jobovy/orbit-in-bar-frame.ipynb

## orbit-in-bar-frame.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\n",
    "import astropy.units as u\n",
    "from galpy import potential\n",
    "from galpy.orbit import Orbit\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Making a movie of an Orbit near the bar's cororation resonance including the shape of the bar\n",
    "\n",
    "First, let's set up a few things:\n",
    "* The background potential: ``MWPotential2014``\n",
    "* The bar potential: ``SoftenedNeedleBarPotential``\n",
    "* An orbit near its corotation radius\n",
    "\n",
    "To make sure we get outputs in physical units (kpc, km/s, etc.), we'll turn on physical outputs. We start with defining the potential:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "background_potential = potential.MWPotential2014\n",
    "potential.turn_physical_on(background_potential,ro=8.,vo=220.)\n",
    "Omegab= 40.*u.km/u.s/u.kpc\n",
    "bar_potential= potential.SoftenedNeedleBarPotential(amp=1e10*u.Msun,\n",
    "                                                    a=5.*u.kpc,\n",
    "                                                    b=1.*u.kpc,\n",
    "                                                    c=1.*u.kpc,\n",
    "                                                    pa=25.*u.deg,\n",
    "                                                    omegab=Omegab)\n",
    "total_potential = background_potential + bar_potential"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we plot the surface density and approximate it with an ellipse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/bovy/Repos/galpy/galpy/util/plot.py:682: UserWarning: The following kwargs were not used by contour: 'aspect'\n",
      "  cont = pyplot.contour(\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "potential.plotSurfaceDensities(\n",
    "    bar_potential,justcontours=True,ncontours=5,nxs=101,nys=101\n",
    ");\n",
    "plt.gca().set_aspect('equal')\n",
    "# Draw an ellipse in the x-y plane with the same aspect ratio as the bar\n",
    "# potential.\n",
    "plt.gca().add_patch(Ellipse((0,0), 1.4, 1.4/5., angle=25, fill=False, color='r'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ellipse model is good (not perfect) so we'll use it to plot the shape of the bar.\n",
    "\n",
    "Next, we set up an orbit near the corotation radius:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2D orbit\n",
    "Rc= potential.lindbladR(background_potential,bar_potential.OmegaP(),m='corot')\n",
    "orb= Orbit([Rc,15.*u.km/u.s,potential.vcirc(background_potential,Rc,quantity=True),0.*u.rad])\n",
    "ts= numpy.linspace(0.,0.5,1001)*u.Gyr\n",
    "orb.integrate(ts,total_potential)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The orbit in the inertial frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x28771c580>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "orb.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The orbit in the bar frame (to do this, we need to temporarily turn physical outputs off and calculate physical positions ourselves by multiplying by 8):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "orb.turn_physical_off()\n",
    "orb.plot(d1=f'8.*R*cos(phi-{bar_potential.OmegaP()}*t)',\n",
    "         d2=f'8.*R*sin(phi-{bar_potential.OmegaP()}*t)')\n",
    "orb.turn_physical_on(ro=8.,vo=220.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now an animation of the orbit in the frame of the bar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img3c638630cbce4f4dba914b3589373c7d\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider3c638630cbce4f4dba914b3589373c7d\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim3c638630cbce4f4dba914b3589373c7d.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim3c638630cbce4f4dba914b3589373c7d.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select3c638630cbce4f4dba914b3589373c7d\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_3c638630cbce4f4dba914b3589373c7d\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_3c638630cbce4f4dba914b3589373c7d\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_3c638630cbce4f4dba914b3589373c7d\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_3c638630cbce4f4dba914b3589373c7d\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_3c638630cbce4f4dba914b3589373c7d\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_3c638630cbce4f4dba914b3589373c7d\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img3c638630cbce4f4dba914b3589373c7d\";\n",
       "    var slider_id = \"_anim_slider3c638630cbce4f4dba914b3589373c7d\";\n",
       "    var loop_select_id = \"_anim_loop_select3c638630cbce4f4dba914b3589373c7d\";\n",
       "    var frames = new Array(99);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAGwCAYAAADITjAqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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