{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "db41e62a", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:34.939985Z", "iopub.status.busy": "2025-12-11T04:10:34.939738Z", "iopub.status.idle": "2025-12-11T04:10:35.342426Z", "shell.execute_reply": "2025-12-11T04:10:35.341568Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "id": "7ed8d9b6", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:35.344328Z", "iopub.status.busy": "2025-12-11T04:10:35.344077Z", "iopub.status.idle": "2025-12-11T04:10:35.351094Z", "shell.execute_reply": "2025-12-11T04:10:35.350352Z" }, "nbsphinx": "hidden" }, "outputs": [], "source": [ "%run nb_setup" ] }, { "cell_type": "markdown", "id": "760587cb", "metadata": {}, "source": [ "# Integrate an orbit with uncertainties in Milky Way model" ] }, { "cell_type": "markdown", "id": "472a4e5e", "metadata": {}, "source": [ "`gala` provides a simple mass model for the Milky Way based on recent\n", "measurements of the enclosed mass compiled from the literature. See the\n", "[Defining a Milky Way potential\n", "model](define-milky-way-model.html) documentation for more\n", "information about how this model was defined.\n", "\n", "In this example, we will use the position and velocity and uncertainties of\n", "the Milky Way satellite galaxy \"Draco\" to integrate orbits in a Milky Way mass\n", "model starting from samples from the error distribution over initial\n", "conditions defined by its observed kinematics. We will then compute\n", "distributions of orbital properties like orbital period, pericenter, and\n", "eccentricity.\n", "\n", "Let's start by importing packages we will need:" ] }, { "cell_type": "code", "execution_count": 3, "id": "72f250e3", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:35.352873Z", "iopub.status.busy": "2025-12-11T04:10:35.352704Z", "iopub.status.idle": "2025-12-11T04:10:36.500796Z", "shell.execute_reply": "2025-12-11T04:10:36.499886Z" } }, "outputs": [], "source": [ "\n", "import astropy.coordinates as coord\n", "import astropy.units as u\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# Gala\n", "import gala.dynamics as gd\n", "import gala.potential as gp\n" ] }, { "cell_type": "markdown", "id": "9e9178df", "metadata": {}, "source": [ "We will also set the default Astropy Galactocentric frame parameters to the\n", "values adopted in Astropy v4.0:" ] }, { "cell_type": "code", "execution_count": 4, "id": "9cfea305", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.503233Z", "iopub.status.busy": "2025-12-11T04:10:36.502946Z", "iopub.status.idle": "2025-12-11T04:10:36.508967Z", "shell.execute_reply": "2025-12-11T04:10:36.508265Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coord.galactocentric_frame_defaults.set(\"v4.0\")" ] }, { "cell_type": "markdown", "id": "1da0fe6b", "metadata": {}, "source": [ "For the Milky Way model, we'll use the built-in potential class in `gala` (see\n", "above for definition):" ] }, { "cell_type": "code", "execution_count": 5, "id": "ce20d2ec", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.510703Z", "iopub.status.busy": "2025-12-11T04:10:36.510514Z", "iopub.status.idle": "2025-12-11T04:10:36.522447Z", "shell.execute_reply": "2025-12-11T04:10:36.521753Z" } }, "outputs": [], "source": [ "potential = gp.MilkyWayPotential(version=\"latest\")" ] }, { "cell_type": "markdown", "id": "c14b3a4a", "metadata": {}, "source": [ "For the sky position and distance of Draco, we'll use measurements from\n", "[Bonanos et al. 2004](https://arxiv.org/abs/astro-ph/0310477). For proper\n", "motion components, we'll use the recent HSTPROMO measurements ([Sohn et al.\n", "2017](https://arxiv.org/abs/1707.02593)) and the line-of-sight velocity from\n", "[Walker et al. 2007](https://arxiv.org/abs/0708.0010)." ] }, { "cell_type": "code", "execution_count": 6, "id": "0f90690a", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.524383Z", "iopub.status.busy": "2025-12-11T04:10:36.524170Z", "iopub.status.idle": "2025-12-11T04:10:36.541332Z", "shell.execute_reply": "2025-12-11T04:10:36.540365Z" } }, "outputs": [], "source": [ "icrs = coord.SkyCoord(\n", " ra=coord.Angle(\"17h 20m 12.4s\"),\n", " dec=coord.Angle(\"+57° 54′ 55″\"),\n", " distance=76 * u.kpc,\n", " pm_ra_cosdec=0.0569 * u.mas / u.yr,\n", " pm_dec=-0.1673 * u.mas / u.yr,\n", " radial_velocity=-291 * u.km / u.s,\n", ")\n", "\n", "icrs_err = coord.SkyCoord(\n", " ra=0 * u.deg,\n", " dec=0 * u.deg,\n", " distance=6 * u.kpc,\n", " pm_ra_cosdec=0.009 * u.mas / u.yr,\n", " pm_dec=0.009 * u.mas / u.yr,\n", " radial_velocity=0.1 * u.km / u.s,\n", ")" ] }, { "cell_type": "markdown", "id": "b868b62d", "metadata": {}, "source": [ "Let's start by transforming the measured values to a Galactocentric reference\n", "frame so we can integrate an orbit in our Milky Way model. We'll do this using\n", "the velocity transformation support in\n", "[`astropy.coordinates`](http://docs.astropy.org/en/stable/coordinates/velocities.html).\n", "We first have to define the position and motion of the sun relative to the\n", "Galactocentric frame, and create an\n", "[`astropy.coordinates.Galactocentric`](http://docs.astropy.org/en/stable/api/astropy.coordinates.Galactocentric.html#astropy.coordinates.Galactocentric)\n", "object with these parameters. We could specify these things explicitly, but\n", "instead we will use the default values that were recently updated in Astropy:" ] }, { "cell_type": "code", "execution_count": 7, "id": "bbc77544", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.543020Z", "iopub.status.busy": "2025-12-11T04:10:36.542803Z", "iopub.status.idle": "2025-12-11T04:10:36.547429Z", "shell.execute_reply": "2025-12-11T04:10:36.546778Z" } }, "outputs": [ { "data": { "text/plain": [ ", galcen_distance=8.122 kpc, galcen_v_sun=(12.9, 245.6, 7.78) km / s, z_sun=20.8 pc, roll=0.0 deg)>" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "galcen_frame = coord.Galactocentric()\n", "galcen_frame" ] }, { "cell_type": "markdown", "id": "9559b0e1", "metadata": {}, "source": [ "To transform the mean observed kinematics to this frame, we simply do:" ] }, { "cell_type": "code", "execution_count": 8, "id": "1252c797", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.549302Z", "iopub.status.busy": "2025-12-11T04:10:36.549132Z", "iopub.status.idle": "2025-12-11T04:10:36.557581Z", "shell.execute_reply": "2025-12-11T04:10:36.557010Z" } }, "outputs": [], "source": [ "galcen = icrs.transform_to(galcen_frame)" ] }, { "cell_type": "markdown", "id": "47115855", "metadata": {}, "source": [ "That's it! Now we have to turn the resulting `Galactocentric` object into\n", "orbital initial conditions, and integrate the orbit in our Milky Way model.\n", "We'll use a timestep of 0.5 Myr and integrate the orbit backwards for 10000\n", "steps (5 Gyr):" ] }, { "cell_type": "code", "execution_count": 9, "id": "0b043faa", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.559469Z", "iopub.status.busy": "2025-12-11T04:10:36.559295Z", "iopub.status.idle": "2025-12-11T04:10:36.567854Z", "shell.execute_reply": "2025-12-11T04:10:36.566958Z" } }, "outputs": [], "source": [ "w0 = gd.PhaseSpacePosition(galcen.data)\n", "orbit = potential.integrate_orbit(w0, dt=-0.5 * u.Myr, n_steps=10000)" ] }, { "cell_type": "markdown", "id": "085241c7", "metadata": {}, "source": [ "Let's visualize the orbit:" ] }, { "cell_type": "code", "execution_count": 10, "id": "2445f345", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:36.569457Z", "iopub.status.busy": "2025-12-11T04:10:36.569286Z", "iopub.status.idle": "2025-12-11T04:10:37.096657Z", "shell.execute_reply": "2025-12-11T04:10:37.095657Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 411, "width": 1099 } }, "output_type": "display_data" } ], "source": [ "fig = orbit.plot()" ] }, { "cell_type": "markdown", "id": "1459ba6d", "metadata": {}, "source": [ "With the `orbit` object, we can easily compute quantities like the pericenter,\n", "apocenter, or eccentricity of the orbit:" ] }, { "cell_type": "code", "execution_count": 11, "id": "c12a9337", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.098726Z", "iopub.status.busy": "2025-12-11T04:10:37.098472Z", "iopub.status.idle": "2025-12-11T04:10:37.126112Z", "shell.execute_reply": "2025-12-11T04:10:37.125167Z" } }, "outputs": [ { "data": { "text/plain": [ "(, , )" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "orbit.pericenter(), orbit.apocenter(), orbit.eccentricity()" ] }, { "cell_type": "markdown", "id": "bd0d7dee", "metadata": {}, "source": [ "We can also use these functions to get the time of each pericenter or\n", "apocenter - let's plot the time of pericenter, and time of apocenter over the\n", "time series of the Galactocentric radius of the orbit:" ] }, { "cell_type": "code", "execution_count": 12, "id": "e6f9a562", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.127841Z", "iopub.status.busy": "2025-12-11T04:10:37.127659Z", "iopub.status.idle": "2025-12-11T04:10:37.298948Z", "shell.execute_reply": "2025-12-11T04:10:37.298126Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$r$ [$\\\\mathrm{kpc}$]')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 434, "width": 573 } }, "output_type": "display_data" } ], "source": [ "plt.plot(orbit.t, orbit.spherical.distance, marker=\"None\")\n", "\n", "per, per_times = orbit.pericenter(return_times=True, func=None)\n", "apo, apo_times = orbit.apocenter(return_times=True, func=None)\n", "\n", "for t in per_times:\n", " plt.axvline(t.value, color=\"#67a9cf\")\n", "\n", "for t in apo_times:\n", " plt.axvline(t.value, color=\"#ef8a62\")\n", "\n", "plt.xlabel(\"$t$ [{}]\".format(orbit.t.unit.to_string(\"latex\")))\n", "plt.ylabel(\"$r$ [{}]\".format(orbit.x.unit.to_string(\"latex\")))" ] }, { "cell_type": "markdown", "id": "fd29eca9", "metadata": {}, "source": [ "Now we'll sample from the error distribution over the distance, proper\n", "motions, and radial velocity, compute orbits, and plot distributions of mean\n", "pericenter and apocenter:" ] }, { "cell_type": "code", "execution_count": 13, "id": "71530c20", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.300905Z", "iopub.status.busy": "2025-12-11T04:10:37.300709Z", "iopub.status.idle": "2025-12-11T04:10:37.306343Z", "shell.execute_reply": "2025-12-11T04:10:37.305545Z" } }, "outputs": [], "source": [ "n_samples = 128\n", "\n", "rng = np.random.default_rng(42)\n", "dist = (\n", " rng.normal(icrs.distance.value, icrs_err.distance.value, n_samples)\n", " * icrs.distance.unit\n", ")\n", "\n", "pm_ra_cosdec = (\n", " rng.normal(icrs.pm_ra_cosdec.value, icrs_err.pm_ra_cosdec.value, n_samples)\n", " * icrs.pm_ra_cosdec.unit\n", ")\n", "\n", "pm_dec = (\n", " rng.normal(icrs.pm_dec.value, icrs_err.pm_dec.value, n_samples) * icrs.pm_dec.unit\n", ")\n", "\n", "rv = (\n", " rng.normal(icrs.radial_velocity.value, icrs_err.radial_velocity.value, n_samples)\n", " * icrs.radial_velocity.unit\n", ")\n", "\n", "ra = np.full(n_samples, icrs.ra.degree) * u.degree\n", "dec = np.full(n_samples, icrs.dec.degree) * u.degree" ] }, { "cell_type": "code", "execution_count": 14, "id": "c4298f10", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.307966Z", "iopub.status.busy": "2025-12-11T04:10:37.307795Z", "iopub.status.idle": "2025-12-11T04:10:37.311797Z", "shell.execute_reply": "2025-12-11T04:10:37.310946Z" } }, "outputs": [], "source": [ "icrs_samples = coord.SkyCoord(\n", " ra=ra,\n", " dec=dec,\n", " distance=dist,\n", " pm_ra_cosdec=pm_ra_cosdec,\n", " pm_dec=pm_dec,\n", " radial_velocity=rv,\n", ")" ] }, { "cell_type": "code", "execution_count": 15, "id": "a4fd9e1f", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.313403Z", "iopub.status.busy": "2025-12-11T04:10:37.313222Z", "iopub.status.idle": "2025-12-11T04:10:37.317202Z", "shell.execute_reply": "2025-12-11T04:10:37.316420Z" } }, "outputs": [ { "data": { "text/plain": [ "(128,)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "icrs_samples.shape" ] }, { "cell_type": "code", "execution_count": 16, "id": "7b26a2e3", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.318789Z", "iopub.status.busy": "2025-12-11T04:10:37.318585Z", "iopub.status.idle": "2025-12-11T04:10:37.326630Z", "shell.execute_reply": "2025-12-11T04:10:37.325863Z" } }, "outputs": [], "source": [ "galcen_samples = icrs_samples.transform_to(galcen_frame)" ] }, { "cell_type": "code", "execution_count": 17, "id": "4c394229", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.328297Z", "iopub.status.busy": "2025-12-11T04:10:37.328126Z", "iopub.status.idle": "2025-12-11T04:10:37.371852Z", "shell.execute_reply": "2025-12-11T04:10:37.370878Z" } }, "outputs": [], "source": [ "w0_samples = gd.PhaseSpacePosition(galcen_samples.data)\n", "orbit_samples = potential.integrate_orbit(w0_samples, dt=-1 * u.Myr, n_steps=4000)" ] }, { "cell_type": "code", "execution_count": 18, "id": "bbb9f916", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.373642Z", "iopub.status.busy": "2025-12-11T04:10:37.373413Z", "iopub.status.idle": "2025-12-11T04:10:37.377688Z", "shell.execute_reply": "2025-12-11T04:10:37.376838Z" } }, "outputs": [ { "data": { "text/plain": [ "(4001, 128)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "orbit_samples.shape" ] }, { "cell_type": "code", "execution_count": 19, "id": "81f8f3a1", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:37.379381Z", "iopub.status.busy": "2025-12-11T04:10:37.379206Z", "iopub.status.idle": "2025-12-11T04:10:39.193312Z", "shell.execute_reply": "2025-12-11T04:10:39.192275Z" } }, "outputs": [], "source": [ "peris = orbit_samples.pericenter(approximate=True)\n", "\n", "apos = orbit_samples.apocenter(approximate=True)\n", "\n", "eccs = orbit_samples.eccentricity(approximate=True)" ] }, { "cell_type": "code", "execution_count": 20, "id": "f1da908a", "metadata": { "execution": { "iopub.execute_input": "2025-12-11T04:10:39.195280Z", "iopub.status.busy": "2025-12-11T04:10:39.195067Z", "iopub.status.idle": "2025-12-11T04:10:39.553707Z", "shell.execute_reply": "2025-12-11T04:10:39.552486Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'eccentricity')" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "image/png": { "height": 371, "width": 980 } }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(12, 4), sharey=True)\n", "\n", "axes[0].hist(peris.to_value(u.kpc), bins=np.linspace(20, 80, 32))\n", "axes[0].set_xlabel(\"pericenter [kpc]\")\n", "\n", "axes[1].hist(apos.to_value(u.kpc), bins=np.linspace(60, 140, 32))\n", "axes[1].set_xlabel(\"apocenter [kpc]\")\n", "\n", "axes[2].hist(eccs.value, bins=np.linspace(0.3, 0.5, 41))\n", "axes[2].set_xlabel(\"eccentricity\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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 }