star_distribution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b87529bc-f6d7-4e1e-903c-1493b7df38b4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import unyt\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets\n",
    "import rebound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "231c1e4a-ac8b-4046-8805-c559c4bebbbe",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "radius = 2 * unyt.ly\n",
    "nstars = 25\n",
    "bh_mass = 1e7\n",
    "t_final = 10000 * unyt.year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "47ae033a-dedc-4d50-9b3f-4c25caf764fe",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "xyz_init = unyt.ly * np.random.normal(loc = 0.0, scale = radius.in_units(\"ly\").v / 2.5, size = (nstars, 3))\n",
    "xyz_init.convert_to_units(\"AU\")\n",
    "masses = np.random.normal(loc = 2.5, scale = 1.0, size = nstars)\n",
    "masses = np.maximum(masses, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ab02f036-f274-4283-a400-899316d7140a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.units = ('day', 'AU', 'Msun')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "48e2850a-b308-4c3d-9353-2a693d1d4e99",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5851bbdb-2ca9-452a-8228-5771ea3ec6e5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000000.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bh_mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "21a7bd86-513a-4025-bc5b-9e00271634af",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sim.add(m = bh_mass, x = 0, y = 0, z = 0)\n",
    "for i in range(nstars):\n",
    "    sim.add(x = xyz_init[i,0], y = xyz_init[i,1], z = xyz_init[i,2], m = masses[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9826308f-7cf7-49aa-b9ad-f5b8fb3e1604",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def output_orbits(output_fn):\n",
    "    sim.save_to_file(output_fn, interval = t_final.in_units(\"day\").v / 500)\n",
    "    sim.integrate(t_final.in_units(\"day\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ea3f779-d3ff-47f5-ae9e-9e38a857bc55",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(7305.0)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_final.in_units(\"day\").v / 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ad22b625-001b-4e4a-a574-c5b09ca19f0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "!rm output.bin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c39b549-f52e-42b4-a60e-c07b1aeb1023",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "output_orbits(\"output.bin\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8638313c-6a34-4382-962d-1de8a273cfc1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3652500.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim.t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c98a8f51-42b4-468d-bf43-b03a43d2d518",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import hashlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "66686f3d-6583-4dc7-939c-f38a3de08d15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "676ce44a71e34dc8ba4a173bbf5ecbe0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='sim_index', max=500), Output()), _dom_classes=('widget-i…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sims = rebound.Simulationarchive(\"output.bin\")\n",
    "xyz_final = np.zeros((nstars + 1, 3), dtype=\"f8\")\n",
    "\n",
    "xyz_data = {}\n",
    "\n",
    "@ipywidgets.interact(sim_index = (0, len(sims) - 1, 1))\n",
    "def plot_it(sim_index = 0):\n",
    "    sim = sims[sim_index]\n",
    "    sim.serialize_particle_data(xyz = xyz_final)\n",
    "    xyz_data[sim_index] = xyz_final.copy() - xyz_final[0,:]\n",
    "    plt.scatter(xyz_final[:,0], xyz_final[:,1])\n",
    "    plt.xlim(-radius.in_units(\"AU\"), radius.in_units(\"AU\"))\n",
    "    plt.ylim(-radius.in_units(\"AU\"), radius.in_units(\"AU\"))\n",
    "    plt.title(f\"Time: {(sim.t * unyt.day).in_units(\"yr\"):0.1f} - {hashlib.md5(xyz_final.tobytes()).hexdigest()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "027c7afd-57aa-45e4-9394-2fd0d59e6231",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3652500.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sims[-1].t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e387111f-a836-4b76-b87f-b0dcaed9274a",
   "metadata": {},
   "outputs": [],
   "source": [
    "pos0 = xyz_data[0] * unyt.AU\n",
    "posf = xyz_data[max(xyz_data.keys())] * unyt.AU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "15efce5a-8820-40e4-af58-05a900601ee2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "unyt_array([[ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 4.54068864e-03,  8.75331389e-03, -4.77308003e-04],\n",
       "       [-9.92672802e-01, -6.73521553e-02, -6.27244543e-01],\n",
       "       [-4.15054557e-03, -3.42593969e-03, -4.50053708e-02],\n",
       "       [-4.65323541e-01, -1.09264624e-01,  3.23800112e-01],\n",
       "       [-2.59857722e-01,  1.43935608e-01,  8.95889498e-02],\n",
       "       [-2.60344589e-02, -8.29214744e-02,  1.07228716e-01],\n",
       "       [-3.31453672e-01, -3.60508112e-01,  3.76360471e-01],\n",
       "       [ 2.80154058e-01,  2.85096267e-01, -2.09095493e-01],\n",
       "       [ 1.38698038e-02,  6.63859297e-03, -3.08114666e-02],\n",
       "       [ 1.98103806e-03,  2.84541121e-03,  4.42289387e-03],\n",
       "       [-5.22201590e-03,  7.82887346e-03,  2.51875533e-03],\n",
       "       [-5.27507444e-02, -1.18087017e-01, -7.17559827e-02],\n",
       "       [-4.59162258e-01, -2.14492768e-01,  3.83028854e-01],\n",
       "       [-2.24926784e-01, -1.27286507e-01,  3.82691683e-02],\n",
       "       [-5.77614350e-02, -1.08504969e-02,  6.18369318e-02],\n",
       "       [-2.45436856e+03,  5.83879974e+03, -1.76103740e+03],\n",
       "       [ 1.87806701e-01, -3.47703225e-01,  1.11181883e-01],\n",
       "       [ 7.76244760e-04, -4.93308393e-04,  1.02023067e-03],\n",
       "       [-1.21414547e-01, -2.10892704e-01,  8.41964328e-03],\n",
       "       [ 1.30702033e-01,  7.59403241e-03,  7.79612199e-02],\n",
       "       [-3.51916284e-01,  3.25895215e-01,  1.62272823e-01],\n",
       "       [-1.84706063e-02,  4.82695100e-03,  9.95490177e-04],\n",
       "       [ 4.00994678e-02,  5.78861640e-02, -1.58146743e-02],\n",
       "       [-2.69521045e-02, -2.63708778e-03,  3.81912226e-02],\n",
       "       [-8.62559225e-03,  3.22731267e-02,  2.39083245e-02]], 'ly')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(posf - pos0).in_units(\"ly\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "bcb4a380-618e-44b0-b6b4-2ec1b6213b0b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x7f71e831e030>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hexbin(xyz_final[:,0], xyz_final[:,1], gridsize = 32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d543e3dc-f347-489d-8e54-178ddfc0af1d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "rebound",
   "language": "python",
   "name": "rebound"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}