Plot_SMS_mound_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "561a49da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Critical density today [MSun/pc**3]  1.275588996364624e-07\n",
      "Critical density at z = 15 0.00016177490369340906  [Msun/pc**3]\n",
      "Virial radius at z = 15 903.628836641711  [pc]\n"
     ]
    }
   ],
   "source": [
    "#%%\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from copy import copy\n",
    "import os\n",
    "\n",
    "from tqdm import tqdm\n",
    "#os.chdir('/Users/daniele/Dropbox/Fisica/2023/EvolvingDensities-main/')\n",
    "\n",
    "from scipy.interpolate import interp1d, UnivariateSpline, interpn\n",
    "from matplotlib.colors import LogNorm, Normalize\n",
    "from mpl_toolkits.axes_grid1.axes_divider import make_axes_locatable\n",
    "from astropy.cosmology import Planck18\n",
    "from evolving_densities import Density, smooth_Bspline\n",
    "from polytropic import PolytropicSolver\n",
    "from colourmap_maker import lch_colour_map, luv_colour_map\n",
    "\n",
    "from timeit import default_timer as timer\n",
    "\n",
    "rgb_palette = np.array([[255, 97, 229], [241, 0, 123], \n",
    "                        [151, 0, 71], [54, 3, 27], \n",
    "                        [179, 126, 12], [255, 190, 11], \n",
    "                        [250, 237, 185], [86, 235, 215],\n",
    "                        [0, 128, 117], [0, 59, 59]], dtype = np.float32)/255\n",
    "\n",
    "rgb_palette_dict = {'purple pizzazz': rgb_palette[0], 'flickr pink': rgb_palette[1],\n",
    "                    'jazzberry jam': rgb_palette[2], 'dark sienna': rgb_palette[3],\n",
    "                    'dark goldenrod': rgb_palette[4], 'amber': rgb_palette[5],\n",
    "                    'blond': rgb_palette[6], 'turquiose': rgb_palette[7],\n",
    "                    'pine green': rgb_palette[8], 'rich black': rgb_palette[9]}\n",
    "\n",
    "#%%\n",
    "import sys\n",
    "from importlib import reload\n",
    "reload(sys.modules['evolving_densities'])\n",
    "from evolving_densities import Density\n",
    "\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": False\n",
    "})\n",
    "\n",
    "#%%\n",
    "\n",
    "G_N = 4.302e-3 #Units of (pc/solar mass) (km/s)^2\n",
    "c_light = 2.9979e05 #km/s\n",
    "G_N_Mpc = 1e-6*4.302e-3 #(Mpc/solar mass) (km/s)^2\n",
    "\n",
    "r_array = np.geomspace(1e-10, 1e3, num = 1301)\n",
    "\n",
    "h = 0.678\n",
    "Omega_DM = 0.1186/(h**2)\n",
    "H0 = 100.0*h #(km/s) Mpc^-1\n",
    "H0_peryr = 67.8*(3.24e-20)*(60*60*24*365)\n",
    "ageUniverse = 13.799e9 #y\n",
    "Omega_L = 0.692\n",
    "Omega_m = 0.308\n",
    "Omega_r = 9.3e-5\n",
    "\n",
    "z_eq = 3375.0\n",
    "rho_eq = 1512.0 #Solar masses per pc^3\n",
    "sigma_eq = 0.005 #Variance of DM density perturbations at equality\n",
    "lambda_max = 3.0 #Maximum value of lambda = 3.0*z_dec/z_eq (i.e. binaries decouple all the way up to z_dec = z_eq)\n",
    "\n",
    "def Hubble(z):\n",
    "    return H0_peryr*np.sqrt(Omega_L + Omega_m*(1+z)**3 + Omega_r*(1+z)**4)\n",
    "\n",
    "def Hubble2(z):\n",
    "    return H0*np.sqrt(Omega_L + Omega_m*(1+z)**3 + Omega_r*(1+z)**4)\n",
    "\n",
    "rho_critical_today_Mpc = 3.0*H0**2/(8.0*np.pi*G_N_Mpc) #Solar masses per Mpc^3\n",
    "rho_critical_today = rho_critical_today_Mpc / 1.e18\n",
    "\n",
    "def rho_critical_Mpc(z):\n",
    "    return 3.0*Hubble2(z)**2/(8*np.pi*G_N_Mpc) #Solar masses per pc^3\n",
    "\n",
    "def rho_critical(z):\n",
    "    return 3.0*Hubble2(z)**2/(8*np.pi*G_N_Mpc*1.e18) #Solar masses per pc^3\n",
    "\n",
    "print(\"Critical density today [MSun/pc**3] \", rho_critical(0))\n",
    "\n",
    "M_halo = 1.E8\n",
    "z = 15\n",
    "## Concentration\n",
    "c = 3. #https://arxiv.org/pdf/1502.00391.pdf Fig. 7\n",
    "\n",
    "#R_vir = 1E3 #0.784*(Planck18.Om0/Planck18.Om(15))**(-1/3) * (M_halo*1E-8*Planck18.h)**(1/3) * (10/(z + 1)) / Planck18.h *1E3\n",
    "## Virial radius in pc\n",
    "R_vir = (3.*M_halo/(4.*np.pi*200.*rho_critical(z)))**(1./3)  #pc\n",
    "\n",
    "print(\"Critical density at z = 15\", rho_critical(z), \" [Msun/pc**3]\")\n",
    "print(\"Virial radius at z = 15\", R_vir, \" [pc]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9377a84f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r_poly: 4.446341891734883e-06\n",
      "> Creating Density objects...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/zr/f2d9jr713t9f5hjyf3917rrm0000gn/T/ipykernel_69688/589720592.py:17: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  return rho_0_prime * (R_s/r) / (1 + r/R_s)**2 * np.exp(-r/R_vir)\n",
      "/var/folders/zr/f2d9jr713t9f5hjyf3917rrm0000gn/T/ipykernel_69688/589720592.py:17: RuntimeWarning: divide by zero encountered in scalar divide\n",
      "  return rho_0_prime * (R_s/r) / (1 + r/R_s)**2 * np.exp(-r/R_vir)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "> ...Done.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+9wtI9ZmHrAn7oBGA+W81wBcdakEQgJ+P30D/5SeQkqmTunQiIrIQBiSiRwQ7FTRTgmF3ekj20ACZemSNDkOa/yIY/76DjwOr48c+jWGrkuPg5fvotfgI7iTx5G0iopKIAYkoF3ntcrAN6w+b1T0hlLWFMeou0posRuZXu9CmigvWD2wGV3s1LtxNQbeFh3HhbrLUJRMRkZkxIBHlQRAEKN/xg935oVC8URcwGKGdfABpDb5H7X+Ssfnjl1HNzQ53kzPRa9ERHLp8X+qSiYqFwMBADBs2LN/zX7t2DYIgIDIy0qzthoeHQxAEJCYm5nsZqS1fvhzOzs4WX09x7BtLYEAiegZZOXvYrn8TNr++DcHDHsYL95De/Ae4zTmMTQOaokkVF6Rk6RHy03Fs+fuW1OUSWb1ff/21QDeO9fT0xJ07d1C3bl0AT//yLmi7RM/DgESUD8puPrA//ymU7/oCRhHa8eFQBC3D8pbV0MW3AvRGEcPWR+LHv65KXSqRVXNxcYGDg0O+55fL5fDw8IBC8ex7Ixa0XaLnYUAiyiehjA1sVvWCzbregLMGxhO3oG+8CNOTdejf3BsAMGF7NCbtiIbRWOrvAU2Up9yHwry9vTFp0iT0798fDg4O8PLywg8//GD6/L+H2K5du4bWrVsDAMqUKQNBENC3b9882121ahUaN24MBwcHeHh44O2330Z8fHyBar1w4QJatGgBjUYDHx8f7NmzB4IgYMuWLaZ5vvzyS9SsWRO2traoWrUqRo8eDZ3u3ytco6Ki0Lp1azg4OMDR0RGNGjXCyZMnn7rOxMREfPjhh3B3d4dGo0HdunWxbdu2p86/aNEiVKtWDSqVCrVq1cKqVavy7Lv/ti8IAsLDw03TduzYgZo1a8LGxgatW7fGtWvXCtRPJRVvV05UQMre9SBv7oWMkE0w7L0K7Udb8XmXl+D2USNMPXAVPxy4inspWZjWsz6Ucv4NQkVDFEWk66QZesJWqYQgCC+8/MyZMzF+/Hh89dVX2LhxIwYNGoRWrVqhVq1aOebz9PTEpk2b0KNHD8TExMDR0RE2NjZ5tqnT6TB+/HjUqlUL8fHxCA0NRd++fbFjx4581WQwGNC1a1d4eXnh2LFjSElJweeff/7EfA4ODli+fDkqVKiAM2fOYMCAAXBwcMAXX3wBAHjnnXfQoEEDLFq0CHK5HJGRkVAqlXmu02g0omPHjkhJScHq1atRrVo1nD9/HnK5PM/5N2/ejE8//RRz5sxBUFAQtm3bhn79+qFSpUqmIPk8N2/eRPfu3TF48GAMHDgQJ0+ezHM7SyMGJKIXIKvkBNvdfaGdcwRZo3bB8PsFvHvqNlxntMfI07ex+e9beJCmxaJ3GsJOzV8zsrx0nQ72k7+RZN2poybATqV64eU7deqEjz/+GED2HpnZs2dj3759TwQkuVwOFxcXAEC5cuWeecJy//79Ta+rVq2KefPmwd/fH6mpqbC3t39uTbt378aVK1cQHh4ODw8PAMDEiRPRrl27HPN9882/fe7t7Y3hw4dj3bp1poB048YNjBgxAi+99BIAoEaNGk9d5549e3D8+HFER0ejZs2aptqfZsaMGejbt6+p70JDQ3H06FHMmDEj3wHp8R6omTNnAgBq1aqFM2fOYOrUqflaviTjn7dEL0iQyaAObQ67E4Mgq+UK8VYygt/9FYs0atgo5Thw8R7eXnIUD1KzpC6VyKrVr1/f9FoQBHh4eBT4cFhuERER6NKlC7y8vODg4IBWrVoByA4s+RETEwNPT09TOAKAJk2aPDHf+vXr0bx5c3h4eMDe3h7ffPNNjnWEhobigw8+QFBQEKZMmYIrV648dZ2RkZGoVKmSKRw9T3R0NJo3b55jWvPmzREdHZ2v5R+3ERAQkGNas2bN8r18ScY/bYkKSV7fA3YnByFz0FboVkeh6dh9+KlbbXxc3xVR/ySh5+IjWNm/CTxdbKUulUowW6USqaMmSLbuwsh9yEkQBBiNL347n7S0NAQHByM4OBhr1qyBm5sbbty4geDgYGi12kLV+l9HjhzBO++8g2+//RbBwcFwcnLCunXrTHtjAGDcuHF4++23sX37dvzxxx8YO3Ys1q1bh27duj3R3tMOF74omSx7H4go/ntOpE6iw7DFEfcgEZmBYK+GZmVPaJZ2A2yUqLM5GivWnUdFGyVi76eh+6LDOH+bA0qS5QiCADuVSpJHYc4/KijVo0N5BoPhqfNcuHABDx48wJQpU/DKK6/gpZdeKvAeqVq1auHmzZuIi4szTTtx4kSOeQ4fPozKlSvj66+/RuPGjVGjRg1cv/7kDa1r1qyJzz77DLt27UL37t2xbNmyPNdZv359/PPPP7h48WK+aqxduzYOHTqUY9qhQ4fg4+MDAHBzcwMA3Llzx/R57vGkateujePHj+eYdvTo0Xytv6RjQCIyE0EQoOrfCHbHP4Ksthu8Yx5gxcyjqCmT4V5KFnr/7wiOXHkgdZlExVrlypUhCAK2bduGe/fuITU19Yl5vLy8oFKpMH/+fFy9ehVbt24t8BhJ7dq1Q7Vq1RASEoLTp0/j0KFDpvONHgfCGjVq4MaNG1i3bh2uXLmCefPmYfPmzaY2MjIyMGTIEISHh+P69es4dOgQTpw4gdq1a+e5zlatWqFly5bo0aMHdu/ejdjYWPzxxx/YuXNnnvOPGDECy5cvx6JFi3Dp0iXMmjULv/76K4YPHw4ge49U06ZNMWXKFERHR2P//v05zpkCgI8++giXLl3CiBEjEBMTg7Vr12L58uUF6quSigGJyMzkdd1hd2IQlCENUC5Fi59mHUXjdL1pQMkdZ+48vxEiylPFihXx7bffYuTIkXB3d8eQIUOemMfNzQ3Lly/Hhg0b4OPjgylTpmDGjBkFWo9cLseWLVuQmpoKf39/fPDBB/j6668BABqNBgDw2muv4bPPPsOQIUPg5+eHw4cPY/To0TnaePDgAfr06YOaNWvijTfeQMeOHfHtt98+db2bNm2Cv78/3nrrLfj4+OCLL7546t6yrl27Yu7cuZgxYwbq1KmD//3vf1i2bBkCAwNN8/z000/Q6/Vo1KgRhg0bhgkTch6G9fLywqZNm7Blyxb4+vpi8eLFmDRpUoH6qqQSxP8enCylkpOT4eTkhKSkJDg6OkpdDpUQoihCt+QkModsQ5bRiFFv18WeCvYQBODb1+qgTzNvqUukYiwzMxOxsbGoUqWK6QubLOvQoUNo0aIFLl++jGrVqkldTqnxrJ91S35/cw8SkYUIggDVQH/YHvgAGg8HTF99Br3O3oMoAmN+O4cZf8aAf58QWa/Nmzdj9+7duHbtGvbs2YOBAweiefPmDEelBAMSkYUpmnrCLuJjqF7xxjfbL2PwX9mXAC/YdxkjN52B3vDiV+sQkeWkpKRg8ODBeOmll9C3b1/4+/vjt99+k7osKiK8zJ+oCMjc7WG7px+yvvwTH84+jLJpOkwIror1J2/iQZoW899qABtV3qPlEpE0+vTpgz59+khdBkmEe5CIioiglEMzqxNs1vZCz0sJmLU5BiqDEXui4/Du0mNITDff+CxERFQ4DEhERUz5li/sjnyItjoR/1t3Hg6ZekRcT0CvxUdwOzFD6vKIiAgMSESSkNf3gN3xQWhStSyWrzmLcilZuBSfih6LDuNiXIrU5RERlXoMSEQSkbnZwXZ3X/j0qItVq86iyoN03EnKRK9Fh3Hy2kOpyyMiKtUYkIgkJKgU0Cx6DVUmt8eKn6NR/1YKkjL1eGfJMew+H/f8BoiIyCIYkIgkJggCVIObosJv72DJzqtoeTkBWQYjPlx5EuuO5+/O40REZF4MSERWQtG2GtyOfIi50Q/Q9XQ8jABG/noG88MucUBJokf69u2Lrl27mt4HBgZi2LBhktWTX8Wlzv/y9vbGnDlzLL4ea+0bBiQiKyKrXhbOhz/EREGO94/8AwCYufsiRv92FgYjQxIRUVFhQCKyMoKTBrZb38WIxl4YuTsWgihi9dEbGLI6Apm6vG9aSURE5sWARGSFBLkMmpkd0X9AE0zbdhkKgxF/nI9D3x+OIjlTJ3V5RC/MaDRi2rRpqF69OtRqNby8vDBx4kTT52fOnEGbNm1gY2ODsmXLYuDAgUhNTc13+6tWrULjxo3h4OAADw8PvP3224iPjzd9Hh4eDkEQsH37dtSvXx8ajQZNmzbF2bNnTfNcv34dXbp0QZkyZWBnZ4c6depgx44dps/Pnj2Ljh07wt7eHu7u7njvvfdw//590+dpaWno06cP7O3tUb58ecycOTNftU+YMAHlypWDg4MDPvjgA4wcORJ+fn6mz0+cOIF27drB1dUVTk5OaNWqFU6dOmX6XBRFjBs3Dl5eXlCr1ahQoQKGDh36zHX+/vvv8Pf3h0ajgaurK7p16/bUeW/cuIHXX38d9vb2cHR0xBtvvIG4uH8vJsl9+BMAhg0bhsDAwEL3jRQYkIismOqjJug261V8v+0K7LL0OHozEb3nHUR8cqbUpZGVEUURmaJRkkdBzpEbNWoUpkyZgtGjR+P8+fNYu3Yt3N3dAWR/eQYHB6NMmTI4ceIENmzYgD179mDIkCH5bl+n02H8+PGIiorCli1bcO3aNfTt2/eJ+UaMGIGZM2fixIkTcHNzQ5cuXaDTZf/xMXjwYGRlZeHAgQM4c+YMpk6dCnt7ewBAYmIi2rRpgwYNGuDkyZPYuXMn4uLi8MYbb+Roe//+/fjtt9+wa9cuhIeH5wgyeVmzZg0mTpyIqVOnIiIiAl5eXli0aFGOeVJSUhASEoKDBw/i6NGjqFGjBjp16oSUlOyx0zZt2oTZs2fjf//7Hy5duoQtW7agXr16T13n9u3b0a1bN3Tq1Al///03wsLC0KRJkzznNRqNeP311/Hw4UPs378fu3fvxtWrV9G7d+9nblduL9I3UuG92IisnCK4BtpueAvL3v0Fg1pUQjSA7rMPYOXHL6Oqm73U5ZGVyIKIkAcXJVn3irI1oYHw3PlSUlIwd+5cLFiwACEhIQCAatWqoUWLFgCAtWvXIjMzEytXroSdnR0AYMGCBejSpQumTp1qClLP0r9/f9PrqlWrYt68efD390dqaqop5ADA2LFj0a5du+z6V6xApUqVsHnzZrzxxhu4ceMGevToYQoXVatWNS23YMECNGjQAJMmTTJN++mnn+Dp6YmLFy+iQoUKWLp0KVavXo22bdvmaP9Z5s+fj/fffx/9+vUDAIwZMwa7du3KsfesTZs2OZb54Ycf4OzsjP3796Nz5864ceMGPDw8EBQUBKVSCS8vr6cGHgCYOHEi3nzzTXz77bemab6+vnnOGxYWhjNnziA2Nhaenp4AgJUrV6JOnTo4ceIE/P39n7l9AJCamvpCfSMV7kEiKgbkdd3ReGdfrD5zH54JmfgnQ4cec/5C1M1EqUsjyrfo6GhkZWWZvhzz+tzX19cUjgCgefPmMBqNiImJydc6IiIi0KVLF3h5ecHBwQGtWrUCkH146L+aNWtmeu3i4oJatWohOjoaADB06FBMmDABzZs3x9ixY3H69GnTvFFRUdi3bx/s7e1Nj5deegkAcOXKFVy5cgVarRYBAQFPtP8sMTExT4SZ3O/j4uIwYMAA1KhRA05OTnB0dERqaqpp23r16oWMjAxUrVoVAwYMwObNm6HX65+6zsjIyKf+W+QWHR0NT09PUzgCAB8fHzg7O5v67XletG+kwj1IRMWEzMMBL/0RgjX9f8WHWXpEe9jjrYWH8H0/fwTWKid1eSQxNQSsKFtTsnXnh42NjUXreHyILjg4GGvWrIGbmxtu3LiB4OBgaLX5vxn0Bx98gODgYGzfvh27du3C5MmTMXPmTHzyySdITU017dHKrXz58rh8+bI5NymHkJAQPHjwAHPnzkXlypWhVqvRrFkz07Z5enoiJiYGe/bswe7du/Hxxx9j+vTp2L9/P5RK5RPtmfvfQyaTPXG49fFhy+KIe5CIihHBVgXPtW9glYczml5LRDqAD346jl+PXZe6NJKYIAjQCDJJHoKQv4BUo0YN2NjYICwsLM/Pa9eujaioKKSlpZmmHTp0CDKZLF97GS5cuIAHDx5gypQpeOWVV/DSSy/lOEH7v44ePWp6nZCQgIsXL6J27dqmaZ6envjoo4/w66+/4vPPP8eSJUsAAA0bNsS5c+fg7e2N6tWr53jY2dmhWrVqUCqVOHbs2BPtP0utWrVw4sSJHNNyvz906BCGDh2KTp06oU6dOlCr1TlODgeyQ0+XLl0wb948hIeH48iRIzhz5kye66xfv/5T/y1yq127Nm7evImbN2+app0/fx6JiYnw8fEBALi5ueHOnTs5louMjDS9ftG+kQoDElExI8hkcJ0SjB+DaqJj9H3oBQGhm8/ihz8uSF0a0TNpNBp8+eWX+OKLL7By5UpcuXIFR48exdKlSwEA77zzDjQaDUJCQnD27Fns27cPn3zyCd577718nX/k5eUFlUqF+fPn4+rVq9i6dSvGjx+f57zfffcdwsLCcPbsWfTt2xeurq6mK7CGDRuGP//8E7GxsTh16hT27dtnCk+DBw/Gw4cP8dZbb+HEiRO4cuUK/vzzT/Tr1w8GgwH29vZ4//33MWLECOzdu9fUvkz27K/bTz75BEuXLsWKFStw6dIlTJgwAadPn84RPmvUqIFVq1YhOjoax44dwzvvvJNjL9Dy5cuxdOlSnD17FlevXsXq1athY2ODypUr57nOsWPH4ueff8bYsWMRHR1tOiE9L0FBQahXrx7eeecdnDp1CsePH0efPn3QqlUrNG7cGED2OVInT57EypUrcenSJYwdOzbH1YEv2jdSsc6qiOi57D/wx9yhzfHu6ey/kCftv4IJa07ByAElyYqNHj0an3/+OcaMGYPatWujd+/epr08tra2+PPPP/Hw4UP4+/ujZ8+eaNu2LRYsWJCvtt3c3LB8+XJs2LABPj4+mDJlCmbMmJHnvFOmTMGnn36KRo0a4e7du/j999+hUqkAAAaDAYMHD0bt2rXRoUMH1KxZE99//z0AoEKFCjh06BAMBgPat2+PevXqYdiwYXB2djZ90U+fPh2vvPIKunTpgqCgILRo0QKNGjV6Zu3vvPMORo0aheHDh6Nhw4aIjY1F3759odFoTPMsXboUCQkJaNiwId577z0MHToU5cr9e3jd2dkZS5YsQfPmzVG/fn3s2bMHv//+O8qWLZvnOgMDA7FhwwZs3boVfn5+aNOmDY4fP57nvIIg4LfffkOZMmXQsmVLBAUFoWrVqli/fr1pnuDgYIwePRpffPEF/P39kZKSgj59+uRo50X6RiqCyHsYIDk5GU5OTkhKSoKjo6PU5RAViP5cHBZ+vh2z/bL/wu7qWQbTP2oKpZx//5RkmZmZiI2NRZUqVXJ8idKzhYeHo3Xr1khISICzs7PU5TxTu3bt4OHhgVWrVkldiqSe9bNuye9v/g9KVMwp6rjjk2W9MPHMPciNIrbcTED/6eFIy3r61StEZF3S09Mxa9YsnDt3DhcuXMDYsWOxZ88e03AIVPQYkIhKAFl5B7y9/i0svJYMjdaAvxIz8ObEPXiQmiV1aUSUD4IgYMeOHWjZsiUaNWqE33//HZs2bUJQUJDUpZVaPMQGHmKjkkPUGXBs6O/4SAkk2ipRWQRWjWgFL1cOKFnS8BAblRY8xEZEhSYo5Qj4/nX87OqA8klZuC4A3afsw7nrD6UujYioWGFAIiphBEFA7TFt8UtjL9S4l477Chl6zz+EI1G3pS6NiKjYKBEBKSYmBn5+fqaHjY0NtmzZInVZRJLyfL8x1vesj0a3UpCqkKHP6lPYtveS1GURERULJeJWI7Vq1TKN1pmamgpvb2/TTQiJSjOXjrWwysMBn0zfjzAvR3zyZwwe3E9HyBt535CSiIiylYg9SP+1detWtG3bNsfNDolKM9sGFbB4Skf0upEMURAw9tQ/mPb9kSfumURERP+yioB04MABdOnSBRUqVIAgCHkeHlu4cCG8vb2h0WgQEBDw1NE+f/nlF/Tu3dvCFRMVL0ovZ0z9visG30oFAHx/4yG+mLwPeoNR4sqIiKyTVQSktLQ0+Pr6YuHChXl+vn79eoSGhmLs2LE4deoUfH19ERwc/MRNCJOTk3H48GF06tSpKMomKlZkzjYYvrQHxiVpITOK2JCcgYHf/IkMLQeUJCLKzSoCUseOHTFhwgR069Ytz89nzZqFAQMGoF+/fvDx8cHixYtha2uLn376Kcd8v/32G9q3b//cMUGysrKQnJyc40FUGggqBUK+74q5KiVUeiP2ika8M/IPJCRlSF0aUYF4e3ujfv368PPzQ+vWraUuh0ogqwhIz6LVahEREZFjNFGZTIagoCAcOXIkx7z5Pbw2efJkODk5mR6enp5mr5vIWgmCgC4TgrGsclk4ZOpxSiVDz7G7cPsO/1Cg4uXw4cOIjIzEvn37pC6FSiCrD0j379+HwWCAu7t7junu7u64e/eu6X1SUhKOHz+O4ODg57Y5atQoJCUlmR43b940e91E1q75Jy/j56beKJeqxRWNAt2n7kPMhfjnL0hEVApYfUDKLycnJ8TFxUGlUj13XrVaDUdHxxwPotKo7pu+2NC9PrwTM3FXo0CvH47ixOHrUpdFJZw5LswRBAGtWrWCv78/1qxZ88TyrVq1giAImDRpUo7poigiICAAgiDgu+++M9s23bt3D4MGDYKXlxfUajU8PDwQHByMQ4cOAQD69u0LQRDw0UcfPbHs4MGDIQgC+vbtm+/2yPKsPiC5urpCLpcjLi4ux/S4uDh4eHhIVBVRyVG5TTVsGNQM9e9nIFklx3u/nsau389LXRaVYOa4MOfgwYOIiIjA1q1bMWnSJJw+fdr0mSiK+Pvvv1G5cmWcOXMmR9srVqzA7dvZo8o3bNjQbNvUo0cP/P3331ixYgUuXryIrVu3IjAwEA8ePDDN4+npiXXr1iEj499z/jIzM7F27Vp4eXkVuD2yMNHKABA3b96cY1qTJk3EIUOGmN4bDAaxYsWK4uTJk82yzqSkJBGAmJSUZJb2iIqjlOsJ4rv9fhErf7lNrDrid3HtshNSl0TPkJGRIZ4/f17MyMiQupRCedr/+YMHDza9NxgMYoUKFZ76f/7w4cPFZcuWmd7HxMSIAMQxY8aIderUMU1PTk4WPTw8xG+++UYEIN6+fdss25CQkCACEMPDw586T0hIiPj666+LdevWFVevXm2avmbNGrF+/fri66+/LoaEhOS7vdLkWT/rlvz+too9SKmpqYiMjDSNhh0bG4vIyEjcuHEDABAaGoolS5ZgxYoViI6OxqBBg5CWloZ+/fpJWDVRyWLv5YylM1/F6/czYJAJGHUhDnNn/cUBJalI5efCnLS0NKSkpADI/v7Yu3cv6tSpY5o/IiICtra2eOuttxATEwOtVgsAGD9+PBo3bgw3Nzd4eHigfPnyZqnZ3t4e9vb22LJlC7Kysp45b//+/bFs2TLT+59++umJ77KCtEeWYxUB6eTJk2jQoAEaNGgAIDsQNWjQAGPGjAEA9O7dGzNmzMCYMWPg5+eHyMhI7Ny584kTt4mocFRlbDF74ev4ICn7C2V2fDLGjNsDAweUtHqiKEJM00rzMGOIzs+FOXFxcWjRogV8fX3RtGlT9OnTB/7+/qZ5T506hfr166NWrVrQaDS4cOECLl26hEWLFmHWrFk4deqUWQ+vKRQKLF++HCtWrICzszOaN2+Or776Ksdhv8feffddHDx4ENevX8f169dx6NAhvPvuuy/cHlmOVdyLLTAw8Lm/YEOGDMGQIUOKqCKi0kumVuLrha+j3Jc7MUkuYlWWFve//AOzJ7WHRqWUujx6mnQdUuzNd9JxQTikjgHsnn+BjLlUrVoVUVFRT/38cQASBAH169fHmTNn8PPPP2PQoEGoUaMGIiIinjru3ovq0aMHXn31Vfz11184evQo/vjjD0ybNg0//vhjjpOv3dzc8Oqrr2L58uUQRRGvvvoqXF1dX7g9shyr2INERNZFkMkwcHonzHKyhcJgxB8KIGTEDiQnckBJsixzXJjz3z1Efn5+mDNnDk6ePInRo0cjMzMTFy5ceOoepC1btqBz585o3749li5dWqDaNRoN2rVrh9GjR+Pw4cPo27cvxo4d+8R8/fv3N+0h6t+/f6HbI8uwij1IRGSduo9qDZclx/Fx9F0cs1HgjdF/YuWXgShXyVnq0ig3W2X2nhyJ1m0uKpUKjRo1QlhYGLp27QoAMBqNCAsLy9dRhKtXryIxMdEUgBo0aIDvv/8eP/30ExwcHHDs2DHo9Xo0atToiWXXrFmD7du3Y9GiRVCr1Zg6dSomTpyIr7/++oW2xcfHJ88hDDp06ACtVgtBEPI1dt/z2iPLYEAiomcKHNAEa7ecQ/+9l3DBTonu08Kx4sNmqFaH5wBaE0EQivQwV2Gkpqbi8uXLpvePL8xxcXGBl5cXQkNDERISgsaNG6NJkyaYM2dOvi/MiYiIgEqlQt26dQEAISEh6Nq1K8qWLQsge++Sm5tbnndQ+OGHH7Bnzx4oldmBb+bMmWjXrh2GDh0KBweHp67zwYMH6NWrF/r374/69evDwcEBJ0+exLRp0/D6668/Mb9cLkd0dLTpdWHbI8tgQCKi5/LrWgcbXe3Q5+e/8Y+DCr2WHMXSHvXR4JUqUpdGxdDJkydz3D8tNDQUQHaYWb58OXr37o179+5hzJgxuHv3Lvz8/PJ9Yc6pU6dQt25dU8hRKpU5zvE5deqU6YKg/3rw4AG8vLygVCrx448/4uDBg1i+fDkCAgJw8eLFPPc4PWZvb4+AgADMnj0bV65cgU6ng6enJwYMGICvvvoqz2WeNUDxi7RH5ieIvIYXycnJcHJyQlJSEkfVJnqGuPNx6DvvIKKdNbDRGfB9i6po3a2u1GWVSpmZmYiNjUWVKlWee4Nuej6j0Yj27dtjz549SEpKQnp6OsqXL49evXph4cKFKFeunNQlllrP+lm35Pc3T9Imonxz93HHujHt0DQhExlKOQYcjsWmH48/f0EiKyeTyfDyyy9j1qxZcHJyQvny5fHLL7/Azs6O4aiUYkAiogJxquCI5dNfRcckLfRyGT6/fA//mxoudVlEhTZmzBjEx8fD19cXfn5+2L1791Nvh0IlHw+xgYfYiF6EQavHuC92YJUm+yTT9wUZvpoQDLmcf3cVBR5io9KCh9iIqFiRqxT4dlZnfK7MvtZjqWjEZ59vgzZTJ3FlRESFx4BERC9MJpPhk/HBmFLOEXKjiK0aOd7/fBvSEjigJBEVbwxIRFRob4a+gkV1ykOjM+AvBxXe/PoP3L+eIHVZREQvjAGJiMyifUgjrGpbE06ZepxxVKPntHDciLotdVlERC+EAYmIzMa/00v45a0G8EjT4ZqDCj2WHse5fVekLouIqMAYkIjIrGoFeOHXoS1QI0WLe7ZKvLn1LA5tPCN1WUREBcKARERmV6GGKzaMCUKjZC1S1Ar0O3oN2/53TOqyiIjyjQGJiCzC2d0Bq6d1Qts0HbQKGT65eg/LJ++TuiwionxhQCIii7GxV2PxzM54QydCFASMS0rHtJF/wGg0Sl0aEdEzMSARkUUpVQpMmd4JQ1TZd1f/HkaM/GwbdFkcUJKIrBcDEhFZnEwmw/Dv2uNbNwcIoohfbOT46LNtyEjigJJEZJ0YkIioyIR83hLza3tApTcizFGFd0b+gYRbSVKXRcWQt7c36tevDz8/P7Ru3VrqcqgEYkAioiLVuW9jLGtZDfZaA045qfHGxDDcPh8ndVlUDB0+fBiRkZHYt48n/5P5MSARUZFr/poP1veoD7d0HS45qtF90WHEHLomdVlEkgkMDMSwYcOkLoP+gwGJiCRRp7k3Nn3YFN6pWty1U+GNDVE4/vt5qcuiInDgwAF06dIFFSpUgCAI2LJlyxPzLFy4EN7e3tBoNAgICMDx48dzfC4IAlq1agV/f3+sWbPmieVbtWoFQRAwadKkHNNFUURAQAAEQcB3331ntm3q27cvBEGAIAhQqVSoXr06vvvuO+j1erOtIzeGKstiQCIiyXjV8cCmka1RL0WLJI0CfcIvY9fyCKnLIgtLS0uDr68vFi5cmOfn69evR2hoKMaOHYtTp07B19cXwcHBiI+PN81z8OBBREREYOvWrZg0aRJOnz5t+kwURfz999+oXLkyzpzJOYr7ihUrcPt29j0CGzZsaNbt6tChA+7cuYNLly7h888/x7hx4zB9+nSzrqOgtFqtpOsvzhiQiEhSZSs5Y93EDnglRYdMpRyDzt/BzzMPSF0WWVDHjh0xYcIEdOvWLc/PZ82ahQEDBqBfv37w8fHB4sWLYWtri59++sk0T8WKFQEA5cuXR6dOnXDq1CnTZ5cuXUJKSgpCQkJyBKSUlBSMGjUKffv2BQA0atTIrNulVqvh4eGBypUrY9CgQQgKCsLWrVsBAFlZWRg6dCjKlSsHjUaDFi1a4MSJE3m2s3LlSpQtWxZZWVk5pnft2hXvvfcegOw9Vvv378fcuXNNe66uXbuGwMBADBkyBMOGDYOrqyuCg4Pztf7Hyw0ZMgROTk5wdXXF6NGjIYqiaR6j0YjJkyejSpUqsLGxga+vLzZu3GjWPrQmDEhEJDk7ZxssnfUqXs80wCATMOpeCuaP3sUBJUshrVaLiIgIBAUFmabJZDIEBQXhyJEjALL3QKWkpAAAUlNTsXfvXtSpU8c0f0REBGxtbfHWW28hJibGtBdl/PjxaNy4Mdzc3ODh4YHy5ctbdFtsbGxM6/7iiy+wadMmrFixAqdOnUL16tURHByMhw8fPrFcr169YDAYTOEKAOLj47F9+3b0798fADB37lw0a9YMAwYMwJ07d3Dnzh14enoCyN5LplKpcOjQISxevDjf61+xYgUUCgWOHz+OuXPnYtasWfjxxx9Nn0+ePBkrV67E4sWLce7cOXz22Wd49913sX//fvN3nhVQSF0AEREAqNRKzJ7VGW7f7MKPRgNm6nSIH74D46Z2hFwpl7o8qyeKIjJ0BknWbaOUQxAEs7R1//59GAwGuLu755ju7u6OCxcuAADi4uJMe58MBgMGDBgAf39/07ynTp1C/fr1UatWLWg0Gly4cAE2NjZYtGgRTp06hYkTJ5r98Np/iaKIsLAw/Pnnn/jkk0+QlpaGRYsWYfny5ejYsSMAYMmSJdi9ezeWLl2KESNG5FjexsYGb7/9NpYtW4ZevXoBAFavXg0vLy8EBgYCAJycnKBSqWBrawsPD48cy9eoUQPTpk0zvc/v+j09PTF79mwIgoBatWrhzJkzmD17NgYMGICsrCxMmjQJe/bsQbNmzQAAVatWxcGDB/G///0PrVq1Mn9HSowBiYishkwmwzeTOsBtyj5MTkzHKpWA+8N+x+ypHaGxV0tdnlXL0BngM+ZPSdZ9/rtg2KqK7uukatWqiIqKeurnp06dQsOGDSEIAurXr48zZ87g559/xqBBg1CjRg1EREQ89fBeYWzbtg329vbQ6XQwGo14++23MW7cOFy5cgU6nQ7Nmzc3zatUKtGkSRNER0fn2dbj0Hfr1i1UrFgRy5cvN50I/jy5Dx3md/1NmzbN0X6zZs0wc+ZMGAwGXL58Genp6WjXrl2OtrVaLRo0aPDcmoojBiQisjofjmwN1/8dw5eX4/GHgxIJI7bjh2/bw7GcvdSlkYW5urpCLpcjLi7n2FhxcXFP7Cl5mlOnTuHtt98GAPj5+WHOnDm4efMmfv75Z2RmZuLChQtP3YO0ZcsW/Pjjj9Bqtejduzfef//9fNfeunVrLFq0CCqVChUqVIBC8eJfsQ0aNICvry9WrlyJ9u3b49y5c9i+fXu+lrWzs3vh9T5NamoqAGD79u2m878eU6tL5h8vDEhEZJV6fBgAlw2n8fHRazjqpEbvsbuw/POWcK/uKnVpVslGKcf574IlW7e5qFQqNGrUCGFhYejatSuA7JODw8LCMGTIkOcuf/XqVSQmJpoCUIMGDfD999/jp59+goODA44dOwa9Xp/nCdpr1qzB9u3bsWjRIqjVakydOhUTJ07E119/na/a7ezsUL169SemV6tWzXROUOXKlQEAOp0OJ06ceOZl+h988AHmzJmDW7duISgoyHSO0WMqlQoGw/MPq+Z3/ceOHcux3NGjR1GjRg3I5XL4+PhArVbjxo0bJfJwWl4YkIjIarXuVR9ry9ri/d/OIdpJjR5z/sKKvv6o1riS1KVZHUEQivQwV2Gkpqbi8uXLpvexsbGIjIyEi4sLvLy8EBoaipCQEDRu3BhNmjTBnDlzkJaWhn79+j237YiICKhUKtStWxcAEBISgq5du6Js2bIAsvcuubm5PRE2AOCHH37Anj17oFRm31h55syZaNeuHYYOHQoHB4cX3l47OzsMGjQII0aMMG3jtGnTkJ6e/sw9VG+//TaGDx+OJUuWYOXKlU987u3tjWPHjuHatWuwt7eHi4tLodZ/48YNhIaG4sMPP8SpU6cwf/58zJw5EwDg4OCA4cOH47PPPoPRaESLFi2QlJSEQ4cOwdHRESEhIS/cP9aqePw2EVGp1aBNdWxwsUHI0uP4x16FXqtOYtmDdPgG15S6NHpBJ0+ezHH/tNDQUADZYWb58uXo3bs37t27hzFjxuDu3bvw8/PDzp07nzhxOy+nTp1C3bp1TSFHqVTC1dU1x+d5nTPz4MEDeHl5QalU4scff8TBgwexfPlyBAQE4OLFi4UeEmDKlCkwGo147733kJKSgsaNG+PPP/9EmTJlnrqMk5MTevToge3bt5v2pv3X8OHDERISAh8fH2RkZCA2NrZQ6+/Tpw8yMjLQpEkTyOVyfPrppxg4cKDp8/Hjx8PNzQ2TJ0/G1atX4ezsjIYNG+Krr756sU6xcoL430EOSqnk5GQ4OTkhKSkJjo6OUpdDRHmIu/YQIdP344KDCrZaAxY19kKrt/2kLksymZmZiI2NRZUqVaDRaKQup9gzGo1o37499uzZg6SkJKSnp6N8+fLo1asXFi5ciHLlyklSV9u2bVGnTh3MmzfPousJDAw0na9lbZ71s27J72+Og0RExYK7twt++a49AlK0SFfJ8f7fN/HrgsNSl0UlhEwmw8svv4xZs2bByckJ5cuXxy+//AI7OztJwlFCQgI2b96M8PBwDB48uMjXTwxIRFSMOJa1w4rpr6JDuh56uQyh/yTgh/FhUpdFJcSYMWMQHx8PX19f+Pn5Yffu3U+9HYqlNWjQAH379sXUqVNRq1YtSWoo7XiIDTzERlTcGPQGjP1qJ1Y/+hNvgAEYNaUDZPLSM6AkD7FRacFDbERE+SRXyDF+aieE2maPv7JEDoQO2wZtBm/MSUTmwYBERMWSIAgYOiYIkyo4Q24UscVOgQ9CtyHtYbrUpRFRCcCARETF2ttDm2NR/QrQ6Iw44KTGW1/vxP3rCVKXRUTFHAMSERV77d9tiFVBNeGYpcdpJzV6TQvHzag7UpdFRMUYAxIRlQj+HWvhlzcbwD1dh1gHFXr8eAznw69KXRYRFVMMSERUYrwU4IVfh7RA9RQt4u2U6P3bGRzedFbqsiyKFyJTSSfVzzgDEhGVKBVrumLj6CA0SNEiRa1A3yOx2P7DcanLMrvHt9JIT+dJ6VSyPf4Zf/wzX1Q4DhI4DhJRSZSRkomPv9qJfXZKyIwixrnYo8/IQKnLMqs7d+4gMTER5cqVg62tLQRBkLokIrMRRRHp6emIj4+Hs7Mzypcv/8Q8lvz+ZkACAxJRSaXT6jFq5E5sVGUHhyEyOUIntIdMVjJ2nouiiLt37yIxMVHqUogsxtnZGR4eHnn+AcCAZGEMSEQll9FoxIyxu/G9Tg8A6J1hwMTpnaBQKSSuzHwMBgN0Op3UZRCZnVKphPwZI+QzIFkYAxJRybds5gF8F58MURAQlKzFgikdoHG0kbosIioE3mqEiKiQ+n3eEnNruUOpN2KPowrvfPkHkm4nSV0WEVkpBiQiKjVe6++PZS2qwj7LgAgnNXpOCMOdC3FSl0VEVogBiYhKlRZd62Bd93pwzdDhkqMa3RcexsXD16Qui4isDAMSEZU6dV+pgk0DmqJyqhZ37FR445conNx+QeqyiMiKMCARUalUua4HNn7ZGnWTtUjUKPDu3ovYsyJC6rKIyEowIBFRqeXm6Yx1k4LRIkWLTKUcH567g3Wz/5K6LCKyAgxIRFSq2Tvb4qdZndEl0wCDTMDIuGQsGLMLRqNR6tKISEIMSERU6qnUSsyZ2Rn9hez/EmdodRg3fAcMOoPElRGRVBiQiIgAyOUyjJncEV8+GjxypUrA0GG/IytNK3FlRCQFBiQiov8Y9FUbzPAuC4XBiO0OSvQdvg0p8alSl0VERYwBiYgol54fNcUP/l6w0RlwxEmN3mN3If7KA6nLIqIixIBERJSHNm/4Ym3H2iiTqcd5JzV6zDqAqxH/SF0WERURBiQioqdoEFQDG/o0RsU0LW46qNBz5Umc3n1R6rKIqAgwIBERPUP1hhWx6bOWqJWixUMbJd764wL+WhcldVlEZGElJiB5e3ujfv368PPzQ+vWraUuh4hKEI+qZfHLuPbwT9EiTSVHv4gb2LLwsNRlEZEFlZiABACHDx9GZGQk9u3bJ3UpRFTCOLnZYdX0V9E+XQ+9XIbPbjzEjxP2Sl0WEVlIiQpIRESWpLFV4ftZnfG2ARAFARNSMzDpix0wGjigJFFJYxUB6cCBA+jSpQsqVKgAQRCwZcuWJ+ZZuHAhvL29odFoEBAQgOPHj+f4XBAEtGrVCv7+/lizZk0RVU5EpY1CIceEqR0xzEYNAPhBJmL4sG3QZeokroyIzMkqAlJaWhp8fX2xcOHCPD9fv349QkNDMXbsWJw6dQq+vr4IDg5GfHy8aZ6DBw8iIiICW7duxaRJk3D69OmiKp+IShmZTIZhY4MwobwTZEYRv9op8MFn25CekC51aURkJoIoiqLURfyXIAjYvHkzunbtapoWEBAAf39/LFiwAABgNBrh6emJTz75BCNHjnyijREjRqBOnTro27dvnuvIyspCVlaW6X1ycjI8PT2RlJQER0dHs24PEZVsO1edwqdRt5ClkME3KQs/jWqDsl7OUpdFVCokJyfDycnJIt/fVrEH6Vm0Wi0iIiIQFBRkmiaTyRAUFIQjR44AyN4DlZKSAgBITU3F3r17UadOnae2OXnyZDg5OZkenp6elt0IIiqxOrzXECvb1IBjph5RTmr0nLIXN0/fkbosIiokqw9I9+/fh8FggLu7e47p7u7uuHv3LgAgLi4OLVq0gK+vL5o2bYo+ffrA39//qW2OGjUKSUlJpsfNmzctug1EVLIFdHoJ69/0g3uaDrGOavRYcgzn91+VuiwiKgSF1AWYQ9WqVREVlf+B29RqNdRqtQUrIqLSpnbTythUxhZ95h3EVQcVem85gyUP09G0W12pSyOiF2D1e5BcXV0hl8sRFxeXY3pcXBw8PDwkqoqI6EmVarlh0zdt4ZesRYpagZBDsfhjyfHnL0hEVsfqA5JKpUKjRo0QFhZmmmY0GhEWFoZmzZpJWBkR0ZPKlHfE2ikdEZiqQ5ZChsGX4rFq2n6pyyKiArKKgJSamorIyEhERkYCAGJjYxEZGYkbN24AAEJDQ7FkyRKsWLEC0dHRGDRoENLS0tCvXz8JqyYiyputowZLZnVG9ywjjDIBox+mYtbXO2E0GqUujYjyySou8w8PD8/z/mkhISFYvnw5AGDBggWYPn067t69Cz8/P8ybNw8BAQFmWb8lLxMkotLLaDRi2pjdWKzXAwDezDRgwrROUKhKxOmfRJKz5Pe3VQQkqTEgEZElLZ2+HxPup0AUBLRP1mLe1I7QOGikLouo2CvV4yARERV3749ohbk13KHUG7HLUYX3vtiBpLspUpdFRM/AgEREVARe+8AfPzWvAjutASec1Oj13W7cuRD//AWJSBIMSEREReSVbnWx7vW6cE3X4aKjGj0WHMKlo9elLouI8sCARERUhOq1qopNAwLglarFbXsVeq2LRMT2C1KXRUS5MCARERWxyvXKY+OIQNRJ1iJRo8A7ey8ibOUpqcsiov9gQCIikkC5ymWwfmIwmqdokamU48Mzt/DLnINSl0VEjzAgERFJxL6MLX6a0RldMgzQy2X44m4Svh+7Gxx9hUh6DEhERBJS2ygxZ1Zn9H303/G0LC2+Hb4dBr1B4sqISjcGJCIiicnlMoyb0hFfONgAAJYrBXw67HdkpWklroyo9GJAIiKyEh9/3QbTvVygMBixzV6JfsO3IeVeqtRlEZVKDEhERFak18fN8L9GXtDoDDjspMabY3Yh/uoDqcsiKnUYkIiIrEzbN32xtsNLKJOpxzknNXrOPIBrp25JXRZRqcKARERkhRq2q4kN7zVChTQdbjio0GP5CZzZc0nqsohKDQYkIiIrVb1RJWwa9gpqpmjxwFaJN3dE46/1p6Uui6hUYEAiIrJi5auVxYax7eCfokWaSo7+J65j6/dHpC6LqMRjQCIisnJO5eyxamontE/TQ6eQ4dPrD7B04l6pyyIq0RiQiIiKAY29Gt/P7oy39IAoCBifkoEpX+6A0WiUujSiEokBiYiomFAo5Jg4rSOGalQAgMWCiBHDfocuUydxZUQlDwMSEVExIpPJEDquHcZ7OEFmFLHJVoGBoduQnpghdWlEJQoDEhFRMfTesBZYUKc81Hoj9jmq8PaoP/DwZqLUZRGVGAUKSLt27UJ8fLylaiEiogLoFNIIKwKrwyFLj0gnNXpO3ot/zt6VuiyiEkEQRVHM78y2trbIysqCu7s7/Pz80KBBA7Rr1w6BgYEWLNHykpOT4eTkhKSkJDg6OkpdDhFRgZw/fA1910Ui3lYJ9zQdlvfyRe2WVaQui8jiLPn9XaA9SCkpKYiKisL06dNRt25dHDt2DB06dEDr1q2RlpZm1sKIiCh/fF72xqZBzVAlRYs4OyV6/3oax7ack7osomKtQHuQ4uPjUa5cuSemde/eHS1atMCUKVPMXmBR4B4kIioJHt5ORr8JYYhyVEGtN2JubQ90eN9f6rKILMaS398FCkgymQweHh7w9fU1Pfz8/JCWloZOnToV2/OTGJCIqKRIT87Ex1/tRLi9EjKjiPFuDnhnRCupyyKyCKsJSFeuXEFUVBROnz6NqKgoREVF4dq1a1CpVNDpdHjrrbcQEBAAPz8/vPLKK2Yt1JIYkIioJNFl6fDlyJ34VZ19FsUwhQJDv2sHmYwXLlPJYjUBKS/JycnYt28funXrhrfeegsxMTE4f/480tPTzVWjxTEgEVFJYzQaMWX0LvxgMAAA3s404Lvpr0KhlEtcGZH5WE1AcnFxgZ+fn+nwWr169WBvb49Zs2Zh7969uHTpEgDAYDBALi8+v4QMSERUUv04bT8mPkiBKAhon6LFvCmdoHFQS10WkVlYTUDasmWL6dBaZGQkrl27BiD78v9ffvkFnTp1MmtxRYUBiYhKst+WHMfnF+Ogl8vgn5SFH8e2g5OHg9RlERWa1QSk3FJSUnDnzh1UrFgRdnZ25qyrSDEgEVFJd2DTGQw6FIs0lRy1krKw4rOW8KjpKnVZRIViNeMg5ebg4ICaNWsW63BERFQatOxRDz+/VhdlM3SIcVKjx7y/cPn4TanLIrJavKSBiKiUqB9YFZveD4Bnqha37FXoteYUTv0RI3VZRFaJAYmIqBTxrl8eG4cHwidFiwQbBd7ZHYO9q09JXRaR1WFAIiIqZdy9y2D9+GA0S9EiQyXHwKhb2Dj3kNRlEVkVBiQiolLIwcUWy2d0xqvpeujlMgy/k4hF43ajkEPjEZUYDEhERKWU2kaJebM6I0QUAABTM7UYP3wHDHqDxJURSY8BiYioFJMr5Bg3pSOG22sAAD8pgWHDfoc2XStxZUTSYkAiIirlBEHAkG/aYppnGciNIn63V6Lf59uQej9V6tKIJMOAREREAIA3Br+MHxpUgkZnwCEnNd4cvQv3Yh9KXRaRJBiQiIjIpO1bfljT/iU4Z+px1kmNnjP24/rft6Qui6jIMSAREVEOjYJrYsM7DVE+TYfrDir0WHYCZ/delrosoiLFgERERE+o4e+JXz9tgRopWty3VeLN38/j4C+npS6LqMgwIBERUZ7KV3fFxrFBaJysRapajn7Hr2Pr4qNSl0VUJBiQiIjoqZzKOWD1tE4IStNBp5Dh09j7+GnSXqnLIrI4BiQiInomjb0ai2d3QW+dCFEQ8F1yBqaN/ANGo1Hq0ogshgGJiIieS6GQY/L0TvhErQQAfA8jvhz2O3SZOokrI7IMBiQiIsoXmUyGz79tj+/KOUJmFLHBVoGBoduQkZghdWlEZseAREREBdIn9BXM9/GASm/EPkcV3hn5BxJuJUldFpFZMSAREVGBvdq3MZa3qg6HLANOOavRa2IYbp27K3VZRGbDgERERC/k5S61sb5nfZRL1+Gyoxo9Fh9BzMFYqcsiMgsGJCIiemE+zb2x6aNmqJKqxV07FXptPI3jv52XuiyiQmNAIiKiQvH0ccfGka1RP1mLZI0CfQ5cxs5lJ6Uui6hQGJCIiKjQylZyxs+TO6Blqg6ZSjkGR9/FzzMOSF0W0QtjQCIiIrOwc7LBjzNfRddMAwwyAaPup2DuN39yQEkqlhiQiIjIbFRqJWbN6owBMjkAYLZejzGfb4dBZ5C4MqKCYUAiIiKzkslk+HpSB3ztbAcAWK2WYfCwrchMzZK4MqL8Y0AiIiKLGDAyELOrukJhMGKngwohI7YjOS5F6rKI8oUBiYiILKbbwAAsDfCGrdaAY05qvDFuN+Iu3Ze6LKLnYkAiIiKLatWzHtZ2qQOXDB0uOKnRfe5fuHLiptRlET0TAxIREVmcX+tq2NSvCSqlanHLXoVeqyPw984YqcsieioGJCIiKhJV/Cpg0/BA1E7R4qGNEm/visG+NX9LXRZRngRRFEWpiyisxMREBAUFQa/XQ6/X49NPP8WAAQPyvXxycjKcnJzQskxNKAT5C9UgCMILLZe97AsvWugGClN3YZcv7LpL63YXavFivd38WSv4soVatcW2Wy7TINXvXZzzzD6Bu+2hA3iQcDTfyxdm3flZViaXQyZ79CyXQy6T/ftanvO1IJNBLpdD9mh6Xq8VSiWUahVUKhWUajVUalX2e3Ue71XZ723sbGHrYAdbB3vY2tvB1sEOSpXqhberpHr8/Z2UlARHR0eztl0iApLBYEBWVhZsbW2RlpaGunXr4uTJkyhbtmy+ln/cwY1k5SEXuFONiMjS5DIVynX8HJG1vQEALfb+hUsRq4HChroSTKlS/Sc02cLO0RHOri5wdi0D57IucCxbJvt9WRc4u7rAxd0VbhU9oFKrpS7dYiwZkBRmbU0icrkctra2AICsrCyIoogXyX0rTv4BB3uHgi1UiHhZmGxaHJdFMaz5RZct1J8dxWxbC7tsadveF162BP5fYzQYsXb9TWx0tMXBNq/g7YYN0estLwhymWQ/U0ajEUaD8dGzAQaDEUaj4dFrQ/Zn/339aD6jwfho2pOv9TodtFla6LK00Gqzsp8fv8/SQpeVZXqv0+mgzcxERloG0lNSkZGahqzM7PGjdFotkh5okfQgoUDbVKacK9w9K8C9Unm4e1ZAuYrlUam6NyrXrIZK1b1LdIAqDKvYg3TgwAFMnz4dERERuHPnDjZv3oyuXbvmmGfhwoWYPn067t69C19fX8yfPx9NmjQxfZ6YmIhWrVrh0qVLmD59OgYPHpzv9VsygRIR0dOJoogFE/ZiZlomAOD1VB2mT+8ElQ0PJz2m1+mQnpqG9JS0R8+pSE9JQ2pyMpIeJCDpfgIS7z9E4oOHSLz/EEn3HyLxQQIe3IkzhaunkclkKO/tCa+aVeFdqzpq+tVBrQZ1Ufml6lAorH8fSok/xPbHH3/g0KFDaNSoEbp37/5EQFq/fj369OmDxYsXIyAgAHPmzMGGDRsQExODcuXK5WgrLi4O3bt3x6+//gp3d/d8rZ8BiYhIWuvmH8LXNxNgkAl4JSkLiyd0gF1ZW6nLKtZEUUTSgwTE3byNuH9uI/6fO9mvb97CzUuxuH7xKtKS8x64U22jQY36PnipUT3Uf9kfDVs2hVsFjyLegucr8QHpvwRBeCIgBQQEwN/fHwsWLACQvQvU09MTn3zyCUaOHPlEGx9//DHatGmDnj175rmOrKwsZGX9m6qTk5Ph6enJgEREJKHda/7GJ6f+QaZShnpJWVg2sjVcK5eRuqwSSxRFPIy7h+sxV3D94hXERl/Cxb/PIubvs0hPTXti/krVKqNBy6ZoFPgymgW3hrOriwRV51SqA5JWq4WtrS02btyYIzSFhIQgMTERv/32G+Li4mBrawsHBwckJSWhefPm+Pnnn1GvXr081zFu3Dh8++23T0xnQCIiktbJnTF4f+cFJGkU8E7OwsqBAfDyqyh1WaWK0WjEP5evIfrUaZw/Hom/Dx7DpchzMBqNpnkEQUDdgIZo3qktXunSDtXqvlT4q0VfQKkOSLdv30bFihVx+PBhNGvWzDTfF198gf379+PYsWM4fvw4Bg4caDo5e/Dgwfjwww+fug7uQSIisl4xx28iZFUE7top4Zauw/Ju9VCndTWpyyrVUpOScfrwSZzafwRHd+/HpajzOT6v4lMT7Xu/jvZvvo5K1byLrC4GpOcEpMLiOUhERNbl9qX7CJnzFy45qOCQpcfi5lXRvGfeRwWo6MXdvI1Df+zFoe17cGz3Aei0WtNndfz90HXAO2j/ZldobG0sWoclv7+tftAfV1dXyOVyxMXF5ZgeFxcHDw/rO2GMiIgKr0INV2wYHYRGyVqkqBXod/Qatv2v8H8Qk3m4e1ZA94HvYuZvy/HH7b/xzY8z0SSoJWQyGc6diMTEgSPwqmcjzPxsDGKjL0ld7gux+oCkUqnQqFEjhIWFmaYZjUaEhYXl2KNEREQli7OHA1ZP7Yi2qTpoFTJ8cvUeVkzZJ3VZlIuDsxO69O2N+TvXYtuNkxgy+StUrFoZqUnJ+GX+T3izXmuEvhaCqEMnpC61QKwiIKWmpiIyMhKRkZEAgNjYWERGRuLGjRsAgNDQUCxZsgQrVqxAdHQ0Bg0ahLS0NPTr10/CqomIyNJsHDRYPKsz3tCJEAUBYxPTMX3kHzlOGCbrUdajHN4b8TE2XvgLc7evRsvXgiGTyXBoRxgGtuqGDwN74Oif4YUbCLSIWMU5SOHh4WjduvUT00NCQrB8+XIAwIIFC0wDRfr5+WHevHkICAgwy/p5DhIRkXUzGo2YNXY3Fuj0AIA3MgyYNL0TFCrrH8ywtLtx6SpWz1iE7Ss3Qq/TAQAatmyKwZO/Qt2AhoVqu1SdpC0FBiQiouJhxcwDGBefDFEQ0DZZiwWTO8DGybInApN5xP1zG2tn/YBf/7cK2kdXkrfu3gkfTxgJr5pVX6hNBiQLY0AiIio+ti07idBzd6BVyNAoKQtLv2kL54pOUpdF+XT3xi0s+W4WdqzcAKPRCIVSifeGD0LfUZ8U+Kq3Un0VGxER0X917tcYy16pBnutARFOavSaGIbb5+OevyBZBQ+vihj940ysPrULzTq0hl6nw7LJ8/Bm/TY4uG2P1OWZMCAREVGx0/x1H6zvXg9u6TpcclSjx/eHcfHQNanLogKoVvclzP59JaZuXAJ3zwq4c+0mPu/aF1+9+RES7z+UujwGJCIiKp7qtKiCTR82hXeqFnfsVei1IQonfj///AXJagiCgMCuHbH+bDj6jPgYcoUCYRu34S3ftvjr992S1saARERExZZXHQ9sGtka9ZK1SNIo8F74ZexaHiF1WVRANna2GDz5Kyw9tBVVfGriYdw9DO/WD+M/+DzPG+cWBQYkIiIq1spWcsa6SR3wSooWmUo5Bp2/g3UzD0hdFr2A2o3qY8XxHXgn9EMIgoBty9ejX9NXceXshSKvhQGJiIiKPTtnGyyd1RmvZxpgkAkYeS8F80fv4oCSxZBao8HQaaOxaO9GuFX0wLULl9GvWWfsWLWxSOtgQCIiohJBpVZi9qzO+EDI/mqbqdNh7OfbYdAZJK6MXkSDVwKw6uSfCGjXClkZmfi23zBM+nBEjhvjWhIDEhERlRgymQzfTO6IUU62AIBVahk+GfY7MlOzJK6MXkQZt7KYvW0lBoz9HIIg4LelP+OT4LeK5Co3BiQiIipxPhzVGjO9y0JhMGKHgxJ9R2xHcnyq1GXRC5DL5fhg9GeY/ftK2Dk64O+/jqH/y10QG33JoutlQCIiohKpx0dNscS/Mmx0Bhx1UqP32F2Iu3xf6rLoBTXr0Bo/HvwNFap44dbV6/igxes4ufeQxdbHW42AtxohIirJ/g67jPe3nsNDGwU8U7RY0c8fVRtXkrosekEJ9x7gix4f4PThExDlMpzQ3uStRoiIiAqqQdvq2NC3MSqlaXHTQYWeq04i6s+LUpdFL6iMW1ks3L0O7d98HUa93mLrYUAiIqISr1qDitgU2govpWjx0EaJt/68gP1rI6Uui16QSq3GtyvnY8iUry22DgYkIiIqFdyruOCXb9sjIFmLdJUc7/99E78uOCx1WfSCZDIZun/4nuXat1jLREREVsbR1Q4rZryKDul66OUyhP6TgB/Gh0ldFlkhBiQiIipVNLYqLJzVGe8+Gj9yUlomJo7YDqOBA0rSvxiQiIio1JEr5Bg/rRNCbdUAgCVy4PNh26DNKJpRmsn6MSAREVGpJAgCho4JwqQKzpAbRWy2U+CD0G1Ie5AudWlkBRiQiIioVHt7aHMsql8BGp0BB5zUeOubnXhwPUHqskhiDEhERFTqtX+3IVa2rQnHTD1OO6nRc+o+3Dx9R+qySEIMSERERACadHoJv7zVAO7pOsQ6qtFjyTGcD78qdVkkEQYkIiKiR14K8MKvg5ujeooW8XZK9P7tDI78elbqskgCDEhERET/UbGWGzaObosGyVqkqBUIORyLHUuOS10WFTEGJCIiolycPRyxdmpHtE7VQauQYcileKycEi51WVSEGJCIiIjyYOOgwQ+zOqOn1gijTMCYxDTM/GonjEaj1KVREWBAIiIiegqlSoFpM17Fx0oFAGC+0YBRn22DXmu5u8iTdWBAIiIiegaZTIYvxgdjrKs9BFHEehs5Bg37HZnJGVKXRhbEgERERJQP/Ya3wtya7lDqjdjtqMK7X/6BpNtJUpdFFsKARERElE+vve+PZS2qwj7LgJNOavScEIY7F+KkLossgAGJiIioAFp0rYN13evBNUOHS45q9FhwGJcOX5e6LDIzBiQiIqICqvtKFWwa0BSVU7W4ba9Cr18icXJbtNRlkRkxIBEREb2AynU9sPHL1qibrEWiRoF3913CnhURUpdFZsKARERE9ILcPJ2xblIwWqRokamU48Nzd7B+9l9Sl0VmwIBERERUCPbOtvhpZmd0yTDAIBPwZVwyFo7dxQElizkGJCIiokJSaZSYM6sz+j/6Wp2epcO3w3fAoDNIXBm9KAYkIiIiM5DLZRgzpSO+dLQBAKxQCRg67HdkpWklroxeBAMSERGRGQ36qg1mVC4LhcGI7Q5K9Bu+DSnxqVKXRQXEgERERGRmPQc1xQ+NvWCjM+Cwkxq9x+5C/JUHUpdFBcCAREREZAFtevtibcfaKJOpx3knNXrOOoDYiH+kLovyiQGJiIjIQhoE1cCG9xqhYpoWNxxU6LniJE7vvih1WZQPDEhEREQWVL1RJWwa1hK1UrR4YKvEW39cwF/roqQui56DAYmIiMjCPKqVxS/j2sM/RYs0lRz9Im7gt4WHpS6LnoEBiYiIqAg4udlh1fRX0T5dD71chmE3HuLHCWFSl0VPwYBERERURDS2Knw/qzPeNgCiIGBCaiYmfbEDRgMHlLQ2DEhERERFSKGQY8LUjhhmowYA/CATMXzYNugydRJXRv/FgERERFTEZDIZho0NwgQPJ8iMIn61U+CDz7YhPSFd6tLoEQYkIiIiibw7rAW+r1cBar0R+51UeOurnXhwI1HqsggMSERERJLq8F5DrGxdA46ZekQ5qdFryl78c+aO1GWVegxIREREEgt49SWs7+0H9zQdrjqq0f2HY4g+cFXqsko1BiQiIiIrULtZZWwa3BxVU7SIt1Pijc1ncHTzWanLKrUYkIiIiKxEpZfcsOmbtvBL1iJFrUDIoVjs/PG41GWVSgxIREREVqRMeUesndIRgak6ZClk+PhiPFZP2y91WaUOAxIREZGVsXXUYMmszuieZYRRJuCbh6mY9dVOGI1GqUsrNRiQiIiIrJBSpcCMma/iI4UCADDPaMDXodug1+olrqx0YEAiIiKyUjKZDCMnBGN0WXsIooifNXJ8POx3ZKZkSl1aiceAREREZOXeH9EKc2u4Q6k3YpejCu99sQNJd5KlLqtEY0AiIiIqBl77wB8/Na8CO60BJ5zU6PXdHty5EC91WSUWAxIREVEx8Uq3ulj3el24putw0UmNHgsO4fLRG1KXVSIxIBERERUj9VpVxaYBAfBK1eK2vQq9fv4bEdsvSF1WiVNiAlK3bt1QpkwZ9OzZU+pSiIiILKpyvfLYOCIQdZK1SLBR4J29FxG28pTUZZUoJSYgffrpp1i5cqXUZRARERWJcpXLYP3EYDRP0SJTKceHZ27hlzkHpS6rxCgxASkwMBAODg5Sl0FERFRk7MvY4qcZndElwwC9XIYv7ibh+7G7IYqi1KUVe1YRkA4cOIAuXbqgQoUKEAQBW7ZseWKehQsXwtvbGxqNBgEBATh+nPemISIiUtsoMWdWZ/R99JU+LUuLb4dvh0FvkLiy4k0hdQEAkJaWBl9fX/Tv3x/du3d/4vP169cjNDQUixcvRkBAAObMmYPg4GDExMSgXLlyZqvjoUEHvUFntvYEQcj/vGZba8HbM/+6S+t2F2DeAvxsmH3dZl1zwdosyM+GOdctPH6Yud+JrIVcLsO4KR1RbuJeTEvJwHKlgPvDfsfMqZ2gtlNJXV6xJIhWth9OEARs3rwZXbt2NU0LCAiAv78/FixYAAAwGo3w9PTEJ598gpEjR5rmCw8Px4IFC7Bx48ZnriMrKwtZWVmm98nJyfD09ES3qyegdLA37wYRkdWQAZBDyH4WhH/fCwLkAGR49CwIpvkefyaHALkgQAkBStOzzPRaJQhQPJqmymM+lSBAI8igFmTQCDJo8O97OYMbmdGG749gVOx96OUyvJyUhR/Gt4e9a8n8bktOToaTkxOSkpLg6Oho1ratYg/Ss2i1WkRERGDUqFGmaTKZDEFBQThy5MgLtTl58mR8++23T0yXP3qYQ0FSp7kTqlUlXiIrYgRgfPwb8t+/DSX+pVE+CksaQfg3QD16qAUZbE0POewEGWxl8jynqSFwLxmh18fN4LIuCoNPXMdhJzV6j96FZSNaoVzVslKXVqxYfUC6f/8+DAYD3N3dc0x3d3fHhQv/jvsQFBSEqKgopKWloVKlStiwYQOaNWuWZ5ujRo1CaGio6f3jPUhLy9Y0ewItKfK7o9ES3zP5bdMy6y6l210M/r0LMq+I7GBkEEVTSDIAj95nvzaKj54fzff4tfE/8+kB6EQjdKIIHUToRBFaiNCLInSi0fRai+z3/74WkSUakQURmaIRWaIRmaIRj+/Lnt2WASmF7FAZYApNto9Ck70gg70gh4NMnuPZXiaHw6Nne0EOBYNVidL2TV+sLWuD97dH45yTGj1nHsDK9/3h3bCS1KUVG1YfkPJrz549+Z5XrVZDrVZbsJqSJ79/lZa8/2JL3hblSynd7KIkiiL0EJEp5gxNptePwlSmaES60YB00Yg00Yh0Mfv142npj6ZlBzogVTQiVXwUvQpwjq5NnkFKBgdBDkeZAk6yR8+CHE4yBewEGfdWWbmG7Wpig4st+iw/iRsOKvRcfhLLHmagXlANqUsrFqw+ILm6ukIulyMuLi7H9Li4OHh4eEhUFRFR4Qim85MAh0Ie3BdFEVkQc4SmtEdBKtVoQKpoQMqj51SjASn/eU4Xsw86ZohGZIhG3DPm70IVOWAKTKYA9Sg8OcoePQtyOD96rxKs4qLpUqd6o0rY5GyDkFkHcNFBhTd3RGPxgwy80ru+1KVZPasPSCqVCo0aNUJYWJjpxG2j0YiwsDAMGTJE2uKIiKyAIAjZJ33LZXAp4LJGUcwOTo/CVEquEJUsGpBs1CPZmP2c9ChUGQAkGPVIgB4wZD13PTaCDGVkCjjLFCjz6OEsyE2vH39mwz1TZle+WllsGNsOH3y7GyccVOh/4jpmPkjDax/nfRoKZbOKgJSamorLly+b3sfGxiIyMhIuLi7w8vJCaGgoQkJC0LhxYzRp0gRz5sxBWloa+vXrJ2HVRETFn0wQ4Cgo4Ajk+yoVnWhEstGApEfhKcloQJJRj2Tx0XOO9wboIWbvoTJocdugfWbbaghPBimZAi6PnsvKFCgrV0LNPVIF4lTOHqumdsLQUTuxy06BT68/wP2Je9H/6zZSl2a1rOIy//DwcLRu3fqJ6SEhIVi+fDkAYMGCBZg+fTru3r0LPz8/zJs3DwEBAWZZvyUvEyQiKs1EMTscJRr12XucHj0SRcO/rx89Zzw+dyof7AUZysqUpsBUVqZ44r2SIeoJer0Bo0fuxM+Pdo98JAr4YnIHyGTFs68s+f1tFQFJagxIRETSyxSNT4Sm/75+aNTjgUGHrHxev+gkyOGSK0C5ypUoJ1PCTa6EkyAvlYfzjEYj5nwXhnmZ2XvzeqTrMWVaJyg1SokrKzgGJAtjQCIiKh5EUUS6aMQDow4PjPrsh0H3xHttPkKUCgLc/hOYTM9yFdxkStiX8POhVs05iLG3E2GUCWidpMXCyR1g62wjdVkFwoBkYQxIREQlhyiKSP1viDI8Dk863DPocM+ow0Oj/rkRykaQwU2mRDm50vRcXq6Cx6MAVRLGjtqxIgKfnbmNLIUMfklZ+OmrNnDxdJa6rHxjQLIwBiQiotJFL4q4b9Qh/lFgumfQIf7xs0GLRPHZg0jJALjJ/g1MHnIlPOQqlJer4FrMwtPRbdEYEHYRKWoFqiVnYcXHL6NS3eIxjA4DkoUxIBER0X9pRaNpb1P8o/AUZ9DirkGHuwbtMw/hyZEdnh4HpopyFSoq1KgkV8FRZhUXjz/h/OFr6LsuEvG2Srin6bDiDV+89EoVqct6LgYkC2NAIiKi/DKKIhKNetwxaHHXmB2Y7hi0iMtHeHIQ5DkCU0W5GhXlKpSVKSQ/3+lmdBz6LDiMWAcVHDP1+DGwOpp0rSNpTc/DgGRhDEhERGQORlFEglGPu4/C022DFrf0WfjHoH3mKOU2ggwV5CpUkqtRWaFGZbkalRUaOMjMdQv1/Hl4Oxn9JoQhylEFtd6IubU90OF9/yKtoSAYkCyMAYmIiCwtUzSaAtMtgxb/GLKf4wzap942r4xM8SgsZQemynI1ystVkFtwb1N6ciY+/monwu2VkBtFfOfmgHdGtLLY+gqDAcnCGJCIiEgqelHEXYMWtwxZuGHQ4ro+Ezf0WYh7yh4nJQRUkqtQRaFBVYUG1ZQ28JKrzXpiuC5Lhy9H7sSv6uwBJIfJFRg6vp3VDSjJgGRhDEhERGRtMowG3DBk4bo+K8dzZh4jjishoLJCjWqPQ5PCBhXlKsgKEZqMRiOmjN6FHwzZ+7feyTTg22mdoFBZz4nmDEgWxoBERETFgVEUEW/U4bo+C7H6TFzRZ+CKPhNpeYQmNQRUUWhQS2mDWkpb1FLYwP4Fzmn6cdp+THyQAlEQEJysxdypnaBxUJtjcwqNAcnCGJCIiKi4EkURcUYdrugzcVWfiSu6DFzVZ+Z5S5ZKchVqKR4FJqUN3GXKfF0999uS4/j8Yhz0chmaJGVhydh2cPJwsMTmFAgDkoU97uA31/wEla3tC7VR2CO/hb28s9DrL2QLhT30zfUXdv0S//xw/Vx/sV7/iy8vCIBSJodSLoNCJodSJoNSLodCJns0/fHrnNM1CgXsVCrYKlWwVSph9+jZVqmCUl74K9eMoojbBi0u6TMQo8tAjD4Dtw3aJ+ZzFuSorbRFPZUd6ipt4S5XPbXNA5vOYNChWKSp5KiVlIUVn7WER03XQtdaGAxIFva4gzFyKKCxjt2GRERUOill8kdhSQknjQ3KaGzgYmODMja2/77W2KKMjQ1cbW1R3t4R5R0c4WZrB/kzTqJONupNYSnm0V6m3DdccZMpUfdRYKqjtIVzroEtT4dfRb/Np/HARomKqVqs6NMY1Zt4WqQf8oMBycIed/D4XduhsbMr8PKF6cLCdr5U6y7sj41U65a2vwuxbCELl2rdhVlvaV136f23Lp7/lxlFETqjEXqjATqDEXrRCJ3BAJ3RAL3x8Wuj6bXeaITOaECmXo80rRbpOi3SdTqk6bQwFrIWuSCDu709yts7oLyDIyrYO8LbuQyqlHFB1TIuqOLsAldbO9MeN61oxGV9Js5p03BWl45L+ownhhvwkqvRQGWHhip71FTYQCYIuHb6Dt774Shu2qvgkqHD0g610aBjrULV/qIYkCyM5yAREZGURFGE1mBAmu4/oUmrRWJmBhIyM5CQkYGHGen/vs5MR0JGBu6lp+FOSjLi09LyFVLtVSpUcXZBdRdX+LiVg4+bO3zc3PGSqxsglyNal46zunSc1abhmiEr57KCDH4qezRU2aPCbS0Gz/gL5x1UsNEasLChJ9q828BS3fNUDEgWxoBERETFmd5oQFxqKu6kJuNOSgrupCbjVnIyriUl4GrCA8QmJOBWStJTl5cJAqqWcUEdNw80LF8BjStUQi2P8rijFHBKl4ZIbWqOK+VkAGqlynB22lmcdFRDYTBiSiUX9Py0eRFs7b8YkCyMAYmIiEq6TL0O1xMTcDXhIS49vI/z9+Jw7l4czsXHISEzI89lKjk6oVH5SvCv6Inq3pWR5WyHKH06/nl0wreQaYBhSjRO2NsAAD7XKDFkbLsiu68cA5KFMSAREVFpJYoi4tNSce5eHE7H3UHEnVuIuP0PLty/98RhO7VcgYBKnmhavQbcKnvivp0SV/WZUE29gIPK7IucOmZq8fak1giwcYRKsOzI2wxIFsaARERElFNKViYi797Byds3ceSfGzhw/Sri0lJzzKOSy9Gq1kuoV6c2Mn6+ix267CEKmialw/arOmhaxgWBaifUUGgssleJAcnCGJCIiIieTRRFXHp4H39dj8WBG7HYf+0qricl5Jina3w1nLarCINMgG9COhw+rwGdiwaV5Cq015RBS7UjbF5gNO+nYUCyMAYkIiKighFFERcf3MMfl2Pwx+UY7L92FVkGPQJuuiDRyQeZSjlqJKTDc2AVpFW2BwDYCDIEqp3QXuOMCorCjzvIgGRhDEhERESFk6bVYt+1y/jtwnmc3XsVaWJNJNsoUSEpAw510+H6uh/0mn9H6vZX2aOrTVlUV9q88DoZkCyMAYmIiMh8dAYDft1+ArN23UacvRpl07TQGs7gXmNHBDRpDI17WdM9muopbdHVpizqKG0LfJ4SA5KFMSARERGZ353L99Fn9l+45KCCXZYejqnncbRSAhzKOMHXvyEqVPc2BSUfpS3esXUr0B4lBiQLY0AiIiKyjKT4FLw/bg9OOqqg1BvxpiYDq1yv4HpSAmwd7OHTsD6q+tQEHt1HLkDlgDft3FDhGTfOfYwBycIYkIiIiCwnMzULQ0b9gT12SgiiiNFONnB43Q0zjxzAsVs3YGtvh7pNGsL7peqAIEAOoJONC3raukLzjLGUGJAsjAGJiIjIsvR6A77+8g+sV2YfUvsYMnw+sT2O3rqJaYfDsTXmPBxdnOHbzB/lvT0BAGVlCvS1c4e/yj7P85MYkCyMAYmIiMjyjEYjZn+7B/OzdACAXul6TJrWCUqNEsdv3cA3e//E7quXUL5yJTRq2Qy2jg4AgCYqewyw94CjTJGjPQYkC2NAIiIiKjorZ/2FcXeTYJQJaJOkxcLJHWDjnH1y9v5rVzBi9w6cir+N2o18UbthfQgyGZwEOT50KI9GKntTOwxIFsaAREREVLS2Lz+Jz87egVYhQ8PELCwd3RZlKjoBAIyiEUtPncDIsD9gtNMgIKgVnMqWAQB01JTBu3bloBAEBiRLY0AiIiIqeod/j8aHey8hRS1H9eQsrBj8MirW8TB9/iA9DV/s3oHlZ06hXkBD1GpQDwDwksIGnzlWhCw1nQHJkhiQiIiIpHH+0DX0XR+JeFslPNK0WNHbD7VaVMkxz7aL5/HB1o2Ql3NBQNuWUKpVKCNT4CPRAQ1cPSzy/f30a+eIiIiILMynuTc2fdQMVVK1uGunwhsbT+P4b+dyzNO5pg/Ofvw5GintsHvDViQ9TECCUY/Jyf9YrC4GJCIiIpKUp487No5sjfrJWiRpFOhz4Ar+/Olkjnlcbe2w5c0QfNmwGfZu3IY71/+BDpY7CMaARERERJIrW8kZP0/ugJapOmQq5fj4wl38PONAjnlkggzftGyLLb3eReTu/YiOiLJYPQxIREREZBXsnGzw48xX0TXTAINMwKj7KZj3zZ8wGo055utUozb+6jsI6VduWKwWnqQNnqRNRERkTYxGIyZ/swtLjAYAwHtZRoyb1glypTzHfPcTHsLNpSxP0iYiIqKSTyaT4etJHfC1sx0AYJVahsHDtiIzNSvHfCq5Iq/FzVODxVomIiIiKoQBIwMxu6orFAYjdjqoEDJiO5LjUopk3QxIREREZLW6DQzA0gBv2GoNOOakRu9xuxF36b7F18uARERERFatVc96WNulDlwydIh2UqPH3L9w5cRNi66TAYmIiIisnl/ratjUrwkqpWrxj70KvVZH4PTuSxZbHwMSERERFQtV/Cpg0/BA1E7R4qGNEu/vZUAiIiIigrt3Gaz/rj2apmiRoZI/f4EXxIBERERExYpjWTssn/4q+giWizEMSERERFTsaGxV+GJcO4u1z4BERERElAsDEhEREVEuDEhEREREuTAgEREREeXCgERERESUCwMSERERUS4MSERERES5MCARERER5cKARERERJQLAxIRERFRLgxIRERERLkwIBERERHlwoBERERElItC6gKsgSiKAIDk5GSJKyEiIqL8evy9/fh73JwYkAA8ePAAAODp6SlxJURERFRQDx48gJOTk1nbZEAC4OLiAgC4ceOG2Tu4NElOToanpydu3rwJR0dHqcsp1tiX5sO+NA/2o/mwL80nKSkJXl5epu9xc2JAAiCTZZ+K5eTkxB9WM3B0dGQ/mgn70nzYl+bBfjQf9qX5PP4eN2ubZm+RiIiIqJhjQCIiIiLKhQEJgFqtxtixY6FWq6UupVhjP5oP+9J82JfmwX40H/al+ViyLwXREtfGERERERVj3INERERElAsDEhEREVEuDEhEREREuTAgEREREeXCgERERESUCwNSAc2YMQN16tRB3bp1sXr1aqnLKbZiYmLg5+dnetjY2GDLli1Sl1UseXt7o379+vDz80Pr1q2lLqfYSkxMROPGjeHn54e6detiyZIlUpdUrHXr1g1lypRBz549pS6lWGG/mYc5fp95mX8BnDlzBiEhITh8+DBEUUTr1q2xc+dOODs7S11asZaamgpvb29cv34ddnZ2UpdT7Hh7e+Ps2bOwt7eXupRizWAwICsrC7a2tkhLS0PdunVx8uRJlC1bVurSiqXw8HCkpKRgxYoV2Lhxo9TlFBvsN/Mwx+8z9yAVQHR0NJo1awaNRgMbGxv4+vpi586dUpdV7G3duhVt27ZlOCJJyeVy2NraAgCysrIgiiL49+OLCwwMhIODg9RlFDvsN/Mwx+9ziQpIBw4cQJcuXVChQgUIgpDnIZuFCxfC29sbGo0GAQEBOH78eL7br1u3LsLDw5GYmIiEhASEh4fj1q1bZtwC62HpvvyvX375Bb179y5kxdapKPpREAS0atUK/v7+WLNmjZkqtz5F0ZeJiYnw9fVFpUqVMGLECLi6upqpeutSlL/fpQn71XzM0ZeF/X0uUQEpLS0Nvr6+WLhwYZ6fr1+/HqGhoRg7dixOnToFX19fBAcHIz4+3jTP4+OVuR+3b9+Gj48Phg4dijZt2qB79+5o2rQp5HJ5UW1ekbJ0Xz6WnJyMw4cPo1OnThbfJikURT8ePHgQERER2Lp1KyZNmoTTp08XybYVtaLoS2dnZ0RFRSE2NhZr165FXFxckWxbUSuq3+/Sxhz9StnM0ZeF/n0WSygA4ubNm3NMa9KkiTh48GDTe4PBIFaoUEGcPHnyC63j/fffF7dt21aYMosFS/blypUrxXfeecccZVq9oviZHD58uLhs2bJCVFk8FEVfDho0SNywYUNhyiwWLNmX+/btE3v06GGOMoudwvRrae63vJjjZ/RFfp9L1B6kZ9FqtYiIiEBQUJBpmkwmQ1BQEI4cOZLvdh6n05iYGBw/fhzBwcFmr9XamasvgZJ9eO15zNGPaWlpSElJAZB9svvevXtRp04di9RrzczRl3Fxcaa+TEpKwoEDB1CrVi2L1GvNzPn7Tf9iv5pPfvrSHL/PCvOVbN3u378Pg8EAd3f3HNPd3d1x4cKFfLfz+uuvIykpCXZ2dli2bBkUilLThSbm6sukpCQcP34cmzZtMneJxYI5+jEuLg7dunUDkH3VxoABA+Dv72/2Wq2dOfry+vXrGDhwoOlkzk8++QT16tWzRLlWzVy/30FBQYiKikJaWhoqVaqEDRs2oFmzZuYut9jIb7+y354vP31pjt/n0vftXkhM+ubj5ORUYs/xKCpVq1ZFVFSU1GWUCE2aNEFkZKTUZZQYe/bskbqEYon9Zh7m+H0uNYfYXF1dIZfLn/hCjouLg4eHh0RVFU/sS/NgP5oP+9J82JeWwX41n6Lqy1ITkFQqFRo1aoSwsDDTNKPRiLCwMO6+LCD2pXmwH82HfWk+7EvLYL+aT1H1ZYk6xJaamorLly+b3sfGxiIyMhIuLi7w8vJCaGgoQkJC0LhxYzRp0gRz5sxBWloa+vXrJ2HV1ol9aR7sR/NhX5oP+9Iy2K/mYxV9WaBr3qzcvn37RABPPEJCQkzzzJ8/X/Ty8hJVKpXYpEkT8ejRo9IVbMXYl+bBfjQf9qX5sC8tg/1qPtbQl7wXGxEREVEupeYcJCIiIqL8YkAiIiIiyoUBiYiIiCgXBiQiIiKiXBiQiIiIiHJhQCIiIiLKhQGJiIiIKBcGJCIiIqJcGJCIiIiIcmFAIiIiIsqFAYmISoQHDx6gXLlyuHbtmlnae/PNNzFz5kyztEVExQ/vxUZEJUJoaChSUlKwZMkSs7R39uxZtGzZErGxsXBycjJLm0RUfHAPEhEVK3q9/olp6enpWLp0Kd5//32zradu3bqoVq0aVq9ebbY2iaj4YEAiIqt17do1CIKAX375Ba+88grUajW2bt36xHw7duyAWq1G06ZNTdMCAwMxZMgQDBkyBE5OTnB1dcXo0aPx353mRqMR06ZNQ/Xq1aFWq+Hl5YWJEyeaPu/SpQvWrVtn2Y0kIqvEgEREVisqKgoAMH36dIwZMwbnzp1D27Ztn5jvr7/+QqNGjZ6YvmLFCigUChw/fhxz587FrFmz8OOPP5o+HzVqFKZMmYLRo0fj/PnzWLt2Ldzd3U2fN2nSBMePH0dWVpYFto6IrJlC6gKIiJ4mMjISdnZ22LBhA7y9vZ863/Xr11GhQoUnpnt6emL27NkQBAG1atXCmTNnMHv2bAwYMAApKSmYO3cuFixYgJCQEABAtWrV0KJFC9PyFSpUgFarxd27d1G5cmWzbx8RWS/uQSIiqxUVFYXXXnvtmeEIADIyMqDRaJ6Y3rRpUwiCYHrfrFkzXLp0CQaDAdHR0cjKyspzj9RjNjY2ALLPcSKi0oUBiYisVmRkJAIDA587n6urKxISEgrU9uPw8ywPHz4EALi5uRWobSIq/hiQiMgqJScn49q1a2jQoMFz523QoAHOnz//xPRjx47leH/06FHUqFEDcrkcNWrUgI2NDcLCwp7a7tmzZ1GpUiW4uroWfAOIqFhjQCIiqxQVFQW5XI569eo9d97g4GCcO3fuib1IN27cQGhoKGJiYvDzzz9j/vz5+PTTTwEAGo0GX375Jb744gusXLkSV65cwdGjR7F06VLT8n/99Rfat29v3g0jomKBJ2kTkVWKiopCrVq18jy3KLd69eqhYcOG+OWXX/Dhhx+apvfp0wcZGRlo0qQJ5HI5Pv30UwwcOND0+ejRo6FQKDBmzBjcvn0b5cuXx0cffQQAyMzMxJYtW7Bz507zbxwRWT2OpE1EJcL27dsxYsQInD17FjKZDIGBgfDz88OcOXNeqL1FixZh8+bN2LVrl3kLJaJigXuQiKhEePXVV3Hp0iXcunULnp6ehW5PqVRi/vz5ZqiMiIojBiQiKjGGDRtmtrY++OADs7VFRMUPD7ERERER5cKr2IiIiIhyYUAiIiIiyoUBiYiIiCgXBiQiIiKiXBiQiIiIiHJhQCIiIiLKhQGJiIiIKBcGJCIiIqJcGJCIiIiIcmFAIiIiIsqFAYmIiIgol/8D8vbd+dkU23QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Number of particles in the sample\n",
    "#---------------------------------\n",
    "N_particles = int(1e6)\n",
    "\n",
    "\n",
    "#Calculate adiabatic phase-space from scratch\n",
    "#---------------------------------\n",
    "FROM_SCRATCH = False\n",
    "\n",
    "\n",
    "R_s = R_vir/c\n",
    "a_NFW = np.log(1 + c) - c/(1 + c)\n",
    "rho_halo = M_halo/(4/3 * np.pi * R_vir**3)\n",
    "rho_0_prime = rho_halo*c**3/(3*a_NFW)\n",
    "\n",
    "def rho_NFW(r):\n",
    "    return rho_0_prime * (R_s/r) / (1 + r/R_s)**2 * np.exp(-r/R_vir)\n",
    "\n",
    "#input(\"Press Enter to continue...\")\n",
    "\n",
    "rho_0_gas_i = 1E-23 * (3.0857E18)**3 / (1.9885E33) # M_sun/pc^3\n",
    "r_c_i = 1E1\n",
    "def rho_gas_initial(r):\n",
    "    return rho_0_gas_i / (1 + r/r_c_i)**2\n",
    "\n",
    "rho_0_gas_f = 1E-15 * (3.0857E18)**3 / (1.9885E33) # M_sun/pc^3\n",
    "r_c_f = 1E-3\n",
    "def rho_gas_final(r):\n",
    "    return rho_0_gas_f / (1 + r/r_c_f)**2\n",
    "\n",
    "plt.figure()\n",
    "plt.loglog(r_array, rho_NFW(r_array), c = rgb_palette_dict['rich black'])\n",
    "plt.loglog(r_array, rho_gas_initial(r_array), c = rgb_palette_dict['pine green'])\n",
    "plt.loglog(r_array, rho_gas_final(r_array), c = rgb_palette_dict['turquiose'])\n",
    "plt.ylim(bottom = 1E-4)\n",
    "#plt.show()\n",
    "\n",
    "#%%\n",
    "\n",
    "#rho_M_data = np.genfromtxt('/Users/daniele/Dropbox/Fisica/2023/EvolvingDensities-main/rho_M.csv', delimiter = ',')\n",
    "rho_M_data = np.genfromtxt('rho_M.csv', delimiter = ',')\n",
    "\n",
    "logrho_M_interp = interp1d(rho_M_data[:, 0], np.log10(rho_M_data[:, 1]), kind = 'quadratic', bounds_error = False,\n",
    "                           fill_value = (np.log10(rho_M_data[0, 1]), 0))\n",
    "rho_M_interp = lambda x: 10**logrho_M_interp(x) * (3.0857E18)**3 / (1.9885E33)\n",
    "\n",
    "x_test = np.linspace(0, np.max(rho_M_data[:, 0]), num = 1000)\n",
    "x_test = np.append(x_test, np.max(rho_M_data[:, 0]) - np.logspace(-8, -1, num = 1000))\n",
    "x_test = np.unique(x_test)\n",
    "\n",
    "r_reconstructed = [0]\n",
    "M_tot = 1E5 # M_sun\n",
    "\n",
    "for i in range(len(x_test) - 1):\n",
    "\n",
    "    dM = (x_test[i + 1] - x_test[i]) * M_tot # M_sun\n",
    "\n",
    "    rho = (rho_M_interp(x_test[i]) + rho_M_interp(x_test[i + 1]))/2 \n",
    "\n",
    "    r = r_reconstructed[-1]\n",
    "\n",
    "    dr = np.cbrt(3*dM/(4*np.pi*rho) + r**3) - r\n",
    "\n",
    "    r_reconstructed.append(r + dr)\n",
    "\n",
    "    #if i%100 == 0: print(r_reconstructed[-1], dr)\n",
    "\n",
    "r_reconstructed = np.array(r_reconstructed)\n",
    "\n",
    "rho_SMS_bloated_interp = interp1d(np.array(r_reconstructed), rho_M_interp(x_test), fill_value = (rho_M_interp(x_test[0]), 0), bounds_error = False)\n",
    "\n",
    "m_proto = M_tot\n",
    "n = 3\n",
    "rho_c = 1. * (3.0857E18)**3 / (1.9885E33) # M_sun/pc^3\n",
    "poly_solver = PolytropicSolver(n)\n",
    "r_array_poly, rho_array_poly = poly_solver(rho_c, m_proto)\n",
    "rho_proto_poly_interp = interp1d(r_array_poly, rho_array_poly, fill_value = (rho_array_poly[0], 0), bounds_error = False)\n",
    "\n",
    "r_poly = np.min(r_array_poly[rho_array_poly <= 0])\n",
    "print(\"r_poly:\", r_poly)\n",
    "\n",
    "r_core = 5E-7\n",
    "\n",
    "#%%\n",
    "\n",
    "plt.figure()\n",
    "plt.loglog(r_array, rho_NFW(r_array), c = rgb_palette_dict['dark sienna'], label = 'initial NFW')\n",
    "#plt.loglog(r_array, rho_gas_initial(r_array), c = rgb_palette_dict['pine green'], label = 'initial gas cloud')\n",
    "#plt.loglog(r_array, rho_gas_final(r_array), c = rgb_palette_dict['turquiose'], label = 'collapsed gas cloud')\n",
    "#plt.loglog(r_array, rho_SMS_bloated_interp(r_array), c = rgb_palette_dict['flickr pink'], ls=\"--\", label = r'$10^5 M_\\odot$ SMS, Hosokawa solution')\n",
    "plt.loglog(r_array_poly, rho_proto_poly_interp(r_array_poly), c = rgb_palette_dict['pine green'], label = r'$10^5 M_\\odot$ SMS, Lane-Emden solution')\n",
    "# plt.loglog(r_array, rho_proto_poly_interp(r_array), c = rgb_palette_dict['flickr pink'])\n",
    "plt.xlim(1E-9, 1E3)\n",
    "plt.ylim(bottom = 1E-4)\n",
    "plt.xlabel(r'$r$ (pc)')\n",
    "plt.ylabel(r'$\\rho$ ($M_\\odot$ pc$^{-3}$)')\n",
    "plt.legend()\n",
    "plt.savefig('./figures/density_NFW_gas_star_densities.pdf')\n",
    "\n",
    "#%%\n",
    "\n",
    "print(\"> Creating Density objects...\")\n",
    "\n",
    "N_part = int(1e2) #\n",
    "density_NFW = Density('density_NFW_SMS', rho_NFW, r_array, N_particles = N_part)\n",
    "density_NFW.setup_potentials()\n",
    "psi_NFW = density_NFW.get_psi()\n",
    "M_tot_NFW = density_NFW.M_enclosed(r_array[-1])\n",
    "rho_initial = density_NFW(r_array)\n",
    "\n",
    "density_gas_initial = Density('density_gas_initial', rho_gas_initial, r_array, N_particles = int(5E0))\n",
    "density_gas_initial.setup_potentials()\n",
    "psi_gas_i = density_gas_initial.get_psi()\n",
    "M_tot_gas_i = density_gas_initial.M_enclosed(r_array[-1])\n",
    "\n",
    "density_gas_final = Density('density_gas_final', rho_gas_final, r_array, N_particles = int(5E0))\n",
    "density_gas_final.setup_potentials()\n",
    "psi_gas_f = density_gas_final.get_psi()\n",
    "M_tot_gas_f = density_gas_final.M_enclosed(r_array[-1])\n",
    "\n",
    "print(\"> ...Done.\")\n",
    "\n",
    "density_proto_poly = Density('density_proto_poly', rho_proto_poly_interp, r_array, N_particles = int(5E0))\n",
    "density_proto_poly.setup_potentials()\n",
    "psi_proto_poly = density_proto_poly.get_psi()\n",
    "M_tot_proto_poly = density_proto_poly.M_enclosed(r_array[-1])\n",
    "\n",
    "density_SMS_bloated = Density('density_SMS_bloated', rho_SMS_bloated_interp, r_array, N_particles = int(5E0))\n",
    "#density_SMS_bloated.smoothen_density()\n",
    "density_SMS_bloated.setup_potentials()\n",
    "psi_SMS_bloated = density_SMS_bloated.get_psi()\n",
    "M_tot_SMS_bloated = density_SMS_bloated.M_enclosed(r_array[-1])\n",
    "\n",
    "#%%\n",
    "plt.figure()\n",
    "plt.loglog(r_array, psi_NFW(r_array), c = rgb_palette_dict['dark sienna'], label = 'initial NFW')\n",
    "plt.loglog(r_array, psi_gas_i(r_array), c = rgb_palette_dict['pine green'], label = 'initial gas cloud')\n",
    "plt.loglog(r_array, psi_gas_f(r_array), c = rgb_palette_dict['turquiose'], label = 'collapsed gas cloud')\n",
    "plt.loglog(r_array, psi_SMS_bloated(r_array), c = rgb_palette_dict['flickr pink'], label = r'$10^5 M_\\odot$ SMS')\n",
    "plt.loglog(r_array, psi_proto_poly(r_array), c = 'C0', label = r'$10^5 M_\\odot$ Polytrope')\n",
    "plt.xlim(1E-9, 1E3)\n",
    "plt.legend()\n",
    "plt.xlabel('$r$ (pc)')\n",
    "plt.ylabel(r'$\\psi$')\n",
    "plt.savefig('./figures/density_NFW_gas_star_potentials.pdf')\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5b5e7010",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">------- NOTE THAT WE'RE USING A FACTOR OF 2 TO FUDGE THE RESULTS: CHECK WHERE IT COMES FROM!\n",
      "> Supermassive star formation...\n",
      "> Loading grids from file...\n",
      "  C_CONTIGUOUS : True\n",
      "  F_CONTIGUOUS : False\n",
      "  OWNDATA : True\n",
      "  WRITEABLE : True\n",
      "  ALIGNED : True\n",
      "  WRITEBACKIFCOPY : False\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#%%\n",
    "m_BH = M_tot\n",
    "r_S = 2*G_N*m_BH/c_light**2\n",
    "def psi_BH(r):\n",
    "    return G_N*m_BH/r\n",
    "\n",
    "#r_sp = 0.122 * R_s * ( m_BH / ( rho_0_prime * R_s**3 ) )**(1./(3.-1))\n",
    "\n",
    "gamma_PL = 1.\n",
    "r_0   = R_s\n",
    "rho_0 = rho_0_prime/4.\n",
    "gamma_sp_GS = (9. - 2.*gamma_PL)/(4. - gamma_PL)\n",
    "\n",
    "\n",
    "alpha_gamma = 0.293 * (gamma_PL)**(4./9.)\n",
    "\n",
    "def g_GS(r):\n",
    "    return (1. - 2.*r_S/r)**3.\n",
    "\n",
    "r_sp_GS = alpha_gamma * r_0 * (m_BH / (rho_0 * r_0**3.))**(1./(3. - gamma_PL))\n",
    "\n",
    "print(\">------- NOTE THAT WE'RE USING A FACTOR OF 2 TO FUDGE THE RESULTS: CHECK WHERE IT COMES FROM!\")\n",
    "rho_R = 0.5*rho_0*(r_sp_GS/r_0)**(-gamma_PL)\n",
    "\n",
    "def rho_GS(r):\n",
    "    return rho_0_prime * (R_s/r) / (1 + r/R_s)**2 * np.exp(-r/R_vir) + g_GS(r) * rho_R*(r_sp_GS/r)**(gamma_sp_GS)\n",
    "\n",
    "rho_GS_array = rho_GS(r_array)\n",
    "\n",
    "\n",
    "#plt.figure()\n",
    "\n",
    "#plt.loglog(r_array, psi_SMS_bloated(r_array))\n",
    "#plt.loglog(r_array, psi_SMS_bloated(r_array))\n",
    "#plt.loglog(r_array, psi_BH(r_array))\n",
    "#plt.loglog(r_array, -psi_SMS_bloated(r_array) + psi_BH(r_array))\n",
    "#plt.loglog(r_array, +psi_SMS_bloated(r_array) - psi_BH(r_array))\n",
    "#plt.show()\n",
    "\n",
    "# delta_psi = lambda r: psi_SMS_bloated(r) - psi_proto_poly(r)\n",
    "print(\"> Supermassive star formation...\")\n",
    "\n",
    "if ((FROM_SCRATCH) or (not os.path.isfile(\"f_grid.npy\"))):\n",
    "    print(\"> Calling Adiabatic Growth...\")\n",
    "    #BJK: Use refinement=15\n",
    "    density_after_SMS, E_grid, L_grid, f_grid = density_NFW.adiabatic_growth(psi_proto_poly, refinement = 15, figures = False, return_DF=True)\n",
    "    #######################################################################################################################\n",
    "    #######################################################################################################################\n",
    "    #######################################################################################################################\n",
    "\n",
    "    rho_array = density_after_SMS(r_array)\n",
    "\n",
    "    np.save(\"r_array.npy\", r_array)\n",
    "    np.save(\"rho_array.npy\", rho_array)\n",
    "    np.save(\"E_grid.npy\", E_grid)\n",
    "    np.save(\"L_grid.npy\", L_grid)\n",
    "    np.save(\"f_grid.npy\", f_grid)\n",
    "    \n",
    "    _psi = psi_NFW(r_array) + psi_proto_poly(r_array)\n",
    "    \n",
    "    T_orb_grid = 0.0*f_grid\n",
    "    for i, E in enumerate(tqdm(E_grid[:,0])):\n",
    "        for j, L in enumerate(L_grid[0,:]):\n",
    "            vr_sq_grid = 2*_psi - 2*E - L**2/r_array**2\n",
    "            inds = vr_sq_grid > 0\n",
    "            \n",
    "            if ((np.sum(inds) > 0) and (np.sum(inds) < 100)):\n",
    "                _r = np.geomspace(np.min(r_array[inds]), np.max(r_array[inds]), 250)\n",
    "                _psi_new = psi_NFW(_r) + psi_proto_poly(_r)\n",
    "                vr_sq_grid = 2*_psi_new - 2*E - L**2/_r**2\n",
    "                inds = vr_sq_grid > 0\n",
    "            \n",
    "                integ = 0.0*vr_sq_grid\n",
    "                integ[inds] = 1/np.sqrt(vr_sq_grid[inds])\n",
    "                T_orb_grid[i,j] = np.trapz(integ, _r, axis=-1)\n",
    "            else:\n",
    "                integ = 0.0*vr_sq_grid\n",
    "                integ[inds] = 1/np.sqrt(vr_sq_grid[inds])\n",
    "                T_orb_grid[i,j] = np.trapz(integ, r_array, axis=-1)\n",
    "\n",
    "    np.save(\"T_orb_grid.npy\", T_orb_grid)\n",
    "\n",
    "else:\n",
    "    print(\"> Loading grids from file...\")\n",
    "    r_array   = np.load(\"r_array.npy\")\n",
    "    rho_array = np.load(\"rho_array.npy\")\n",
    "    E_grid    = np.load(\"E_grid.npy\")\n",
    "    L_grid    = np.load(\"L_grid.npy\")\n",
    "    f_grid    = np.load(\"f_grid.npy\")\n",
    "    \n",
    "    T_orb_grid    = np.load(\"T_orb_grid.npy\")\n",
    "\n",
    "print(f_grid.flags)\n",
    "\n",
    "f_grid[np.isnan(f_grid)] = 0.0\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50214ee4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shapes\n",
      "(3473, 2000)\n",
      "(3473, 2000)\n",
      "(3473, 2000)\n",
      "(3473, 2000)\n",
      "Running interpn\n",
      "Total: 8.446484770080919e-05\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Calculating density profile: 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████| 1000000/1000000 [00:30<00:00, 33022.62it/s]\n",
      " 93%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████▎        | 934416/1000000 [05:34<00:24, 2722.84it/s]"
     ]
    }
   ],
   "source": [
    "def lin_sampler(x_min, x_max, N):\n",
    "    u = np.random.rand(N)\n",
    "    x = (x_max - x_min)*u + x_min\n",
    "    return x\n",
    "\n",
    "def log_sampler(x_min, x_max, N):\n",
    "    return np.exp(lin_sampler(np.log(x_min), np.log(x_max), N))\n",
    "\n",
    "#Sampling E, L points\n",
    "#--------------------\n",
    "\n",
    "Lmin = 1e-8\n",
    "\n",
    "E_samps = lin_sampler(np.min(E_grid[:,0]), np.max(E_grid[:,0]), N_particles)\n",
    "L_samps = log_sampler(Lmin, np.max(L_grid[0,:]), N_particles)\n",
    "\n",
    "deltaE = np.max(E_grid[:,0]) - np.min(E_grid[:,0])\n",
    "deltaL = np.max(L_grid[0,:]) - Lmin\n",
    "\n",
    "deltalogE = np.log(np.max(E_grid[:,0])) - np.log(np.min(E_grid[:,0]))\n",
    "deltalogL = np.log(np.max(L_grid[0,:])) - np.log(Lmin)\n",
    "\n",
    "_psi = psi_NFW(r_array) + psi_proto_poly(r_array)\n",
    "\n",
    "print(\"Shapes\")\n",
    "print(E_grid.shape)\n",
    "print(L_grid.shape)\n",
    "print(T_orb_grid.shape)\n",
    "print(f_grid.shape)\n",
    "\n",
    "points = (E_grid[:,0], L_grid[0,:])\n",
    "#new_points = np.array((E_samps, L_samps)).T\n",
    "new_points = (E_samps, L_samps)\n",
    "\n",
    "\n",
    "print(\"Running interpn\")\n",
    "\n",
    "f_E_L = interpn(points,  (4*np.pi)**2*(L_grid*T_orb_grid)*f_grid, new_points, bounds_error=False, fill_value=0.0)\n",
    "\n",
    "p_samps = 1/(L_samps)\n",
    "#p_samps = 1/(E_samps*L_samps)\n",
    "#p_samps = 1.0\n",
    "weights = (1/p_samps)*f_E_L\n",
    "\n",
    "Vol = deltaE*deltalogL\n",
    "\n",
    "print(\"Total:\", Vol*np.sum(weights)/N_particles/M_halo)\n",
    "\n",
    "_psi = psi_NFW(r_array) + psi_proto_poly(r_array)\n",
    "\n",
    "# Reconstructing Density Profile\n",
    "#-------------------------------\n",
    "\n",
    "T_orb_samps = 0.0*E_samps\n",
    "P_r_A = 0.0*r_array\n",
    "\n",
    "for i in tqdm(range(N_particles),desc=\"Calculating density profile\"):\n",
    "    if (weights[i] > 0):\n",
    "        E = E_samps[i]\n",
    "        L = L_samps[i]\n",
    "        vr_sq_grid = 2*_psi - 2*E - L**2/r_array**2\n",
    "        inds = vr_sq_grid > 0\n",
    "        integ = 0.0*vr_sq_grid\n",
    "        \n",
    "        if ((np.sum(inds) > 0) and (np.sum(inds) < 100)):\n",
    "            _r = np.geomspace(np.min(r_array[inds]), np.max(r_array[inds]), 250)\n",
    "            _psi_new = psi_NFW(_r) + psi_proto_poly(_r)\n",
    "            vr_sq_grid = 2*_psi_new - 2*E - L**2/_r**2\n",
    "            inds = vr_sq_grid > 0\n",
    "        \n",
    "            integ = 0.0*vr_sq_grid\n",
    "            integ[inds] = 1/np.sqrt(vr_sq_grid[inds])\n",
    "            T_orb_samps[i] = np.trapz(integ, _r, axis=-1)\n",
    "            \n",
    "            integ2 = np.interp(r_array, _r, integ, left=0.0, right=0.0)\n",
    "            \n",
    "        else:\n",
    "            integ = 0.0*vr_sq_grid\n",
    "            integ[inds] = 1/np.sqrt(vr_sq_grid[inds])\n",
    "            T_orb_samps[i] = np.trapz(integ, r_array, axis=-1)\n",
    "            integ2 = 1.0*integ\n",
    "        \n",
    "        if (T_orb_samps[i] > 0):\n",
    "            P_r_A += (Vol/N_particles)*weights[i]*integ2/T_orb_samps[i]\n",
    "        \n",
    "#P_r_A = (Vol/N_particles)*np.sum(weights[:,np.newaxis]*integ/T_orb_samps[:,np.newaxis], axis=0)\n",
    "\n",
    "rho_r_A = P_r_A/(4*np.pi*r_array**2)\n",
    "\n",
    "\n",
    "#Sampling r-positions\n",
    "#--------------------\n",
    "\n",
    "r_samps = 0.0*E_samps\n",
    "\n",
    "psi_fun = lambda x: psi_NFW(x) + psi_proto_poly(x)\n",
    "for i in tqdm(range(N_particles)):\n",
    "    found = False\n",
    "    if (weights[i] < 1e-20):\n",
    "        r_samps[i] = 1.0\n",
    "        continue\n",
    "        \n",
    "    _Nr = 1000\n",
    "    while not found:\n",
    "        _rs = log_sampler(np.min(r_array), np.max(r_array), _Nr)\n",
    "        vr_sq = 2*psi_fun(_rs) - 2*E_samps[i] - L_samps[i]**2/_rs**2\n",
    "        inds = vr_sq > 0\n",
    "        #print(inds)\n",
    "        if np.sum(inds) > 0:\n",
    "            found = True\n",
    "        else:\n",
    "            _Nr *= 10\n",
    "        #print(weights[i])\n",
    "        if (_Nr > 10000):\n",
    "            r_samps[i] = 1.0\n",
    "            weights[i] = 0.0\n",
    "            found = True\n",
    "        #assert(_Nr < 100000)\n",
    "        \n",
    "    #assert(np.sum(inds) > 0)\n",
    "    \n",
    "    if (np.sum(inds) == 0):\n",
    "        continue\n",
    "    \n",
    "    i1 = np.random.choice(np.arange(len(_rs))[inds])\n",
    "    r_samps[i] = _rs[i1]\n",
    "    if (T_orb_samps[i] > 0):\n",
    "        weights[i] *= (_rs[i1]/np.sqrt(vr_sq[i1]))/T_orb_samps[i]\n",
    "    else:\n",
    "        weights[i] = 0\n",
    "    \n",
    "#Instantaneous BH formation\n",
    "#--------------------------\n",
    "\n",
    "E_f_samps = E_samps - psi_proto_poly(r_samps) + psi_BH(r_samps)\n",
    "\n",
    "_psi = psi_NFW(r_array) + psi_BH(r_array)\n",
    "\n",
    "T_orb_samps_B = 0.0*E_samps\n",
    "P_r_B = 0.0*r_array\n",
    "P_r_C = 0.0*r_array\n",
    "\n",
    "#Reconstructing density profile\n",
    "#------------------------------\n",
    "\n",
    "#def L_c(E):\n",
    "#    E2 = 1 - E/c_light**2\n",
    "#    return np.sqrt(32*(G_N*m_BH/c_light)**2/(36*E2**2 - 27*E2**4 - 8 + E2*(9*E2**2 - 8)**(3/2)))\n",
    "\n",
    "for i in tqdm(range(N_particles),desc=\"Calculating density profile\"):\n",
    "    #_psi = psi_NFW(_r1) + psi_SMS_bloated(_r1)\n",
    "    if (weights[i] > 0):\n",
    "        E = E_f_samps[i]\n",
    "        L = L_samps[i]\n",
    "        vr_sq_grid = 2*_psi - 2*E - L**2/r_array**2\n",
    "        inds = vr_sq_grid > 0\n",
    "        integ = 0.0*vr_sq_grid\n",
    "        if ((np.sum(inds) > 0) and (np.sum(inds) < 100)):\n",
    "            _r = np.geomspace(np.min(r_array[inds]), np.max(r_array[inds]), 250)\n",
    "            _psi_new = psi_NFW(_r) + psi_BH(_r)\n",
    "            vr_sq_grid = 2*_psi_new - 2*E - L**2/_r**2\n",
    "            inds = vr_sq_grid > 0\n",
    "        \n",
    "            integ = 0.0*vr_sq_grid\n",
    "            integ[inds] = 1/np.sqrt(vr_sq_grid[inds])\n",
    "            T_orb_samps_B[i] = np.trapz(integ, _r, axis=-1)\n",
    "            \n",
    "            integ2 = np.interp(r_array, _r, integ, left=0.0, right=0.0)\n",
    "            r_peri = np.min(_r[inds])\n",
    "            \n",
    "        else:\n",
    "            integ = 0.0*vr_sq_grid\n",
    "            integ[inds] = 1/np.sqrt(vr_sq_grid[inds])\n",
    "            T_orb_samps_B[i] = np.trapz(integ, r_array, axis=-1)\n",
    "            integ2 = 1.0*integ\n",
    "            r_peri = np.min(r_array[inds])\n",
    "        \n",
    "        \n",
    "        if (T_orb_samps_B[i] > 0):\n",
    "            contrib = (Vol/N_particles)*weights[i]*integ2/T_orb_samps_B[i]\n",
    "            P_r_B += contrib\n",
    "            #if (L > L_c(E)):\n",
    "            if (r_peri > 2*r_S):\n",
    "                P_r_C += contrib\n",
    "\n",
    "rho_r_B = P_r_B/(4*np.pi*r_array**2)\n",
    "rho_r_C = P_r_C/(4*np.pi*r_array**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "23c3bd89",
   "metadata": {},
   "outputs": [],
   "source": [
    "#--------------------\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "plt.loglog(r_array, rho_initial, c = rgb_palette_dict['dark sienna'], label = 'NFW')\n",
    "#plt.loglog(r_array, rho_GS_no_r_S, c = rgb_palette_dict['amber'], label = r'GS, $m_{BH} = 10^5 M\\odot$') #density_GS_pred\n",
    "# plt.loglog(r_array, rho_after_proto, c = rgb_palette_dict['purple pizzazz'], label = 'after isothermal collapse')\n",
    "plt.loglog(r_array, rho_array, c = rgb_palette_dict['flickr pink'], label = 'After SMS formation')\n",
    "plt.loglog(r_array, rho_GS_array, c = rgb_palette_dict['amber'], label = 'GS profile')\n",
    "#plt.loglog(r_array, rho_r,c='C1', linestyle=':')\n",
    "plt.loglog(r_array, rho_r_A,c='C2', linestyle='--', label=\"After SMS formation (sampled)\")\n",
    "plt.loglog(r_array, rho_r_B,c='C3', linestyle=':',lw=2, label=\"After DCBH formation (all)\")\n",
    "plt.loglog(r_array, rho_r_C,c='C4', linestyle=':',lw=2, label=\"After DCBH formation (uncaptured)\")\n",
    "plt.axvline(r_core, c = rgb_palette_dict['turquiose'], ls = '--')\n",
    "plt.axvline(2*r_S, c = 'k', ls = '--')\n",
    "plt.axvline(3*r_S, c = 'k', ls = '--')\n",
    "plt.axvline(4*r_S, c = 'k', ls = '--')\n",
    "plt.ylim(1E0, 1E25)\n",
    "plt.xlim(1E-9, 1E3)\n",
    "plt.legend()\n",
    "plt.ylabel(r'$\\rho$ [$M_\\odot$pc$^{-3}$]')\n",
    "plt.xlabel(r'$r$ (pc)')\n",
    "plt.savefig('./figures/density_NFW_rho_SMS.pdf')\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "#fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 9))\n",
    "plt.loglog(r_array, rho_GS_array, c = rgb_palette_dict['amber'], label = 'GS Profile')\n",
    "plt.loglog(r_array, rho_array, c = rgb_palette_dict['flickr pink'], label = 'After SMS formation')\n",
    "plt.loglog(r_array, rho_r_C, c=rgb_palette_dict['dark goldenrod'], linestyle='-',lw=2, label=\"After DCBH formation\")\n",
    "plt.axvline(2*r_S, c = 'k', ls = '--')\n",
    "plt.axvline(r_poly, c = 'k', ls = '--')\n",
    "plt.text(1.4*r_S, 8e19, r\"$2 r_\\mathrm{s}$\", rotation=90)\n",
    "plt.text(0.7*r_poly, 8e19, r\"$r_\\mathrm{SMS}$\", rotation=90)\n",
    "plt.ylim(1E14, 1E21)\n",
    "plt.xlim(1E-8, 1E-5)\n",
    "plt.legend()\n",
    "plt.ylabel(r'$\\rho_\\mathrm{DM}$ [$M_\\odot$pc$^{-3}$]')\n",
    "plt.xlabel(r'$r$ [pc]')\n",
    "plt.savefig('./figures/density_NFW_rho_SMS_zoom.pdf')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "df8a2ad1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import UnivariateSpline\n",
    "from scipy.signal import savgol_filter\n",
    "#\n",
    "#rho_array_smooth  = savgol_filter(rho_array_cut, 10, 3)\n",
    "#rho_r_C_smooth    = savgol_filter(rho_r_C_cut, 10, 3)\n",
    "#\n",
    "interval_start = 2*r_S\n",
    "interval_end = 10*r_poly\n",
    "print(interval_start)\n",
    "print(interval_end)\n",
    "indices_in_interval = np.where((r_array >= interval_start) & (r_array <= interval_end))[0]\n",
    "small_value = 1.e15\n",
    "#\n",
    "rho_array_cut = np.zeros(len(r_array))\n",
    "rho_r_C_cut = np.zeros(len(r_array))\n",
    "#\n",
    "rho_array_cut[:] = rho_array[:]\n",
    "rho_r_C_cut[:]   = rho_r_C[:]\n",
    "print(rho_array_cut)\n",
    "#\n",
    "rho_array_cut[~np.isin(np.arange(len(r_array)), indices_in_interval)] = small_value\n",
    "#\n",
    "rho_array_smooth  = savgol_filter(rho_array_cut, 30, 3)\n",
    "#\n",
    "rho_r_C_cut[~np.isin(np.arange(len(r_array)), indices_in_interval)] = small_value\n",
    "#\n",
    "rho_r_C_smooth  = savgol_filter(rho_r_C_cut, 30, 3)\n",
    "#\n",
    "print(rho_array)\n",
    "print(rho_array_cut)\n",
    "#\n",
    "spline_interpolation_rho = UnivariateSpline(r_array, np.log(rho_array_cut), s=3)\n",
    "spline_interpolation_rC  = UnivariateSpline(r_array, np.log(rho_r_C_cut), s=3)\n",
    "#\n",
    "log_rho_interpolated   = spline_interpolation_rho(r_array)\n",
    "log_r_C_interpolated   = spline_interpolation_rC(r_array)\n",
    "\n",
    "##\n",
    "plt.figure()\n",
    "plt.xlim(1E-8, 1E-5)\n",
    "plt.loglog(r_array, log_rho_interpolated, c = rgb_palette_dict['flickr pink'], label = 'logRho1')\n",
    "plt.loglog(r_array, np.log(np.abs(rho_array_smooth)), c = \"red\", ls=\"--\", label = 'logRho1_smooth')\n",
    "plt.loglog(r_array, log_r_C_interpolated, c = rgb_palette_dict['dark goldenrod'], label = 'logRho2')\n",
    "plt.loglog(r_array, np.log(np.abs(rho_r_C_smooth)), c = \"brown\", ls=\"--\", label = 'logRho2_smooth')\n",
    "#plt.ylim(1E0, 1E25)\n",
    "#plt.xlim(1E-9, 1E3)\n",
    "#plt.legend()\n",
    "plt.show()\n",
    "\n",
    "##\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 9))\n",
    "ax1.loglog(r_array, rho_GS_array, c = rgb_palette_dict['amber'], label = 'GS Profile')\n",
    "ax1.loglog(r_array, rho_array, c = rgb_palette_dict['flickr pink'], label = 'After SMS formation')\n",
    "#ax1.loglog(r_array, rho_array_smooth, c = \"red\", linestyle=\"--\", label = 'After SMS formation')\n",
    "ax1.loglog(r_array, rho_r_C, c=rgb_palette_dict['dark goldenrod'], linestyle='-',lw=2, label=\"After DCBH formation\")\n",
    "#ax1.loglog(r_array, rho_r_C_smooth, c=\"brown\", linestyle='--',lw=2, label=\"After DCBH formation\")\n",
    "ax1.axvline(2*r_S, c = 'k', ls = '--')\n",
    "ax1.axvline(r_poly, c = 'k', ls = '--')\n",
    "ax1.text(1.4*r_S, 8e19, r\"$2 r_\\mathrm{s}$\", rotation=90)\n",
    "ax1.text(0.7*r_poly, 8e19, r\"$r_\\mathrm{SMS}$\", rotation=90)\n",
    "ax1.set_ylim(1E14, 1E21)\n",
    "ax1.set_xlim(1E-8, 1E-5)\n",
    "ax1.legend()\n",
    "ax1.set_ylabel(r'$\\rho_\\mathrm{DM}$ [$M_\\odot$pc$^{-3}$]')\n",
    "ax1.set_xlabel(r'$r$ [pc]')\n",
    "#\n",
    "interval_start_2 = 2*r_S\n",
    "interval_end_2 = 10*r_poly\n",
    "print(interval_start_2)\n",
    "print(interval_end_2)\n",
    "indices_in_interval_2 = np.where((r_array >= interval_start_2) & (r_array <= interval_end_2))[0]\n",
    "#slope_1 = np.gradient(log_rho_interpolated, np.log(r_array))\n",
    "#slope_2 = np.gradient(log_r_C_interpolated,   np.log(r_array))\n",
    "slope_1 = np.gradient(np.log(np.abs(rho_array_smooth)), np.log(r_array))\n",
    "slope_2 = np.gradient(np.log(np.abs(rho_r_C_smooth)),   np.log(r_array))\n",
    "spline_slope_1 = UnivariateSpline(r_array, np.abs(slope_1), s=3)\n",
    "spline_slope_2 = UnivariateSpline(r_array, np.abs(slope_2), s=3)\n",
    "slope_1_interp = spline_slope_1(r_array)\n",
    "slope_2_interp = spline_slope_2(r_array)\n",
    "#\n",
    "interval_start_ = 5*r_S\n",
    "interval_end_ = 0.5*r_poly\n",
    "indices_in_interval_ = np.where((r_array >= interval_start_) & (r_array <= interval_end_))[0]\n",
    "#\n",
    "slope_1_cut = np.abs(slope_1[:])\n",
    "slope_1_cut[~np.isin(np.arange(len(r_array)), indices_in_interval_)] = 0.\n",
    "slope_2_cut = np.abs(slope_2[:])\n",
    "slope_2_cut[~np.isin(np.arange(len(r_array)), indices_in_interval_)] = 0.\n",
    "#\n",
    "slope_1_interp_cut = np.abs(slope_1_interp[:])\n",
    "slope_1_interp_cut[~np.isin(np.arange(len(r_array)), indices_in_interval_)] = 0.\n",
    "slope_2_interp_cut = np.abs(slope_2_interp[:])\n",
    "slope_2_interp_cut[~np.isin(np.arange(len(r_array)), indices_in_interval_)] = 0.\n",
    "#\n",
    "slope_1[~np.isin(np.arange(len(r_array)), indices_in_interval_2)] = 0.01\n",
    "slope_2[~np.isin(np.arange(len(r_array)), indices_in_interval_2)] = 0.01\n",
    "ax2.plot(r_array, slope_1_cut, c = rgb_palette_dict['flickr pink'], ls=\":\")\n",
    "ax2.plot(r_array, slope_1_interp_cut, c = rgb_palette_dict['flickr pink'], ls=\"-\")\n",
    "ax2.plot(r_array, slope_2_cut, c = rgb_palette_dict['dark goldenrod'], linestyle=':',lw=2)\n",
    "ax2.plot(r_array, slope_2_interp_cut, c = rgb_palette_dict['dark goldenrod'], ls=\"-\")\n",
    "ax2.set_xscale(\"log\")\n",
    "ax2.set_ylabel(\"Log Slope\")\n",
    "ax2.set_xlim(1E-8, 1E-5)\n",
    "ax2.set_ylim(4E-1, 3E0)\n",
    "plt.tight_layout()\n",
    "plt.savefig('./figures/density_NFW_rho_SMS_zoom_2.pdf')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93c0d354",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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