vela_C/code/2_S_dispersion_subregions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# File Contents:\n",
    "- Determining the gamma value of each of the 4 regions of Vela-C with S-dispersion\n",
    "\n",
    "*see file #1*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#imports\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "\n",
    "import aplpy\n",
    "import numpy as np\n",
    "from astropy.io import fits\n",
    "from astropy.visualization import astropy_mpl_style\n",
    "from astropy.wcs import WCS\n",
    "from astropy.utils.data import get_pkg_data_filename\n",
    "import math as m\n",
    "import scipy.optimize as opt\n",
    "import statistics as st\n",
    "\n",
    "matplotlib.rcParams['figure.figsize'] = (15, 7)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "hill_data = fits.getdata('fits_files/VelaC_500_hill_regs_regrid_30as_pix.fits', ext = 0)\n",
    "var_Q_data = fits.getdata('fits_files/VelaC_500_intermediate_regrid_30as_pix_var_Q.fits', ext = 0)\n",
    "var_U_data = fits.getdata('fits_files/VelaC_500_intermediate_regrid_30as_pix_var_U.fits', ext = 0)\n",
    "ang_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_ang.fits', ext=0)\n",
    "I_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_I.fits', ext=0)\n",
    "p_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_p.fits', ext=0)\n",
    "polint_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_polint.fits', ext = 0)\n",
    "Q_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_Q.fits', ext=0)\n",
    "S_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_S.fits', ext = 0)\n",
    "s2n_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_s2n_polint.fits', ext = 0)\n",
    "U_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_U.fits', ext = 0)\n",
    "var_polint_data = fits.getdata('fits_files_2/VelaC_500_intermediate_regrid_30as_pix_var_polint.fits', ext=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# S-corrected p for entire cloud"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = np.logical_and(hill_data>0, polint_data>3*np.sqrt(var_polint_data))\n",
    "s = S_data[np.logical_not(np.isnan(S_data))]\n",
    "s_median = np.logical_and(S_data<st.median(s), mask)\n",
    "\n",
    "i_good = mask.nonzero()\n",
    "p_good = p_data[i_good]\n",
    "s_good = p_data[s_median]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/bb/r56hppg12fn6k8mzjncdy1b00000gn/T/ipykernel_56850/194442918.py:5: RuntimeWarning: invalid value encountered in arccos\n",
      "  gammas = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good]\n",
      "/var/folders/bb/r56hppg12fn6k8mzjncdy1b00000gn/T/ipykernel_56850/194442918.py:6: RuntimeWarning: invalid value encountered in arccos\n",
      "  gammap = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12a5eca10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 7))\n",
    "\n",
    "p_max = 0.15\n",
    "p_0 = (3*p_max)/(3+p_max)\n",
    "gammas = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good]\n",
    "gammap = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good]\n",
    "\n",
    "hists, bins, patches = plt.hist(gammas, 90, range= (0,90), histtype = 'step', label = 's-corrected$\\gamma_{obs}$')\n",
    "histp, bins, patches = plt.hist(gammap, 90, range= (0,90), histtype = 'step', label = '$\\gamma_{obs}$')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Misc "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "mask2 = np.logical_and(hill_data==2, polint_data>3*np.sqrt(var_polint_data))\n",
    "mask3 = np.logical_and(hill_data==3, polint_data>3*np.sqrt(var_polint_data))\n",
    "mask4 = np.logical_and(hill_data==4, polint_data>3*np.sqrt(var_polint_data))\n",
    "mask5 = np.logical_and(hill_data==5, polint_data>3*np.sqrt(var_polint_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# S-corrected for S mean of each subregion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 Center-Ridge "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.317666119975689"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 7))\n",
    "\n",
    "s2 = S_data[mask2]\n",
    "s_median2 = np.logical_and(S_data<st.median(s2), mask2)\n",
    "s_good2 = p_data[s_median2]\n",
    "gammas2 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good2]\n",
    "hists2, bins, patches = plt.hist(gammas2, 90, range= (0,90),  histtype = 'step', label = 's-corrected')\n",
    "\n",
    "i_good2 = mask2.nonzero()\n",
    "p_good2 = p_data[i_good2]\n",
    "gamma2 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good2]\n",
    "hist2, bins, patches = plt.hist(gamma2, 90, range= (0,90), histtype = 'step', label = '$\\gamma_{obs}$ mask = 2')\n",
    "plt.legend()\n",
    "\n",
    "st.median(s2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 Center-Nest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1120ac590>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 7))\n",
    "\n",
    "s3 = S_data[mask3]\n",
    "\n",
    "s_median3 = np.logical_and(S_data<st.median(s3), mask3)\n",
    "s_good3 = p_data[s_median3]\n",
    "gammas3 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good3]\n",
    "hists3, bins, patches = plt.hist(gammas3, 90, range= (0,90),  histtype = 'step', label = 's-corrected')\n",
    "\n",
    "i_good3 = mask3.nonzero()\n",
    "p_good3 = p_data[i_good3]\n",
    "gamma3 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good3]\n",
    "hist3, bins, patches = plt.hist(gamma3, 90, range= (0,90), histtype = 'step', label = 'mask = 3')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 South-Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x129a4ca10>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 7))\n",
    "\n",
    "s4 = S_data[mask4]\n",
    "s_median4 = np.logical_and(mask4, S_data<st.median(s4))\n",
    "s_good4 = p_data[s_median4]\n",
    "gammas4 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good4]\n",
    "hists4, bins, patches = plt.hist(gammas4, 90, range= (0,90),  histtype = 'step', label = 's-corrected')\n",
    "\n",
    "i_good4 = mask4.nonzero()\n",
    "p_good4 = p_data[i_good4]\n",
    "gamma4 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good4]\n",
    "hist4, bins, patches = plt.hist(gamma4, 90, range= (0,90), histtype = 'step', label = 'mask = 4')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 South-Nest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/bb/r56hppg12fn6k8mzjncdy1b00000gn/T/ipykernel_56850/2364114856.py:6: RuntimeWarning: invalid value encountered in arccos\n",
      "  gammas5 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good5]\n",
      "/var/folders/bb/r56hppg12fn6k8mzjncdy1b00000gn/T/ipykernel_56850/2364114856.py:11: RuntimeWarning: invalid value encountered in arccos\n",
      "  gamma5 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good5]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12a9c8150>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 7))\n",
    "\n",
    "s5 = S_data[mask5]\n",
    "s_median5 = np.logical_and(S_data<st.median(s5), mask5)\n",
    "s_good5 = p_data[s_median5]\n",
    "gammas5 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in s_good5]\n",
    "hists5, bins, patches = plt.hist(gammas5, 90, range= (0,90),  histtype = 'step', label = 's-corrected')\n",
    "\n",
    "i_good5 = mask5.nonzero()\n",
    "p_good5 = p_data[i_good5]\n",
    "gamma5 = [(1/2)*np.arccos(((2*p_obs*(1+(2/3)*p_0))/(p_0*(1+p_obs)))-1)*180/np.pi for p_obs in p_good5]\n",
    "hist5, bins, patches = plt.hist(gamma5, 90, range= (0,90), histtype = 'step', label = 'mask = 5')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12a990690>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H3pKsLOWMGasyh4NgDUCdQLAGAABqTIsYq9qxNhEA1CmhcXGEZADqLYI1AACAOiy3MFeOYs/uJKmqrALP11Ty9Rw10UtVlObkVOkOHgAAUDsRrAEAANRRuYW56re4n5xlTp/NYQmxyB5mr/Zx7WF2WUIsyliT4fdeqqo0J0fb+14hw+n5526yWBRi93/vAACgagjWAAAA6ihHsUPOMqemdpuqZFuyT+awh9kVa42t9nFjrbFa3G9xle6281UvVVXmcMhwOhU3Y7rMyZ597uySCABA7USwBgAAUMcl25KV0ijF321UWaw1NiCCMm+Zk5NladvW320AAAAfCvJ3AwAAAAAAAEBtRLAGAAAAAAAAeCGgg7WpU6fqvPPOU8OGDRUTE6P+/fvrl19+cas5cuSIhg0bpkaNGslqtWrAgAHau3evnzoGAAAAAABAfRHQwdrq1as1bNgwffvtt1q+fLlKS0t12WWXqaioyFVz//3366OPPtI777yj1atXKycnR9dcc40fuwYAAAAAAEB9ENCbFyxbtszt9YIFCxQTE6ONGzfq4osvVkFBgf75z3/qrbfeUs+ePSVJ8+fPV5s2bfTtt9/qb3/7mz/aBgAAAAAAQD0Q0Hes/VVBQYEkKTo6WpK0ceNGlZaWKj093VXTunVrnXXWWVq7du1JxykuLtbBgwfdfgAAAAAAAICqqDXBWkVFhUaOHKmuXbuqXbt2kqQ9e/bIbDYrKirKrbZJkybas2fPSceaOnWqbDab6ychIcGXrQMAAAAAAKAOqjXB2rBhw7Rp0ya9/fbbpz1WRkaGCgoKXD+7du2qhg4BAAAAAABQnwT0GmvHDB8+XEuWLNGXX36pM88803W8adOmKikpUX5+vttda3v37lXTpk1POl5YWJjCwsJ82TIAAAAAAADquIAO1gzD0IgRI/TBBx9o1apVSkpKcjvfqVMnhYaGauXKlRowYIAk6ZdfftHOnTvVpUsXf7QMAAAA+F7+Lunwfs9qGzSSolj6pLpsyyv0qM4eYVZ8lMXH3QAA/C2gg7Vhw4bprbfe0uLFi9WwYUPXumk2m00Wi0U2m0233XabHnjgAUVHRysyMlIjRoxQly5d2BEUAAAAdVP+LmnO+VLpYc/qQxtIw74jXDtN9gizLKHBGrkw06N6S2iwVoxKI1wDgDouoIO1uXPnSpK6d+/udnz+/PkaMmSIJOmZZ55RUFCQBgwYoOLiYvXq1UsvvPBCDXcKAAAA1JDD+4+Gate8LJ3R6tS1+36V3h969BqCtdMSH2XRilFpchSVVFq7La9QIxdmylFUQrAGAHVcQAdrhmFUWhMeHq45c+Zozpw5NdARAAAAECDOaCXFpfq7i3olPspCUAYAcBPQwRoAAKjfPF3LyNM6AAAAoDoRrAEAgIBT1bWMpKPrGdkjzL5rCgAAAPgLgjUAABBwqrKW0THswAcAAICaRrAGAAACEmsZAQAAINARrAEAAAD+lr/r6M6dntj3q297AQAAHiNYAwAAAPwpf5c053yp9LDn14Q2kBo08l1PAADAIwRrAAAAgD8d3n80VLvmZemMVp5d06CRFJXg274AAEClCNYAAACAQHBGKyku1d9dAACAKiBYAwAAAAC4ySrI8rjWHmZXrDXWh90AQOAiWAMAAAAASDoakllCLMpYk+HxNZYQixb3W0y4BqBeIlgDAAAAAEiSYq2xWtxvsRzFDo/qswqylLEmQ45iB8EagHqJYA0AAAAA4BJrjSUkAwAPEawBAACv7M53ylFU4lHttrxCH3cD+FZpTo7KHJ7dwVOS5fnaVAAAoHYjWAMAAFW2O9+p9Jmr5Swt9/gaS2iw7BFmH3YF+EZpTo62971ChtPp8TUmi0UhdrsPuwIAAIGAYA0AAFSZo6hEztJyzRqUqhYxVo+usUeYFR9l8XFnQPUrczhkOJ2KmzFd5uRkj64JsdsVGhfn484AAIC/EawBAACvtYixql28zd9tADXCnJwsS9u2/m4DAAAEEII1AAAA1EuerpvGmmkAAOBkCNYAAABQ71R13TTWTAMAACdCsAYAAIB6p6rrprFmGgAAOBGCNQAAANRbrJsGAABOB8EaAABw2Z3vlKOopNK6bXmFNdANAAAAENgI1gAAgKSjoVr6zNVylpZ7VG8JDZY9wuzjrgAAAIDARbAGAAAkSY6iEjlLyzVrUKpaxFgrrbdHmBUfZamBzgAAAIDARLAGAADctIixql28zd9tAAAAAAGPYA0AAAAA8H/yd0mH93tWe3CHT1sBgEBHsAYAAAAAOCp/lzTnfKn0sGf15lApPlY6tFdqlOLb3gAgABGsAQAAAACOOrz/aKh2zcvSGa0qr9+5WvrlFelIge97A4AARLAGAAAAAHB3RispLrXyOh4FBVDPEawBAFDNduc75Sgq8bie3TUBALVdVtFuaf/mygsLsmXyfTsAUGMI1gAAqEa7851Kn7laztJyj6+xhAZrxag0wjUAQK1jD7XKUlGhjE3zpE3zKq1P2mNomqR9zn1K8H17AOBzBGsAAFQjR1GJnKXlmjUoVS1irJXWb8sr1MiFmXIUlRCsAQBqnVjLGVr8e64c170qNa58TbbfN34pzZ+tQyWHaqA7APA9gjUAAHygRYxV7eJt/m4DAACfiy0vV2xkome7glqzfN4PANQkgjUAAALAtrxCj+pYjw25hblyFDs8qs0q4D9gAX/y9O92qR7+/b7jdzltP1daFmK3KzQurgYaAgDvEKwBAOBH9gizLKHBGrkw06N61mOr33ILc9VvcT85y5weX2MJscgeZvdhVwD+qqp/t0v16O93W0MdCZXCJ83WDs2utNxksaj50iWEawACFsEaAAB+FB9l0YpRaR7tIsp6bHAUO+Qsc2pqt6lKtiV7dI09zK5Ya6yPOwPwZ1X5u12qZ3+/N22s+4cG64XOTyrJlnTK0pKsLOWMGasyh4NgDUDAIlgDAMDP4qMsdf8/pFCtkm3JSvFkLSMAfsPf7Se332aSzk6Whb/HANQBBGsAAJfd+U6P/9f1+rQWTFU+l6qsp1MTanPvAKrRvl89r23QSIpK8F0vAADUIQRrAABJRwOY9Jmr5Swt96i+vqwFU9XPRTr62dgjzD7syjO1uXcA1aRBIym0gfT+UM+vCW0gDfuOcA0AAA8QrAEAJEmOohI5S8s1a1CqWsRYT1lbn9aCqcrnckyg3M1Xm3sHUE2iEo6GZIf3e1a/79ejIdzh/QRrAAB4gGANAOCmRYxV7eJt/m4j4NTmz6U29w6gGkQlEJIBAOAjBGsAAAAAvJe/y/M74iTWcKurPF3H7+AOn7YBADWNYA0AAACAd/J3SXPOl0oPe34Na7jVLVVdx88cKsXHSof2SuwKCqAOIFgDAAAA4J3D+4+Gate8LJ3RqvJ61nCre6q6jt/O1dIvr0hHCnzbFwDUEII1AAAAAKfnjFZSXKq/u4C/VGUdPx4FBVDHEKwBAOqE3flOOYpKPKqt7TtfbssrrNY6+F9uYa4cxY5K67IKsmqgG1SLqqw75unaVDXJ054CsXcAAGoQwRoAoNbbne9U+szVcpaWe1RvCQ3WilFptS5cs0eYZQkN1siFmR5fYwkNlj3C7LumcNpyC3PVb3E/OcucHtVbQiyyh9l93BVOi7frjjVo5LuePFXV9bKkwOkdAAA/IFgDANR6jqISOUvLNWtQqlrEWE9Zuy2vUCMXZspRVFLrgrX4KItWjErz+M48qfbfnVcfOIodcpY5NbXbVCXbkiutt4fZFWuNrYHO4LWqrjsmBc5OmVVdL0sKnN4BAPADgjUAQJ3RIsaqdvE2f7fhU/FRFoKyOirZlqwUdsirW2rrumNVWS8LAIB6jmANAAAAqExtXzMN9Vst//6WZHm+vmSI3a7QuDgfdgMA7gjWAAAAgFOpzWumAbX4+xtit8tksShnzFiPrzFZLGq+dAnhGoAaQ7AGAAAAnEptXjMNqMXf39C4ODVfukRljsp3TZaO3tmWM2asyhwOgjUANYZgDQAAAPBEbV0zDZBq7fc3NC6OkAxAQCNYAwDUiN35TnazBKpDVdZKkqp+50lVx68KX98FU5Xe/8j+///3Vymn9NS1AbjmFAAACAwEawAAn9ud71T6zNVylpZ7fI0lNFgrRqURrgF/5u1aScO+8yzQ8mb8qqhKL1VV1d4PhEpqLL0/VIquJFiTAmbNKQAAEFgI1gAAPucoKpGztFyzBqWqRYy10vpteYUauTBTjqISgjXgz6q6VtK+X48GR4f3exZmebMWk6eq2ktVVbX3X7Olzx46Wt8qqfL6AFlzCgAABBaCNQBAjWkRY1W7eJu/2wBqP1+vlVRL12KS5HnvjtCj/7dxKymurU9bAgAAdRfBGgCgXtqWV1itdcCflebkeLyLnQqy1ajA8G1Dnq4RxlpiQO3h6ZqC/F4DgE8RrAEA6hV7hFmW0GCNXJjp8TWW0GDZI8y+awp1SmlOjrb3vUKG0+lRvUnSM6GSLvlDqu4lvBo0Oro22PtDPb+GtcSAwFfVNQX5vQYAnyFYAwDUK/FRFq0YlcYOpfCZModDhtOpuBnTZU5OrrQ++8c1Cp80W0bBoepvJirh6GYBvtxFFEDNq+qagvxeA4DPEKwBAOqd+CgLQRl8zpycLEtbD9buKsj2bSNRCfwHNVBX1eb1EAGgjiBYAwB4jXXK4EtVWqdMUojdrtC4OB92hBrn6RpSkrTvV5UWBavs1+z/25jgFEqysk6zOdSIqnwHpKrfmVXV8X0kfF+h2pqyFb7PJpkq3z2bddMAIHAQrAEAqox1yuBrVV2nTJJMFouaL11CuFZXVHENqdKiYG3/OEbGRw95PIXJYlGI3e5th/C1qq4jJh1dS2zYd56Fa96M7yMtJC0Nk/RBFS5i3TQACAgEawCAKmOdMvhaVdcpK8nKUs6YsSpzOAjW6ooqriFV9mu2jI8e8vg7I3GXY8Cr6jpi+349ulHH4f2eBWtVHd+Htv1RqPveztTs61P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      "text/plain": [
       "<Figure size 1500x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hists2, bins, patches = plt.hist(gammas2, 90, range= (0,90),  histtype = 'step', label = 'Center-Ridge')\n",
    "hists3, bins, patches = plt.hist(gammas3, 90, range= (0,90),  histtype = 'step', label = 'Center-Nest')\n",
    "hists4, bins, patches = plt.hist(gammas4, 90, range= (0,90),  histtype = 'step', label = 'South-Ridge')\n",
    "hists5, bins, patches = plt.hist(gammas5, 90, range= (0,90),  histtype = 'step', label = 'South-Nest')\n",
    "plt.xlabel('Inclination angle $\\gamma_{obs}$')\n",
    "plt.ylabel('Counts')\n",
    "plt.title('S-corrected values of inclination angle')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}