{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "107e4ef2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:06.865023Z",
     "iopub.status.busy": "2026-08-11T01:27:06.864851Z",
     "iopub.status.idle": "2026-08-11T01:27:07.290359Z",
     "shell.execute_reply": "2026-08-11T01:27:07.289463Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "78b6ded6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:07.292593Z",
     "iopub.status.busy": "2026-08-11T01:27:07.292333Z",
     "iopub.status.idle": "2026-08-11T01:27:07.300232Z",
     "shell.execute_reply": "2026-08-11T01:27:07.299315Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%run ../tutorials/nb_setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16be264b",
   "metadata": {},
   "source": [
    "# Defining the MilkyWayPotential model\n",
    "\n",
    "## Introduction\n",
    "\n",
    "`gala` provides simplified mass models for the Milky Way to use in orbit integration or dynamical calculations. Some of these mass models come from other publications or packages (e.g., the Law and Majewski 2010 model `LM10Potential`). Some of the potential models are defined and provided by Gala. This document describes how we determined the parameters of the Gala Milky Way models.\n",
    "\n",
    "We determine parameters of the Gala Milky Way models using compilations of enclosed mass measurements of the Milky Way and measurements of the mass structure of the Galactic disk. We then fit for the parameters of a multi-component model (e.g., disk, bulge, halo, etc.) using these measurements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6d004f7f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:07.302202Z",
     "iopub.status.busy": "2026-08-11T01:27:07.302034Z",
     "iopub.status.idle": "2026-08-11T01:27:08.162613Z",
     "shell.execute_reply": "2026-08-11T01:27:08.161697Z"
    }
   },
   "outputs": [],
   "source": [
    "import astropy.units as u\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from astropy.constants import G\n",
    "from astropy.io import ascii\n",
    "from scipy.optimize import leastsq\n",
    "\n",
    "import gala.potential as gp\n",
    "from gala.units import galactic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "361db562",
   "metadata": {},
   "source": [
    "## `MilkyWayPotential` version 1 (circa 2017)\n",
    "\n",
    "This model was previously just known as `MilkyWayPotential` in Gala, now known as \"version 1,\" and represents an older model based on measurements that are now out of date. We still describe the process of fitting for this model, for completeness.\n",
    "\n",
    "The source data for this model was compiled from published values and is included with Gala:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3ad90814",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:08.165165Z",
     "iopub.status.busy": "2026-08-11T01:27:08.164829Z",
     "iopub.status.idle": "2026-08-11T01:27:08.177593Z",
     "shell.execute_reply": "2026-08-11T01:27:08.176604Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><i>Table length=16</i>\n",
       "<table id=\"table140190154433856\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>r</th><th>Menc</th><th>Menc_err_neg</th><th>Menc_err_pos</th><th>ref</th></tr></thead>\n",
       "<thead><tr><th>float64</th><th>float64</th><th>float64</th><th>float64</th><th>str27</th></tr></thead>\n",
       "<tr><td>0.01</td><td>30000000.0</td><td>10000000.0</td><td>10000000.0</td><td>Feldmeier et al. (2014)</td></tr>\n",
       "<tr><td>0.12</td><td>800000000.0</td><td>200000000.0</td><td>200000000.0</td><td>Launhardt et al. (2002)</td></tr>\n",
       "<tr><td>8.1</td><td>89502860861.52429</td><td>4994562473.797714</td><td>4858963492.608627</td><td>Bovy et al. (2012)</td></tr>\n",
       "<tr><td>8.3</td><td>110417867208.19055</td><td>4475949382.696884</td><td>4387023236.020782</td><td>McMillan (2011)</td></tr>\n",
       "<tr><td>8.4</td><td>102421035406.90356</td><td>16733918715.629944</td><td>15468328224.531876</td><td>Koposov et al. (2010)</td></tr>\n",
       "<tr><td>19.0</td><td>208023299175.30438</td><td>44317988008.38101</td><td>34833267089.920685</td><td>Kuepper et al. (2015)</td></tr>\n",
       "<tr><td>50.0</td><td>539884832748.48975</td><td>19995734543.31433</td><td>268490735257.4718</td><td>Wilkinson &amp; Evans (1999)</td></tr>\n",
       "<tr><td>50.0</td><td>529886965173.18726</td><td>9997867269.659302</td><td>38536752776.21277</td><td>Sakamoto et al. (2003)</td></tr>\n",
       "<tr><td>50.0</td><td>399914690706.92847</td><td>109976539940.53711</td><td>72696676468.2511</td><td>Smith et al. (2007)</td></tr>\n",
       "<tr><td>50.0</td><td>419910425325.7268</td><td>39991469076.968506</td><td>38172735113.64386</td><td>Deason et al. (2012)</td></tr>\n",
       "<tr><td>60.0</td><td>399914690957.5188</td><td>69985070910.63354</td><td>64344945146.92987</td><td>Xue et al. (2008)</td></tr>\n",
       "<tr><td>80.0</td><td>689852841359.0248</td><td>299936018002.3314</td><td>110361048549.1029</td><td>Gnedin et al. (2010)</td></tr>\n",
       "<tr><td>100.0</td><td>1399701417307.7747</td><td>899808054059.3811</td><td>831336271726.1903</td><td>Watkins et al. (2010)</td></tr>\n",
       "<tr><td>120.0</td><td>539884832260.29584</td><td>199957345314.72906</td><td>123854764645.32489</td><td>Battaglia et al. (2005)</td></tr>\n",
       "<tr><td>150.0</td><td>750000000000.0</td><td>250000000000.0</td><td>250000000000.0</td><td>Deason et al. (2012)</td></tr>\n",
       "<tr><td>200.0</td><td>679854974257.2006</td><td>409912558030.05396</td><td>313652012195.06256</td><td>Bhattacherjee et al. (2014)</td></tr>\n",
       "</table></div>"
      ],
      "text/plain": [
       "<Table length=16>\n",
       "   r           Menc        ...    Menc_err_pos                ref            \n",
       "float64      float64       ...      float64                  str27           \n",
       "------- ------------------ ... ------------------ ---------------------------\n",
       "   0.01         30000000.0 ...         10000000.0     Feldmeier et al. (2014)\n",
       "   0.12        800000000.0 ...        200000000.0     Launhardt et al. (2002)\n",
       "    8.1  89502860861.52429 ...  4858963492.608627          Bovy et al. (2012)\n",
       "    8.3 110417867208.19055 ...  4387023236.020782             McMillan (2011)\n",
       "    8.4 102421035406.90356 ... 15468328224.531876       Koposov et al. (2010)\n",
       "   19.0 208023299175.30438 ... 34833267089.920685       Kuepper et al. (2015)\n",
       "   50.0 539884832748.48975 ...  268490735257.4718    Wilkinson & Evans (1999)\n",
       "   50.0 529886965173.18726 ...  38536752776.21277      Sakamoto et al. (2003)\n",
       "   50.0 399914690706.92847 ...   72696676468.2511         Smith et al. (2007)\n",
       "   50.0  419910425325.7268 ...  38172735113.64386        Deason et al. (2012)\n",
       "   60.0  399914690957.5188 ...  64344945146.92987           Xue et al. (2008)\n",
       "   80.0  689852841359.0248 ...  110361048549.1029        Gnedin et al. (2010)\n",
       "  100.0 1399701417307.7747 ...  831336271726.1903       Watkins et al. (2010)\n",
       "  120.0 539884832260.29584 ... 123854764645.32489     Battaglia et al. (2005)\n",
       "  150.0     750000000000.0 ...     250000000000.0        Deason et al. (2012)\n",
       "  200.0  679854974257.2006 ... 313652012195.06256 Bhattacherjee et al. (2014)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mwdata1 = ascii.read(\"data/MW_mass_enclosed.csv\")\n",
    "mwdata1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53f9d71d",
   "metadata": {},
   "source": [
    "We can now plot the above data and uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "deff9ff9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:08.179406Z",
     "iopub.status.busy": "2026-08-11T01:27:08.179178Z",
     "iopub.status.idle": "2026-08-11T01:27:08.906079Z",
     "shell.execute_reply": "2026-08-11T01:27:08.905065Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 590
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"tight\")\n",
    "\n",
    "ax.errorbar(\n",
    "    mwdata1[\"r\"],\n",
    "    mwdata1[\"Menc\"],\n",
    "    yerr=(mwdata1[\"Menc_err_neg\"], mwdata1[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(r\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cbee64e",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "We now need to assume some form for the potential. We use a four component potential model consisting of a Hernquist\n",
    "([1990](https://ui.adsabs.harvard.edu/#abs/1990ApJ...356..359H/abstract))\n",
    "bulge and nucleus, a Miyamoto-Nagai\n",
    "([1975](https://ui.adsabs.harvard.edu/#abs/1975PASJ...27..533M/abstract))\n",
    "disk, and an NFW\n",
    "([1997](https://ui.adsabs.harvard.edu/#abs/1997ApJ...490..493N/abstract))\n",
    "halo. We fix the parameters of the disk and bulge to be consistent with\n",
    "previous work ([Bovy\n",
    "2015](https://ui.adsabs.harvard.edu/#abs/2015ApJS..216...29B/abstract) -\n",
    "please cite that paper if you use this potential model) and vary the scale\n",
    "mass and scale radius of the nucleus and halo, respectively. We'll fit for\n",
    "these parameters in log-space, so we'll first define a function that returns a\n",
    "`gala.potential.CCompositePotential` object given these four parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3121c5e3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:08.907896Z",
     "iopub.status.busy": "2026-08-11T01:27:08.907692Z",
     "iopub.status.idle": "2026-08-11T01:27:08.912117Z",
     "shell.execute_reply": "2026-08-11T01:27:08.911286Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_potential(log_M_h, log_r_s, log_M_n, log_a):\n",
    "    mw_potential = gp.CCompositePotential()\n",
    "    mw_potential[\"bulge\"] = gp.HernquistPotential(m=5e9, c=1.0, units=galactic)\n",
    "    mw_potential[\"disk\"] = gp.MiyamotoNagaiPotential(\n",
    "        m=6.8e10 * u.Msun, a=3 * u.kpc, b=280 * u.pc, units=galactic\n",
    "    )\n",
    "    mw_potential[\"nucl\"] = gp.HernquistPotential(\n",
    "        m=np.exp(log_M_n), c=np.exp(log_a) * u.pc, units=galactic\n",
    "    )\n",
    "    mw_potential[\"halo\"] = gp.NFWPotential(\n",
    "        m=np.exp(log_M_h), r_s=np.exp(log_r_s), units=galactic\n",
    "    )\n",
    "\n",
    "    return mw_potential"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97f3fc0d",
   "metadata": {},
   "source": [
    "We now need to specify an initial guess for the parameters - let's do that (by\n",
    "making them up), and then plot the initial guess potential over the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0386796c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:08.913920Z",
     "iopub.status.busy": "2026-08-11T01:27:08.913732Z",
     "iopub.status.idle": "2026-08-11T01:27:08.926101Z",
     "shell.execute_reply": "2026-08-11T01:27:08.925199Z"
    }
   },
   "outputs": [],
   "source": [
    "# Initial guess for the parameters- units are:\n",
    "#     [Msun, kpc, Msun, pc]\n",
    "x0 = [np.log(6e11), np.log(20.0), np.log(2e9), np.log(100.0)]\n",
    "init_potential = get_potential(*x0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6b047edc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:08.927777Z",
     "iopub.status.busy": "2026-08-11T01:27:08.927590Z",
     "iopub.status.idle": "2026-08-11T01:27:09.778474Z",
     "shell.execute_reply": "2026-08-11T01:27:09.777515Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 590
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.logspace(-3, 3, 256) * u.kpc\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"tight\")\n",
    "\n",
    "ax.errorbar(\n",
    "    mwdata1[\"r\"],\n",
    "    mwdata1[\"Menc\"],\n",
    "    yerr=(mwdata1[\"Menc_err_neg\"], mwdata1[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "# Use symmetry coordinates for spherical mass_enclosed calculation\n",
    "fit_menc = init_potential.mass_enclosed(R=r)\n",
    "ax.loglog(r.value, fit_menc.value, marker=\"\", color=\"#3182bd\", linewidth=2, alpha=0.7)\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(r\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3eefc286",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "It looks pretty good already! But let's now use least-squares fitting to\n",
    "optimize our nucleus and halo parameters. We first need to define an error\n",
    "function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4d208ddb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:09.780540Z",
     "iopub.status.busy": "2026-08-11T01:27:09.780152Z",
     "iopub.status.idle": "2026-08-11T01:27:09.784183Z",
     "shell.execute_reply": "2026-08-11T01:27:09.783209Z"
    }
   },
   "outputs": [],
   "source": [
    "def err_func(p, r, Menc, Menc_err):\n",
    "    pot = get_potential(*p)\n",
    "    model_menc = pot.mass_enclosed(R=r * u.kpc).to(u.Msun).value\n",
    "    return (model_menc - Menc) / Menc_err"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7908f3e4",
   "metadata": {},
   "source": [
    "Because the uncertainties are all approximately but not exactly symmetric,\n",
    "we'll take the maximum of the upper and lower uncertainty values and assume\n",
    "that the uncertainties in the mass measurements are Gaussian (a bad but simple\n",
    "assumption):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a68d1743",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:09.785888Z",
     "iopub.status.busy": "2026-08-11T01:27:09.785717Z",
     "iopub.status.idle": "2026-08-11T01:27:10.208552Z",
     "shell.execute_reply": "2026-08-11T01:27:10.207615Z"
    }
   },
   "outputs": [],
   "source": [
    "err = np.max([mwdata1[\"Menc_err_pos\"], mwdata1[\"Menc_err_neg\"]], axis=0)\n",
    "p_opt, ier = leastsq(err_func, x0=x0, args=(mwdata1[\"r\"], mwdata1[\"Menc\"], err))\n",
    "assert ier in range(1, 4 + 1), \"least-squares fit failed!\"\n",
    "fit_potential = get_potential(*p_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "045395fe",
   "metadata": {},
   "source": [
    "Now we have a best-fit potential! Let's plot the enclosed mass of the fit potential over the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4c6afd50",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:10.210699Z",
     "iopub.status.busy": "2026-08-11T01:27:10.210347Z",
     "iopub.status.idle": "2026-08-11T01:27:10.907989Z",
     "shell.execute_reply": "2026-08-11T01:27:10.907050Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 590
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.logspace(-3, 3, 256) * u.kpc\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"tight\")\n",
    "\n",
    "ax.errorbar(\n",
    "    mwdata1[\"r\"],\n",
    "    mwdata1[\"Menc\"],\n",
    "    yerr=(mwdata1[\"Menc_err_neg\"], mwdata1[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "fit_menc = fit_potential.mass_enclosed(R=r)\n",
    "ax.loglog(r.value, fit_menc.value, marker=\"\", color=\"#3182bd\", linewidth=2, alpha=0.7)\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(r\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab415224",
   "metadata": {},
   "source": [
    "This potential model can be loaded and used in Gala with:\n",
    "```\n",
    "import gala.potential as gp\n",
    "potential = gp.MilkyWayPotential(version=\"v1\")\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49b5fa1d",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## `MilkyWayPotential` version 2 (circa 2022)\n",
    "\n",
    "This model was previously known as `MilkyWayPotential2022` in Gala, now known as `MilkyWayPotential` \"version 2,\" and represents an updated model of the Milky Way based on more recent measurements of the halo and disk structure.\n",
    "\n",
    "The source data for this model was compiled from published values and is included with Gala — here we use the Eilers et al. (2019) circular velocity measurements from APOGEE for mass enclosed measurements within the disk region:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f92ae231",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:10.909784Z",
     "iopub.status.busy": "2026-08-11T01:27:10.909601Z",
     "iopub.status.idle": "2026-08-11T01:27:10.918958Z",
     "shell.execute_reply": "2026-08-11T01:27:10.918119Z"
    }
   },
   "outputs": [],
   "source": [
    "eilers = ascii.read(\"data/Eilers2019-circ-velocity.txt\")\n",
    "\n",
    "mwdata2 = mwdata1.copy()\n",
    "\n",
    "# remove old measurements within disk region:\n",
    "mwdata2.remove_rows([2, 3, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa2a81c9",
   "metadata": {},
   "source": [
    "Here we convert the circular velocity measurements to enclosed mass measurements, to be consistent with the other input data. We also adopt a 5% uncertainty on the enclosed mass measurements:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e97587b4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:10.920809Z",
     "iopub.status.busy": "2026-08-11T01:27:10.920632Z",
     "iopub.status.idle": "2026-08-11T01:27:10.933197Z",
     "shell.execute_reply": "2026-08-11T01:27:10.932379Z"
    }
   },
   "outputs": [],
   "source": [
    "eilers_r = eilers[\"R\"][eilers[\"R\"] < 15] * u.kpc\n",
    "eilers_v = eilers[\"v_c\"][eilers[\"R\"] < 15] * u.km / u.s\n",
    "eilers_M = (eilers_v**2 * eilers_r / G).to(u.Msun)\n",
    "for r, M in zip(eilers_r, eilers_M):\n",
    "    mwdata2.add_row(\n",
    "        [r.value, M.value, 0.05 * M.value, 0.05 * M.value, \"Eilers et al. (2019)\"]\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b5eb8ab5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:10.934958Z",
     "iopub.status.busy": "2026-08-11T01:27:10.934788Z",
     "iopub.status.idle": "2026-08-11T01:27:11.532109Z",
     "shell.execute_reply": "2026-08-11T01:27:11.531061Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 590
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.logspace(-3, 3, 256) * u.kpc\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"tight\")\n",
    "\n",
    "ax.errorbar(\n",
    "    mwdata2[\"r\"],\n",
    "    mwdata2[\"Menc\"],\n",
    "    yerr=(mwdata2[\"Menc_err_neg\"], mwdata2[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(r\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73d0ce49",
   "metadata": {
    "lines_to_next_cell": 2
   },
   "source": [
    "For hte new model, we use the same bulge component as with v1, but we now use a mixture of Miyamoto-Nagai disk models to represent an approximately radially exponential and vertically sech^2 disk density profile:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b0d38dc7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:11.534004Z",
     "iopub.status.busy": "2026-08-11T01:27:11.533812Z",
     "iopub.status.idle": "2026-08-11T01:27:11.538115Z",
     "shell.execute_reply": "2026-08-11T01:27:11.537320Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_potential_v2(log_M_h, log_r_s, log_M_n, log_a, log_M_d):\n",
    "    mw_potential = gp.CCompositePotential()\n",
    "\n",
    "    # Fixed bulge component\n",
    "    mw_potential[\"bulge\"] = gp.HernquistPotential(m=5e9, c=1.0, units=galactic)\n",
    "\n",
    "    # Scale radius and height are fixed to Bland-Hawthorn & Gerhard (2016) values\n",
    "    mw_potential[\"disk\"] = gp.MN3ExponentialDiskPotential(\n",
    "        m=np.exp(log_M_d) * u.Msun,\n",
    "        h_R=2.6 * u.kpc,\n",
    "        h_z=300 * u.pc,\n",
    "        units=galactic,\n",
    "        sech2_z=False,\n",
    "    )\n",
    "\n",
    "    mw_potential[\"nucl\"] = gp.HernquistPotential(\n",
    "        m=np.exp(log_M_n), c=np.exp(log_a) * u.pc, units=galactic\n",
    "    )\n",
    "    mw_potential[\"halo\"] = gp.NFWPotential(\n",
    "        m=np.exp(log_M_h), r_s=np.exp(log_r_s), units=galactic\n",
    "    )\n",
    "\n",
    "    return mw_potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b305a9c3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:11.539793Z",
     "iopub.status.busy": "2026-08-11T01:27:11.539619Z",
     "iopub.status.idle": "2026-08-11T01:27:11.552104Z",
     "shell.execute_reply": "2026-08-11T01:27:11.551258Z"
    }
   },
   "outputs": [],
   "source": [
    "x0 = [np.log(6e11), np.log(20.0), np.log(2e9), np.log(100.0), np.log(4e10)]\n",
    "init_potential_v2 = get_potential_v2(*x0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5c40462f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:11.553824Z",
     "iopub.status.busy": "2026-08-11T01:27:11.553656Z",
     "iopub.status.idle": "2026-08-11T01:27:11.557071Z",
     "shell.execute_reply": "2026-08-11T01:27:11.556192Z"
    }
   },
   "outputs": [],
   "source": [
    "def err_func_v2(p, r, Menc, Menc_err):\n",
    "    pot = get_potential_v2(*p)\n",
    "    xyz = np.zeros((3, len(r)))\n",
    "    xyz[0] = r\n",
    "    model_menc = pot.mass_enclosed(xyz).to(u.Msun).value\n",
    "    return (model_menc - Menc) / Menc_err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "99e07b11",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:11.558788Z",
     "iopub.status.busy": "2026-08-11T01:27:11.558619Z",
     "iopub.status.idle": "2026-08-11T01:27:12.172798Z",
     "shell.execute_reply": "2026-08-11T01:27:12.171748Z"
    }
   },
   "outputs": [],
   "source": [
    "err = np.max([mwdata2[\"Menc_err_pos\"], mwdata2[\"Menc_err_neg\"]], axis=0)\n",
    "p_opt, ier = leastsq(err_func_v2, x0=x0, args=(mwdata2[\"r\"], mwdata2[\"Menc\"], err))\n",
    "assert ier in range(1, 4 + 1), \"least-squares fit failed!\"\n",
    "\n",
    "fit_potential_v2 = get_potential_v2(*p_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "319ff17c",
   "metadata": {},
   "source": [
    "Here is the fitted potential compared to the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "763ba10f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:12.174717Z",
     "iopub.status.busy": "2026-08-11T01:27:12.174530Z",
     "iopub.status.idle": "2026-08-11T01:27:12.783672Z",
     "shell.execute_reply": "2026-08-11T01:27:12.782702Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 590
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.logspace(-3, 3, 256) * u.kpc\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"tight\")\n",
    "\n",
    "ax.errorbar(\n",
    "    mwdata2[\"r\"],\n",
    "    mwdata2[\"Menc\"],\n",
    "    yerr=(mwdata2[\"Menc_err_neg\"], mwdata2[\"Menc_err_pos\"]),\n",
    "    marker=\"o\",\n",
    "    markersize=2,\n",
    "    color=\"k\",\n",
    "    alpha=1.0,\n",
    "    ecolor=\"#aaaaaa\",\n",
    "    capthick=0,\n",
    "    linestyle=\"none\",\n",
    "    elinewidth=1.0,\n",
    ")\n",
    "\n",
    "fit_menc = fit_potential_v2.mass_enclosed(R=r)\n",
    "ax.loglog(r.value, fit_menc.value, marker=\"\", color=\"#3182bd\", linewidth=2, alpha=0.7)\n",
    "\n",
    "ax.set_xlim(1e-3, 10**2.6)\n",
    "ax.set_ylim(7e6, 10**12.25)\n",
    "\n",
    "ax.set_xlabel(\"$r$ [kpc]\")\n",
    "ax.set_ylabel(r\"$M(<r)$ [M$_\\odot$]\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "ax.set_yscale(\"log\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08482951",
   "metadata": {},
   "source": [
    "And a comparison of the circular velocity curve between v1 and v2, compared to the Eilers et al. (2019) data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f6bdc000",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-11T01:27:12.785664Z",
     "iopub.status.busy": "2026-08-11T01:27:12.785459Z",
     "iopub.status.idle": "2026-08-11T01:27:13.103036Z",
     "shell.execute_reply": "2026-08-11T01:27:13.101979Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$v_c$')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 590
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mwpot_v1 = gp.MilkyWayPotential(version=\"v1\")\n",
    "\n",
    "r_grid = np.linspace(0.5, 30, 128)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4), layout=\"tight\")\n",
    "ax.plot(\n",
    "    r_grid,\n",
    "    fit_potential_v2.circular_velocity(R=r_grid),\n",
    "    marker=\"\",\n",
    "    lw=2,\n",
    "    label=\"v2\",\n",
    "    color=\"tab:blue\",\n",
    ")\n",
    "ax.plot(\n",
    "    r_grid,\n",
    "    mwpot_v1.circular_velocity(R=r_grid),\n",
    "    marker=\"\",\n",
    "    label=\"v1\",\n",
    "    linestyle=\"--\",\n",
    "    color=\"tab:orange\",\n",
    ")\n",
    "ax.scatter(\n",
    "    eilers[\"R\"][eilers[\"R\"] < 15],\n",
    "    eilers[\"v_c\"][eilers[\"R\"] < 15],\n",
    "    marker=\"o\",\n",
    "    s=8,\n",
    "    color=\"k\",\n",
    ")\n",
    "ax.legend(loc=\"best\", fontsize=16)\n",
    "ax.set_xlabel(\"$R$ [kpc]\")\n",
    "ax.set_ylabel(\"$v_c$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed85e8e6",
   "metadata": {},
   "source": [
    "Note that the parameters of this fit were further tweaked (as described in [Hunt et al. 2022](https://ui.adsabs.harvard.edu/abs/2022MNRAS.516L...7H/abstract)) to provide a better match to the vertical phase spiral morphology."
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "custom_cell_magics": "kql"
  },
  "kernelspec": {
   "display_name": "gala",
   "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": "3.12.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}