K-Coefficient Paper Plots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "sexual-shape",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from astropy.modeling.models import NFW\n",
    "import astropy.units as u\n",
    "from astropy import cosmology\n",
    "import sympy as sp\n",
    "data = pd.read_csv(\"/Users/shreyanakum/Desktop/K Coefficient/Paper HI Column Density & Redshift of Observational Data MODIFIED - Sheet1.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e5848d1",
   "metadata": {},
   "source": [
    "# Diffusivity Coefficient from SDSS Data w/ Error Bars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "affected-orchestra",
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffusivity_coefficient(N_H, circular_velocity, halo_mass, M_star_i, star_formation_rate):\n",
    "    nums = 1e18 * 1e30\n",
    "    v_circ_norm = 200/circular_velocity\n",
    "    N_H_fr = np.power(10, N_H)\n",
    "    #return_value = nums * np.power(N_H_fr, -1) * (M_star_i) / np.power(v_circ_norm, 2)\n",
    "    return nums * np.power(N_H_fr, -1) * (1/star_formation_rate) * np.power(v_circ_norm, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "26eb4136",
   "metadata": {},
   "outputs": [],
   "source": [
    "def error_dy_value(N_H_low,N_H_high):\n",
    "    for x in range(0,33):\n",
    "        N_H_amt_low = diffusivity_coefficient(N_H_low[x], velocity_vals, predictedM, M_star_d, sfr)\n",
    "        N_H_amt_high = diffusivity_coefficient(N_H_high[x], velocity_vals, predictedM, M_star_d, sfr)\n",
    "        return ((N_H_amt_high-N_H_amt_low))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7e350fee",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def sfr_atm(age, stellar_mass): \n",
    "    return stellar_mass/age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3f8c6d2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "diff_coeffs = []\n",
    "for i in range(0,33): \n",
    "    diff_coeffs.append(diffusivity_coefficient(N_H[i], velocity_vals[i], predictedM[i], M_star_d[i], sfr[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "1a059f4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.863313023320381e+28, 2.918029187265663e+28, 1.0633321821074404e+29, 1.9504643751374936e+28, 1.1570558894212647e+30, 1.148059177411108e+27, 6.325760157508916e+27, 2.417033109915669e+29, 2.465422735674595e+28, 1.6719577991360764e+27, 2.4994129573374594e+29, 1.0099176881907184e+28, 1.4990331524745091e+29, 5.362538500903624e+29, 2.608201335180833e+30, 7.087889762752873e+27, 8.055675606171463e+28, 9.96469135428087e+28, 5.627945145048884e+28, 2.578824046263642e+28, 1.1398359259432645e+31, 8.055941130662073e+29, 7.37486430712444e+28, 3.900496431171076e+29, 9.070416431660122e+27, 3.800011068111928e+29, 2.4185722006010198e+30, 1.697514137126323e+27, 1.710824840558586e+30, 1.0385160156430671e+28, 3.335096555475075e+28, 1.120789719451305e+30, 6.805182421175025e+28]\n",
      "33\n"
     ]
    }
   ],
   "source": [
    "print(diff_coeffs)\n",
    "print(len(diff_coeffs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "02f79799",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.863313023320381e+28, 2.918029187265663e+28, 1.0633321821074404e+29, 1.9504643751374936e+28, 1.1570558894212647e+30, 1.148059177411108e+27, 6.325760157508916e+27, 2.417033109915669e+29, 2.465422735674595e+28, 1.6719577991360764e+27, 2.4994129573374594e+29, 1.0099176881907184e+28, 1.4990331524745091e+29, 5.362538500903624e+29, 2.608201335180833e+30, 7.087889762752873e+27, 8.055675606171463e+28, 9.96469135428087e+28, 5.627945145048884e+28, 2.578824046263642e+28, 1.1398359259432645e+31, 8.055941130662073e+29, 7.37486430712444e+28, 3.900496431171076e+29, 9.070416431660122e+27, 3.800011068111928e+29, 2.4185722006010198e+30, 1.697514137126323e+27, 1.710824840558586e+30, 1.0385160156430671e+28, 3.335096555475075e+28, 1.120789719451305e+30, 6.805182421175025e+28]\n"
     ]
    }
   ],
   "source": [
    "print(diff_coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "aa0688b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = data['R']\n",
    "N_H = data['N_H']\n",
    "M_star_d = data['log M_*']\n",
    "#sfr = data['SFR']\n",
    "galaxy_age = data['Age Gyr']\n",
    "sfr = sfr_atm(galaxy_age,M_star_d)\n",
    "velocity_vals = np.array([134.05430348763306, 510.21258348149706, 183.43068548075482, 618.451524921208, 110.04104426428928, 513.2321384813996, 234.47085431245546, 230.4213140053146, 102.33555196284, 435.22941800909996, 119.21853483839298, 154.43032711839197, 149.4959744149872, 181.09407352030155, 159.3110992310241, 330.3523655693238, 197.2776795711477, 227.49075690415384, 185.00543166922802, 146.1938044781218, 124.30436763865931, 107.24392367586164, 236.78327050423655, 150.3368062665032, 265.06291167573903, 189.91927258930735, 163.88186723392656, 346.2770941360653, 116.13182974316351, 524.9985013624732, 180.67373358423535, 129.57960283661137, 241.937639758548])\n",
    "\n",
    "y = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr)\n",
    "plt.scatter(R, y, s=20, alpha=0.6, edgecolor='black', linewidth=1)\n",
    "#plt.plot(R, y, zorder=100)\n",
    "#N_H_low = data['log N_H low']\n",
    "#y = diffusivity_coefficient(N_H_low, velocity_vals, predictedM, M_star_d, sfr)\n",
    "#plt.scatter(R, y, s=20, alpha=0.6, edgecolor='black', linewidth=1, color='orange')\n",
    "\n",
    "#N_H_high = data['log N_H high']\n",
    "#y = diffusivity_coefficient(N_H_high, velocity_vals, predictedM, M_star_d, sfr)\n",
    "#plt.scatter(R, y, s=20, alpha=0.6, edgecolor='black', linewidth=1)\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.ylim(1e27,1e33)\n",
    "plt.xlabel('Impact Parameter (kpc)')\n",
    "plt.ylabel('Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ff7637b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = data['R']\n",
    "N_H = data['N_H']\n",
    "M_star_d = data['log M_*']\n",
    "galaxy_age = data['Age Gyr']\n",
    "sfr = sfr_atm(galaxy_age,M_star_d)\n",
    "velocity_vals = np.array([134.05430348763306, 510.21258348149706, 183.43068548075482, 618.451524921208, 110.04104426428928, 513.2321384813996, 234.47085431245546, 230.4213140053146, 102.33555196284, 435.22941800909996, 119.21853483839298, 154.43032711839197, 149.4959744149872, 181.09407352030155, 159.3110992310241, 330.3523655693238, 197.2776795711477, 227.49075690415384, 185.00543166922802, 146.1938044781218, 124.30436763865931, 107.24392367586164, 236.78327050423655, 150.3368062665032, 265.06291167573903, 189.91927258930735, 163.88186723392656, 346.2770941360653, 116.13182974316351, 524.9985013624732, 180.67373358423535, 129.57960283661137, 241.937639758548])\n",
    "\n",
    "y = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr)\n",
    "\n",
    "plt.scatter(R, y)\n",
    "#plt.scatter(R, y, linewidth = 2, linestyle = 'dashed')\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.ylim(1e27,1e33)\n",
    "plt.xlabel('Impact Parameter (kpc)')\n",
    "plt.ylabel('Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f64452fa",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'N_H_low' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/y8/tjhxjlzj4rq0l60s_sy7fl2m0000gn/T/ipykernel_8012/2428764571.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0msfr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msfr_atm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgalaxy_age\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mM_star_d\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdiffusivity_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_H\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvelocity_vals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpredictedM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mM_star_d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msfr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0my_high\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdiffusivity_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_H_low\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvelocity_vals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpredictedM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mM_star_d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msfr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0my_low\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdiffusivity_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_H_high\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvelocity_vals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpredictedM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mM_star_d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msfr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'N_H_low' is not defined"
     ]
    }
   ],
   "source": [
    "galaxy_age = data['Age Gyr']\n",
    "sfr = sfr_atm(galaxy_age,M_star_d)\n",
    "y = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr)\n",
    "y_high = diffusivity_coefficient(N_H_low, velocity_vals, predictedM, M_star_d, sfr)\n",
    "y_low = diffusivity_coefficient(N_H_high, velocity_vals, predictedM, M_star_d, sfr)\n",
    "\n",
    "dy = error_dy_value(N_H_low,N_H_high)\n",
    "plt.yscale('log')\n",
    "plt.ylim(1e27,1e33)\n",
    "plt.errorbar(R, y, yerr =[y-y_low,y_high-y], fmt='.k');\n",
    "plt.xlabel('Impact Parameter (kpc)')\n",
    "plt.ylabel('Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fe1a7824",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'N_H_low' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/y8/tjhxjlzj4rq0l60s_sy7fl2m0000gn/T/ipykernel_8012/1085783927.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0msfr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msfr_atm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgalaxy_age\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mM_star_d\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdiffusivity_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_H\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvelocity_vals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpredictedM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mM_star_d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msfr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0my_high\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdiffusivity_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_H_low\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvelocity_vals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpredictedM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mM_star_d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msfr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0my_low\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdiffusivity_coefficient\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_H_high\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvelocity_vals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpredictedM\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mM_star_d\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msfr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'N_H_low' is not defined"
     ]
    }
   ],
   "source": [
    "galaxy_age = data['Age Gyr']\n",
    "sfr = sfr_atm(galaxy_age,M_star_d)\n",
    "y = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr)\n",
    "y_high = diffusivity_coefficient(N_H_low, velocity_vals, predictedM, M_star_d, sfr)\n",
    "y_low = diffusivity_coefficient(N_H_high, velocity_vals, predictedM, M_star_d, sfr)\n",
    "\n",
    "#----\n",
    "sfr_2 = data['SFR']\n",
    "y_t = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr_2)\n",
    "y_high_t = diffusivity_coefficient(N_H_low, velocity_vals, predictedM, M_star_d, sfr_2)\n",
    "y_low_t = diffusivity_coefficient(N_H_high, velocity_vals, predictedM, M_star_d, sfr_2)\n",
    "\n",
    "dy = error_dy_value(N_H_low,N_H_high)\n",
    "plt.yscale('log')\n",
    "plt.ylim(1e27,1e33)\n",
    "plt.errorbar(R, y, yerr =[(y-y_low),(y_high-y)], fmt='.k');\n",
    "\n",
    "dy = error_dy_value(N_H_low,N_H_high)\n",
    "plt.yscale('log')\n",
    "plt.ylim(1e27,1e33)\n",
    "plt.errorbar(R, y_t, yerr =[y_t-y_low_t,y_high_t-y_t], fmt='.c');\n",
    "\n",
    "\n",
    "plt.xlabel('Impact Parameter (kpc)')\n",
    "plt.ylabel('Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f200834",
   "metadata": {},
   "source": [
    "# More Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ffd834f",
   "metadata": {},
   "source": [
    "Diffusivity Coeff. vs. Stellar Mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9e887df9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Hzl5DRKbOkrptPlrUOg6ZBo8+47B204PBnESGJloIUlNTUVJSIkUWonqxpG6bllTUyPyIXhpycnJCaGgoPDw8MG7cOPTr149dSMkkWNLU3lyvgoxJtBBMnjwZkydPxi+//IItW7Zg+fLlGDduHKZNmwZXV1cpMhLpZClTe1tSUSPzI1oISktLsW/fPuzZswcKhQJLlixBdXU1QkND8dlnn0mRkeipLGVqb0spamR+RAvB+PHj8dprr2HDhg1o2bKl9vkLFy4YNBiRNbKUokbmRbQQHDhwoNY9gVu3bsHDwwPz5s0zaDAiIpKGaCFITEzE9u3bcf/+fVRWVqJt27bYt2+fFNksEgcMEZGpEe0+mpWVhaysLIwcORL79+/Hc889J0Uui3TixElMnx2GhbEbMX12GE6ePGnsSERPVFZWhoKCAo5jsBKiLQI3NzfI5XKoVCp4e3tz0rkGsrRRsGS5OMLZ+oi2CFq0aIGMjAw4OTkhISEBSqVSilwWhwOGyBxwhLN1Ei0EYWFh6N27N8LDw+Hh4YENGzZIkcviWNIoWLJc/MJinUQvDb311lv44osvAADBwcEGD2SpOGCIzAFHOFsn0ULQuHFjbNu2DT4+PrCxedCAeOmllwwezBJxwBCZOn5hsU6ihaBJkya4cOFCrQFkLAQNxwFDZOr4hcX6iBaC2NhYAMB3332H/v37GzwQERkfv7BYlzqvR5CSkmLIHEREZCR1LgR/XMSeiIgsQ50KQUVFBebOnYtbt24ZOg9ZGY5gJTI+0XsEGzduhFKpRGRkJObMmYNu3brhjTfekCIbWTiOYCUyDaItgsOHDyMyMhIA8MEHH+Dw4cMGD0WWjyNYiUyHaCGQyWRQq9UAgPv37/NeAekFR7ASmQ7RS0NBQUEYOXIkOnXqhMuXL+Mf//iHFLnIwnEEK5HpEC0EEyZMwMCBA3H16lV4eXmhadOmUuQiC8cRrESmQ2ch2Lx5M0JDQzF//vxaK5QBQEJCgt4CHDt2DLt370ZlZSVCQ0ORn5+PzMxMuLm5Ye7cuXBxcdHbsci0cAQrkWnQWQgGDBgA4MGlIUOqqKjAmjVrkJeXhyNHjiAvLw9r1qzBhQsXsGfPHkyZMsWgxyfj4gjW2riCHRmDzkLQpUsXAEDLli2RmZmJqqoq7WsvvPCC3gIMGDAA5eXlSEtLw8KFCxEQEIClS5eiRYsWsLW11dtxiEwdu9OSsYj2GgoNDcW9e/cgl8u1f/Tpzp07WL16NebMmQN3d3cUFRUhOjoavXr1QsuWLfV6LCJTZWrdaTnQz7qI3ixu2bIlZs+e3aCdnz59GvHx8UhLS4NGo0FUVBQuXrwIuVyO6OhoeHt7IzY2FiUlJUhISMCgQYPQuHFjREZGwtbWFitXrmzQcYnMzZO60974vTut1JeI2DKxPjJBZGDAF198gcLCQnTo0EH73OjRo0V3nJycjL1798LJyQnp6en4+uuvcfjwYcTFxSE3Nxdbt25FUlJSvQPn5OSgUaNG9d5OSpWVlXB0dDR2DFHmkhMwn6wNzalSqfBu7AY07z0GLk09oCy5haJjuxG9aB6cnZ0lyyl1jobmNEWmnrW8vBwBAQFPfE20RbB//360a9cO+fn5APBYDyJd2rRpg8TERISHhwN4cALv27cvAKB79+44d+5cnfbzJL6+vg3eVgp5eXkmnxEwn5yA+WR9lpyrIudi7aYUlP/enXZV5Fz07NlTzwkf0JWzoKAALs1awrNdZwCAm1sTlP/cAs2aNUPbtm0NkuVpzOX3Dph+1pycHJ2viRYCuVyOFStW1PugQ4YMwbVr17SPlUplra6gtra2qK6uhp2daAQiq6Cv7rTP0vOIA/2sk+hZuFWrVti6dSu6du2qbQ00ZIUyFxcXqFQq7WONRsMiQPQHz9qd9lmv73Ogn3USPRNXV1ejoKAABQUF2ucaUgj8/f2RmZmJwMBA5ObmolOnTvXeBxHp9mjPo4ff5tduSkFqYpd6nch79eqF92Na4/Lly2jXrh1atWplwNRkCuq0VGVNTQ0EQUBubi78/PwadKDBgwcjOzsbQUFBEAQBMTExDdoPET2ZvnoesdeQ9REtBOvWrYOXlxd+++03nD9/Hs2bN0dcXFyddu7p6Yn09HQAgI2NDbuDEhmQPq7vP2xVuAUMg529A6rvVzWoVUHmRbQQ5OTkICwsDMHBwUhLS8O0adOkyEVE9aSP6/vFxcUoLlXi/L92QuaogFBZhuecZUYZz0DSES0EGo0GZ86cgaenJ9RqNUpKSqTIRUQN8Kw9j+RyOfJ/uYQWgW/DxaMNlLeu4PL+TXqfUYBMi2ghGDVqFFatWoWYmBisW7cOU6dOlSIXETXQs/Q8UqvV6Ni1G+5VlOHe1YuQaarRwfd57eJUZJlEC8GUKVMQGBiIq1evYubMmVyPgEiHsrIyFBYWwtPT02wvo7i7u6OJkx3ad2kLubMb1Kq7KCk9w3EEFq5OI4vff/99tG/fHr/88gtmzZqFUaNGSZGNyGw87GlTdh9QfJZhtj1tHr3PoOE4AqshWgi2bduGXbt2wdnZGUqlEtOmTWMhIHrEo/33m9k6wKbGvHvacMEg61OnxesfTjbl4uICBwcHg4ci88Cpih94Uv99ze/9982VQqFA27ZtWQSshGiLoE2bNoiLi0PPnj3xww8/oE2bNlLkIhPHQUf/82j/fdg6cH4eMjuiLYKYmBh4eXnh6NGj8PLywqpVq6TIRSbM1BZRMbaH19VvZX+Jywc/x63sL3ldnczKU1sER44cQZ8+fTBlyhRcuHABt27dgr29vVTZyESZ0iIqpuLhdfXjx4/jxRdftNrPgcyTzhbB9u3bsXHjxlozhm7atAk7d+6UJBiZrlqXQgBeCvmdQqFA69atWQTI7OgsBLt378a2bdu0awh06dIFqamp2rmDyHo9eink539/wkshRGZO56UhR0fHx3oIOTs7G2W5OjI97GJIZDl0FgJ7e3uUlJTUGklcUlKCmpoaSYKR6XvWRVSIyDToLAShoaEICQnB6NGj4eXlhevXryMjIwNhYWFS5iMyG5YwxQRZJ533CHr27IkPPvgAZWVl+Pbbb6FUKrFx40b85S9/kTIfkVk4ceIkps8OQ/zHGZg+OwwnT540diSiOntq91EvLy/MmjVLqixEZsnSppgg6yM6oIyIns4Sp5gg/TL16VhEp5ggoqfjFBP0NOYwHYtoIVAqlUhOTkZRURFefvlldO7cGd7e3lJkIzILj07dXKoW4CqXcVwFAah92fDhOtKmeNlQ9NLQ4sWL4eXlhYKCAjRr1gxLliyRIhdZCVNvMtfVg3EV6xA2fQJSE9eZ3Dc+Mg5zuWwo2iK4e/cuxo8fj71798Lf3x+CIEiRyyDKyso4AMqEmEOTuT44xQT90aOXDR+2CEzxsmGd7hHk5+cDAG7cuAEbG/O8v2xpJx1zZy5NZqJn8ehlwxsmvOKbaCF49913sXjxYuTn52POnDlYvny5FLn0iicd08MZTMlamMN0LKKFoFOnTmY/4yhPOqbHXJrMRPpg6tOxiBaCjRs34vPPP4etra32uSNHjhg0lL7xpGN6zKXJTGQNRAtBZmYmMjMz4ejoKEUeg+BJxzSZQ5OZyFQYsrOLaCFwd3eHnZ35jzvjScc0mXqTmcgUGLqzi84z/Pz58yGTyXD79m2MGTMGHTt2hEwmAwAkJCToLYCUeNIhInMjRWcXnYUgKChILwcgIqKGk6Kzi85BAQEBAejevTs+/fRT9OjRA927d4efnx82btyolwMTEZE4KdYI19ki+PLLL7Flyxbcvn0bQ4cOBQDY2NggICBAbwcnIqKnk6Kzi85CMHHiREycOBEZGRkYP3683g5IRET1Y+jOLqLdgVgEiIiMz5CdXcxz4iAiItIbnYVgw4YNAICDBw9KFoaIiKSn89LQoUOH4OHhgbS0tMfmzp40aZLBgxERkTR0FoKYmBhkZ2dDrVajqKjIYAGOHTuG3bt3o7KyEqGhoVCr1di1axeUSiWmT5+Orl27GuzYRET0lELg5+cHPz8/9OnTB23atMGVK1fg6emJpk2b6jVARUUF1qxZg7y8PBw5cgTOzs7a9Q9atGih12MREdHjRG8WX7t2DZMmTcKWLVswadIk7NmzR68BBgwYgIqKCqSlpWHMmDF4/vnnkZKSghkzZuC7777T67GIiIzB1JdkFe0+um3bNuzatQvOzs5QKpWYNm0aRo0apbcAd+7cQXx8PObMmQN3d3dER0dj3bp1aNq0qbZlQJaLy4eSpTOH1RFFC4FMJoOzszMAwMXFBQ4ODnXe+enTpxEfH4+0tDRoNBpERUXh4sWLkMvliI6Ohre3N2JjY1FSUoKEhAQMGjQIw4cPR3h4OOzt7REeHt7wn4xMnjn8ByF6FuayOqJoIWjTpg3i4uLQs2dP/PDDD2jTpk2ddpycnIy9e/fCyckJwINuqGq1Gjt37kRubi7i4uKQlJSEtWvXPrbtoEGD6vljkLkxl/8g1DBs6T1gLqsjihaCmJgY7Ny5E0ePHkX79u2xYMGCOu24TZs2SExM1H6rz8nJQd++fQEA3bt3x7lz5xocOi8vr8HbSqGystLkMwLGzVlYWIiy+0AzWwfcvXsHsHVAqVrA8ePH0bp168fez89UvwyZ88zZs/h45x7AUQFUlmH6pFH405/+1KB9mcvnCTw5q0qlgvL2dVy7fBEuTT2gLLkFVfEN3L59GxUVFUZK+jjRQmBnZ4cpU6bUe8dDhgzBtWvXtI+VSiVcXFy0j21tbVFdXd2gRW98fX3rvY2U8vLyTD4jYNycnp6eUHyWAZuaKm2LwFUuw4svvvjEb0r8TPXLUDnLysqwbM37aD/0de3v9f/t/xLDhg1r0Ddgc/k8Ad1ZV0XOxdpNKSj/fcK4VZFz0bNnT8nz5eTk6HxNsqXHXFxcoFKptI81Go1FrHxGDcPlQy2TuVwKkZI5rI4oeib+47f20tJSuLq61vtA/v7+yMzMRGBgIHJzc9GpU6d674Msizn8B6H6eXTu/IctAn3PnW+OTH11RJ2FoKioCEqlEhEREVi7di0EQYBGo0FERAQyMjLqfaDBgwcjOzsbQUFBEAQBMTExzxScLIOp/weh+rHElp413PjWWQhOnz6Nbdu24b///S+WLl0K4MHCNC+99FKdd+7p6Yn09HTttitXrnzGuERk6iyppWctXZx1FoJBgwZh0KBB+O6779C/f38pMxGRmbOElp41dXHWWQg2b96M0NBQ7NmzB3v37q31WkJCgsGDEZHxWMPlEDHWdONbZyEYMGAAACAoKEiyMERkfNZyOUSMNd341lkIunTpAgBo2bIlMjMzUVVVpX3thRdeMHwyIpKcNV0OEWOJN751Ee0+GhoaildffbVBXUaJyLxY0+WQurCkG99PI1oIWrZsidmzZ0uRhYiMzJouh9SVJdz4FiNaCF555RXEx8ejQ4cO2udGjx5tyExEZCTWdDmE/ke0EOzfvx/t2rXTrg0gk8kMHoqIjMdaLofQ/4gWArlcjhUrVkiRhYhMhDVcDqH/ES0ErVq1wtatW9G1a1dta6A+o4uJiMi01WnSuYKCAhQUFGifYyEgIrIcOgvBw1lHeVmIiMiy6SwEERERSEhIwNChQ7WXhARBgEwmw6FDhyQLSEREhqWzEDycT+jw4cO1nn/0EhEREZk/m/pusHDhQkPkICIiI6l3IRAEwRA5iIjISOpdCDigjIjIsui8RzB//vzHTvqCIODq1asGD0VERNLRWQh0rUPA9QmIiCyLzkLANQeIiKxDve8REBGRZREtBJcvX5YiBxERGYloIViyZIkUOYiIyEhEJ51r1KgRYmJi4OPjAxubB3Vj0qRJBg9GRETSEC0EPXr0APBgLVMiIrI8ooVg1qxZOHr0KK5duwY/Pz/4+PhIkYuIiCQiWgjWr1+PGzduID8/H/b29vjwww+xfv16KbIREZEERG8W5+TkYO3atWjUqBHGjBmDa9euSZGLiIgkIloIampqUFVVBZlMhpqaGu0NYyIisgyil4amTZuGsWPHoqSkBBMmTMDf//53KXIRET2zsrIyFBcXw93dHQqFwmj7MHWihSAgIADbt2/Hr7/+Ck9PTzRt2lSKXEREz+TEiZNYtzkFgoMLZFVKhL8dgl69ekm+D3MgWggWLVoEtVqNV155BU2aNGEhICKTV1ZWhnWbU+DRZxxc3VugtPgG1m5KQWpilzp/q9fHPsyFaCFISUmBUqlEVlYWwsLCUFlZiX/+858SRCMiapji4mIIDi5wdW8BAHB1b4EbcmcUFxfX+SSuj32YC9FCcPDgQRw9ehSnT59Gq1at8NJLL0mRi4iowdzd3SGrUqK0+Ib227yNWgV3d3dJ92EuRAtBfHw8HBwc8MYbb6Bv375wdXWVIhcRUYMpFAqEvx2CtZtScEPuDBu1CuFvh9Trm7w+9mEuRAvBv//9b1y7dg1HjhzBrFmzUFlZifT0dCmyERE1WK9evZCa2OWZevzoYx/mQLQQnD9/Ht999x2OHj0KR0dHDBs2TIpcRETPTKFQPPPJWx/7MHWihWDz5s149dVXkZSUZPEfBhGRIZj6WATRQhAXF4fNmzdj3759aNu2LUJDQ+Hm5qa3AMeOHcPu3btRWVmJ0NBQ/Oc//8GFCxdQUFCAkSNHYsqUKXo7FhGR1MxhLEKdFqZp1aoV5s2bh9atWyMyMlKvASoqKrBmzRq89dZbOHLkCF5//XWsXLkSHTt2xOTJk/V6LCIiKT06FqHjkGnw6DMOazeloKyszNjRahEtBHfu3EFwcDB8fX0xbdo0lJaW6jXAgAEDUFFRgbS0NIwZMwYAsG/fPgwePJjzGhGRWXvSWATN72MRTInombaqqgpFRUUAgNu3b0Oj0eg1wJ07d7B69WrMmTNH2z/3hx9+QN++ffV6HCIiqT06FgGAyY5FEL1H8M477yAoKAgKhQJKpRKrVq2q885Pnz6N+Ph4pKWlQaPRICoqChcvXoRcLkd0dDS8vb0RGxuLkpISJCQkYNCgQRg6dChqamogk8me6QcjIjI2cxmLIBMEQajLG0tKStC0aVP8+uuv8Pb2Fn1/cnIy9u7dCycnJ6Snp+Prr7/G4cOHERcXh9zcXGzduhVJSUn1DpyTk4NGjRrVezspVVZWwtHR0dgxRJlLTsB8sjKnfplLTuDpWVUqFe7evQs3Nzc4OztLnOyB8vJyBAQEPPE10RbBQw8nm1uwYAEyMjJE39+mTRskJiYiPDwcwIMT+MPLPd27d8e5c+fqeujH+Pr6NnhbKeTl5Zl8RsB8cgLmk5U59ctccgKmnzUnJ0fna/W+G1vHBgSGDBkCO7v/1RmlUgkXFxftY1tbW1RXV9f38EREpGf1LgQNvXbv4uIClUqlfazRaGoVCiIiMg6dZ+L58+c/dtIXBAFXr15t0IH8/f2RmZmJwMBA5ObmolOnTg3aDxER6ZfOQhAUFFSv58UMHjwY2dnZCAoKgiAIiImJadB+iIhIv3QWghdeeOGZd+7p6amdqdTGxgYrV6585n0SEZF+1bn7qKl42p1vIiLSTVf3UbMrBEREpF+czIeIyMqxEBARWTl25K8ntVqNRYsW4erVq3BxccGyZcvQtm1bAEBRURHmz5+vfW9eXh4WLFiAyZMnY/To0dr5RTw9PREbG2uwjI/O8fTrr78iMjISMpkMHTt2xPLly2vN6qprDiix7aTOef/+fSxevBiFhYVQq9WYOXMmBg4ciPPnz+Ott97S/g4mT56MwMBAo+UE8MTftRSfZ32z7tq1C7t37wbwYHLJvLw8ZGdn4+rVq5J+pgDwzTff4N///jcSEhIee296ejp27NgBOzs7zJw5E6+88goqKysRFhaG4uJiODs7Y82aNdrZD4yV85NPPsG+ffsAAP3798esWbMgCAL69eun/Sy7d++OBQsW6D3nMxOoXtLS0oR3331XEARByM/PF6ZPn/7E9506dUoIDg4WqqurhcrKSmHUqFGS5Pvwww+FESNGCBMmTBAEQRDefPNN4T//+Y8gCIKwdOlS4euvv671/gMHDggRERGCIAjCjz/+KLz11lt12k7qnBkZGUJ0dLQgCIJQUlIi9O/fXxAEQUhPTxdSUlL0mu1Zcur6XRv682xI1kdFRUUJO3bsEARB+s901apVwpAhQ4S5c+c+9t5bt24JI0aMEKqqqoTS0lLt31NTU4UPPvhAEARB+Oqrr4RVq1YZNeeVK1eEMWPGCNXV1UJNTY0wadIkIS8vTygoKBDefPNNvWfTN14aqqdLly6hX79+AIB27dohPz//sfcIgoBVq1YhKioKtra2uHDhAioqKjB9+nRMnToVubm5Bsv3cI6nh86fP6/tCtyvXz8cPXq01vt1zQEltp3UOYcOHYp33nlH+9jW1hYAcO7cOXz77beYMmUKFi9eDKVSadScun7Xhv48G5L1obNnz+LSpUuYNGkSAOk/U39/f0RFRT3xvWfOnEGPHj0gl8uhUCjQpk0bXLhwoda/2379+uHYsWN6zVjfnC1atMBHH30EW1tb2NjYoLq6Gg4ODjh//jxu3ryJ4OBgzJgxA5cvX9Z7Tn1gIagnX19fZGZmQhAE5Obm4ubNm6ipqan1nsOHD6Njx45o164dAMDR0REhISFISUnBihUrsHDhQoPNs/THOZ4EQdCOEHd2dn5sZSRdc0CJbSd1TmdnZ7i4uECpVGLOnDmYO3cuAMDPzw/h4eH4/PPP4eXlhU2bNhk1p67ftaE/z4ZkfWjr1q14++23tY+l/kwDAwN1Tl2jVCprTdns7OwMpVJZ63mpPs+n5bS3t0fTpk0hCALWrFmDrl27wsfHB82bN8cbb7yBtLQ0vPnmmwgLC9N7Tn1gIaincePGwcXFBVOnTkVmZiaef/557bfTh/bu3YuJEydqH/v4+OC1116DTCaDj48P3NzctIv9GNqj14RVKhVcXV1rva5rDiix7aTOCQDXr1/H1KlTMWrUKIwcORLAgxHr3bp10/79p59+MmpOXb9rqT/PumQFgNLSUly+fBn/93//p31O6s/0af7471OlUkGhUNR6XqrPU0xVVRUWLlwIlUqF5cuXAwC6deuGgQMHAgB69uyJmzdv1nniTimxENTT2bNnERAQgLS0NAwaNAheXl6Pvef8+fPw9/fXPs7IyEBcXBwA4ObNm1AqlWjevLkkebt27Yrjx48DALKystCzZ89ar/v7+yMrKwsAas0BJbad1Dlv376N6dOnIywsDOPHj9c+HxISgjNnzgAAjh07hueff96oOXX9rqX+POuSFQBOnjyJv/zlL7Wek/ozfRo/Pz/k5OSgqqoKZWVlyM/PR6dOneDv74/vvvsOwIOfTddAKakIgoDQ0FB07twZK1eu1H453LhxI7Zt2wbgwWXDVq1ameSiWywE9eTt7Y0vvvgCkyZNwvvvv4/IyEj861//ws6dOwE8WMDH2dm51i97/PjxKCsrw+TJkzFv3jzExMRINvNqREQEEhMTMWnSJNy/fx9DhgwBAISHh+O3337D4MGDIZfLERQUhNjYWCxatOip2xkr55YtW1BaWorNmzcjODgYwcHBqKysRFRUFGJiYhAcHIxTp04hNDTUqDl1/a6l/jzrkhUA/vvf/8LT07PWdlJ/pk/y8ccf49ChQ2jevDmCg4Px17/+FdOmTcO8efPg4OCAyZMn45dffsHkyZOxc+dOzJo1S/KMj+Y8ePAgTpw4ge+//1777/PHH3/EG2+8gZMnT+Jvf/sbYmNjDdpb8FlwZDERkZVji4CIyMqxEBARWTkWAiIiK8dCQERk5VgIiIisHAsBmbzjx49j3rx5Bj9OeHg4Jk6cWGvakMrKSkRGRmL69OkICQnBO++8gzt37gB4MAHZzZs3de4vMjISWVlZ2LVrF+Lj4+ud5/jx4+jcuTP2799f6/mRI0ciMjKy3vsj0oWFgOh3R44cQXp6Otq3b6997ssvv0SzZs2QmpqKlJQU9OjRQzvlwqeffqr3eXj+qF27dvjqq6+0jy9evIiKigqDHpOsD6ehJrOVnZ2N9957Dw4ODnBzc0NMTAwUCgVWrFiBc+fOoVmzZigsLERSUlKtQVNP2m79+vUoLS3FzJkzkZSUpH1v69atkZGRAX9/f7zwwgsIDg6GIAj49ttvkZeXh4iICGzfvh07d+7EV199BZlMhsDAQEydOvWJmRMSEnDu3DmoVCq0b98esbGxSExMxI8//ojy8nKsXr26ViHq0qULCgoKUFpaCldXV+zduxcjR47E9evXAQCfffYZvv76a1RXV0OhUCAxMRGFhYVYtGgR7OzsYGtri7Vr18Le3h5z586FIAi4f/8+VqxYgc6dOxvoN0PmhoWAzJIgCFi6dCm++OILPPfcc9i2bRuSkpIQEBCAu3fvIiMjAyUlJXj11VfrtF1UVBS++eabWkUAAF5++WWo1WpkZGRg0aJF6NSpE9599128/PLL8PX1RVRUFK5cuYL9+/dj+/btkMlkeP311/HSSy89llmpVMLV1RUff/wxNBoNhg8frr201K5dO7z77rtP/FkHDx6Mb775BmPHjsWZM2cwY8YMXL9+HRqNBnfv3sUnn3wCGxsbhISE4OzZs7hw4QKef/55REZG4ocffsC9e/fw22+/QaFQICEhAZcuXTJ4S4bMCwsBmaU7d+7AxcUFzz33HACgV69eWL9+PZo0aYLu3bsDAJo2baqdAVZsO11+/PFH9O7dG6+++ipqamqwZ88eLFq0CLt27dK+5+eff8Zvv/2G119/HQBw7949XLly5bF9OTg4oKSkBPPnz0ejRo1QXl6O+/fvA3gwWZ0uI0eORFRUFLy8vGrNF2RjYwN7e3vt/m7cuIHq6mqMHz8eycnJ+Mc//gGFQoF58+ahX79+KCgoQGhoqHaBF6KHeI+AzFKTJk2gVCpx69YtAMCJEyfQtm1bdOzYUbsGwL1791BQUFCn7XTZt28fPvroIwAPpuju3Lkz5HI5AEAmk0EQBLRr1w4dOnTAp59+irS0NIwdO1Y7ed+jsrKycP36daxfvx7z589HZWWldibKp61W5uXlhfLycqSlpeG1117TPn/hwgUcPHgQ7733HpYuXQqNRgNBEHDo0CEEBARg27ZtGDp0KD766CMcP34cHh4eSE1NxcyZM59a/Mj6sEVAZiE7Oxtjx47VPk5ISEB0dDRmz54NmUyGxo0bIzY2Fk2aNEFWVhaCgoLQrFkzODo6wt7eXrudTCZ74na6zJ07F6tWrcKoUaPg5OSERo0aYfXq1QCAHj16IDw8HKmpqejduzcmT54MtVoNPz8/bYvjUX5+fti8eTMmTpwIuVwOLy8vbUESExgYiD179sDHxwdXr14F8GACRCcnJ4wdOxZyuRzNmzfHrVu30L17d4SFhSExMRE2NjZYtGgRWrVqhXnz5mHbtm2wsbGptf4AESedI4uSn5+PCxcuYPjw4bhz5w5GjBiBzMxM7bd4InocCwFZlPLycixYsADFxcWoqanB3/72N4wZM8bYsYhMGgsBEZGV481iIiIrx0JARGTlWAiIiKwcCwERkZVjISAisnIsBEREVu7/Axc/jMDDtyMVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = data['R']\n",
    "N_H = data['N_H']\n",
    "M_star_d = data['log M_*']\n",
    "galaxy_age = data['Age Gyr']\n",
    "sfr = sfr_atm(galaxy_age,M_star_d)\n",
    "velocity_vals = np.array([134.05430348763306, 510.21258348149706, 183.43068548075482, 618.451524921208, 110.04104426428928, 513.2321384813996, 234.47085431245546, 230.4213140053146, 102.33555196284, 435.22941800909996, 119.21853483839298, 154.43032711839197, 149.4959744149872, 181.09407352030155, 159.3110992310241, 330.3523655693238, 197.2776795711477, 227.49075690415384, 185.00543166922802, 146.1938044781218, 124.30436763865931, 107.24392367586164, 236.78327050423655, 150.3368062665032, 265.06291167573903, 189.91927258930735, 163.88186723392656, 346.2770941360653, 116.13182974316351, 524.9985013624732, 180.67373358423535, 129.57960283661137, 241.937639758548])\n",
    "\n",
    "y = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr)\n",
    "plt.yscale('log')\n",
    "plt.scatter(M_star_d, y, s=20, alpha=0.6, edgecolor='black', linewidth=1)\n",
    "plt.xlabel('Log of Stellar Mass')\n",
    "plt.ylabel('Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4125d131",
   "metadata": {},
   "source": [
    "Diffusivity Coeff. vs. Redshift"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d7005090",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+HZt33B0E+CAsVyWiVqKJYM+ePaipqZEiFjKBqRd0lqsSUSvRR0Oenp6Ii4tD9+7dMX36dIwcOZIlpDbE1HUFWK5KRK1EE8ELL7yAF154AV9//TV2796NdevWYfr06Zg7dy58fHykiJEeoCMXdJarEhFgQCKoq6vD0aNHcfjwYSgUCqxevRrNzc2Ii4vDvn37pIiRRHTkgs5pqIlINBHMmDEDzz33HLZu3YqAgADd65cvX7ZoYGQcXtCJyFSiieD48eP39AncunUL3bt3x+LFiy0aGBERSUM0EWzbtg379+/HnTt30NjYiD59+uDo0aNSxEbUIRw1TWQY0fLR06dP4/Tp05g0aRKOHTuGhx9+WIq4iDrkk08KMecPixG3ZjPm/GExCgsLrR0Skc0STQS+vr6Qy+VQq9UIDg7mpHNk85RKJVZtTMc38hDc8g/HN/IQrNyYLjrIjshZiSaCHj16IDc3F56ensjIyIBKpZIiLiKTXb9+HVcratGlfwS6BA1El/4RuPr9bVy/ft3aoRHZJNE+guXLl0OlUmHChAk4dOgQtm7dKkVcRB0iNKnR0qBCJ/fOaGlQQduktnZIRDZLNBG88soreP/99wEAsbGxFg+IqKOCg4PRP+hh3Pj4fXTy8ceduioMCOqB4OBga4dGZJNEE0GXLl2wd+9ehISEwMXl7pOkJ5980uKBEZlKoVAgbd0KbPzzLjRqtfBQ+GL1oj+wcohID9FE8NBDD+Hy5cv3DCBjIiBbN2TIEGTv5vQZRIYQTQSpqakAgI8++ghPPfWUxQMiMheOtiYyjMHrEWRlZVkyDiIishKDE8HPF7EnIiLHYFAiaGhowKJFi3Dr1i1Lx0Nkt5RKJW7evMmBa2R3RPsItm/fDpVKhRUrVmDhwoV47LHH8Lvf/U6K2IjsRuu60co7gGJfrkHrRhPZCtE7glOnTmHFihUAgDfffBOnTp2yeFBE9qTtutEho180eN1oIlshmghkMhk0Gg0A4M6dO+wrIPoZU9eNJrIVoo+GYmJiMGnSJISGhuKbb77Bb3/7WyniIrIbbdeNhqu7wetGE9kK0UQwc+ZMjB49Gjdu3ECvXr3QtWtXKeIishtt142u0wjwkcsMXjeayBboTQQ7d+5EXFwclixZcs8KZQCQkZFhtgDOnTuHQ4cOobGxEXFxcbh27Rry8/Ph6+uLRYsWwdvb22zHIrKU1nWjz58/j6FDhzIJkF3RmwhGjRoF4O6jIUtqaGjApk2bUFpaijNnzqC0tBSbNm3C5cuXcfjwYcyePdtsx+KKVWRJCoUCgYGBPLfI7uhNBIMGDQIABAQEID8/H01NTbr3nnjiCbMFMGrUKNTX1yM7OxvLli1DZGQk1qxZgx49esDV1dVsx2kt7xPcvSFrUrG8j4joJ6JVQ3Fxcfjxxx8hl8t1/8zp9u3b2LhxIxYuXAg/Pz9UVlYiOTkZQ4YMQUBAgFmO0ba8b8D4uSzvszNKpRJlZWX8/0VkIaKdxQEBAXjttddM2nlJSQnS09ORnZ0NrVaLxMREXLlyBXK5HMnJyQgODkZqaipqamqQkZGBMWPGoEuXLlixYgVcXV2RlJRk0nF/7n7lfRU/lffxNt628U6OyPJEE8HTTz+N9PR09O/fX/falClTRHecmZmJI0eOwNPTEwBw4sQJaDQaHDx4EMXFxUhLS8OuXbuwefPmdtsOGzbsgfsuLS0VPX5barUaqqrvUf7NFXh37Q5VzS2oqytQVVVl0BrMjY2NRh/TGVi6XdRqNdZu+jO6DZuq+/+2Ju3PSF65GF5eXhY7bkfwXGmPbdKerbWJaCI4duwY+vbti2vXrgFAuwoifXr37o1t27YhPj4eAFBUVIQRI0YAAMLDw3Hx4kVTY0ZYWJjR22xYsQibd2ShXu4FF40aG1YsQlRUlEHblpaWmnRMR2fpdikrK4O3fwCC+g4EAPj6PoT6r3rA398fffr0sdhxO4LnSntsk/as0SZFRUV63xNNBHK5HOvXrzf6oOPHj0d5ebnuZ5VKdU8pqKurK5qbm+HmJhqCWbSW97FqyH60Hajl49eDA7XaYAUcmZPoVbhnz55466238Mgjj+juBkxZoczb2xtq9X8XENdqtZIlgVZcqMS+tB2oVfHTnRwHarHfhMxP9Erc3NyMsrIylJWV6V4zJRFEREQgPz8f0dHRKC4uRmhoqNH7IPtmyrdY3sndq20FXOtd0uYdWdizbZDTtw2ZzqClKltaWiAIAoqLizF48GCTDjR27FgUFBQgJiYGgiAgJSXFpP2QferIt1jeyf0XK+DIEkQTwZYtW9CrVy989913uHTpErp164a0tDSDdh4UFIScnBwAgIuLi9nKQcm+OMu32NaFaYKCgiz2udhvQpYgOqCsqKgIMTEx+Pzzz5GVlYXvv/9eirjIgTjDNM2ffFKIea8tR/o7uZj32nIUFhZa5Dit/Sa3Cv6Gr/75V9wq+Bv7TajDRO8ItFotLly4gKCgIGg0GtTU1EgRFzkQR/8W2/aOx9/VHS4tTRa942G/CZmbaCKYPHkyNmzYgJSUFGzZsgVz5syRIi5yII5e/dP2jqe29rYkz+3Zb0LmJJoIZs+ejejoaNy4cQN/+MMfuB4BmcSRv8VyYRrbwfEVpjFoZPEbb7yBfv364euvv8aCBQswefJkKWIjB+Oo32K5MI1t4PgK04kmgr179yIvLw9eXl5QqVSYO3cuEwHRz3BhGutylso0SzFo8frWCb68vb3h7u5u8aCI2rKXaai5MI31OENlmiWJ3hH07t0baWlpiIqKwqefforevXtLERcRAN7uk2EcvTLN0kTvCFJSUtCrVy+cPXsWvXr1woYNG6SIi4gLCpHBOL6iYx54R3DmzBkMHz4cs2fPxuXLl3Hr1i106tRJqtjIyXE6BTKGI1emWZreO4L9+/dj+/bt98wYumPHDhw8eFCSwIjuKcsEeLtPohQKBfr06cMkYCS9ieDQoUPYu3evbg2BQYMGYc+ePbq5g4gsjbf7RNLQ+2jIw8OjXYWQl5eXzS4RSI6Jt/tElqc3EXTq1Ak1NTX3jCSuqalBS0uLJIERtXLUgWhEtkJvIoiLi8P8+fMxZcoU9OrVC99//z1yc3OxfPlyKeMjC+OQfCLSmwiioqLw5ptv4vDhw/jwww8RGBiI7du3IzAwUMr4yIJYo09EgEj5aK9evbBgwQKpYiEJcUg+EbUSHVBGjolD8s2vdYUyDngjeyM6xQQ5Jg7JN6/Wx2zKO4BiXy4fs5FdEU0EKpUKmZmZqKysxK9//WsMHDgQwcHBUsRGFuToi8VISeoVyojMTTQRrFq1CiNHjkRhYSH8/f2xevVq7Nu3T4rYyMKkrtF31Aola6xQRmROoomgtrYWM2bMwJEjRxAREQFBEKSIiyQiVY2+I1cocYUyMkZrX1JQUJDNfFEwqI/g2rVrAICKigq4uLB/mYzj6BVKXKGMDGWrfUmiieBPf/oTVq1ahWvXrmHhwoVYt26dFHGRA3GGWUS5QhmJseW+JNFEEBoayhlHqUOcpUKJK5TRg9hyX5JoIti+fTvee+89uLq66l47c+aMRYMix8IKJSLb7ksSTQT5+fnIz8+Hh4eHFPGQg+Isovo5ajUV3cuW+5JEE4Gfnx/c3DjujDqOs4i258jVVNSerfYl6b3CL1myBDKZDFVVVZg6dSoGDBgAmUwGAMjIyJAsQCJH5ejVVHR/ttiXpDcRxMTESBkHkdNxhmoqsg96BwVERkYiPDwc7777Lh5//HGEh4dj8ODB2L59u5TxETksrslMtkLvHcHf/vY37N69G1VVVZgwYQIAwMXFBZGRkZIFR+TIWE1FtkJvInj++efx/PPPIzc3FzNmzJAyJiKnwWoqsgWi5UBMAkSWxWoqsjZOHERE5OT0JoKtW7cCAE6cOCFZMEREJD29j4ZOnjyJ7t27Izs7u93yhbNmzbJ4YEREJA29iSAlJQUFBQXQaDSorKy0WADnzp3DoUOH0NjYiLi4OGg0GuTl5UGlUmHevHl45JFHLHZsIiJ6QCIYPHgwBg8ejOHDh6N379749ttvERQUhK5du5o1gIaGBmzatAmlpaU4c+YMvLy8dOsf9OjRw6zHIiKi9kQ7i8vLyzFr1izs3r0bs2bNwuHDh80awKhRo9DQ0IDs7GxMnToVjz76KLKysvDyyy/jo48+MuuxiMg+KJVKlJWVQalUWjsUpyBaPrp3717k5eXBy8sLKpUKc+fOxeTJk80WwO3bt5Geno6FCxfCz88PycnJ2LJlC7p27aq7MyAi58GJ+O7PkrPUiiYCmUwGLy8vAIC3tzfc3d0N3nlJSQnS09ORnZ0NrVaLxMREXLlyBXK5HMnJyQgODkZqaipqamqQkZGBMWPG4JlnnkF8fDw6deqE+Ph40z8ZEdkdTsR3f5ZOjqKJoHfv3khLS0NUVBQ+/fRT9O7d26AdZ2Zm4siRI/D09ARwtwxVo9Hg4MGDKC4uRlpaGnbt2oXNmze323bMmDFGfgyi9jjPv/3hRHztSZEcRRNBSkoKDh48iLNnz6Jfv35YunSpQTvu3bs3tm3bpvtWX1RUhBEjRgAAwsPDcfHiRZODLi0tNXlbUzQ2Nkp+THtgy+1y4Ysv8M7Bw4CHAmhUYt6syfjFL35h8ePacptYizFtolaroar6HuXfXIF31+5Q1dyCuroCVVVVaGhosHCk0jGmTW7evAnlHcDf1R21tbfvrm6mEXD+/HkEBgaaJR7RRODm5obZs2cbvePx48ejvLxc97NKpYK3t7fuZ1dXVzQ3N5u06E1YWJjR23REaWmp5Me0B7baLkqlEms3vYF+E17SfYP6f8f+hokTJ1r8W6Wttok1GdsmG1YswuYdWaj/aSK+DSsWISoqyoIRSs+YNgkKCoJiXy5cWpp057OPXGb0wjZFRUV635Ns6TFvb2+o1Wrdz1qtliufkUXw8YJ940R895JillrRK/HPv7XX1dXBx8fH6ANFREQgPz8f0dHRKC4uRmhoqNH7IDJE23n+W79BcZ5/+8KJ+O5l6eSoNxFUVlZCpVIhISEBmzdvhiAI0Gq1SEhIQG5urtEHGjt2LAoKChATEwNBEJCSktKhwIn06eg3KHYyky2yZHLUmwhKSkqwd+9e/N///R/WrFkD4O7CNE8++aTBOw8KCkJOTo5u26SkpA6GS2QYU79BsYadnJHeRDBmzBiMGTMGH330EZ566ikpYyIyC2O/QbGGnZyV3kSwc+dOxMXF4fDhwzhy5Mg972VkZFg8MFuhVCpx8+bNuz33vBg4NHYyk7PSmwhGjRoFAIiJiZEsGFvT+phAeQdQ7MvlYwIHx05mclZ6E8GgQYMAAAEBAcjPz0dTU5PuvSeeeMLykVlZ28cE/q7ucGlp4mMCB8fF5MlZiZaPxsXFYdy4cSaVjNqzto8Jamtv8zGBk2ANOzkj0UQQEBCA1157TYpYbErbxwRwdedjAifCGnZyNqKJ4Omnn0Z6ejr69++ve23KlCmWjMkmtH1MUKcR4COX8TEBETkk0URw7Ngx9O3bV7c2gEwms3hQtqL1McH58+eNnteDiMheiCYCuVyO9evXSxGLTVIoFAgMDGQSICKHJZoIevbsibfeeguPPPKI7m7AmNHFRERk2wyadK6srAxlZWW615gIiIgch95E0DrrqDM/FiIicgZ6E0FCQgIyMjIwYcIE3SMhQRAgk8lw8uRJyQIkIiLL0psIWucTOnXq1D2vt31ERERE9s/F2A2WLVtmiTiIiMhKjE4EgiBYIg4iIrISoxOBMw0oIyJyBnr7CJYsWdLuoi8IAm7cuGHxoIiISDp6E4G+dQiceX0CIiJHpDcROMOaA0REZEIfARERORbRRPDNN99IEQcREVmJaCJYvXq1FHEQEZGViE4617lzZ6SkpCAkJAQuLnfzxqxZsyweGBERSUM0ETz++OMA7q7hS0REjkc0ESxYsABnz55FeXk5Bg8ejJCQECniIiIiiYgmgtdffx0VFRW4du0aOnXqhLfffhuvv/66FLEREZEERDuLi4qKsHnzZnTu3BlTp05FeXm5FHEREZFERBNBS0sLmpqaIJPJ0NLSouswJiIixyB6VZ87dy6mTZuGr7/+GjNnzsTs2bOliItsnFKpxM2bN6FUKo3apqyszKhtiMjyRPsIIiMjsX//fly/fh1BQUHo2rWrFHGRDfvkk0Js2ZkF5R1AsS8X8a/Ox5AhQwzaRnD3hqxJZdA2RCQN0USwcuVKaDQaPP3003jooYeYCJycUqnElp1Z6D58Ovxd3eHS0oTNO7KwZ9sgKBQK0W18/HqgrrpCdBsiko7oo6GsrCzs2rULPXr0wPLlyzFlyhQJwiJbVV1dDcHdGz5+PQAAPn49oJV7PXCciSnbEJF0RO8ITpw4gbNnz6KkpAQ9e/bEk08+KUVcZKP8/Pwga1KhrroCcHVHXXUFXDRq+Pn5GbRN6x2B2DZEJB3RRJCeng53d3f87ne/w4gRI+Dj4yNFXGSjFAoF4l+dj807slCnEeAjlyH+1fkPfMTTdpsKuRdcNGrRbYhIOqKJ4J///CfKy8tx5swZLFiwAI2NjcjJyZEiNrJRQ4YMwZ5tg3D+/HkMHTrUoAt66zbV1dXw8/NjEiCyIaKJ4NKlS/joo49w9uxZeHh4YOLEiVLERTZOoVAgMDDQqAu6QqFgAiCyQaKJYOfOnRg3bhx27drFP2KiB2gdWxEUFMS/FbIrookgLS0NO3fuxNGjR9GnTx/ExcXB19fXbAGcO3cOhw4dQmNjI+Li4vCf//wHly9fRllZGSZNmsQBbGQXTBlbQWQrDFqYpmfPnli8eDECAwOxYsUKswbQ0NCATZs24ZVXXsGZM2fw0ksvISkpCQMGDMALL7xg1mMRWULbcRIho19E9+HTsXlHFkdQk90QTQS3b99GbGwswsLCMHfuXNTV1Zk1gFGjRqGhoQHZ2dmYOnUqAODo0aMYO3Ys5zUiu8BxEmTvRK+0TU1NqKysBABUVVVBq9WaNYDbt29j48aNWLhwoa6u/NNPP8WIESPMehwiS7lnbAXAcRJkd0T7CP74xz8iJiYGCoUCKpUKGzZsMHjnJSUlSE9PR3Z2NrRaLRITE3HlyhXI5XIkJycjODgYqampqKmpQUZGBsaMGYMJEyagpaUFMpmsQx+MSCqmjK0gsiUyQRAEQ36xpqYGXbt2xfXr1xEcHCz6+5mZmThy5Ag8PT2Rk5ODf/3rXzh16hTS0tJQXFyMt956C7t27TI64KKiInTu3Nno7TqisbERHh4ekh7THrBd7qVWq/HDDz/g4YcfhpeXl7XDsRk8T9qzRpvU19cjMjLyvu+J3hG0ap1sbunSpcjNzRX9/d69e2Pbtm2Ij48HcPcC3vq4Jzw8HBcvXjT00O2EhYWZvK0pSktLJT+mPWC7tMc2aY9t0p412qSoqEjve0b3xhp4A4Hx48fDze2/eUalUsHb21v3s6urK5qbm409PBERmZnRicDUZ/fe3t5Qq9W6n7Va7T2JgoiIrEPvlXjJkiXtLvqCIODGjRsmHSgiIgL5+fmIjo5GcXExQkNDTdoPERGZl95EEBMTY9TrYsaOHYuCggLExMRAEASkpKSYtB8iIjIvvYngiSee6PDOg4KCdDOVuri4ICkpqcP7JCIi8zK4fNRWPKjnm4iI9NNXPmp3iYCIiMyLk/kQETk5JgIiIifn9IX8+uZAaquhoQG/+c1vsHHjRvTr1w8AMGXKFN1cMkFBQUhNTZU8dksRa5N//OMf2Lt3L1xdXREaGorExEQAEG1He2ZKm7i4uDj0eQKIt8vx48fx9ttvQyaTYdasWZg5c6ZBf3P2zJQ2Aax8TRGc3PHjx4WEhARBEATh888/F1555ZV73r9w4YIwdepU4X/+53+Eq1evCoIgCI2NjcLkyZOlDlUyD2qThoYGYfTo0UJ9fb0gCIKwePFi4cSJE6LtaO9MaRNHP08E4cHt0tzcLIwdO1aoq6sTmpubhXHjxgnV1dVOfa7oaxNrnytO/2hIbA4kjUaDHTt2oG/fvrrXLl++jIaGBsybNw9z5sxBcXGxlCFb3IPaRC6X48CBA/D09AQANDc3w93d3axzSdkiU9rE0c8T4MHt4urqimPHjkGhUKC2thYA4OXl5dTnir42sfa54vSJQGwOpMjISAQEBNyzjYeHB+bPn4+srCysX78ey5Ytc6h5kx7UJi4uLvD39wcAZGdno76+HsOHD3f4uaRMaRNHP08A8b8fNzc3/Otf/8LkyZMRFRUFNzc3pz5XgPu3ibXPFadPBKbMgRQSEoLnnnsOMpkMISEh8PX11S3e4wjE2kSr1WLTpk0oKCjAtm3bIJPJHH4uKVPaxNHPE8Cwv59x48bh9OnTuHPnDj744AOnP1eA9m1i7XPF6RNBREQETp8+DQAGz4GUm5uLtLQ0AMAPP/wAlUqFbt26WTROKYm1ydq1a9HU1ISdO3fqHoeY0o72xJQ2cfTzBHhwu6hUKvzv//4vNBoNXFxc4OnpCRcXF6c+V/S1ibXPFacfUNbaw//VV1/p5kD68ssvUV9fj1mzZul+LzY2FomJiejXrx80Gg1WrlyJ7777DjKZDMuWLUNERIQVP4V5PahNHnvsMUyfPh1RUVG6SQnnzJmD0aNHt9umtcLKEZjSJk899ZRDnyeA+N/PwYMHkZubCzc3NwwcOBBr1qyBTCZz2nNFX5u0tLRY9Vxx+kRAROTsnP7REBGRs2MiICJyckwEREROjomAiMjJMREQETk5JgKinzl//jyGDRuG2NhYxMbGYtq0aVi4cCE0Go3B+1ixYoWulrxVZWWlboK+EydO4Nlnn8W7776Lf//73/jhhx/M+RGIjMJEQHQfv/rVr5CdnY3s7Gzk5eWhU6dOOHXqVIf22a1bN10iyM/Px5IlSzBnzhy8++67UKlUZoiayDSOM66byEI0Gg1u3bqFLl26ICMjA4WFhRAEAS+99BImTpyI9957Dx988IFu1GxCQgIA4ODBg/jLX/4ClUqFxMREdO3aFUuWLMHvf/97fPjhh7hw4QKuXLmC0tJSJCQkYP/+/ZDL5Vb+tOSMmAiI7uM///kPYmNjUV1dDRcXFzz//PPQaDQoLy/HgQMH0NTUhOeffx7Dhw9HXl4e1qxZg/DwcOzfv183Wdijjz6KuLg45OXlIS8vD7/97W8BAKNHj8a///1vREdHY+TIkTh79iwSExOZBMhqmAiI7uNXv/oVtm7ditu3b2PevHkICgrCV199hUuXLiE2NhbA3emmv/vuO6SmpmLPnj1IT09HeHg4WgfrP/roowAAf39/NDY2Wu2zEIlhHwHRAzz00EPYsmUL/vSnP8Hf3x9Dhw5FdnY29u7di4kTJyIoKAg5OTlYv3499u3bh9LSUnz++ecAoJt3SIxMJgNneiFrYiIgEtG/f3/ExsYiPz8fnTt3xosvvohp06YBuDvl8MCBAzFjxgzMmTMHXbt2xS9/+Uuj9v/4448jPj5et1AJkdQ46RwRkZPjHQERkZNjIiAicnJMBERETo6JgIjIyTEREBE5OSYCIiInx0RAROTkmAiIiJzc/weN5Xj1xhLErAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R = data['R']\n",
    "N_H = data['N_H']\n",
    "M_star_d = data['log M_*']\n",
    "galaxy_age = data['Age Gyr']\n",
    "redshift_z = data['z']\n",
    "sfr = sfr_atm(galaxy_age,M_star_d)\n",
    "velocity_vals = np.array([134.05430348763306, 510.21258348149706, 183.43068548075482, 618.451524921208, 110.04104426428928, 513.2321384813996, 234.47085431245546, 230.4213140053146, 102.33555196284, 435.22941800909996, 119.21853483839298, 154.43032711839197, 149.4959744149872, 181.09407352030155, 159.3110992310241, 330.3523655693238, 197.2776795711477, 227.49075690415384, 185.00543166922802, 146.1938044781218, 124.30436763865931, 107.24392367586164, 236.78327050423655, 150.3368062665032, 265.06291167573903, 189.91927258930735, 163.88186723392656, 346.2770941360653, 116.13182974316351, 524.9985013624732, 180.67373358423535, 129.57960283661137, 241.937639758548])\n",
    "\n",
    "y = diffusivity_coefficient(N_H, velocity_vals, predictedM, M_star_d, sfr)\n",
    "plt.yscale('log')\n",
    "plt.scatter(redshift_z, y, s=20, alpha=0.6, edgecolor='black', linewidth=1)\n",
    "plt.xlabel('Reshift')\n",
    "plt.ylabel('Lower Limit of the Cosmic-ray Diffusivity (cm²/s)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bc433bb",
   "metadata": {},
   "source": [
    "# Finding Halo Mass from Stellar Mass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ef4cbfc",
   "metadata": {},
   "source": [
    "Function that returns halo mass vs. stellar mass plot based on given precision and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "db81abf4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def halo_mass(precision, logm):\n",
    "    halo_mass_list = np.logspace(10, 15, precision)\n",
    "    print (halo_mass_list)\n",
    "    \n",
    "    galaxy_mass_R = []\n",
    "    for x in halo_mass_list:\n",
    "        M1 = np.power(10, 11.884)\n",
    "        beta = -1.057\n",
    "        gamma = 0.556\n",
    "        mMot = 2*0.02820\n",
    "        MMo = x/M1\n",
    "        galaxy_mass_R.append(x*mMot*(np.power((np.power(MMo, beta) + np.power(MMo, gamma)), -1)))\n",
    "    \n",
    "    predicted_M = []\n",
    "    for x in logm:\n",
    "        halo_mass_list = np.logspace(10, 15, precision)\n",
    "        predicted_stellar_mass_list = np.log10(galaxy_mass_R)\n",
    "        mask = predicted_stellar_mass_list >= x\n",
    "        predicted_M.append(halo_mass_list[mask][0])\n",
    "        \n",
    "    #print(predicted_stellar_mass_list)\n",
    "    plt.plot(np.log10(halo_mass_list), predicted_stellar_mass_list)\n",
    "    plt.xlabel(\"Halo Mass\")\n",
    "    plt.ylabel(\"Stellar Mass\")\n",
    "    return predicted_M"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bcbee49",
   "metadata": {},
   "source": [
    "The Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8c737aab",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00000000e+10 1.00115207e+10 1.00230547e+10 ... 9.97699834e+14\n",
      " 9.98849255e+14 1.00000000e+15]\n",
      "[517811173014.0411, 24257077952194.38, 1355854919822.7415, 40584559456616.19, 337406010890.65454, 24257077952194.38, 2470240705666.254, 2470240705666.254, 260100695898.87378, 14598775553950.787, 337406010890.65454, 606985501810.7432, 606985501810.7432, 1069554502462.7122, 719756703787.5809, 14598775553950.787, 1787414276899.6643, 2470240705666.254, 1069554502462.7122, 606985501810.7432, 445825511476.55164, 337406010890.65454, 2470240705666.254, 719756703787.5809, 3612066818361.2085, 1355854919822.7415, 868348122047.7374, 8898051796489.426, 295560957415.6108, 24257077952194.38, 1069554502462.7122, 517811173014.0411, 2470240705666.254]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7ff1cc69ceb0>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "logm = data['log M_*']\n",
    "predictedM = halo_mass(10000, logm)\n",
    "print(predictedM)\n",
    "plt.scatter(np.log10(predictedM), logm, color = 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b62834bc",
   "metadata": {},
   "source": [
    "# Finding Circular Velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "db5cffdb",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.178112e+11\n",
      "0.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.425708e+13\n",
      "1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.355855e+12\n",
      "2.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.058456e+13\n",
      "3.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.374060e+11\n",
      "4.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.425708e+13\n",
      "5.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.470241e+12\n",
      "6.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.470241e+12\n",
      "7.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.601007e+11\n",
      "8.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.459878e+13\n",
      "9.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.374060e+11\n",
      "10.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.069855e+11\n",
      "11.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.069855e+11\n",
      "12.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.069555e+12\n",
      "13.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.197567e+11\n",
      "14.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.459878e+13\n",
      "15.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.787414e+12\n",
      "16.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.470241e+12\n",
      "17.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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q1QwaNIh58+Y5ZBzN1ERE/kQ2pW5iw08bSrSPjIwMvE542R73atSL7g2733Kb+vXrk5ubi8ViwWQy2T7SVdoUaiIi4nBeXl6cPn2axx57jIsXL7J48WKHjKNQExH5E+nesLvdWZU9xfnw9YoVK2jfvj3Dhw/nzJkzPPXUU3z88cdUrFixRLXcSKEmIiIOV7lyZSpUqABAlSpVyMnJITc3t9THUaiJiIjD9evXj3HjxhETE0N2djZDhw7Fy8vL/oZFpFATERGH8/b2Zv78+Q4fR5f0i4iIYSjURETEMBRqIiJiGAo1ERExDIWaiIgYhkJNREQMQ5f0i4iIw5nNZsaOHcsvv/yCj48PEyZM4N577y31cTRTExERh1uzZg1eXl6sWbOGuLg4Jk+e7JBxNFMTEfkTubRxI5fXrS/ZTjIyOPGHu4FUCQ+jas+et9zk2LFjhISEANCgQQNSU1NLVkMBNFMTERGHa9q0KYmJiVitVg4cOMDZs2d170cRESmZqj172p1V2ZOSkkK9It6lPzw8nNTUVJ588klatWrFX/7yF9zc3EpUR340UxMREYc7dOgQgYGBxMfH88gjj1CnTh2HjKOZmoiIOFy9evWYP38+y5cvx9fXl6lTpzpkHIWaiIg4nJ+fHytWrHD4ODr8KCIihqFQExERw1CoiYiIYSjURETEMBRqIiJiGAo1ERExDLuhdvnyZRITE9mwYQPbtm3DZDI5oy4RETGY77//ntjYWABOnDhBdHQ0MTExTJw4EYvFUipjFBhqFy5cYNy4cTz77LN8+eWXHD9+nMTERAYOHMj48eM5f/58qRQgIiLG9/bbbxMXF0dWVhYA06dP5+WXX2blypVYrVa2bNlSKuMU+OHrN954g2eeeYb69evftC41NZU333yTiRMnlkoRIiLiHEd2niEl6UyJ9pGRkcERr322x02DatHkwVq33KZu3bosXLiQUaNGAfDvf/+bNm3aABASEkJSUhKdOnUqUV1wi1CbMGFCgRs1bNhQgSYiIoX26KOPcurUKdtjq9WKi4sLAN7e3ly9erVUxrF7m6w9e/Zw7do1LBYLkydP5uWXX6Zbt26lMriIiDhXkwftz6rsSUlJoWkR79J/I1fX/3/2Kz09ncqVK5dof7b92nvC7Nmzuffee4mPj2f16tWsXr26WANZLBYmTJhAVFQUsbGxnDhxIs/6rVu3Eh4eTlRUFGvWrAEgOzubkSNHEhMTQ+/evUvtmKuIiJStZs2asWvXLgC2b9/OAw88UCr7tRtqFStWpFq1ari7u1O9enXMZnOxBtq8eTNms5mEhASGDx/OjBkzbOuys7OZPn06y5cvJz4+noSEBNLS0ti0aRNVq1Zl5cqVvP322w77+m8REXGu0aNHs3DhQqKiosjOzubRRx8tlf3aPfzo7e1N//79iYmJ4YMPPqBWreJNW5OTkwkODgagRYsWHD582LYuNTWVunXrUqVKFQACAwPZu3cvnTt3ztOoI75QTkREnKN27dq2I3H169fn/fffL/UxCgy106dPc88997BgwQJOnjyJv78/P/74IxEREcUayGQy4ePjY3vs5uZGTk4O7u7umEwmfH19beu8vb0xmUx4e3vbth0yZAgvv/xygftPSUkpVl2lJTMzs8xrKG1G68lo/TT5379G6slorxGoJ2crMNTeeecdTp8+jb+/Pw899BBWq5WAgIBiD+Tj40N6errtscViwd3dPd916enptpA7c+YMgwYNIiYm5pYXqJT0pGVJlcaJ0/LGaD0ZrR8AK2X/t1+ajPgaqSfHSE5Oznd5gaEWFxcHwLFjx0hMTGT58uVUrlyZ4OBgunTpUuQCWrVqRWJiIl26dOHAgQN5ArJhw4acOHGCS5cu4eXlxd69exk4cCDnz59nwIABTJgwgXbt2hV5TBER+XOxe07N398ff39/4PdbZn377bfFGqhTp04kJSXRp08frFYr06ZN4+OPPyYjI4OoqCjGjBnDwIEDsVqthIeHU7NmTaZMmcKVK1dYtGgRixYtAn7/VLqnp2exahAREWOzG2rXL+P/41WPjz/+eJEHcnV1ZdKkSXmWNWzY0PZzaGgooaGhedbHxcXZZowiIiL22A219957j6VLl9quTBQRESmv7IZa48aNqVWrli6nFxGRcs9uqD344IM88sgj1KlTx3avrvfee88ZtYmIiBSJ3VBLSEhg3rx5eT5HJiIiUh7ZDbWaNWty//3357n5pIiISHlkN9TMZjM9evSgUaNGtq8JmDNnjsMLExERKSq7ofbss886ow4REZESs3tM8dy5c7Rp04Y2bdpw7733snTpUmfUJSIiUmR2Z2obN27E29sbs9nM66+/zpAhQ5xRl4iISJHZDbU33niD5557jqysLFatWoWfn58z6hIRESmyAkNt2LBhtgtDPD09OXjwIFOnTgV0oYiIiJRPBYZanz598jweMGCAw4sREREpiQJD7ejRo0RHR9u+8+yPcnJyWLlyJU8++aRDixMRESmKAkOtadOmPP300/j7+9O4cWPuvPNOrly5wvfff8+xY8cYPHiwM+sUERGxq8BQe+CBB1ixYgVJSUns3r2bQ4cO4efnR6dOnRg/frztfJuIiEh5Yffqx6CgIIKCgpxRi4iISInoho4iImIYCjURETEMu6H27LPPsnnzZnJzc51Rj4iISLHZDbVRo0axb98+wsLCmD17NsePH3dCWSIiIkVnN9QaNmzIqFGjeOedd/jvf/9L165d6d+/P4cOHXJGfSIiIoVm9+rHbdu2sWHDBn7++We6d+/OuHHjyMnJ4ZlnnmHTpk3OqFFERKRQ7Ibapk2biI6Opm3btnmW68PXIiJS3tg9/FilSpU8gTZq1CgA/v73vzuuKhERkWIocKb2wQcf8NZbb3H58mW+/PJLAKxWK/7+/k4rTkREpCgKDLW+ffvSt29fFi9ezHPPPefMmkRERIqlwFBLTEykY8eOVK1alYSEhDzroqKiHF6YiIhIURUYapcuXQLg/PnzzqpFRESkRAq8UKRXr14AdOvWjXvvvZfBgweTmZlJz549nVWbiIhIkdi9+nH06NFUr14dgA4dOvCPf/zD4UWJiIgUR6FuaHz9kv7WrVtjsVgcWpCIiEhx2f3wdeXKlUlISKBFixYcPHgQb29vZ9QlIiJSZHZnajNmzODYsWO89tprpKamMm3aNGfUJSIiUmR2Z2p+fn4EBQVRo0YN6tevj5+fnzPqEhERKTK7M7U5c+awfv16KlSowMaNG5kxY0axBrJYLEyYMIGoqChiY2M5ceJEnvVbt24lPDycqKgo1qxZU6htRERE/sjuTG3Pnj2sXr0agKeeeorIyMhiDbR582bMZjMJCQkcOHCAGTNm8NZbbwGQnZ3N9OnTWbt2LZUqVSI6OpqOHTuyf//+ArcRERG5kd1Qy8nJwWKx4OrqitVqxcXFpVgDJScnExwcDECLFi04fPiwbV1qaip169alSpUqAAQGBrJ3714OHDhQ4DYiIiI3shtqXbp0ITo6mr/+9a8cPHiQLl26FGsgk8mEj4+P7bGbmxs5OTm4u7tjMpnw9fW1rfP29sZkMt1ymxulpKQUq67SkpmZWeY1lDaj9WS0fpr8718j9WS01wjUk7PZDbUBAwbQvn17fv75Z3r37k1AQECxBvLx8SE9Pd322GKx2MLpxnXp6en4+vrecpsbNW3atFh1lZaUlJQyr6G0Ga0no/UDYKXs//ZLkxFfI/XkGMnJyfkuLzDU5syZc9Ohxh9++AGAYcOGFbmAVq1akZiYSJcuXThw4ECecGzYsCEnTpzg0qVLeHl5sXfvXgYOHIiLi0uB24iIiNyowFBr0KBBqQ7UqVMnkpKS6NOnD1arlWnTpvHxxx+TkZFBVFQUY8aMYeDAgVitVsLDw6lZs2a+24iIiBSkwFC7fkPjnJwcNmzYwJkzZ2jbti2NGjUq1kCurq5MmjQpz7KGDRvafg4NDSU0NNTuNiIiIgWx+zm1iRMn8uuvv5KUlER6ejqjR492Rl0iIiJFZjfUTp48yUsvvYSHhwehoaFcvXrVGXWJiIgUmd1Qy83N5cKFC7i4uGAymXB1LdSN/UVERJzO7iX9L7/8MtHR0aSlpREVFaXvUxMRkXKrwFCLiYkhKiqKxx57jC+++IILFy5wxx13FPuOIiIiIo5W4LHECRMmcOjQIbp168a0adO4ePGiAk1ERMq1AmdqTZo0IS4uDrPZzJYtW5gxYwaZmZn07t2bHj16OLNGERGRQrF71YeHhwePPfYYU6ZMoUWLFkydOtUZdYmIiBTZLS8UyczM5IsvvuCjjz7i6tWr9O7dm61btzqrNhERkSIpMNRGjx7Nzp07CQ0NZcSIETRr1syZdYmIiBRZgaHWpk0bXn31VTw9PZ1Zj4iISLEVGGrh4eHOrENERKTEdHsQERExDLuhtmzZMmfUISIiUmJ2Q23btm3k5uY6oxYREZESsXvvx4sXLxIcHEzt2rVxcXHBxcWF1atXO6M2ERGRIrEbaosXL3ZGHSIiIiVmN9RycnL4/PPPyc7OBuDcuXP6NmoRESmX7J5Tu/5N1/v27ePUqVNcunTJ0TWJiIgUi91Q8/T05Nlnn6VmzZrMmDGD8+fPO6MuERGRIrMbalarlbS0NDIyMsjIyODy5cvOqEtERKTI7Iba4MGD+eqrr+jevTsPP/wwISEhzqhLRESkyOxeKNK6dWtat24NwMMPP+zwgkRERIqrwFBr3759gRt9++23DilGRESkJAoMNQWXiIjcbuwefhw7duxNy6ZPn+6QYkRERErCbqh16dIF+P0qyB9++IFz5845vCgREZHisBtqwcHBtp9DQkIYMGCAQwsSEREpLruh9sdza+fOndOHr0VEpNyyG2qffvqp7eeKFSsybdo0hxYkIiJSXHZDbeTIkaSkpBAUFMT7779P3bp1nVGXiIhIkdm9o8jw4cO5evUqAFWqVGHkyJEOL0pERKQ47IbatWvX6Ny5MwDdunXj2rVrDi9KRESkOOyGWoUKFUhKSsJkMrFjxw5cXe1uIiIiUibsnlObMmUKM2fOZMqUKfj7+xf7C0IzMzMZOXIkv/32G97e3sycORM/P788z1mzZg2rV6/G3d2d559/no4dO3L16lVGjhyJyWQiOzubMWPG0LJly2LVICIixmY31FauXMmiRYtKPNCqVasICAjgxRdf5NNPP2XRokXExcXZ1qelpREfH8+6devIysoiJiaGoKAg3nnnHR588EH69evHzz//zPDhw9mwYUOJ6xEREeOxeywxNTWVK1eulHig5ORk2we5Q0JC2LFjR571Bw8epGXLlnh4eODr60vdunU5cuQI/fr1o0+fPgDk5uZSsWLFEtciIiLGZHemlpqaStu2bfHz88PFxQWwf7PjDz/8kHfffTfPsmrVquHr6wuAt7e37YrK60wmk2399eeYTCYqV64M/D6TGzlyJOPGjct3zJSUFHutOFRmZmaZ11DajNaT0fpp8r9/jdST0V4jUE/OZjfUEhMTi7zTiIgIIiIi8iwbPHgw6enpAKSnp9vC6jofHx/b+uvPuR5yR48eZdiwYYwaNYo2bdrkO2bTpk2LXGdpSklJKfMaSpvRejJaPwBWyv5vvzQZ8TVST46RnJyc7/ICQ23RokW88MILDBs2zDZDu27OnDlFLqBVq1Zs27aN5s2bs337dgIDA/Osb968OfPmzSMrKwuz2UxqaioBAQEcO3aMl156iXnz5tGkSZMC9i4iInKLUAsNDQWwnc8qqejoaEaPHk10dDQVKlSwBeM777xD3bp1efjhh4mNjSUmJgar1crQoUOpWLEic+bMwWw2M3XqVOD3Gd1bb71VKjWJiIixFBhqTZo0ISEhgfDwcNzd3dm7dy8//fQT0dHRxRqoUqVKLFiw4Kbl/fv3t/0cGRlJZGRknvUKMBERKawCr35cuHAhSUlJZGdnA3DXXXeRlJTEm2++6bTiREREiqLAUNu+fTvz58+nUqVKANSuXZu5c+eydetWpxUnIiJSFAWGmpeX100XiFSoUAFvb2+HFyUiIlIcBYaap6cnv/zyS55lv/zyy01BJyIiUl4UeKHIiBEjeOGFF2jXrh116tTh119/5dtvv2XmzJnOrE9ERKTQCpypNWrUiJUrV9KsWTOuXbvGX/7yF1atWkWzZs2cWZ+IiEih3fKOIr6+vvTs2dNJpYiIiJSMvhxNREQMQ6EmIiKGoVATERHDUKiJiIhhKNRERMQwFGoiImIYCjURETEMhZqIiBiGQk1ERAxDoSYiIoahUBMREcNQqImIiGEo1ERExDAUaiIiYhgKNRERMQyFmoiIGIZCTUREDEOhJiIihqFQExERw1CoiYiIYSjURETEMBRqIiJiGAo1ERExDIWaiIgYhkJNREQMQ6EmIiKGoVATERHDcFqoZWZm8uKLLxITE8MzzzzDhQsXbnrOmjVrCAsLIzIyksTExDzrUlNTCQwMJCsry1kli4jIbcZpobZq1SoCAgJYuXIlPXv2ZNGiRXnWp6WlER8fz+rVq1m2bBmvv/46ZrMZAJPJxMyZM/Hw8HBWuSIichtyWqglJycTHBwMQEhICDt27Miz/uDBg7Rs2RIPDw98fX2pW7cuR44cwWq1Mn78eIYNG0alSpWcVa6IiNyG3B2x0w8//JB33303z7Jq1arh6+sLgLe3N1evXs2z3mQy2dZff47JZOKNN96gQ4cONGnS5JZjpqSklFL1xZOZmVnmNZQ2o/VktH6u/xdhpJ6M9hqBenI2h4RaREQEEREReZYNHjyY9PR0ANLT06lcuXKe9T4+Prb115/j6+vLpk2buOuuu1i3bh1paWkMGDCADz744KYxmzZt6oBOCi8lJaXMayhtRuvJaP0AWCn7v/3SZMTXSD05RnJycr7LHRJq+WnVqhXbtm2jefPmbN++ncDAwDzrmzdvzrx588jKysJsNpOamkpAQABfffWV7TmhoaEsX77cWSWLiMhtxmmhFh0dzejRo4mOjqZChQrMmTMHgHfeeYe6devy8MMPExsbS0xMDFarlaFDh1KxYkVnlSciIgbgtFCrVKkSCxYsuGl5//79bT9HRkYSGRlZ4D62bt3qkNpERMQY9OFrERExDIWaiIgYhkJNREQMQ6EmIiKGoVATERHDUKiJiIhhKNRERMQwFGoiImIYCjURETEMhZqIiBiGQk1ERAxDoSYiIoahUBMREcNQqImIiGEo1ERExDAUaiIiYhgKNRERMQyFmoiIGIZCTUREDEOhJiIihqFQExERw1CoiYiIYSjURETEMBRqIiJiGAo1ERExDIWaiIgYhovVarWWdREllZycXNYliIiIkwUGBt60zBChJiIiAjr8KCIiBqJQExERw1CoiYiIYSjUiuj7778nNjYWgJSUFGJiYoiNjWXgwIGcP38egG3bthEZGUlkZCSvvPIK5f20ZWF6WrZsGWFhYYSHh/PVV1+VZbl2/bGfY8eOER0dTZ8+fXjllVfIzc0FYM2aNYSFhREZGUliYmJZllsohelpxYoVREREEBERwRtvvFGW5dpVmH4ALBYLTz/9NKtWrSqrUgutMD3dTu8NhemnXL4vWKXQli5dau3atas1IiLCarVarX379rX+8MMPVqvVal21apV12rRp1qtXr1off/xx62+//Wbb5vrP5VFherp8+bK1Q4cO1qysLOulS5esDz30UFmWfEs39vP8889bd+/ebbVardbRo0dbv/zyS+u5c+esXbt2tWZlZVmvXLli+7m8KkxPJ0+etPbq1cuak5Njzc3NtUZFRVlTUlLKsuwCFaaf6+bMmWPt3bu3deXKlWVSa2EVpqfb6b2hMP2U1/cFzdSKoG7duixcuND2+PXXX6dp06YA5ObmUrFiRfbv309AQAAzZ84kJiaGO++8Ez8/v7Iq2a7C9FSpUiXuvvturl27xrVr13BxcSmrcu26sZ+FCxfSunVrzGYzaWlpVKtWjYMHD9KyZUs8PDzw9fWlbt26HDlypAyrvrXC9HTXXXfxz3/+Ezc3N1xdXcnJyaFixYplWHXBCtMPwOeff46LiwshISFlVWqhFaan2+m9oTD9lNf3BYVaETz66KO4u7vbHteoUQOAffv28f7779OvXz8uXrzIrl27GDFiBG+//Tbvvvsu//nPf8qqZLsK0xNArVq1ePzxx+nVqxdPPvlkWZRaKDf24+bmxunTp+natSsXL16kfv36mEwmfH19bc/x9vbGZDKVRbmFUpieKlSogJ+fH1arlZkzZ9KsWTPq169fhlUXrDD9/Pjjj3zyySe89NJLZVhp4RWmp9vpvaEw/UD5fF9QqJXQZ599xsSJE1m6dCl+fn5UrVqV+++/n+rVq+Pt7c0DDzxASkpKWZdZJDf2tH37ds6dO8eWLVv4+uuv2bx5MwcPHizrMgvtnnvu4csvvyQ6OpoZM2bg4+NDenq6bX16enqekLsd3NgTQFZWFiNGjCA9PZ2JEyeWcYVFc2M/Gzdu5OzZszz11FNs2LCBFStWsH379rIus0hu7Ol2f2+4sZ/y+r6gUCuBjz76iPfff5/4+Hjq1KkDwH333cePP/7IhQsXyMnJ4fvvv8ff37+MKy28/HqqUqUKnp6eeHh4ULFiRXx9fbly5UoZV1o4zz33HMePHwd+n5G5urrSvHlzkpOTycrK4urVq6SmphIQEFC2hRZBfj1ZrVZeeOEFGjduzKRJk3BzcyvbIosgv35GjRrFhx9+SHx8PL169aJfv363xWHI6/Lr6XZ+b8ivn/L6vuBu/ymSn9zcXKZOnUqtWrV48cUXAWjdujVDhgxh+PDhPP300wB07tz5tnnDvFVP3333HZGRkbi6utKqVSuCgoLKuNrC+b//+z/GjBlDhQoVqFSpElOmTKF69erExsYSExOD1Wpl6NCh5fb8U37y62nz5s3s3r0bs9nMN998A8CwYcNo2bJlGVdrX3793O7y68nPz++2fW/Ir58aNWqUy/cF3SZLREQMQ4cfRUTEMBRqIiJiGAo1ERExDIWaiIgYhkJNREQMQ6EmUop27dpFu3btiI2NJTY2lrCwMIYMGYLZbC7U9tu3b2fMmDEADB48uES1mM1mRo4cicViITQ0lKysrGLtJy0tjUmTJpWoFhFnUaiJlLIHH3yQ+Ph44uPjWb9+PRUqVGDr1q1F3k9J77S/YsUKHnvsMVxdS/af+fU7YOzevbtE+xFxBoWaiAOZzWbOnTtHlSpVyM3N5R//+AcDBw4kLCyMefPmAZCamkpUVBT9+vXL8xUr1z/IGhsbS2pqKgCrVq1i4cKFZGVl8dxzz/HEE0/Qu3dvdu3alWdcq9XKpk2bCA4OzrN81apVDB48GLPZTJcuXZgwYQLR0dE899xzZGRkkJmZydChQ4mKiiIsLIz9+/cD0LVrV9577z1H/ZpESo3uKCJSynbu3ElsbCy//fYbrq6uREZG0q5dO06dOkWLFi2IiIggKyuLkJAQXn75ZebPn8+QIUMICgpi6dKl/Pzzz3bHOHnyJOfPn2fFihX89ttvtlsYXXf8+HF8fHyoUKGCbVl8fDwpKSnMnz8fNzc3MjMz6datG61bt2bWrFkkJCTg4uLCPffcw9y5c/nxxx/57rvvaNmyJf7+/uzbt6+0f1UipU6hJlLKHnzwQebOncvFixcZMGAAtWvXBqBq1aocOnSInTt34uPjYzvP9tNPP9G8eXMAWrVqdctQu34DoEaNGtG3b1+GDRtGTk6O7cscr7t48SJ33nlnnmU7duzAzc3Ndl9Id3d3WrdubRv3+g2Dr99jMSAgwHYbp+vbWSyWEh/OFHEk/XWKOMgdd9zB7NmziYuL49y5c6xfvx5fX1/mzJnDgAEDyMzMxGq10qBBA9thvsOHD9+0Hw8PD9LS0gD44YcfADh69Cjp6eksXbqUGTNmMHny5DzbVKtW7aabyy5atIjKlSvbDnHm5OTYvkcuOTkZf39/GjZsyKFDhwD45ZdfGD58OPB7mLq7uyvQpNzTTE3Egfz9/YmNjWXKlCm8+OKLDBs2jOTkZCpVqkS9evU4d+4cEydOZOjQoSxbtgw/P7+bbq785JNPMmnSJGrVqmX7vrt7772XN998k40bN1KhQgWGDBmSZ5t69erZ7gb/x+/FiouLIyIignbt2gHw9ttv8+uvv3L33XczdOhQrFYr48aN44knniA3N5dx48YBv4doixYtHPibEikduqGxiEEtWbKEBg0a0KlTp3zXh4aG8q9//atQ31Awa9YsQkNDeeCBB0q7TJFSpWMJIgb11FNP8fnnn2OxWEq0n7S0NEwmkwJNbguaqYmIiGFopiYiIoahUBMREcNQqImIiGEo1ERExDAUaiIiYhj/D/lKYlWzwCQzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.069555e+12\n",
      "18.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.069855e+11\n",
      "19.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.458255e+11\n",
      "20.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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J3MLGHzeW6z4fb/I4PRv3vO1rGjZsSGFhISaTCYPBYPkql70o1ERExG68vb05d+4c3bt35/LlyyxZssSu4ynURET+AHo27mlzVmUPK1eupGPHjowZM4bz58/z1FNPsXXrVqpUqWKX8RRqIiJiN/7+/lSqVAmAgIAACgoKKCwstNt4CjUREbGbQYMGMXHiRGJiYsjPz2fUqFF4e3vbbTyFmoiI2I2Pjw8LFy502Hg6pV9ERFyGQk1ERFyGQk1ERFyGQk1ERFyGQk1ERFyGQk1ERFyGTukXERG7MRqNTJgwgTNnzuDr60tCQgINGjSw23iaqYmIiN2kpKTg7e1NSkoK8fHxTJkyxa7jaaYmIvIHcGXTJn5dv6Fc9xkQ2YdqvXvf9jXHjx8nLCwMgEaNGpGZmVmuNdxMMzUREbGb4OBgUlNTMZvNHDx4kAsXLujajyIicmeq9e5tc1ZlD5GRkWRmZjJw4EBat27N/fffj4eHh93G00xNRETs5vDhw4SEhJCUlESXLl2oW7euXcfTTE1EROymfv36LFy4kBUrVuDn50diYqJdx1OoiYiI3QQGBrJy5UqHjafDjyIi4jIUaiIi4jIUaiIi4jIUaiIi4jIUaiIi4jIUaiIi4jJshtqvv/5KamoqGzduZOfOnRgMBkfUJSIiLuS7774jNjYWgFOnThEdHU1MTAyTJ0/GZDKV2zjFhtqlS5eYOHEizzzzDJ999hknT54kNTWVoUOHMmnSJH7++edyK0JERFzX22+/TXx8PHl5eQBMnz6dkSNHsnr1asxmM9u3by+3sYr98vUbb7zB008/TcOGDW9Zl5mZyZtvvsnkyZPLrRAREbGfo3vOk5F2vlz3GdyhNs0frm3zdfXq1eP1119n3LhxAHz//fe0bdsWgLCwMNLS0ujatWu51FRsqCUkJBS7UePGjRVoIiJSIo8++ihnz561PDebzbi5uQHg4+PDtWvXym0sm5fJ2rdvHzk5OZhMJqZMmcLIkSPp0aNHuRUgIiL21/zhks2qHMHd/f9/8pWdnY2/v3/57dvWC2bPnk2DBg1ISkpi7dq1rF27tkwDmUwmEhISiIqKIjY2llOnTlmt37FjB5GRkURFRZGSkgJAfn4+Y8eOJSYmhr59+5brcVcREakYLVq0YO/evQDs2rWLhx56qNz2bTPUqlSpQvXq1fH09KRGjRoYjcYyDbRt2zaMRiPJycmMGTOGGTNmWNbl5+czffp0VqxYQVJSEsnJyWRlZbFlyxaqVavG6tWrefvtt+1+G3AREbG/8ePH8/rrrxMVFUV+fj6PPvpoue3b5uFHHx8fBg8eTExMDO+//z61a5dt+pqenk5oaCgArVq14siRI5Z1mZmZ1KtXj4CAAABCQkLYv38/3bp1s3qz9ryxnIiI2E+dOnUsR+EaNmzIqlWr7DJOsaF27tw5/vznP7No0SJOnz5NUFAQ//73v+nXr1+ZBjIYDPj6+lqee3h4UFBQgKenJwaDAT8/P8s6Hx8fDAYDPj4+lm1HjBjByJEji91/RkaG5XFubq7VcymeelUyztan5v/986gT1QTO1ydnpT6VTFn6VGyovfPOO5w7d46goCD+/ve/Yzabadq0aZmL8/X1JTs72/LcZDLh6elZ5Lrs7GxLyJ0/f55hw4YRExNz2xNUgoODLY8zMjKsnkvx1KuScdY+OVtNztonZ6M+lUxRfUpPT7/tNsWGWnx8PADHjx8nNTWVFStW4O/vT2hoKBEREaUurnXr1qSmphIREcHBgwetArJx48acOnWKK1eu4O3tzf79+xk6dCg///wzQ4YMISEhgfbt25d6TBER+WOx+ZlaUFAQQUFBwG+XzPrqq6/KNFDXrl1JS0tjwIABmM1mpk2bxtatW7l+/TpRUVHExcUxdOhQzGYzkZGR1KpVi6lTp3L16lUWL17M4sWLgd++me7l5VWmGkRExLXZDLUbp/H//qzH//mf/yn1QO7u7rz22mtWyxo3bmx5HB4eTnh4uNX6+Ph4y4xRRETEFpuh9t5777Fs2TLLmYkiIiLOymaoNWvWjNq1a+t0ehERcXo2Q+3hhx+mS5cu1K1b13K9rvfee88RtYmIiJSKzVBLTk5mwYIFVt8jExERcUY2Q61WrVr85S9/sboApYiIiDOyGWpGo5FevXrRpEkTy60C5s6da/fCRERESstmqD3zzDOOqENEROSO2TymePHiRdq2bUvbtm1p0KABy5Ytc0RdIiIipWZzprZp0yZ8fHwwGo3MmzePESNGOKIuERGRUrMZam+88QbPPvsseXl5rFmzhsDAQEfUJSIiUmrFhtro0aMtJ4Z4eXlx6NAhEhMTAZ0oIiIizqnYUBswYIDV8yFDhti9GBERkTtRbKgdO3aM6Ohoyz3Pfq+goIDVq1czcOBAuxYnIiJSGsWGWnBwMP/85z8JCgqiWbNm3HvvvVy9epXvvvuO48ePM3z4cEfWKSIiYlOxofbQQw+xcuVK0tLS+Oabbzh8+DCBgYF07dqVSZMmWT5vExERcRY2z37s0KEDHTp0cEQtIiIid0QXdBQREZehUBMREZdhM9SeeeYZtm3bRmFhoSPqERERKTOboTZu3DgOHDhAnz59mD17NidPnnRAWSIiIqVnM9QaN27MuHHjeOedd/jPf/7DY489xuDBgzl8+LAj6hMRESkxm2c/7ty5k40bN3LixAl69uzJxIkTKSgo4Omnn2bLli2OqFFERKREbIbali1biI6Opl27dlbL9eVrERFxNjYPPwYEBFgF2rhx4wD4xz/+Yb+qREREyqDYmdr777/PW2+9xa+//spnn30GgNlsJigoyGHFiYiIlEaxofbEE0/wxBNPsGTJEp599llH1iQiIlImxYZaamoqnTt3plq1aiQnJ1uti4qKsnthIiIipVVsqF25cgWAn3/+2VG1iIiI3JFiTxR5/PHHAejRowcNGjRg+PDh5Obm0rt3b0fVJiIiUio2z34cP348NWrUAKBTp068/PLLdi9KRESkLEp0QeMbp/S3adMGk8lk14JERETKyuaXr/39/UlOTqZVq1YcOnQIHx8fR9QlIiJSajZnajNmzOD48ePMmTOHzMxMpk2b5oi6RERESs3mTC0wMJAOHTpQs2ZNGjZsSGBgoCPqEhERKTWbM7W5c+eyYcMGKlWqxKZNm5gxY0aZBjKZTCQkJBAVFUVsbCynTp2yWr9jxw4iIyOJiooiJSWlRNuIiIj8ns2Z2r59+1i7di0ATz31FP379y/TQNu2bcNoNJKcnMzBgweZMWMGb731FgD5+flMnz6ddevWUbVqVaKjo+ncuTPffvttsduIiIjczGaoFRQUYDKZcHd3x2w24+bmVqaB0tPTCQ0NBaBVq1YcOXLEsi4zM5N69eoREBAAQEhICPv37+fgwYPFbiMiInIzm6EWERFBdHQ0f/3rXzl06BARERFlGshgMODr62t57uHhQUFBAZ6enhgMBvz8/CzrfHx8MBgMt93mZhkZGZbHubm5Vs+leOpVyThbn5r/98+jTlQTOF+fnJX6VDJl6ZPNUBsyZAgdO3bkxIkT9O3bl6ZNm5apOF9fX7Kzsy3PTSaTJZxuXpednY2fn99tt7lZcHCw5XFGRobVcymeelUyztonZ6vJWfvkbNSnkimqT+np6bfdpthQmzt37i2HGn/44QcARo8eXeriWrduTWpqKhERERw8eNAqHBs3bsypU6e4cuUK3t7e7N+/n6FDh+Lm5lbsNiIiIjcrNtQaNWpUrgN17dqVtLQ0BgwYgNlsZtq0aWzdupXr168TFRVFXFwcQ4cOxWw2ExkZSa1atYrcRkREpDjFhtqNCxoXFBSwceNGzp8/T7t27WjSpEmZBnJ3d+e1116zWta4cWPL4/DwcMLDw21uIyIiUhyb31ObPHkyP/30E2lpaWRnZzN+/HhH1CUiIlJqNkPt9OnTvPjii1SuXJnw8HCuXbvmiLpERERKzWaoFRYWcunSJdzc3DAYDLi7l+jC/iIiIg5n85T+kSNHEh0dTVZWFlFRUbqfmoiIOK1iQy0mJoaoqCi6d+/Op59+yqVLl7jnnnvKfEUREREReyv2WGJCQgKHDx+mR48eTJs2jcuXLyvQRETEqRU7U2vevDnx8fEYjUa2b9/OjBkzyM3NpW/fvvTq1cuRNYqIiJSIzbM+KleuTPfu3Zk6dSqtWrUiMTHREXWJiIiU2m1PFMnNzeXTTz9l8+bNXLt2jb59+7Jjxw5H1SYiIlIqxYba+PHj2bNnD+Hh4bz00ku0aNHCkXWJiIiUWrGh1rZtW1599VW8vLwcWY+IiEiZFRtqkZGRjqxDRETkjunyICIi4jJshtry5csdUYeIiMgdsxlqO3fupLCw0BG1iIiI3BGb1368fPkyoaGh1KlTBzc3N9zc3Fi7dq0jahMRESkVm6G2ZMkSR9QhIiJyx2yGWkFBAZ988gn5+fkAXLx4UXejFhERp2TzM7Ubd7o+cOAAZ8+e5cqVK/auSUREpExshpqXlxfPPPMMtWrVYsaMGfz888+OqEtERKTUbIaa2WwmKyuL69evc/36dX799VdH1CUiIlJqNkNt+PDhfP755/Ts2ZNHHnmEsLAwR9QlIiJSajZPFGnTpg1t2rQB4JFHHrF7QSIiImVVbKh17Nix2I2++uoruxQjIiJyJ4oNNQWXiIjcbWwefpwwYcIty6ZPn26XYkRERO6EzVCLiIgAfjsL8ocffuDixYt2L0pERKQsbIZaaGio5XFYWBhDhgyxa0EiIiJlZTPUfv/Z2sWLF/XlaxERcVo2Q+2jjz6yPK5SpQrTpk2za0EiIiJlZTPUxo4dS0ZGBh06dGDVqlXUq1fPEXWJiIiUms0riowZM4Zr164BEBAQwNixY+1elIiISFnYDLWcnBy6desGQI8ePcjJybF7USIiImVhM9QqVapEWloaBoOB3bt34+5ucxMREZEKYfMztalTpzJz5kymTp1KUFBQmW8Qmpuby9ixY/nll1/w8fFh5syZBAYGWr0mJSWFtWvX4unpyXPPPUfnzp25du0aY8eOxWAwkJ+fT1xcHA8++GCZahAREddmM9RWr17N4sWL73igNWvW0LRpU1544QU++ugjFi9eTHx8vGV9VlYWSUlJrF+/nry8PGJiYujQoQPvvPMODz/8MIMGDeLEiROMGTOGjRs33nE9IiLiemweS8zMzOTq1at3PFB6errli9xhYWHs3r3bav2hQ4d48MEHqVy5Mn5+ftSrV4+jR48yaNAgBgwYAEBhYSFVqlS541pERMQ12ZypZWZm0q5dOwIDA3FzcwNsX+z4gw8+4N1337VaVr16dfz8/ADw8fGxnFF5g8FgsKy/8RqDwYC/vz/w20xu7NixTJw4scgxMzIyLI9zc3Otnkvx1KuScbY+Nf/vn0edqCZwvj45K/WpZMrSJ5uhlpqaWupC+vXrR79+/ayWDR8+nOzsbACys7MtYXWDr6+vZf2N19wIuWPHjjF69GjGjRtH27ZtixwzODjY8jgjI8PquRRPvSoZZ+2Ts9XkrH1yNupTyRTVp/T09NtuU2yoLV68mOeff57Ro0dbZmg3zJ07t9TFtW7dmp07d9KyZUt27dpFSEiI1fqWLVuyYMEC8vLyMBqNZGZm0rRpU44fP86LL77IggULaN68eTF7FxERuU2ohYeHA1g+z7pT0dHRjB8/nujoaCpVqmQJxnfeeYd69erxyCOPEBsbS0xMDGazmVGjRlGlShXmzp2L0WgkMTER+G1G99Zbb5VLTSIi4lqKDbXmzZuTnJxMZGQknp6e7N+/nx9//JHo6OgyDVS1alUWLVp0y/LBgwdbHvfv35/+/ftbrVeAiYhISRV79uPrr79OWloa+fn5APzpT38iLS2NN99802HFiYiIlEaxobZr1y4WLlxI1apVAahTpw7z589nx44dDitORESkNIoNNW9v71tOEKlUqRI+Pj52L0pERKQsig01Ly8vzpw5Y7XszJkztwSdiIiIsyj2RJGXXnqJ559/nvbt21O3bl1++uknvvrqK2bOnOnI+kREREqs2JlakyZNWL16NS1atCAnJ4f777+fNWvW0KJFC0fWJyIiUmK3vaKIn58fvXv3dlApIiIid0Y3RxMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZehUBMREZfhsFDLzc3lhRdeICYmhqeffppLly7d8pqUlBT69OlD//79SU1NtVqXmZlJSEgIeXl5jipZRETuMg4LtTVr1tC0aVNWr15N7969Wbx4sdX6rKwskpKSWLt2LcuXL2fevHkYjUYADAYDM2fOpHLlyo4qV0RE7kIOC7X09HRCQ0MBCAsLY/fu3VbrDx06xIMPPkjlypXx8/OjXr16HD16FLPZzKRJkxg9ejRVq1Z1VLkiInIX8rTHTj/44APeffddq2XVq1fHz88PAB8fH65du2a13mAwWNbfeI3BYOCNN96gU6dONG/e/LZjZmRkWB7n5uZaPZfiqVcl42x9uvG34agT1QTO1ydnpT6VTFn6ZJdQ69evH/369bNaNnz4cLKzswHIzs7G39/far2vr69l/Y3X+Pn5sWXLFv70pz+xfv16srKyGDJkCO+///4tYwYHB1seZ2RkWD2X4qlXJeOsfXK2mpy1T85GfSqZovqUnp5+223sEmpFad26NTt37qRly5bs2rWLkJAQq/UtW7ZkwYIF5OXlYTQayczMpGnTpnz++eeW14SHh7NixQpHlSwiIncZh4VadHQ048ePJzo6mkqVKjF37lwA3nnnHerVq8cjjzxCbGwsMTExmM1mRo0aRZUqVRxVnoiIuACHhVrVqlVZtGjRLcsHDx5sedy/f3/69+9f7D527Nhhl9pERMQ16MvXIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMhRqIiLiMtzMZrO5oou4U+np6RVdgoiIOEhISEix61wi1ERERECHH0VExIUo1ERExGUo1ERExGV4VnQBdyo/P5+4uDjOnTuHu7s7U6ZMwWg0MnnyZDw8PGjQoAGJiYm4u/+x89toNDJhwgTOnDmDr68vCQkJuLm5ERcXh5ubG02aNGHy5Ml/+D5B0b3KyclhypQpeHh4ULlyZWbOnMm9995b0aVWqKL61KBBAwC2bt3KqlWrSE5OrtginUBRffLz8yM+Pp6rV69SWFjIrFmzqFevXkWXWqGK+3tX2t/ld32o7dy5k4KCAtauXUtaWhoLFizAZDIxbNgwOnXqxJgxY/jiiy8IDw+v6FIrVEpKCt7e3qSkpHDixAmmTJlCpUqVGDlyJO3atSMhIYHt27fTtWvXii61whXVq7y8PCZNmkRwcDBr167l7bffZsKECRVdaoUqqk/Lly8nIyODdevWoXPQflNUn2rUqEGPHj2IiIhgz549nDhx4g8fakX1ycvLq9S/y+/6f5Y3bNiQwsJCTCYTBoMBT09PgoODuXLlCmazmezsbDw97/rsvmPHjx8nLCwMgEaNGpGZmcn3339P27ZtAQgLC+Prr7+uyBKdRlG9mjdvHsHBwQAUFhZSpUqViizRKRTVp8uXLzNnzhwmTpxYwdU5j6L6dODAAS5cuMCgQYPYunWr5e/hH1lRfSrL7/K7PtS8vb05d+4c3bt3Z9KkScTGxlqmqd27d+eXX36hXbt2FV1mhQsODiY1NRWz2czBgwe5cOECZrMZNzc3AHx8fLh27VoFV+kciupV9erVAThw4ACrVq1i0KBBFVukE7i5T+fPn2fChAlMnDgRHx+fii7PaRT183Tu3Dn8/f1ZuXIltWvX5u23367oMitcUX2qV69eqX+X3/WhtnLlSjp27Minn37K5s2biYuLIzExkffff59PPvmE3r17M2PGjIous8JFRkbi6+vLwIEDSU1N5f7777c6Np2dnY2/v38FVug8iuqVh4cHH3/8MZMnT2bZsmUEBgZWdJkV7uY+ubm5cebMGV555RVGjx7N8ePHSUxMrOgyK1xRP0/VqlWzHEYLDw/nyJEjFVxlxSuqT9OnTy/17/K7PtT8/f3x8/MDICAggIKCAvz8/PD19QWgZs2aXL16tSJLdAqHDx8mJCSEpKQkunTpQt26dWnRogV79+4FYNeuXTz00EMVXKVzKKpXmzdvZtWqVSQlJVG3bt2KLtEp3Nyn7t2789FHH5GUlMS8efMICgri5ZdfrugyK1xRP08hISHs3LkTgH379hEUFFTBVVa8ovoUEBBQ6t/ld/0VRbKzs5k4cSJZWVnk5+czcOBAateuzZw5c/D09KRSpUpMmTKFOnXqVHSpFerSpUuMHj2anJwc/Pz8SExM5Pr160yaNIn8/HwaNWrE1KlT8fDwqOhSK1xRverRowe1a9e2zGbbtGnDiBEjKrjSilVUn2rVqgXA2bNnGT16NCkpKRVcZcUrqk8FBQXEx8eTk5ODr68vc+fOJSAgoKJLrVBF9enMmTOl/l1+14eaiIjIDXf94UcREZEbFGoiIuIyFGoiIuIyFGoiIuIyFGoiIuIyFGoi5WTv3r20b9+e2NhYYmNj6dOnDyNGjMBoNJZo+127dhEXFwfA8OHD76gWo9HI2LFjMZlMhIeHk5eXV6b9ZGVl8dprr91RLSKOpFATKUcPP/wwSUlJJCUlsWHDBipVqsSOHTtKvZ833njjjupYuXIl3bt3v+O7LtSoUQMfHx+++eabO9qPiKMo1ETsxGg0cvHiRQICAigsLOTll19m6NCh9OnThwULFgCQmZlJVFQUgwYNYs2aNZZtO3ToAEBsbCyZmZkArFmzhtdff528vDyeffZZnnzySfr27Wu5KswNZrOZLVu2EBoaarV8zZo1DB8+HKPRSEREBAkJCURHR/Pss89y/fp1cnNzGTVqFFFRUfTp04dvv/0WgMcee4z33nvPXm0SKVe6fL1IOdqzZw+xsbH88ssvuLu7079/f9q3b8/Zs2dp1aoV/fr1Iy8vj7CwMEaOHMnChQsZMWIEHTp0YNmyZZw4ccLmGKdPn+bnn39m5cqV/PLLL5w8edJq/cmTJ/H19aVSpUqWZUlJSWRkZLBw4UI8PDzIzc2lR48etGnThlmzZpGcnIybmxt//vOfmT9/Pv/+97/5+uuvefDBBwkKCuLAgQPl3SoRu1CoiZSjhx9+mPnz53P58mWGDBliuaRPtWrVOHz4MHv27MHX19fyOduPP/5Iy5YtAWjduvVtQ+3GxX+aNGnCE088wejRoykoKCA2NtbqdZcvX77lBqa7d+/Gw8PDchk0T09P2rRpYxl3165dAJZbfzRt2pSmTZsCWLYzmUy6iaw4Pf2EitjBPffcw+zZs4mPj+fixYts2LABPz8/5s6dy5AhQ8jNzcVsNtOoUSPLYb6irtReuXJlsrKyAPjhhx8AOHbsGNnZ2SxbtowZM2YwZcoUq22qV69+y4VfFy9ejL+/v+UQZ0FBAUePHgUgPT2doKAgGjduzOHDhwE4c+YMY8aMAX4LU09PTwWa3BU0UxOxk6CgIGJjY5k6dSovvPACo0ePJj09napVq1K/fn0uXrzI5MmTGTVqFMuXLycwMPCWm48OHDiQ1157jdq1a1OzZk0AGjRowJtvvsmmTZuoVKnSLRdWrl+/PpcuXaKgoMDqporx8fH069eP9u3bA/D222/z008/cd999zFq1CjMZjMTJ07kySefpLCw0HKjz2PHjtGqVSs7dkqk/OiCxiIuaOnSpTRq1IiuXbsWuT48PJx//etfJbqD96xZswgPD9etieSuoOMJIi7oqaee4pNPPsFkMt3RfrKysjAYDAo0uWtopiYiIi5DMzUREXEZCjUREXEZCjUREXEZCjUREXEZCjUREXEZ/w8JP9Wcap/+YgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.374060e+11\n",
      "21.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.470241e+12\n",
      "22.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.197567e+11\n",
      "23.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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ne8PuN92nfv36FBQUYLFYMJlMto90lTeFmoiIOJyXlxenT5+ma9euXLhwgSVLljhkHIWaiMifSPeG3e2uqhxh5cqVtG/fntGjR3PmzBmefPJJNm/eTKVKlcp1HIWaiIg4nJ+fHxUqVADA39+f/Px8CgoKyn0chZqIiDjcwIEDmTBhAjExMeTl5TFy5Ei8vLzKfRyFmoiIOJy3tzcLFixw+Di6pV9ERAxDoSYiIoahUBMREcNQqImIiGEo1ERExDAUaiIiYhi6pV9ERBzObDYzfvx4fvrpJ3x8fEhISKBevXrlPo5WaiIi4nDJycl4eXmRnJxMfHw8kydPdsg4WqmJiPyJXNy4kd/Wp5TrMf0je1G1Z8+b7nP06FHCwsIAaNCgAZmZmeVawzVaqYmIiMMFBQWRmpqK1Wpl//79nD17Vs9+FBGRsqnas6fdVZUjREZGkpmZyYABA2jZsiX3338/Hh4e5T6OVmoiIuJwBw8eJDg4mMTERDp16kTt2rUdMo5WaiIi4nB169ZlwYIFrFixAl9fX6ZOneqQcRRqIiLicAEBAaxcudLh4+j0o4iIGIZCTUREDEOhJiIihqFQExERw1CoiYiIYSjURETEMOyG2m+//UZqaiobNmxg+/btmEwmZ9QlIiIG89133xEbGwvAiRMniI6OJiYmhkmTJmGxWMpljGJD7fz580yYMIGnn36azz77jOPHj5OamsqQIUOYOHEiv/zyS7kUICIixvfWW28RHx9Pbm4uANOnT2fEiBGsXr0aq9XK1q1by2WcYj98/frrr/PUU09Rv379G9oyMzN54403mDRpUrkUISIiznF41xky0s6U6zGDQmrStG3Nm+5Tp04dFi1axNixYwH4/vvvad26NQBhYWGkpaXRuXPnMtdSbKglJCQU26lhw4YKNBERuWWPPvoop06dsr22Wq24ubkB4O3tzeXLl8tlHLuPydqzZw9Xr17FYrEwefJkRowYQbdu3cplcBERca6mbe2vqpzB3f3/X/3Kzs7Gz8+vfI5rb4fZs2dTr149EhMTWbt2LWvXri3VQBaLhYSEBKKiooiNjeXEiROF2rdt20ZkZCRRUVEkJycDkJeXx5gxY4iJiaF3797lds5VRERur2bNmrF7924AduzYwUMPPVQux7UbapUqVaJatWp4enpyzz33YDabSzXQli1bMJvNJCUlMXr0aGbMmGFry8vLY/r06axYsYLExESSkpLIyspi06ZNVK1aldWrV/PWW2857Ou/RUTEucaNG8eiRYuIiooiLy+PRx99tFyOa/f0o7e3N4MGDSImJoZVq1ZRs2bplq3p6emEhoYC0KJFCw4dOmRry8zMpE6dOvj7+wMQHBzM3r176dKlS6E36ogvlBMREeeoVauW7Uxc/fr1ee+998p9jGJD7fTp09x3330sXLiQkydPEhgYyH/+8x/69OlTqoFMJhM+Pj621x4eHuTn5+Pp6YnJZMLX19fW5u3tjclkwtvb29Z3+PDhjBgxotjjZ2RklKouo8vJydHclIErz1/T//152EXrA9eeP1enuSudYkPt7bff5vTp0wQGBvLwww9jtVpp3LhxqQfy8fEhOzvb9tpiseDp6VlkW3Z2ti3kzpw5w9ChQ4mJibnpDSpBQUGlrs3IMjIyNDdlcCfMnyvXdyfMn6vS3N1cenp6kduLDbX4+HgAjh49SmpqKitWrMDPz4/Q0FAiIiJKXEDLli1JTU0lIiKC/fv3FwrIhg0bcuLECS5evIiXlxd79+5lyJAh/PLLLwwePJiEhATatWtX4jFFROTPxe41tcDAQAIDA4HfH5n11VdflWqgzp07k5aWRr9+/bBarUybNo3Nmzdz5coVoqKiiIuLY8iQIVitViIjI6lRowZTpkzh0qVLLF68mMWLFwO/fyq9cuXKpapBRESMzc1qtVpvtsO12/j/eNfjxx9/7PDCSiI9PZ3g4ODbXYZL0imMsnHp+fvfB1e5+f/Ct5VLz5+L09zdXHF/79tdqb377rssW7bMdmeiiIiIq7Ibak2aNKFmzZq6nV5ERFye3VBr27YtnTp1onbt2rZndb377rvOqE1ERKRE7IZaUlIS8+fPL/Q5MhEREVdkN9Rq1KjBX//610IPnxQREXFFdkPNbDbTo0cPGjVqZPuagLlz5zq8MBERkZKyG2pPP/20M+oQEREpM7vnFM+dO0fr1q1p3bo19erVY9myZc6oS0REpMTsrtQ2btyIt7c3ZrOZ1157jeHDhzujLhERkRKzG2qvv/46zzzzDLm5uaxZs4aAgABn1CUiIlJixYbaqFGjbDeGVK5cmQMHDjB16lRAN4qIiIhrKjbU+vXrV+j14MGDHV6MiIhIWRQbakeOHCE6Otr2nWd/lJ+fz+rVqxkwYIBDixMRESmJYkMtKCiIf/7znwQGBtKkSRPuvvtuLl26xHfffcfRo0cZNmyYM+sUERGxq9hQe+ihh1i5ciVpaWl88803HDx4kICAADp37szEiRNt19tERERchd27H0NCQggJCXFGLSIiImWiBzqKiIhhKNRERMQw7Iba008/zZYtWygoKHBGPSIiIqVmN9TGjh3Lvn376NWrF7Nnz+b48eNOKEtERKTk7IZaw4YNGTt2LG+//Tb//e9/eeyxxxg0aBAHDx50Rn0iIiK3zO7dj9u3b2fDhg0cO3aM7t27M2HCBPLz83nqqafYtGmTM2oUERG5JXZDbdOmTURHR9OmTZtC2/XhaxERcTV2Tz/6+/sXCrSxY8cC8I9//MNxVYmIiJRCsSu1VatW8eabb/Lbb7/x2WefAWC1WgkMDHRacSIiIiVRbKg98cQTPPHEEyxZsoRnnnnGmTWJiIiUSrGhlpqaSseOHalatSpJSUmF2qKiohxemIiISEkVG2oXL14E4JdffnFWLSIiImVS7I0ijz/+OADdunWjXr16DBs2jJycHHr27Oms2kRERErE7t2P48aN45577gGgQ4cOvPTSSw4vSkREpDRu6YHG127pb9WqFRaLxaEFiYiIlJbdD1/7+fmRlJREixYtOHDgAN7e3s6oS0REpMTsrtRmzJjB0aNHmTNnDpmZmUybNs0ZdYmIiJSY3ZVaQEAAISEhVK9enfr16xMQEOCMukRERErM7kpt7ty5pKSkUKFCBTZu3MiMGTNKNZDFYiEhIYGoqChiY2M5ceJEofZt27YRGRlJVFQUycnJt9RHRETkj+yu1Pbs2cPatWsBePLJJ+nbt2+pBtqyZQtms5mkpCT279/PjBkzePPNNwHIy8tj+vTprFu3jipVqhAdHU3Hjh359ttvi+0jIiJyPbuhlp+fj8Viwd3dHavVipubW6kGSk9PJzQ0FIAWLVpw6NAhW1tmZiZ16tTB398fgODgYPbu3cv+/fuL7SMiInI9u6EWERFBdHQ0f/vb3zhw4AARERGlGshkMuHj42N77eHhQX5+Pp6enphMJnx9fW1t3t7emEymm/a5XkZGRqnqMrqcnBzNTRm48vw1/d+fh120PnDt+XN1mrvSsRtqgwcPpn379hw7dozevXvTuHHjUg3k4+NDdna27bXFYrGF0/Vt2dnZ+Pr63rTP9YKCgkpVl9FlZGRobsrgTpg/V67vTpg/V6W5u7n09PQitxcbanPnzr3hVOMPP/wAwKhRo0pcQMuWLUlNTSUiIoL9+/cXCseGDRty4sQJLl68iJeXF3v37mXIkCG4ubkV20dEROR6xYZagwYNynWgzp07k5aWRr9+/bBarUybNo3Nmzdz5coVoqKiiIuLY8iQIVitViIjI6lRo0aRfURERIpTbKhde6Bxfn4+GzZs4MyZM7Rp04ZGjRqVaiB3d3deffXVQtsaNmxo+zk8PJzw8HC7fURERIpj93NqkyZN4ueffyYtLY3s7GzGjRvnjLpERERKzG6onTx5khdeeIGKFSsSHh7O5cuXnVGXiIhIidkNtYKCAs6fP4+bmxsmkwl391t6sL+IiIjT2b2lf8SIEURHR5OVlUVUVJS+T01ERFxWsaEWExNDVFQUXbt25dNPP+X8+fPcddddpX6iiIiIiKMVey4xISGBgwcP0q1bN6ZNm8aFCxcUaCIi4tKKXak1bdqU+Ph4zGYzW7duZcaMGeTk5NC7d2969OjhzBpFRERuid27PipWrEjXrl2ZMmUKLVq0YOrUqc6oS0REpMRueqNITk4On376KR988AGXL1+md+/ebNu2zVm1iYiIlEixoTZu3Dh27dpFeHg4L774Is2aNXNmXSIiIiVWbKi1bt2aV155hcqVKzuzHhERkVIrNtQiIyOdWYeIiEiZ6fEgIiJiGHZDbfny5c6oQ0REpMzshtr27dspKChwRi0iIiJlYvfZjxcuXCA0NJRatWrh5uaGm5sba9eudUZtIiIiJWI31JYsWeKMOkRERMrMbqjl5+fzySefkJeXB8C5c+f0bdQiIuKS7F5Tu/ZN1/v27ePUqVNcvHjR0TWJiIiUit1Qq1y5Mk8//TQ1atRgxowZ/PLLL86oS0REpMTshprVaiUrK4srV65w5coVfvvtN2fUJSIiUmJ2Q23YsGF8/vnndO/enUceeYSwsDBn1CUiIlJidm8UadWqFa1atQLgkUcecXhBIiIipVVsqLVv377YTl999ZVDihERESmLYkNNwSUiIncau6cfx48ff8O26dOnO6QYERGRsrAbahEREcDvd0H+8MMPnDt3zuFFiYiIlIbdUAsNDbX9HBYWxuDBgx1akIiISGnZDbU/Xls7d+6cPnwtIiIuy26offTRR7afK1WqxLRp0xxakIiISGnZDbUxY8aQkZFBSEgI7733HnXq1HFGXSIiIiVm94kio0eP5vLlywD4+/szZswYhxclIiJSGnZD7erVq3Tp0gWAbt26cfXqVYcXJSIiUhp2Q61ChQqkpaVhMpnYuXMn7u52u4iIiNwWdq+pTZkyhZkzZzJlyhQCAwNL/QWhOTk5jBkzhl9//RVvb29mzpxJQEBAoX2Sk5NZu3Ytnp6ePPvss3Ts2JHLly8zZswYTCYTeXl5xMXF8eCDD5aqBhERMTa7obZ69WoWL15c5oHWrFlD48aNef755/noo49YvHgx8fHxtvasrCwSExNZv349ubm5xMTEEBISwttvv03btm0ZOHAgx44dY/To0WzYsKHM9YiIiPHYPZeYmZnJpUuXyjxQenq67YPcYWFh7Ny5s1D7gQMHePDBB6lYsSK+vr7UqVOHw4cPM3DgQPr16wdAQUEBlSpVKnMtIiJiTHZXapmZmbRp04aAgADc3NwA+w87fv/993nnnXcKbatWrRq+vr4AeHt72+6ovMZkMtnar+1jMpnw8/MDfl/JjRkzhgkTJhQ5ZkZGhr238qeUk5OjuSkDV56/pv/787CL1geuPX+uTnNXOnZDLTU1tcQH7dOnD3369Cm0bdiwYWRnZwOQnZ1tC6trfHx8bO3X9rkWckeOHGHUqFGMHTuW1q1bFzlmUFBQiev8M8jIyNDclMGdMH+uXN+dMH+uSnN3c+np6UVuLzbUFi9ezHPPPceoUaNsK7Rr5s6dW+ICWrZsyfbt22nevDk7duwgODi4UHvz5s2ZP38+ubm5mM1mMjMzady4MUePHuWFF15g/vz5NG3atJiji4iI3CTUwsPDAWzXs8oqOjqacePGER0dTYUKFWzB+Pbbb1OnTh0eeeQRYmNjiYmJwWq1MnLkSCpVqsTcuXMxm81MnToV+H1F9+abb5ZLTSIiYizFhlrTpk1JSkoiMjIST09P9u7dy48//kh0dHSpBqpSpQoLFy68YfugQYNsP/ft25e+ffsWaleAiYjIrSr27sdFixaRlpZGXl4eAH/5y19IS0vjjTfecFpxIiIiJVFsqO3YsYMFCxZQpUoVAGrVqsW8efPYtm2b04oTEREpiWJDzcvL64YbRCpUqIC3t7fDixIRESmNYkOtcuXK/PTTT4W2/fTTTzcEnYiIiKso9kaRF198keeee4527dpRu3Ztfv75Z7766itmzpzpzPpERERuWbErtUaNGrF69WqaNWvG1atXuf/++1mzZg3NmjVzZn0iIiK37KZPFPH19aVnz55OKkVERKRs9OVoIiJiGAo1ERExDIWaiIgYhkJNREQMQ6EmIiKGoVATERHDUKiJiIhhKNRERMQwFGoiImIYCjURETEMhZqIiBiGQk1ERAxDoSYiIoahUBMREcNQqImIiGEo1ERExDAUaiIiYhgKNRERMQyFmoiIGIZCTUREDEOhJiIihqFQExERw1CoiYiIYSjURETEMBRqIiJiGAo1ERExDIWaiIgYhtNCLScnh+eff56YmBieeuopzp8/f8M+ycnJ9OrVi759+5KamlqoLTMzk+DgYHJzc51VsoiI3GGcFmpr1qyhcePGrF69mp49e7J48eJC7VlZWSQmJrJ27VqWL1/Oa6+9htlsBsBkMjFz5kwqVqzorHJFROQO5LRQS09PJzQ0FICwsDB27txZqP3AgQM8+OCDVKxYEV9fX+rUqcPhw4exWq1MnDiRUaNGUaVKFWeVKyIidyBPRxz0/fff55133im0rVq1avj6+gLg7e3N5cuXC7WbTCZb+7V9TCYTr7/+Oh06dKBp06Y3HTMjI6OcqjeWnJwczU0ZuPL8Xfs/4rCL1geuPX+uTnNXOg4JtT59+tCnT59C24YNG0Z2djYA2dnZ+Pn5FWr38fGxtV/bx9fXl02bNvGXv/yF9evXk5WVxeDBg1m1atUNYwYFBTngndz5MjIyNDdlcCfMnyvXdyfMn6vS3N1cenp6kdsdEmpFadmyJdu3b6d58+bs2LGD4ODgQu3Nmzdn/vz55ObmYjabyczMpHHjxnz++ee2fcLDw1mxYoWzShYRkTuM00ItOjqacePGER0dTYUKFZg7dy4Ab7/9NnXq1OGRRx4hNjaWmJgYrFYrI0eOpFKlSs4qT0REDMBpoValShUWLlx4w/ZBgwbZfu7bty99+/Yt9hjbtm1zSG0iImIM+vC1iIgYhkJNREQMQ6EmIiKGoVATERHDUKiJiIhhKNRERMQwFGoiImIYCjURETEMhZqIiBiGQk1ERAxDoSYiIoahUBMREcNQqImIiGEo1ERExDAUaiIiYhgKNRERMQyFmoiIGIZCTUREDEOhJiIihqFQExERw1CoiYiIYSjURETEMBRqIiJiGAo1ERExDIWaiIgYhkJNREQMw81qtVpvdxFllZ6efrtLEBERJwsODr5hmyFCTUREBHT6UUREDEShJiIihqFQExERw/C83QVI+cnLyyMuLo7Tp0/j7u7O5MmTadiwIQCbN2/mvffeIykp6TZX6bqKmr+qVasSHx/PpUuXKCgoYNasWdSpU+d2l+qSipo/s9nMpEmT8PDwoF69ekydOhV3d/0ufT2z2cz48eP56aef8PHxISEhATc3N+Li4nBzc6NRo0ZMmjRJc3cLFGoGsn37dvLz81m7di1paWnMnz+fRYsWkZGRwbp169A9QTdX1Px5e3vTrVs3IiIi2LVrF8eOHVOoFaOo+bNYLAwdOpQOHTowevRovvjiC8LDw293qS4nOTkZLy8vkpOTOXbsGJMnT6ZChQqMGDGCNm3akJCQwNatW+ncufPtLtXlKfYNpH79+hQUFGCxWDCZTHh6enLhwgXmzJnDhAkTbnd5Lq+o+du3bx9nz55l4MCBbN68mdatW9/uMl1WUfMXFBTExYsXsVqtZGdn4+mp36OLcvToUcLCwgBo0KABmZmZfP/997b/3sLCwvj6669vZ4l3DIWagXh5eXH69Gm6du3KxIkT6d+/Py+99BITJkzA29v7dpfn8q6fv9jYWE6fPo2fnx8rV66kZs2avPXWW7e7TJdV1PxdO+XYtWtXfv31V9q0aXO7y3RJQUFBpKamYrVa2b9/P2fPnsVqteLm5gaAt7c3ly9fvs1V3hn0a5OBrFy5kvbt2zN69GjOnDnDww8/TO3atXn55ZfJzc3l6NGjTJ06lZdeeul2l+qSrp+/J598kqpVq9pOl4WHhzNv3rzbXKXrKmr+Ll++zKpVq2jUqBGrVq1ixowZTJo06XaX6nIiIyPJzMxkwIABtGzZkvvvv59z587Z2rOzs/Hz87uNFd45tFIzED8/P3x9fQHw9/fnvvvuY9OmTSQmJvLaa68RGBioQLuJ6+cvPz+fFi1asH37dgD27NlDYGDg7SzRpRU1f76+vvj4+ABQvXp1Ll26dDtLdFkHDx4kODiYxMREOnXqRO3atWnWrBm7d+8GYMeOHTz00EO3uco7g54oYiDZ2dlMmDCBrKws8vLyGDBgAN26dQPg1KlTjBo1iuTk5Ntcpesqav5atmxJfHw8V69excfHh7lz5+Lv73+7S3VJRc1fzZo1mTNnDp6enlSoUIHJkydTq1at212qyzl//jyjRo3i6tWr+Pr6MnXqVK5cucLEiRPJy8ujQYMGTJkyBQ8Pj9tdqstTqImIiGHo9KOIiBiGQk1ERAxDoSYiIoahUBMREcNQqImIiGEo1ETK0e7du2nXrh2xsbHExsbSq1cvhg8fjtlsvqX+O3bsIC4uDoBhw4aVqRaz2cyYMWOwWCyEh4eTm5tbquNkZWXx6quvlqkWEWdRqImUs7Zt25KYmEhiYiIpKSlUqFCBbdu2lfg4r7/+epnqWLlyJV27di3zk93vuecevL29+eabb8p0HBFnUKiJOJDZbObcuXP4+/tTUFDASy+9xJAhQ+jVqxfz588HIDMzk6ioKAYOHMiaNWtsfUNCQgCIjY0lMzMTgDVr1rBo0SJyc3N55pln6N+/P71797Y9eeIaq9XKpk2bCA0NLbR9zZo1DBs2DLPZTEREBAkJCURHR/PMM89w5coVcnJyGDlyJFFRUfTq1Ytvv/0WgMcee4x3333XUdMkUm707EeRcrZr1y5iY2P59ddfcXd3p2/fvrRr145Tp07RokUL+vTpQ25uLmFhYYwYMYIFCxYwfPhwQkJCWLZsGceOHbM7xsmTJ/nll19YuXIlv/76K8ePHy/Ufvz4cXx8fKhQoYJtW2JiIhkZGSxYsAAPDw9ycnLo1q0brVq1YtasWSQlJeHm5sZ9993HvHnz+M9//sPXX3/Ngw8+SGBgIPv27SvvqRIpdwo1kXLWtm1b5s2bx4ULFxg8eLDtsVBVq1bl4MGD7Nq1Cx8fH9t1th9//JHmzZsD0LJly5uG2rUHADVq1IgnnniCUaNGkZ+fT2xsbKH9Lly4wN13311o286dO/Hw8LA9asnT05NWrVrZxt2xYweA7StQGjduTOPGjQFs/SwWi76oUlya/usUcZC77rqL2bNnEx8fz7lz50hJScHX15e5c+cyePBgcnJysFqtNGjQwHaa79ChQzccp2LFimRlZQHwww8/AHDkyBGys7NZtmwZM2bMYPLkyYX6VKtW7YaHBy9evBg/Pz/bKc78/HwOHz4MQHp6OoGBgTRs2JCDBw8C8NNPPzF69Gjg9zD19PRUoInL00pNxIECAwOJjY1lypQpPP/884waNYr09HSqVKlC3bp1OXfuHJMmTWLkyJEsX76cgIAAKlWqVOgYAwYM4NVXX6VmzZpUr14dgHr16vHGG2+wceNGKlSowPDhwwv1qVu3LufPnyc/P7/QF3PGx8fTp08f2rVrB8Bbb73Fzz//zL333svIkSOxWq1MmDCB/v37U1BQYPty2SNHjtCiRQsHzpRI+dADjUUMaunSpTRo0IDOnTsX2R4eHs6///3vG0K0KLNmzSI8PFxffyIuT+cSRAzqySef5JNPPsFisZTpOFlZWZhMJgWa3BG0UhMREcPQSk1ERAxDoSYiIoahUBMREcNQqImIiGEo1ERExDD+Hz4B0TP5hFnhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.612067e+12\n",
      "24.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.355855e+12\n",
      "25.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.683481e+11\n",
      "26.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.898052e+12\n",
      "27.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.955610e+11\n",
      "28.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.425708e+13\n",
      "29.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.069555e+12\n",
      "30.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.178112e+11\n",
      "31.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n",
      "/opt/anaconda3/lib/python3.9/site-packages/astropy/units/quantity.py:486: RuntimeWarning: invalid value encountered in sqrt\n",
      "  result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.470241e+12\n",
      "32.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "redshift_d = data['z']\n",
    "impact_parameter_d = data['R']\n",
    "counter = 0;\n",
    "for mass, redshift, impact_parameter in zip(predictedM, redshift_d, impact_parameter_d): \n",
    "    for concentration in range(6,11,1): \n",
    "        cosmo = cosmology.Planck15\n",
    "        massfactor = (\"critical\", 200)\n",
    "        \n",
    "        n = NFW(mass=mass, concentration=concentration, redshift=redshift, cosmo=cosmo, massfactor=massfactor)\n",
    "        \n",
    "        radii = range(-1,3,1000) * u.kpc\n",
    "        \n",
    "        # NFW circular velocity distribution\n",
    "        n_result = n.circular_velocity(radii)\n",
    "        \n",
    "        # Plot creation\n",
    "        X = plt.plot(radii, n_result, '-', label = concentration)\n",
    "        plt.xscale('linear')\n",
    "        v = plt.axvline(x = impact_parameter, color = 'red')\n",
    "        counter = counter+1\n",
    "        \n",
    "    # Display plot\n",
    "    plt.tight_layout(rect=[0, 0.03, 1, 0.95])\n",
    "    print(\"%e\"%mass)\n",
    "    print((counter-5)/5)\n",
    "    leg = plt.legend(loc='upper right')\n",
    "    plt.xlabel(\"Radius (kpc)\")\n",
    "    plt.ylabel(\"Circular Velocity (km/s)\")\n",
    "    plt.title(\"NFW Circular Velocity Profile\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c3844d3",
   "metadata": {},
   "source": [
    "Circular Velocity Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b899e88d",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "83 134.05430348763306 km / s\n",
      "77 510.21258348149706 km / s\n",
      "112 183.43068548075482 km / s\n",
      "135 618.451524921208 km / s\n",
      "101 110.04104426428928 km / s\n",
      "83 513.2321384813996 km / s\n",
      "91 234.47085431245546 km / s\n",
      "121 230.4213140053146 km / s\n",
      "92 102.33555196284 km / s\n",
      "91 435.22941800909996 km / s\n",
      "60 119.21853483839298 km / s\n",
      "44 154.43032711839197 km / s\n",
      "23 149.4959744149872 km / s\n",
      "44 181.09407352030155 km / s\n",
      "53 159.3110992310241 km / s\n",
      "18 330.3523655693238 km / s\n",
      "154 197.2776795711477 km / s\n",
      "132 227.49075690415384 km / s\n",
      "32 185.00543166922802 km / s\n",
      "20 146.1938044781218 km / s\n",
      "93 124.30436763865931 km / s\n",
      "112 107.24392367586164 km / s\n",
      "37 236.78327050423655 km / s\n",
      "87 150.3368062665032 km / s\n",
      "35 265.06291167573903 km / s\n",
      "88 189.91927258930735 km / s\n",
      "83 163.88186723392656 km / s\n",
      "39 346.2770941360653 km / s\n",
      "47 116.13182974316351 km / s\n",
      "102 524.9985013624732 km / s\n",
      "34 180.67373358423535 km / s\n",
      "97 129.57960283661137 km / s\n",
      "46 241.937639758548 km / s\n",
      "\n",
      "[134.05430348763306, 510.21258348149706, 183.43068548075482, 618.451524921208, 110.04104426428928, 513.2321384813996, 234.47085431245546, 230.4213140053146, 102.33555196284, 435.22941800909996, 119.21853483839298, 154.43032711839197, 149.4959744149872, 181.09407352030155, 159.3110992310241, 330.3523655693238, 197.2776795711477, 227.49075690415384, 185.00543166922802, 146.1938044781218, 124.30436763865931, 107.24392367586164, 236.78327050423655, 150.3368062665032, 265.06291167573903, 189.91927258930735, 163.88186723392656, 346.2770941360653, 116.13182974316351, 524.9985013624732, 180.67373358423535, 129.57960283661137, 241.937639758548]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[<Quantity 134.05430349 km / s>, <Quantity 510.21258348 km / s>, <Quantity 183.43068548 km / s>, <Quantity 618.45152492 km / s>, <Quantity 110.04104426 km / s>, <Quantity 513.23213848 km / s>, <Quantity 234.47085431 km / s>, <Quantity 230.42131401 km / s>, <Quantity 102.33555196 km / s>, <Quantity 435.22941801 km / s>, <Quantity 119.21853484 km / s>, <Quantity 154.43032712 km / s>, <Quantity 149.49597441 km / s>, <Quantity 181.09407352 km / s>, <Quantity 159.31109923 km / s>, <Quantity 330.35236557 km / s>, <Quantity 197.27767957 km / s>, <Quantity 227.4907569 km / s>, <Quantity 185.00543167 km / s>, <Quantity 146.19380448 km / s>, <Quantity 124.30436764 km / s>, <Quantity 107.24392368 km / s>, <Quantity 236.7832705 km / s>, <Quantity 150.33680627 km / s>, <Quantity 265.06291168 km / s>, <Quantity 189.91927259 km / s>, <Quantity 163.88186723 km / s>, <Quantity 346.27709414 km / s>, <Quantity 116.13182974 km / s>, <Quantity 524.99850136 km / s>, <Quantity 180.67373358 km / s>, <Quantity 129.57960284 km / s>, <Quantity 241.93763976 km / s>]\n"
     ]
    }
   ],
   "source": [
    "graph_vals = []\n",
    "redshift_d = data['z']\n",
    "impact_parameter_d = data['R']\n",
    "velocity_vals = [134.05430348763306, 510.21258348149706, 183.43068548075482, 618.451524921208, 110.04104426428928, 513.2321384813996, 234.47085431245546, 230.4213140053146, 102.33555196284, 435.22941800909996, 119.21853483839298, 154.43032711839197, 149.4959744149872, 181.09407352030155, 159.3110992310241, 330.3523655693238, 197.2776795711477, 227.49075690415384, 185.00543166922802, 146.1938044781218, 124.30436763865931, 107.24392367586164, 236.78327050423655, 150.3368062665032, 265.06291167573903, 189.91927258930735, 163.88186723392656, 346.2770941360653, 116.13182974316351, 524.9985013624732, 180.67373358423535, 129.57960283661137, 241.937639758548]\n",
    "for mass, redshift, impact_parameter in zip(predictedM, redshift_d, impact_parameter_d):\n",
    "    cosmo = cosmology.Planck15\n",
    "    massfactor = (\"critical\", 200)\n",
    "        \n",
    "    n = NFW(mass=mass, concentration=10, redshift=redshift, cosmo=cosmo, massfactor=massfactor)\n",
    "\n",
    "    radii = range(1,300,10) * u.kpc\n",
    "\n",
    "    # NFW circular velocity distribution\n",
    "    n_result = n.circular_velocity(impact_parameter)\n",
    "\n",
    "    # Plot creation\n",
    "    plt.scatter(impact_parameter, n_result)\n",
    "    print(impact_parameter, n_result)\n",
    "    graph_vals.append(n_result)\n",
    "\n",
    "# Display plot\n",
    "plt.tight_layout(rect=[0, 0.03, 1, 0.95])\n",
    "plt.xlabel(\"Impact Parameter\")\n",
    "plt.ylabel(\"Circular Velocity (km/s)\")\n",
    "plt.title(\"NFW Circular Velocity Profile\")\n",
    "print()\n",
    "print(velocity_vals)\n",
    "plt.show()\n",
    "print(graph_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "14d97375",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[517811173014.0411, 24257077952194.38, 1355854919822.7415, 40584559456616.19, 337406010890.65454, 24257077952194.38, 2470240705666.254, 2470240705666.254, 260100695898.87378, 14598775553950.787, 337406010890.65454, 606985501810.7432, 606985501810.7432, 1069554502462.7122, 719756703787.5809, 14598775553950.787, 1787414276899.6643, 2470240705666.254, 1069554502462.7122, 606985501810.7432, 445825511476.55164, 337406010890.65454, 2470240705666.254, 719756703787.5809, 3612066818361.2085, 1355854919822.7415, 868348122047.7374, 8898051796489.426, 295560957415.6108, 24257077952194.38, 1069554502462.7122, 517811173014.0411, 2470240705666.254]\n"
     ]
    }
   ],
   "source": [
    "print(predictedM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6e0f87f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#PG. 20 has the sfr / Use this for Data for Explain why question is important"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1fc4867a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "11.714171417141714\n",
      "13.384838483848384\n",
      "12.132213221322132\n",
      "13.608360836083609\n",
      "11.528152815281528\n",
      "13.384838483848384\n",
      "12.392739273927393\n",
      "12.392739273927393\n",
      "11.415141514151415\n",
      "13.164316431643165\n",
      "11.528152815281528\n",
      "11.783178317831783\n",
      "11.783178317831783\n",
      "12.029202920292029\n",
      "11.857185718571857\n",
      "13.164316431643165\n",
      "12.252225222522252\n",
      "12.392739273927393\n",
      "12.029202920292029\n",
      "11.783178317831783\n",
      "11.64916491649165\n",
      "11.528152815281528\n",
      "12.392739273927393\n",
      "11.857185718571857\n",
      "12.557755775577558\n",
      "12.132213221322132\n",
      "11.938693869386938\n",
      "12.94929492949295\n",
      "11.47064706470647\n",
      "13.384838483848384\n",
      "12.029202920292029\n",
      "11.714171417141714\n",
      "12.392739273927393\n"
     ]
    }
   ],
   "source": [
    "for item in predictedM: \n",
    "    print(np.log10(item))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2eb538ce",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e01d26f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1c328fdd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e78cb490",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9850d55",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "634f8bf2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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