{ "cells": [ { "cell_type": "markdown", "id": "intro-title", "metadata": { "papermill": { "duration": 0.004813, "end_time": "2026-06-30T01:18:56.693452+00:00", "exception": false, "start_time": "2026-06-30T01:18:56.688639+00:00", "status": "completed" }, "tags": [] }, "source": [ "# The Potential of N-body Simulations\n", "\n", "galpy can set up and work with the frozen potential of an N-body simulation. This allows you to study the properties of such potentials, investigate orbits, and calculate action-angle coordinates using the galpy framework. Currently, this functionality uses axisymmetrized versions of the snapshots. The use of this functionality requires [pynbody](https://github.com/pynbody/pynbody)." ] }, { "cell_type": "code", "execution_count": 1, "id": "setup-imports", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:18:56.702482Z", "iopub.status.busy": "2026-06-30T01:18:56.702271Z", "iopub.status.idle": "2026-06-30T01:18:58.964424Z", "shell.execute_reply": "2026-06-30T01:18:58.963598Z" }, "papermill": { "duration": 2.267718, "end_time": "2026-06-30T01:18:58.965425+00:00", "exception": false, "start_time": "2026-06-30T01:18:56.697707+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", "import numpy\n", "from matplotlib import pyplot as plt\n", "import pynbody\n", "from galpy.potential import (\n", " SnapshotRZPotential,\n", " InterpSnapshotRZPotential,\n", " KeplerPotential,\n", ")" ] }, { "cell_type": "markdown", "id": "snapshot-simple", "metadata": { "papermill": { "duration": 0.003231, "end_time": "2026-06-30T01:18:58.972235+00:00", "exception": false, "start_time": "2026-06-30T01:18:58.969004+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Simple example: SnapshotRZPotential\n", "\n", "As a first, simple example we look at the potential of a single simulation particle, which should correspond to galpy's `KeplerPotential`. We can create such a single-particle snapshot using `pynbody` and then get its potential in galpy:" ] }, { "cell_type": "code", "execution_count": 2, "id": "de8863bf", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:18:58.980178Z", "iopub.status.busy": "2026-06-30T01:18:58.979812Z", "iopub.status.idle": "2026-06-30T01:18:58.983739Z", "shell.execute_reply": "2026-06-30T01:18:58.982983Z" }, "papermill": { "duration": 0.009026, "end_time": "2026-06-30T01:18:58.984527+00:00", "exception": false, "start_time": "2026-06-30T01:18:58.975501+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "s = pynbody.new(star=1)\n", "s[\"mass\"] = 1.0\n", "s[\"eps\"] = 0.0\n", "sp = SnapshotRZPotential(s, num_threads=1)" ] }, { "cell_type": "markdown", "id": "10ba1cec", "metadata": { "papermill": { "duration": 0.006231, "end_time": "2026-06-30T01:18:58.994177+00:00", "exception": false, "start_time": "2026-06-30T01:18:58.987946+00:00", "status": "completed" }, "tags": [] }, "source": [ "With these definitions, this snapshot potential should be the same as `KeplerPotential` with an amplitude of one, which we can verify:" ] }, { "cell_type": "code", "execution_count": 3, "id": "0eafa44d", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:18:59.001890Z", "iopub.status.busy": "2026-06-30T01:18:59.001683Z", "iopub.status.idle": "2026-06-30T01:18:59.008835Z", "shell.execute_reply": "2026-06-30T01:18:59.007855Z" }, "papermill": { "duration": 0.012007, "end_time": "2026-06-30T01:18:59.009517+00:00", "exception": false, "start_time": "2026-06-30T01:18:58.997510+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Potentials: -0.9090909090909091 -0.9090909090909091 0.0\n", "R forces: -0.8264462809917354 -0.8264462809917353 -1.1102230246251565e-16\n" ] } ], "source": [ "from galpy.potential import KeplerPotential\n", "\n", "kp = KeplerPotential(amp=1.0)\n", "print(\"Potentials: \", sp(1.1, 0.0), kp(1.1, 0.0), sp(1.1, 0.0) - kp(1.1, 0.0))\n", "print(\n", " \"R forces: \",\n", " sp.Rforce(1.1, 0.0),\n", " kp.Rforce(1.1, 0.0),\n", " sp.Rforce(1.1, 0.0) - kp.Rforce(1.1, 0.0),\n", ")" ] }, { "cell_type": "markdown", "id": "0e059d91", "metadata": { "papermill": { "duration": 0.003335, "end_time": "2026-06-30T01:18:59.016449+00:00", "exception": false, "start_time": "2026-06-30T01:18:59.013114+00:00", "status": "completed" }, "tags": [] }, "source": [ "`SnapshotRZPotential` instances can be used wherever other galpy potentials can be used (note that the second derivatives have not been implemented, such that functions depending on those will not work). For example, we can plot the rotation curve:" ] }, { "cell_type": "code", "execution_count": 4, "id": "c5770f78", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:18:59.024322Z", "iopub.status.busy": "2026-06-30T01:18:59.023947Z", "iopub.status.idle": "2026-06-30T01:18:59.556668Z", "shell.execute_reply": "2026-06-30T01:18:59.555736Z" }, "papermill": { "duration": 0.537573, "end_time": "2026-06-30T01:18:59.557450+00:00", "exception": false, "start_time": "2026-06-30T01:18:59.019877+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sp.plotRotcurve();" ] }, { "cell_type": "markdown", "id": "interp-snapshot", "metadata": { "papermill": { "duration": 0.003352, "end_time": "2026-06-30T01:18:59.565352+00:00", "exception": false, "start_time": "2026-06-30T01:18:59.562000+00:00", "status": "completed" }, "tags": [] }, "source": [ "## InterpSnapshotRZPotential\n", "\n", "Because evaluating the potential and forces of a snapshot is computationally expensive, most useful applications of frozen N-body potentials employ interpolated versions of the snapshot potential. These can be set up in galpy using `InterpSnapshotRZPotential`.\n", "\n", "To illustrate its use we will make use of one of `pynbody`'s example snapshots, `g15784`. This snapshot is used in the [pynbody quickstart tutorial](https://pynbody.readthedocs.io/latest/tutorials/quickstart.html) and can be downloaded from [Zenodo](https://zenodo.org/records/12687409).\n", "\n", "Once you have downloaded the testdata, load and prepare the snapshot:" ] }, { "cell_type": "code", "execution_count": 5, "id": "fc2e057e", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:18:59.573474Z", "iopub.status.busy": "2026-06-30T01:18:59.573259Z", "iopub.status.idle": "2026-06-30T01:19:00.851867Z", "shell.execute_reply": "2026-06-30T01:19:00.850993Z" }, "papermill": { "duration": 1.285248, "end_time": "2026-06-30T01:19:00.854106+00:00", "exception": false, "start_time": "2026-06-30T01:18:59.568858+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "pynbody.halo : Unable to load AHF substructure file; continuing without. To expose the underlying problem as an exception, pass ignore_missing_substructure=False to the AHFCatalogue constructor\n" ] } ], "source": [ "s = pynbody.load(\"gasoline_ahf/g15784.lr.01024.gz\")\n", "\n", "# Get the main galaxy, center, and align face-on\n", "h = s.halos()\n", "h0 = h[0]\n", "pynbody.analysis.faceon(h0)\n", "\n", "# Convert to physical units with G=1\n", "s.physical_units(mass=\"kpc km**2 s**-2 G**-1\")" ] }, { "cell_type": "markdown", "id": "dd3b6de6", "metadata": { "papermill": { "duration": 0.006068, "end_time": "2026-06-30T01:19:00.866535+00:00", "exception": false, "start_time": "2026-06-30T01:19:00.860467+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can now load an interpolated version of this snapshot's potential into galpy:" ] }, { "cell_type": "code", "execution_count": 6, "id": "842edc19", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:19:00.879804Z", "iopub.status.busy": "2026-06-30T01:19:00.879482Z", "iopub.status.idle": "2026-06-30T01:19:58.709570Z", "shell.execute_reply": "2026-06-30T01:19:58.708813Z" }, "papermill": { "duration": 57.838153, "end_time": "2026-06-30T01:19:58.710799+00:00", "exception": false, "start_time": "2026-06-30T01:19:00.872646+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "spi = InterpSnapshotRZPotential(\n", " h0,\n", " rgrid=(numpy.log(0.01), numpy.log(20.0), 101),\n", " logR=True,\n", " zgrid=(0.0, 10.0, 101),\n", " interpPot=True,\n", " zsym=True,\n", ")" ] }, { "cell_type": "markdown", "id": "034421df", "metadata": { "papermill": { "duration": 0.003376, "end_time": "2026-06-30T01:19:58.717860+00:00", "exception": false, "start_time": "2026-06-30T01:19:58.714484+00:00", "status": "completed" }, "tags": [] }, "source": [ "where we further assume that the potential is symmetric around the mid-plane ($z=0$). Depending on the size of the simulation, this instantiation can take a long time. This potential instance has *physical* units (and thus the `rgrid=` and `zgrid=` inputs are given in kpc if the simulation's distance unit is kpc). For example, if we ask for the rotation curve:" ] }, { "cell_type": "code", "execution_count": 7, "id": "ac6589bf", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:19:58.725813Z", "iopub.status.busy": "2026-06-30T01:19:58.725475Z", "iopub.status.idle": "2026-06-30T01:20:04.740151Z", "shell.execute_reply": "2026-06-30T01:20:04.739099Z" }, "papermill": { "duration": 6.019765, "end_time": "2026-06-30T01:20:04.741040+00:00", "exception": false, "start_time": "2026-06-30T01:19:58.721275+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spi.plotRotcurve(\n", " Rrange=[0.01, 19.9],\n", " xlabel=r\"$R\\,(\\mathrm{kpc})$\",\n", " ylabel=r\"$v_c(R)\\,(\\mathrm{km\\,s}^{-1})$\",\n", ");" ] }, { "cell_type": "markdown", "id": "natural-units", "metadata": { "papermill": { "duration": 0.003426, "end_time": "2026-06-30T01:20:04.748982+00:00", "exception": false, "start_time": "2026-06-30T01:20:04.745556+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Converting to natural units\n", "\n", "Because galpy works best in a system of *natural units*, we can convert the interpolated snapshot potential to natural units using `normalize()`. For example, using the circular velocity at $R = 10$ kpc:" ] }, { "cell_type": "code", "execution_count": 8, "id": "3b5e4e27", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:20:04.757013Z", "iopub.status.busy": "2026-06-30T01:20:04.756812Z", "iopub.status.idle": "2026-06-30T01:20:04.775919Z", "shell.execute_reply": "2026-06-30T01:20:04.775018Z" }, "papermill": { "duration": 0.024106, "end_time": "2026-06-30T01:20:04.776540+00:00", "exception": false, "start_time": "2026-06-30T01:20:04.752434+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vcirc at R=10 kpc: 294.6732646339408\n" ] } ], "source": [ "print(\"Vcirc at R=10 kpc:\", spi.vcirc(10.0))\n", "spi.normalize(R0=10.0)" ] }, { "cell_type": "markdown", "id": "3b870ed5", "metadata": { "papermill": { "duration": 0.003762, "end_time": "2026-06-30T01:20:04.784188+00:00", "exception": false, "start_time": "2026-06-30T01:20:04.780426+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can then plot the rotation curve again, keeping in mind that the distance unit is now $R_0$:" ] }, { "cell_type": "code", "execution_count": 9, "id": "cd89ffa1", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:20:04.792390Z", "iopub.status.busy": "2026-06-30T01:20:04.792139Z", "iopub.status.idle": "2026-06-30T01:20:10.545547Z", "shell.execute_reply": "2026-06-30T01:20:10.544318Z" }, "papermill": { "duration": 5.758435, "end_time": "2026-06-30T01:20:10.546248+00:00", "exception": false, "start_time": "2026-06-30T01:20:04.787813+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spi.plotRotcurve(Rrange=[0.01, 1.99])" ] }, { "cell_type": "markdown", "id": "9a2b3f4a", "metadata": { "papermill": { "duration": 0.003791, "end_time": "2026-06-30T01:20:10.554771+00:00", "exception": false, "start_time": "2026-06-30T01:20:10.550980+00:00", "status": "completed" }, "tags": [] }, "source": [ "In particular, `spi.vcirc(1.)` now returns `1.0`. We can also plot the potential:" ] }, { "cell_type": "code", "execution_count": 10, "id": "3314acc8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:20:10.562934Z", "iopub.status.busy": "2026-06-30T01:20:10.562742Z", "iopub.status.idle": "2026-06-30T01:20:25.108944Z", "shell.execute_reply": "2026-06-30T01:20:25.108109Z" }, "papermill": { "duration": 14.551182, "end_time": "2026-06-30T01:20:25.109605+00:00", "exception": false, "start_time": "2026-06-30T01:20:10.558423+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spi.plot(rmin=0.01, rmax=1.9, nrs=51, zmin=-0.99, zmax=0.99, nzs=51)\n", "plt.gca().set_aspect(1.0);" ] }, { "cell_type": "markdown", "id": "dba03c17", "metadata": { "papermill": { "duration": 0.00386, "end_time": "2026-06-30T01:20:25.117688+00:00", "exception": false, "start_time": "2026-06-30T01:20:25.113828+00:00", "status": "completed" }, "tags": [] }, "source": [ "This simulation's potential is quite spherical, which is confirmed by looking at the flattening:" ] }, { "cell_type": "code", "execution_count": 11, "id": "4d699a67", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:20:25.126677Z", "iopub.status.busy": "2026-06-30T01:20:25.126483Z", "iopub.status.idle": "2026-06-30T01:20:25.153067Z", "shell.execute_reply": "2026-06-30T01:20:25.152246Z" }, "papermill": { "duration": 0.032405, "end_time": "2026-06-30T01:20:25.154008+00:00", "exception": false, "start_time": "2026-06-30T01:20:25.121603+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Flattening at R=1.0, z=0.1: 0.8631229510097886\n", "Flattening at R=1.5, z=0.1: 0.9430920419468051\n" ] } ], "source": [ "print(f\"Flattening at R=1.0, z=0.1: {spi.flattening(1.0, 0.1)}\")\n", "print(f\"Flattening at R=1.5, z=0.1: {spi.flattening(1.5, 0.1)}\")" ] }, { "cell_type": "markdown", "id": "96b24fdc", "metadata": { "papermill": { "duration": 0.00405, "end_time": "2026-06-30T01:20:25.162307+00:00", "exception": false, "start_time": "2026-06-30T01:20:25.158257+00:00", "status": "completed" }, "tags": [] }, "source": [ "The epicycle and vertical frequencies can also be interpolated by setting the `interpepifreq=True` or `interpverticalfreq=True` keywords when instantiating the `InterpSnapshotRZPotential` object." ] }, { "cell_type": "markdown", "id": "17c2de27", "metadata": { "papermill": { "duration": 0.003752, "end_time": "2026-06-30T01:20:25.170062+00:00", "exception": false, "start_time": "2026-06-30T01:20:25.166310+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Estimating action-angle coordinates in the N-body simulation\n", "\n", "Once we have set up the interpolated potential of an N-body simulation, we can\n", "use galpy's action-angle machinery to compute actions for simulation particles.\n", "This is a powerful way to characterize the orbital structure of the simulated\n", "galaxy. Here we use `actionAngleStaeckel`, the most accurate general method\n", "for axisymmetric potentials. We need to re-instantiate the interpolated\n", "potential with `enable_c=True` so the action-angle calculation can use the\n", "fast C implementation:" ] }, { "cell_type": "code", "execution_count": 12, "id": "1c6dba6d", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:20:25.179018Z", "iopub.status.busy": "2026-06-30T01:20:25.178825Z", "iopub.status.idle": "2026-06-30T01:21:22.819607Z", "shell.execute_reply": "2026-06-30T01:21:22.818794Z" }, "papermill": { "duration": 57.646486, "end_time": "2026-06-30T01:21:22.820633+00:00", "exception": false, "start_time": "2026-06-30T01:20:25.174147+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "spi_c = InterpSnapshotRZPotential(\n", " h0,\n", " rgrid=(numpy.log(0.01), numpy.log(20.0), 101),\n", " logR=True,\n", " zgrid=(0.0, 10.0, 101),\n", " interpPot=True,\n", " zsym=True,\n", " enable_c=True,\n", ")\n", "spi_c.normalize(R0=10.0)" ] }, { "cell_type": "markdown", "id": "98f5d82e", "metadata": { "papermill": { "duration": 0.004121, "end_time": "2026-06-30T01:21:22.829947+00:00", "exception": false, "start_time": "2026-06-30T01:21:22.825826+00:00", "status": "completed" }, "tags": [] }, "source": [ "Now we load a pristine copy of the simulation (because the normalization\n", "above can lead to some inconsistent behavior in pynbody) and select star\n", "particles in a radial ring near $R = 8\\,\\mathrm{kpc}$:" ] }, { "cell_type": "code", "execution_count": 13, "id": "ccc232fc", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:21:22.839037Z", "iopub.status.busy": "2026-06-30T01:21:22.838833Z", "iopub.status.idle": "2026-06-30T01:21:24.231761Z", "shell.execute_reply": "2026-06-30T01:21:24.230717Z" }, "papermill": { "duration": 1.398486, "end_time": "2026-06-30T01:21:24.232484+00:00", "exception": false, "start_time": "2026-06-30T01:21:22.833998+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "pynbody.halo : Unable to load AHF substructure file; continuing without. To expose the underlying problem as an exception, pass ignore_missing_substructure=False to the AHFCatalogue constructor\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Selected 12926 star particles\n" ] } ], "source": [ "sc = pynbody.load(\"gasoline_ahf/g15784.lr.01024.gz\")\n", "hc = sc.halos()\n", "hc0 = hc[0]\n", "pynbody.analysis.faceon(hc0)\n", "sc.physical_units()\n", "\n", "# Select stars in a radial ring near R = 8 kpc\n", "sn = pynbody.filt.BandPass(\"rxy\", \"7 kpc\", \"9 kpc\")\n", "R, vR, vT, z, vz = [\n", " numpy.ascontiguousarray(hc0.s[sn][x]) for x in (\"rxy\", \"vr\", \"vt\", \"z\", \"vz\")\n", "]\n", "\n", "# Convert to natural units\n", "ro, vo = 10.0, spi_c.vcirc(1.0, use_physical=False) * 294.67\n", "R /= ro\n", "z /= ro\n", "vR /= vo\n", "vT /= vo\n", "vz /= vo\n", "print(f\"Selected {len(R)} star particles\")" ] }, { "cell_type": "markdown", "id": "537f84a3", "metadata": { "papermill": { "duration": 0.004054, "end_time": "2026-06-30T01:21:24.241643+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.237589+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can integrate a random orbit from this selection to see what it looks like:" ] }, { "cell_type": "code", "execution_count": 14, "id": "d22126f1", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:21:24.250821Z", "iopub.status.busy": "2026-06-30T01:21:24.250608Z", "iopub.status.idle": "2026-06-30T01:21:24.476369Z", "shell.execute_reply": "2026-06-30T01:21:24.475473Z" }, "papermill": { "duration": 0.231885, "end_time": "2026-06-30T01:21:24.477638+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.245753+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.orbit import Orbit\n", "\n", "numpy.random.seed(1)\n", "ii = numpy.random.permutation(len(R))[0]\n", "o = Orbit([R[ii], vR[ii], vT[ii], z[ii], vz[ii]])\n", "ts = numpy.linspace(0.0, 100.0, 1001)\n", "o.integrate(ts, spi_c)\n", "o.plot();" ] }, { "cell_type": "markdown", "id": "4e2204e6", "metadata": { "papermill": { "duration": 0.00449, "end_time": "2026-06-30T01:21:24.488055+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.483565+00:00", "status": "completed" }, "tags": [] }, "source": [ "Now compute actions for all selected particles using `actionAngleStaeckel`:" ] }, { "cell_type": "code", "execution_count": 15, "id": "26080bbf", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:21:24.498263Z", "iopub.status.busy": "2026-06-30T01:21:24.498042Z", "iopub.status.idle": "2026-06-30T01:21:24.599956Z", "shell.execute_reply": "2026-06-30T01:21:24.599469Z" }, "papermill": { "duration": 0.11139, "end_time": "2026-06-30T01:21:24.604090+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.492700+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.actionAngle import actionAngleStaeckel\n", "\n", "aAS = actionAngleStaeckel(pot=spi_c, delta=0.45, c=True)\n", "jr, lz, jz = aAS(R, vR, vT, z, vz)" ] }, { "cell_type": "markdown", "id": "17b4602f", "metadata": { "papermill": { "duration": 0.004791, "end_time": "2026-06-30T01:21:24.613859+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.609068+00:00", "status": "completed" }, "tags": [] }, "source": [ "Plot the distribution of angular momentum $L_z$ vs. radial action $J_R$:" ] }, { "cell_type": "code", "execution_count": 16, "id": "6edb5863", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:21:24.624148Z", "iopub.status.busy": "2026-06-30T01:21:24.623943Z", "iopub.status.idle": "2026-06-30T01:21:24.844143Z", "shell.execute_reply": "2026-06-30T01:21:24.843304Z" }, "papermill": { "duration": 0.226323, "end_time": "2026-06-30T01:21:24.844827+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.618504+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.util import plot as galpy_plot\n", "\n", "galpy_plot.scatterplot(\n", " lz,\n", " jr,\n", " \"k.\",\n", " xlabel=r\"$L_z$\",\n", " ylabel=r\"$J_R$\",\n", " xrange=[0.0, 1.3],\n", " yrange=[0.0, 0.6],\n", ");" ] }, { "cell_type": "markdown", "id": "81695d91", "metadata": { "papermill": { "duration": 0.00471, "end_time": "2026-06-30T01:21:24.855712+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.851002+00:00", "status": "completed" }, "tags": [] }, "source": [ "The curved shape is a selection effect: low angular-momentum stars can only\n", "enter the selected radial ring if they have highly eccentric orbits (and\n", "therefore large $J_R$). The density gradient in angular momentum reflects the\n", "falling surface density of the disk. We can also look at the distribution of\n", "radial and vertical actions:" ] }, { "cell_type": "code", "execution_count": 17, "id": "09d4009a", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:21:24.866279Z", "iopub.status.busy": "2026-06-30T01:21:24.866058Z", "iopub.status.idle": "2026-06-30T01:21:24.993030Z", "shell.execute_reply": "2026-06-30T01:21:24.992004Z" }, "papermill": { "duration": 0.13313, "end_time": "2026-06-30T01:21:24.993638+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.860508+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(6, 6))\n", "ax.plot(jr, jz, \"k,\")\n", "ax.set_xlabel(r\"$J_R$\")\n", "ax.set_ylabel(r\"$J_z$\")\n", "ax.set_xlim(0.0, 0.4)\n", "ax.set_ylim(0.0, 0.2);" ] }, { "cell_type": "markdown", "id": "6f7f1843", "metadata": { "papermill": { "duration": 0.004807, "end_time": "2026-06-30T01:21:25.003808+00:00", "exception": false, "start_time": "2026-06-30T01:21:24.999001+00:00", "status": "completed" }, "tags": [] }, "source": [ "For more on action-angle coordinates and the different methods available for\n", "computing them, see the [action-angle tutorials](../action_angle/introduction.ipynb)." ] } ], "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": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 149.894289, "end_time": "2026-06-30T01:21:25.725376+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/potentials/nbody_snapshots.ipynb", "output_path": "doc/source/tutorials/potentials/nbody_snapshots.ipynb", "parameters": {}, "start_time": "2026-06-30T01:18:55.831087+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }