{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4b1cde21",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:06.427057Z",
     "iopub.status.busy": "2025-12-11T03:38:06.426877Z",
     "iopub.status.idle": "2025-12-11T03:38:06.821759Z",
     "shell.execute_reply": "2025-12-11T03:38:06.821011Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8c648b64",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:06.823922Z",
     "iopub.status.busy": "2025-12-11T03:38:06.823699Z",
     "iopub.status.idle": "2025-12-11T03:38:06.830653Z",
     "shell.execute_reply": "2025-12-11T03:38:06.829935Z"
    },
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
    "%run ../tutorials/nb_setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "648eb16a",
   "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": "0045f910",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:06.832572Z",
     "iopub.status.busy": "2025-12-11T03:38:06.832403Z",
     "iopub.status.idle": "2025-12-11T03:38:07.724374Z",
     "shell.execute_reply": "2025-12-11T03:38:07.723510Z"
    }
   },
   "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": "101d32c0",
   "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": "c70283af",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:07.726223Z",
     "iopub.status.busy": "2025-12-11T03:38:07.725942Z",
     "iopub.status.idle": "2025-12-11T03:38:07.737437Z",
     "shell.execute_reply": "2025-12-11T03:38:07.736758Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><i>Table length=16</i>\n",
       "<table id=\"table140605115601488\" 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": "5b45f1f0",
   "metadata": {},
   "source": [
    "We can now plot the above data and uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5db6f754",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:07.739338Z",
     "iopub.status.busy": "2025-12-11T03:38:07.739141Z",
     "iopub.status.idle": "2025-12-11T03:38:08.466998Z",
     "shell.execute_reply": "2025-12-11T03:38:08.466098Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 589
      }
     },
     "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": "7c5c5d29",
   "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": "27458325",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:08.468711Z",
     "iopub.status.busy": "2025-12-11T03:38:08.468533Z",
     "iopub.status.idle": "2025-12-11T03:38:08.472554Z",
     "shell.execute_reply": "2025-12-11T03:38:08.471840Z"
    }
   },
   "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": "6b59e79a",
   "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": "1371d403",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:08.474134Z",
     "iopub.status.busy": "2025-12-11T03:38:08.473970Z",
     "iopub.status.idle": "2025-12-11T03:38:08.485429Z",
     "shell.execute_reply": "2025-12-11T03:38:08.484735Z"
    }
   },
   "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": "1a86e298",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:08.487086Z",
     "iopub.status.busy": "2025-12-11T03:38:08.486919Z",
     "iopub.status.idle": "2025-12-11T03:38:09.443061Z",
     "shell.execute_reply": "2025-12-11T03:38:09.442062Z"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 589
      }
     },
     "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": "b5b88fdd",
   "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": "35c25ff4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:09.444887Z",
     "iopub.status.busy": "2025-12-11T03:38:09.444629Z",
     "iopub.status.idle": "2025-12-11T03:38:09.447770Z",
     "shell.execute_reply": "2025-12-11T03:38:09.447073Z"
    }
   },
   "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": "d3d7916e",
   "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": "ff617f0f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:09.449579Z",
     "iopub.status.busy": "2025-12-11T03:38:09.449403Z",
     "iopub.status.idle": "2025-12-11T03:38:09.853011Z",
     "shell.execute_reply": "2025-12-11T03:38:09.852142Z"
    }
   },
   "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": "9d061a48",
   "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": "bea898de",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:09.855150Z",
     "iopub.status.busy": "2025-12-11T03:38:09.854956Z",
     "iopub.status.idle": "2025-12-11T03:38:10.496193Z",
     "shell.execute_reply": "2025-12-11T03:38:10.495198Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 589
      }
     },
     "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": "e4550dfa",
   "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": "79264c6d",
   "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": "1886f8da",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:10.498276Z",
     "iopub.status.busy": "2025-12-11T03:38:10.498063Z",
     "iopub.status.idle": "2025-12-11T03:38:10.507020Z",
     "shell.execute_reply": "2025-12-11T03:38:10.506370Z"
    }
   },
   "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": "3ec9984b",
   "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": "d09c812d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:10.508878Z",
     "iopub.status.busy": "2025-12-11T03:38:10.508704Z",
     "iopub.status.idle": "2025-12-11T03:38:10.520529Z",
     "shell.execute_reply": "2025-12-11T03:38:10.519614Z"
    }
   },
   "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": "4353cb80",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:10.522218Z",
     "iopub.status.busy": "2025-12-11T03:38:10.521915Z",
     "iopub.status.idle": "2025-12-11T03:38:11.157090Z",
     "shell.execute_reply": "2025-12-11T03:38:11.156188Z"
    },
    "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": 589
      }
     },
     "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": "a9740357",
   "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": "e1aca6b5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:11.159090Z",
     "iopub.status.busy": "2025-12-11T03:38:11.158732Z",
     "iopub.status.idle": "2025-12-11T03:38:11.163357Z",
     "shell.execute_reply": "2025-12-11T03:38:11.162639Z"
    }
   },
   "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": "457f90a4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:11.165236Z",
     "iopub.status.busy": "2025-12-11T03:38:11.165039Z",
     "iopub.status.idle": "2025-12-11T03:38:11.176493Z",
     "shell.execute_reply": "2025-12-11T03:38:11.175777Z"
    }
   },
   "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": "11c66674",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:11.178325Z",
     "iopub.status.busy": "2025-12-11T03:38:11.178132Z",
     "iopub.status.idle": "2025-12-11T03:38:11.181464Z",
     "shell.execute_reply": "2025-12-11T03:38:11.180695Z"
    }
   },
   "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": "c1c0dc37",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:11.183186Z",
     "iopub.status.busy": "2025-12-11T03:38:11.182992Z",
     "iopub.status.idle": "2025-12-11T03:38:11.762961Z",
     "shell.execute_reply": "2025-12-11T03:38:11.762119Z"
    }
   },
   "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": "84213290",
   "metadata": {},
   "source": [
    "Here is the fitted potential compared to the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "60e05cbd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:11.764869Z",
     "iopub.status.busy": "2025-12-11T03:38:11.764678Z",
     "iopub.status.idle": "2025-12-11T03:38:12.500511Z",
     "shell.execute_reply": "2025-12-11T03:38:12.499611Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 390,
       "width": 589
      }
     },
     "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": "0b7e1018",
   "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": "0f70fa94",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-11T03:38:12.502317Z",
     "iopub.status.busy": "2025-12-11T03:38:12.502006Z",
     "iopub.status.idle": "2025-12-11T03:38:12.720625Z",
     "shell.execute_reply": "2025-12-11T03:38:12.719760Z"
    }
   },
   "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": 589
      }
     },
     "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": "7cceab20",
   "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": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}