{ "cells": [ { "cell_type": "markdown", "id": "e806dfaf", "metadata": {}, "source": [ "# How to use `vcdisk`" ] }, { "cell_type": "markdown", "id": "52579cad", "metadata": {}, "source": [ "This page demonstrates how to use `vcdisk` in typical use cases in Astronomy." ] }, { "cell_type": "markdown", "id": "e102a8f5", "metadata": {}, "source": [ "## What is `vcdisk`?" ] }, { "cell_type": "markdown", "id": "760d87a7", "metadata": {}, "source": [ "`vcdisk` uses the method of [Casertano (1983)](https://ui.adsabs.harvard.edu/abs/1983MNRAS.203..735C/) to solve Poisson's equation on the mid-plane of a thick axisymmetric galaxy disk. This is a fast and efficient way to compute the circular velocity of a stellar/gas disk with an arbitrary surface density distribution." ] }, { "cell_type": "markdown", "id": "843186ec", "metadata": {}, "source": [ "## Why do we need `vcdisk`?" ] }, { "cell_type": "markdown", "id": "6a5b1929", "metadata": {}, "source": [ "The most typical use case for `vcdisk` is in rotation curve modelling. Specifically, this module allows to compute *the contribution to the circular velocity of the observed baryonic components of a disk galaxy*, e.g. the stellar disk, the gas disk, the stellar bulge.\n", "\n", "If we have some kinematical observations that allowed us to measure the rotational velocities of some material in circular orbits in the disk of a spiral galaxy (e.g. cold gas), the observed rotation curve can be decomposed into several dynamically important components in the galaxy\n", "![Rotation curve decomposition](vrot.png)\n", "where $V_{\\rm DM}$ is the contribution from dark matter, $V_{\\star,\\rm disk}$ from the stellar disk, $V_{\\rm gas, disk}$ from the gas disk etc. \n", "While the left-hand side of this equation usually comes from observations, and the contribution of DM is the unknown that is often what we want to constrain, for all the other terms there is ``vcdisk``!\n", "\n", "``vcdisk`` calculates the contribution to the gravitational field of an axisymmetric component whose radial surface density distribution is known. For instance, the surface density profiles of stellar ($\\Sigma_{\\star, \\rm disk}$) and gaseous disks ($\\Sigma_{\\star, \\rm disk}$) can be directly obtained from galaxy images in appropriate wavebands and these can then be used as input for ``vcdisk`` to calculate $V_{\\rm disk}(R, \\Sigma_{\\rm disk}(R))$.\n", "\n", "While the method of Casertano (1983) is designed for thick disks it works for all flattened axisymmetric distribution. Hence, it is ideal also to derive the contribution to the circular velocity of a flattened (pseudo-)bulge." ] }, { "cell_type": "markdown", "id": "5dedd674", "metadata": {}, "source": [ "## Example 1: analytic surface density" ] }, { "cell_type": "markdown", "id": "7ef6dbbf", "metadata": {}, "source": [ "### Import `vcdisk`" ] }, { "cell_type": "code", "execution_count": 1, "id": "5e702f02", "metadata": {}, "outputs": [], "source": [ "from vcdisk import vcdisk\n", "\n", "import numpy as np\n", "import matplotlib.pylab as plt" ] }, { "cell_type": "markdown", "id": "5ebce6af", "metadata": {}, "source": [ "### Exponential thick disk" ] }, { "cell_type": "markdown", "id": "566f9bf0", "metadata": {}, "source": [ "Let's start with the case of a thick disk with a classical exponential surface density." ] }, { "cell_type": "code", "execution_count": 2, "id": "c666c1a2", "metadata": {}, "outputs": [], "source": [ "md, rd = 1e10, 2.0 # mass, scalelength of the disk\n", "r = np.linspace(0.1, 30.0, 50) # radii samples\n", "\n", "def expdisk_sb(r, md, rd):\n", " # exponential disk surface density\n", " return md / (2*np.pi*rd**2) * np.exp(-r/rd)\n", "\n", "sb_exp = expdisk_sb(r, md, rd)\n", "\n", "# run vcdisk\n", "vdisk = vcdisk(r, sb_exp)" ] }, { "cell_type": "code", "execution_count": 3, "id": "57c4d80b", "metadata": {}, "outputs": [ { "data": { "image/png": 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lpbm8MH150LFEEoaGJROYmgRFRCLyC4vYvGMP2VlpdGiWFXSc0DIzbjyhFz8b0wd3+Pkrn/H3qUuDjiWSEFQ0J4HKmgRvfmGOmgRFpMFYuLYQgL7tsjWfuQauGd1z786Bv37jC56cvCTgRCLhF9OOgGaWCZxDpAlw73vd/bcxHqcP8EK5p7oD/+PuD8RyHNmnrEnw+ekr+O2/5vPa7FVMX7pJOwmKSIOwaG/RnBNwksRx5ajuZKal8Os3vuDOt+azu7iUH4/uEXQskdCKdaT5DeBMoBjYXu4WE3df5O6D3X0wcCiwA3gt1uPIN5kZFw7vzL+u106CItKwLFi7FYA+WmouJhcf2ZW7zx6IGdwzfiH3vrMIdw86lkgoxTTSDHRy9zFxznA88JUaCuOnZ5tIk+C97yzisYlf88CEPCblbeCBCwZzUG7joOOJiMTdonLTMyQ2Y4d3JiMthVtfnsfD73/J1p17+M0ZA0hJ0TQXkfJiHWmeUn4b7TgZC/yz4pNmdpWZzTCzGfn5+XE+ZfLLSEvhF6f247krv9kk+MYcNQmKSHIpLiklb/02AHqraK6Vs4d24i/fH0pGagrPTF3GT1+aq28oRSqItWgeCcw0s0XRzU4+O5DNTcwsA/gO8FLF19z9cXcf5u7DWrfWmpu1NSLaJHhS/0iT4I3PR5oEC9UkKCJJYunG7ewuLqVj80bkZKUHHSdhnTygHU9ddhiNM1J5dfYqrnluFkXFJUHHEgmNWIvmU4BewEnAGUQ2PTnjAM5/CjDL3dcdwDGkGi2aZPDYxYfyu+8OJCs9hddmr+LUhyYxc9nmoKOJiBywhZqaETcje7Xi71ccTk5WGu/MX8cVf53B9qLioGOJhEJMRXMdbG5yIZVMzZD4MzO+d3hn3rp+FAd3zGHFpp2c/9hUHpyQp6/gRCSh7Z3P3F5Fczwc2qUFL/zoSFo1zWTylxv4/hPT2LR9d9CxRAIXU9FsZv9T2a02JzazxsCJwKu1eb/UTlmT4I+O7k5JqXP/hMWM1U6CIpLAFqyJFM19tNxc3PRrn8NLVx9Jx+aNmLOigHMfmaK/J6TBi3V6Rvll5kqITK/oWpsTu/sOd2/p7ltq836pvYpNgjPUJCgiCWzRushyc5qeEV/dWjXh1WuOol/7HL7esJ2zH5nC56v0V7Y0XLFOz7i33O0uYDTQsU6SSZ0bUWEnQTUJikii2VZUzIpNO8lITaFbqyZBx0k6bXOyeOFHR3BUj5bkFxZxwWNTmZSnFa2kYTrQbbQbE9nNTxJU2U6C324S3BR0NBGRapXNZ+7RpinpqQf6V5pUJicrnb9ePpzvHNKB7btLuPzp6bw+W99MSsMT65zmz6JLzc0zsy+ARcCDdRNN6kvlTYLaSVBEwk+bmtSPjLQUHrhgMD8c1Y3iUuemF+bw5w++1O6B0qDE+s/ysiXmziCy7FwHd/9T3FNJICo2CT4wIU9NgiISaou0fXa9SUkxfnlaf351Wj/M4A9vL+KWF+dqLWdpMGItmocDm6LLzF0OvGhmQ+MfS4KiJkERSSQLNNJc764c1Z1HLzqURumRTVC+N24aG7YVBR1LpM7FWjT/2t0LzWwkcDLwDPBI/GNJ0LSToIiEnbuXm56h5ebq08kD2vHyj4+kfbMsZi7bzFl//njv/xciySrWornsO5jTgEfc/Q0gI76RJCy0k6BIYjGznwedoT6t21rElp17aNYonbY5mUHHaXAGdGjGG9eO4JCDmrNy807OeWQKHyxcH3QskToTa9G8ysweA84H/mNmmbU4hiSQ8k2CAzpoJ0GRMDGzF8vdXgKuDDpTfVqwdt/6zGYWcJqGqU1OFi9cdQSnD2rPtqJifvDMdP78wZeUlqpBUJJPrAXv+cDbwBh3LwBygVvLXjSzFvGLJmHSs01TXr3mKK7SToIiYbLV3c+P3s4DJgQdqD5p5YxwyEpP5eELh3DzCb2BSIPgVX+fwZadms4nySXWzU12uPur7p4XfbzG3d8p9yvvxTWdhEpmWir/79R+PHuFmgRFQuKuCo9/GUiKgJQVzdo+O3hmxo0n9OKpSw8jJyuNCQvW850/TWbBmq1BRxOJm3hPrdD3Yw3AyF5qEhQJA3dfAmBmraKPG9SuRGUFWd/2GmkOi2P7tuGt60fRv30Oyzbu4Lt/+ZjXZq8MOpZIXMS7aNYkpgZCTYIiofJU0AHq256SUr7K3wZA77YqmsOkc8vGvHrNUZx7aCd27Snl5hfm8svXPmPXHq3nLIlNTXxSa1U1CT70Xh4lagIRqU8N7lu+JRu2s6fEOSi3EU0z04KOIxVkpafyh3MH8bvvDiQjNYXnpi3njIc1XUMSm6ZnyAGr2CR437uLGfv4VFZuVpOgSD1pcP9K3Ts1Q/OZQ6tsYOXVa46ie+sm5K3fxpl//pinP16i7bclIcW7aD4+zseTBFGxSXD60s2c8oCaBEXqSYMbsNDKGYnj4I7NeOv6kVw4vDO7i0u541/z+cFfp2sXQUk4NSqazezN/d3Kfq+hNaHIt1XWJPgTNQmK1LVfxOMgZtbczF42s4VmtsDMjjSzXDN718zyovehWFp038oZKpoTQeOMNP7v7IE8etFQmjVK54NF+Yx5YJI2Q5GEUtOR5iOBTsAk4I/AvRVuIntVbBJ8VU2CInXK3T83s/PMLBvAzH5lZq+a2dAYD/UgMN7d+wKHAAuA24D33L0XkWVFb4tn9tpaqO2zE9KYg9sz/qZRHNE9lw3birj8r9O57ZV5bCsqDjqaSLVqWjS3A/4fcDCRi+qJwAZ3/8jdP6qrcJK4tJOgSL37tbsXmtlI4GTgGeCRmr7ZzHKAo4EnAdx9d3QTqzOjxyJ6f1YcM9fK1l17WFWwk4y0FLq2bBx0HIlR+2aNeO7KI/jlqf3ISEvh+ekrGPPARKZ+tTHoaCL7VaOi2d1L3H28u18KHAF8CXxoZtfXaTpJeNpJUKTelK3ndRrwiLu/AWTE8P7uQD7wtJnNNrMnzKwJ0Nbd10BkQyugTTxD18bi6ChzrzZNSUvVIlCJKDXF+OHR3Xnr+pEc3DGHlZt3cuG4T7jjX19oaToJrRpfbcws08zOBp4FrgUeAl6tq2CSPMo3CbbJ1k6CInVklZk9BpwP/MfMMomt2TsNGEqk4B4CbCeGqRhmdpWZzTCzGfn5+bHkjtlCzWdOGr3bZvPaNSO48fhepKYYT3+8lFMfmsTs5ZrOJ+FT00bAZ4ApRC6od7j7Ye5+p7ur6pEaG9mrFeNvOpoTtZOgSF04H3gbGBOdVpEL3BrD+1cCK919WvTxy0Su+evMrD1A9L7Szi13f9zdh7n7sNatW9fyf0LNrIguZ9m9VZM6PY/Uj/TUFG4+sTevXzOCXm2a8nX+ds55ZAr3jF9IUbFGnSU8ajoKcTHQG7gRmGJmW6O3QjPTSuVSY7lNMnhcOwmKxJ2773D3V909L/p4jbu/E8P71wIrzKxP9KnjgfnAm8Cl0ecuBd6IY+xaWV2wC4AOzRsFnETiaWCnZvzr+pH86JjuADzy4Vec8fBk5q0sCDaYSFRN5zSnuHt29JZT7pbt7rVqXa5saaPaHEcSj5oERULreuA5M5sHDAZ+B9wNnGhmeUSawO8OLl7EmoKdQKShTJJLVnoqvzilHy9dfRTdWjVh8bptfPcvU7j3nUXsLtbfDxKsIDsoKlvaSBoQNQmKhIu7z4lOsRjk7me5+2Z33+jux7t7r+h94Ovxr44WzR010py0Du3Sgv/cMIorRnaj1J2H3/+S0x6apBU2JFCBFM37WdpIGhg1CYpILIpLSlm7dRdm0LZZZtBxpA41ykjl16f354WrjqRry8bkrd/GheM+4abnZ7N+666g40kDVNNGwCPNLJ7btFa1tFH5c9ZbJ7YEr7ImQe0kKFJzZjbMzF4zs1lmNs/MPotOs0gq6wuLKHVo1TSTzLTUoONIPRjeLZfxNx3NT07sTWZaCq/PWc3x937EU5OXaEqf1KuajjRfCsw0s+fN7DIza3eA5612aaP67MSWcKjYJPjq7FWc9tBkZmnpIZGaeA54GjgHOAM4PXqfVMqmZqgJsGHJSk/lhuN78e7Nx3B83zYUFhXz27fmc/rDk5ny5Yag40kDUdNGwKvdfShwO9AC+KuZTTWz35nZ0WYW6z/3q1raSBq4ik2Cyzft4LxHp/LQe3mUlHrQ8UTCLN/d33T3Je6+rOwWdKh4W7V3PnNWwEkkCJ1bNubJyw7jiUuG0alFIxauLeR7T0zjsqc/ZeFaLeYldSumOc3uvtDd73f3McBxwGTgPGDa/t/5reNUtbSRCPDtJsH73l3M2MensnKzmgRFqvCb6FS3C83s7LJb0KHibc2WyFxWrZzRsJ3Qvy3v3nwMt57ch6aZaXy4KJ9THpzET1+ay5otO4OOJ0mq1o2A7r7T3f/j7te7+7BaHKKypY1E9qrYJDh96WZOeXASb85dHXQ0kTC6nMi1dAyRaRllUzSSiqZnSJlGGalce2xPPrp1NJcd1ZVUM16euZLRf/iQe8YvZKt6YiTOAltyrrKljYLKIuH2jSbBXcXc8M/ZahIU+bZDotfUS9398ujtB0GHirfVmp4hFbRsmsnt3xnAhJ8cw2mD2lNUXMojH37FMb//gKc/XqL1nSVuglynWaTG1CQoUq1PzKx/0CHqWtlugJqeIRV1bdWEP39vKK9dcxTDu+ayecce7vjXfE647yPemrcad/XFyIGJqWg2s+vMrEVdhRHZHzUJiuzXSGCOmS1K5iXnVm/R9AzZvyGdW/DCj47giUuG0bNNU5Zv2sF1/5jNWX/+mI+/3KDiWWot1pHmdsB0M3vRzMbEee1mkRpRk6BIpcYAvYCTSNIl53bsLqZgxx4y0lJo2SQj6DgSYmbGCf3bMv7GUfzf2QNpnZ3J3JVb+P4T0zjv0alMystX8Swxi3X1jF8RuSg/CVwG5EWXnetRB9lEqqQmQZFvaVV+qbnocnODgg4VT/umZmSRkqIxG6leWmoKFw7vzEe3jubWk/vQvHE6M5Zt5uInP+WcR6bw4aL1Kp6lxmKe0+yRP11ro7diIus2v2xmv49zNpFqVdok+KKaBKVBGmdmA8semNmFwK8CzBN3e1fO0HxmiVHjjDSuPbYnk39+HD8b04cWjdOZtbyAy56ezll/mcL4z9dqmp9UK9Y5zTeY2Uzg98DHwEB3/zFwKJFdqETqXVmT4F3fPTjSJDhLTYLSIJ0LPGNm/czsh8A1RKZqJA0tNycHqmlmGteMjhTPvzilLy2bZDB3RQFXPzuTE+77iOemLWPXnpKgY0pIxTrS3Ao4291PdveX3H0PgLuXkoTrgUriMDO+f3gX3rp+JP3bq0lQGh53/xoYC7xCpIA+yd23BJsqvlZHNzbRcnNyoJpkpvGjY3ow6efHcvsZ/enUohFLNmznl699zoi73+eh9/LYvH130DElZGItmjMrbstqZvcAuPuCuKUSqaWebbJ57dqj+OGobmoSlAahbJWM6EoZLwO5QFdgWrKtnlE20txeI80SJ40z0rhsRDc+/OloHr5wCAM7NmPj9t3c9+5ijrz7PX71+mcs2bA96JgSErEWzSdW8twp8QgiEi+Zaan88rT+/P2K4WoSlIagbJWMstvh7FtBI6lWz9D0DKkraakpnHFIB968bgT/+OHhjO7Tml17Snn2k+Ucd++HXPnMDKZ9vVFNgw1cWk1+ycx+TGR+XPcKIxfZROY2i4TOqF6tGX/T0fzs5XlMWLCOG/45mw8XreeO7wwgOys96HgicVHx279kpt0Apa6ZGUf1aMVRPVqRt66QJycv4dXZq5iwYB0TFqxjUKdmXHZUV04d2J6s9NSg40o9s5r8q8nMmhFZJeP/gNvKvVTo7pvqKNtew4YN8xkzZtT1aSRJuTv/+HQ5d741n117Sumc25gHxg5maGft0yP1w8xmuvuwoHPUl7q4Zrs7fX49nt3FpXxxx8k0yazRmI/IAcsvLOLvnyzj2U+WsSk6z7lZo3TOGdqJ7x3emZ5tmgacUOKtqmt2jaZnuPsWd1/q7hdWWAe0zgtmkQOlJkFJZmZ2ZEPYaGrj9t3sLi6lWaN0FcxSr1pnZ/KTE3sz5bbjuPvsgQzq1IwtO/fw1MdLOOG+j7jgsam8MWcVRcVadSPZ1ahoNrPJ0ftCM9savRWWPa7biCLxUdYkqJ0EJclcCsw0s+fN7DIzaxd0oLqg+cwStKz0VMYO78yb143kX9eN5MLhB9E4I5VpSzZx4/NzOOJ373HnW/P5cn1h0FGljtRoekbQND1D4m1y3gZ+8uIc1hcWkZ2Vxl3fHch3DukQdCxJUvUxPcPM+hJpzD4ZaAZ8AIwHPnb3eh0Cq4tr9vjP13L1szM5vm8bnrzssLgeW6S2Cnft4fU5q/nntOXMX7NvDHFYlxaMHd6Z0wa2p1GG5j4nmgOanlHuIOeZWXb051+Z2atmNiReIUXqS2U7Cd7y4ly2FRUHHU2kVtx9obvf7+5jgOOAycB5wLRgk8WHRpoljLKz0rn4iC78+4aRvHndCC4c3pkmGanMWLaZn740l8PumsCtL81lylcbKNV0wIQX65Jzv3b3QjMbSWQ04xng0fjHEql7FXcSfGXWSk59cBKztZOgJDh33+nu/3H365OlAVFFs4SZmTGoU3P+7+yBfPrLE7jnnIEMPqg524qKeWnmSr43bhoj73mfe8YvZPE6Td9IVLEWzWVf8Z0GPOLubwAZ8Y0kUn8qaxI899GpPKwmQZFQWRPdDbCDlpuTkGuSmcYFh3Xm9WtH8N4tx3D9cT3p1KIRq7fs4pEPv+Kk+ydy6oOTePSjr1gV/cegJIZYi+ZVZvYYcAHwHzPLrMUxREKnYpPgvWoSFAmVVRpplgTUo3VTbjmpDxNvPZYXf3QkFw7vTE5WGvPXbOXu/y5kxN3vc+4jU/j71KVs3FYUdFypRkyNgGbWGBgDfObuedEu7UHu/k5dBQQ1Akr9mpSXzy0vzlWToMRNPTUCXgc85+6Bzy+qi2v28LsmsL6wiI9vO46OKpwlgRUVl/DRonzenLuaCQvWsWtPKQCpKcbh3XI5ZWB7Th7QljbZ+lYlKFVds2Nd7LIEyALOM7Py763TolmkPlW1k+BvzzyYplofVsKrHTDdzGYBTwFveyIsj1QDu4tLyd9WRIpB2+zMoOOIHJDMtFROGtCOkwa0Y1tRMRPmr+ONOauYlLeBKV9tZMpXG/mfNz7nsC65nDKwHScPaKdvWEIi1pHm8UABMIt985tx93vjnqwcjTRLECrbSfDBsYMZop0EJUb1tSNgdJOTk4DLgWHAi8CT7v5VXZ+7vHhfs1ds2sGo339A+2ZZTP3F8XE7rkiYbNmxhwkL1vHfz9cyMS+f3cWle18b2LEZJ/Vvy8kHt6NXm6Y0gP2MAhWvkeZO0eWM4hFoKVBIpPguTpYOb0keZU2Ch3fL5fp/zmHBmq2c++hUbjq+F9cc25PUFF20JFzc3c1sLbAWKAZaAC+b2bvu/rNg09We5jNLQ9CscTrnHNqJcw7txLaiYt5fuJ7/fraGDxfl89mqLXy2agv3vruYri0bc2L/thzfry2HdmlBeqpay+pLrEXzFDMb6O6fxen8x7r7hjgdS6RO9GyTzevXHsUf317EuElLuPfdxUzMy+f+CwbTqUXjoOOJAGBmNxDZHXAD8ARwq7vvMbMUIA9I2KJ5zZZI0dy+meZ4SsPQNDON7xzSge8c0oFde0qYnLeBd+avZcKC9SzduINxk5YwbtIScrLSOLp3a47v14Zjercht4kWNKtLsRbNI4HLzGwJUAQYkcGNQXFPJhIimWmp/PK0/hzduzW3vDiX6Us3c8qDk/jddwdyhpoEJRxaAWe7+7LyT7p7qZmdHlCmuFhdEFluTg2A0hBlpadyQv+2nNC/LSWlzsxlm3nni7W8v2g9X+dv5615a3hr3hpSDAYf1JzRfdowuk9rDu7QjBR9IxpXsRbNp8Tx3A68Y2YOPObuj5d/0cyuAq4C6Ny5cxxPK1J7FZsEr//nbD5clM8dZw5Qk6AELbNiwWxm97j7z919QVCh4kHTM0QiUlOM4d1yGd4tl1+d3p+lG7bz/sL1fLBoPZ98vZFZywuYtbyA+95dTMsmGRzduzWj+7RmZM9WtGyqJtoDFVMjYFxPbNbB3VebWRvgXeB6d59Y2e+qEVDCxt15btpy/vffahKU6tXTknOz3H1ohefmBfFNYLyv2Zc//SkfLMpn3CXDOLF/27gdVySZbCsqZsqXG/hwcT4fLcr/1sYp/dvnMKpXK0b0bMXwbrlkpacGlDT84tIIGO3M/j7Q3d1/a2adgXbu/mmsgdx9dfR+vZm9BgwHKi2aRcLGzLjoiC4c0V1NghIsM/sxcA3Q3czmlXspG/g4mFTxVTY9Q3OaRarWNDNt71J27s5X+dv4cFE+Hy7K59Olm5i/Zivz12zlsYlfk5GWwrAuLRjRsxVH9mjJoI7NSFNDYbVi/T75L0ApcBzwWyKrX7wCHBbLQcysCZDi7oXRn0+KHk8koVTWJDgpbwP3jx2s+ZdSX/4B/Bf4P+C2cs8XuvumYCLF1+roiJn+mxKpGTOjZ5tserbJ5spR3dm1p4QZSzcz+csNfPzlBj5fvWXvmtAQKbiHd8vlqB4tObJHS/q1y9F86ErEWjQf7u5DzWw2gLtvNrPatGq2BV6LrjOYBvzD3cfX4jgigavYJPjp0k2MeWCimgSlXrj7FmALcGHQWerC1l17KCwqplF6Ks0bpwcdRyQhZaWnMrJXK0b2agXApu27mfrVRqZ8tYGpX23k6+jc6PcXrgcgJyuNw7rmcnj3XA7v1pIBHXI0Ek3sRfMeM0sl0sSHmbUmMvIcE3f/Gjgk1veJhJmaBCUIZjbZ3UeaWSHRa3PZS0RWN8oJKFpcrCmbmtE8Sxs6iMRJbpMMThvUntMGtQciyzpO/WojH3+5kU++3siqgp28t3A970WL6CYZqQzt0oLDuuYyrGsLhhzUgkYZDW9OdKx/kz8EvAa0NbO7gHOBX8U9lUiCym2SwbhLDt3bJPjKrJXMWLaJB8cOYfBBzYOOJ0nI3UdG77ODzlIXNDVDpO61b9aIs4d24uyhnQBYuXkHny7ZxLSvNzFtyUaWbtzBpLwNTMqLbK2RlmIc3LEZh3VtwaFdchnapTltspO/5yCmotndnzOzmUDZPqZnJfpSRiLxVlmT4DmPTOHmE3rx49FqEpRwi36bOANY5e6nm1ku8ALQFVgKnO/um+srz97l5pqpaBapL51aNKZTi8Z7i+h1W3cxY+lmpi/dxPSlm1iwZitzVhQwZ0UB4yYtAeCg3EYc2rkFh3ZpwZDOLejbLjvppnTUqGg2s59U8dIpZnaKu98Xx0wiSaFik+Af31nMxMVqEpS6YWbPADe6e0H0cQvgXnf/QYyHuhFYAJRN67gNeM/d7zaz26KPfx6f1NXbuxtg8+QfxRIJq7Y5Wd+YzlG4aw+zlxcwfekmZi3fzJzlBazYtJMVm3by+pzVAGSlpzCoY3MGd27O4IOaM6Rzc9on+D9+azrSXPa1Xx8iK2W8GX18BlomTqRKahKUejSorGCGvY3aQ2I5gJl1Ak4D7gLKBkvOBEZHf34G+JB6LJrLlpvTxiYi4ZGdlc7RvVtzdO/WAJSUOovWFjJz+WZmLt3E7BUFLNu4g0+XbuLTpfsW8WmTncmgTs0ZfFAzBnVqzqBOzWjeOHG2/q5R0ezudwCY2TvAUHcvjD6+HXipztKJJAk1CUo9SDGzFmVTJ6LTKmL9w/UA8DP2DZQAtHX3NQDuvia6IdW31NUurqs0p1kk9FJTjP4dcujfIYeLj+gCRFbomLuigNnLNzN7RQFzVxSwvrCICQvWMWHBur3v7dKyMQM7Ntt7G9CxGc0ahXOlnFgvqJ2B3eUe7yYyz01EqlFZk+D0pZu0k6DEy73AFDN7Ofr4PCIjxjViZqcD6919ppmNjvXk7v448DhEdgSM9f1V2Ts9QxubiCSU3CYZHNu3Dcf2jfw7u7TUWbpxO/NWbmHOigLmrSzgi9VbWbZxB8s27uCteWv2vrdry8Yc3LEZAzo04+COOQzo0IzcJsGPSMdaNP8d+DS6g58D3yXydZ2I1EBVOwmqSVAOlLv/zcxmENl8CuBsd58fwyFGAN8xs1OBLCDHzJ4F1plZ++goc3tgfXyTV62k1Fm7RdMzRJJBSorRvXVTurduyllDOgKwp6SUxesK+XzVFj5btYXPVm1lwZqtLN24g6UVCukOzbLo36FZZES7fQ4DOuTQqUWjel2KMtbVM+4ys/8Co6JPXe7us+MfSyS5lTUJ/mH8Ip6YrCZBiZt0ouszR3+uMXf/BfALgOhI80/d/SIz+wNwKXB39P6NOObdr43bi9hT4rRonE5WesNbE1Yk2aWnpjCgQ2RE+YLo3tJlhfQXq7fyxaotfL46Ukiv3rKL1Vt2fWNqR3ZmGv3a59CvfTZ92+fQt102fdpl0zijbqY9xnxUd58FzKqDLCINSmZaKr86Pdok+JKaBOXAmNmNwA+BV4gUzs+a2ePu/vABHvpu4EUzuwJYTmTaR73YvH0PAC2bZtbXKUUkYOULaYYdBES+dVqyYTtfrN7C/DVbWbCmkPmrt7JhW9G3mg3NoEtuY/q2y6Fv+2yuPqZH3P7RrQ4kkYAd3bs1428cxc9fmceEBevVJCi1dQVwuLtvBzCze4CpQMxFs7t/SGSVDNx9I/vW5q9Xm7ZHWmhaaPtskQYtNcXo2aYpPds05czBHfc+v75w194CetHarSxcW8iX67ftnd4xKS+fG47rFbcc+htZJARaNs1k3CXDeHbacv73rX07CT5wgZoEpcYMKCn3uCT6XMIq2BEpmhNpSSoRqT9tsrNok53FMdGl7wB2F5fyVf42Fq7dypYde0iJY69QTEWzRWZbfx/o7u6/NbPOQDt3/zRuiUQaKDPj4iO6cES3XG54Xk2CErOngWnRRm0DzgKeCjTRAdq8IzI9I1dFs4jUUEZaSnSec071vxyjWPc3/AtwJHBh9HEh8Oe4JhJp4Hq1jTQJXjmyGyWlzh/fWcyF4z7Zu16tSGWiO7NeDmyM3i519/uDTXVgNpeNNDfR9AwRCV6s0zMOd/ehZjYb9u44pSEAkTj7VpPgkk2c8sBEfnf2QE4fpCZB2cfMComslrH3qXKvubvHf7ilnpRNz2ihkWYRCYFYR5r3mFkq0Qu0mbUGSuOeSkSASJPg2zcdzQn92rJ1VzHX/WM2P31pLtuKioOOJiHh7tnunlPull3ulrAFM+ybnqFGQBEJg1iL5oeA14A2ZnYXMBn4XdxTicheZTsJ/u9ZB5OVnsLLM1dy2kOTmL18c9DRROrU5u1qBBSR8IipaHb354CfAf8HrAHOcveX6iKYiOxTtpPgW9ePpF/7HJZt3MG5j07lT+/nUVIatx2LJYFZxEVm9j/Rx53NbHjQuQ7EZk3PEJEQiXWkGXdf6O5/dvc/ufuCugglIpUr20nwG02Cj6tJUIAkbNQuKFs9Q42AIhICMRXNZvaMmTUv97iFmSX0kkYiiaasSfBvPxhO6+zMvTsJ/mvu6qCjSbAOd/drgV0QadQGEnqIdrPWaRaREIl1pHmQuxeUPYhelIfENZGI1EjZToIn9GtD4a5irv/nbG55UU2CDVhSNWqXljpbdkZGmps30kiziAQv1qI5xcz2bk9mZrloV0GRwJTtJHjnWQeTmZbCK7MiTYJzVhQEHU3qX1mjdttkaNTeumsPpQ7ZWWmkpcY8k1BEJO5ivRLdC0wxszvN7E5gCvD72pzYzFLNbLaZvVWb94tIRNlOguWbBM95ZIqaBBueNsAfiBTKCd+ovWm7mgBFJFxiXT3jb8A5wDpgPXC2u/+9lue+EVAjoUiclO0keIV2EmyocoBHgbFEpmhsCjbOgdm7RnMTFc0iEg61+c5rDfApMBdoZWZHx3oAM+sEnAY8UYvzi0gVMtNS+XX5JsHoToJvzVOTYLJz9zvcfQBwLdAB+MjMJgQcq9b27Qao+cwiEg6xrp5xJTAReBu4I3p/ey3O+wCR9Z4TtklFJMzKmgSP79tGOwk2POuBtcBGIlM2EtK+3QA10iwi4RDrSPONwGHAMnc/lsjKGfmxHMDMTgfWu/vMan7vKjObYWYz8vNjOoWIEGkSfOLSYdx55gAy0/btJKgmweRkZj82sw+B94BWwA/dfVCwqWqvYO9ycxppFpFwiLVo3uXuuwDMLNPdFwJ9YjzGCOA7ZrYUeB44zsyerfhL7v64uw9z92GtW7eO8RQiAtEmwSO78q/rR9K3XbaaBJNbF+Amdx/g7r9x9/lBBzoQ2g1QRMIm1qJ5ZXRzk9eBd83sDSCmyZLu/gt37+TuXYk0rLzv7hfFmENEYtC7bTZvXDdCTYJJzN1vc/c5QeeIl03by6ZnaKRZRMKhRkWzmZWtkPGhuxe4++3Ar4EngbPqJpqIxFNZk+AzahKUBLC3EVCrZ4hISNR0pPlQM+sC/CC6dXYu8BmRxfOb1vbk7v6hu59e2/eLSOyOKbeToJoEJaw0PUNEwqamRfOjwHigLzAzeptR7l5EEkjFnQTVJChhUxBdPUONgCISFjUqmt39IXfvBzzl7t3dvVv5+zrOKCJ1QDsJSphppFlEwibWRsDf1UkKEQmMdhKUsHF3Nm/XOs0iEi6xFs2v10UIEQmWdhKUMNmxu4TdJaVkpafQKCM16DgiIkDsRfMnZnZYnSQRkcAdrSZBCQFNzRCRMIq1aD6WSOH8lZnNM7PPzGxeXQQTkWCoSVCCtq8JUEWziIRHWoy/f0qdpBCRUClrEjyiWy43PD+HBWu2cs4jU7j5hF78eHRPUlMs6IiSxPaNNGvlDBEJj1iL5kureP63BxpERMKnrEnw9+MX8eTkJfzxncVMzNvA/RcMpmPzRkHHkyS1eYeaAEUkfGKdnrG93K2EyMhz1zhnEpEQKb+TYKumahKUurd5e2SkWWs0i0iYxFQ0u/u95W53AaOBjnWSTERC5ZjerXn7plEc31dNglK3yqZn5GoLbREJkVhHmitqDGhzE5EGomXTTJ64dBh3njlATYJSZ9QIKCJhFFPRXLZaRvT2BbAIeLBuoolIGJkZFx/ZlX9dP5K+7bJZtnEH5z4yhT9/8KV2EpS4UCOgiIRRrCPNpwNnRG8nAR3c/U9xTyUiode7bTavXzuCK0Z2o7jU+cPbi/jeuE9YrZ0E5QCpEVBEwijWonk4sMndlwGXAy+a2dD4xxKRRJCV/s0mwWlLNjHmgYn8e96aoKNJAivYoUZAEQmfWIvmX7t7oZmNBE4GngEeiX8sEUkkFZsEr/3HLG59aS7b1SQotbBpuxoBRSR8Yi2aS6L3pwGPuPsbgK5qIvKtJsGX1CQotaRGQBEJo1iL5lVm9hhwPvAfM8usxTFEJElVbBJcqiZBidHu4lK2FRWTmmLkZMW6/5aISN2JteA9H3gbGOPuBUAucGu8Q4lIYitrEvzBCDUJSmwKdkbnMzdKx0zbtYtIeMS6uckOd3/V3fOij9e4+zt1E01EEllWeir/c4aaBBOFmR1kZh+Y2QIz+8LMbow+n2tm75pZXvS+RV3m2Dc1Q02AIhIumlohInWqqiZB7SQYOsXALe7eDzgCuNbM+gO3Ae+5ey/gvejjOlO2hbaWmxORsFHRLCJ1Tk2C4Rf95nBW9OdCYAHQETiTyEpJRO/Pqsscezc20coZIhIyKppFpF5oJ8HEYWZdgSHANKCtu6+BSGENtKniPVeZ2Qwzm5Gfn1/rc+/b2ETTM0QkXGJqTTazn1Ty9BZgprvPieE4WcBEIDOa4WV3/00sWUQkMZU1Cf5+/CKe+ngJf3h7ERMX53P/BYPp0LxR0PEaPDNrCrwC3OTuW2vajOfujwOPAwwbNqzW/wrat4W2RppFJFxiHWkeBlxN5Cu7jsBVwGhgnJn9LIbjFAHHufshwGBgjJkdEWMWEUlQZU2Cf738MDUJhoiZpRMpmJ9z91ejT68zs/bR19sD6+syg9ZoFpGwirVobgkMdfdb3P0WIkV0a+Bo4LKaHsQjtkUfpkdv+n5WpIEZ3acN428axXHaSTBwFhlSfhJY4O73lXvpTeDS6M+XAm/UZY59jYCaniEi4RJr0dwZ2F3u8R6gi7vvJDJ6XGNmlmpmc4iMWrzr7tMqvB6X+XEiEm6tmmby5KXD+G2FJsG5ahKsbyOAi4HjzGxO9HYqcDdwopnlASdGH9cZNQKKSFjFut3SP4BPzOwNwIDTgX+aWRNgfiwHcvcSYLCZNQdeM7OD3f3zcq/HZX6ciISfmXHJkV05ontLbvjnbBauLeScR6Zw84m9ufqYHqSmaJOLuubuk4lc1ytzfH3l2NcIqKJZRMIl1s1N7gR+CBREb1e7+2/dfbu7f782AaI7C34IjKnN+0UkeWgnQdnXCKjpGSISLrVZcq4YKI3e76nNSc2sdXSEGTNrBJwALKzNsUQkuahJsGFTI6CIhFVMRXN0W9XngFZE1up81syur8V52wMfmNk8YDqROc1v1eI4IpKkRvdpU+lOgmoSTF6lpU5BdKRZ22iLSNjEOqf5CuBwd98OYGb3AFOBh2M5iLvPI7JwvohIlcp2Enz2k2X8778X8NLMlUxfuokHxw7hkIOaBx1P4qxwVzGlDtlZaaSnau8tEQmXWK9KBpSUe1xC1Y0jIiIHrOJOgks37uAc7SSYlDZpYxMRCbFYi+angWlmdruZ3UFki9Wn4h9LROSbKmsS/P4TahJMJmoCFJEwi3X1jPuAy4GN0dul7n5/XQQTEamorEnwmR8Mp1XTTD75ehOnPDiJ/3ymJsFksG8+s0aaRSR8ajSn2cwK+eaOfVbuNXf3nHgHExGpyjG9W/P2TaP42cvzeG/heq55bhbnHdqJ278zgCaZsbZqSFhs3l62RrNGmkUkfGo00uzu2e6eU+6WXe6mgllE6l1Zk6B2EkwemzXSLCIhpvZkEUlYZTsJqkkwOZSt0ZyrLbRFJIRUNItIwitrErx8RFftJJjANqkRUERCTEWziCSFrPRUfnPGgG/sJKgmwcSiRkARCTMVzSKSVEb3acP4m0ZxXN82bNm5h2uem8XPXtZOgolgXyOgimYRCR8VzSKSdFo1zeTJck2CL85Qk2Ai2KwttEUkxFQ0i0hSqqpJ8C8fqkkwrNQIKCJhpqJZRJJaxSbB34/XToJh5O7ldgRU0Swi4aOiWUSSXsUmQe0kGD4795RQVFxKZloKjTJSg44jIvItKppFpMFQk2B4bd6hJkARCTcVzSLSoFTWJHj6w5PVJBiwzdvVBCgi4aaiWUQanIpNgks2bFeTYMAKNNIsIiGnollEGqyqmgTXbFGTYH0rawLUyhkiElYqmkWkQausSXDMA2oSrG9ao1lEwk5Fs4gIahIMmnYDFJGwU9EsIhKlJsHgaKRZRMJORbOISDlqEgxGgTY2EZGQC6RoNrODzOwDM1tgZl+Y2Y1B5BARqUplTYIXPzmN4pLSoKMlpc3aQltEQi6okeZi4BZ37wccAVxrZv0DyiIiUqmyJsGno02Cgzo1Jy1VX9DVhcy0FLKz0mihollEQiotiJO6+xpgTfTnQjNbAHQE5geRR0Rkf46NNgnmZGm+bV15/JJhQUcQEdmvQIrm8sysKzAEmBZwFBGRKrVqmhl0BBERCVCg3zOaWVPgFeAmd99a4bWrzGyGmc3Iz88PJqCIiIiICAEWzWaWTqRgfs7dX634urs/7u7D3H1Y69at6z+giIiIiEhUUKtnGPAksMDd7wsig4iIiIhITQU10jwCuBg4zszmRG+nBpRFRERERGS/glo9YzJgQZxbRERERCRWWnBURERERKQaKppFRERERKph7h50hmqZWT6wLMa3tQI21EGcupaouSFxsyt3/UrU3FD77F3cvcEsA9TArtmQuNmVu34lam5I3OxxvWYnRNFcG2Y2w90TboupRM0NiZtduetXouaGxM4edon82SZqduWuX4maGxI3e7xza3qGiIiIiEg1VDSLiIiIiFQjmYvmx4MOUEuJmhsSN7ty169EzQ2JnT3sEvmzTdTsyl2/EjU3JG72uOZO2jnNIiIiIiLxkswjzSIiIiIicaGiWURERESkGklZNJvZGDNbZGZfmtltQeepKTNbamafmdkcM5sRdJ6qmNlTZrbezD4v91yumb1rZnnR+xZBZqxKFdlvN7NV0c99jpmdGmTGypjZQWb2gZktMLMvzOzG6POh/tz3kzvUn7mZZZnZp2Y2N5r7jujzof68E5Wu2XUvUa/bumbXL12zqzlPss1pNrNUYDFwIrASmA5c6O7zAw1WA2a2FBjm7qFeQNzMjga2AX9z94Ojz/0e2OTud0f/0mvh7j8PMmdlqsh+O7DN3f8YZLb9MbP2QHt3n2Vm2cBM4CzgMkL8ue8n9/mE+DM3MwOauPs2M0sHJgM3AmcT4s87EemaXT8S9bqta3b90jV7/5JxpHk48KW7f+3uu4HngTMDzpRU3H0isKnC02cCz0R/fobIf2ShU0X20HP3Ne4+K/pzIbAA6EjIP/f95A41j9gWfZgevTkh/7wTlK7Z9SBRr9u6ZtcvXbP3LxmL5o7AinKPV5IA/4dHOfCOmc00s6uCDhOjtu6+BiL/0QFtAs4Tq+vMbF70q8BQfV1WkZl1BYYA00igz71Cbgj5Z25mqWY2B1gPvOvuCfV5JxBds4OTyH+eQ339KE/X7PpRH9fsZCyarZLnEmUOygh3HwqcAlwb/VpK6t4jQA9gMLAGuDfQNPthZk2BV4Cb3H1r0HlqqpLcof/M3b3E3QcDnYDhZnZwwJGSla7ZEqvQXz/K6Jpdf+rjmp2MRfNK4KByjzsBqwPKEhN3Xx29Xw+8RuRry0SxLjoXqmxO1PqA89SYu6+L/sdWCowjpJ97dJ7WK8Bz7v5q9OnQf+6V5U6UzxzA3QuAD4ExJMDnnYB0zQ5OQv55TpTrh67ZwajLa3YyFs3TgV5m1s3MMoCxwJsBZ6qWmTWJTrrHzJoAJwGf7/9dofImcGn050uBNwLMEpOy/6CivksIP/dok8OTwAJ3v6/cS6H+3KvKHfbP3Mxam1nz6M+NgBOAhYT8805QumYHJyH/PIf9+gG6Zte3+rpmJ93qGQDRpVAeAFKBp9z9rmATVc/MuhMZqQBIA/4R1txm9k9gNNAKWAf8BngdeBHoDCwHznP30DVvVJF9NJGvnBxYCvyobA5UWJjZSGAS8BlQGn36/xGZaxbaz30/uS8kxJ+5mQ0i0jSSSmRw4UV3/62ZtSTEn3ei0jW77iXqdVvX7Pqla3Y150nGollEREREJJ6ScXqGiIiIiEhcqWgWEREREamGimYRERERkWqoaBYRERERqYaKZhERERGRaqholqRgZqPN7K3oz98xs9vidNwLzeyXFZ67zMz+FI/ji4g0RLpmSyJKCzqASFWii6xbdAeiGnP3N4nf5ghjgIfidCwRkaSla7YkO400S6iYWVczW2BmfwFmAQeZ2SNmNsPMvjCzO8r97hgzW2hmk4Gzyz2/d1TBzP5qZueWe21b9L69mU00szlm9rmZjaokixFZzH3WfvKeZmZTzaxV9FyPmtkkM1tsZqdHfyfVzP5oZp+Z2Twzu/5APycRkTDQNVsaEo00Sxj1AS5392sAzOyX7r7JzFKB96I7/ywGxgHHAV8CL8R4ju8Bb7v7XdHjNq7kd4YAc72KHYDM7LvAT4BT3X1z5HpNV+AYoAfwgZn1BC4HugFD3L3YzHJjzCoiEma6ZkuDoKJZwmiZu39S7vH5ZnYVkT+v7YH+RL4lWeLueQBm9ixwVQznmA48ZWbpwOvuPqeS3xkD/LeK9x8LDANOcvet5Z5/MfrVZJ6ZfQ30BU4AHnX3YoAwbZkqIhIHumZLg6DpGRJG28t+MLNuwE+B4919EPBvICv6ck32gC8m+uc8+tVdBoC7TwSOBlYBfzezSyp570nAO1Uc92sgG+hd4fmKmRywGmYVEUlEumZLg6CiWcIuh8gFeYuZtQVOiT6/EOhmZj2ijy+s4v1LgUOjP58JpAOYWRdgvbuPA54EhpZ/k5k1A9LcfWMVx11GZE7e38xsQLnnzzOzlGiu7sAiIhfxq80sLXpsfdUnIslK12xJWiqaJdTcfS4wG/gCeAr4OPr8LiJf7f072lSyrIpDjAOOMbNPgcPZNyIyGphjZrOBc4AHK7zvRGBCNdkWAd8HXir3F8Ei4CMiXxFeHc35BLAcmGdmc4nMzRMRSTq6Zksysyrmy4s0aGb2BPBEhXl61b3nr8Bb7v5ynQUTEZFv0TVb6oMaAUUq4e5XBp1BRERqRtdsqQ8aaRYRERERqYbmNIuIiIiIVENFs4iIiIhINVQ0i4iIiIhUQ0WziIiIiEg1VDSLiIiIiFTj/wPmvMPp0ENBcgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_sb_vdisk(ax, r, sb, vdisk, label=None):\n", " ax[0].plot(r, np.log10(sb), lw=2)\n", " ax[0].set_xlabel(\"radius / kpc\");\n", " ax[0].set_ylabel(\"log surface density / M_sun kpc\"+\"$^{2}$\");\n", "\n", " ax[1].plot(r, vdisk, lw=2, label=label)\n", " ax[1].set_xlabel(\"radius / kpc\");\n", " ax[1].set_ylabel(\"velocity / km s\"+\"$^{-1}$\");\n", " if label is not None: ax[1].legend()\n", "\n", "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk)" ] }, { "cell_type": "markdown", "id": "ab42a3c1", "metadata": {}, "source": [ "We can explore how does $V_{\\rm disk}$ change when changing the scaleheight of the disk $z_0$ for instance:" ] }, { "cell_type": "code", "execution_count": 4, "id": "40696380", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk, label='z0=0.3 kpc')\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk(r, sb_exp, z0=0.1), label='z0=0.1 kpc')\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk(r, sb_exp, z0=0.8), label='z0=0.8 kpc')" ] }, { "cell_type": "markdown", "id": "c5c8e1b5", "metadata": {}, "source": [ "### Sersic profile" ] }, { "cell_type": "markdown", "id": "435a02b8", "metadata": {}, "source": [ "Let's compare to other popular analytic surface density profiles. Probably the most used in Astronomy is the [Sersic (1968)](https://ui.adsabs.harvard.edu/abs/1968adga.book.....S) profile, which is often used to describe all sorts of stellar components, including disks and bulges." ] }, { "cell_type": "code", "execution_count": 5, "id": "c71444c4", "metadata": {}, "outputs": [], "source": [ "def sersic(r, Ie, Re, n):\n", " bn = 2*n -1./3. +4./405./n # Ciotti & Bertin (1999): https://ui.adsabs.harvard.edu/abs/1999A%26A...352..447C/\n", " return Ie * np.exp(-bn * ((r/Re)**(1/n)-1))" ] }, { "cell_type": "markdown", "id": "e768d47e", "metadata": {}, "source": [ "Let's take as a reference the model:" ] }, { "cell_type": "code", "execution_count": 6, "id": "5bcb800e", "metadata": {}, "outputs": [], "source": [ "sb_sers_disk = sersic(r, 0.743e8, 1.678*rd, 1.0)" ] }, { "cell_type": "markdown", "id": "cf5472a5", "metadata": {}, "source": [ "which is equivalent to the exponential disk that we have above. Let's now compare the circular velocities of disks with Sersic surface brightnesses with different index $n$, while keeping the total luminosity fixed." ] }, { "cell_type": "code", "execution_count": 7, "id": "1631bc2d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# here the profiles are renormalized to yield the same total mass = 1e10 Msun\n", "# see e.g. Eq.(2) in Graham & Driver (2005): https://ui.adsabs.harvard.edu/abs/2005PASA...22..118G\n", "sb_sers_n4 = sersic(r, 0.392e8, 1.678*rd, 4.0)\n", "sb_sers_n3 = sersic(r, 0.449e8, 1.678*rd, 3.0)\n", "sb_sers_n2 = sersic(r, 0.545e8, 1.678*rd, 2.0)\n", "\n", "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sb_sers_disk, vcdisk(r, sb_sers_disk), label='Sersic: n=1')\n", "plot_sb_vdisk(ax, r, sb_sers_n2, vcdisk(r, sb_sers_n2), label='Sersic: n=2')\n", "plot_sb_vdisk(ax, r, sb_sers_n3, vcdisk(r, sb_sers_n3), label='Sersic: n=3')\n", "plot_sb_vdisk(ax, r, sb_sers_n4, vcdisk(r, sb_sers_n4), label='Sersic: n=4')" ] }, { "cell_type": "markdown", "id": "74f01e6a", "metadata": {}, "source": [ "### User-defined vertical density profile" ] }, { "cell_type": "markdown", "id": "d76510dd", "metadata": {}, "source": [ "`vcdisk` allows us to specify our own vertical density profile, if we so choose. This can be easily done through the `rhoz` argument." ] }, { "cell_type": "code", "execution_count": 8, "id": "4333761f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def rhoz_gauss(z, m, std): return np.exp(-0.5*(z-m)**2/std**2) / np.sqrt(2*np.pi*std**2)\n", "\n", "def plot_rhoz(ax, z, rhoz, label=None):\n", " ax.plot(z, rhoz, lw=2, label=label)\n", " ax.legend()\n", " ax.set_xlabel(\"radius / kpc\");\n", " ax.set_ylabel(\"vertical density / M_sun kpc\"+\"$^{2}$\");\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(6,4))\n", "z = np.linspace(0,3)\n", "plot_rhoz(ax, z, np.exp(-z/0.3) / (2*0.3), label='exp')\n", "plot_rhoz(ax, z, rhoz_gauss(z, 0., 0.8), label='gauss')" ] }, { "cell_type": "code", "execution_count": 9, "id": "06f0b0e3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk)\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk(r, sb_exp, rhoz=rhoz_gauss, rhoz_args={'m':0.0, 'std':0.8}))" ] }, { "cell_type": "markdown", "id": "5b7dd1c4", "metadata": {}, "source": [ "### Flaring disk" ] }, { "cell_type": "markdown", "id": "72f875b9", "metadata": {}, "source": [ "We can also have a flaring disk, i.e. one where the vertical density depends also on radius $\\rho_z=\\rho_z(z,R)$. We can work out this case as well with `vcdisk` by specifying how $\\rho_z$ depends on $R$." ] }, { "cell_type": "code", "execution_count": 10, "id": "44279f7d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def rhoz_exp_flaring(z, R, z00, Rs):\n", " z0R = z00+np.arcsinh(R**2/Rs**2)\n", " return np.exp(-z/z0R) / (2*z0R)\n", "\n", "fig, ax = plt.subplots(figsize=(6,4))\n", "z = np.linspace(0,3)\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 0.0, 0.1, 0.8), label='R=0')\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 0.5, 0.1, 0.8), label='R=0.5')\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 1.0, 0.1, 0.8), label='R=1')\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 1.5, 0.1, 0.8), label='R=1.5')\n", "plt.ylim(None,2);" ] }, { "cell_type": "code", "execution_count": 11, "id": "745345ef", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk)\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk(r, sb_exp, rhoz=rhoz_exp_flaring, rhoz_args={'z00':0.1, 'Rs':0.8}, flaring=True))" ] }, { "cell_type": "markdown", "id": "fcfda35e", "metadata": {}, "source": [ "## Example 2: observed surface brightness" ] }, { "cell_type": "markdown", "id": "fb9c3c48", "metadata": {}, "source": [ "Let's say that, instead of having just simple galaxy images from which we can derive an analytic approximation for the galaxy surface brightness, we have a detailed galaxy image from which we can measure the intensity in elliptical annuli. This is for instance the case of nearby galaxies such as [NGC 2403](http://cdsportal.u-strasbg.fr/?target=ngc2403), that I use here as an example.\n", "\n", "I use data taken from the [SPARC](http://astroweb.cwru.edu/SPARC/) database for this galaxy, which I include in this package as the `NGC2403_rotmod.dat` file. Here are reported measurements of the intensity at 3.6$\\mu$m taken with the *SPITZER* space telescope in elliptical annuli for this target." ] }, { "cell_type": "code", "execution_count": 12, "id": "7060aac6", "metadata": {}, "outputs": [], "source": [ "rad, _, _, _, _, _, sb_n2403, _ = np.genfromtxt('NGC2403_rotmod.dat', unpack=True)\n", "# convert SB to Msun / kpc^2\n", "sb_n2403 *= 1e6" ] }, { "cell_type": "markdown", "id": "f39e2ff5", "metadata": {}, "source": [ "Now we can very easily use `vcdisk` to calculate $V_{\\star, \\rm disk}$ for this galaxy, and we can evena compare it to some analytic profiles." ] }, { "cell_type": "code", "execution_count": 13, "id": "84d306ee", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/lposti/anaconda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log10\n", " \n" ] }, { "data": { "image/png": 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t2pUbbriB1q1bs3bt2j/P26lTJ5YuXUpycjI33XQTLVu2pFmzZkyaNAmA1NRU+vbtS3x8PNdccw2pqan58v3658tRihk/l3BVz16sbXE+j3w5mjbHf6KXzoOFw9CNk5E+n0LF5k7HNMaY/LJfRMqr6l4RKQ8c8OzfBVTO87xKwJ5CT3cu9q+BtET2Shl2aRzPnlfV6UR/KV0dbp4OEwfD+u8I/KYvo7s8x9WZzVm5K5HrRixgzG1tiAkPcjqp8XXPRBXQcf+9j/3SpUsZOXIkCxcuRFVp3bo1559/Phs3buTjjz+mXbt23HTTTbz//vvcdNNNTJgwgQ0bNiAiHDt2DIB7772X+++/n/bt27Njxw66devG+vXr/zz+nDlzCAkJ4c0332TMmDE8++yz7N27lz179tCiRQv+85//0LlzZz755BOOHTtGq1atuPDCC/nwww8JDQ1l1apVrFq1iubN86dms5bm/6FhxVI8d9+drGn9OpdmvMjanKrIse3kjLwY1k5wOp4xxuSX74ABnq8HAJPy7O8rIkEiUh2oDSxyIN/Z2+ZuuZqXVZfY8CDOr+NDreAAQeHQZxRc8DigBM14kjFVJ9GgbCibDyZz/ceLSEzNdDqlMf8wZ84crrjiCsLCwggPD+fKK69k9uzZVK5cmXbt2gHQv39/5syZQ2RkJMHBwdxyyy2MHz+e0FD3/Og///wzd911F02bNqVnz54cP36cpCR3n/6ePXsSEhICwNVXX83YsWMBGDNmDH369AFg2rRpvPzyyzRt2pROnTqRlpbGjh07mDVrFv379wcgPj6e+Pj4fPmeT9vSLCIXAVcD/1XVFSIySFWH58vZi4DgAD+e7NGAefXLMPibGtyV8j5X8xuMvRH94xek8+MQUc7pmMYYc0ZE5CugExArIruAp4GXgTEicjOwA+gDoKprRWQMsA7IAu5U1WxHgp+t7e6ieUFOfa5sXhF/Px9sK3K54PxHoHQNmHA7QUuHM772Hnpl3cC6vccZOHIRn93cmrAg+3DY/Iv/0SJcUP5tet6TV9gUEfz9/Vm0aBEzZszg66+/5r333uOXX34hJyeH+fPn/1kc5xUW9lc3qooVKxITE8OqVav45ptv+PDDD//M8O2331K3bt3T5sgPZ3L1uAN4GOgvIp2BpvmeoghoWzOW7+/vwvxGz/JM5g2kqz+yfDT6Vjws+cTpeMYYc0ZUtZ+qllfVAFWtpKofq+phVe2iqrU9t0fyPP8FVa2pqnVVdYqT2b2Wk4NunwfAwpz6XNW8ksOBTqNxb/cAwaAogjf9wHdRr1M/KpNlO44x6LMlpGcVrb9XTPHWsWNHJk6cSEpKCsnJyUyYMIEOHTqwY8cO5s+fD8BXX31F+/btOXHiBImJiVxyySW89dZbrFixAoCuXbvy3nvv/XnM3P2n0rdvX1599VUSExNp3LgxAN26dePdd9/9s4Bfvnz5n9m++OILANasWcOqVavy5Xs+k6L5oKoeU9WHgK5Ay3w5cxEUFRLAm32bkXDNY1wrrzA5uxWSnU7Ojw/BtjlOxzPGGJPXoY1I6hH2amlC4mpSt1yE04lOr3pHuOkniKxI0J5FTAp5jviwY8z94zAPjFlJTo4tvmV8Q/Pmzbnxxhtp1aoVrVu35pZbbiE6Opr69eszatQo4uPjOXLkCIMHDyYpKYkePXoQHx/P+eefz5tvuldlfuedd1iyZAnx8fE0aNCADz744F/P17t3b77++muuvvrqP/c9+eSTZGZmEh8fT6NGjXjyyScBGDx4MCdOnCA+Pp5XX32VVq3yZ6ZMOd3qdyLSS1Un5bl/t6q+my9nP0MJCQmaH/Pr5ad9iWk8PG4lbbe+y2D/70n0j0HuXU5kRAF1xjfGFFkislRVE5zOUVh85pq99FP4/l6+zz6PLee/x70X1nY60Zk7vge+6AP715AVEst1KQ+yML0qA9tV46keDQrko2dTtKxfv5769es7HaPIO9X7+G/X7NO2NOctmD33C7Vg9lXlooIZfVMrwro/wxqtQVTWYT5++1kWbDnsdDRjjDFAzg73mMVlObW5NL6IjT2JrAADJ0P18/FPPcSXAf9Ha/9NjJy7jeGztjidzpgSyasRESIySkRK5bkfLSIltkOviHBD+1rEXPIEANdkTuCGj+bw4uT11vfMGGMclrZ1AQCHS8VTq0wR6JpxsuAouG4cNO6DX1YKn4e8TkPZxktTNjB+2S6n0xlT4ng7jDheVY/l3lHVo0CzfE1UBJVveQUaV48KcoRb/X5k+Kwt9HpvLuv32hLcxhjjiNSjhB7fTLoGULVRG6fTnD3/QLj8A6jfk4DMJMaFv0ZN2c0j41Yx63cfW3nRFLrTdbE1/5u375+3RbNLRKJz74hIaWyBFHC5kG4vAvBQwLdcWmoHG/Yl0eu9uQyftZlsG7hhjDGFSnctBWCNVqNTAx+fNeN0/Pzhqo+h1oWEZB5lQvirlNP93P75UlbvKvypxoxvCA4O5vDhw1Y4nyVV5fDhwwQHB5/xa7wteIcC80VkrOd+H+AFL4+BiNwP3IJ7OdbVwEBVLdrrhdbqAq1uQxZ9yHuZT3NRrXu4/48mvDh5AzPWH2Do1U2oFB3qdEpjjCkRjvw+lxhgvV9d+lUu5XScc+cfCFd/Bl/0JnL7XCaGv8olSY8z8NNFfDu4LVVjfGBpcFOoKlWqxK5duzh40D5xOFvBwcFUqnTmf1R7VTSr6mgRWQJ09uy6UlXXeXMMEakI3AM0UNVUz8T5fYFPvTmOT+r6PGRnIEtHcvmu17igYjOuOzaIhVuh+1uzeaZnQ65qXtFGPRtjTAFL3ryQGEArtMDPVUyuuYGh0O9rGN2T2D3LGR/+KpedeIwbPlnEuNvbEhdhy22XJAEBAVSvXt3pGCWKtwMBg4HuQBfgAqCbZ5+3/IEQEfEHQoE9Z3EM3+MfCJe95f4YLbwcUYeX813gE9xdYy8n0rN4aOxK7vhiGUeSM5xOaowxxZcqpY6tAaB8w/YOh8lnwZHQfzzE1adS1nbGhr3GkcOHGPjpIk6kZzmdzphizds+zaOBhsA7wHtAfeAzbw6gqruB13Ev1boXSFTVaSc/T0QGicgSEVlS5D56aNwb7lwANbvgSj3MA3sfZkrj34gLymLKmn10e2sWv2484HRKY4wpltIPbSMyJ5HDGkHz+CZOx8l/oaXhhokQXZ1a2Zv5MnQom3cf4DZbNdCYAuVt0VxXVW9W1V892yCgjjcH8Awk7AVUByoAYSLS/+TnqepwVU1Q1YS4uDgvY/qAkGi4dgx0eAhRpf6mD1kQ+gD/LT2W+smLuGvkLJ6YuJqUDGsZMMaY/LR11SwAtgTWoXR4Me2yEFEOBnwHkRVpnLOekSFvs/iPfTxoqwYaU2C8LZqXi8h5uXdEpDUw18tjXAhsVdWDqpoJjAfaenmMosHPH7o8CTf+CBWa45d6iEtTJjA68BWWBA2mxdJHeeqN91ix44jTSY0xpthI/GMhAGlxTZ0NUtBKVYEbJkFYHOfpSoYFvcdPq3by3A/rbEYFYwqAt0Vza2CeiGwTkW3AfOB8EVktIqvO8Bg7gPNEJFTcI+K6AOu9zFG0VGsHt/4CN/8Mbe+Bii0IkQyu8JvL62lPE/3xecwY/QKZmdbX2RhjzlXYwZUARNc+7zTPLAZia8P1EyG4FF1kMUMDhzNq3hben7nZ6WTGFDveTjnX/VxPqKoLRWQcsAzIApYDw8/1uD5PBCq3dG8AR7eRtewLkheOpmrGPqpueZUtL48loPeHVK7f2tmsxhhTRCWlpFE9cxMI1Gjawek4haNcI/fgwNE96ZUxhxMBQTw+9SbiwoO4umVlp9MZU2x429Icq6rb8264VwnM/fqMqOrTqlpPVRup6vWqmu5ljqIvuhr+XR4nasg6NnZ8lz1ShhrZW4n7+lLmjnvHPlozxpizsGH1EsIknQOuMoRGl3c6TuGp1AKu/Qb8g7nObwb/8f+SxyasYvq6/U4nM6bY8LZo/khEGufeEZF+wBP5G6mEcflRt/MNhN2/hPmlLiVYMmm35knGvXU/+xNTnU5njDFFyqHf5wNwuFTj0zyzGKrWHq75HFwBDPL/kbvkW+76chmLttq4GWPyg7dFc29glIjUF5FbgTuArvkfq+SJioyizX1fsqbJk+Qg9EkcyfI3r2Tqsk1ORzPGmCLDb89yAPwrtXA4iUNqXwS9P0bFxf0B33K9fs/Noxazbs9xp5MZU+R5VTSr6hbcq/d9i7uA7qqqtvB9Pmp0xUMcv+xjUiWE7syjxsRevDx6EsfTMp2OZowxPi0tM5vyKe5x5eUbtHM4jYMa9EJ6vQ/AEwFf0CtzCgNGLmLH4RSHgxlTtJ1R0Zw7O4ZnhoxxQGmgGrDQi1kzzBkq1eIqgu+YxbGwGtR27ebOzbfx8tBXWbDlsNPRjDHGZ63dfoB6bCcHIbx6CW1pztW0H1w6FIDnA0bSMXk613+ykINJJW8IkTH55UxbmnsAl+XZWuPulpF73+QziatDqXtmk1SrJxGSyouZr7J95E0M/W6xrfhkjDGnsHP9IgIkm4NBVSEowuk4zmt5C3R9HoBXA4fT8OgvDPhkkX1yacxZOqOi+eQZM04xg4YpCEHhRFw3muyuL5ElgVzjN5N+S6/m2TffZf1e659mjDF5ZexYDEBKcV/UxBtt74ZOj+FHDu8E/pdy+2dy66glpGVa44sx3vJ2IKApbCL4tb0D/zvmkBzbhApyhBeTn2bl+zfyyYxVZNtyqcYYA0DkYXdvwdDqrRxO4mPOfxTa3oM/2QwLfBv/7b9xz1fLycrOcTqZMUWKFc1FRVxdwgb/QkanJ8mSAPr6zaDrrCt44d1h7DxigzuMMSXbwaR0amf9DkBs3bYOp/ExInDRc9DyVoLIZETgGxxZ/xsPjV1pDS/GeMGrollEgkTkWhH5j4g8lbsVVDhzEj9/Ajs9hP/tszge3YhKcoinjj7GirevZvLshbYgijGmxFqzeQc1XXvJIAC/cg2djuN7RODiV6HpdYSQzqeBr7F95W88PmG1/e4w5gx529I8CeiFe/nr5DybKUxlGxB510xS2g8hC38uk9l0+fkSZrx1C0cP7nU6nTHGFLqDGxe4b8Prgn+gw2l8lMsFPd+FRlcRLqmMDnyZDUt+5dnv11nhbMwZ8LZorqSq16jqq6o6NHcrkGTmf/MLIPTCx/C7ZwnbK/YgSLK4MHEcAf9tzpZvn4UM+1vGGFOC7FkKQFa5Zg4H8XEuP7hiODS8gghJ5bPAl1g+/2denbrRCmdjTsPbonle3mW0jfOkdHWq3voF+/pOY0VQC8JJocbqNzj+amPSF34COTbQwxhTvKkqsYlrAIioaYMAT8vPH64cAQ0u9xTOLzP3t2m898sfTiczxqd5WzS3B5aKyEbPYierbXET31CuXmsaPzqDH5oOY3VODSKzDhM05X6OjeoL6UlOxzPGmAKzNzGNBuou+KJrnedwmiLCzx+uGgENehEpKXwe+BLTf57CR7O2OJ3MGJ/lbdF8MVCbvxY2yV30xPgAP5fQ4/Jr8b/9V14OfYjjGkqp7VM5/FYHMg/87nQ8Y4wpEJv++J1ycpRkCUNiajkdp+jwC4CrPob6Pf8snL+b8iOj5m1zOpkxPsmrotkWNyka6lcoxX33/4cvmnzK7zkViUndSvqwTuxdPNHpaMYYk+8S/1gIwIGI+u7BbubM+QVA70+g/mWewvlFxn3/PZ/M2ep0MmN8jrdTzj11qq2gwpmzFxzgx+Aru3H02in85mpNuCZT9ocbWf7546j1czbGFCN+e5cDNgjwrPkFQO+RUK8HUZLCF4Ev8OOPExgx27pqGJOXt3+S551mLht3d41q+ZzJ5KPW9arS7OHvmRx3CwDN/niPJa9dxoFDhxxOZowx+SP2+FoAImq2djhJEZZbODe4nEjP4MBfpoxl2MzNTiczxmd42z1jaJ7tBaATULFAkpl8ExkSxCV3DmVpu2EkEULL1Dkkv9eBub9NczqaMcack8TkdOrlbAKgTN02Dqcp4vwD3X2cm1xLqKQzMuA1Fk37ivd+2eR0MmN8wrl2/goFauRHEFPwWnbtR/rAGewOqEp19tD6l2uY9u7dHE+2OZ2NMUXT9k2riJIUDrticJWq5HScos/PH3r9FxJuJkgyGR7wBut+Hs1bP9tgcmO87dO82jPV3CoRWQtsBN4umGimIMRWbUiFhxewrur1uFC6Hh7NvtfbsXLJXKejGWMcJiL3i8haEVkjIl+JSLCIlBaR6SKyyXMb7XTOvJL+mA/AnjBbOjvfuFxw6VBoezcBks27Ae+y45ePeWOaLYBiSjZvW5pzp5i7DPe0cxVU9b18T2UKlASG0mDge+y9chz7XGWpo1up//1l/DJiCGnp6U7HM8Y4QEQqAvcACaraCPAD+gJDgBmqWhuY4bnvM/z3ulcCTCnb3OEkxYwIXPR/0Okx/ER5I/ADjvw2jP/7YT05OVY4m5LJ26K5FXDEM83cQGCMiHh9pRKRuiKyIs92XETu8/Y45txUbHIhMQ8vYWW5qwiUbDrvGsaWVzvwx7oVTkczxjjDHwgREX/c3e/2AL2AUZ7HRwGXOxPt1OISVwMQXM1WAsx3ItBpiLt4Bp4PGEnIgjd5aMwKMrNtFiZT8nhbND+pqkki0h7ohvsCOszbk6rqRlVtqqpNgRZACjDB2+OYcxcQEkmT2z9hc7fRHJQYGmRvpMI3XZn15ctk20XRmBJDVXcDrwM7gL1AoqpOA8qq6l7Pc/YCZU71ehEZJCJLRGTJwYMHCydz+gmqZG0lS12Ub2ArARaYdvfApW+gCA8HjKHpmhcYPHoRaZnZTiczplB5WzTn/g+5FBimqpOAwHPM0AXYbIukOKtmm16E3b+YFdHdCJV0Ov7+Eitf6crunTbBvTG+REQeLaDjRuNuVa4OVADCRKT/mb5eVYeraoKqJsTFxRVExH84vGkR/uSwSaoSF126UM5ZYrW8Gbl6FDl+QdzgP52rtjzBzSPmkJia6XQyYwqNt0XzbhH5ELgamCwiQWdxjJP1Bb46eacTrRYlXWhkDE3vHcOadm+TSDjNMxYTOqID877/xAZ/GOMQERmTZxsL3FJAp7oQ2KqqB1U1ExgPtAX2i0h5T5bywIECOr/XEje5BzDvCm2AiDicpgRo0AvX9RPIDozkYr/F3LP3EW7+4GcOJKU5ncyYQuFtwXs1MBXorqrHgNLAw7kPejuqWkQCgZ7A2JMfc6LVwrg1uuhGcgbPZ21oS6IlibZL72fB0D4cOWx/vBjjgOOqerVn6wP8XEDn2QGcJyKh4q5AuwDrge+AAZ7nDAAmFdD5vea/y718dmJcgsNJSpBq7fC7+SeywsvT2rWB548+zB3vf8+OwylOJzOmwHm7uEmKqo5X1U2e+3s9fd5yzfDy/BcDy1R1v5evMwUsumwVGjw0jRWNnyBVA2lzYjrp757Hst++czqaMSXNCyfdf7wgTqKqC4FxwDJgNe7fD8OBl4GLRGQTcJHnvvNycog7tgIAqWqLmhSqsg3xv2U6WaXrUM+1k3dSHuHB979h1a5jTiczpkCda9eKk3n7+Vg/TtE1w/gGcbloetXDJA6YwR8BdSjPIZr+cgOz3ruNZFsQxZhCoapbAUQk1nP/SAGe62lVraeqjVT1elVNV9XDqtpFVWt7bgvs/F45tJHQ7CR2awzlq9R2Ok3JU6oy/rdMJatSayrIEUZk/Yc3P/yIGeutDcwUX/ldNJ9xx1cRCcXdajE+nzOYfFauRjzVH5nL0mqDyEHoeOhr9r3ehnXL5zkdzZiS5BOnA/gS3e5e1GRJTl1qlQl3OE0JFVoa/wGTyKnbgyhJYbjrJX7+/FU+m7/N6WTGFIj8LprPmKerR4yqJjqVwZw5v4BAWtz4GjuvmMguVwVq6nZqTryM30Y+QWamjZ42phDYSLc80rfMAWC1qz5xEUEOpynBAkJwXfMZ2vZeAiSblwJGkPbjY7z4w2pbBMUUO053zzBFTPWm5xP30EKWlbmSIMni/O3vsuGVC9i2eb3T0Ywp7qwCyaWKbHd/0nWgdHObOcNpLhfS9Tno+S454s+t/pNpufAeHvh8rs3lbIqV/C6au+Tz8YwPCgqNpPkdI9nQ+WMOU4rGWauJGX0Bc8a+Q44tiGJMQbHKMNfRbQSl7OWohhNYrqHTaUyu5jfgumEimYFRXOS3jEF/3MFdH3zP4RPpTiczJl+cUdEsIt/9ry33eT4zQMQUinodexN4z0JWRXQkQlJpv/ZJlr7eg/17dzkdzZji6DGnA/iM7e75mRfl1KNG2QiHw5i/qd6BgNt+JSOqOg1c23nx0L0MeWcka3ZbT0xT9J1pS3MboBIwG/cyq0NP2kwJFVG6HPEPfMfKhJdJIoSWqXPx+7Ati6Z+4XQ0Y4oVVV0jIn1EJAJARJ4QkfEi0tzpbIVum7toXphTn5pxNgjQ58TUJPC2X8io3I4ycoz30h9nzIfPMWm5NaiYou1Mi+ZywH+ARsDbuGe9OKSqv6nqbwUVzhQRIjTpMZj0W2azPqgJsSTSav4dzH/zWhKP2YcPxuSjJ1U1SUTaA92AUcAwhzMVvm3uQYALc+pTIzbM4TDmlEJLEzhgItkJtxIkWTznGkHat3fyyg8ryLJufKaIOqOiWVWzVfUnVR0AnAf8AcwUkbsLNJ0pUmIr1abeo7+ypN7DpGsAbRJ/5MRb57F63k9ORzOmuMgdVXUpMExVJwGBDuYpfMd2QOIOEjWMDVShculQpxOZf+MfiF+P19HLPyDLFcQ1/jPpvmggD434kWMpGU6nM8ZrZzwQUESCRORK4HPgTuAdbI5lcxJx+ZHQ9wkO9JvKFv8aVGQ/Dab2Ze4Hd5GWlup0PGOKut0i8iFwNTBZRIJwcOpQR2zL7c9cl3JRYQQH+DkcyJyONO2H/60/kxZemSauLTy5ZzDPvP0+6/cedzqaMV4504GAo4B5QHPgWVVtqar/p6q7CzSdKbIq12tBlUfms6jSQADa7fuMXa+24Y81ixxOZkyRdjUwFeiuqseA0sDDjiYqbJ6uGQty6lMt1lqZi4zy8QTfMYu0qhcQI0kMTXuGycMeZdySHU4nM+aMnWkLxfVAHeBeYJ6IHPdsSSJifyqaU/IPDKbVLW+x5bKx7JFy1MrZSuWxlzD3s2fIzra5O43xlmdRqPGquslzf6+qTnM6V6Ha/ld/5mox1p+5SAktTfCAb8lq/xB+ojzo+pLSk67nqS9/JTk9y+l0xpzWmfZpdqlqhGeLzLNFqGpkQYc0RVvthIuIfmAhS2J6EiSZtNv8JutevoDd2353OpoxpihJ3AVHt5HmCmOdVqO6DQIselx++F/4JNr3K9IDoujst4K7Nt7I02+9x7o91gZnfFvJ6gtnHBMSUYqEuz9jdccPOEwUjTNXEjmyIwsnvIfm2EhqY8wZ8KwCuCGwETm4qGotzUWW1LuEoLvmk1LhPMrIMV5NeYY5H9zJ5/P+QNUWvzS+yYpmU6gad+6H350LWBHWjghJpfXKx1n++mUcOWDd440xp7FrCQCLsmsBUN36NBdtURUJvWUymR0fAxEGub6j0U9X89SnP5CYmul0OmP+4UwHArYREVvC1eSLUnEVaPLgDyxp+gJJGkLzlDnw/nms/NkWRDHmfxGRBBGZICLLRGSViKwWkVVO5yo0e5YBMDulKi7BppsrDlx+BHQeguumKaSElKepazOPbLuVt954ngWbDzmdzpi/OdOW5gHAUhH5WkRuFJFyBRnKFH/icpFw+V2cuGkWqwObUprjNJlzB0ve7kdyoi2IYsy/+AIYCVwFXAb08NwWf1kZsNf998HK7OqUjwohyN+mmys2qpxH6D3zSa55KRGSytOZb3Hk0368NWke6Vk2cNz4hjMdCHi7qjYHngGigU9FZL6IvCgiHUXErlzmrJSvWoeGj/7CvNoPk6YBJBydTNJbrdi44Eenoxnjiw6q6nequlVVt+duTocqFAfWQXY6KRHVOU4YlUuHOJ3I5LeQaML6f0FWj3fIcIVyid8irlt2DS+9+YbN6Wx8gld9mlV1g6q+qardgc7AHKAPsLAgwpmSweXnR9vrnmBP32ls9KtNOT1I3Z+uZemHt5GZlux0PGN8ydMiMkJE+onIlbmb06EKxe6lAOyPaABA5WjrmlEsieCfMIDAuxeQVO484uQ4zyQ/z/ph1/HJzyvIzrFBgsY5Zz0QUFVTVXWyqt6tqgn5GcqUTDXqN6fao3OZVfFWMtWPFnu/Zt9rrdi5Zo7T0YzxFQOBpkB33N0ycrtoFH+e/sx/BNQFrD9zsRddlYhBU8i48EUyJZArXbPoPvsKXnz3fbYftsYU4wybPcP4lKDAIDre+jobL/2WbVKRytm7KDe2J8tHDyEnM8PpeMY4rYmqJqjqAFUd6NlucjpUodi3GoDVOdUAqGJFc/HnchHY/k4C7pjL8Zh4KsgRnjz6Hxa9fR2fTF9GZrZNV2oKlxXNxic1anUBMQ8sYFbpPgRINs22DGPra+05uHWN09GMcdICEWngdIhCl5MDB92LIS1OLgtgfZpLkrg6RN7xK6ntHyNLAujj+pWec3rx5tDnWbXzqNPpTAniVdEsIneJSHRBhTEmr4iISDreM4JFHT9lLzHUzNhIxKhOrJ7wGtjk96Zkag+sEJGNJWrKuWPbICsVIsqz4Zj715b1aS5h/PwJuXAI/nfM41iZlsTKcR5JGcqxjy7jvXHTbBluUyi8bWkuBywWkTEi0t3mbjaFoVXnK/C/cwFzwi4imEwar3yeta935/hBWxDFlDjdgdpAV0rSlHMHNgCQFVOXoymZBPm7iIsIcjiUcURcHUrdPo30S98h1S+Sjq7V3LL6Wj577V5mrtvldDpTzHk7e8YTuC/YHwM3Aps8087V9PbEIlJKRMaJyAYRWS8ibbw9hik54uLK0O6hscxq+jrHNIyGyQvI+u95rJv5jdPRjClMsXmnmvNMNxfvdKgCd3A9AInh7l81lUuHYm02JZjLRVDLAYTcv4yjNa8gWDK5Petzyn/djaEffsSOwylOJzTFlNd9mtW9KPw+z5aFe97mcSLyqpeHehv4SVXrAU2A9d5mMSWLiNDx8ls5PvA3VgU0oTTHaTBzEEv/O4C0ZJvD05QIH4lI49w7ItIPeMLBPIXD09K8N6g6AJWjrT+zAcLjiL7+U7KvG09iSGXqunbx4N6HWPd2L0Z89yupGbYoislf3vZpvkdElgKvAnOBxqo6GGiBe4WqMz1OJNARd4s1qpqhqse8yWJKrirVatPg0V+YXf0+0tWfFgcncmDoefyxYrbT0YwpaL2BUSJSX0RuBe7A3VWjePO0NG+VyoBNN2f+zq92F6IeWMKJdkNIl2C6uxbRf2kfvnrlNqYs24LaGBiTT7xtaY4FrlTVbqo6VlUzAVQ1B+/mCq0BHARGishyz2T9YXmfICKDRGSJiCw5ePCglzFNcefv70+HAc+y7Yrv2eaqTJWc3VSd0IuFnw4hOyvT6XjGFAhV3QL0Bb7FXUB3VdVEZ1MVsJxsOLQJgPVZFQCoWMpams1JAoIJv+gxgu5bxuHqPQmWTG7KHkv8pAt5951X2GgrCpp84G3RHHTykq0i8gqAqnrTvcIfaA4MU9VmQDIwJO8TVHW4Zz7ShLi4OC9jmpKibtO2lH1wAfPj3FPTtd42jD9eac+ezTY1nSk+cmfJ8MyUMQ4oDVQDFhb72TOO74asNAgvx5YkPwAqWNFs/k1URWIGfEb2jVM4ElmPinKYe46+RNKwLvx39JfsP57mdEJThHlbNF90in0Xn8V5dwG7VDV3+e1xuItoY7wWEhZOmztHsLLzKPYTQ93MDZQa3Zml415Dc2zye1Ms5M6Skbu15q8ZNIr37BlHPe000VXZk5gKWNFsTs+vWltK3zePlG5vcMK/FAmu37lzy2BWDr2MkZOmccKmqDNn4YyKZhEZLCKrgbq5rR2ebSvgdSuHqu4DdopIXc+uLsA6b49jTF5NOl5O0N0LWBzRhVBJp8Wa51nzWleO7Nt++hcb48NOnjHjFDNoFF/HdrhvS1VhzzF30WzdM8wZcfkR2uZmwh9azdGEe8mQILrKIq5fdg0/vdyPsb8ttVUFjVfOtKX5S9ytGd/x99aOFqra/yzPfTfwheejxabAi2d5HGP+VCqmDAkPfMuihKEkEkbj1MW4PmjLqqmfOh3NGHM2PEVzVmQVDp3IIMBPKGNzNBtvBEcS3eM5Au9fycE6fRGB3jqNS365mC9fuZ2flm4kJ8cGC5rTO6OiWVUTVXWbqvY7qYXjyNmeWFVXePosx6vq5apqa2GafCEitOpxCym3zGVlUAtKcYL4+fey8s0rST5mg0pN0SMibUrsYlLH3A3pRwPLAVAuKhiXq2S+FeYcRZYn7toPcd0xj/3lOxMm6QzI+IbzvruAz169i+nL/7CZNsz/dKbdM+Z4bpNE5LhnS8q9X7ARjTk75StVp/EjPzOn7n9I0SCaJM4g9e2WbJoz3uloxnhrALBURL4WkRtFpJzTgQqNp6V5n6ssABWirGuGOTdSpj5lb5tA5g2T2R/dglKSzIC0z0mYeD6jX72Hmas2W/FsTulMW5rbe24jVDXSs0Xk3i/YiMacPZefi/b9HmXftTNY69eAWD1K7Z8HsmrYADJTivdMXab4UNXbVbU58AzuBaU+FZH5nhVZO4qIn7MJC5BnIOCO7FjA+jOb/BNQox1l75lBRv9J7C/VnGg5wYDU0TT5tiOfvXYvs9bYHM/m77xd3KSPiER4vn5CRMaLSLOCiWZM/qlRtzG1Hv2NX6vcRbr6E79/Ikdeb8mu5dOcjmbMGVPVDar6pqp2BzoDc4A+wML//cozIyKlRGSciGwQkfWebiGlRWS6iGzy3Ebnx7nOSFYGJO0BcbEpvRQAFW01QJOfRAis1Ymy9/5CxrUT2BfVlGg5wQ0po2g8tgNfvjKYqYvWkm19ng3eTzn3pKomiUh7oBswCvgg/2MZk/+CAgO54KYX+L3Xj2yUGpTN2U+FiVezeuTd5GTY3J2maFHVVFWdrKp3q2pCPh32beAnVa0HNAHW455Df4aq1gZmcNKc+gXq+G7QHIiowK7j7inCbLo5UyBECKzTmXL3zSSt37d/Fs/XpX1Fhx8vYMKL/Zn020LSs2xp7pLM26I596flUtwLk0wCAvM3kjEFq3Hz86jw0Fymx91IDkLj7aPZ+VobDm5e5nQ0YxwjIpFAR+BjAFXNUNVjQC/cDSR4bi8vtFDH8szR7JlurnxUcKGd3pRAIgTXvZBy980k/fof2R3XgVBJp3fWD1zyy8X8/OKVjJs83eZ5LqG8LZp3i8iHwDXAZBEJOotjGOO4iLBQLrrzbRZ3/oqdlKNq5hYiP+vKmm9fAlsQxZRMNYCDwEgRWS4iI0QkDCirqnsBPLdlTvViERkkIktEZMnBg/k0S82xne7bqMrs86zkZi3NplCIEFSzPRXv/IGsQbPZWakHLlEuzZlJ70W9WfbihXz5xUh2Hk52OqkpRN4WvFcDU4FunhaIaODh/A5lTGFpc353gu+ex2/hFxNEJo1Wv8zG17twfH/xXi/CFE0iclcB9in2x70y6zBVbQYk40VXDFUd7plGNCEuLi5/Ep3Y7z52RDn2JbqL5rKR1tJsCpd/hXgq3/IFrnuXs6v29WQQSEdZzrWb7iP17ZZ88f6zLPtjtw0aLAHOpntGMNBHRJ4CBgHn5XsqYwpRXEwMHR/8it+av80RjaBuyjJ0WFs2zBjtdDRjTlYOWCwiY0Skez7P3bwL2KWquYMKx+EuoveLSHkAz+2BfDzn/5Z8CID0oNKkZGQTGuhHZLB/oZ3emLwkuhqVrnuPwIc3sC/hEY75x1LHtZvrDrxB9c9a8e2rtzJ1/lIysuzTyuLK26J5EtATyMLdCpG7GVOkiQjn97yR5JtmsySwJVGcoN7su1n2bn/Skm0qcuMbVPUJoDbufsc3Aps8087VzIdj7wN2ikhdz64uwDrcK8EO8OwbgPv3QOFIdnfzOCpRAJSLDKakrvFifEhYDOV6PE6pxzaQeMkw9oY1IFpO0Dt1LF1+upDZL1zMmDGfsftoitNJTT7z9k/2Sp6pjowplipXrU75R6Yy86uXafPHmzQ//D07hi4jo9dH1GrSzul4xqCqKiL7gH24GzCigXEiMl1VHznHw98NfCEigcAWYCDuxpUxInIzsAP3FHeFI9ndqH0wx1M02yBA40v8AohqdS1RLfuRvnUB+6a/SaW90+miC2DdAraseYFvYntRsdPNtG1U21ayLAa8LZrniUhjVV1dIGmM8QH+/n50uv5xfl/VhYCJt1I9ZwcZ43sye9W9tL32Cfz8bOyrcYaI3IO7tfcQMAJ4WFUzRcQFbALOqWhW1RXAqaav63Iuxz1rnu4Ze7PCgQwrmo1vEiGoRhuq3tYGTdzN7l8/ImzNZ9TI2kuNIx+Q9u3HTJ3UntT4G2h/wcWUibTBrEWVt7/92+NeynWjiKwSkdUisqogghnjtDrx51Huwfksjr2CQMmiw+ahrHilK7t27nA6mim5YoErVbWbqo5V1UwAVc0BejgbrQB4umfszAgH3N0zjPFlElWRipc/Q6nHNnK816fsiG5DsGRycfavXLl8IIlDWzD27YeZuXQ1mdnW97mo8bZovhh3f7quwGW4L9KX5XcoY3xFSFg4Le/6lLUdhpFIOC0yFhM0ogOzvv/MRkobJwSp6t+mdhGRVwBUdb0zkQpITjakHAZga4q7WLY5mk2R4edPZLMrqHLvT2TftZzt9W4h0S+a2rKbPkeH0/67jsx7vivjvviQzfuOOp3WnCGvimZV3X6qraDCGeMrGna5FgbP5feQJsTJMTouvYulr/Xk8D5rdTaF6qJT7Lu40FMUhpQj7tUAQ6LZm+ReSMKmmzNFkV9sDar2HUrUfzaR2Gs022I7gQjn62J6b3qEyGHxfPfKAH786UeOnkh3Oq75H7wqmsWtv2e6OUSkioi0KphoxviWqLLVqP3QL6xuNIQUgkhImUXQB61Z/92btiCKKVAiMlhEVgN1PV3jcretQPHsIufpmkFYGfZ65mguH2V9QU0R5hdAVLNeVLtrEn4Prmdny/+wL6gacXKcnqkTuXTBtRx5rSkT376PX+cvIi3Tluz2Nd52z3gfaAP089xPAv6br4mM8WHi50/j3o9x/Ka5LA06j3BSqL/sGba/3oGUXTY+1hSYL3F3hfvOc5u7tVDV/k4GKzB/Fs1x7PesBlg2KsjBQMbkH4koS+VLH6XckBWk3TiNzTX6c9xVipqyh8uPjuSCqRex/oU2TBz+LIvXbCA7x7oD+gJvZ89orarNRWQ5gKoe9UxNZEyJUq5Kbco8MoWfJ35M41UvUDVlDVkjzmdv/G2U7/ks+Nt/C5N/VDURSOSvBoviz1M0Z4fGcCQ5A3+XEBtmRbMpZkQIrtaamtVaQ/bbHFs7jUPzPqPSvhk0YyPN9mwke+ybLHE1Zm+li6ncri/N6lS36esc4m3RnCkifoACiEgcYJ9LmxLJ5efiwqtuZVPCJSz88mF6pE2m/Kr32bf5F0oP+JzAMrWdjmiKCRGZo6rtRSQJz/U39yHcUzdHOhSt4HiK5pSA0gCUiQiyQsEUb37+lIq/hFLxl0D6CfYuGkfq0jFUObaA1roKdq4i86vXWeBqwoGql1CtbR/ia1W1/xeFyNui+R1gAlBWRF4AegNP5HsqY4qQ2lUrUuXhz/hywrd0XPMfqiRvIPX99uy74EXKdbwJbAUzc45Utb3nNsLpLIXGUzQf9ysFQJwNAjQlSVA45TvcCB1uRFOOsGv+WDJWfkuV44tpq8tg2zIytr7EQldjDlTqSoVWV9GsQR38bR2BAuVV0ayqX4jIUv6a6P7yYjfNkTFnIcjfj/59rmZpfCs2jrmLi7JnE/LrA2xeN43qAz7EFVrK6YjGFC25S2jjXg2wTIR1zTAlk4SWplKX26DLbeiJg+yY9w3Zq8dTJWk5bXQF7FxBzo7XWCH12FWuC7Etr6J5fBOCA/ycjl7snFHRLCIP/MtDF4vIxar6hrcnFpFtuAcSZgNZqnqqVaiMKVJa1K1G0kPj+frzN7hs1xvU3P8TB4a2xtXnY2LrtXc6niniRGQUcK+qHvPcjwaGqupNjgYrCCfcRfPBHHfPEyuajQEJj6NK17ug611o8iF2LviWjNWTqHxsIc1ZT/N96+H799jwXVU2l+5AUINLaXreBcRG2Mwz+eFMW5pzPxKsC7TEPYIb3KO3Z53D+S9Q1UPn8HpjfE5ESCB9bx3CrPnnEzf1DupnbyHr68vYWG8wdXs/Df72y9+ctfjcghn+HIzdzME8BSf1CAD7skIBKBNh3TOMyUvCYqmc2wKdlsjeJd9zYsUEKh2aQz3ZTr2j22Hu5xyYU4qfQ1qTWfMiarXpSa2KZRDrNnhWzqhoVtVnAURkGtBcVZM8958BxhZYOmOKsI5t2nCg3kx+Gvkg3Y+Ppe6G/7L/le8Iu/Jtwut3Of0BjPknl4hEq+pRABEpjfdjU4qGtEQA9qS5/8gsE2l/bBrzbyQ4ivLt+0P7/pCZxuG1Mzi47Dtid/9CmewDXJg2FdZOJX3NYyzya8ihch2Jjr+Eps0SCA0KcDp+keHtxbYKkJHnfgZQ7SzPrcA0EVHgQ1UdfpbHMcZnlYmOotv9H/HzlIupvvAJambuhG+u5EC1XpTp/TqEl3E6oilahgLzRGSc534f4AUH8xSc1GMA7Ej1FM3WPcOYMxMQTEzTS4lpeimokrJrFbsWjCdoyzQqp66ndc4K2LMC9rzDzillmBfRmpyaF1Gz1cXUqBBnrdD/g7dF82fAIhGZgLvovQIYdZbnbqeqe0SkDDBdRDao6p9dPURkEDAIoEqVKmd5CmOcJyJceMlVbGvRmc9HP03vE19SZtsk0t6cgd9FzxDQ6iZw2YANc3qqOlpElgCdPbuuVNV1TmYqMJ6W5u3J/kCWdc8w5myIEFq5CXUqNwGeJSfpINuXfE/qup+ocGg+lTlA5RPfw8rvSV/hzzJXPQ6UaUdY/YtolNCB0uH2/y4vUfVulRkRaQ508NydparLzzmEu5vHCVV9/VSPJyQk6JIlS871NMY4Lis7hy+m/EbVRc/QybUCgJS4JoT2HQkxNZ0NZwqMiCzNr8HOItIE6Ii74WK2qq7Mj+Pmp3O+Zmelw/NlwOVPC77icEomC//ThbI27Zwx+Scnm8TNC9mz5HtCtv9KlbQNuPJMA39YI1gb1IzkSh2IbdKdxg0alpgZOf7tmu11XzhVXQYsO8cwYYBLVZM8X3cFnjuXYxpTFPj7uRjQ4wJWN2nGM1+8z22pH1H+4EpSP+hM4A3j8avcwumIxoeJyL3ArcC3uBc2+VxEhqvqu84my2eeVmYNLsXhI5mIQEyYrbJpTL5y+RFVuy1RtdsCkJN8hB3LpnBi3XTKHJhLbPYBOmbMgi2zYMsLbB9flk1hLciq0p7yTbvSoHZNAkrYvNBODSApC0zw9JvxB75U1Z8cymJMoWtcuRS1H3yUN3+4kDbLHqITK0n95BKO9xxJ2WaXOB3P+K6bgdaqmgwgIq8A84HiVTR7+jNnB7qnm4sJC7JFG4wpYK6w0lTpcB10uA5USdv3OzuX/EDO5l+plLiUquynaspk2DAZNvyHjVqF7ZHN0artKB/fhfo1qxf7ItqRollVtwBNnDi3Mb4iOMCPx65oxez6XzNlzG1cnDML/4n9mbf9Jdr0GmSDMcypCO657XNle/YVL2nHAEgPsDmajXGECMHl61L7srrAg5CdxfGtS9m74if8ts+mUtJK6soO6ibtgDUTYQ38rpXZHtGM7CptKde4M/Vr1yLIv3h15/CqaBb3b/HrgBqq+pyIVAHKqeqiAklnTAnQoV4Fjj04lhkj7qLL0bG0XfEIX+3YzoUDnybOigXzdyOBhZ7B2AJcDnziaKKC4OmekeoKB6CsTTdnjLP8/Ims1ZrIWq3d97PSObxxLgdX/0zAzvlUSl5DHdlJnRM7Yd13sA62anm2hjYmvUIrouufT4OGTYkMKdrdrLxtaX4fyME9cvs53Cv6fYt7wRNjzFkqFRZMl3tHsHZsFRquHUq/I//l4zf2UqX3S1zUsJzT8YyPUNU3RGQm0A530TxAVVc4GqogeLpnnPAUzfbHozE+xj+ImIadiWnomcgnK52jmxawf/UM/HfOo2LSKqrLXqqn7oXN02Dz8xz6PpI5gY1IKtOC0BptqdG4DZXiShWpT1W9LZpbq2pzEVkOf65GVbT/bDDGhzTs8xRHK1QmcvoD3KzjGff1If6v4YPcf0V7woOK5xoW5vREJAnIO9WR5HlMVTWy8FMVIE/3jCR1rwZoRbMxPs4/iOj65xNd/3z3/exMjm9dxr7Vv5KzYz7lElcQm3OM9pnzYPc82P0u6bMCWCU12B8VD5VaUaZhR+rVru3TM3R4+1s4U0T88Fy8RSQOd8uzMSafRLcbSE5MObLG3EhvZpG+fh6/bOpAlUsfomHz9k7HMw5Q1QinMxQqT9F81FM0x4Zb0WxMkeIX8PfuHKqkH9jE7pW/krZlLqUOL6dC5g6asBESN0LiWFgLuzWWrUH1SIptSmj1VlRp2JZq5WN9pjXa26L5HWACUEZEXgB6A0/keypjSjhXvYtx3TqNE1NfIHTbNC7O/hW++5XtM1tQofuDBNS7GFzFe5SyKcE8fZoPZ4UAEGNFszFFmwhBZetQo2sd4DYANOUo+9fP5ciG2QTsXUKFE2upKIeomDEH9syBPZA1x8UGqcqe8IZklW1KZM3W1GjQnLKlwh35NrwqmlX1CxFZCnTBMwhFVdcXSDJjSrryTQi/cQwZBzazavzL1Nv7HVWPL4Ux15IRVY3A8x+CptfaaoIlSIkZjO3p03wg0100x4ZbL0BjihsJjaZcix6Ua9HDvSMnm5Q969izZjbp2xcReXglFTK2UZ+t1D+xFU78AJshZWoQK13VORjRgOzyzYiu3ZqadeOJiQgp8Mxns7jJBmBDAWQxxpxCYJmaJNz+Ect+f5x5Y9/k8owfqJS4Db67C104DOn6PNTsfNrjmGKhZAzG9rQ078twrwAYZy3NxhR/Lj9CKzWmVqXGwB0AaPoJDm1axMEN82DPcmIS11Amex9NdAMc3wDHx8NGOPF9MCtcNTgUUY+ccvFE1WxJ9XpNKROVvy3S3k45Nwq4V1WPee5HA0NV9aZ8TWWM+YfmdapR56GhvPDdAFKXj+WhgDFU2r8WPrsCal0IF/0flG3gdExTsErGYGxPn+bdae5vzfo0G1MySVA4sY06E9vor4ahnBOH2b9xPkc3LcS1dzlxSeuIyTlMU10Hx9e5C+nfIXVyIKtd1aj54M+EhkflSx5vW5rjcwtm+POC3SxfkhhjTis8yJ+X+jRnesOK9BnXnl7p33FnwCQi/vgZNv8Cza6HCx6HiLJORzUFo2QMxva0NO9ND8bPJUSFBDgcyBjjK1zhMZRv0YPyud06gOykA+zfuIBjm5cg+1YRc3wdZbL3U14P5lvBDN4XzS4RiVbVowAiUvosjmGMOUcXNShL0/sv5LHxZTh/fSfu9f+W/v4z8Fs2ClaPg0uHQtN+Tsc0+S93MHbZYj0Y29On+TihxIQF4nL5xsh5Y4xv8osoQ4WEnlRI6PnnvpzkI7j2bcnX83hb8A4F5onIOM/9PsAL+ZrIGHNG4iKC+OiGBL5ZXJbnfohmVHo3ng3+mg6ZS2Di7bB7CXR7CfyL36f3JVgZ4DUgnuI8GNvT0pyoYVSwrhnGmLPgCitN6Zql8/eY3jxZVUcDVwH7gQPAlar6Wb4mMsacMRGhb6sqTLm3A6UqN+D61AcYknkLWRIAi0fAp5fA8T1OxzT5JxL4AOiLu4vGEWfjFICcnD+L5iRCibWFTYwxPuJsJnrdCywCVgKxItIxfyMZY7xVNSaMMbe14eFudRmnXbgq7Un2SyzsWgwfdoSts52OaPKBqj6rqg2BO4EKwG8i8rPDsfJXhnvxw0y/ULLxIzbMPikxxvgGr4pmEbkFmAVMBZ713D6T/7GMMd7y93Nx5wW1mHhnO5LjmnJx6vPMzWkEyQfR0b1g3rugevoDmaLgALAPOIy7y0bxkXYcgHR/9yKI1tJsjPEV3rY034t7PtDtqnoB0Aw4mO+pjDFnrVHFKH64uz0928ZzQ8ajvJ/VE9FsmPYEfHsL5GQ7HdGcJREZLCIzgRlALHCrqsY7myqfpScBkCq5S2hbS7Mxxjd4OxAwTVXTRAQRCVLVDSJSt0CSGWPOWnCAH8/0bMiF9cvy0NgwVp6oydCADwhfMw6Nq4uc/4jTEc3ZqQrcp6ornA5SYDxF8wlyVwO0lmZjjG/wtqV5l4iUAiYC00VkEmCjjIzxUe1rxzL1vo4ENu7F4Mx7Acj59SWObpjlcDJzNlR1SEEXzCLiJyLLReQHz/3SIjJdRDZ5bqML8vy5RXOSuluaY6xoNsb4iDMqmkUkd4aMmap6TFWfAZ4EPgYuL5hoxpj8EBUawLv9mtH76hv4hJ74kUPa1wOZsXyj09GMb7oXyDuN3RBghqrWxt0tZEiBnj3dPXPGsRz3EtoxNhDQGOMjzrSluYWIVAVuEpFoz6Imq4E5QP4u7G2MKRC9mlbk4nv+yx8BdSnPITLG38kjY1dwIj3L6WjGR4hIJeBSYESe3b2AUZ6vR1HQDSWeluaj2e4W5tJWNBtjfMSZFs0fAD8B9YClnm1JnltjTBFQvnQkNW7/hgz/cC72W0zAilF0f2sWi7YWv+l+zVl5C3iEvy/NXVZV9wJ4bk85W4eIDBKRJSKy5ODBcxgf7imaD2da0WyM8S1nVDSr6juqWh/4RFVrqGr1vLcFnNEYk49cMdUJvPwdAJ4K+JywYxu5Zvh8XvlpAxlZOad5tSmuRKQHcEBVl57N61V1uKomqGpCXFzc2QfxFM3HNZjQQD+CA/zO/ljGGJOPvB0I+GJ+nfjkwSbGmELU6Cpodj1BZPBlqQ8JIZ1hMzfT679z2bgvyel0xhntgJ4isg34GugsIp8D+0WkPIDn9kCBpsgzENBamY0xvsTbonliPp775MEmxpjCdPErEFuHmNSt/NZ4KlVKh7J+73Eue28OI2ZvISfHFkIpSVT1MVWtpKrVcC/T/Yuq9ge+AwZ4njYAmFSgQTyLmyQRYkWzMcaneDtP8wIRaamqi8/lpHkGm7wAPHAuxzLGnKXAMOg9Ej7qTNzvX/NrhT/YQQYHT6TDdPh9tj/VY8MJ8j/N39Y3/VQ4eY1TXgbGiMjNwA6gT4GeLd1dNJ9QK5qNMb7F26L5AuB2z8d3yYAAehYrUr2Fe7BJxL89QUQGAYMAqlSp4uXhjTFnpFwjuPhl+OF+/PYsoTpQPbdGzsBmYS+hVHUmMNPz9WGgS6GdPM/iJrGhVjQbY3yHt0Xzxed6wryDTUSk0789T1WHA8MBEhIS7HNiYwpKwk1Q/Xw4sf/PXcdSM/nwt80s2XYUgDY1Y7i1Q3UiggOcSmlKityiWUOoYy3Nxhgf4m3RPOBf9j/nxTFyB5tcAgQDkSLyuafvnDHGCTE13ZtHKeCRuh0Zs2Qnz36/jsV/ZPPNgUxe692AjnXOYWYEY04nd/YMQom2otkY40O8HQiYnGfLxt3yXM2bA/yPwSbGGB8iIlzTsgpT7u1Ai6rR7D+ezg2fLOLpSWtIzch2Op4prvL0abbVAI0xvsSrollVh+bZXgA6ARULJJkxxidUjQljzG1teLhbXfxdwqj52+nx7mxW7TrmdDRTHOXp02wDAY0xvsTbluaThQJnvbiJqs5U1R7nmMEYU8D8XMKdF9Ri4p3tqFUmnM0Hk7ny/Xm8O2MTWdm2IIrJJznZkHGCHIRkgq1oNsb4FK+KZhFZLSKrPNtaYCPwdsFEM8b4mkYVo/jh7vYMbFeNrBxl6PTf6fPhfLYdSnY6mikOMk4AkEIIisuKZmOMT/F2IGDeVuEsYL+qZuVjHmOMjwsO8OPpyxrSpV5ZHh63kuU7jnHx27N5okd9rm1VBRFxOqIpqvLMnAFY0WyM8Sneds9oBRxR1e3AQNwT3jfP/1jGGF/XvnYsP93bkV5NK5Camc3jE9Zw06eLOZCU5nQ0U1R5VgM8rsH4uYRIm+LQGONDvC2an1TVJBFpD3QDRgHD8j+WMaYoiAoN4O2+zXinXzMig/35deNBur81m6lr9zkdzRRFeQYBlgoJwOWyTy2MMb7D26I5d56pS4FhqjoJsM/PjCnhejapwNT7O9KhdixHkjO47bOlPDx2JUlpmU5HM0VJnu4ZpUKtldkY41u8LZp3i8iHwNXAZBEJOotjGGOKofJRIYwa2IqnL2tAkL+LsUt3cfHbs1m09YjT0UxR4Zmj+TihRNsS2sYYH+NtwXs1MBXorqrHgNLAw/kdyhhTNLlcwsB21fnxnvY0qhjJrqOpXDN8Pq/8tIGMLJuazpyGp6U5WUMoZUWzMcbHeLu4SYqqjlfVTZ77e1V1WsFEM8YUVbXKRDB+cDvu7lwLAYbN3Eyv/85l474kp6MZX5a3T7N1zzDG+BjrWmGMKRCB/i4e7FqXsbe3pWpMKOv3Hueyd+cwYvYWcnLU6XjGF3nmaT5BMNFWNBtjfIwVzcaYAtWiajST7+lAv1ZVyMjO4fkf13PdiIXsPpbqdDTja/7snhFs3TOMMT7HimZjTIELC/LnpSsbM+KGBGLDA5m/5TDd35zFhOW7ULVWZ+ORWzRb9wxjjA/yakVAEXngFLsTgaWquiJfEhljiq0LG5TlpyodeWz8aqav28/936zk53UHeOGKRtayaP7qnqHBNnuGMcbneNvSnADcDlT0bIOATsBHIvJI/kYzxhRHseFBDL++Ba9eFU9YoB8/rt5L1zdn8dvvB52OZpyW7i6araXZGOOLvC2aY4Dmqvqgqj6Iu4iOAzoCN+ZzNmNMMSUiXN2yMlPu7UhC1WgOJKUz4JNFPDVpDakZ2ac/gCme/hwIGEKpEGtpNsb4Fm+L5ipARp77mUBVVU0F0vMtlTGmRKgSE8o3t7Xhke51CfATRs/fzqXvzmbVrmNORzNO+HNFwGCiw6yl2RjjW7wtmr8EFojI0yLyDDAX+EpEwoB1+R3OGFP8+bmEOzrVYsId7ahdJpwtB5O58v15vDNjE1nZtiBKSaIZebpnWEuzMcbHeLu4yf8BtwLHPNvtqvqcqiar6nX5H88YU1I0qhjF93e35+b21cnKUd6Y/ju9P5jP1kPJTkczhcXTpznTL5SQQD+HwxhjzN+dzZRzWUCO5zYzf+MYY0qy4AA/nuzRgC9uaU35qGBW7DzGJW/P5ouF221quhJAPd0zAkIiHU5ijDH/5FXRLCL3Al8AsUAZ4HMRubsgghljSq52tWL56b6OXN60AqmZ2Tw+YQ03fbqYA0lpTkczBSU7C1dWKjkqBIVGOJ3GGGP+wduW5puB1qr6tKo+BZyHu7uGMcbkq6iQAN7q24x3+zUjMtifXzcepNubs/hpzV6no5mC8Gd/5mBKhVl/ZmOM7/G2aBYg73xQ2Z59xhhTIC5rUoFp959Ph9qxHE3J5PbPl/HQ2JUkpVnvsGIlT9FsC5sYY3yRt0XzSGChiDwjIs8CC4FPvD2piASLyCIRWSkiaz3HMsaYUyoXFcyoga145rIGBPm7GLd0F93fms3CLYedjmbyS+7CJhpsC5sYY3ySt7NnvAEMBA57tgGq+uZZnDcd6KyqTYCmQHcROe8sjmOMKSFcLuHGdtX58Z72NKoYye5jqfT9aAEvTVlPepYtiFLk5VnYJDLEimZjjO/xP5MniUgSkHfouuR5TFXVq6HO6h4Gf8JzN8Cz2dB4Y8xp1SoTwfjB7Xj3l03899c/+PC3Lfy28SBv9W1KvXI260KR9efCJiFEWdFsjPFBZ9TSrKoRqhqZZ4vIs53VbykR8RORFcABYLqqLjzp8UEiskRElhw8ePBsTmGMKaYC/V082LUu4wa3pVpMKBv2JdHz3bl8NGsLOTn293eR5Cmakwm2otkY45POZp7mfKGq2araFKgEtBKRRic9PlxVE1Q1IS4uzpGMxhjf1rxKND/e04F+raqQkZ3DC5PXc+2IBew+lup0NOOtPN0zrGg2xvgix4rmXKp6DJgJdHc2iTGmKAoL8uelKxvz8YAEYsMDWbDlCN3fnMWE5btsQZSiJM9AwMhgK5qNMb7HkaJZROJEpJTn6xDgQmCDE1mMMcVDl/plmXpfR7o2KEtSehb3f7OSO79cxtHkDKejmTORkds9w1qajTG+yamW5vLAryKyCliMu0/zDw5lMcYUEzHhQXx4fQte6x1PWKAfk1fvo9tbs/jtdxsX4fM8Lc0n1Po0G2N8kyNFs6quUtVmqhqvqo1U9Tknchhjih8RoU9CZX66ryMtq0VzICmdAZ8s4qlJa0jNsKnp/o2IVBaRX0VkvWf+/Hs9+0uLyHQR2eS5jS6QAHkWN7Gi2Rjjixzv02yMMQWhculQvh7Uhke71yPATxg9fzuXvjOblTuPOR3NV2UBD6pqfeA84E4RaQAMAWaoam1ghud+vtPcKecIISL4jGZDNcaYQmVFszGm2PJzCYM71WTine2oUzacLYeSuXLYPN7+eRNZ2TlOx/MpqrpXVZd5vk4C1gMVgV7AKM/TRgGXF8T5s1LdRXO2fxj+fvaryRjje+zKZIwp9hpWiOK7u9pzS/vqZOcob/78O70/mM+WgydO/+ISSESqAc2AhUBZVd0L7sIaKPMvrzmnufWzU4+7vwgMP7vQxhhTwKxoNsaUCMEBfjzRowFf3tKaClHBrNh5jEvfmcPnC7bb1HR5iEg48C1wn6oeP9PXnevc+mmB0ezWGLKDS3n9WmOMKQxWNBtjSpS2tWKZcl9HrmhWkdTMbJ6YuIaBny7mwPE0p6M5TkQCcBfMX6jqeM/u/SJS3vN4edyruOa7tW3eoF36u+yPaFgQhzfGmHNmRbMxpsSJCgngzWua8t61zYgKCWDmxoN0e2sWP63Z63Q0x4iIAB8D61X1jTwPfQcM8Hw9AJhUEOdPTM0EsIVNjDE+y4pmY0yJ1SO+AlPv60iH2rEcTcnk9s+X8eCYlRxPy3Q6mhPaAdcDnUVkhWe7BHgZuEhENgEXee7nu+OeotmmmzPG+Cqb18cYU6KViwpm9E2t+GzBdl74cT3fLtvFgi2HeePqJrSuEeN0vEKjqnMA+ZeHuxT0+ROtaDbG+DhraTbGlHgiwg1tqvHjPR2IrxTF7mOp9P1oAS9NXk96li2IUhisaDbG+Dormo0xxqNWmXC+HdyWezrXQoAPZ22h13tzWb/3jCeRMGfpz6I51IpmY4xvsqLZGGPyCPBz8UDXuowb3JZqMaFs2JdEr/fmMnzWZrJzbGq6gnI8LQuwgYDGGN9lRbMxxpxC8yrR/HhPB65tXYWM7BxenLyB6z9eaCsJFhDrnmGM8XVWNBtjzL8IC/LnxSsa88mNCcSGB9Gkcilb4rmAhAS4iAz2t+4ZxhifZbNnGGPMaXSuV5ap95UiwroOFJgPr09wOoIxxvxPVjQbY8wZiAkPcjqCMcYYB9nnjMYYY4wxxpyGFc3GGGOMMcachhXNxhhjjDHGnIYVzcYYY4wxxpyGFc3GGGOMMcachhXNxhhjjDHGnIYVzcYYY4wxxpyGqKrTGU5LRA4C2714SSxwqIDiFDX2XrjZ+/AXey/+UljvRVVVjSuE8/gEu2afE3sv/mLvxV/svXBz9JpdJIpmb4nIElW15aWw9yKXvQ9/sffiL/Ze+Ab7d/iLvRd/sffiL/ZeuDn9Plj3DGOMMcYYY07DimZjjDHGGGNOo7gWzcOdDuBD7L1ws/fhL/Ze/MXeC99g/w5/sffiL/Ze/MXeCzdH34di2afZGGOMMcaY/FRcW5qNMcYYY4zJN1Y0G2OMMcYYcxrFqmgWke4islFE/hCRIU7ncZKIbBOR1SKyQkSWOJ2nMInIJyJyQETW5NlXWkSmi8gmz220kxkLy7+8F8+IyG7Pz8YKEbnEyYyFQUQqi8ivIrJeRNaKyL2e/SXy58KX2HX7LyX1um3X7L/YNfsvvnjdLjZFs4j4Af8FLgYaAP1EpIGzqRx3gao2LYFzO34KdD9p3xBghqrWBmZ47pcEn/LP9wLgTc/PRlNVnVzImZyQBTyoqvWB84A7PdeHkvpz4RPsun1KJfG6/Sl2zc71KXbNzuVz1+1iUzQDrYA/VHWLqmYAXwO9HM5kHKCqs4AjJ+3uBYzyfD0KuLwwMznlX96LEkdV96rqMs/XScB6oCIl9OfCh9h129g1Ow+7Zv/FF6/bxalorgjszHN/l2dfSaXANBFZKiKDnA7jA8qq6l5w/0cEyjicx2l3icgqz0eBJeJjz1wiUg1oBizEfi6cZtftv7Pr9l/s/+bfldhrNvjOdbs4Fc1yin0leT69dqraHPfHnneKSEenAxmfMQyoCTQF9gJDHU1TiEQkHPgWuE9Vjzudx9h1+yR23TanUmKv2eBb1+3iVDTvAirnuV8J2ONQFsep6h7P7QFgAu6PQUuy/SJSHsBze8DhPI5R1f2qmq2qOcBHlJCfDREJwH3h/UJVx3t228+Fs+y6nYddt//G/m96lNRrNvjedbs4Fc2LgdoiUl1EAoG+wHcOZ3KEiISJSETu10BXYM3/flWx9x0wwPP1AGCSg1kclXux8biCEvCzISICfAysV9U38jxkPxfOsuu2h123/8H+b3qUxGs2+OZ1u1itCOiZhuUtwA/4RFVfcDaRM0SkBu5WCgB/4MuS9F6IyFdAJyAW2A88DUwExgBVgB1AH1Ut9oMt/uW96IT7Yz4FtgG35fYPK65EpD0wG1gN5Hh2/wd3/7gS93PhS+y67VaSr9t2zf6LXbP/4ovX7WJVNBtjjDHGGFMQilP3DGOMMcYYYwqEFc3GGGOMMcachhXNxhhjjDHGnIYVzcYYY4wxxpyGFc3GGGOMMcachhXNplgQkU4i8oPn654iMiSfjttPRB4/ad+NIvJefhzfGGNKIrtmm6LI3+kAxvwbz8Tm4lkF6Yyp6nfk3wIJ3YF38ulYxhhTbNk12xR31tJsfIqIVBOR9SLyPrAMqCwiw0RkiYisFZFn8zy3u4hsEJE5wJV59v/ZqiAin4pI7zyPnfDclheRWSKyQkTWiEiHU2QR3BPKL/sfeS8VkfkiEus51wciMltEfheRHp7n+InI6yKyWkRWicjd5/o+GWOML7BrtilJrKXZ+KK6wEBVvQNARB5X1SMi4gfMEJF44HfgI6Az8AfwjZfnuBaYqqoveI4beornNANW6r+sACQiVwAPAJeo6lH39ZpqwPlATeBXEakFDASqA81UNUtESnuZ1RhjfJlds02JYEWz8UXbVXVBnvtXi8gg3D+v5YEGuD8l2aqqmwBE5HNgkBfnWAx8IiIBwERVXXGK53QHpvzL6y8AEoCuqno8z/4xno8mN4nIFqAecCHwgapmAZSEpWCNMSWKXbNNiWDdM4wvSs79QkSqAw8BXVQ1HvgRCPY8fCZrwGfh+Tn3fHQXCKCqs4COwG7gMxG54RSv7QpM+5fjbgEigDon7T85kwJyhlmNMaYosmu2KRGsaDa+LhL3BTlRRMoCF3v2bwCqi0hNz/1+//L6bUALz9e9gAAAEakKHFDVj4CPgeZ5XyQiUYC/qh7+l+Nux90nb7SINMyzv4+IuDy5agAbcV/EbxcRf8+x7aM+Y0xxZddsU2xZ0Wx8mqquBJYDa4FPgLme/Wm4P9r70TOoZPu/HOIj4HwRWQS05q8WkU7AChFZDlwFvH3S6y4Cfj5Nto3AdcDYPL8INgK/4f6I8HZPzhHADmCViKzE3TfPGGOKHbtmm+JM/qW/vDElmoiMAEac1E/vdK/5FPhBVccVWDBjjDH/YNdsUxhsIKAxp6CqtzidwRhjzJmxa7YpDNbSbIwxxhhjzGlYn2ZjjDHGGGNOw4pmY4wxxhhjTsOKZmOMMcYYY07DimZjjDHGGGNOw4pmY4wxxhhjTuP/AZCniCJuADgOAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vd_n2403 = vcdisk(rad, sb_n2403, z0=0.4) # z0=0.4 kpc from Fraternali et al. (2002): https://ui.adsabs.harvard.edu/abs/2002AJ....123.3124F\n", "sb_exp_n2403 = expdisk_sb(rad, 1.004e10, 1.39) # numbers taken from http://astroweb.cwru.edu/SPARC/\n", "\n", "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, rad, sb_exp_n2403, vcdisk(rad, sb_exp_n2403), label='exp-disk')\n", "plot_sb_vdisk(ax, rad, sb_n2403, vd_n2403, label='observed')" ] }, { "cell_type": "markdown", "id": "2503de91", "metadata": {}, "source": [ "The $V_{\\star, \\rm disk}$ curve obtained with `vcdisk` directly from the ellipse photometry of NGC 2403 is much more structured between $1-5\\rm \\,kpc$, which is where the surface brightness has dips and peaks. \n", "*Capturing this rich structure is* **essential** *to rotation curve modelling*." ] }, { "cell_type": "code", "execution_count": null, "id": "ce124cc4", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.13" } }, "nbformat": 4, "nbformat_minor": 5 }