{ "cells": [ { "cell_type": "markdown", "id": "a1b2c3d4e5f6", "metadata": { "papermill": { "duration": 0.00546, "end_time": "2026-06-02T01:10:19.919940+00:00", "exception": false, "start_time": "2026-06-02T01:10:19.914480+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Orbit Examples\n", "\n", "This notebook gives some detailed orbit examples,\n", "including the eccentricity distribution of thick-disk stars, integrating the LMC orbit with dynamical friction, and taking the barycentric acceleration\n", "due to the LMC into account for Milky-Way orbits." ] }, { "cell_type": "code", "execution_count": 1, "id": "b2c3d4e5f6a7", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:19.930177Z", "iopub.status.busy": "2026-06-02T01:10:19.929962Z", "iopub.status.idle": "2026-06-02T01:10:23.060451Z", "shell.execute_reply": "2026-06-02T01:10:23.058607Z" }, "papermill": { "duration": 3.136853, "end_time": "2026-06-02T01:10:23.061598+00:00", "exception": false, "start_time": "2026-06-02T01:10:19.924745+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)\n", "\n", "import numpy\n", "import copy\n", "from astropy import units\n", "from matplotlib import pyplot as plt\n", "from galpy.orbit import Orbit\n", "from galpy.potential import MWPotential2014, ChandrasekharDynamicalFrictionForce\n", "from galpy.util import conversion" ] }, { "cell_type": "markdown", "id": "e2dad8a4", "metadata": { "papermill": { "duration": 0.007814, "end_time": "2026-06-02T01:10:23.077969+00:00", "exception": false, "start_time": "2026-06-02T01:10:23.070155+00:00", "status": "completed" }, "tags": [] }, "source": [ "## The eccentricity distribution of the Milky Way's thick disk\n", "\n", "A straightforward application of galpy's orbit-integration capabilities is to\n", "derive the eccentricity distribution for a set of thick-disk stars. We use the\n", "SDSS/SEGUE thick-disk sample compiled by\n", "[Dierickx et al. (2010)](https://ui.adsabs.harvard.edu/abs/2010ApJ...725L.186D/abstract),\n", "which we download from Vizier:" ] }, { "cell_type": "code", "execution_count": 2, "id": "652d9dad", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:23.096165Z", "iopub.status.busy": "2026-06-02T01:10:23.095406Z", "iopub.status.idle": "2026-06-02T01:10:23.191194Z", "shell.execute_reply": "2026-06-02T01:10:23.190260Z" }, "papermill": { "duration": 0.105913, "end_time": "2026-06-02T01:10:23.191891+00:00", "exception": false, "start_time": "2026-06-02T01:10:23.085978+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Loaded 31535 thick-disk stars from local cache: dierickx_2010_thick_disk.fits\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "WARNING: UnitsWarning: 'log(cm.s**-2)' did not parse as fits unit: 'log' is not a recognized function If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html [astropy.units.core]\n", "WARNING: UnitsWarning: 'log(Sun)' did not parse as fits unit: 'log' is not a recognized function If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html [astropy.units.core]\n" ] } ], "source": [ "import os\n", "\n", "from astropy.table import Table\n", "\n", "from galpy.potential import LogarithmicHaloPotential\n", "\n", "# Cache the Vizier query result locally so re-runs of this notebook don't\n", "# repeat the catalog download, which is occasionally slow or unavailable.\n", "_dierickx_cache = \"dierickx_2010_thick_disk.fits\"\n", "\n", "if os.path.exists(_dierickx_cache):\n", " dierickx = Table.read(_dierickx_cache)\n", " print(\n", " f\"Loaded {len(dierickx)} thick-disk stars from local cache: {_dierickx_cache}\"\n", " )\n", "else:\n", " from astroquery.vizier import Vizier\n", "\n", " v = Vizier(columns=[\"*\"], row_limit=-1)\n", " result = v.get_catalogs(\"J/ApJ/725/L186\")\n", " dierickx = result[\"J/ApJ/725/L186/table2\"]\n", " print(f\"Downloaded {len(dierickx)} thick-disk stars\")\n", " dierickx.write(_dierickx_cache, format=\"fits\", overwrite=True)" ] }, { "cell_type": "markdown", "id": "d32a6ef7", "metadata": { "papermill": { "duration": 0.004487, "end_time": "2026-06-02T01:10:23.201024+00:00", "exception": false, "start_time": "2026-06-02T01:10:23.196537+00:00", "status": "completed" }, "tags": [] }, "source": [ "Set up the phase-space coordinates as `(RA, Dec, distance, pmRA, pmDec, vlos)`\n", "and initialize orbits in a `LogarithmicHaloPotential` (a spherical potential with\n", "a flat rotation curve). All stars are formally bound in this potential\n", "(which has an infinite escape velocity), but a handful have such extreme\n", "kinematics that their orbits cause numerical issues, so we filter those out:" ] }, { "cell_type": "code", "execution_count": 3, "id": "a6b7c6db", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:23.215235Z", "iopub.status.busy": "2026-06-02T01:10:23.215013Z", "iopub.status.idle": "2026-06-02T01:10:23.267586Z", "shell.execute_reply": "2026-06-02T01:10:23.266744Z" }, "papermill": { "duration": 0.062809, "end_time": "2026-06-02T01:10:23.268461+00:00", "exception": false, "start_time": "2026-06-02T01:10:23.205652+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Keeping 31491 of 31535 orbits (removed 44 extreme outliers)\n" ] } ], "source": [ "vxvv = numpy.column_stack(\n", " [\n", " numpy.array(dierickx[\"RAJ2000\"], dtype=float),\n", " numpy.array(dierickx[\"DEJ2000\"], dtype=float),\n", " numpy.array(dierickx[\"Dist\"], dtype=float) / 1e3, # pc -> kpc\n", " numpy.array(dierickx[\"pmRA\"], dtype=float),\n", " numpy.array(dierickx[\"pmDE\"], dtype=float),\n", " numpy.array(dierickx[\"HRV\"], dtype=float),\n", " ]\n", ")\n", "\n", "lp = LogarithmicHaloPotential(normalize=1.0)\n", "all_orbits = Orbit(vxvv, radec=True, ro=8.0, vo=220.0, solarmotion=\"hogg\")\n", "\n", "# Filter out stars with extreme energies that cause numerical issues\n", "E = all_orbits.E(pot=lp, use_physical=False)\n", "keep = E < 3.0\n", "orbits = all_orbits[keep]\n", "e_dierickx = numpy.array(dierickx[\"e\"], dtype=float)[keep]\n", "print(\n", " f\"Keeping {keep.sum()} of {len(keep)} orbits (removed {(~keep).sum()} extreme outliers)\"\n", ")" ] }, { "cell_type": "markdown", "id": "397d03da", "metadata": { "papermill": { "duration": 0.012153, "end_time": "2026-06-02T01:10:23.286658+00:00", "exception": false, "start_time": "2026-06-02T01:10:23.274505+00:00", "status": "completed" }, "tags": [] }, "source": [ "Now we compute eccentricities in two ways: (a) by integrating each orbit for\n", "many dynamical times and finding the actual peri- and apocenter, and (b)\n", "analytically using the [Staeckel approximation](./fast_characterization.ipynb),\n", "which avoids orbit integration entirely:" ] }, { "cell_type": "code", "execution_count": 4, "id": "f238e272", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:23.298981Z", "iopub.status.busy": "2026-06-02T01:10:23.298745Z", "iopub.status.idle": "2026-06-02T01:10:30.271454Z", "shell.execute_reply": "2026-06-02T01:10:30.269802Z" }, "papermill": { "duration": 6.980509, "end_time": "2026-06-02T01:10:30.272846+00:00", "exception": false, "start_time": "2026-06-02T01:10:23.292337+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Analytic eccentricities (Staeckel approximation, very fast)\n", "e_ana = orbits.e(analytic=True, pot=lp, delta=0.01)\n", "\n", "# Numerical eccentricities (orbit integration)\n", "ts = numpy.linspace(0.0, 20.0, 1001)\n", "orbits.integrate(ts, lp)\n", "e_int = orbits.e()" ] }, { "cell_type": "markdown", "id": "8733a01e", "metadata": { "papermill": { "duration": 0.010335, "end_time": "2026-06-02T01:10:30.294315+00:00", "exception": false, "start_time": "2026-06-02T01:10:30.283980+00:00", "status": "completed" }, "tags": [] }, "source": [ "The eccentricity distribution of the thick disk peaks around $e \\approx 0.25$:" ] }, { "cell_type": "code", "execution_count": 5, "id": "d614613d", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:30.317435Z", "iopub.status.busy": "2026-06-02T01:10:30.317102Z", "iopub.status.idle": "2026-06-02T01:10:30.665930Z", "shell.execute_reply": "2026-06-02T01:10:30.664866Z" }, "papermill": { "duration": 0.362558, "end_time": "2026-06-02T01:10:30.667584+00:00", "exception": false, "start_time": "2026-06-02T01:10:30.305026+00:00", "status": "completed" }, "tags": [] }, "outputs": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(e_int, bins=50, range=(0, 1), density=True)\n", "plt.xlabel(r\"$\\mathrm{Eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{Density}$\");" ] }, { "cell_type": "markdown", "id": "c299c1d3", "metadata": { "papermill": { "duration": 0.010811, "end_time": "2026-06-02T01:10:30.689916+00:00", "exception": false, "start_time": "2026-06-02T01:10:30.679105+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can compare galpy's integrated eccentricities with those published by\n", "Dierickx et al. (2010). The agreement is excellent for most stars:" ] }, { "cell_type": "code", "execution_count": 6, "id": "30e227f2", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:30.713360Z", "iopub.status.busy": "2026-06-02T01:10:30.713085Z", "iopub.status.idle": "2026-06-02T01:10:30.903319Z", "shell.execute_reply": "2026-06-02T01:10:30.902252Z" }, "papermill": { "duration": 0.203972, "end_time": "2026-06-02T01:10:30.905050+00:00", "exception": false, "start_time": "2026-06-02T01:10:30.701078+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(e_dierickx, e_int, \"k,\")\n", "plt.plot([0, 1], [0, 1], \"r-\", lw=0.8)\n", "plt.xlabel(r\"$\\mathrm{Dierickx\\ et\\ al.\\ eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{galpy\\ integrated\\ eccentricity}$\")\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "id": "a0ba9ff9", "metadata": { "papermill": { "duration": 0.011035, "end_time": "2026-06-02T01:10:30.928370+00:00", "exception": false, "start_time": "2026-06-02T01:10:30.917335+00:00", "status": "completed" }, "tags": [] }, "source": [ "The analytic Staeckel estimates are equally good:" ] }, { "cell_type": "code", "execution_count": 7, "id": "ac71a49f", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:30.951467Z", "iopub.status.busy": "2026-06-02T01:10:30.951245Z", "iopub.status.idle": "2026-06-02T01:10:31.134960Z", "shell.execute_reply": "2026-06-02T01:10:31.133935Z" }, "papermill": { "duration": 0.196677, "end_time": "2026-06-02T01:10:31.136431+00:00", "exception": false, "start_time": "2026-06-02T01:10:30.939754+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(e_dierickx, e_ana, \"k,\")\n", "plt.plot([0, 1], [0, 1], \"r-\", lw=0.8)\n", "plt.xlabel(r\"$\\mathrm{Dierickx\\ et\\ al.\\ eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{galpy\\ analytic\\ eccentricity}$\")\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "id": "2bbc9de0", "metadata": { "papermill": { "duration": 0.011399, "end_time": "2026-06-02T01:10:31.159604+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.148205+00:00", "status": "completed" }, "tags": [] }, "source": [ "Because the `LogarithmicHaloPotential` is spherical, the Staeckel\n", "approximation is essentially exact. Comparing the integrated and analytic\n", "eccentricities directly confirms this:" ] }, { "cell_type": "code", "execution_count": 8, "id": "3378e9a9", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:31.183489Z", "iopub.status.busy": "2026-06-02T01:10:31.183269Z", "iopub.status.idle": "2026-06-02T01:10:31.359656Z", "shell.execute_reply": "2026-06-02T01:10:31.358697Z" }, "papermill": { "duration": 0.189639, "end_time": "2026-06-02T01:10:31.360990+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.171351+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(e_int, e_ana, \"k,\")\n", "plt.plot([0, 1], [0, 1], \"r-\", lw=0.8)\n", "plt.xlabel(r\"$\\mathrm{Integrated\\ eccentricity}$\")\n", "plt.ylabel(r\"$\\mathrm{Analytic\\ eccentricity}$\")\n", "plt.xlim(0, 1)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "id": "c3d4e5f6a7b8", "metadata": { "papermill": { "duration": 0.01096, "end_time": "2026-06-02T01:10:31.383279+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.372319+00:00", "status": "completed" }, "tags": [] }, "source": [ "## LMC orbit with dynamical friction\n", "\n", "The Large Magellanic Cloud (LMC) is a massive satellite of the Milky Way, so its\n", "orbit is significantly affected by dynamical friction -- a frictional force of\n", "gravitational origin that occurs when a massive object travels through a sea of\n", "low-mass objects (halo stars and dark matter; see Section 19.4.1 in [galaxiesbook.org](https://galaxiesbook.org/chapters/IV-03.-Hierarchical-Galaxy-Formation_4-Dynamical-processes.html#Dynamical-friction)). We investigate the LMC's past and\n", "future orbit using `ChandrasekharDynamicalFrictionForce`.\n", "\n", "First, we load the current phase-space coordinates for the LMC using `Orbit.from_name`.\n", "Because the LMC is unbound in the default ``MWPotential2014``, we increase the\n", "halo mass by 50% (corresponding to a Milky Way halo mass of approximately\n", "1.2 x 10^12 Msun). We use `copy.deepcopy` to avoid modifying the global potential." ] }, { "cell_type": "code", "execution_count": 9, "id": "f6a7b8c9d0e1", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:31.407670Z", "iopub.status.busy": "2026-06-02T01:10:31.407453Z", "iopub.status.idle": "2026-06-02T01:10:31.419030Z", "shell.execute_reply": "2026-06-02T01:10:31.417916Z" }, "papermill": { "duration": 0.025356, "end_time": "2026-06-02T01:10:31.420124+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.394768+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "o = Orbit.from_name(\"LMC\")\n", "\n", "# Make a deep copy to avoid modifying the global MWPotential2014\n", "mwp = copy.deepcopy(MWPotential2014)\n", "mwp[2] *= 1.5 # increase halo mass by 50%" ] }, { "cell_type": "markdown", "id": "a7b8c9d0e1f2", "metadata": { "papermill": { "duration": 0.009498, "end_time": "2026-06-02T01:10:31.439343+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.429845+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Orbit without dynamical friction\n", "\n", "First, integrate the LMC orbit backward for 10 Gyr without dynamical friction:" ] }, { "cell_type": "code", "execution_count": 10, "id": "b8c9d0e1f2a3", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:31.458673Z", "iopub.status.busy": "2026-06-02T01:10:31.458324Z", "iopub.status.idle": "2026-06-02T01:10:31.787659Z", "shell.execute_reply": "2026-06-02T01:10:31.786739Z" }, "papermill": { "duration": 0.340175, "end_time": "2026-06-02T01:10:31.789166+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.448991+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts = numpy.linspace(0.0, -10.0, 1001) * units.Gyr\n", "o.integrate(ts, mwp)\n", "o.plot(d1=\"t\", d2=\"r\");" ] }, { "cell_type": "markdown", "id": "c9d0e1f2a3b4", "metadata": { "papermill": { "duration": 0.012342, "end_time": "2026-06-02T01:10:31.814248+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.801906+00:00", "status": "completed" }, "tags": [] }, "source": [ "The LMC is bound with an apocenter just over 200 kpc.\n", "\n", "### Adding dynamical friction (M = 5 x 10^10 Msun)\n", "\n", "Now add dynamical friction assuming an LMC mass of 5 x 10^10 Msun:" ] }, { "cell_type": "code", "execution_count": 11, "id": "d0e1f2a3b4c5", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:31.839134Z", "iopub.status.busy": "2026-06-02T01:10:31.838911Z", "iopub.status.idle": "2026-06-02T01:10:42.756719Z", "shell.execute_reply": "2026-06-02T01:10:42.755361Z" }, "papermill": { "duration": 10.931057, "end_time": "2026-06-02T01:10:42.757968+00:00", "exception": false, "start_time": "2026-06-02T01:10:31.826911+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator dopr54_c instead)\n" ] } ], "source": [ "cdf = ChandrasekharDynamicalFrictionForce(\n", " GMs=5e10 * units.Msun, rhm=5.0 * units.kpc, dens=mwp\n", ")\n", "\n", "# Make a copy of the orbit for the dynamical friction integration\n", "odf = o()\n", "odf.integrate(ts, mwp + cdf)" ] }, { "cell_type": "code", "execution_count": 12, "id": "e1f2a3b4c5d6", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:42.785082Z", "iopub.status.busy": "2026-06-02T01:10:42.784818Z", "iopub.status.idle": "2026-06-02T01:10:43.375363Z", "shell.execute_reply": "2026-06-02T01:10:43.374399Z" }, "papermill": { "duration": 0.606015, "end_time": "2026-06-02T01:10:43.377034+00:00", "exception": false, "start_time": "2026-06-02T01:10:42.771019+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "o.plot(d1=\"t\", d2=\"r\", label=r\"$\\mathrm{No\\ DF}$\")\n", "odf.plot(\n", " d1=\"t\", d2=\"r\", overplot=True, label=r\"$\\mathrm{DF},\\ M=5\\times10^{10}\\,M_\\odot$\"\n", ")\n", "plt.ylim(0.0, 660.0)\n", "plt.legend(fontsize=17.0);" ] }, { "cell_type": "markdown", "id": "f2a3b4c5d6e7", "metadata": { "papermill": { "duration": 0.012935, "end_time": "2026-06-02T01:10:43.403948+00:00", "exception": false, "start_time": "2026-06-02T01:10:43.391013+00:00", "status": "completed" }, "tags": [] }, "source": [ "Dynamical friction removes energy from the LMC's orbit, so the past apocenter\n", "is now around 500 kpc rather than 200 kpc, and the orbital period is much longer.\n", "\n", "### A more massive LMC (M = 10^11 Msun)\n", "\n", "Recent observations suggest the LMC may be even more massive (> 10^11 Msun).\n", "We can change the mass in the existing `ChandrasekharDynamicalFrictionForce`\n", "object without re-solving the Jeans equation (necessary to initialize the dynamical-friction object):" ] }, { "cell_type": "code", "execution_count": 13, "id": "a3b4c5d6e7f8", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:43.429616Z", "iopub.status.busy": "2026-06-02T01:10:43.429399Z", "iopub.status.idle": "2026-06-02T01:10:43.446158Z", "shell.execute_reply": "2026-06-02T01:10:43.445190Z" }, "papermill": { "duration": 0.03023, "end_time": "2026-06-02T01:10:43.447430+00:00", "exception": false, "start_time": "2026-06-02T01:10:43.417200+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "cdf.GMs = 1e11 * units.Msun\n", "\n", "odf2 = o()\n", "odf2.integrate(ts, mwp + cdf)" ] }, { "cell_type": "code", "execution_count": 14, "id": "b4c5d6e7f8a9", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:43.471258Z", "iopub.status.busy": "2026-06-02T01:10:43.471043Z", "iopub.status.idle": "2026-06-02T01:10:43.833037Z", "shell.execute_reply": "2026-06-02T01:10:43.831979Z" }, "papermill": { "duration": 0.375967, "end_time": "2026-06-02T01:10:43.834838+00:00", "exception": false, "start_time": "2026-06-02T01:10:43.458871+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "o.plot(d1=\"t\", d2=\"r\", label=r\"$\\mathrm{No\\ DF}$\", yrange=[0.0, 660.0])\n", "odf.plot(\n", " d1=\"t\", d2=\"r\", overplot=True, label=r\"$\\mathrm{DF},\\ M=5\\times10^{10}\\,M_\\odot$\"\n", ")\n", "odf2.plot(\n", " d1=\"t\", d2=\"r\", overplot=True, label=r\"$\\mathrm{DF},\\ M=1\\times10^{11}\\,M_\\odot$\"\n", ")\n", "plt.legend(fontsize=17.0);" ] }, { "cell_type": "markdown", "id": "c5d6e7f8a9b0", "metadata": { "papermill": { "duration": 0.013663, "end_time": "2026-06-02T01:10:43.862816+00:00", "exception": false, "start_time": "2026-06-02T01:10:43.849153+00:00", "status": "completed" }, "tags": [] }, "source": [ "With a mass of 10^11 Msun, the LMC barely completes a full orbit over 10 Gyr!\n", "\n", "### Future orbit: merging timescale\n", "\n", "Let's see what happens in the future with the massive LMC. We flip the sign of\n", "the integration times (limiting to 9 Gyr to avoid numerical issues at very\n", "small radii):" ] }, { "cell_type": "code", "execution_count": 15, "id": "d6e7f8a9b0c1", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:43.889076Z", "iopub.status.busy": "2026-06-02T01:10:43.888860Z", "iopub.status.idle": "2026-06-02T01:10:45.735988Z", "shell.execute_reply": "2026-06-02T01:10:45.734950Z" }, "papermill": { "duration": 1.860967, "end_time": "2026-06-02T01:10:45.737647+00:00", "exception": false, "start_time": "2026-06-02T01:10:43.876680+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "odf2.integrate(numpy.linspace(0.0, 9.0, 1001) * units.Gyr, mwp + cdf)\n", "odf2.plot(d1=\"t\", d2=\"r\");" ] }, { "cell_type": "markdown", "id": "e7f8a9b0c1d2", "metadata": { "papermill": { "duration": 0.014637, "end_time": "2026-06-02T01:10:45.766740+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.752103+00:00", "status": "completed" }, "tags": [] }, "source": [ "The LMC merges with the Milky Way in about 4 Gyr after a few more pericenter\n", "passages. Mass loss (not included here) would somewhat increase the merging\n", "timescale, but the merger is inevitable. \n", "\n", "This example also illustrates thhe continuation of an existing orbit integration when \n", "integrating starting from one of the previous integrations edges. The `integrate` method continues the integration from the last point of the previous integration, so we can seamlessly continue the integration into the future. See [Continuing integrations](./integration_and_plotting.ipynb#Continuing-integrations) for more details.\n", "\n", "
\n", "\n", "**Warning**\n", "\n", "When using dynamical friction, if the radius gets very small the\n", "integration can become erroneous, leading to unphysical kicks. Always inspect\n", "the full orbit to check whether a merger has happened.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "f8a9b0c1d2e3", "metadata": { "papermill": { "duration": 0.011308, "end_time": "2026-06-02T01:10:45.792133+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.780825+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Barycentric acceleration due to the LMC\n", "\n", "The LMC is so massive that it pulls the center of the Milky Way towards it,\n", "meaning the Galactocentric reference frame is not truly inertial. We can\n", "account for this using `NonInertialFrameForce`.\n", "\n", "Our approach: (1) compute the LMC orbit assuming the MW is at rest, (2) compute\n", "the acceleration at the origin due to the LMC along that orbit, (3) use\n", "`NonInertialFrameForce` with that acceleration." ] }, { "cell_type": "code", "execution_count": 16, "id": "a9b0c1d2e3f4", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:45.811330Z", "iopub.status.busy": "2026-06-02T01:10:45.811093Z", "iopub.status.idle": "2026-06-02T01:10:45.815370Z", "shell.execute_reply": "2026-06-02T01:10:45.814049Z" }, "papermill": { "duration": 0.014616, "end_time": "2026-06-02T01:10:45.816370+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.801754+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import (\n", " HernquistPotential,\n", " MovingObjectPotential,\n", " NonInertialFrameForce,\n", " evaluateRforces,\n", " evaluatephitorques,\n", " evaluatezforces,\n", ")" ] }, { "cell_type": "markdown", "id": "b0c1d2e3f4a5", "metadata": { "papermill": { "duration": 0.007517, "end_time": "2026-06-02T01:10:45.831611+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.824094+00:00", "status": "completed" }, "tags": [] }, "source": [ "We already computed the LMC orbit with dynamical friction above. Now we\n", "re-compute it over 10 Gyr backward using the massive LMC setup:" ] }, { "cell_type": "code", "execution_count": 17, "id": "c1d2e3f4a5b6", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:45.848494Z", "iopub.status.busy": "2026-06-02T01:10:45.848173Z", "iopub.status.idle": "2026-06-02T01:10:45.879119Z", "shell.execute_reply": "2026-06-02T01:10:45.877996Z" }, "papermill": { "duration": 0.040777, "end_time": "2026-06-02T01:10:45.880105+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.839328+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Re-integrate LMC orbit backward with the heavy LMC\n", "o_lmc = Orbit.from_name(\"LMC\")\n", "ts_back = numpy.linspace(0.0, -10.0, 1001) * units.Gyr\n", "o_lmc.integrate(ts_back, mwp + cdf)" ] }, { "cell_type": "markdown", "id": "d2e3f4a5b6c7", "metadata": { "papermill": { "duration": 0.010068, "end_time": "2026-06-02T01:10:45.900452+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.890384+00:00", "status": "completed" }, "tags": [] }, "source": [ "Define the LMC as a `HernquistPotential` and create a `MovingObjectPotential`\n", "that follows its orbit:" ] }, { "cell_type": "code", "execution_count": 18, "id": "e3f4a5b6c7d8", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:45.919756Z", "iopub.status.busy": "2026-06-02T01:10:45.919365Z", "iopub.status.idle": "2026-06-02T01:10:45.927410Z", "shell.execute_reply": "2026-06-02T01:10:45.926222Z" }, "papermill": { "duration": 0.018214, "end_time": "2026-06-02T01:10:45.928347+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.910133+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "# Hernquist potential for LMC: rhm = (1+sqrt(2)) * a, amp = 2 x mass\n", "lmcpot = HernquistPotential(\n", " amp=2e11 * units.Msun, a=5.0 * units.kpc / (1.0 + numpy.sqrt(2.0))\n", ")\n", "moving_lmcpot = MovingObjectPotential(o_lmc, pot=lmcpot)" ] }, { "cell_type": "markdown", "id": "f4a5b6c7d8e9", "metadata": { "papermill": { "duration": 0.008967, "end_time": "2026-06-02T01:10:45.946480+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.937513+00:00", "status": "completed" }, "tags": [] }, "source": [ "Compute the acceleration of the Galactic center due to the LMC by evaluating\n", "the force from `moving_lmcpot` at a small offset from the origin (to avoid\n", "numerical issues in cylindrical coordinates):" ] }, { "cell_type": "code", "execution_count": 19, "id": "a5b6c7d8e9f0", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:45.962798Z", "iopub.status.busy": "2026-06-02T01:10:45.962339Z", "iopub.status.idle": "2026-06-02T01:10:45.969473Z", "shell.execute_reply": "2026-06-02T01:10:45.968125Z" }, "papermill": { "duration": 0.015744, "end_time": "2026-06-02T01:10:45.970424+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.954680+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "loc_origin = 1e-4 # small offset in R\n", "ax = lambda t: evaluateRforces(\n", " moving_lmcpot, loc_origin, 0.0, phi=0.0, t=t, use_physical=False\n", ")\n", "ay = lambda t: (\n", " evaluatephitorques(moving_lmcpot, loc_origin, 0.0, phi=0.0, t=t, use_physical=False)\n", " / loc_origin\n", ")\n", "az = lambda t: evaluatezforces(\n", " moving_lmcpot, loc_origin, 0.0, phi=0.0, t=t, use_physical=False\n", ")" ] }, { "cell_type": "markdown", "id": "b6c7d8e9f0a1", "metadata": { "papermill": { "duration": 0.007814, "end_time": "2026-06-02T01:10:45.986249+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.978435+00:00", "status": "completed" }, "tags": [] }, "source": [ "Set up the `NonInertialFrameForce` with the origin's acceleration. We can pass\n", "the acceleration functions directly: by default (`cinterp=True`),\n", "`NonInertialFrameForce` builds a fast cubic-spline interpolation of them in C\n", "over each orbit integration's time range, so these (relatively expensive)\n", "functions are evaluated only when setting up an integration rather than being\n", "called from C at every integration step. This makes the C orbit integration\n", "much faster and removes the need to manually pre-interpolate the acceleration." ] }, { "cell_type": "code", "execution_count": 20, "id": "c7d8e9f0a1b2", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:46.001601Z", "iopub.status.busy": "2026-06-02T01:10:46.001149Z", "iopub.status.idle": "2026-06-02T01:10:46.006692Z", "shell.execute_reply": "2026-06-02T01:10:46.005354Z" }, "papermill": { "duration": 0.013935, "end_time": "2026-06-02T01:10:46.007630+00:00", "exception": false, "start_time": "2026-06-02T01:10:45.993695+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "nip = NonInertialFrameForce(a0=[ax, ay, az])" ] }, { "cell_type": "markdown", "id": "d8e9f0a1b2c3", "metadata": { "papermill": { "duration": 0.006533, "end_time": "2026-06-02T01:10:46.020579+00:00", "exception": false, "start_time": "2026-06-02T01:10:46.014046+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Effect on the Sun's orbit\n", "\n", "Compare the Sun's past orbit with and without the barycentric correction.\n", "When including the non-inertial correction, we must also include the LMC's\n", "gravitational potential (`moving_lmcpot`) to keep the model self-consistent:" ] }, { "cell_type": "code", "execution_count": 21, "id": "e9f0a1b2c3d4", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:46.034909Z", "iopub.status.busy": "2026-06-02T01:10:46.034437Z", "iopub.status.idle": "2026-06-02T01:10:46.706610Z", "shell.execute_reply": "2026-06-02T01:10:46.705675Z" }, "papermill": { "duration": 0.68056, "end_time": "2026-06-02T01:10:46.707554+00:00", "exception": false, "start_time": "2026-06-02T01:10:46.026994+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: You specified integration times as a Quantity, but are evaluating at times not specified as a Quantity; assuming that time given is in natural (internal) units (multiply time by unit to get output at physical time)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sunts = numpy.linspace(0.0, -3.0, 301) * units.Gyr\n", "\n", "osun_inertial = Orbit()\n", "osun_inertial.integrate(sunts, mwp)\n", "osun_inertial.plotx(label=r\"$\\mathrm{Inertial}$\")\n", "\n", "osun_noninertial = Orbit()\n", "osun_noninertial.integrate(sunts, mwp + nip + moving_lmcpot)\n", "osun_noninertial.plotx(overplot=True, label=r\"$\\mathrm{Non-inertial}$\")\n", "plt.legend(fontsize=18.0, loc=\"upper left\", framealpha=0.8);" ] }, { "cell_type": "markdown", "id": "f0a1b2c3d4e5", "metadata": { "papermill": { "duration": 0.014082, "end_time": "2026-06-02T01:10:46.736604+00:00", "exception": false, "start_time": "2026-06-02T01:10:46.722522+00:00", "status": "completed" }, "tags": [] }, "source": [ "There is essentially no difference for the Sun, because its orbit is close to\n", "the Galactic center where the LMC's pull on the origin is largely cancelled\n", "by the direct attraction to the LMC.\n", "\n", "### Effect on a distant dwarf galaxy (Fornax)\n", "\n", "For objects orbiting far in the halo, the effect is more significant:" ] }, { "cell_type": "code", "execution_count": 22, "id": "a1b2c3d4e5f0", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:46.763377Z", "iopub.status.busy": "2026-06-02T01:10:46.763162Z", "iopub.status.idle": "2026-06-02T01:10:47.560756Z", "shell.execute_reply": "2026-06-02T01:10:47.559623Z" }, "papermill": { "duration": 0.81088, "end_time": "2026-06-02T01:10:47.561749+00:00", "exception": false, "start_time": "2026-06-02T01:10:46.750869+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fornaxts = numpy.linspace(0.0, -10.0, 101) * units.Gyr\n", "\n", "ofornax_inertial = Orbit.from_name(\"Fornax\")\n", "ofornax_inertial.integrate(fornaxts, mwp)\n", "ofornax_inertial.plotr(label=r\"$\\mathrm{Inertial}$\")\n", "\n", "ofornax_noninertial = Orbit.from_name(\"Fornax\")\n", "ofornax_noninertial.integrate(fornaxts, mwp + nip + moving_lmcpot)\n", "ofornax_noninertial.plotr(overplot=True, label=r\"$\\mathrm{Non-inertial}$\")\n", "plt.autoscale()\n", "plt.legend(fontsize=18.0, loc=\"lower right\", framealpha=0.8);" ] }, { "cell_type": "markdown", "id": "b2c3d4e5f0a1", "metadata": { "papermill": { "duration": 0.011936, "end_time": "2026-06-02T01:10:47.586446+00:00", "exception": false, "start_time": "2026-06-02T01:10:47.574510+00:00", "status": "completed" }, "tags": [] }, "source": [ "For Fornax, the past orbit differs significantly when the barycentric\n", "acceleration is taken into account. The abrupt change around -8 Gyr is caused\n", "by the LMC's previous pericenter passage in our model.\n", "\n", "### Checking the acceleration: displacement, velocity, and force\n", "\n", "We can verify the acceleration is realistic by integrating it to get the\n", "displacement and velocity of the MW center, and comparing to the results of\n", "[Vasiliev et al. (2021)](https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.2279V/abstract):" ] }, { "cell_type": "code", "execution_count": 23, "id": "c3d4e5f0a1b2", "metadata": { "execution": { "iopub.execute_input": "2026-06-02T01:10:47.611483Z", "iopub.status.busy": "2026-06-02T01:10:47.611263Z", "iopub.status.idle": "2026-06-02T01:10:48.146898Z", "shell.execute_reply": "2026-06-02T01:10:48.145705Z" }, "papermill": { "duration": 0.549259, "end_time": "2026-06-02T01:10:48.148259+00:00", "exception": false, "start_time": "2026-06-02T01:10:47.599000+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import integrate\n", "\n", "vo, ro = 220.0, 8.0\n", "int_ts_phys = numpy.linspace(-3.0, 0.0, 101)\n", "int_ts = int_ts_phys / conversion.time_in_Gyr(vo, ro)\n", "\n", "ax4plot = ax(int_ts)\n", "ay4plot = ay(int_ts)\n", "az4plot = az(int_ts)\n", "\n", "vx4plot = integrate.cumulative_trapezoid(ax4plot, x=int_ts, initial=0.0)\n", "vy4plot = integrate.cumulative_trapezoid(ay4plot, x=int_ts, initial=0.0)\n", "vz4plot = integrate.cumulative_trapezoid(az4plot, x=int_ts, initial=0.0)\n", "\n", "xx4plot = integrate.cumulative_trapezoid(vx4plot, x=int_ts, initial=0.0)\n", "xy4plot = integrate.cumulative_trapezoid(vy4plot, x=int_ts, initial=0.0)\n", "xz4plot = integrate.cumulative_trapezoid(vz4plot, x=int_ts, initial=0.0)\n", "\n", "plt.figure(figsize=(11, 3.5))\n", "\n", "plt.subplot(1, 3, 1)\n", "plt.plot(\n", " int_ts_phys, xx4plot * ro, color=(0.5, 0.5, 247.0 / 256.0), lw=2.0, label=r\"$x$\"\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " xy4plot * ro,\n", " color=(111.0 / 256, 180.0 / 256, 109.0 / 256),\n", " lw=2.0,\n", " label=r\"$y$\",\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " xz4plot * ro,\n", " color=(239.0 / 256, 135.0 / 256, 132.0 / 256),\n", " lw=2.0,\n", " label=r\"$z$\",\n", ")\n", "plt.xlabel(r\"$\\mathrm{time}\\,(\\mathrm{Gyr})$\")\n", "plt.ylabel(r\"$\\mathrm{displacement}\\,(\\mathrm{kpc})$\")\n", "plt.legend(frameon=False, fontsize=18.0)\n", "\n", "plt.subplot(1, 3, 2)\n", "plt.plot(int_ts_phys, vx4plot * vo, color=(0.5, 0.5, 247.0 / 256.0), lw=2.0)\n", "plt.plot(\n", " int_ts_phys, vy4plot * vo, color=(111.0 / 256, 180.0 / 256, 109.0 / 256), lw=2.0\n", ")\n", "plt.plot(\n", " int_ts_phys, vz4plot * vo, color=(239.0 / 256, 135.0 / 256, 132.0 / 256), lw=2.0\n", ")\n", "plt.xlabel(r\"$\\mathrm{time}\\,(\\mathrm{Gyr})$\")\n", "plt.ylabel(r\"$\\mathrm{velocity}\\,(\\mathrm{km\\,s}^{-1})$\")\n", "\n", "plt.subplot(1, 3, 3)\n", "plt.plot(\n", " int_ts_phys,\n", " -ax4plot * conversion.force_in_kmsMyr(vo, ro) * 1000.0,\n", " color=(0.5, 0.5, 247.0 / 256.0),\n", " lw=2.0,\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " -ay4plot * conversion.force_in_kmsMyr(vo, ro) * 1000.0,\n", " color=(111.0 / 256, 180.0 / 256, 109.0 / 256),\n", " lw=2.0,\n", ")\n", "plt.plot(\n", " int_ts_phys,\n", " -az4plot * conversion.force_in_kmsMyr(vo, ro) * 1000.0,\n", " color=(239.0 / 256, 135.0 / 256, 132.0 / 256),\n", " lw=2.0,\n", ")\n", "plt.xlabel(r\"$\\mathrm{time}\\,(\\mathrm{Gyr})$\")\n", "plt.ylabel(r\"$\\mathrm{acceleration}\\,(\\mathrm{km\\,s}^{-1}\\,\\mathrm{Gyr}^{-1})$\")\n", "\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "d4e5f0a1b2c3", "metadata": { "papermill": { "duration": 0.015133, "end_time": "2026-06-02T01:10:48.179491+00:00", "exception": false, "start_time": "2026-06-02T01:10:48.164358+00:00", "status": "completed" }, "tags": [] }, "source": [ "The main trends and magnitudes are consistent with Figure 10 of Vasiliev et al.\n", "(2021), confirming that our simple approximation gives a reasonable estimate of\n", "the Galactocentric reference frame's acceleration." ] } ], "metadata": { "kernelspec": { "display_name": "py313", "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": "3.13.12" }, "papermill": { "default_parameters": {}, "duration": 30.40779, "end_time": "2026-06-02T01:10:49.111596+00:00", "environment_variables": {}, "exception": null, "input_path": "examples.ipynb", "output_path": "examples.ipynb", "parameters": {}, "start_time": "2026-06-02T01:10:18.703806+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }