
    "    Thus, Sun's average temperature is 5460 K."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "..The Polar star's peak wavelength is 3500 Angstroms.\n",
    "\n",
    "    Convert this length to meters:\n",
    "    1 meter = 1010 Angstroms\n",
    "    3500 Angstroms (1 m/ 1010 Angstroms) = 3.5 x (10^(-7)) m.\n",
    "    Insert this length into the peak wavelength equation:\n",
    "    λpeak T = 2.897 x (10^(-3)) m K.\n",
    "    to get T : (3.5 x (10^(-7)) m) T = 2.897 x (10^(-3)) m K.\n",
    "    Now, solve for T: \n",
    "    T = (2.897 x (10^(-3)) m K) / (3.5 x (10^(-7)) m) = 8534 K\n",
    "    Thus, Polar star's average temperature is 8534 K."
   ]
  },
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   "source": []
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