Gr8 stars kinematics/dynamics

GR8-stars.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "b5d14139",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pathlib\n",
    "\n",
    "import astropy.coordinates as coord\n",
    "import astropy.table as at\n",
    "import astropy.units as u\n",
    "import gala.dynamics as gd\n",
    "import gala.potential as gp\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from pyia import GaiaData\n",
    "\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "844de63a",
   "metadata": {},
   "outputs": [],
   "source": [
    "path = pathlib.Path(\"~/data/Misc/gr8stars_paper1_results_revision7.csv\").expanduser()\n",
    "\n",
    "tbl = at.Table.read(path)\n",
    "tbl.rename_column(\"ra_j2000\", \"ra\")\n",
    "tbl.rename_column(\"dec_j2000\", \"dec\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9fa46a90",
   "metadata": {},
   "outputs": [],
   "source": [
    "g = GaiaData(tbl)\n",
    "c = g.get_skycoord()\n",
    "\n",
    "galcen = c.transform_to(coord.Galactocentric(galcen_distance=8.275 * u.kpc))\n",
    "w = gd.PhaseSpacePosition(galcen.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "319c26eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "vR = w.cylindrical.v_rho\n",
    "vphi = (w.cylindrical.rho * w.cylindrical.pm_phi).to(\n",
    "    u.km / u.s, equivalencies=u.dimensionless_angles()\n",
    ")\n",
    "vz = w.v_z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "062f27de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$\\\\sqrt{v_R^2 + v_z^2}$ [km/s]')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 368,
       "width": 584
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 5))\n",
    "ax.hist2d(\n",
    "    -vphi.to_value(u.km / u.s),\n",
    "    np.sqrt(vR**2 + vz**2).to_value(u.km / u.s),\n",
    "    bins=(np.linspace(-300, 300, 128), np.linspace(0, 300, 128)),\n",
    "    norm=mpl.colors.LogNorm(),\n",
    "    cmap=\"magma\",\n",
    ")\n",
    "ax.set_xlabel(r\"$-v_\\phi$ [km/s]\")\n",
    "ax.set_ylabel(r\"$\\sqrt{v_R^2 + v_z^2}$ [km/s]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c6799f48",
   "metadata": {},
   "outputs": [],
   "source": [
    "Rg = -w.angular_momentum()[2] / (229 * u.km / u.s)\n",
    "Rg = Rg.to(u.kpc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c35680a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Guiding radius $R_g$ [kpc]')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 368,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 5))\n",
    "ax.hist(Rg.to_value(u.kpc), bins=np.linspace(2, 12, 64))\n",
    "ax.set_xlabel(\"Guiding radius $R_g$ [kpc]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa48fe00",
   "metadata": {},
   "source": [
    "# Orbits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "8d5664b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "mw = gp.MilkyWayPotential(version=\"v2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "5d17354f",
   "metadata": {},
   "outputs": [],
   "source": [
    "orbits = mw.integrate_orbit(w, dt=2 * u.Myr, t1=0, t2=500 * u.Myr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a0b6ee30",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/aprice-whelan/projects/scratch/.venv/lib/python3.12/site-packages/numpy/_core/fromnumeric.py:3860: RuntimeWarning: Mean of empty slice.\n",
      "  return _methods._mean(a, axis=axis, dtype=dtype,\n",
      "/Users/aprice-whelan/projects/scratch/.venv/lib/python3.12/site-packages/numpy/_core/_methods.py:145: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  ret = ret.dtype.type(ret / rcount)\n"
     ]
    }
   ],
   "source": [
    "zmax = orbits.zmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "5fd3a76d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$z_{\\\\rm max}$ [kpc]')"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 368,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 5))\n",
    "ax.hist(zmax.to_value(u.kpc), bins=np.linspace(0, 5, 64))\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_xlabel(r\"$z_{\\rm max}$ [kpc]\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a644bc0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "scratch",
   "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": "3.12.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}