{
"cells": [
{
"cell_type": "markdown",
"id": "e7d996ee-25b8-467c-b755-6b8d5d7ed2e6",
"metadata": {},
"source": [
"# Some examples of lenstool usage on Jupyter Notebook\n",
"\n",
"## The SIS model (Singular Isothermal Sphere)\n",
"In this notebook we will showcase lensing modelling with Lenstool using the SIS model."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "2ec98e29-83d0-4169-86e0-33f6dcdf7cdf",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"'8.6.1'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from astropy.io import fits\n",
"import matplotlib.pyplot as plt\n",
"from astropy.wcs import WCS\n",
"from astropy.table import Table\n",
"from matplotlib.patches import Ellipse\n",
"from matplotlib.patches import Circle\n",
"import os\n",
"import matplotlib.cm as cm\n",
"from matplotlib.colors import Normalize\n",
"import numpy\n",
"import lenstool\n",
"from lenstool.potentials import sis\n",
"lenstool.__version__"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a261dee0",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"lt = lenstool.Lenstool()\n",
"lt.add_lens(sis(0.,0.,0.3,800))\n",
"lt.set_cosmology(70, 0.3, 0.7, -1)\n",
"lt.set_field(50)\n",
"lt.set_grid(1000, 1)"
]
},
{
"cell_type": "markdown",
"id": "7868fad7-52ca-45a3-ac4e-e0481d1f2edd",
"metadata": {
"tags": []
},
"source": [
"## The inputs\n",
"\n",
"We will first define the lens model. In this example, the lens is a single SIS potential. It is centered at (0,0) and has a redshift of 0.3.\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0880def5-0182-482d-a3ad-763269e1e3f1",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"
Table length=1 \n",
"
\n",
"type n x y z \n",
"int64 str1 float64 float64 float64 \n",
"1 1 0.0 0.0 0.3 \n",
"
"
],
"text/plain": [
"\n",
" type n x y z \n",
"int64 str1 float64 float64 float64\n",
"----- ---- ------- ------- -------\n",
" 1 1 0.0 0.0 0.3"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lt.get_lenses()"
]
},
{
"cell_type": "markdown",
"id": "c70fc0a2-d357-4b60-a078-90950fa24603",
"metadata": {},
"source": [
"## The source definition\n",
"The source properties are coordinates in arcsec, size, redshift, orientation angle and magnitude (brightness).\n",
"These parameters must be given directly in the code .\n",
"Here we study a circular source of redshift 1 and magnitude 20. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "761a9d04-506b-4daa-90a7-b6d71f3a9813",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 0.6789067 -9.7 3.5 3.5 0.0 1.0 20.0 \n",
"
"
],
"text/plain": [
"\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64\n",
"---- --------- ------- ------- ------- ------- ------- -------\n",
" 1a 0.6789067 -9.7 3.5 3.5 0.0 1.0 20.0"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = Table(names=['n','x','y','a','b','theta','z','mag'], dtype=['str',*['float',]*7])\n",
"tab.add_row(['1a', 0.6789067, -9.7, 3.5, 3.5, 0, 1.0, 20])\n",
"tab.meta['iref'], tab.meta['ref_ra'], tab.meta['ref_dec'] = 3, 0, 0\n",
"lt.set_sources(tab)\n",
"lt.get_sources()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "68b2638d-98e9-4509-8746-2ec008e0ebbc",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
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XERGB4OBg81Jfq9KFCxdgNBoRGhoqWR8aGgq9Xm+1/E6dOsHPzw8JCQmYNm2auSULAHr06IGcnBzs3LkTubm58Pf3x6BBg3D69GlF58DuPCIiIrKLSYPuvNrBNs+dO4egoCDzej8/vwb30cm6XYUQFuvkDhw4gKtXr+LTTz/F3Llzcdddd+GJJ54AAAwcOBADBw40bzto0CD07dsXa9euxZo1a+w+FwZR1LSaaw4Uc55U03k5/t4RJua52GTrPdpccqaYI2WVSXjBpHKwzNr9g4KCJEFUfUJCQuDt7W3R6nT+/HmL1im5qKgoAEDPnj3x448/YtGiReYgSs7Lywv9+vVT3BLFb3YiIiJySb6+voiPj0dBQYFkfUFBAZKSkuwuRwhRb85V3edLS0vRoUMHRfVjSxQRERHZxQgdjCoHy1S6f2ZmJtLS0pCQkIDExERs3LgR5eXlmDp1KgAgKysLFRUV2LJlCwDg9ddfR+fOndGjRw8At8eNevXVVzFjxgxzmYsXL8bAgQMRHR0Ng8GANWvWoLS0FK+//rqiujGIIiIiIrto2Z1nr9TUVFy8eBFLlixBZWUl4uLisGvXLkRGRgIAKisrUV5e/r/yTSZkZWWhrKwMPj4+6NatG/74xz/i2WefNW9z+fJlTJkyBXq9HsHBwejTpw/279+P/v37K6qbTgh2+Lo7g8GA4OBgJGMMfHQtnF0dKeZANStq8pbcVbPNt2ouOVJ1ueDP5S1xE4XYgaqqKpv5RWrU/s4sPvIg/Fupa3+5cfUWFg7Y2+h1bgpsiSIiIiK7GKG8O66+MjwFgygiIiKyizO681yZ55wJERERURNiSxSRFjw0B6o55jgppfQaeUwOFefea5aMwgtGlS1Javd3JQyiiIiIyC4COphU5kQJlfu7Es8JB4mIiIiaEFuiiIiIyC7szpNiEEXaaw5jQ7lxDhTznJxLyfV3q/yp5pAjxXn1YBI6mIS67xC1+7sS9/0lICIiInIitkQRERGRXYzwglFl+4va/V0JgygiIiKyC7vzpBhEkXqemgPlpnlPzHnyHLZeS5fOmbL2+fGUfCnmSDV7DKKIiIjILiZ4waSyO07t/q6EQRQRERHZxSh0MKrsjlO7vythEEXKsfvOpXhs911jvh4e0p0kf+1dunuvLk8dDoHde80OgygiIiKyCxPLpRhEERERkV2E8IJJ5YjjwoNGLPecMyEiIiJqQmyJInJxbpXz5C55ZVrW04Xyedx6SARyC0boYITKxHKV+7sSBlFERERkF5NQn9PkSbG8m/zZSERERORa2BJFREREdjFpkFiudn9XwiCKbOO4UE3KpXKgXPQauRSl18iJOVR131sulR/FcaPchgk6mFTmNKnd35XwG5KIiIjIAWyJIiIiIrtw2hcpBlFERERkF+ZESTGIoubDhfN7nJYH5cLXxGPZuuZNlA/k0vPueWqOFHkcBlFERERkFxM0mDvPgxLLGUQRERGRXYQGd+cJDwqi2JZPRERE5AC2RJElTxkXyoXyfZw69pMLXQcJVxoPS86Z+UHWXq9GzA1y6Xn3PCVHygPGjTIJDbrzeHceERERNTe8O0/Kc86EiIiIqAmxJYqIiIjswu48KQZR5DlcKPen2eZAuXKekxJKzqMpc4WcmBvkUuNKeUqOlBvi3HlSrvOrQ0RERORGGEQRERGRXWq789QuSq1fvx5RUVHw9/dHfHw8Dhw40OC2Bw8exKBBg9CuXTsEBASgR48eWL16tcV277//PmJjY+Hn54fY2Fhs375dcb0YRBEREZFdnBFE5eXlISMjA/PmzUNJSQkGDx6MESNGoLy8vN7tAwMDMX36dOzfvx8nT57E/PnzMX/+fGzcuNG8TVFREVJTU5GWloYvv/wSaWlpeOyxx3DkyBFFddMJ4YYDVZCEwWBAcHAwkjEGProWygvguFCaa9KcqMY8b0/JcXIljZlL1IS5QS41156n5EQ58HN8S9xEIXagqqoKQUFBjVCp22p/Z0bsfgYtAn1VlXXzWg0+Gf6W3XUeMGAA+vbtiw0bNpjXxcTEYOzYsVi+fLldxxw3bhwCAwPx//7f/wMApKamwmAw4JNPPjFvM3z4cLRp0wa5ubl2n4vr/OoQERGRS9OyJcpgMEiW6upqi+PV1NSguLgYKSkpkvUpKSk4fPiwXXUuKSnB4cOHMWTIEPO6oqIiizKHDRtmd5m1GEQRERGRXbQMoiIiIhAcHGxe6mtVunDhAoxGI0JDQyXrQ0NDodfrrda1U6dO8PPzQ0JCAqZNm4bJkyebn9Pr9Q6VKccgSgPLly9Hv3790Lp1a9x5550YO3YsTp06JdlGCIFFixYhPDwcAQEBSE5Oxtdffy3ZpkuXLigsLERhYSG6dOnShGfgxnRe/1ucWg2dZNG4cOuLGl4664uGdDqd2y6aasxr3pjvFYtDNeJ7XnllXOJ7gJQ5d+4cqqqqzEtWVlaD28o/h0IIm5/NAwcO4PPPP8cbb7yB7Oxsi246R8qU4ztOA/v27cO0adPw6aefoqCgALdu3UJKSgquXbtm3ubll1/GqlWrsG7dOhw9ehRhYWEYOnQorly54sSaExER2U/gf2NFObrUZn4FBQVJFj8/P4vjhYSEwNvb26KF6Pz58xYtSXJRUVHo2bMnnnnmGTz33HNYtGiR+bmwsDCHypRjEKWB3bt3Y+LEibjnnnvQu3dvbN68GeXl5SguLgZwO7rNzs7GvHnzMG7cOMTFxeGdd97B9evXsXXrVifXnoiIyD5NfXeer68v4uPjUVBQIFlfUFCApKQku8sRQkhyrhITEy3KzM/PV1QmwBHLG0VVVRUAoG3btgCAsrIy6PV6SRKbn58fhgwZgsOHD+PZZ591Sj2JiIhcXWZmJtLS0pCQkIDExERs3LgR5eXlmDp1KgAgKysLFRUV2LJlCwDg9ddfR+fOndGjRw8At8eNevXVVzFjxgxzmbNmzcJ9992HFStWYMyYMdixYwf27t2LgwcPKqobgyiNCSGQmZmJX/ziF4iLiwMAc5NhfUlsZ8+eNT8+c+ZMvf+Xq72ToZZDXYLuOqyBi+Q8NGoOSGOfYyPWXfP8IRdh7bw0HyWm7uuj9TACdd9bGg8L4DLTwrjzlDB132cK31cVFRWS34XaLjKtOWPuvNTUVFy8eBFLlixBZWUl4uLisGvXLkRGRgIAKisrJWNGmUwmZGVloaysDD4+PujWrRv++Mc/ShoskpKSsG3bNsyfPx8LFixAt27dkJeXhwEDBiiqG4MojU2fPh3Hjh2rN5rVIokNAEaPHo19+/Y5XEciIvIssbGxksdDhgxBYWGh5sdx1gTE6enpSE9Pr/e5nJwcyeMZM2ZIWp0a8utf/xq//vWvFdelLgZRGpoxYwZ27tyJ/fv3o1OnTub1YWFhAG63SHXo0MG83pEkNgDYuXOnRUuU/ANERETNx4kTJ9C6dWvz48YceJP+h0GUBoQQmDFjBrZv347CwkJERUVJno+KikJYWBgKCgrQp08fALcHENu3bx9WrFih+HjyZtq6ARURETU/HTt2bJLAyVktUa6KQZQGpk2bhq1bt2LHjh1o3bq1OQcqODgYAQEB0Ol0yMjIwLJlyxAdHY3o6GgsW7YMLVu2xPjx451ce7KX2+ZBaVjvRs158nJivpvJ8bwZW9dEVc6U/LXTMs+okXOH6n5eXGqKGFJFCB2EyiBI7f6uhEGUBmrn80lOTpas37x5MyZOnAgAmDNnDn7++Wekp6fj0qVLGDBgAPLz8yXNr0REROQ+GERpwJ6/NHU6HRYtWiQZ7IuIiMid1A6YqbYMT8EgioiIiOzCnCgpBlHNhbuO3+Mi40K5FRU5UNrPE+cmr5+SeirMn9I0Z6oxc6Q8lbuOGyV/32g9HhlpgkEUERER2YWJ5VIMooiIiMgu7M6TcpO2diIiIiLXwpYooga4zbhQzsyBUpPz5Mp5etbyT2yds8qcKaflSDVi7pDLzKtHqrE7T4pBFBEREdlFaNCd50lBFLvziIiIiBzAligiIiKyi4D60RY8qTOXQRTRf3lqDpSqvCelOU9a5jk15hhTtvKWlJyH/BdFZc6UtdfLZr4Uc6SokZmgg44jlpuxO4+IiIjIAWyJIiIiIrvw7jwpBlGeypVvH7fGU6Z5Yfed+rIbk9K6WOuCUzo9h/zYCoZEUDwcgpt07zUpdz0PF5kGxiR00HGwTTMGUURERGQXITRILPegFDgX+tOQiIiIyH2wJYqIiIjswpwoKQZR1Gw16pAGajRlvWzlBinNr1KQa6R6yplGZJFrZO285DlNts7LVtkKp41RpO57y4WGFeCQB+SuGEQRERGRXdgSJcUgioiIiOzCu/OkmFhORERE5AC2RJFzcVyo21TkQSnOLbKW32OrLIXjK1mtm9rcL2vXXOXYPzoruyvKlwJs50xZK0/hFDE2x42SHEflGFLuOt6SnKecRxPhEAdSDKKIiIjILreDKLU5URpVxgV4SDMAERERUdNiSxQRERHZhXfnSTGIInIzrpQDZbMu1vKelOaRKcqh8pY+VJrv49VwXoy1fCnAjpwpJTlSCseQUpUjRWQH8d9FbRmegt15RERERA5gSxQRERHZhd15UgyiiIiIyD7sz5NgEOVJdDrlc501I5rOlefEcaFsl61iPjytc6CsXSdb10DL97K3jbGZ5EzW6i3LS5LlW9nMS1KSI9WU8+y50LhRnEvPDub3ic6jghJ3wyCKiIiI7KNBdx48qDuPieVERERkl9oRy9UuSq1fvx5RUVHw9/dHfHw8Dhw40OC2H3zwAYYOHYr27dsjKCgIiYmJ2LNnj2SbnJwc6HQ6i+XGjRuK6sUgioiIiFxWXl4eMjIyMG/ePJSUlGDw4MEYMWIEysvL691+//79GDp0KHbt2oXi4mLcf//9ePjhh1FSUiLZLigoCJWVlZLF399fUd3YnUfk4hSPC6VEY+dA1X3eVlnW9tWaPMdGnr9jLYdKni/V2DlSKnDcKNKaM+7OW7VqFSZNmoTJkycDALKzs7Fnzx5s2LABy5cvt9g+Oztb8njZsmXYsWMH/va3v6FPnz7m9TqdDmFhYcpPoA62RBEREZF9hE6bBYDBYJAs1dXVFoerqalBcXExUlJSJOtTUlJw+PBhu6psMplw5coVtG3bVrL+6tWriIyMRKdOnTBq1CiLlip7MIgiIiKiJhcREYHg4GDzUl+r0oULF2A0GhEaGipZHxoaCr1eb9dxVq5ciWvXruGxxx4zr+vRowdycnKwc+dO5Obmwt/fH4MGDcLp06cVnQO786hpqR0agCypGdLAYlMNu+/kx7axrcWxG7MbUyft1rLoXrC4pb5OF5v8cmvdvSfdWPq4KYc8aK40HKrBEzmaGC4vAwDOnTuHoKAg83o/P78G96nvc2NPqkNubi4WLVqEHTt24M477zSvHzhwIAYOHGh+PGjQIPTt2xdr167FmjVr7D0VBlFERERkJw0H2wwKCpIEUfUJCQmBt7e3RavT+fPnLVqn5PLy8jBp0iS89957ePDBB61u6+XlhX79+iluiXKoWWD58uX405/+ZLH+T3/6E1asWOFIkUREREQSvr6+iI+PR0FBgWR9QUEBkpKSGtwvNzcXEydOxNatW/HQQw/ZPI4QAqWlpejQoYOi+jkURL355pvo0aOHxfp77rkHb7zxhiNFEhERkYurvTtP7aJEZmYm3n77bfzpT3/CyZMn8dxzz6G8vBxTp04FAGRlZWHChAnm7XNzczFhwgSsXLkSAwcOhF6vh16vR1VVlXmbxYsXY8+ePfj+++9RWlqKSZMmobS01FymvRzqztPr9fVGa+3bt0dlZaUjRRJpTtNpXm4X6Pi+CuqiekgDm3lNCs5DTQ6UbHudt5f1beX10jJHSp7EIXuss5h6RZYzZaz7SLatyhwpC3Wvg7UpYQDFySl131s2hzvQchoYlXlFnAbGxTTx5U9NTcXFixexZMkSVFZWIi4uDrt27UJkZCQAoLKyUjJm1Jtvvolbt25h2rRpmDZtmnn9U089hZycHADA5cuXMWXKFOj1egQHB6NPnz7Yv38/+vfvr6huDgVREREROHToEKKioiTrDx06hPDwcEeKJCIiIqpXeno60tPT632uNjCqVVhYaLO81atXY/Xq1arr5VAQNXnyZGRkZODmzZv45S9/CQD4+9//jjlz5mD27NmqK0VERESuxxmDbboyh4KoOXPm4KeffkJ6ejpqamoAAP7+/njhhReQlZWlaQWJiIjIRWh4d54ncCiI0ul0WLFiBRYsWICTJ08iICAA0dHRVsd4ICKNKMlpssEi/0rDHChAlgcl39bbW/ZYYU6UtRwpGzlQFo+NsrKMkiQoyXlI86MAtTlSOtnuqqZm4bhRRE1K1bexXq/HTz/9hG7dusHPz4/zMhEREXk0nUaLZ3AoiLp48SIeeOAB3H333Rg5cqT5jrzJkyczJ4qIiMhTCY0WD+FQEPXcc8+hRYsWKC8vR8uWLc3rU1NTsXv3bs0qR0REROSqHMqJys/Px549e9CpUyfJ+ujoaJw9e1aTihE1J6rHhrJGwxwqRTlQ8u3lOVA+sseyegp5WfLzsDb2lnwcIVlukM5oY/wluTo5UvJztJkjpebP7kbMcVI0hx9RLSaWSzgURF27dk3SAlXrwoULTC4nIiLyVEJ3e1Fbhodw6E/U++67D1u2bDE/1ul0MJlMeOWVV3D//fdrVjkiIiIiV+VQS9Qrr7yC5ORkfP7556ipqcGcOXPw9ddf46effsKhQ4e0riMRERG5ACEUzzZUbxmewqEgKjY2FseOHcOGDRvg7e2Na9euYdy4cZg2bZriGZCJPJLW8/ZZozCfSpILo3RcKDlb40bVzYOS5UAJeU6UjZwp4SPLRbKS6yWfC093S/pY3JIlMsnHhWqwZMttLa6BPEfKYg46+8eNspmnpHIuPUXUzqVHnoE5URIOBVEAEBYWhsWLF2tZFyIiIiK3YXcQdezYMbsL7dWrl0OVISIiIhfGxHIJu4Ooe++9FzqdDkIISXdAbXNz3XVGeXM3ERERuT2duL2oLcNT2B1ElZWVmf9fUlKC559/Hr/73e+QmJgIACgqKsLKlSvx8ssva19LouZMy3Ge1JKPC2Ux956srnXHVLJ4Tpbz5Cf9OhK+0scm2fOmFg1fF6+b0jwjr+pbkse6Gmm9ddWyAuT5Pt51HsvyjnSyx0KeV2Y5kFTT4Vx6RI3K7iAqMjLS/P9HH30Ua9aswciRI83revXqhYiICCxYsABjx47VtJJERETkAphYLuFQYvnx48cRFRVlsT4qKgonTpxQXSkiIiJyQcyJknAoiIqJicHSpUuxadMm+Pv7AwCqq6uxdOlSxMTEaFpBcnPyrg134q51b8xpXmwNaWDlscU0LvIhDGTdd7da+Uoe32wle75lw+fpc13abdXiqnRbn6uyahplXXLyIRLqPrZ1zvJrZPGD4ZrTwDQqiy5ON6k3IK27O9WbmoRDQdQbb7yBhx9+GBEREejduzcA4Msvv4ROp8NHH32kaQWJiIjIRbA7T8KhIKp///4oKyvDn//8Z/zrX/+CEAKpqakYP348AgMDta4jERERuQIGURIOD7bZsmVLTJkyRcu6EBEREbkNh4Oo+lRWVuLmzZvo3LmzlsUS2UXXlFOteCq119BavpAsn0c+jYt8CAN5DtS1MGkO1dWIhuva6pz0uUC99Hn5EAi6m7JpX27JcnjqnofCaXYs2JomhmySf9YFp6BpOmyJktA0iPrlL3+Jb775hoNtEhEReSLenSehaRC1ZcsWXL9+XcsiiYiIiFySpvdw9+vXD0OGDNGySLeyfv16REVFwd/fH/Hx8Thw4ID5OSEEFi1ahPDwcAQEBCA5ORlff/21ZP8uXbqgsLAQhYWF6NKlSxPXnoiIyLraaV/ULp5C05ao5iwvLw8ZGRlYv349Bg0ahDfffBMjRozAiRMn0LlzZ7z88stYtWoVcnJycPfdd2Pp0qUYOnQoTp06hdatWzu7+tRcNfZYWJKcKFkeiyxHSj6Ni3wcKHkO1L+eWd/gYXu8lS557GeQliUfN8pLVheL/Dq1eVDWWLwGTIcgF8acKAmHvkHbtGmDtm3b2rU0F6tWrcKkSZMwefJkxMTEIDs7GxEREdiwYQOEEMjOzsa8efMwbtw4xMXF4Z133sH169exdetWZ1ediIiIHOBQS9SCBQuwdOlSDBs2TDIB8Z49e7BgwYJmFTwBQE1NDYqLizF37lzJ+pSUFBw+fBhlZWXQ6/VISUkxP+fn54chQ4bg8OHDePbZZ5u6ykRERKSSQ0HUoUOHsGTJEkyfPt28bubMmVi3bh327t2LDz/8UKv6uYULFy7AaDQiNDRUsj40NBR6vR56vd78WP782bNnzY/PnDlT7/+JiIhcgQ7qc5o85948B4OoPXv2YMWKFRbrhw0bZtEa05zoZHkTQgjJOlvP28tgMMBgMJgfX7lyRXEZRETkOSoqKiS/C0FBQQgKCnJijZoHh3Ki2rVrh+3bt1us//DDD9GuXTvVlXI3ISEh8Pb2Nrc41Tp//jxCQ0MRFhYGAA0+r9To0aMRERFhXmJjYx2vPBERub3Y2FjJ78Lo0aMb50C140SpXTyEQy1RixcvxqRJk1BYWGjOifr000+xe/duvP3225pW0B34+voiPj4eBQUFeOSRR8zrCwoKMGbMGERFRSEsLAwFBQXo06cPgNt5VPv27au3Rc+WnTt3WrREMZAiImq+Tpw4IbnTu9FaoXh3noRDQdTEiRMRExODNWvW4IMPPoAQArGxsTh06BAGDBigdR3dQmZmJtLS0pCQkIDExERs3LgR5eXlmDp1KnQ6HTIyMrBs2TJER0cjOjoay5YtQ8uWLTF+/HjFx5I309YNqIiIqPnp2LEju++cwOFxogYMGIB3331Xy7q4tdTUVFy8eBFLlixBZWUl4uLisGvXLkRGRgIA5syZg59//hnp6em4dOkSBgwYgPz8fI4RRc4lTLIV3vVu5nj5df7klM1vpjNJjy2fz87nuvSxfD48+VhQ0m2lx5KXZTF3nqwu8rpKzkNrFq8BkQtjS5SEw0HUd999h82bN+P7779HdnY27rzzTuzevRsRERG45557tKyj20hPT0d6ev1f7DqdDosWLcKiRYuatlJEREQa0WLEcU8asdyhxPJ9+/ahZ8+eOHLkCN5//31cvXoVAHDs2DEsXLhQ0woSERERuSKHgqi5c+di6dKlKCgogK+vr3n9/fffj6KiIs0qR0RERC5EaLQoZG1uWrkPPvgAQ4cORfv27REUFITExETs2bPHYrv3338fsbGx8PPzQ2xsbL2jDtjiUHfe8ePH652upH379rh48aIjRRKpJuQ5N/L5z8g2eS6Qt8JrKM8dkuREyfKQbsnylKpvSR7L57cLlI4QYjEfXl3yHKgWV6Vly48lr4u8rpLzUJsfJb/GpJj8s05NyAk5UbbmppXbv38/hg4dimXLluGOO+7A5s2b8fDDD+PIkSPmO+SLioqQmpqKP/zhD3jkkUewfft2PPbYYzh48KCiG+Qcaom64447UFlZabG+pKQEHTt2dKRIIiIiIgvW5qatT3Z2NubMmYN+/fqZ74aPjo7G3/72N8k2Q4cORVZWFnr06IGsrCw88MADyM7OVlQ3h4Ko8ePH44UXXoBer4dOp4PJZMKhQ4fw/PPPY8KECY4USURERC6uNrFc7QL8b/aN2qW6utrieLVz09adexb439y09jCZTLhy5YpkXt+ioiKLMocNG2Z3mbUcCqJeeukldO7cGR07dsTVq1cRGxuL++67D0lJSZg/f74jRRIREZGr03DE8oiICAQHB5uX5cuXWxzO1ty09li5ciWuXbuGxx57zLxOr9erKrOWQzlRLVq0wLvvvos//OEP+OKLL2AymdCnTx9ER0c7Uhx5MvkYODqH4nbncNe6y/N5vFTUW57/I89Fkd+rbCUnSmeU1kvcMkqLqpHmX/lclRYlH9tJnjNlbVuLHKga6WPI62JUkBNl6xppOcaU/LV1F+48FpY7193FnTt3TjJAqJ+fX4PbOjr3bG5uLhYtWoQdO3bgzjvv1KTMuhweJwoAunbtiq5du6opgoiIiNyFhonl9kySbGtuWmvy8vIwadIkvPfee3jwwQclz4WFhWkyn62mf1rv2LEDW7Zs0bJIIiIichFa5kTZo+7ctHUVFBQgKSmpwf1yc3MxceJEbN26FQ899JDF84mJiRZl5ufnWy2zPqpaouReeOEFnD59msnlRFrSsntOLVnXhpDNxm4xfYqxzvPyZnKjrAtNllOqM8qGrLgp3d7LynWQ18NiCANZ9528LhbXvG73nkl+DeTddy7U/eOu3X9EdVibmxYAsrKyUFFRYW7Eyc3NxYQJE/Daa69h4MCB5hangIAABAcHAwBmzZqF++67DytWrMCYMWOwY8cO7N27FwcPHlRUN02/jf/1r3/BKP8yIiIiIs/ghME2U1NTkZ2djSVLluDee+/F/v37JXPTVlZWory83Lz9m2++iVu3bmHatGno0KGDeZk1a5Z5m6SkJGzbtg2bN29Gr169kJOTg7y8PEVjRAGATlj8GUXuxmAwIDg4GMm6sfDRtXB2daxrwuRszQfbVFJ3hcdWlMwob4Gxta9se8mx5PWUn6PF87LH3tIJi3XyutV93ke6rZA9lpdlub20bNGILVE6+fN1H8u2FRatVrJ9bSaeNzz5scXXs62WJaXbS3ZV+FOgZMBLjVvnmnSwTVdqWazHLXETheJDVFVV2cwvUqP2d6brgmXw9vdXVZbxxg18/4cXG73OTcGhX7Tdu3dLmrxef/113HvvvRg/fjwuXbqkWeWIiIiIXJVDQdTvfvc7GAwGALengJk9ezZGjhyJ77//HpmZmZpWkMgtmYR0aUxCSBebmwvzYlFPYZIuts7DYn/ZYjT+b7klXXTy5eYtyYKam5JFd0O6eN2oaXCRb2tRluxY8rrI6yo5D/k5Kr5G1q+x5PXR+LVXpSnf0+S6nNCd58ocSiwvKytDbGwsgNsT+I0aNQrLli3DF198gZEjR2paQSIiInIRGg5x4Akcaony9fXF9evXAQB79+41D53etm1bcwsVERERkSdzqCXqF7/4BTIzMzFo0CB89tlnyMvLAwB888036NSpk6YVJCIiItegdJynhsrwFA4FUevWrUN6ejr++te/YsOGDejYsSMA4JNPPsHw4cM1rSBRc1A3/0XptAM2NeY0MJCNmSS7MU3nXedYtoY/8ZaNCyWvt/y6WLtOtqZmkT+WT/Ni5Q47YTEljJUpYtRqxHGeeGM2kXoOBVGdO3fGRx99ZLF+9erVqitERERE5A4cHrHcaDTiww8/xMmTJ6HT6RATE4MxY8bAWz7WCxEREXkGJpZLOBREffvttxg5ciQqKirQvXt3CCHwzTffICIiAh9//DG6deumdT2JiIjIyZgTJeVQEDVz5kx069YNn376Kdq2bQsAuHjxIp588knMnDkTH3/8saaVJKI6NMxxkufF6OQpOF7y0bTlI5rLS2w4R0qSHwXYHtlbSQ6ULbZyouTXVPa8JA/KVg6UghHJb+/uHjlURGTJoSBq3759kgAKANq1a4c//vGPGDRokGaVIyIiIhfjQS1JajkURPn5+eHKlSsW669evQpfX1/VlSIiIiIXxJwoCYeCqFGjRmHKlCnYtGkT+vfvDwA4cuQIpk6ditGjR2taQSIi4HZvXnzPcIx6IBo9uoXAz88H167XoPh4JT76+zc4XfaTs6tIRM2MQ0HUmjVr8NRTTyExMREtWrQAANy8eRNjxozBa6+9pmkFiRwln+ld56Vy/KW6uS06hXlI8jwZK3WxyFNSmgtkK7eobt6MrXwqi3o7niMlH0NKfg10VurdsUMQfp95Pzp3vAPfnbmInXtO4vrPN3FHcACSk6KQcl83fHH8Byxfsw9Xr9VYPyfAMudJSV6Tyhwom6zlNanMn1KUf6V2fjz5dVBVlAc1Xbg5JpZLORRE3XHHHdixYwe+/fZbnDhxAgAQGxuLu+66S9PKERF17BCElYtG4HLVDTy3cBf+dfo/kue3/KUEA+MjMPOZRLy8YBieX7wb13++6aTaEnk4dudJOHxbz6ZNmzB27Fg8+uijePTRRzF27Fi8/fbbWtaNiJo5nQ5Y8Nz9uFx1A88v/sQigAIAkxA4/Hk55izZjZB2gZj22wFOqCkRNUcOBVELFizArFmz8PDDD+O9997De++9h4cffhjPPfcc5s+fr3UdiaiZ6n1PB0R2ugNrNxXZ7KYrr6jCn/9aivsGRqHNHQFNVEOi5qW2O0/t4ikc6s7bsGED3nrrLTzxxBPmdaNHj0avXr0wY8YMLF26VLMKkoeR50kozS0iS7bGjbKVIyXZ1EY+lqocKfn8dLJjy98LXjqMerA7ys7+hK9O6husc117932L36b2xfDku7D1gy8b3tBWHpNc3euiMgdKUV6SrW05LpT2NMzl8kjszpNw6BfMaDQiISHBYn18fDxu3bqlulJERABwd7cQfFp8zu7tr12vwbETetzdNaQRa0VEdJtDQdSTTz6JDRs2WKzfuHEjfvOb36iuFBERAPj7+eDnG8qSxK/fuAk/f4enBSUia4RGi4dw+Jtm06ZNyM/Px8CBAwEAn376Kc6dO4cJEyYgMzPTvN2qVavU15KoGVM95IE1NroCte3eszHMg3wMBKHD1WvVaBPsbzlFjBVt7wiAwXDD+j42u8msPK91910jdslpOqUMETjEgZxDQdRXX32Fvn37AgC+++47AED79u3Rvn17fPXVV+btNP2yJ6Jm52jJOQxJ6opNf/4Mt27ZDjZC72yFuB5heO3NA01QOyJq7hwKov75z39qXQ8iIgsf7zmJ0cPvwX2JXfGPA9/a3H708Htw7XoNCg9+1wS1I2qGmFguwVujiMhlnf33ZRz67AymTU7CXV3bWd12SFJXPPJQHLZ//BWqa+zv/iMiBZgTJcEgypMI8b+FLAiTkCwqC5MuSpmEdNGSySRd5Ky9T2zsK4SQLJb7y85Lfp3qLvJt5YvRBBhNeDX7nzj378t4ZdEopD7SG8Gt/STn0DEsCP/324F4Ydb9+MeBb5H71y+k5yj+V5Z5sXVsJfVWfI0a7/VRRe17Uu1nQlKUhp9VT8Xve5fAW1iIyKX9fOMmXlj4EZ79bSLG/6oPnny0L77+14+4/nMN2twRgJi7Q2G4cgNbtn2OvO2l/E0hakRMLJdiEEVELq+6+hbWbDyIP209ipT770aP6Dvh7+cD/Y9X8NGekzhQ9D1q2IVH1PiYEyXBIIqI3MbVq9X44G/HnV0NIiIADKKI3I7icaOsjQVla0oYheNIyemspcbIx5SyRd7QZG3KILVTd1jJw1E89pKt3CVr5SnMe+K4UNTY2J0nxSCKiIiI7MPuPAnenUdERETkALZEERERkX3YEiXBIIqcS567Yi3PxZWpPY+6OTjyOeVsHVpNjpQsx0lxjpScgpwpq/lSdmm8u/EU5RYpHa9Jw7n0VOVAaTFWmifwlPNoIrr/LmrL8BRu+otFRERE5FxsiSIiIiL7sDtPgi1RREREZJfaIQ7ULkqtX78eUVFR8Pf3R3x8PA4cONDgtpWVlRg/fjy6d+8OLy8vZGRkWGyTk5MDnU5nsdy4cUNRvRhEUbPlsvNzNea8ehbHUjCPW32LrfIUzMPnSoua81J9zRpTU72vFHLZzyK5hLy8PGRkZGDevHkoKSnB4MGDMWLECJSXl9e7fXV1Ndq3b4958+ahd+/eDZYbFBSEyspKyeLv76+obgyiiIiIyD5Co0WBVatWYdKkSZg8eTJiYmKQnZ2NiIgIbNiwod7tu3Tpgtdeew0TJkxAcHBwg+XqdDqEhYVJFqUYRBEREZH9NAqgDAaDZKmurrY4VE1NDYqLi5GSkiJZn5KSgsOHD6s6jatXryIyMhKdOnXCqFGjUFJSorgMBlFERETU5CIiIhAcHGxeli9fbrHNhQsXYDQaERoaKlkfGhoKvV7v8LF79OiBnJwc7Ny5E7m5ufD398egQYNw+vRpReXw7jxPZWu8H1fFcaMsyXNEbIwjpXjcKMmxrM+VV8/BpI+tHUtpvo+tY6uhZe6R1nPpWT2U0mNpmF/kKeMpuet5uMi8iFrOnXfu3DkEBQWZ1/v5+TW8j+y7RQih7LtNZuDAgRg4cKD58aBBg9C3b1+sXbsWa9assbscBlFERERkHw2HOAgKCpIEUfUJCQmBt7e3RavT+fPnLVqn1PDy8kK/fv0Ut0S56Z/5RERE5Ol8fX0RHx+PgoICyfqCggIkJSVpdhwhBEpLS9GhQwdF+7Eliui/5LdW6xROv2KjcOljJ3bvSaqhZIqY+tiaNsYatcduTKqmU1FXb6dO5SKpSONdfw5j4L607M6zV2ZmJtLS0pCQkIDExERs3LgR5eXlmDp1KgAgKysLFRUV2LJli3mf0tJSALeTx//zn/+gtLQUvr6+iI2NBQAsXrwYAwcORHR0NAwGA9asWYPS0lK8/vrriurGIIqIiIjs44QRy1NTU3Hx4kUsWbIElZWViIuLw65duxAZGQng9uCa8jGj+vTpY/5/cXExtm7disjISJw5cwYAcPnyZUyZMgV6vR7BwcHo06cP9u/fj/79+yuqm06o+rOHXIHBYEBwcDCSMQY+uhb1b+QuieVyTkws17QlyrJw7cpSUU81iZm3j63iPFz5PcmWKM9tifKwxPJb4iYKsQNVVVU284vUqP2d6TlpGbx9lQ1IKWesuYHjm15s9Do3BbZEERERkV2c0Z3nyhhEETXAU3OkJNVQMxwCoDxnSnpwZcdyFRrnarHlidyKE7rzXBnvziMiIiJyAFuiiIiIyD5siZJgEEVERER2YU6UFIOo5oLTwDQfGuZIyWmeM1VXY07zYksjjkml6Q3QzC1SzsPuxiPXwiCKiIiI7MPuPAm3+rP+0qVLSEtLM8/4nJaWhsuXL0u22blzJ+6++250794df/vb3yTPlZeX4+GHH0ZgYCBCQkIwc+ZM1NTUSLY5fvw4hgwZgoCAAHTs2BFLliyR/CWZk5OD5ORk8+O33noLgwcPRps2bdCmTRs8+OCD+Oyzzyzqvn79ekRFRcHf3x/x8fE4cOCA5Pnk5GTk5OTgzJkz6sfuISIiagQ6ITRZPIVbBVHjx49HaWkpdu/ejd27d6O0tBRpaWnm56urqzFt2jSsX78e69atQ3p6OqqrqwEARqMRDz30EK5du4aDBw9i27ZteP/99zF79mzz/gaDAUOHDkV4eDiOHj2KtWvX4tVXX8WqVasarFNhYSGeeOIJ/POf/0RRURE6d+6MlJQUVFRUmLfJy8tDRkYG5s2bh5KSEgwePBgjRoywGGGViIiI3IfbdOedPHkSu3fvxqeffooBAwYAuN0KlJiYiFOnTqF79+6oqamBl5cX7r33XgCAt7c3bt68CT8/P+Tn5+PEiRM4d+4cwsPDAQArV67ExIkT8dJLLyEoKAjvvvsubty4gZycHPj5+SEuLg7ffPMNVq1ahczMzHpbiN59913J47feegt//etf8fe//x0TJkwAAKxatQqTJk3C5MmTAQDZ2dnYs2cPNmzYgOXLlzfWJSON1R3rRvPRzOvmbWid96UiR0pO85ypupw5V54KjTrpQ2PmQDVyrhDHhvJQ7M6TcJuWqKKiIgQHB5sDKAAYOHAggoODcfjwYQBA69at8fTTT6NDhw4IDw9Heno6WrVqZd4/Li7OHEABwLBhw1BdXY3i4mLzNkOGDIGfn59kmx9++ME8344t169fx82bN9G2bVsAQE1NDYqLi5GSkiLZLiUlxVxvIiIid1B7d57axVO4TUuUXq/HnXfeabH+zjvvhF6vNz9euHAhMjIy4OXlhdatW0v2Dw0Nlezbpk0b+Pr6mvfX6/Xo0qWLZJvaffR6PaKiojBx4kRMnDixwXrOnTsXHTt2xIMPPggAuHDhAoxGo8WxQ0NDJfUuLCw0/5/TGRIREbk+pwdRixYtwuLFi61uc/ToUQD1dxUIISzWBwcH11uOPfvLt6kNaOzppnj55ZeRm5uLwsJC+PtLJ2isr1xHuz4MBgMMBoP58ZUrVxwqh4iIPENFRYXkdyEoKKhxJvdld56E04Oo6dOn4/HHH7e6TZcuXXDs2DH8+OOPFs/95z//sWjlqU9YWBiOHDkiWXfp0iXcvHnTvH9YWJikdQgAzp8/DwA2j/Hqq69i2bJl2Lt3L3r16mVeHxISAm9v73rLtafe9Rk9ejT27dvn0L5mdVu73OluQBcZN8pt5tWrT926a5zbZa0V1Z3vOm3S1mE3zYNymRwodx0XClA1NlRsbKzk8ZAhQyQ9HFrhYJtSTg+iQkJCEBISYnO7xMREVFVV4bPPPkP//v0BAEeOHEFVVRWSkpLs2v+ll15CZWUlOnToAADIz8+Hn58f4uPjzdu8+OKLqKmpga+vr3mb8PBwi26+ul555RUsXboUe/bsQUJCguQ5X19fxMfHo6CgAI888oh5fUFBAcaMGWOz3vXZuXOnRUuU/ANERETNx4kTJyQpLI3SCkUWnB5E2SsmJgbDhw/HM888gzfffBMAMGXKFIwaNQrdu3e3uX9KSgpiY2ORlpaGV155BT/99BOef/55PPPMM+Y32/jx47F48WJMnDgRL774Ik6fPo1ly5bh97//fYN/Rb/88stYsGABtm7dii5duphbnFq1amVOas/MzERaWhoSEhKQmJiIjRs3ory8HFOnTnXoWsibaesGVERE1Px07NixaQIndudJuE0QBdweTmDmzJnmO91Gjx6NdevW2bWvt7c3Pv74Y6Snp2PQoEEICAjA+PHj8eqrr5q3CQ4ORkFBAaZNm4aEhAS0adMGmZmZyMzMbLDc9evXo6amBr/+9a8l6xcuXIhFixYBAFJTU3Hx4kUsWbIElZWViIuLw65duxAZGanwChARETkPu/OkdIK3grk9g8GA4OBgJGMMfHQtlBfgxrkqEi40r57m40hZP1jjld2U59FcuGnOk+WhXOinw53zoOpy4Of4lriJQuxAVVVVo7ZE1f7OxKe+BG9ff9s7WGGsuYHivHmNXuem4FYtUURERORE7M6TYBBFREREdvOk7ji1GESRZROyp3TvNReNOSSC0i6b5tj958xuLU/pxmqumE3j9hhEERERkX2EUB/8eVDwyCCKiIiI7MK786Rc53YmIiIiIjfClijyHC4yJQzQyNPC2D649HFTXgcl+UGunD/lSrfv1+XEHCgOaUAAeHeeDIMoIiIisovOdHtRW4anYHceERERkQPYEkVERET2YXeeBIMosuQp40a5cI6UXKPmTFnLH3HmVDmulGPjSpyU7+NSOU9ynpID5QG39vPuPCl25xERERE5gC1RREREZB8OtinBIIqIiIjswu48KQZR1Hy4UI6UXN18FKeOKSXnQtfIY7hIfg9zoIjUYxBFRERE9uHdeRIMooiIiMgu7M6TYls9ERERubT169cjKioK/v7+iI+Px4EDBxrctrKyEuPHj0f37t3h5eWFjIyMerd7//33ERsbCz8/P8TGxmL79u2K68UgimyrvRtDi7syXIkwSRcXIUxCsji5MsqW5siNrpHLvK/kXOgaacoTvzvl5+TookBeXh4yMjIwb948lJSUYPDgwRgxYgTKy8vr3b66uhrt27fHvHnz0Lt373q3KSoqQmpqKtLS0vDll18iLS0Njz32GI4cOaKobjohPOWVbb4MBgOCg4ORjDHw0bVo/AO66+CbtrhoEnWTJpqr5aLXsFG50Y++ywVPtdzoGirSBD+vt8RNFGIHqqqqEBQU1GjHqf2dSRyxBD4t/FWVdevmDRR98nu76zxgwAD07dsXGzZsMK+LiYnB2LFjsXz5cqv7Jicn495770V2drZkfWpqKgwGAz755BPzuuHDh6NNmzbIzc21+1ya4TceEREROZvBYJAs1dXVFtvU1NSguLgYKSkpkvUpKSk4fPiww8cuKiqyKHPYsGGKy2QQRURERPYRGi0AIiIiEBwcbF7qa1W6cOECjEYjQkNDJetDQ0Oh1+sdPg29Xq9Jmbw7j8jFOXXePaW07JZpzK5BD+0+ctnuOvIYWt6dd+7cOUl3np+fX8P7yNJIhBAW6xTXQ4MyGUQRERFRkwsKCrKZExUSEgJvb2+LFqLz589btCQpERYWpkmZ7M4jIiIi+5iENoudfH19ER8fj4KCAsn6goICJCUlOXwaiYmJFmXm5+crLpMtUURERGQfJ4xYnpmZibS0NCQkJCAxMREbN25EeXk5pk6dCgDIyspCRUUFtmzZYt6ntLQUAHD16lX85z//QWlpKXx9fREbGwsAmDVrFu677z6sWLECY8aMwY4dO7B3714cPHhQUd0YRJFy8tt2PWXIAxeeW88aeR6MS+VIqeGheUtactscKE99bTliUKNITU3FxYsXsWTJElRWViIuLg67du1CZGQkgNuDa8rHjOrTp4/5/8XFxdi6dSsiIyNx5swZAEBSUhK2bduG+fPnY8GCBejWrRvy8vIwYMAARXXjOFEeoMnHiZLzlCBKzk2CKDmPCaLIJgZRLsYJP6dNPU7UoAcXw8dH5ThRt27g0N6FjV7npsCWKCIiIrKPFqOve1DbDYMoUq+5dO/V5cKtVG41JAJZ5bYtTYDntjbV5UHBADmGQRQRERHZRctxojwBgygiIiKyjxPuznNlrtsnQUREROTC2BJF2qubJ+Ap+VFybjocAqAsz4b5U9pz6zwna5gD1SzohIBO5XVQu78rYRBFRERE9jH9d1Fbhodwnz+fiYiIiFwIW6KIiIjILuzOk2IQRaQFN86RskZp/k5zzKHy2BwnW5pDDhRZ4t15Ep7xTU9ERETUxNgSRURERPbhtC8SDKKIiIjILhyxXIpBFDUuT51XzxYPzZGypTHzg9TkWzXbvCUtNdccKA9qNSHtMYgiIiIi+7A7T4JBFBEREdlFZ7q9qC3DUzSPPgYiIiIijbElipoWc6Tq10xyptRgXlMja645T3Ie1NXUKNidJ8EgioiIiOzDwTYl+OcvERERkQPYEkVERER24dx5UgyiyLmaa46UXN18FOZHUVNgDtRtHvSD3iSYEyXBb2siIiIiB7AlioiIiOwjAKhtxPSchigGUeRi2L3H4RBIO+yys+RBXUnOwJwoKX4bExERETmALVFERERkHwENEss1qYlLYBBFRERE9uHdeRIMosi1MUfKktI8F+ZQeQ7mOCnnQT/Y5HoYRBEREZF9TADU/i3rQX8LMIgiIiIiu/DuPCm28xMRERE5gC1R5F6YI6WctTwa5ku5HuY9qeNBrRwuiYnlEgyiiIiIyD4MoiT4ZygRERGRA9gSRURERPZhS5QEW6LIvdV+oD3oQ9mkhEndQpZ4TZsevweajkmjRaH169cjKioK/v7+iI+Px4EDB6xuv2/fPsTHx8Pf3x9du3bFG2+8IXk+JycHOp3OYrlx44aiejGIagTLly+HTqdDRkaGeZ0QAosWLUJ4eDgCAgKQnJyMr7/+WrJfly5dUFhYiMLCQnTp0qVpK01EROSC8vLykJGRgXnz5qGkpASDBw/GiBEjUF5eXu/2ZWVlGDlyJAYPHoySkhK8+OKLmDlzJt5//33JdkFBQaisrJQs/v7+iurGIEpjR48excaNG9GrVy/J+pdffhmrVq3CunXrcPToUYSFhWHo0KG4cuWKk2pKRESkTO04UWoXJVatWoVJkyZh8uTJiImJQXZ2NiIiIrBhw4Z6t3/jjTfQuXNnZGdnIyYmBpMnT8bTTz+NV199VXouOh3CwsIki1IMojR09epV/OY3v8Fbb72FNm3amNcLIZCdnY158+Zh3LhxiIuLwzvvvIPr169j69atTqwxERGRAnW7TtUsAAwGg2Sprq62OFxNTQ2Ki4uRkpIiWZ+SkoLDhw/XW8WioiKL7YcNG4bPP/8cN2/eNK+7evUqIiMj0alTJ4waNQolJSWKLweDKA1NmzYNDz30EB588EHJ+rKyMuj1esmL6ufnhyFDhjT4JiAH1PMhpUamNv/HWblB7lpvuo2fdY8QERGB4OBg87J8+XKLbS5cuACj0YjQ0FDJ+tDQUOj1+nrL1ev19W5/69YtXLhwAQDQo0cP5OTkYOfOncjNzYW/vz8GDRqE06dPKzoH3p2nkW3btuGLL77A0aNHLZ6rfaHre1HPnj1rfnzmzJl6/09EROQSTALQqQxcTbf3P3fuHIKCgsyr/fz8GtxFJxtYWQhhsc7W9nXXDxw4EAMHDjQ/P2jQIPTt2xdr167FmjVr7DwRBlGaOHfuHGbNmoX8/HyrSWlK3wQNqW36rMW8KiKi5q2iokLyuxAUFCQJUDSj4RAH9tQxJCQE3t7eFq1O58+ft2iYqBUWFlbv9j4+PmjXrl29+3h5eaFfv36KW6LYnaeB4uJinD9/HvHx8fDx8YGPjw/27duHNWvWwMfHx/xCK3kTWDN69GhERESYl9jYWE3Og4iI3FNsbKzkd2H06NHOrpImfH19ER8fj4KCAsn6goICJCUl1btPYmKixfb5+flISEhAixYt6t1HCIHS0lJ06NBBUf3YEqWBBx54AMePH5es++1vf4sePXrghRdeQNeuXREWFoaCggL06dMHwO1kuX379mHFihWKj7dz506LligGUvWw9dcS591zbcwvar6Y56TYiRMn0Lp1a/PjRmmFAgBokYembP/MzEykpaUhISEBiYmJ2LhxI8rLyzF16lQAQFZWFioqKrBlyxYAwNSpU7Fu3TpkZmbimWeeQVFRETZt2oTc3FxzmYsXL8bAgQMRHR0Ng8GANWvWoLS0FK+//rqiujGI0kDr1q0RFxcnWRcYGIh27dqZ12dkZGDZsmWIjo5GdHQ0li1bhpYtW2L8+PGKjydvAq0bUBERUfPTsWPHRgyc6nDCiOWpqam4ePEilixZgsrKSsTFxWHXrl2IjIwEAFRWVkrGjIqKisKuXbvw3HPP4fXXX0d4eDjWrFmDX/3qV+ZtLl++jClTpkCv1yM4OBh9+vTB/v370b9/f0V1YxDVRObMmYOff/4Z6enpuHTpEgYMGID8/HzJXw5ERERkKT09Henp6fU+l5OTY7FuyJAh+OKLLxosb/Xq1Vi9erXqejGIaiSFhYWSxzqdDosWLcKiRYucUh+qh/yvIXbvETkHu+/ch0lAaXdc/WV4BgZRREREZB8txkPzoHxH3p1HRERE5AC2RBEREZF9nJBY7soYRBHVYo4UUdPwoB/RZoc5URLsziMiIiJyAFuiiIiIyD7szpNgEEVERET2EdAgiNKkJi6BQRRRQ6x9UTBfisg6D2ptIGoIgygiIiKyD7vzJBhEERERkX1MJgAqB8s0cbBNIiIiomaNLVFEjrDVHM2cKfJ0HtQlQwqwO0+CQRQRERHZh0GUBLvziIiIiBzAligiIiKyD6d9kWAQRdQYmDNF7s6DulxIO0KYIIS6u+vU7u9K2J1HRERE5AC2RBEREZF9hFDfHedBrZwMooiIiMg+QoOcKAZRRKQK5+UjZ/OgHzIiZ2EQRURERPYxmQCdysRwD0osZxBFRERE9mF3ngSDKCJXw+ERSCse9GNF5IoYRBEREZFdhMkEobI7z5PGiWIQRURERPZhd54EB9skIiIicgBboojcjdK/4phD5Tk86C94clMmAejYElWLQRQRERHZRwgAaoc48Jwgit15RERERA5gSxQRERHZRZgEhMruPOFBLVEMoog8nZovLOZTac+DfkCoGRImqO/O85whDtidR0REROQAtkQRERGRXdidJ8UgioiIiOzD7jwJBlEeoDaq/3/n1iEoKMjJtSEioqZiMBgQEbGjyVp3buGm6gHLb+GmNpVxAQyiPMCVK1cAABEREU6uCREROcOVK1cQHBzcaOX7+voiLCwMB/W7NCkvLCwMvr6+mpTlTDrhSZ2TzZTJZMIPP/yA1q1bQ8e7qexWUVGB2NhYnDhxAh07dnR2dchBfB09A19HxwghcOXKFYSHh8PLq3HvFbtx4wZqamo0KcvX1xf+/v6alOVMbInyAF5eXujUqZOzq+F2DAYDAKB169bsBnVjfB09A19HxzVmC1Rd/v7+HhH4aIlDHBARERE5gEEUERERkQMYRFGzFRQUhCFDhrDrwM3xdfQMfB3JHTGxnIiIiMgBbIkil3XmzBkkJCQ4uxpE1AB+Rqm5YxBFRERE5AAGUeTSbt68iaeeegoxMTFITU3VfFTeM2fOoHfv3pg4cSJiY2Pxf//3f/jwww8xYMAA3HPPPTh9+rSmx7t69SqGDx+Onj17omfPntizZ4+m5ZMUr3fja8zPKD+f5OoYRJHTrV+/HlFRUfD390d8fDwOHDhgfu7kyZPIysrCiRMn8OOPP+LgwYN272vvNrXHOH78OAoLC3Ho0CEcOXIEM2bMwLp16xSVtXz5cvTr1w+tW7fGnXfeibFjx+LUqVPm5/fs2YN27drh+PHjOHbsGBITEx2+bs2FrWtu7Xleb+tsvV83bNiAXr16ISgoCEFBQUhMTMQnn3wiKcPaZ3TRokXQ6XSSJSwszPz8lStXkJGRgcjISAQEBCApKQlHjx6tt3xbn09bxwKAW7duYf78+YiKikJAQAC6du2KJUuWwGS6PZcb3y+kmCByom3btokWLVqIt956S5w4cULMmjVLBAYGirNnz4qysjIRFxdn3jYjI0Ns2bLFrn3t3UZ+jEceeUTs3r1bCCHEoUOHxOjRoxUdb9iwYWLz5s3iq6++EqWlpeKhhx4SnTt3FlevXhVCCHHq1CkREREhfve734nDhw9rfDU9j61rbut5Xm/rbL1fd+7cKT7++GNx6tQpcerUKfHiiy+KFi1aiK+++koIYfn5kX9GFy5cKO655x5RWVlpXs6fP29+/rHHHhOxsbFi37594vTp02LhwoUiKChI/Pvf/663fGufT1vHEkKIpUuXinbt2omPPvpIlJWViffee0+0atVKZGdnCyH4fiHlGESRU/Xv319MnTpVsq5Hjx5i7ty5oqysTMTHx5vXz549W2zevNmufe3dRn6MX/3qV+Kf//ynEEKIoqIi8dBDDyk6ntz58+cFALFv3z7zugsXLoh33nlH9OvXT6xdu7bBfcn2NbfnNeH1tl9971e5Nm3aiLffflsIYfn5kX9GFy5cKHr37l1vOdevXxfe3t7io48+kqzv3bu3mDdvXr3lW/t8WjtWrYceekg8/fTTknXjxo0TTz75pPkx3y+kBLvzyGlqampQXFyMlJQUyfqUlBQcPnxY9b5qyteqrlVVVQCAtm3bAgB++OEHBAYGYsKECZg1axZKS0sV1aM5sXXN7XlNeL2Vkb9f6zIajdi2bRuuXbumqJvr9OnTCA8PR1RUFB5//HF8//33AG53rRmNRotpRAICAiy67dUeq9YvfvEL/P3vf8c333wDAPjyyy9x8OBBjBw5EgDfL6Qc584jp7lw4QKMRiNCQ0Ml60NDQ6HX61Xvq6Z8LeoqhEBmZiZ+8YtfIC4uDgBw/PhxPP/88/D29kZAQAA2bdqkqB7Nia1rbs9rwuttv/rer8Dta5iYmIgbN26gVatW2L59O2JjY+0qc8CAAdiyZQvuvvtu/Pjjj1i6dCmSkpLw9ddfo127dkhMTMQf/vAHxMTEIDQ0FLm5uThy5Aiio6MV19/WsQDghRdeQFVVFXr06AFvb28YjUa89NJLeOKJJ8znyvcLKeLspjBqvioqKgQAi9yDpUuXiu7du6veV035WtQ1PT1dREZGinPnzik6Ft1m65pr+fpSw+/X6upqcfr0aXH06FExd+5cERISIr7++muHjnH16lURGhoqVq5cKYQQ4ttvvxX33XefACC8vb1Fv379xG9+8xsRExOj+nzkxxJCiNzcXNGpUyeRm5srjh07JrZs2SLatm0rcnJyVB+Pmie2RJHThISEwNvb26Il5/z58xatC47sq6Z8tXWdMWMGdu7cif3796NTp06KjkW32brmWr6+zZ2196uvry/uuusuAEBCQgKOHj2K1157DW+++abi4wQGBqJnz57moQm6deuGffv24dq1azAYDOjQoQNSU1MRFRWl+pzkxwKA3/3ud5g7dy4ef/xxAEDPnj1x9uxZLF++HE899ZTqY1Lzw5wochpfX1/Ex8ejoKBAsr6goABJSUmq91VTvqN1FUJg+vTp+OCDD/CPf/xDkx+D5srWNdfy9W2uHHm/CiFQXV3t0PGqq6tx8uRJdOjQQbI+MDAQHTp0wKVLl7Bnzx6MGTPGofJtHev69evw8pL+7Hl7e5uHOCBSzMktYdTM1d6ivmnTJnHixAmRkZEhAgMDxZkzZzTZV035jhzv//7v/0RwcLAoLCyU3Gp9/fp1xccj29dcy9e3ObL1fs3KyhL79+8XZWVl4tixY+LFF18UXl5eIj8/367yZ8+eLQoLC8X3338vPv30UzFq1CjRunVr8+uze/du8cknn4jvv/9e5Ofni969e4v+/fuLmpoaxedi61hCCPHUU0+Jjh07moc4+OCDD0RISIiYM2eO4uMRCcEhDsgFvP766yIyMlL4+vqKvn37Wr292pF91ZSvtCwA9S51b/smZWxdcy1f3+bG1vv16aefNl/b9u3biwceeMDuAEoIIVJTU0WHDh1EixYtRHh4uBg3bpwknyovL0907dpV+Pr6irCwMDFt2jRx+fJlh87F1rGEEMJgMIhZs2aJzp07C39/f9G1a1cxb948UV1d7dAxiXRCaDyPBhEREVEzwJwoIiIiIgcwiCIiIiJyAIMoIiIiIgcwiCIiIiJyAIMoIiIiIgcwiCIiIiJyAIMoIiIiIgcwiCIiIiJyAIMoIiIiIgcwiCIiIiJyAIMoIiIiIgcwiCIiIiJyAIMoIiIrbt686ewqEJGLYhBFRJpITk7G9OnTMX36dNxxxx1o164d5s+fDyEEAODSpUuYMGEC2rRpg5YtW2LEiBE4ffq0ef+zZ8/i4YcfRps2bRAYGIh77rkHu3btavB4NTU1mDNnDjp27IjAwEAMGDAAhYWFkm1ycnLQuXNntGzZEo888ghWrlyJO+64o8Eyz5w5A51Oh7/85S9ITk6Gv78//vznP+PixYt44okn0KlTJ7Rs2RI9e/ZEbm6uqutFRO6PQRQRaeadd96Bj48Pjhw5gjVr1mD16tV4++23AQATJ07E559/jp07d6KoqAhCCIwcOdLc0jNt2jRUV1dj//79OH78OFasWIFWrVo1eKzf/va3OHToELZt24Zjx47h0UcfxfDhw82B2ZEjR/D0008jPT0dpaWluP/++7F06VK7zuOFF17AzJkzcfLkSQwbNgw3btxAfHw8PvroI3z11VeYMmUK0tLScOTIEZVXjIjcmiAi0sCQIUNETEyMMJlM5nUvvPCCiImJEd98840AIA4dOmR+7sKFCyIgIED85S9/EUII0bNnT7Fo0SK7jvXtt98KnU4nKioqJOsfeOABkZWVJYQQ4oknnhDDhw+XPJ+amiqCg4MbLLesrEwAENnZ2TbrMHLkSDF79my76ktEnoktUUSkmYEDB0Kn05kfJyYm4vTp0zhx4gR8fHwwYMAA83Pt2rVD9+7dcfLkSQDAzJkzsXTpUgwaNAgLFy7EsWPHGjzOF198ASEE7r77brRq1cq87Nu3D9999x0A4OTJk0hMTJTsJ3/ckISEBMljo9GIl156Cb169UK7du3QqlUr5Ofno7y83K7yiMgz+Ti7AkTUfAkhzEHX5MmTMWzYMHz88cfIz8/H8uXLsXLlSsyYMcNiP5PJBG9vbxQXF8Pb21vyXG0XoPhvLpYjAgMDJY9XrlyJ1atXIzs7Gz179kRgYCAyMjJQU1Pj8DGIyP2xJYqINPPpp59aPI6OjkZsbCxu3bolySG6ePEivvnmG8TExJjXRUREYOrUqfjggw8we/ZsvPXWW/Uep0+fPjAajTh//jzuuusuyRIWFgYAiI2Nrbc+jjhw4ADGjBmDJ598Er1790bXrl0lSfFE1DwxiCIizZw7dw6ZmZk4deoUcnNzsXbtWsyaNQvR0dEYM2YMnnnmGRw8eBBffvklnnzySXTs2BFjxowBAGRkZGDPnj0oKyvDF198gX/84x+SAKtHjx7Yvn07AODuu+/Gb37zG0yYMAEffPABysrKcPToUaxYscJ8R9/MmTOxe/duvPzyy/jmm2+wbt067N69W1Lfzz77DD169EBFRYXV87rrrrtQUFCAw4cP4+TJk3j22Weh1+u1vHRE5IYYRBGRZiZMmICff/4Z/fv3x7Rp0zBjxgxMmTIFALB582bEx8dj1KhRSExMhBACu3btQosWLQDczjuaNm0aYmJiMHz4cHTv3h3r1683l33q1ClUVVWZH2/evBkTJkzA7Nmz0b17d4wePRpHjhxBREQEgNv5WW+//TbWrl2Le++9F/n5+Zg/f76kvtevX8epU6dsjgW1YMEC9O3bF8OGDUNycjLCwsIwduxYLS4ZEbkxnVCTOEBE9F/Jycm49957kZ2d7eyqNCgnJwcZGRm4fPmys6tCRB6ALVFEREREDmAQRUREROQAducREREROYAtUUREREQOYBBFRERE5AAGUUREREQOYBBFRERE5AAGUUREREQOYBBFRERE5AAGUUREREQOYBBFRERE5ID/D+ltuSN2QurOAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mass, wcs = lt.g_mass(3, 100, 0.3, 1.0)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs)\n",
"plt.imshow(mass)\n",
"plt.colorbar()\n",
"\n",
"for row in lt.get_sources(): \n",
" ellipse = Ellipse((row['x']/3600.,row['y']/3600.), #conversion from arcsecs to degrees\n",
" width=row['b']/3600, \n",
" height=row['a']/3600,\n",
" edgecolor='pink',\n",
" facecolor='none',\n",
" angle =row['theta']+90,\n",
" transform=plt.gca().get_transform('world')\n",
" )\n",
" \n",
" ax.add_patch(ellipse)"
]
},
{
"cell_type": "markdown",
"id": "1415c18c-2d06-4664-85b6-74de81c5cf23",
"metadata": {},
"source": [
"Here we have displayed the source in pink and the cluster of galaxies that acts as a lens in yellow.\n",
"The colorbar indicates the mass repartition of the cluster in $10^{12}$ Msun/pixel."
]
},
{
"cell_type": "markdown",
"id": "368dd590-3255-4880-aed8-d39ebe3334d5",
"metadata": {
"tags": []
},
"source": [
"## Modelling gravitational lensing\n",
"Using the data from the above source, one or more images can be created corresponding to the gravitational lensing under study."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e8e1174c-fc31-4b84-a6b1-0acae72441f2",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 3, not found 0\r"
]
},
{
"data": {
"text/html": [
"Table length=3 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a -0.14390360326579424 2.056015418854247 3.5000000009029852 0.7418610444825668 94.00368830334747 1.0 21.68436369398107 \n",
"1a -0.14387454674727249 2.057052271183966 3.5000000009029932 0.7423114188365846 94.00087143112768 1.0 21.68370475741009 \n",
"1a 1.5017408667543073 -21.45605858938671 7.741844354807154 3.5000000009029852 184.0036860228906 1.0 19.13805902100179 \n",
"
"
],
"text/plain": [
"\n",
" n x y ... z mag \n",
"str2 float64 float64 ... float64 float64 \n",
"---- -------------------- ------------------ ... ------- -----------------\n",
" 1a -0.14390360326579424 2.056015418854247 ... 1.0 21.68436369398107\n",
" 1a -0.14387454674727249 2.057052271183966 ... 1.0 21.68370475741009\n",
" 1a 1.5017408667543073 -21.45605858938671 ... 1.0 19.13805902100179"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lt.e_lensing()\n",
"lt.get_images()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "7a46324b-9e47-46e9-a62e-e53e1d3fb808",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_images():\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(projection=wcs)\n",
" plt.imshow(mass)\n",
"\n",
" norm = Normalize(min(lt.get_images()['mag']), max(lt.get_images()['mag']))\n",
" for row in lt.get_images(): \n",
" ellipse = Ellipse((row['x']/3600.,row['y']/3600.),\n",
" width=row['b']/3600,\n",
" height=row['a']/3600,\n",
" facecolor = 'none',\n",
" angle =row['theta'] + 90,\n",
" transform=plt.gca().get_transform('world')\n",
" )\n",
" # Assign color to the ellipse based on the magnification\n",
"\n",
" color = cm.ScalarMappable(norm=norm, cmap = 'Wistia').to_rgba(row['mag'])\n",
" ellipse.set_edgecolor(color)\n",
"\n",
" ax.add_patch(ellipse)\n",
"\n",
" # Creating a ScalarMappable object for colorbar\n",
" cmap = cm.ScalarMappable(norm=norm, cmap = 'Wistia')\n",
" cmap.set_array(tab['mag'])\n",
"\n",
" # Adding the colorbar\n",
" colorbar = plt.colorbar(cmap, ax=ax)\n",
" colorbar.set_label('Magnitude')\n",
" plt.colorbar()\n",
" plt.show()\n",
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "3f292095-6882-4a17-bf7c-09a36b7e7562",
"metadata": {},
"source": [
"As we can see, three images are displayed whereas in the SIS model only two images should appear. This happens because due to numerical resolution limits, Lenstool finds two radial images, whereas only one should exist in theory. Note that depending on the grid.number, and grid.polar parameters, this third image is not always detected."
]
},
{
"cell_type": "markdown",
"id": "de9995ed-ffd0-4ab8-b3a8-6ef4391aafc4",
"metadata": {},
"source": [
"### With another source"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "9c7c9a90-ddaa-46a0-84c0-4ad8be109ba5",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 10.6789067 10.7 3.5 3.5 0.0 1.0 20.0 \n",
"
"
],
"text/plain": [
"\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64\n",
"---- ---------- ------- ------- ------- ------- ------- -------\n",
" 1a 10.6789067 10.7 3.5 3.5 0.0 1.0 20.0"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = Table(\n",
" rows=[('1a', 10.6789067, 10.7, 3.5, 3.5, 0, 1.0, 20)],\n",
" names=['n','x','y','a','b','theta','z','mag'], \n",
" dtype=['str',*['float',]*7]\n",
")\n",
"tab.meta['iref'], tab.meta['ref_ra'], tab.meta['ref_dec'] = 3, 0, 0\n",
"lt.set_sources(tab)\n",
"lt.get_sources()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "5cca18a7-406b-4547-9100-a4aecdccf248",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 1, not found 0\r"
]
},
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 19.003780153858134 19.041315591211987 6.228466685230649 3.5000000004546004 135.05652820048417 1.0 19.374217246134503 \n",
"
"
],
"text/plain": [
"\n",
" n x y ... z mag \n",
"str2 float64 float64 ... float64 float64 \n",
"---- ------------------ ------------------ ... ------- ------------------\n",
" 1a 19.003780153858134 19.041315591211987 ... 1.0 19.374217246134503"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "aa541b4d-1242-44c0-8ccc-8d3423695536",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e4f3a585-1aae-48cd-bab5-5ac36199a733",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 1.7 1.7 3.5 3.5 0.0 1.0 20.0 \n",
"
"
],
"text/plain": [
"\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64\n",
"---- ------- ------- ------- ------- ------- ------- -------\n",
" 1a 1.7 1.7 3.5 3.5 0.0 1.0 20.0"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = Table(\n",
" rows=[('1a', 1.7, 1.7, 3.5, 3.5, 0, 1.0, 20)],\n",
" names=['n','x','y','a','b','theta','z','mag'], \n",
" dtype=['str',*['float',]*7]\n",
")\n",
"tab.meta['iref'], tab.meta['ref_ra'], tab.meta['ref_dec'] = 3, 0, 0\n",
"lt.set_sources(tab)\n",
"lt.get_sources()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "4abf75dc-0a3c-441b-b073-8b452a18bd49",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 2, not found 0\r"
]
},
{
"data": {
"text/html": [
"Table length=2 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 10.03309421074721 10.03309421074721 20.656397190255475 3.5000000004537077 134.99999999105756 1.0 18.07253367121692 \n",
"1a -6.633066375294565 -6.633066375294565 13.656071838619273 3.5000000004537037 134.99999999408797 1.0 18.521855628870078 \n",
"
"
],
"text/plain": [
"\n",
" n x y ... z mag \n",
"str2 float64 float64 ... float64 float64 \n",
"---- ------------------ ------------------ ... ------- ------------------\n",
" 1a 10.03309421074721 10.03309421074721 ... 1.0 18.07253367121692\n",
" 1a -6.633066375294565 -6.633066375294565 ... 1.0 18.521855628870078"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "3f6198c4-50b5-450c-9f33-cdc06f70ddd1",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "7e773a81-fe5d-47c6-a351-178d04685b73",
"metadata": {},
"source": [
"By moving the source closer to the lens, the flux can be amplified.\n",
"The second colorbar represents the magnitude values of the obtained images. "
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "a2abbc1e-c704-4d03-8a4b-3685e1efc69d",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 0.6789067 -9.7 5.5 5.5 0.0 1.5 20.0 \n",
"
"
],
"text/plain": [
"\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64\n",
"---- --------- ------- ------- ------- ------- ------- -------\n",
" 1a 0.6789067 -9.7 5.5 5.5 0.0 1.5 20.0"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = Table(\n",
" rows=[('1a', 0.6789067, -9.7, 5.5, 5.5, 0, 1.5, 20)],\n",
" names=['n','x','y','a','b','theta','z','mag'], \n",
" dtype=['str',*['float',]*7]\n",
")\n",
"tab.meta['iref'], tab.meta['ref_ra'], tab.meta['ref_dec'] = 3, 0, 0\n",
"lt.set_sources(tab)\n",
"lt.get_sources()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "d355f6cd-e80d-4f0e-9aed-b169bd4e3262",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 2, not found 0\r"
]
},
{
"data": {
"text/html": [
"Table length=2 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a -0.25707791557222887 3.6729549940005506 5.500000001342865 2.0826060496905985 274.0037237893153 1.5 21.054388909410587 \n",
"1a 1.6149036200952658 -23.072957535127333 13.082585562250514 5.500000001342866 184.00367029497949 1.5 19.059172764025583 \n",
"
"
],
"text/plain": [
"\n",
" n x y ... z mag \n",
"str2 float64 float64 ... float64 float64 \n",
"---- -------------------- ------------------- ... ------- ------------------\n",
" 1a -0.25707791557222887 3.6729549940005506 ... 1.5 21.054388909410587\n",
" 1a 1.6149036200952658 -23.072957535127333 ... 1.5 19.059172764025583"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "a92f6e72-5018-487b-a07b-ae02112e62ec",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "7cafac7c-f48f-4617-affe-ad3cceaab38f",
"metadata": {},
"source": [
"The image obtained for the first source studied is modelled again and the size of the source is increased; it can be seen that the size of the image is also increased. "
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "ee69d2ce-729b-482d-888a-c8d6c78cd349",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 0.6789067 -9.7 3.5 3.5 0.0 15.0 20.0 \n",
"
"
],
"text/plain": [
"\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64\n",
"---- --------- ------- ------- ------- ------- ------- -------\n",
" 1a 0.6789067 -9.7 3.5 3.5 0.0 15.0 20.0"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = Table(\n",
" rows=[('1a', 0.6789067, -9.7, 3.5, 3.5, 0, 15.0, 20)],\n",
" names=['n','x','y','a','b','theta','z','mag'], \n",
" dtype=['str',*['float',]*7]\n",
")\n",
"tab.meta['iref'], tab.meta['ref_ra'], tab.meta['ref_dec'] = 3, 0, 0\n",
"lt.set_sources(tab)\n",
"lt.get_sources()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "aac564d9-5190-4f03-bd0e-70186ae1ba6f",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 2, not found 0\r"
]
},
{
"data": {
"text/html": [
"Table length=2 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 1.8173670426662394 -25.965958656690344 9.369170222656104 3.500000002329488 184.00362385225992 15.0 18.93091728652996 \n",
"1a -0.4595568468859493 6.565971489067192 3.500000002329488 2.369165693006242 274.0036418742858 15.0 20.42368152225295 \n",
"
"
],
"text/plain": [
"\n",
" n x y ... z mag \n",
"str2 float64 float64 ... float64 float64 \n",
"---- ------------------- ------------------- ... ------- -----------------\n",
" 1a 1.8173670426662394 -25.965958656690344 ... 15.0 18.93091728652996\n",
" 1a -0.4595568468859493 6.565971489067192 ... 15.0 20.42368152225295"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "2475403e-f1b8-44a0-b2d5-56ff1bbec8be",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "01b71fb7-b19f-4f6a-89ca-48ba0fee378d",
"metadata": {},
"source": [
"When the redshift is increased, the distance between the images is also increased. "
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "ff7599c5-5c19-4fbb-be58-74330f6df5ef",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/html": [
"Table length=1 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 0.3789067 0.4 3.5 3.5 0.0 1.0 20.0 \n",
"
"
],
"text/plain": [
"\n",
" n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64\n",
"---- --------- ------- ------- ------- ------- ------- -------\n",
" 1a 0.3789067 0.4 3.5 3.5 0.0 1.0 20.0"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = Table(\n",
" rows=[('1a', 0.3789067, 0.4, 3.5, 3.5, 0, 1.0, 20)],\n",
" names=['n','x','y','a','b','theta','z','mag'], \n",
" dtype=['str',*['float',]*7]\n",
")\n",
"tab.meta['iref'], tab.meta['ref_ra'], tab.meta['ref_dec'] = 3, 0, 0\n",
"lt.set_sources(tab)\n",
"lt.get_sources()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "a041946f-41e7-48d4-92ed-70cf0fceab41",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Compute multiple images for source 0...images found 2, not found 0\r"
]
},
{
"data": {
"text/html": [
"Table length=2 \n",
"
\n",
"n x y a b theta z mag \n",
"str2 float64 float64 float64 float64 float64 float64 float64 \n",
"1a 8.483351108269728 8.955704565242334 78.3553353715406 3.500000000478264 136.5515314790598 1.0 16.6249986762484 \n",
"1a -7.725506849912627 -8.155647694845774 71.35961784032675 3.500000000478264 136.5514760544116 1.0 16.72653882184898 \n",
"
"
],
"text/plain": [
"\n",
" n x y ... z mag \n",
"str2 float64 float64 ... float64 float64 \n",
"---- ------------------ ------------------ ... ------- -----------------\n",
" 1a 8.483351108269728 8.955704565242334 ... 1.0 16.6249986762484\n",
" 1a -7.725506849912627 -8.155647694845774 ... 1.0 16.72653882184898"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lt.e_lensing()\n",
"display(lt.get_images())"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "7889b5f7-cd7e-4bb7-af2e-908671e3e069",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_images()"
]
},
{
"cell_type": "markdown",
"id": "e0c55ebf-2b87-4491-bc67-6c1d778b3364",
"metadata": {},
"source": [
"By moving the source closer to the lens again, the images appear streched."
]
},
{
"cell_type": "markdown",
"id": "18652e45-5d3a-44da-becf-acf67bfe3ac9",
"metadata": {},
"source": [
"## Modelling of the Einstein ring\n",
"Now that we have seen the impact of each parameter on the resulting image, we want to model the Einstein ring.\n",
"To do so we can model the brightness map with lenstool."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "63edf362-02a7-4215-aeb8-ee856b4dadc6",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Source plane')"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pix, wcs = lt.e_pixel_image(100)\n",
"source, swcs = lt.e_pixel_source(100)\n",
"fig = plt.figure(figsize=(10,5))\n",
"ax = fig.add_axes([0.15, 0.1, 0.5, 0.5], projection=wcs)\n",
"\n",
"plt.imshow(pix)\n",
"\n",
"ax.autoscale_view()\n",
"ax.set_title('Image plane')\n",
"\n",
"ax = fig.add_axes([0.55, 0.1, 0.5, 0.5], projection=swcs)\n",
"\n",
"plt.imshow(source)\n",
"ax.autoscale_view()\n",
"ax.set_title('Source plane')"
]
},
{
"cell_type": "markdown",
"id": "4c43b61f-fef4-4778-9793-716adbfd1786",
"metadata": {},
"source": [
"## The convergence map\n",
"\n",
"Lenstool can also compute the convergence map of the lens.\n"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "38a003c8-4c7e-4caa-b8f5-6932ba8abd62",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"conv, wcs = lt.g_mass(1, 100, 0.3, 1.0)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs)\n",
"\n",
"s = abs(conv - 1/2) < 0.02\n",
"conv[s] = 10\n",
"plt.imshow(conv)\n",
"plt.colorbar()"
]
},
{
"cell_type": "markdown",
"id": "78004b88-333c-4531-a200-902f9d610829",
"metadata": {},
"source": [
"Here, the yellow circle is the critical line for our SIS model (when the convergence = 1/2)."
]
},
{
"cell_type": "markdown",
"id": "40805fe1-7bba-453d-ba49-ba271245c8e2",
"metadata": {},
"source": [
"## Calculation of the Einstein ring\n",
"We start by using the lensing equations to obtain the radius of the ring created by gravitational lensing. \n",
"$$\\theta_{E} = \\frac{4 \\pi\\sigma_{v}^{2}}{c^{2}}\\frac{D_{LS}}{D_{S}} $$"
]
},
{
"cell_type": "markdown",
"id": "5c08af37-3965-4521-a6c5-8a08f2bd5a2d",
"metadata": {},
"source": [
"We can calculate the distances to the source and to the lens with the redshift data."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "67a325b0-15d6-41b8-892c-fd76827c94b5",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the radius value is: 5.713423457351448e-05\n"
]
}
],
"source": [
"from math import pi\n",
"import astropy.constants as const\n",
"import astropy.units as u\n",
"from astropy.cosmology import FlatLambdaCDM\n",
"\n",
"cosmo= FlatLambdaCDM(70,0.3) # definition of the universe (H0, z_lens)\n",
"dol=cosmo.angular_diameter_distance(0.3) # distance between the observer and the lens\n",
"dos=cosmo.angular_diameter_distance(1) # distance between the observer and the source\n",
"dls=cosmo.angular_diameter_distance_z1z2(0.3,1) # distance between the lens and the source\n",
"sigma = 800 * u.km /u.s\n",
"theta = (4*pi*sigma**2*dls)/(dos*const.c**2)\n",
"theta = theta.to('m2/m2').value\n",
"print(\"the radius value is:\",theta) "
]
},
{
"cell_type": "markdown",
"id": "bf7c412a-f7e8-409e-8b12-eefcc49a15f1",
"metadata": {},
"source": [
"Now that we have the radius we can display the ring. \n",
"To observe the match with the magnification map, it is also possible to directly display the ring on it. "
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "3537a6f2-567d-4e50-86f1-2bf371a4046a",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Magnification map')"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ampli, wcs = lt.g_ampli(1, 100, 1.0)\n",
"\n",
"fig = plt.figure()\n",
"ax = fig.add_axes([0.15, 0.1, 0.8, 0.8], projection=wcs)\n",
"\n",
"plt.imshow(ampli)\n",
"plt.clim((-1,2))\n",
"plt.colorbar()\n",
"\n",
"c = Circle((0,0),\n",
" numpy.degrees(theta),\n",
" edgecolor='pink',\n",
" facecolor='none',\n",
" linewidth=4,\n",
" transform=ax.get_transform('world')\n",
" )\n",
" \n",
" \n",
"ax.add_patch(c)\n",
"ax.set_title('Magnification map')"
]
},
{
"cell_type": "markdown",
"id": "08fc998e-6756-4ecb-a3cb-2d4b74798e2e",
"metadata": {},
"source": [
"Here the Eistein ring is pink and the colorbar indicates the magnification factor."
]
},
{
"cell_type": "markdown",
"id": "46c7c574-fbea-4ef7-9ad2-615e4e659258",
"metadata": {
"tags": []
},
"source": [
"## Display of critical lines\n",
"Another method to represent the critical lines is to use the data calculated by Lenstool, we can then also represent the caustic lines."
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "daed9191-8d97-4d9a-ba67-1dd319202e1b",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"COMP1: critic and caustic lines for source plane at z=1.000\n",
"limitHigh(in arcsec)=10.000 limitLow(in arcsec)=1.000\n",
"xmin=-50.0 ymin=-50.0 xmax=50.0 ymax=50.0\n"
]
},
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Source plane')"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from lenstool import plot\n",
"\n",
"# Compute image plane and source plane surface brightness maps\n",
"pix, wcs = lt.e_pixel_image(100)\n",
"source, swcs = lt.e_pixel_source(100)\n",
"\n",
"# Compute critical and caustic external lines\n",
"tangent, radial = lt.criticnew(1.0)\n",
"critic_int, caustic_int = plot.parse_cline(radial)\n",
"\n",
"fig = plt.figure(figsize=(10,5))\n",
"\n",
"ax = fig.add_axes([0.15, 0.1, 0.5, 0.5], projection=wcs)\n",
"plt.imshow(pix)\n",
"critic_int.set_transform(ax.get_transform('world'))\n",
"ax.add_collection(critic_int)\n",
"ax.autoscale_view()\n",
"ax.set_title('Image plane')\n",
"\n",
"ax = fig.add_axes([0.55, 0.1, 0.5, 0.5], projection=swcs)\n",
"plt.imshow(source)\n",
"caustic_int.set_transform(ax.get_transform('world'))\n",
"ax.add_collection(caustic_int)\n",
"ax.autoscale_view()\n",
"ax.set_title('Source plane')"
]
},
{
"cell_type": "markdown",
"id": "6eca6a0d-bf52-4129-9458-c478ec588447",
"metadata": {},
"source": [
"Here we display the external critical and caustic lines of the lens. \n",
"In the image plane, the critical line is a circle (as we calculated) superposed to the Einstein ring whereas the caustic line in the source plane is a point centered on the source. \n",
"If we were to model the internal lines, it would be the opposite, meaning that the internal critical line would be a point in the image plane and the caustic line a circle in the source plane. However, this point in the image plane is infinitely small, and Lenstool cannot find it, hence it cannot compute the associated caustic line."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bd837c1d",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "lenstool",
"language": "python",
"name": "lenstool"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.8"
}
},
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