{ "cells": [ { "cell_type": "markdown", "id": "fleet-duplicate", "metadata": {}, "source": [ "# Tutorial: $\\gamma\\gamma$ Absorption in the Photon Fields of Line and Thermal Emitters\n", "In this tutorial we will illustrate how to use `agnpy` to compute the $\\gamma\\gamma$ absorption due to the photon fields produced by the BLR and DT photon fields." ] }, { "cell_type": "code", "execution_count": 1, "id": "clear-norway", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import astropy.units as u\n", "from astropy.constants import M_sun\n", "from astropy.coordinates import Distance\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "statistical-ghost", "metadata": {}, "outputs": [], "source": [ "from agnpy.targets import SphericalShellBLR, RingDustTorus, PointSourceBehindJet\n", "from agnpy.absorption import Absorption\n", "from agnpy.utils.plot import load_mpl_rc\n", "\n", "# matplotlib adjustments\n", "load_mpl_rc()" ] }, { "cell_type": "markdown", "id": "sealed-production", "metadata": {}, "source": [ "## Absorption in the photon field of a spehrical shell BLR \n", "Let us consider a BLR composed of a single spherical shell emitting the Ly$\\alpha$ line. Let us take, following Finke (2016) ([see bibliography in the docs](https://agnpy.readthedocs.io/en/latest/bibliography.html)), the following parameters representing the blazar 3C 454.3: $L_{\\rm disk} = 2 \\times 10^{46}\\,{\\rm erg}\\,{\\rm s}^{-1}$, $\\xi_{\\rm li} = 0.1$, $R_{\\rm Ly\\alpha} = 1.1 \\times 10^{17}\\,{\\rm cm}$. The redshift of the source is $z = 0.859$." ] }, { "cell_type": "code", "execution_count": 3, "id": "initial-permission", "metadata": {}, "outputs": [], "source": [ "L_disk = 2 * 1e46 * u.Unit(\"erg s-1\")\n", "xi_line = 0.1\n", "R_line = 1.1 * 1e17 * u.cm\n", "blr = SphericalShellBLR(L_disk, xi_line, \"Lyalpha\", R_line)" ] }, { "cell_type": "markdown", "id": "accredited-finder", "metadata": {}, "source": [ "The `Absorption` class needs, to be initialised: the target instance, the distance from the target $r$ and the redshift of the source (energies have to be converted to the galaxy frame). \n", "Let us actually compare the absorptions for two cases: inside ($r = 0.1 \\times R_{\\rm Ly\\alpha}$) and outside ($r = 10 \\times R_{\\rm Ly\\alpha}$) the BLR." ] }, { "cell_type": "code", "execution_count": 4, "id": "regional-walnut", "metadata": {}, "outputs": [], "source": [ "z = 0.859\n", "r_in_blr = 0.1 * R_line\n", "r_out_blr = 10 * R_line\n", "\n", "# evaluate the two absorptions\n", "abs_in_blr = Absorption(blr, r=r_in_blr, z=z)\n", "abs_out_blr = Absorption(blr, r=r_out_blr, z=z)" ] }, { "cell_type": "markdown", "id": "thick-biodiversity", "metadata": {}, "source": [ "Let us evaluate the absorption in the same energy range considered in Figure 14 of Finke 2016: $[1, 10^5]\\,{\\rm GeV}$" ] }, { "cell_type": "code", "execution_count": 5, "id": "rental-rover", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: divide by zero encountered in true_divide\n", " result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n", "/Users/cosimo/software/miniconda3/envs/gammapy-0.20.1/lib/python3.8/site-packages/astropy/units/quantity.py:613: RuntimeWarning: invalid value encountered in sqrt\n", " result = super().__array_ufunc__(function, method, *arrays, **kwargs)\n" ] } ], "source": [ "E = np.logspace(0, 5) * u.GeV\n", "nu = E.to(\"Hz\", equivalencies=u.spectral())\n", "# evaluate the opacities\n", "tau_in_blr = abs_in_blr.tau(nu)\n", "tau_out_blr = abs_out_blr.tau(nu)" ] }, { "cell_type": "code", "execution_count": 6, "id": "improving-rebel", "metadata": {}, "outputs": [ { "data": { "image/png": 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3nD0GR3hDzkb6L+9u/IYnPtpG2uj+3JCW7Ol9S+f2U0qRcmJfUk7syz1zx/FqVhF/+6yQP7z9NX98bzPnjh/Ij04/kalJcUedPVo6mxFynV+9Fso3e3uf8aPgkqeP+2U5OTmMHTuWDz/88Fufnzlz5lF7VwAeeOABzjrrLABiY9veg1xcXPytK3UnJiby2WefHfV18+fPp6CggAULFjB//nyeffZZ3nvvvTZnHD16NFprlixZwm9+85vjPi8TZIEj/LJu3TqmTJliewzrCvfUcNsr2Qzu05U//nAyERHeXjVbOndO3+4xXDtzONfMSGJt/h7++tkO3t7wDcvXlzJmYE+umjaMeZMH0zXG9w436WyGdG6furo6KioquPfee4+6bfXq1cf9/pqaGrp3737U59t6+/ixLhVzxx13sGDBAq6//nry8/OPOofRzp072b9/P+effz7FxcWcdNJJLF68GIDnnnuO+Ph45s6de9xZA0EWOMIv8o+U74rgNyzNpK6hiReuPi0gF46Uzv5RSjEtOZ5pyfGUVdWx7POd/PWzHdz5Wg6/ezuPy04dwpWnnyidDQm5zu3Y0xIIGzduZOrUqURFHf2/6vbswWlrcQO+PTY7d+489OeioqJjHhe1evVqNmzYwMUXX8x9993HkiVLvnX7+vXrmTVrFh988AGVlZVMmDCBtWvXMm3atKPu65ZbbuH2228nPj6ea6+9lrvuuovHH3+cffv2ERMTw6OPPkqXLl2OHaSD5Bgc4ZfMzEzbI1j36+W5bCiu4r/OH8vJQ/sG5DGks3cSesVy81kj+fiXc3h4wWSG9evOExnbmPWHD7nsz+/z6bY9zp8gLdBke26fnJwcTjrppDZvW716NevWrTvqo3VxA3DgwIE2v/fUU09ly5YtFBQUcPDgQV566SUuuuiio77uq6++4rrrruONN97gL3/5CxUVFdx9991HzXjyyScD0LdvXxYuXMiKFSvafNxFixbx5JNP8tJLL7FgwQKeeuopFi1axHXXXceBAwc8XdyALHCEn1JSUmyPYNXrXxXzt88KuWDiCfx42rCAPY7rnQMhJiqCeZMH8/qi6by+aDrzJg8m65uDLHjyU857eDV//6KQuoaOvWtFtI9sz+3zXQuc9ujevTuXX345Z5xxBl9//TWJiYk888wzREVFsWTJEs4991zGjh3LD3/4Q8aPH3/U99fU1PDKK68wYsQIIiIieP755znxxBOPmrF1gQNw4YUX8tZbb7U5T3JyMiUlJaxYsYLzzjsPgF69egEwduzYTj/PY1Hyk4rvRH+pqamp6enptkcJOVlZWaG3u9kjW3bt56IlH3NC71jeuHF6h68v1REudzZp1cdfkFPbm79+Wkh5dT3xPWK48vRhXHnGicQF4KVHV4XC9rxp06aA/E/XpAMHDhzzZSoTnnvuOV5++WWGDh3K8OHDueOOO3jppZcoLS3llltuYf369Tz55JPU1tYSGRnJPffc862Dn9ty5N9LWloaGRkZGVrrtCO/VhY4yALHH83NzU6eLbO5WXPew6vZUXGA1xdNZ8zAXgF+PDc7m9ba+WBjM8vXl/DU6gI2lVbRJSqCS1ISuWZGEiP6y4Ui/RUK23M4LHC01sc8eNiGjz/+mIcffphnnnmGnj07dx25jixwgnsLCyCl1EKl1HKl1HLkWlSdlpeXZ3sEKzILK/l6135+NmdkwBc34G5n01o7x0RF8IMpibx10wz+es1UTh/ej6WfFXLWQxlc+/yXfCbH6fhFtmczWs9fEyymT5/Oyy+/3OnFTUc5+y4quRaVN5KSkmyPYMWK9aUAzJts5oysrnY27cjOSilmjIxnxsh4vv5mP0+v3sYb60p4f9MuJiX25tqZwzlvwkBPLsfhEtmezfD6oN1QI/9VCr+UlJTYHsG4pmbNWzmlTB7Sh8S+Zi4a6GJnG76r8+iBPfmf+ZNYc+dsbpydzPY9Nfxs2VfMfjCdFz/dIQckd4Bsz2YcPHjQ9ghWyQJH+OXIU4C74IvtFZTtr2fuSScYe0wXO9vQns4JPWO5/dzRrL1rDvddNJ7mZrjn9Q3M+P0HPPrhVvbVNhiYNLTJ9mxGW+fPcYkscIRfampqbI9gXOvLU+dPNLfAcbGzDR3p3C0mih9PG0b6L9L402WT6de9C//zztdM/90H/L+3NrGrKriOfwgmobI9h/pxVs3NzbZH8FRH/z5kgSP8EuzvhPBaU7Nm5YZSUk7sy6A+XY09rmudbelM5+jICL5/8mDe/vlM/nLVqYw7oRdPfrSNmb//kDtfXc+23dUBmDS0hcL2HBsby549cjB5sNBas2fPnmNeX6stbu+/En6Ljg7cuV+C0Wfb9lBefdDzi2kej2udbfGns1KK2WMSmD0mgcwdFTyevo2XvtjJ37/cyXkTBnJDWjITBvf2cNrQFQrbc2JiIkVFRezevdv2KJ3W1NREZGSk7TE8ExsbS2JiYru/XhY4wi/V1dXEx8fbHsOY5TmlKGX25Slwr7MtXnVOOTGOp38cx+Zd+/nf9HzeyC7hrZxvmD26PzfOGUnKiYG5pEeoCIXtOTo6OuTf7bV9+3aGDRtmewxrgn8/oQhqwf6PlJcam5p5e8M3nHpiHAN7t383qRdc6myT151HDejJQ5dNJv32NK6YOpSPt+7hksc/4fInP+XjreXOvvwh27MZrneWBY7wS1FRke0RjFm7bQ8VBw5ygcF3T7VyqbNNgeo8JK4bv7l4Ih/dMZtrZiSxbudernj6My5+7BNWbdrl3EJHtmczXO8sCxzhl+Rks8ei2LRive/lqfMmDDT+2C51tinQnQf2juWeueNY80vfuXTyy6q55vkvOf+RNaxYX0pzsxsLHdmezXC9syxwhF82btxoewQjGpqaeXvjN0xNiiOhl9mXp8CdzraZ6tyvRxduP3c0a+6cw+3njOKbfbUsWprFuX/6iDezS2gK84WObM9muN5ZFjjCL5MmTbI9ghEfby1nb00DF5xk5tIMR3Kls22mO/fuGs2Nc0by8Z1z+M/zx1BZc5Cbln3FOX/M4PWvisN2oSPbsxmudw6LBY5S6gyl1FqlVIZSaplSKvjfgxgmMjMzbY9gxIr1pUQo+N548y9PgTudbbPVuVtMFP8+awSr75jD3ReMZV9tIz//+zrOfiiDVzOLaGwKrxO2yfZshuudw2KBA+wA5mitU4FtwDzL8zgjJSXF9ggBd7CxmXc2fsMZI/rRv6edi9e50DkY2O7cNSaSa2cOZ/Uds7l37jiq6xu57ZVsznwog5e/3ElDmCx0bHd2heudw2KBo7Uu0VrXtvyxEQiPfwVCgAs/IazZupuqukYumGjn5Slwo3MwCJbOXWMiuXpGEh/dMZvFF46jrqGJO/6xnjMfzOCVL3eG/B6dYOkc7lzvHFQLHKXUjUqpL5VS9Uqp5464LU4p9U+l1AGl1A6l1MI2vj8JOA9Ybmhk57nwE8Ly9aVERii+Z+HdU61c6BwMgq1zbHQkV01PIuMXs/n1vPEcbGzmF/9Yz1kPZfDPr4pC9hidYOscrlzvHFQLHKAEuB94to3bHgUOAgOAK4DHlVLjW29USvUCngeu1Fq7fY14g3JycmyPEFD1jU28t3EX00b0I657jLU5wr1zsAjWzrHRkVx5hu/CnvddNJ6ag03c8vdszv5jRki+6ypYO4cb1zsH1aUatNavASilTgEOXXBCKdUduASYoLWuBtYopd4ErgTuVEpFAcuAxVrrr491/0qp9GPcNNmTJ+CgUaNG2R4hoD7aXM7++kbmWji53+HCvXOwCPbOsdGR/HjaMC47dQh/+6yQx9O3ctOyr/jzqi38/KxRnDdhIBERyvaYxxXsncOF652DbQ/OsYwCmrTWmw/7XDbQugfncmAqcK9SKl0pdVlHH6Curo7y8nJKS0spLi6msrKS/Px8amtryc3Npbm5maysLOBfr2tmZWXR3NxMbm4utbW15OfnU1lZSXFxMaWlpZSXl7N9+3aqq6vJy8ujsbGR7Ozsb91H6685OTnU19ezZcsWqqqqKCwspKysjLKyMgoLC6mqqmLLli3U19cfWpUfeR/Z2dk0NjaSl5dHdXU127dvD/hz2r59e9g9p8P/nl5M30BUhGJA4y6rz2nt2rWy7Rl4ToWFhSHxnA7WHuDsoZG8+pMJ3DQrkbIq33l0zvyf91m+bifr168P6r+n1u1Ztr3APqcdO3aE3XM68u+psbGRY1HBeIpwpdT9QKLW+qqWP88EXtFaDzzsa64DrtBap3nweOmpqamp6enp/t6Vc6qqqujVq5ftMQKirqGJlF+/x6lJcTz3k9OszhLOnYNJqHY+UN/IC2t38MRH+eytaWDC4F7cds5o0kb1R6ng26MTqp1DjQud09LSyMjIyGhrLRAqe3CqgSP/lnoB+y3MIg6zd+9e2yMETPrXuzlwsIkLDF85vC3h3DmYhGrn7l2iuD5tBKvvmM2tZ49iR3kNP/nLF8z/37Wszd9je7yjhGrnUON651BZ4GwGopRSIw/73CSg0+ehVkotVEotV0otByaWlZX5O6OTYmPNX7bAlBU5pURHKs4ZZ+/dU63CuXMwCfXOPWOjuenMkaz+5WxuSBvBxpIqLn/qU3709Gd8VVhpe7xDQr1zqHC9c1AtcJRSUUqpWCASiFRKxSqlorTWB4DXgF8ppborpabjO5nfi519LK31Uq31XK31XCAnISHBk+cgwkPtwSZWbdrFrJH96d1NTowtQkufbjHc8b0xrP7lbK6ensTn2yu4+LFPuPb5L8gtqbI9nhBGBNUCB7gbqAXuBH7U8vu7W267AegKlOF7x9T1Wmu3ryQWBOrq6myPEBAffl1GzcEmLrD87qlW4do52IRb5/geXbj3wnFk/CKNhVOHkv71bs5/ZDU3Ls0if3e1tbnCrXOwcr1zsL1NfDGw+Bi3VQDf9+qxWk4U2HqyQHmJqpP69Olje4SAWLG+lJjICM4aN8D2KED4dg424dr5hN5d+X8XT+Sns0bwp1Wbef2rYlZu+IZLpyRy81kjGdSnq9F5wrVzsHG9c7DtwTFGXqLyxq5du2yP4Lmag42syttF6uj+9IoNjpenwrFzMAr3zkP7deOhH07mnZ/P4uyxA/j7lztJeyCdXy/PZU91vbE5wr1zsHC9s7MLHOGNoUOH2h7Bc9t2H6CuoZnpI/rZHuWQcOwcjFzpPHJAT/73yhTeWDSd04bF8cyaAmb94UP++N5m9tc1BPzxXelsm+udZYEj/LJ58+bjf1GIaT01VHRU8PznEY6dg5FrnScN6cNfr53K0munMnJATx5etYVZf/iQp1dvo66hKWCP61pnW1zvHDz/ghsmbxP3xsSJE22P4ATpbIarnaclx/PPG6bx5JUp9O/ZhftXbGL2A+m89HlhQK5c7mpn01zv7OwCR47B8UbrKbRFYElnM1zurJTinPEDWXnzLP542SSiIhV3vpbDuX/6iLc3lOLlWe9d7myS652dXeAIb6SkpNgewQnS2QzpDJERiotPTmTVrWksvnAce2sa+Olfs7j4sU/4dJs3Z0WWzma43lkWOMIvrv+EYIp0NkM6/0tMVARXTU8i447Z/PyskWzZtZ8FT37KVX/53O+TBUpnM1zv7OwCR47B8YbrPyGYIp3NkM5H69Elip+fNYqMO2Zz1bRhfLy1nAv+vJqfv/QVOytqOnWf0tkM1zs7u8CRY3C8kZ2dbXsEJ0hnM6TzscX36MLii8az6tY05k0axBvZJcx5MJ3Fb27s8Dl0pLMZrnd2doEjvDF+/HjbIzhBOpshnY9vaL9u/GnBySz/2QymjYjnuU+2k/o/6Sz5YAu1B9v31nLpbIbrnWWBI/yydetW2yM4QTqbIZ3bb/yg3jx/9WksvXYqSfHdeeDdzaQ98GG73lounc1wvbMscIRfEhMTbY/gBOlshnTuuGnJ8byxaDoPL5hMTFQEd76Ww3kPr+a93F3HfGu5dDbD9c7OLnDkIGNvlJeX2x7BCdLZDOncORERinmTB/P+rancO3cc5dX1XPfCl1z2xKd8VVh51NdLZzNc7+zsAkcOMvZGjx49bI/gBOlshnT2T5eoSK6e4Xtr+Q1pI1hfvJeLH/uEG/6WyfbyA4e+Tjqb4XpnZxc4whsNDYG/MJ+QzqZIZ2/0io3mju+NIf322Vx2yhDe3vANZz2UweI3N1Jx4KB0NsT1zrLAEX5pbvb+OjXiaNLZDOnsrYG9Y/n9pSex8uZZzBjZ8o6rP3zI85+XBvRinsLH9e1ZFjjCL926dbM9ghOksxnSOTBGD+zJcz85jb9dO5Uhcd3437WlzHkgnVczi2hu9u4aV+LbXN+eZYEj/FJRUWF7BCdIZzOkc2BNT45n+c9mcGfaCQDc9ko2c/+8hjVb3D4YNlBc355lgSP8MmjQINsjOEE6myGdAy8iQvHj1LF8cHsav/zeGHZW1PCjZz7jx89+ztff7Lc9XlhxfXt2doEjbxP3RkFBge0RnCCdzZDOZhQUFBAbHcn1aSO+dY2r8x7+iLteW0/Z/jrbI4YF17dnZxc48jZxb4wZM8b2CE6QzmZIZzMO7xzXPYbFF43nvVtTOXvcAJZ9vpPZ/5POn1e1/9IPom2ub8/OLnCEN9atW2d7BCdIZzOksxltdU6K784TV57C3//9dEYk9ODB9zYz50E5ENkfrm/PssARfpkyZYrtEZwgnc2QzmZ8V+epw/vx+g2+Sz9EKMVtr2Rz0aNrWJu/x+CE4cH17VkWOMIvmZmZtkdwgnQ2QzqbcbzOrZd+WHVbKnd8bzTby2u4/KlPufb5L8jfXW1oytDn+vYsCxzhl5SUFNsjOEE6myGdzWhv59joSG5ISyb9F2lcefqJfPj1bs7940csfnMjlQcOBnjK0Of69iwLHOGXrKws2yM4QTqbIZ3N6Gjn+B5d+PX3J/DOz2cys+WMyGkPpPPMmgIONrp9tt7v4vr2LAsc4ZfJkyfbHsEJ0tkM6WxGZzsnJ/TkLz85jReuPo2BvWL59fJczv3TR7y78Ru0lgORj+T69uzsAkfOg+ONvLw82yM4QTqbIZ3N8LfzrFH9WXHTDH5z8QSqahv49xczWfjUZ2ws2efRhOHB9e3Z2QWOnAfHG0lJSbZH8Jwm+H4SDMfOwUg6m+FF56jICK6YeiLpv0jjp6kjyNxRydw/r+GOf2RTViUnCgTZnp1d4AhvlJSU2B4hYBTK9giHhHPnYCKdzfCyc8/YaO48bwyrbkvl/Ikn8PKXRaQ9kM6SD7Y4f8Vy17dnWeAIv8TFxdkewQnS2QzpbEYgOg+J68ajC6fwj5+eQXJCDx54dzNnPpjB/2WXOHt8juvbsyxwhF9qampsj+AE6WyGdDYjkJ1PGRbH6zdM58H5k2hsbuZny75i/v+uJXvn3oA9ZrByfXuWBY7wS0SEbEImSGczpLMZge4cEaG4JCWRD25L46Y5yeQU72Peox9z68vr+GafO8fnuL49u/3shd+io6Ntj+AE6WyGdDbDVOfuXaK49ZzRfHB7GvMmD+K1rGJmP5DOI45cyNP17VkWOMIv1dVy2nQTpLMZ0tkM050H9+nKwwtO5tXrpzF6YE8eem8zZz6YzpthfnyO69uzLHCEX+Lj422P4ATpbIZ0NsNW55QT+/La9dP402WTadZwU8vxOTlF4Xn+HNe3Z1ngCL8UFRXZHsEJ0tkM6WyGzc4REYrvnzyYD25P5aYzR5JTvI+LHm05f87+8Do+x/XtWRY4wi/Jycm2R3CCdDZDOpsRDJ27xURx69mjWHVbKhe0nD9nzgMZPJ6eT31jeByfEwydbXJ2gSOXavDGxo0bbY/gBOlshnQ2I5g6J/btxpKFU3jlp2cwLL4bv387j7Mf+oh3wuD6VsHU2QZnFzhyqQZvTJo0yfYITpDOZkhnM4Kx86nD4nhz0Qz+cMlJ1Bxs4j9ezOSKpz8j75sq26N1WjB2NsnZBY7wRmZmpu0RnCCdzZDOZgRr54gIxQ9PHcKHt6fyH6nD+XJ7Jec/vJp739jA3pqDtsfrsGDtbIoscIRfUlJSbI/gBOlshnQ2I9g794yN5q7zxvLuLbOYM2YAL6zdQdoD6by4djuNTc22x2u3YO8caLLAEX5x/ScEU6SzGdLZjFDpPCy+O0//+BSev/o04nt04Z43NjL3z2v4JL/c9mjtEiqdA0UWOMIvrv+EYIp0NkM6mxFqnVNH9WflzTO5Z+44ivfWsvCpz/jpi5nsrAjuaz2FWmevyQJH+CUnJ8f2CE6QzmZIZzNCsXN0ZATXzEgi/fY0Lj9tKO/kfsOZD2Xw4LtfU3Ow0fZ4bQrFzl6SBY7wy6hRo2yP4ATpbIZ0NiOUO/fr0YXf/mAi/3fjDCYn9uHPH2zlzAczgvKyD6Hc2QuywBF+KSwstD2CE6SzGdLZjHDoPGFwb/7+H6fzyOUnA77LPlz2xKfklgTP28rDobM/ZIEj/DJgwADbIzhBOpshnc0Il85KKS6aNIhVt6XysznJrCvay9w/r+bu13OoPGD/beXh0rmzZIEj/LJ3717bIzhBOpshnc0It87dYqK47ZzRvH9LKmePG8BfPy0k7YF0XrD8tvJw69xRssARfomNjbU9ghOksxnS2Yxw7Ty0XzeeuPIUXrzmNPr37MK9LW8rX5u/x8o84dq5vWSBI4QQQnho5sjD3lZeWcvlT33KoqVZlOyttT2aU8JigaOU6q2U+lwpVa2UmmB7HpfU1dXZHsEJ0tkM6WyGC51b31b+4S/SuOyUIbyVU8qZD2aw5IMt1DWYuVq5C52/S1gscIAa4ALgH7YHcU2fPn1sj+AE6WyGdDbDpc7xPbrw+0tP4vUbpjNqYE8eeHcz5/zxI97P3RXwt5W71LktYbHA0Vo3aK13257DRbt27bI9ghOksxnS2QwXO08a0od/Xj+NP1x6EjUHG7n2hS/5yXNfsG13dcAe08XOhwuqBY5S6kal1JdKqXql1HNH3BanlPqnUuqAUmqHUmqhpTHFYYYOHWp7BCdIZzOksxmudo6IUPzwlCGsui2Nq6cnsXpLOef+6SN+tzKPA/Xenw3Z1c6tgmqBA5QA9wPPtnHbo8BBYABwBfC4Umq8wdlEGzZv3mx7BM8F2clIgfDsHIyksxmud+7dNZp7LxzHyptncuqwOP43I585D6bzxrpiT1+2cr1zlO0BDqe1fg1AKXUKkNj6eaVUd+ASYILWuhpYo5R6E7gSuLO996+USj/GTZM7ObLzJk6caHuEgFHK9gT/Es6dg4l0NkM6+4wa0JO/XTuVlRu+4f7ludz80jr+9lkh9100nrEn9PL7/l3vHGx7cI5lFNCktT58OZoNHNqDo5R6CzgHeEopdVVHH6Curo7y8nJKS0spLi6msrKS/Px8amtryc3Npbm5maysLOBfl6DPysqiubmZ3Nxcamtryc/Pp7KykuLiYkpLSykvL2f79u1UV1eTl5dHY2Mj2dnZ37qP1l9zcnKor69ny5YtVFVVUVhYSFlZGWVlZRQWFlJVVcWWLVuor68/dAG1I+8jOzubxsZG8vLyqK6uZvv27QF/Tl988UXYPaempn+9wyFYntN7770n256B59T6EU7PKRj/nlq353B6Tp39e1JKMeBgCatuS+PSsd1ZV7iXCx5ZzX+/kcOX2Rv9ek5ffvll2G97jY3HfmlPBdvFwQCUUvcDiVrrq1r+PBN4RWs98LCvuQ64Qmud5sHjpaempqamp6f7e1ciDGTv3Mu8Rz/mtz+YyOWnuf0athDCrO3lB/j18lxW5ZXRr3sMvzxvDJdOSSQiIoh2KQeRtLQ0MjIyMtpaC4TKHpxq4Mj9db2A/RZmEYdpXVmLwJLOZkhnM6TzsQ2L784zV53KMz8+hR6xUdzxj/X84PFPWF+0t8P35XrnUFngbAailFIjD/vcJGBjZ+9QKbVQKbVcKbUcmFhWVubvjE5KSUmxPYITpLMZ0tkM6Xx8Z44dwDs/n8Xt54wi75sq5j36MXe9lkNFBy7i6XrnoFrgKKWilFKxQCQQqZSKVUpFaa0PAK8Bv1JKdVdKTQfmAS929rG01ku11nO11nOBnISEBE+eg2taX7MVgSWdzZDOZkjn9omNjuTGOSNZdVsa500YyLLPC5n9QDp//XQHTc3HP7zE9c5BtcAB7gZq8b0z6kctv7+75bYbgK5AGbAMuF5r3ek9OMIb48fLO/VNkM5mSGczpHPHDO7TlceuSOGv10ylX48Y7n59A/MeXUNWYeV3fp/rnYNqgaO1Xqy1Vkd8LG65rUJr/X2tdXet9VCt9VJ/HkteovLG1q1bbY/gBOlshnQ2Qzp3zoyR8bx98yzuPG8M23Yf4AePfcId/8hmT3V9m1/veuegWuCYJC9ReSMxMfH4XyT8Jp3NkM5mSOfOi4mK4KepI1h1WypzTzqBl78sYvYD6bywdvtRL1u53tnZBY7wRnl5ue0RnCCdzZDOZkhn/53QuytLFk7hb9dOJaFXLPe+sZEL/7yGzB0Vh77G9c6ywBF+6dGjh+0RnCCdzZDOZkhn70xPjuetm2byn+ePYceeA1zy+Fpuezmb3fvrne/s7AJHjsHxRkNDg+0RnCCdzZDOZkhnb8VERfDvs0aw6rY0Lpo0iFezipjzYDrLvixp17utwpWzCxw5Bscbzc3NtkdwgnQ2QzqbIZ0DY2DvWB65/GSWXXc6A3vF8mD6Ti5asobMHd/9bqtw5ewCR3ijW7dutkdwgnQ2QzqbIZ0D64wR/Xjr5pncknYi28sPcMnj3/1uq3AlCxzhl4qKiuN/kfCbdDZDOpshnQMvOjKCuSO7suq2NC6cNOjQu61ebOdJAsOBswscOQbHG4MGDbI9ghOksxnS2QzpbMagQYMY2DuWP19+Mktb3m11T8tJAr86zkkCw4GzCxw5BscbBQUFtkdwgnQ2QzqbIZ3NOLzztJZ3W93VcpLAix/7hDtfXU9lB65tFWqcXeAIb4wZM8b2CE6QzmZIZzOksxlHdo6JiuA/Wk4SeMHEE3jpi53MfjCdZZ8X0hyGL1vJAkf4Zd26dbZHcIJ0NkM6myGdzThW5xN6d+XRK6bwwtWn0bdbDHe9lsMPHv+EDcX7zA4YYLLAEX6ZMmWK7RGcIJ3NkM5mSGczjtd51qj+vP3zmdx+zijyvqniwiVruOf1DeyrCY/zFMkCR/glMzPT9ghOkM5mSGczpLMZ7encJSqSG+eM5L1bUjlzzABe/HQHcx5M5x+ZRWgd2i9bObvAkXdReSMlJcX2CE6QzmZIZzOksxkd6TwkrhtP//gUnvnxKXTrEsntr2TzwyfWkvdNVQAnDCxnFzjyLipvZGVl2R7BCdLZDOlshnQ2ozOdzxw7gPduSeWmOclk79zHBY+s4f7luVTXNwZgwsBydoEjvDF58mTbIzhBOpshnc2QzmZ0tnNsdCS3njOad26ZxbQR/Xh6TQFnPpjOivWlIfWylSxwhF/y8vJsj+AE6WyGdDZDOpvhb+ek+O68cPVpPHbFFBSKRUuz+LdnP6eg/IBHEwaWLHCEX5KSkmyP4ATpbIZ0NkM6m+FFZ6UU5088gfdvS+W6mUl8kr+Hc//4EQ+9+zV1DU0eTBk4ssARfikpKbE9gueCcQdsOHYORtLZDOlshpede3SJ4r8uGMeKm2YwaUhvHvlgK2f/MYMP84L3DTrOLnDkXVTeiIuLsz1CwCjbAxwmnDsHE+lshnQ2IxCdxwzsxcv/cQYPzJ9ETX0TP3nuC/7jxS8p2Vvr+WP5y9kFjryLyhs1NTW2R3CCdDZDOpshnc0IVGelFJemJPLBbWlcMXUo7+bu4qyHMngiI5+GpuaAPGZnOLvAEd6IiJBNyATpbIZ0NkM6mxHozr27RfObiyfyzxumM7x/d367Mo8LHlnN5wUVAX3c9pKtTPglOjra9ghOkM5mSGczpLMZpjpPHtKHNxbN4L6LxlO6t44fPrGW217OZk91vZHHPxZZ4Ai/VFdX2x7BCdLZDOlshnQ2w2TnyAjFj6cNY9VtqcybPIhXs4qY82AGSz+zd6VyWeAIv8THx9sewQnS2QzpbIZ0NsNG54ResTy84GT+du1U+nWP4T//ae9K5bLAEX4pKiqyPYITpLMZ0tkM6WyGzc7Tk+NZ2XKl8k2lVfzkuS+obzR73pwoo48mwk5ycrLtEZwgnc2QzmZIZzNsd269Uvm8yYPZsaeGLlGRRh/f2T04ch4cb2zcuNH2CE6QzmZIZzOksxnB0nlIXDdmjDT/cpmzCxw5D443Jk2aZHsEJ0hnM6SzGdLZDNc7O7vAEd7IzMy0PYITpLMZ0tkM6WyG651lgSP8kpKSYnsEJ0hnM6SzGdLZDNc7ywJH+MX1nxBMkc5mSGczpLMZrneWBY7wi+s/IZginc2QzmZIZzNc7ywLHOGXnJwc2yM4QTqbIZ3NkM5muN5ZFjjCL6NGjbI9ghOksxnS2QzpbIbrnWWBI/xSWFhoewQnSGczpLMZ0tkM1zvLAkf4ZcCAAbZHcIJ0NkM6myGdzXC9syxwhF/27t1rewQnSGczpLMZ0tkM1zs7ey0qpdRCYGHLH+VSDZ0UGxtrewQnSGczpLMZ0tkM1zs7uwdHLtUghBBChC9nFzjCG3V1dbZHcIJ0NkM6myGdzXC9syxwhF/69OljewQnSGczpLMZ0tkM1zvLAkf4ZdeuXbZHcIJ0NkM6myGdzXC9syxwhF+GDh1qewQnSGczpLMZ0tkM1zvLAkf4ZfPmzbZHcIJ0NkM6myGdzXC9c4cXOEopt88cJL5l4sSJtkfwnNba9ghHCcfOwUg6myGdzXC9c2f24DyplPqVUqqH59OIkJOZmWl7hIBRyvYE/xLOnYOJdDZDOpvheucOL3C01vOANcCrSqmfKaWcPVmggJSUFNsjOEE6myGdzZDOZrjeubPH4HwC3AXMAb5u2aNzqXdjiVDh+k8IpkhnM6SzGdLZDNc7d3jvi1LqHeAAsBlYATwMNAPjvR1NhALXf0IwRTqbIZ3NkM5muN65M3twfqO1/oHW+k6t9dNa63St9Uda68c9n04EvezsbNsjOEE6myGdzZDOZrjeuTMLnNvkIGPRavx42XFngnQ2QzqbIZ3NcL1z2BxkrJT6jVJqtVLqH0qpbrbnccXWrVttj+AE6WyGdDZDOpvheuewOMhYKTUBGKG1ngm8D1xtaxbXJCYm2h7BCdLZDOlshnQ2w/XOnTnR3zvAC8AP8R1kfA2+RUV/b0frkJnAypbfrwRmWJzFKeXl5bZHcIJ0NkM6myGdzXC983FfXlJKjdZaf33Yp+7XWq9u40s/8ncYpdSNwFXARGCZ1vqqw26LA54BzgHKgbu01ktbbu4LlLb8fh8Q5+8son169JBDsUyQzmZIZzOksxmud27P8TNfAL1a/3CMxY1XSoD7gXOBrkfc9ihwEBgATAZWKKWytdYbgUqgd8vX9QYq2rpzpVT6MR53sj9Du6yhocH2CE6QzmZIZzOksxmud27PS1RtnrBeKTXK41nQWr+mtX4d2HPEY3UHLgHu0VpXa63XAG8CV7Z8yRp8iyJafv24o49dV1dHeXk5paWlFBcXU1lZSX5+PrW1teTm5tLc3ExWVhbwr5MnZWVl0dzcTG5uLrW1teTn51NZWUlxcTGlpaWUl5ezfft2qqurycvLo7Gx8dDb9lrvo/XXnJwc6uvr2bJlC1VVVRQWFlJWVkZZWRmFhYVUVVWxZcsW6uvrycnJafM+srOzaWxsJC8vj+rqarZv3x7w59TQ0BB2z6mpqenQdhEszyk/P1+2PQPPqbm5OeyeUzD+PbUe/BpOzykY/56amprC7jkd+ffU2NjIsajjXVhQKVUPLAY2ABu01gVKqRigQmsdkP1fSqn7gcTWl6iUUicDn2itux72NbcDqVrrC1v+/Ft8x96UAf+mtT7QgcdLT01NTU1PT/fuSTiisrKSvn372h7DU18VVnLxY5/w+0smctmpQ22PA4Rn52Aknc2Qzma40DktLY2MjIwMrXXakbe19yDjEcA9QI5S6gBQBHzq3YjH1QPfsTWH2wf0bP2D1vourfVMrfUlHVncCP9UVLT5aqDwmHQ2QzqbIZ3NcL1ze47BqddaXwuglFLAUHzH5GwK5GBHqOaw44Ba9AL2d/YOlVILgYUtf5xYVlbW2bty2qBBg2yP4ATpbIZ0NkM6m+F65/bswSlq/Y322aG1ztFaH/uFL+9tBqKUUiMP+9wkYGNn71BrvVRrPVdrPRfISUhI8HdGJxUUFNgewQnS2QzpbIZ0NsP1zsdd4Gitx5kYBEApFaWUigUigUilVKxSKqrlJafXgF8ppborpaYD84AXTc0m2jZmzBjbIzhBOpshnc2Qzma43rmzZzIOlLuBWuBO4Ectv7+75bYb8L11vAxYBlzf8hZxYdG6detsj+AE6WyGdDZDOpvheueguI5UK631Ynzv2Grrtgrg+149lhyD440pU6bYHsEJ0tkM6WyGdDbD9c7BtgfHGDkGxxut5ycQgSWdzZDOZkhnM1zv7OwCR3gjJSXF9ghOkM5mSGczpLMZrnd2doGjlFqolFqulFqOvETVaa1nmhSBJZ3NkM5mSGczXO/s7AJHXqLyxuTJk22P4ATpbIZ0NkM6m+F6Z2cXOMIbeXl5tkdwgnQ2QzqbIZ3NcL2zLHCEX5KSkmyP4ATpbIZ0NkM6m+F6Z1ngCL+UlJTYHsEJ0tkM6WyGdDbD9c5BdR4ck+Q8ON6Ii4uzPYLntO0B2hCOnYORdDZDOpvhemdn9+DIQcbeqKmpsT1CwCiU7REOCefOwUQ6myGdzXC9s7MLHOGNiAjZhEyQzmZIZzOksxmud3b72Qu/RUdH2x7BCdLZDOlshnQ2w/XOssARfqmurrY9ghOksxnS2QzpbIbrneUgYx85yLiT4uPjbY/gBOlshnQ2Qzqb4XpnZ/fgyEHG3igqKrI9ghOksxnS2QzpbIbrnZ1d4AhvJCcn2x7BCdLZDOlshnQ2w/XOssARftm4caPtEZwgnc2QzmZIZzNc7ywLHOGXSZMm2R7BCdLZDOlshnQ2w/XOssARfsnMzLQ9ghOksxnS2QzpbIbrneVdVD7yLqpOSklJsT2CE6SzGdLZDOlshuudnd2DI++i8obrPyGYIp3NkM5mSGczXO/s7AJHeMP1nxBMkc5mSGczpLMZrneWBY7wS05Oju0RnCCdzZDOZkhnM1zvLAsc4ZdRo0bZHsEJ0tkM6WyGdDbD9c6ywBF+KSwstD2CE6SzGdLZDOlshuudZYEj/DJgwADbIzhBOpshnc2Qzma43lkWOMIve/futT2CE6SzGdLZDOlshuud5Tw4PnIenE6KjY21PYITpLMZ0tkM6WyG652d3YMj58ERQgghwpezCxzhjbq6OtsjOEE6myGdzZDOZrjeWRY4wi99+vSxPYITpLMZ0tkM6WyG651lgSP8smvXLtsjOEE6myGdzZDOZrjeWRY4wi9Dhw61PYITpLMZ0tkM6WyG651lgSP8snnzZtsjOEE6myGdzZDOZrjeWRY4wi8TJ060PYITpLMZ0tkM6WyG651lgSP8kpmZaXsEz2lte4KjhWPnYCSdzZDOZrjeWRY4wi8pKSm2RwgcZXuAfwnrzkFEOpshnc1wvbMscIRfXP8JwRTpbIZ0NkM6m+F6Z7lUg49cqqGTXP8JwRTpbIZ0NkM6m+F6Z2f34MilGryRnZ1tewQnSGczpLMZ0tkM1zs7u8AR3hg/frztEZwgnc2QzmZIZzNc7ywLHOGXrVu32h7BCdLZDOlshnQ2w/XOssARfklMTLQ9ghOksxnS2QzpbIbrnWWBI/xSXl5uewQnSGczpLMZ0tkM1zvLAkf4pUePHrZHcIJ0NkM6myGdzXC9syxwhF8aGhpsj+AE6WyGdDZDOpvhemdZ4Ai/NDc32x7BCdLZDOlshnQ2w/XOssARfunWrZvtEZwgnc2QzmZIZzNc7ywLHOGXiooK2yM4QTqbIZ3NkM5muN5ZFjjCL4MGDbI9ghOksxnS2QzpbIbrnWWBI/xSUFBgewQnSGczpLMZ0tkM1zvLAkf4ZcyYMbZHcIJ0NkM6myGdzXC9c1gscJRSvZVSnyulqpVSE2zP45J169bZHsEJ0tkM6WyGdDbD9c5hscABaoALgH/YHsQ1U6ZMsT2CE6SzGdLZDOlshuudw2KBo7Vu0Frvtj2HizIzM22P4ATpbIZ0NkM6m+F6Z+MLHKXUjUqpL5VS9Uqp5464LU4p9U+l1AGl1A6l1ELT84mOSUlJsT2CE6SzGdLZDOlshuudbezBKQHuB55t47ZHgYPAAOAK4HGl1HgApdRApdSaNj4GGptcHCUrK8v2CE6QzmZIZzOksxmud44y/YBa69cAlFKnAIeu5a6U6g5cAkzQWlcDa5RSbwJXAndqrb8BZvjz2Eqp9GPcNNmf+3XZ5MmTbY/gBOlshnQ2Qzqb4XrnYDoGZxTQpLXefNjnsoHx7flmpdRbwDnAU0qpqzr64HV1dZSXl1NaWkpxcTGVlZXk5+dTW1tLbm4uzc3Nh1bDra9rZmVl0dzcTG5uLrW1teTn51NZWUlxcTGlpaWUl5ezfft2qqurycvLo7Gxkezs7G/dR+uvOTk51NfXs2XLFqqqqigsLKSsrIyysjIKCwupqqpiy5Yt1NfXk5OT0+Z9ZGdn09jYSF5eHtXV1Wzfvj3gzyk3NzfsnlNTU9Oh7SJYnlN6erpsewaeU15eXtg9p2D8e2rdnsPpOQXj39OmTZvC7jkd+ffU2NjIsSit9TFvDCSl1P1Aotb6qpY/zwRe0VoPPOxrrgOu0FqnBXiW9NTU1NTW/+hE+9XW1tK1a1fbY3gqc0cllzz+CX+49CR+eMoQ2+MA4dk5GElnM6SzGS50TktLIyMjI6OtdUIw7cGpBnod8blewH4Ls4h2KikpsT2CE6SzGdLZDOlshuudjR+D8x02A1FKqZFa6y0tn5sEbAzEg7W8Q6v1XVoTy8rKAvEwYS8uLs72CE6QzmZIZzOksxmud7bxNvEopVQsEAlEKqVilVJRWusDwGvAr5RS3ZVS04F5wIuBmENrvVRrPVdrPRfISUhICMTDhL2amhrbIwSAnZdtv0t4dg4+0tkM6WyG651tvER1N1AL3An8qOX3d7fcdgPQFSgDlgHXa60DsgdHeCMiIphe5fSWsj3AYcK5czCRzmZIZzNc72zjbeKLgcXHuK0C+L6JOeQlKm9ER0fbHsEJ0tkM6WyGdDbD9c7OLu/kJSpvVFdX2x7BCdLZDOlshnQ2w/XOzi5whDfi4+Ntj+AE6WyGdDZDOpvhemdZ4Ai/FBUV2R7BCdLZDOlshnQ2w/XOwfQ2caPkGBxvJCcn2x7BCdLZDOlshnQ2w/XOzu7BkWNwvLFxo7zJzQTpbIZ0NkM6m+F6Z2cXOMIbkyZNsj2CE6SzGdLZDOlshuudZYEj/NJ6ETQRWNLZDOlshnQ2w/XOcgyOjxyD00kpKSm2R3CCdDZDOpshnc1wvbOze3DkGBxvuP4TginS2QzpbIZ0NsP1zs4ucIQ3XP8JwRTpbIZ0NkM6m+F6Z1ngCL/k5OTYHsEJ0tkM6WyGdDbD9c6ywBF+GTVqlO0RnCCdzZDOZkhnM1zv7OwCRym1UCm1XCm1HDnIuNMKCwttj+AE6WyGdDZDOpvhemdnFzhykLE3BgwYYHsEJ0hnM6SzGdLZDNc7O7vAEd7Yu3ev7RGcIJ3NkM5mSOdO0BoO1kBjfbu/xfXOzp4HR3gjNjbW9ghOkM5mSGczpDO+Bcu+Itj9NZR/7fu1Zg801MDBA77FzMHqw/58ANC+7+3SG3r0h+4Jh/2aAN37+37teQLEj3S+syxwhBBCiECq3AG7NsDuPNi92fdr+RZoOHDYFyno2geiu0NMd4jpBr0Tfb+P7tbyue7Q1AAHyqB6N1R/A9/kwMH9bT5sv+4DIGEM9B8N8aMgfiTEj4aeA0EpI0/dJlngCL/U1dXZHsEJ0tkM6WyGE50bD0Lecvjiadjx8b8+HxEN/ZJh5FnQf4xv4dF/tO9z0V0791gNtVBdBgd2+37dVwR7tnCwaD1d92yFgoxvf31MT+g/ChJPgxPPgKFn+Pb8hBlnFzhyqQZv9OnTx/YITpDOZkhnM8K6875iyHwOsp6H6l2+l5NO+w9ImuVb0PQdBpEe/683uiv0PdH3cZiGqiq69uoF9ft9e4zKt0D5Zt9LYrty4bPHfR8AcSP+tdgZegbEDQ/5vTzOLnC01kuBpQBKqfSEhIRUyyOFpF27dtGrVy/bY4Q96WyGdDYj7Dpr7dtL8vlT8PVK0E0wYCLM/k+YON/30pIFhzp36QmDp/g+DlddBoWfQuFa2PEJrFsKX/3Vd1uPATD0dBieBiPOPGrxFAqcXeAIbwwdOtT2CE6QzmZIZzPCpnNDrW9vzRfPwJ4tEBkDEy6BU6+FIadZ3wNy3M49EmDcRb4P8O3pKfrCt+jZ8Qlsfhdy3/DdFj8Kks+C5DPhxOmdfznNIFngCL9s3ryZiRMn2h4j7ElnM6SzGWHROf9DWH4LVBZA76Fw5n/DyVf63tUUJDrcuUtPGDHH9wG+t6QXroWt78PWVfDpY76PqFjfIif5LN9H/Ejri7m2yAJH+CXk/5EKEdLZDOlsRkh3PlAO7/wXrH8JusbBvMdg0gKIiLQ92VH87hzVxfcS1fA0OOd+3/FF+R/4FjzbPoT8VfDOXb7jdcZ9H8bNgxMmBc1iR070J/ySmZlpewQnSGczpLMZIdlZa98xKktO9S1uTloAN34BJ18RlIsbCEDn3oNhypXww+fhF9vg6ndh5u2+d4ateQieTIVHTob3/htKvvI1s0j24Ai/pKSk2B7Bc5b/m2xTOHYORtLZjJDrvCcflv8cCj6Cvklw6bMwYrbtqY4roJ0jo2DoVN/HmfdAWR7kvg4bX4eP/+T76HOib6/O+O/DoCnG9+zIHhzhl5D8SaydVJDsZoXw7hxMpLMZIdO58SB89AA8dobvoNsZt8INa0NicQOGOyeMgbQ7YdGnsOhzmP1fENMDPnkEnpoDj06F5mZz8+DwHhw5D443Qu4nsRAlnc2QzmaEROddufDqNVCWC4NPgQsfhoETbE/VIdY69x8NqXf4Psq3+Pbs1O+HCLP7VJzdgyNXE/dGdna27RGcIJ3NkM5mBH3n6jL426W+Syyc/wBc827ILW4gSDrHj4RZv4Czf2X8oZ3dgyO8MX78eNsjOEE6myGdzQjqzo0H4eV/g6oSWPgyjDrH9kSdFtSdDXB2D47wxtatW22P4ATpbIZ0NiOoO79zl+/cL2feE9KLGwjyzgbIAkf4JTEx0fYITpDOZkhnM4K2c+bzvotjjpvnO6A4xAVtZ0NkgSP8Ul5ebnsEJ0hnM6SzGUHZeefn8NbtkDDed/K+IHoXZWcFZWeDZIEj/NKjRw/bIzhBOpshnc0Ius5VpfD3KyG6Gyz4G3QJsvk6Keg6GyYHGQu/NDQ02B7BCdLZDOlsRlB1bqyHl6+EA2Xwo1chLsn2RJ4Jqs4WyAJH+KXZ8ImbXCWdzZDOZgRNZ61hxW2+K2ifc/+/LjIZJoKmsyXyEpXwS7du3WyP4ATpbIZ0NiNoOn/5DHz1IkycD2fcaHsazwVNZ0tkgSP8UlFRYXsEJ0hnM6SzGUHReccnsPKXMPAkuPCRsDio+EhB0dkiZ1+ikks1eGPQoEG2R3CCdDZDOpthvfO+It/J/GJ7+w4qjgnPPR3WO1vm7B4cuVSDNwoKCmyP4ATpbIZ0NsNq5+Zm+Mc1UFMB85+HPkPtzRJgrm/Pzi5whDfGjBljewQnSGczpLMZVjuv+xvs/NR3IcikmfbmMMD17VkWOMIv69atsz2CE6SzGdLZDGudayrgvXshbjhM/7mdGQxyfXt29hgc4Y0pU6bYHsEJ0tkM6WyGtc6r7oPaCrjkKYiOtTODQa5vz7IHR/glMzPT9ghOkM5mSGczrHQu+tJ3ramxF0HyWeYf3wLXt2dZ4Ai/pKSk2B7BCdLZDOlshvHOzU2w4lbfpRi+91uzj22R69uzLHCEX7KysmyP4ATpbIZ0NsN45y+fhdJsSPsl9HbnCtuub8+ywBF+mTx5su0RnCCdzZDOZhjtXF0Gq34N/cfA6TeYe9wg4Pr2LAsc4Ze8vDzbIzhBOpshnc0w2vnde6B+H1zwIERGm3vcIOD69iwLHOGXpKTwufJuMJPOZkhnM4x13r4G1r8EJy2AYTPMPGYQcX17lgWO8EtJSYntEZwgnc2QzmYY6dzU4LtSeJfecM6vA/94Qcj17VnOgyP8EhcXZ3sEJ0hnM6SzGUY6f/oY7M6D8x+AHm5eisf17Vn24Ai/1NTU2B7BCdLZDOlsRsA77yuG9N/DCZPglKsD+1hBzPXtOSwWOEqpM5RSa5VSGUqpZUopt44ksygiIiw2oW/RtgdoQzh2DkbS2YyAd37nLmiogQsegojIwD5WEHN9ew6XZ78DmKO1TgW2AfMsz+OM6OjwXUsq2wMcJpw7BxPpbEZAO299H3LfgJQfQ+IpgXucEOD69hwWCxytdYnWurblj41As815XFJdXW17BCdIZzOksxkB66w1rLwTusbBmf8dmMcIIa5vz8YXOEqpG5VSXyql6pVSzx1xW5xS6p9KqQNKqR1KqYUdvO8k4DxguYcji+8QHx9vewQnSGczpLMZAetcvhn2bIHTroNubh9gC7I929iDUwLcDzzbxm2PAgeBAcAVwONKqfEASqmBSqk1bXwMbLm9F/A8cKXW+qCRZyIoKiqyPYITpLMZ0tmMgHUu+Mj36/C0wNx/iHF9ezb+NnGt9WsASqlTgEMXBVFKdQcuASZorauBNUqpN4ErgTu11t8AbZ6pSSkVBSwDFmutvz7WYyul0o9x0+SOPxMBkJycbHsEJ0hnM6SzGQHrvC3dd0HNwW4fe9PK9e05mI7BGQU0aa03H/a5bGB8O773cmAqcK9SKl0pdVlHH7yuro7y8nJKS0spLi6msrKS/Px8amtryc3Npbm5+dCFy1ovQZ+VlUVzczO5ubnU1taSn59PZWUlxcXFlJaWUl5ezvbt26muriYvL4/Gxkays7O/dR+tv+bk5FBfX8+WLVuoqqqisLCQsrIyysrKKCwspKqqii1btlBfX09OTk6b95GdnU1jYyN5eXlUV1ezffv2gD+nnJycsHtOTY1Nh7aLYHlO6enpsu0ZeE4bN24Mu+cUjH9Prduzp88pdyO6YDU1CSdTvrdK/p6ystiwYUPYPacj/54aGxs5FqW1nTfFKqXuBxK11le1/Hkm8IrWeuBhX3MdcIXWOi3As6Snpqamtv5HJ9z2xfYK5v/vWh6cP4lLUty58rAQIa04C56aDWf/GqbfZHsaYUhaWhoZGRkZba0TgmkPTjXQ64jP9QL2W5hFtFPryloElnQ2QzqbEZDOBRm+X5NmeX/fIcr17TmYLtWwGYhSSo3UWm9p+dwkYGMgHqzlHVqt79KaWFZWFoiHCXspKSm2R3CCdDZDOpsRkM4FH0HXvjDwJO/vO0S5vj3beJt4lFIqFogEIpVSsUqpKK31AeA14FdKqe5Kqen4Ttj3YiDm0Fov1VrP1VrPBXISEty8Vom/XP8JwRTpbIZ0NsPzzo31sGMtDJsJjp+993Cub882toS7gVrgTuBHLb+/u+W2G4CuQBm+d0Vdr7UOyB4c4Q3Xf0IwRTqbIZ3N8Lxz0RfQWAvDU7293xDn+vZsfIGjtV6stVZHfCxuua1Ca/19rXV3rfVQrfXSQM2hlFqolFqulFqOvETVaa1HzIvAks5mSGczPO+8rfX4mzRv7zfEub49O7svT16i8saoUaNsj+AE6WyGdDbD884FGdBrMPQb4e39hjjXt2dnFzjCG4WFhbZHcIJ0NkM6m+Fp5/r9UJzpe/eUCqZL5Nrn+vYsCxzhlwEDBtgewQnS2QzpbIannXesheZGSJLjb47k+vbs7AJHjsHxxt69e22P4ATpbIZ0NsPTzq3nv5EDjI/i+vbs7AJHjsHxRmxsrO0RnCCdzZDOZnjaeVsG9BsJvQZ5d59hwvXt2dkFjhBCiBB3oBx25cjeG9EmWeAIv9TV1dkewQnS2QzpbIZnnQs+8v0ql2dok+vbczBdqsEouVSDN/r06WN7BCdIZzOksxmedS7IAJTvDMbiKK5vz87uwZFjcLyxa9cu2yM4QTqbIZ3N8KxzwUdwwknQLc6b+wszrm/Pzi5whDeGDh1qewQnSGczpLMZnnTeuxMqtsnbw7+D69uzLHCEXzZv3mx7BCdIZzOksxmedJa3hx+X69uzLHCEXyZOnGh7BCdIZzOksxmedN6WARHRMPQM/+8rTLm+PTu7wJET/XkjMzPT9ghOkM5mSGcz/O6stW8PTuKpENPdm6HCkOvbs7MLHDnI2BspKSm2R3CCdDZDOpvhd+fyzVC9S16eOg7Xt2dnFzjCG+H4E4LWtic4Wjh2DkbS2Qy/O29rOf5GDjD+Tq5vz7LAEX4J558QgunCxOHcOZhIZzP87lyQAdHdYbD8fX0X17dnWeAIv2RnZ9sewQnS2QzpbIZfnZubYPtqOHEaRMV4N1QYcn17lgWO8Mv48eNtj+AE6WyGdDbDr86l66Bunxx/0w6ub8/OLnDkXVTe2Lp1q+0RnCCdzZDOZvjV+dDxN3L9qeNxfXt2doEj76LyRmJiou0RnCCdzZDOZvjVueAj6BoHA9w+x0t7uL49O7vAEd4oLy+3PYITpLMZ0tmMTndurIfCTyFpJkTI/76Ox/XtWbYQ4ZcePXrYHsEJ0tkM6WxGpzvv/Bwaa+Xt4e3k+vYsCxzhl4aGBtsjOEE6myGdzeh050PXn0rzbJZw5vr2LAsc4Zfm5mbbIzhBOpshnc3odOdtGdArEeKGeztQmHJ9e5YFjvBLt27dbI/gBOlshnQ2o1Od6/dDcabv3VPBdBbOIOb69iwLHOGXiooK2yM4QTqbIZ3N6FTnfcWgm2CA2+d26QjXt+co2wPYopRaCCxs+aOcB6eTBg0aZHsEJ0hnM6SzGX51VvJzeXu5vj07u6XIeXC8UVBQYHsEJ0hnM6SzGdLZDNc7O7vAEd4YM2aM7RGcIJ3NkM5mSGczXO8sCxzhl3Xr1tkewQnS2QzpbIZ0NsP1zrLAEX6ZMmWK7RGcIJ3NkM5mSGczXO8sCxzhl8zMTNsjOEE6myGdzZDOZrjeWRY4wi8pKSm2R3CCdDZDOpshnc1wvbMscIRfsrKybI/gBOlshnQ2Qzqb4XpnWeAIv0yePNn2CE6QzmZIZzOksxmud5YFjvBLXl6e7RGcIJ3NkM5mSGczXO8sCxzhl6SkJNsjOEE6myGdzZDOZrjeWRY4wi8lJSW2R3CCdDZDOpshnc1wvbNci8pHrkXVSXFxcbZHcIJ0NkM6myGdzXC9s7N7cORaVN6oqamxPYITpLMZ0tkM6WyG652dXeAIb0REyCZkgnQ2QzqbIZ3NcL2z0lrbnsE6pVRR7969B7v+lrrOaGhoIDo62vYYntpf18jGkn0kJ/QgvkcX2+MA4dk5GElnMzrVuaEGirMgbjj0GhSYwcKMC9vzunXr2LdvX7HWOvHI22SBAyilvgL6A1s7eRcJgD8H8XTk+9vztd/1Nce6ra3PH+9zk1t+XXecebwinc2QzmaEa+e2Pu9K5/Z8fWc6H+u2YOrc1jyB/P7Wr00GdmutTz7qK7TW8uHnB7Dc1Pe352u/62uOdVtbnz/e54B0IF06S2fpLJ2/6/OudG7P13em87FuC6bOplu352vdfoFOCCGEEGFJFjhCCCGECDuywPHGUoPf356v/a6vOdZtbX2+vZ8zRTqbIZ3NCNfObX3elc7t+frOdD7WbcHU2YvH93SbloOMRacppdIBtNZpdicJb9LZDOlshnQ2QzrLHhwhhBBChCHZgyOEEEKIsCN7cIQQQggRdmSBI4QQQoiwIwscIYQQQoQdWeAITyilzlBKrVVKZSillimlog+77XKl1G6b84WLtjorpYYppXYrpdJbPvrbnjPUHWt7VkqlKaVWKaU+VEpdbHvOcHCMbXrGYdvzZqXUH23PGeqO0TlCKfWcUmq1UmqNUmqs7Tm9JAsc4ZUdwBytdSqwDZgHoJSKAC4FdlqcLZy02RnI0FqntXzIYtJ/R3VWSsUCtwHnaa1na63/aXXC8HFUa631mtbtGfgEeN3ifOGirX87JgNdtNYzgbuAW+yN5z1Z4AhPaK1LtNa1LX9sBJpbfr8Q+MdhfxZ++I7O01t+Cvt/SillabywcYzO04Ba4P+UUv9USg20NmAY+Y5tmpY9Z6cBq23MFk6O0bkIaGr5N6MvUG5rvkCQBY74FqXUjUqpL5VS9Uqp5464La7lH/YDSqkdSqmFbXx/EnAesFwpFQn8EPi7keFDiJedgVJ8V9Sdhe8Kuz8I/DMIDR53HoCv84XAU8DigD+BEOJx61ZnA6u01vIDUguPO5cD9UAe8GfgscA/A3NkgSOOVALcDzzbxm2PAgfx/UN/BfC4Ump8641KqV7A88CVWuuDwI+Al+UfpzZ51llrXa+1PqB9J7V6DZgU8OlDh5fb817g45bfrwLGBXb0kONl61bzgVcCNnFo8rLzOUCE1no0cAnwYIBnN0oWOOJbtNavaa1fB/Yc/nmlVHd8/wHco7Wu1lqvAd4Ermy5PQpYBizWWn/d8m3jgH9TSr0NjFRKPWLoaQQ9Lzu3/KPVaiawNfDPIDR4vD1/Doxt2Z0/Gcg38iRChMetW1+eOhVYY+YZhAaPO6vD7qcc6B34Z2COLHBEe40CmrTWmw/7XDbQ+tPB5cBU4N6Wdz5cprX+pdb6HK3194AtWuubDM8cijrcGUhVSmUqpVYDg7F/wb1Q0JnteQ/wTyAD+D3wa5MDh7DObNMAZwEfyB7gdutM5/eAIUqpDOAl4FcmBw60KNsDiJDRA9h3xOf2AT0BtNYvAi8e65u11qcEbrSw0tnO/xfgucJNpzprrR/F9zKAaL/Otl4JrAz4dOGjs/92XNbG58KC7MER7VUN9Dric72A/RZmCWfS2QzpbI60NkM6H0EWOKK9NgNRSqmRh31uErDR0jzhSjqbIZ3NkdZmSOcjyAJHfItSKqrlhGaRQKRSKlYpFaW1PoDvHTq/Ukp1V0pNx3eiqGO+LCWOTTqbIZ3NkdZmSOcO0FrLh3wc+sB3bg99xMfiltvi8J1R9ABQCCy0PW+ofkhn6RxuH9JaOgfbh2qJIoQQQggRNuQlKiGEEEKEHVngCCGEECLsyAJHCCGEEGFHFjhCCCGECDuywBFCCCFE2JEFjhBCCCHCjixwhBBCCBF2ZIEjhBBCiLAjCxwhhBBChB1Z4AghhBAi7MgCRwgRVpRSg5RSRUd8brtS6qwjPneVUmqN2emEEKbIAkcIEW7OB962PYQQwi5Z4AghQoZSqkApdV7L7/sopcqVUj2O+LLzgbc6eL+XKaWqD/uoV0qlezS2EMICWeAIIUJJCTAYQGu9F9gEnN56o1IqGpgFvNeRO9Va/11r3UNr3QMYBGwDlnk0sxDCgijbAwghRAccWuC0iAXUYX+eBWRrrfe38b2vK6UaD/tzDJB1+BcopSKApUC61voJb0YWQtgge3CEEKGkmJYFjlLqFGA4sPqw27/r5anva637tH4AN7TxNb8BegI3eTaxEMIKWeAIIUJJCZColOoJvAgs0lrXHXb7+cCKztyxUmoBcDlwqda6we9JhRBWyUtUQohQUoJvr80/gb9qrV9qvUEplQR00VrndfROlVInA38GztZa7/ZqWCGEPbIHRwgRSoqB0UCG1vo3R9x2AR1899Rh5gF9gTWHvZNqpR9zCiEsU1pr2zMIIYTflFJvAUu01p1d5AghwojswRFChIt04EPbQwghgoPswRFCCCFE2JE9OEIIIYQIO7LAEUIIIUTYkQWOEEIIIcKOLHCEEEIIEXZkgSOEEEKIsCMLHCGEEEKEnf8PzIvdnAzrV4UAAAAASUVORK5CYII=", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# let us plot them\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.loglog(nu, tau_in_blr, label=r\"$r = 0.1 \\times R_{\\rm Ly\\alpha}$\")\n", "ax.loglog(nu, tau_out_blr, label=r\"$r = 10 \\times R_{\\rm Ly\\alpha}$\")\n", "ax.legend()\n", "ax.set_xlabel(r\"$\\nu\\,/\\,{\\rm Hz}$\", fontsize=12)\n", "ax.set_ylabel(r\"$\\tau_{\\gamma \\gamma}$\", fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "personalized-external", "metadata": {}, "source": [ "### Opacity of a misaligned (non-blazar) source\n", "In the default opacity calculation, `agnpy` assumes the line of sight of the observer to be aligned with the jet (i.e. the source is a blazar with $\\mu_s = 1$, where $\\theta_s$ is the viewing angle and $\\mu_s$ its cosine). This brings a considerable simplification in the opacity calculation (see the main documentation). \n", "\n", "For some sources `agnpy` allows the calculation of the opacity for an aribitrary viewing angle (this is possible for BLR, DT and point source behind the blob). Let us assume we are considering a source with the same parameters of 3C 454.3 in the previous example, but with a viewing angle of $20\\,{\\rm deg}$. Let us evaluate the absorption within the BLR for the aligned and misaligned case " ] }, { "cell_type": "code", "execution_count": 7, "id": "imperial-crack", "metadata": {}, "outputs": [], "source": [ "mu_s = np.cos(np.deg2rad(20))\n", "abs_in_blr_mis = Absorption(blr, r=r_in_blr, z=z, mu_s=mu_s)\n", "# evaluate the opacity\n", "tau_in_blr_mis = abs_in_blr_mis.tau(nu)" ] }, { "cell_type": "code", "execution_count": 8, "id": "spread-mountain", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# compare the opacity in the aligned and misaligned case\n", "ax.loglog(\n", " nu, tau_in_blr, label=r\"$r = 0.1 \\times R_{\\rm Ly\\alpha},\\;\\theta_s=0\\,{\\rm deg}$\"\n", ")\n", "ax.loglog(\n", " nu,\n", " tau_in_blr_mis,\n", " label=r\"$r = 0.1 \\times R_{\\rm Ly\\alpha},\\;\\theta_s=20\\,{\\rm deg}$\",\n", ")\n", "ax.legend()\n", "ax.set_xlabel(r\"$\\nu\\,/\\,{\\rm Hz}$\", fontsize=12)\n", "ax.set_ylabel(r\"$\\tau_{\\gamma \\gamma}$\", fontsize=12)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "immediate-harmony", "metadata": {}, "source": [ "### Comparison of the misaligned case with a point source behind the blob\n", "The opacity for the misaligned case, in the limit of large distances, $r >> R_{\\rm Ly\\alpha}$, should reduce to the same opacity produced by a monochromatic point source behind the jet approximating the BLR (in luminosity and emitted energy). \n", "\n", "**Note** this comparison is not possible for the aligned case since for $\\mu_s=1$ there is no absorption from the target photons (factor $(1 - \\mu_s)$ null in the opacity formula)." ] }, { "cell_type": "code", "execution_count": 9, "id": "careful-peter", "metadata": {}, "outputs": [], "source": [ "# point source with the same luminosity as the BLR\n", "ps_blr = PointSourceBehindJet(blr.xi_line * L_disk, blr.epsilon_line)\n", "\n", "# absorption in the limit of very large distances\n", "r_far_blr = 1e2 * R_line\n", "abs_far_blr_mis = Absorption(blr, r=r_far_blr, z=z, mu_s=mu_s)\n", "abs_far_ps_blr_mis = Absorption(ps_blr, r=r_far_blr, z=z, mu_s=mu_s)" ] }, { "cell_type": "code", "execution_count": 10, "id": "white-stevens", "metadata": {}, "outputs": [], "source": [ "# compute the opacities\n", "tau_far_blr_mis = abs_far_blr_mis.tau(nu)\n", "tau_far_ps_blr_mis = abs_far_ps_blr_mis.tau(nu)" ] }, { "cell_type": "code", "execution_count": 11, "id": "advanced-apparel", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# compare the opacity in the aligned and misaligned case\n", "ax.loglog(\n", " nu,\n", " tau_far_blr_mis,\n", " label=r\"$r = 100 \\times R_{\\rm Ly\\alpha},\\;\\theta_s=20\\,{\\rm deg}$\",\n", ")\n", "ax.loglog(nu, tau_far_ps_blr_mis, ls=\"--\", label=\"point source approximating BLR\")\n", "ax.legend()\n", "ax.set_xlabel(r\"$\\nu\\,/\\,{\\rm Hz}$\", fontsize=12)\n", "ax.set_ylabel(r\"$\\tau_{\\gamma \\gamma}$\", fontsize=12)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "female-uruguay", "metadata": {}, "source": [ "## Absorption in the photon field of a ring dust torus \n", "Let us consider a ring dust torus. Following Finke (2016) ([see bibliography in the docs](https://agnpy.readthedocs.io/en/latest/bibliography.html)), we adopt the following parameters: $L_{\\rm disk} = 2 \\times 10^{46}\\,{\\rm erg}\\,{\\rm s}^{-1}$, $\\xi_{\\rm li} = 0.2$, $T_{\\rm dt} = 10^3\\,{\\rm K}$. The redshift of the source is $z = 0.859$." ] }, { "cell_type": "code", "execution_count": 12, "id": "quiet-stretch", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.565247584249853e+19 cm\n" ] } ], "source": [ "dt = RingDustTorus(L_disk, 0.2, 1000 * u.K)\n", "print(dt.R_dt)" ] }, { "cell_type": "markdown", "id": "unsigned-resort", "metadata": {}, "source": [ "Again, let us consider two cases of abosrption: inside ($r = 0.1 \\times R_{\\rm dt}$) and outside ($r = 2 \\times R_{\\rm dt}$) the torus" ] }, { "cell_type": "code", "execution_count": 13, "id": "legendary-elizabeth", "metadata": {}, "outputs": [], "source": [ "r_in_dt = 0.1 * dt.R_dt\n", "r_out_dt = 2 * dt.R_dt\n", "\n", "# define the absorption objects\n", "abs_in_dt = Absorption(dt, r=r_in_dt, z=z)\n", "abs_out_dt = Absorption(dt, r=r_out_dt, z=z)\n", "\n", "# evaluate the opacities\n", "tau_in_dt = abs_in_dt.tau(nu)\n", "tau_out_dt = abs_out_dt.tau(nu)" ] }, { "cell_type": "code", "execution_count": 14, "id": "straight-break", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# let us plot them\n", "ax.loglog(nu, tau_in_dt, label=r\"$r = 0.1 \\times R_{\\rm dt}$\")\n", "ax.loglog(nu, tau_out_dt, label=r\"$r = 2 \\times R_{\\rm dt}$\")\n", "ax.legend()\n", "ax.set_xlabel(r\"$\\nu\\,/\\,{\\rm Hz}$\", fontsize=12)\n", "ax.set_ylabel(r\"$\\tau_{\\gamma \\gamma}$\", fontsize=12)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "timely-technology", "metadata": {}, "source": [ "### Opacity of a misaligned (non-blazar) source\n", "As already explained in the previous opacity calculation, `agnpy` will assume the line of sight of the observer to be aligned with the jet ($\\mu_s = 1$). \n", "Let us perform a comparison with a source with the same dust torus defined above, but with a viewing angle of $20\\,{\\rm deg}$. Let us evaluate the absorption within the DT for the aligned and misaligned case " ] }, { "cell_type": "code", "execution_count": 15, "id": "acting-webster", "metadata": {}, "outputs": [], "source": [ "mu_s = np.cos(np.deg2rad(20))\n", "abs_in_dt_mis = Absorption(dt, r=r_in_dt, z=z, mu_s=mu_s)\n", "# evaluate the opacity\n", "tau_in_dt_mis = abs_in_blr_mis.tau(nu)" ] }, { "cell_type": "code", "execution_count": 16, "id": "systematic-florist", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# compare the opacity in the aligned and misaligned case\n", "ax.loglog(nu, tau_in_dt, label=r\"$r = 0.1 \\times R_{\\rm dt},\\;\\theta_s=0\\,{\\rm deg}$\")\n", "ax.loglog(\n", " nu, tau_in_dt_mis, label=r\"$r = 0.1 \\times R_{\\rm dt},\\;\\theta_s=20\\,{\\rm deg}$\"\n", ")\n", "ax.legend()\n", "ax.set_xlabel(r\"$\\nu\\,/\\,{\\rm Hz}$\", fontsize=12)\n", "ax.set_ylabel(r\"$\\tau_{\\gamma \\gamma}$\", fontsize=12)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "about-method", "metadata": {}, "source": [ "### Comparison of the misaligned case with a point source behind the blob\n", "And again, we can compare the opacity for the misaligned case, in the limit of large distances, $r >> R_{\\rm dt}$, with the opacity produced by a point source behind the jet approximating (in luminosity and emitted energy) the DT. " ] }, { "cell_type": "code", "execution_count": 17, "id": "foreign-amsterdam", "metadata": {}, "outputs": [], "source": [ "# point source approximating the dust torus\n", "ps_dt = PointSourceBehindJet(dt.xi_dt * L_disk, dt.epsilon_dt)\n", "\n", "# absorption in the limit of very large distances\n", "r_far_dt = 100 * dt.R_dt\n", "abs_far_dt_mis = Absorption(dt, r=r_far_dt, z=z, mu_s=mu_s)\n", "abs_far_ps_dt_mis = Absorption(ps_dt, r=r_far_dt, z=z, mu_s=mu_s)" ] }, { "cell_type": "code", "execution_count": 18, "id": "large-conservation", "metadata": {}, "outputs": [], "source": [ "# compute the opacities\n", "tau_far_dt_mis = abs_far_dt_mis.tau(nu)\n", "tau_far_ps_dt_mis = abs_far_ps_dt_mis.tau(nu)" ] }, { "cell_type": "code", "execution_count": 19, "id": "great-shareware", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "# compare the opacity in the aligned and misaligned case\n", "ax.loglog(\n", " nu, tau_far_dt_mis, label=r\"$r = 100 \\times R_{\\rm dt},\\;\\theta_s=20\\,{\\rm deg}$\"\n", ")\n", "ax.loglog(nu, tau_far_ps_dt_mis, ls=\"--\", label=\"point source approximating the DT\")\n", "ax.legend()\n", "ax.set_xlabel(r\"$\\nu\\,/\\,{\\rm Hz}$\", fontsize=12)\n", "ax.set_ylabel(r\"$\\tau_{\\gamma \\gamma}$\", fontsize=12)\n", "\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "vscode": { "interpreter": { "hash": "421e168cb6cfc6aca15f181c3a83240737b07be3ef1f106b08741fd3b71852a7" } } }, "nbformat": 4, "nbformat_minor": 5 }