{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/webbjere/Codes/clustertools/clustertools/analysis/profiles.py:34: FutureWarning: all profiles are setup such that the returned radial bins and profile values are in linear space and not normalized by the effective radius. Previously select profiles had unique returns.\n",
      "  warnings.warn('all profiles are setup such that the returned radial bins and profile values are in linear space and not normalized by the effective radius. Previously select profiles had unique returns.',FutureWarning)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import clustertools as cts\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.8.1.dev0'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import galpy\n",
    "galpy.__version__\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Profiles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load a snapshot of a cluster in file 00000.dat, which has position units of pc and velocity units of km/s in clustercentric coordinates. Stellar masses are in solar units and were generated using a Salpeter IMF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "cluster=cts.load_cluster('snapshot',filename='00000.dat',units='pckms',origin='cluster',ofilename='orbit.dat',ounits='kpckms')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once initialized, many profiles can be measured with ``clustertools``. Profiles can only be called externally via ``profile_name(cluster)``. Every profile has a ``plot=True`` flag that allows for the profile to be plotted in addition to returning the profile data. In many cases, the default is to normalize the radial bins by the cluster's half-mass radius (``normalize=True``)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perhaps the most common measured profile is a globular cluster's density profile, with ``rho_prof`` returning the radial bin locations, the density within each bin, and the number of stars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprof, pprof, nprof=cts.rho_prof(cluster,plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively if one wants to know the mass in each bin:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprof, mprof, nprof=cts.m_prof(cluster,plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the cumulative mass profile is of interest, set ``cumulative=True``"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprof, mprof, nprof=cts.m_prof(cluster,plot=True,cumulative=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another interpretation of the mass profile is the circular velocity profile. For convenience, ``vcirc_prof`` also return the radius of maximal circular velocity and the maximum circular velocity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.07714811938 0.627209383198\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprof, vcprof, rvmax, vmax = cts.vcirc_prof(cluster,plot=True,nrad=None)\n",
    "print(rvmax,vmax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the release of Gaia DR2, it is now possible to analyze the velocity dispersion profiles of globular clusters. The ``sigv_prof`` function allows for both the total velocity dispersion profile to be measured and the velocity dispersion profile over just the radial, tangential or azimuthal direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, sigvprof=cts.sigv_prof(cluster,plot=True)\n",
    "rprofn_r, sigvprof_r=cts.sigv_prof(cluster,coord='r',plot=True)\n",
    "rprofn_phi, sigvprof_phi=cts.sigv_prof(cluster,coord='phi',plot=True)\n",
    "rprofn_theta, sigvprof_theta=cts.sigv_prof(cluster,coord='theta',plot=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ability to measure the radial, tangential, and azimuthal velocity dispersion profiles also leads to the orbital anisotropy profile to be calculated:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV4AAAFeCAYAAADNK3caAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAUdElEQVR4nO3dz3IbV3bH8d+RaS0T/hHX1EB5gISEqrhNhpoHmBLlhbdyKw+QSDVPkFCpLL1gj7daRFLlAULOeMsFoMk2VTYUrmn+SbKTWDxZ4ELTagIgIAKnG8D3U+Uyu3FJX8P0Twenb982dxcAIM6dqicAAIuG4AWAYAQvAAQjeAEgGMELAMEIXgAItlT1BCLdu3fP79+/X/U0ZsrJyYnW19ernsZM4z28nVl9/9rt9i/u3nfiCxW89+/fV6vVqnoaM6XZbPKe3RLv4e3M6vtnZseDXqPVAADBCF4ACEbwYqgsy6qewszjPbydeXz/bJH2amg2mz6LvSIAs8fM2u7e7PcaFS8ABCN4ASAYwQsAwQheAAhG8AJAMIK3Yu3jc33/409qH59XPRUAQRbqluG6aR+f69sfjvTh8kp3l+7o1dNtbW2sVD0tAFNGxVuho86pPlxe6cqlj5dXOuqcVj0lAAEI3gptN9Z0d+mOvjLp66U72m6sVT0lAAFoNVRoa2NFr55u66hzqu3GGm0GYEEQvBXb2lghcIEFQ6sBAIIRvAAQjOAFgGAELwAEI3gBIBjBCwDBCF4ACEbwAlPEJkjohxsogClhEyQMQsU7Y6igZgebIGEQKt4ZsmgVVPv4fKb3sehtgvTx8opNkPAZgneG9KugZjGQRjEPf8iwCRIGIXhnyCJVUPPyhwybIKEfgneGLFIFtUh/yGDxmLtXPYeBzKwh6bGkd5I2JeXufjFg7KaknXT4UNJ35bHNZtNbrdbU5ovJmvUeLxabmbXdvdnvtbpXvPvu/kiSzKwjaU/Ss/IgM1uW1HT3l+n4saQ/SNqKmyqG+ZIQ5WM65lVtl5Olane1d+zuHUlPBgxvSnpROD6UtJkCGRXrXSj71//4L337wxFL4bDwahu86rYWzsonUyB/xt0PJe0WTjXS+YtpTQ6jYz0r8Lk6B++qpIvSuTNJy/0Gu/u7wuE3kl5OZVYYGw/1BD5X9x7v2FJ7YbPXGy46OTlRs/nnXneWZcqyLHB2i2mRVmNgceV5rjzPi6fuDRpb21UN6QLZs2KAmtm5pK3U7x30ffvufu0CnMSqBgBxhq1qqHOr4Z0KF9d6bgjd50oX2biwBqCuahu85YBNF9VeF4+L4Zoq5LeFC2qDVkAAQKXq3uPdTVVsR9LDUgthT9KBpDyF8htJMrPe6x1JnzVcAKAOah28qertrU54W3pttzTOBAAzoLatBgCYVwQvAAQjeAEgGMELAMEIXgAIRvACQDCCFwCCEbwAEIzgBYBgBC8ABCN4ASAYwQsAwQheAAhG8AJAMIIXAIIRvAAQjOAFgGAEb021j8/1/Y8/qX18XvVUAExYrR/9s6jax+f69ocjfbi80t2lO3r1dFtbGytVTwvAhFDxTsgkK9Sjzqk+XF7pyqWPl1c66pxOYIYYBZ80EIGKdwImXaFuN9Z0d+mOPl5e6eulO9purE1wthiETxqIQvBOQL8K9Tb/w25trOjV020ddU613Vjjf/4gk/7vCAxC8E7ANCrUrY0V/qcPxicNRDF3r3oOYZrNprdaran87PbxORXqHOC/IybFzNru3uz3GhXvhFChzgf+OyICqxoAIBjBCwDBCF4ACEbwAkAwghcAghG8kMStskAklpOBW2WBYLWueM2sYWbPzWwn/X15EmPxOTblAWLVveLdd/dHkmRmHUl7kp5NYCwKuFUWiFXb4DWzhqTV3rG7d8zsifqE6ThjcR2b8gCxahu8kjYlnZVPmlnD3Tu3GIs+uFUWiFPn4F2VdFE6dyZp+UvHnpycqNn8854VWZYpy7LbzRIAJOV5rjzPi6fuDRpb5+CduPX1dU1rdzIAi61cyJnZL4PG1nlVQ7/qtl9lO+5YAKhUnYP3nQoXzHoG9GzHGQsAlapt8JZDM61ceF087q3VvWkspo8734DR1b3Hu2tmzyV1JD109+LysD1JB5LyEcZiirjzDRhPrYM3VbIv0+Hb0mu7o47FdPGQSGA8tW01YHb07nz7ysSdb8AIal3xYjZw5xswHoIXE8Gdb8DoaDUAQDCCFwCCEbwAEIzgnRPcwADMDi6uzQFuYABmCxXvHBj30T1Ux0C1qHjnwDiP7qE6BqpH8M6BcW5g4PZeoHoE75wY9QYGHmwJVI/gXTDc3ovbaB+f87szAQTvAuL2XnwJrg9MDqsaAIxk3NUzGIzgDcDyLcwDtv+cHFoNU8bHM8wLrg9MDsE7ZSzfwjzh+sBk0GqYMj6eAbNv0u1CKt4p4+MZMNum0S4keAPw8QyYXdNoF9JqAIAhptEupOIFgCGm0S4keAHgBpNuF9JqAIBgBC8ABCN4ASAYwQsAwQheAAhG8AJAMIIXAILVdh2vmTUkPZb0TtKmpNzdLwaM3ZS0kw4fSvpu0FgAqFptg1fSvrs/kiQz60jak/SsPMjMliU13f1lOn4s6Q+StuKmCgCjq2WrIVW7q71jd+9IejJgeFPSi8LxoaTNFMgAUDu1DF51Wwtn5ZMpkD/j7oeSdgunGun8xbQmBwC3UddWw6qki9K5M0nL/Qa7+7vC4TeSXvYbd3Jyomaz+ek4yzJlWXabeQKAJCnPc+V5Xjx1b9DYugbvF0nthc1eb7hsfX1drVYrdlIAFkK5kDOzXwaNDQ1eM8skPRgy5CC1DvpVt/2q4LK9QaELAHURGrzunt88SlJ3Cdlq+WS6yNaXmT1XushmZsv0eAHUVS0vrpUDNl1Ue108Lq5aSEvI3hbCdtAKCGDmTfrBi4hX5x7vbqpiO5IeuntxDe+epANJeQrlN5JkZr3XO5JGra6BmTGNBy8iXm2DN1W9vdUJb0uv7ZbGmYAFMI0HLyJeLVsNAPqbxoMXEa+2FS+A66bx4EXEI3iBGTPpBy8iHq0GAAhG8AJAMIIXAIIRvAAQjOAFgGAELwAEI3gBIBjBCwDBCF4ACEbwAkAwghcAghG8ABCM4AWAYAQvAAS7MXjN7C8iJgIAi2Jg8JrZ35jZT5L+28xOzexvC6/9tZn91szuR0yyKjxUEMA0DNsI/dfu/ldS93Hpkv7ZzB5I+o2khqQzSU0z+1nS37n7/017spF4qCCAaRkWvO97X6THpv+9mbUkPXf3P/ZeM7MdSX+U9HBak6wCDxUEMC3Deryrfc6dlU+4+6Gkb8zsHyY2qxrgoYIApmVYxXtoZk/d/Yebfoi7d8zs/U3jZgkPFQQwLQOD193fm9kbM/tHSQfu/p/u/pshP8snP71q8VBBANMw9CnD7v4/kv4lrXD4Tt1wPZN06O7/WxrOZ3EAGMFIj3d39z9J+pMkmdlfSnpoZg11g3hF3X7w/rQmCYyqfXxOewi1N1LwFqUq+A/pL0ndNb+StsxsM53quPt/TmSGwIhYAohZMXbw9lOsiCXJzH5lZr9193+fxM8HRsESQMyKiQRvmbu/V2EdMBChtwTw4+UVSwBRa1MJXqAKLAHErCB4MVdYAohZUNttIc2sYWbPzWwn/X15xO9jdQWAWqtt8Erad/eX6Zbkt5L2bvqGtKoim/rMAOAWahm8aY3wp70i3L0j6ckI39qQdDGlaQHARNQyeCVtqs+GPCmQ+zKzx+7+dqqzAoAJqGvwrup65Xomabnf4BTInelOCQAmY15WNWyOUu2enJyo2Wx+Os6yTFlGSxjA7eV5rjzPi6fuDRpr7nGbiplZJunBkCEH7n5oZo8lPXP3R4XvPZe0lfq9xZ+5I6mVNmuXmZ27e9/1RM1m01ut1m3/NQDgRmbWdvdmv9dCK153z28eJUl6pz4bsZdDt+CJmfW+Xk4BfzhkPABUppathrSx+qfj1MN9XTo+c/eLtNysOHZ/jIAHgHB1vbgmSbvpxole2+FZ4bU9lZaXmdmymT1PX+8NWwEBAFUK7fFWjR4vgCjDerx1rngBYC4RvAAQjOAFgGAELwAEI3gBIBjBCwDBCF4ACEbwAkAwghcAghG8ABCM4AWAYAQvAAQjeAEgGMELAMEIXgAIRvACQDCCFwCCEbwAEIzgBYBgBC8ABCN4ASAYwQsAwQheAAhG8AJAMIIXAIIRvAAQjOAFgGAELwAEI3gBIBjBCwDBCF4ACLZU9QQGMbOGpMeS3knalJS7+8WQ8Y8lrUo6k3Th7ocR8wSAcdU2eCXtu/sjSTKzjqQ9Sc/6DUyh23D3lymw30jaCpspAIyhlq2GFJ6rvWN370h6MuRb9tz9ZW+suxO6AGqrlsGrbmvhrHwyBXL53Ga/rwGgruoavKuSLkrnziQt9xnbkHSR2g0dM3tuZjvTnR4AfLk693hHtSpp093fSpKZ5ZLeS1opDzw5OVGz2fx0nGWZsiyLmieAOZbnufI8L566N2isufv0Z9T7h5llkh4MGXLg7oepen3Wu7iWvvdc0lbq9xZ/5o66Pd6twjmX9KA8ttlseqvVmsS/CgAMZWZtd2/2ey204nX3/OZRkrpLyFbLJ8tBmnR0vQVxoT49YgCog1r2ePtUtQ1Jr4vHZrZcGNvpHaexnWFrfgGgSnXu8e6a2XN1K9qH7l5cw7sn6UBSr4LelfQ7M/tZ3VbGr0NnCgBjCO3xVo0eL4Aow3q8tWw1AMA8I3gBIBjBCwDBCF4ACEbwzrn28bm+//EntY/Pq54KgKTOy8lwS+3jc337w5E+XF7p7tIdvXq6ra2Na3dSAwhGxTvHjjqn+nB5pSuXPl5e6ahzWvWUAIjgnWvbjTXdXbqjr0z6eumOthtrVU8JgGg1zLWtjRW9erqto86pthtrtBmAmiB459zWxgqBC9QMrQYACEbwAkAwghcAghG8ABCM4AWAYAQvAAQjeAEgGMELAMEIXgAIRvACQDCCFwCCEbwAEIzgBYBgBC8ABCN4ASAYwQsAwQheAAhG8AJAMIIXAIIRvAAQjOAFgGAELwAEq+3j3c2sIemxpHeSNiXl7n4xZOyOpDNJjWFjAaBqtQ1eSfvu/kiSzKwjaU/SswFjH7v7y96Bme1JejH9KQLA+GrZakgV7Grv2N07kp4M+ZZHpePlKUwLACailsGrbmvhrHwyBXJfZnZgZstmtiPpzTQnBwC3UddWw6qki9K5Mw2oZN39kZm1Jb2X9E/FtkPRycmJms3mp+Msy5Rl2STmC2DB5XmuPM+Lp+4NGlvX4B1LqnJfqHthbd/M1C9819fX1Wq1wucHYP6VCzkz+2XQ2NDgNbNM0oMhQw7c/VD9q9t+VXCv/bDZC1ozO5TUNjNWNgCopdDgdff85lGSukvIVssn00W2sh1Jh8UxZpZrQFADQNVqeXGtHLCpqn1dPDaz5XR4qG74Dv0ZAFAXde7x7prZc0kdSQ/dvbiGd0/Sgbo3SnTMrFMYuyppP366ADCa2gZvqlh7F8jell7bLR1/9joA1FktWw0AMM8IXgAIRvACQDCCFwCCEbwAEIzgBYBgBC8ABCN4ASAYwQsAwQheAAhG8AJAMIIXAIIRvAAQjOAFgGAELwAEI3gBIBjBCwDBCF4ACEbwAkAwghcAghG8ABCM4AWAYAQvAAQjeAEgGMELAMEIXgAIRvACQDCCFwCCEbwAEIzgBYBgBC9G1j4+1/c//qT28XnVUwFm2lLVExjGzHYk7bn71g3jGpIeS3onaVNS7u4X05/h4mgfn+vbH4704fJKd5fu6NXTbW1trFQ9LWAm1bbiTaF7pm6Q3mTf3V+6+6Gkt5L2pjq5BXTUOdWHyytdufTx8kpHndOqpwTMrNoGr7sfuvu7m8alane18H0dSU+mObdFtN1Y092lO/rKpK+X7mi7sVb1lICZVetWw4g21a2MP2NmjRTCmICtjRW9erqto86pthtrtBmAW5iH4F2VdFE6dyZpuTzw5OREzWbz03GWZcqybJpzmytbGysELjBAnufK87x46t6gsfMQvCNbX19Xq9WqehoA5lC5kDOzXwaNDQ1eM8skPRgy5CBdIBtHv+q2XxUMALUQGrzunt88amzvVLi4Vvhn0d8FUEu1XdUwjJk1zGxZuh6waZXD6yrmBQCjqG2PN63jfZS+3tPnbYg9SQeSehX0rpk9l9SR9NDdn0XPFwBGZe5e9RzCNJtN5+IagAhm1nb3Zr/XZrLVgDil5TH4AryHtzOP7x/Bi6Hm8Zc+Gu/h7czj+0fwAkAwghcAgi3UxTUzO5F0XPU8Zsw9SQPvwMFIeA9vZ1bfvw13X+/3wkIFLwDUAa0GAAhG8AJAsNreuYZqmdmmpJ10+FDSdzxO6cuY2T53U34ZM3us7l4sZ5IuvmATrVqix4tr0j4YT3qbGqVf/t/d9Ow7XJf+AGu7u1U9l1mTfu8a7v4y7cHyZl5+BwleXJP2ydh39wfpeFnSuaQVqt7xpPD4vbuzg/yYzOzn3u/gvKHHi2vSx7ndwqlGOn9RyYRmlJk9dve3Vc9jFqVPCte+nhcEL/oqPWj0G0kvq5rLLEofjdkT+ss1JF2kTwwdM3uePonNBS6uYajUZth090dVz2XGbFLt3sqqCu+hmeWS3kuai5YNFS9uskfojidVZnNx9b1CHXWfLiPpU5trOX2SmHlUvBgobS7/In29TI93LE/MPi1kWE7PGzzkkVQj6+j6sxQv1F1WNvNY1YC+Um/tXS8ozCyb0jPz5p6ZOcvJxmdmB5J23f1i3paTUfHimt4vefq6d7qjPz9qCSNI/fEsfb2n7hI9Kt7R7Ur6nZn9rO7TyX9d8XwmhooXAIJxcQ0AghG8ABCM4AWAYAQvAAQjeAEgGMELAMEIXgAIRvACQDCCFwCCEbwAEIy9GoA+0taOjyQdqLsjVm8T7sPSJvHA2AheYLB/k/R7dcP2hZm9kbSmwj6xwJdgkxygJFW7LXWr3N9L+lXamnBHUot9iXFbBC8wgJntS7pw9xdVzwXzhYtrwGA76vZ4gYmi4gX6SJvB/8yTIzANVLxAfzywElND8AL9PVB6/BEwabQaACAYFS8ABCN4ASAYwQsAwQheAAhG8AJAMIIXAIIRvAAQjOAFgGAELwAE+381/L6kYACu1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, betaprof=cts.beta_prof(cluster,plot=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also related to kinematics is the mean velocity and mean square velocity profiles within the cluster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, vprof=cts.v_prof(cluster,plot=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, vprof=cts.v2_prof(cluster,plot=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For an estimate of the dynamical state of cluster, one can measure the radial variation in the stellar mass function using ``alpha_prof`` (Webb, J.J. & Vesperini, E. 2016, MNRAS, 463, 2383). When using ``alpha_prof``, it is important to note:\n",
    "\n",
    "(1) If the mass range is not specified the entire mass spectrum will be used. \n",
    "\n",
    "(2) When plotting, the x-axis will be ln(r) based on (Webb, J.J. & Vesperini, E. 2016, MNRAS, 463, 2383)\n",
    "\n",
    "(3) delta_alpha is calculated to be d(alpha)/d(ln(r/rm)) as per Webb, J.J. & Vesperini, E. 2016, regardless of whether normalize is True or False. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, aprof, dalpha, edalpha, ydalpha, eydalpha=cts.alpha_prof(cluster,mmin=0.1,mmax=0.8, plot=True, normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at how velocity dispersion changes as a function of stellar mass is also a proxy for a cluster's dynamical state, with the power-law slope eta evolving towards (but never reaching) -0.5. An eta of -0.5 corresponds to a state of complete energy equipartition. Similar to ``alpha_prof`` above, one can measure how eta changes with clustercentric distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, eprof, deta, edeta, ydeta, eydeta=cts.eta_prof(cluster,plot=True, normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, an alternative probe for the degree of energy equipartition in a cluster, the meq profile of the cluster can be measured:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rprofn, meqprof, dmeq, edmeq, ydmeq, eydmeq=cts.meq_prof(cluster,plot=True, normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Edit Metadata",
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.1"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}