{ "cells": [ { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.004127, "end_time": "2026-05-16T13:44:29.162150+00:00", "exception": false, "start_time": "2026-05-16T13:44:29.158023+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Three-dimensional Disk Distribution Functions\n", "\n", "The `quasiisothermaldf` class implements the quasi-isothermal distribution function\n", "for three-dimensional disk populations from [Binney 2010](https://ui.adsabs.harvard.edu/abs/2010MNRAS.401.2318B/abstract) (with modifications by [Binney & McMillan 2012](https://ui.adsabs.harvard.edu/abs/2011MNRAS.413.1889B/abstract)). \n", " Research shows that this distribution function provides a good model for the DF of mono-abundance sub-populations (MAPs) of the Milky Way disk (see [Ting et al. 2013](https://ui.adsabs.harvard.edu/abs/2013MNRAS.434..652T/abstract) and [Bovy et al. 2013](https://ui.adsabs.harvard.edu/abs/2013ApJ…779..115B/abstract)).\n", "Unlike the 2D DFs, it is expressed in terms\n", "of action-angle variables $(J_R, L_z, J_z)$ and requires an action-angle calculator." ] }, { "cell_type": "code", "execution_count": 1, "id": "acae54e37e7d407bbb7b55eff062a284", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:29.169836Z", "iopub.status.busy": "2026-05-16T13:44:29.169600Z", "iopub.status.idle": "2026-05-16T13:44:29.535461Z", "shell.execute_reply": "2026-05-16T13:44:29.534580Z" }, "papermill": { "duration": 0.371162, "end_time": "2026-05-16T13:44:29.536645+00:00", "exception": false, "start_time": "2026-05-16T13:44:29.165483+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "id": "9a63283cbaf04dbcab1f6479b197f3a8", "metadata": { "papermill": { "duration": 0.003045, "end_time": "2026-05-16T13:44:29.543176+00:00", "exception": false, "start_time": "2026-05-16T13:44:29.540131+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Setup: potential and action-angle calculator\n", "\n", "We use `MWPotential2014` as the gravitational potential and set up\n", "an `actionAngleAdiabatic` instance to compute actions (note that generally ``actionAngleStaeckel`` is more accurate, but we use `actionAngleAdiabatic` for this demonstration and discuss the Staeckel backend later):" ] }, { "cell_type": "code", "execution_count": 2, "id": "8dd0d8092fe74a7c96281538738b07e2", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:29.550427Z", "iopub.status.busy": "2026-05-16T13:44:29.550160Z", "iopub.status.idle": "2026-05-16T13:44:31.539498Z", "shell.execute_reply": "2026-05-16T13:44:31.538577Z" }, "papermill": { "duration": 1.994224, "end_time": "2026-05-16T13:44:31.540524+00:00", "exception": false, "start_time": "2026-05-16T13:44:29.546300+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import MWPotential2014\n", "from galpy.actionAngle import actionAngleAdiabatic\n", "\n", "aA = actionAngleAdiabatic(pot=MWPotential2014, c=True)" ] }, { "cell_type": "markdown", "id": "72eea5119410473aa328ad9291626812", "metadata": { "papermill": { "duration": 0.003035, "end_time": "2026-05-16T13:44:31.547034+00:00", "exception": false, "start_time": "2026-05-16T13:44:31.543999+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Initializing the quasi-isothermal DF\n", "\n", "The `quasiisothermaldf` takes radial scale lengths and velocity dispersions\n", "as parameters:\n", "\n", "- `hr`: radial scale length of the surface density\n", "- `sr`: radial velocity dispersion at the solar radius\n", "- `sz`: vertical velocity dispersion at the solar radius\n", "- `hsr`: scale length of the radial velocity dispersion\n", "- `hsz`: scale length of the vertical velocity dispersion" ] }, { "cell_type": "code", "execution_count": 3, "id": "8edb47106e1a46a883d545849b8ab81b", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:31.554723Z", "iopub.status.busy": "2026-05-16T13:44:31.554248Z", "iopub.status.idle": "2026-05-16T13:44:32.110662Z", "shell.execute_reply": "2026-05-16T13:44:32.109643Z" }, "papermill": { "duration": 0.561685, "end_time": "2026-05-16T13:44:32.111921+00:00", "exception": false, "start_time": "2026-05-16T13:44:31.550236+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.df import quasiisothermaldf\n", "\n", "qdf = quasiisothermaldf(\n", " hr=1.0 / 3.0, # radial scale length\n", " sr=0.2, # sigma_R at R_0\n", " sz=0.1, # sigma_z at R_0\n", " hsr=1.0, # sigma_R scale length\n", " hsz=1.0, # sigma_z scale length\n", " pot=MWPotential2014,\n", " aA=aA,\n", ")" ] }, { "cell_type": "markdown", "id": "10185d26023b46108eb7d9f57d49d2b3", "metadata": { "papermill": { "duration": 0.002972, "end_time": "2026-05-16T13:44:32.118361+00:00", "exception": false, "start_time": "2026-05-16T13:44:32.115389+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Evaluating the DF at a point\n", "\n", "The DF can be evaluated at a given $(R, v_R, v_T, z, v_z)$ point.\n", "Internally it computes the actions and evaluates $f(J_R, L_z, J_z)$:" ] }, { "cell_type": "code", "execution_count": 4, "id": "8763a12b2bbd4a93a75aff182afb95dc", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:32.125622Z", "iopub.status.busy": "2026-05-16T13:44:32.125370Z", "iopub.status.idle": "2026-05-16T13:44:32.131020Z", "shell.execute_reply": "2026-05-16T13:44:32.130086Z" }, "papermill": { "duration": 0.010856, "end_time": "2026-05-16T13:44:32.132334+00:00", "exception": false, "start_time": "2026-05-16T13:44:32.121478+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f(R=1, vR=0, vT=1, z=0, vz=0) = [514.84583859]\n" ] } ], "source": [ "# DF value at the solar circle moving on a circular orbit\n", "print(\"f(R=1, vR=0, vT=1, z=0, vz=0) =\", qdf(1.0, 0.0, 1.0, 0.0, 0.0))" ] }, { "cell_type": "markdown", "id": "7623eae2785240b9bd12b16a66d81610", "metadata": { "papermill": { "duration": 0.003059, "end_time": "2026-05-16T13:44:32.140041+00:00", "exception": false, "start_time": "2026-05-16T13:44:32.136982+00:00", "status": "completed" }, "tags": [] }, "source": [ "## DF moments\n", "\n", "The `quasiisothermaldf` can compute various moments by marginalizing\n", "over velocity. These integrals use Gauss-Legendre quadrature by default." ] }, { "cell_type": "code", "execution_count": 5, "id": "7cdc8c89c7104fffa095e18ddfef8986", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:32.147403Z", "iopub.status.busy": "2026-05-16T13:44:32.147231Z", "iopub.status.idle": "2026-05-16T13:44:32.522685Z", "shell.execute_reply": "2026-05-16T13:44:32.522081Z" }, "papermill": { "duration": 0.380607, "end_time": "2026-05-16T13:44:32.523932+00:00", "exception": false, "start_time": "2026-05-16T13:44:32.143325+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Surface mass at R=1: 0.5684828858456422\n", "sigma_R^2 at (R=1, z=0): 0.04329359333259306\n", "sigma_T^2 at (R=1, z=0): 0.023214249869379477\n", "sigma_z^2 at (R=1, z=0): 0.04329359333259306\n" ] } ], "source": [ "# Vertically-integrated surface density at R=1\n", "print(\"Surface mass at R=1:\", qdf.surfacemass_z(1.0))\n", "\n", "# Velocity dispersions at (R=1, z=0)\n", "print(\"sigma_R^2 at (R=1, z=0):\", qdf.sigmaR2(1.0, 0.0))\n", "print(\"sigma_T^2 at (R=1, z=0):\", qdf.sigmaT2(1.0, 0.0))\n", "print(\"sigma_z^2 at (R=1, z=0):\", qdf.sigmaR2(1.0, 0.0))" ] }, { "cell_type": "markdown", "id": "b118ea5561624da68c537baed56e602f", "metadata": { "papermill": { "duration": 0.003321, "end_time": "2026-05-16T13:44:32.531643+00:00", "exception": false, "start_time": "2026-05-16T13:44:32.528322+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can also compute the mean actions as a function of position:" ] }, { "cell_type": "code", "execution_count": 6, "id": "938c804e27f84196a10c8828c723f798", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:32.542653Z", "iopub.status.busy": "2026-05-16T13:44:32.542308Z", "iopub.status.idle": "2026-05-16T13:44:34.165685Z", "shell.execute_reply": "2026-05-16T13:44:34.164679Z" }, "papermill": { "duration": 1.631221, "end_time": "2026-05-16T13:44:34.166353+00:00", "exception": false, "start_time": "2026-05-16T13:44:32.535132+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " at (R=1, z=0): 0.03406689383453623\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " at (R=1, z=0): 0.9140887169726567\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " at (R=1, z=0): 0.0017174864094052283\n" ] } ], "source": [ "numpy.random.seed(1)\n", "print(\" at (R=1, z=0):\", qdf.meanjr(1.0, 0.0, mc=True, nmc=10000))\n", "print(\" at (R=1, z=0):\", qdf.meanlz(1.0, 0.0, mc=True, nmc=10000))\n", "print(\" at (R=1, z=0):\", qdf.meanjz(1.0, 0.0, mc=True, nmc=10000))" ] }, { "cell_type": "markdown", "id": "504fb2a444614c0babb325280ed9130a", "metadata": { "papermill": { "duration": 0.003278, "end_time": "2026-05-16T13:44:34.173235+00:00", "exception": false, "start_time": "2026-05-16T13:44:34.169957+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Surface density profile\n", "\n", "Let's compute and plot the surface density as a function of radius:" ] }, { "cell_type": "code", "execution_count": 7, "id": "59bbdb311c014d738909a11f9e486628", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:34.180914Z", "iopub.status.busy": "2026-05-16T13:44:34.180721Z", "iopub.status.idle": "2026-05-16T13:44:40.117200Z", "shell.execute_reply": "2026-05-16T13:44:40.116246Z" }, "papermill": { "duration": 5.941303, "end_time": "2026-05-16T13:44:40.117929+00:00", "exception": false, "start_time": "2026-05-16T13:44:34.176626+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Rs = numpy.linspace(0.3, 2.0, 21)\n", "smass = numpy.array([qdf.surfacemass_z(R) for R in Rs])\n", "plt.semilogy(Rs, smass)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$\\Sigma(R)$\")\n", "plt.title(\"Quasi-isothermal DF surface density profile\");" ] }, { "cell_type": "markdown", "id": "b43b363d81ae4b689946ece5c682cd59", "metadata": { "papermill": { "duration": 0.003579, "end_time": "2026-05-16T13:44:40.125501+00:00", "exception": false, "start_time": "2026-05-16T13:44:40.121922+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can estimate the actual scale length from the DF by taking the log-slope:" ] }, { "cell_type": "code", "execution_count": 8, "id": "8a65eabff63a45729fe45fb5ade58bdc", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:40.133865Z", "iopub.status.busy": "2026-05-16T13:44:40.133656Z", "iopub.status.idle": "2026-05-16T13:44:40.664545Z", "shell.execute_reply": "2026-05-16T13:44:40.663799Z" }, "papermill": { "duration": 0.537418, "end_time": "2026-05-16T13:44:40.666685+00:00", "exception": false, "start_time": "2026-05-16T13:44:40.129267+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated scale length: 0.372 (input: 0.333)\n" ] } ], "source": [ "# Estimate scale length from the DF near R=1\n", "dR = 0.01\n", "sm1 = qdf.surfacemass_z(1.0 - dR)\n", "sm2 = qdf.surfacemass_z(1.0 + dR)\n", "hR_est = -2.0 * dR / numpy.log(sm2 / sm1)\n", "print(f\"Estimated scale length: {hR_est:.3f} (input: {1.0 / 3.0:.3f})\")" ] }, { "cell_type": "markdown", "id": "c3933fab20d04ec698c2621248eb3be0", "metadata": { "papermill": { "duration": 0.003619, "end_time": "2026-05-16T13:44:40.674697+00:00", "exception": false, "start_time": "2026-05-16T13:44:40.671078+00:00", "status": "completed" }, "tags": [] }, "source": [ "The actual scale length of the DF is close to, but not exactly equal to,\n", "the input `hr` because the quasi-isothermal DF is only approximate.\n", "\n", "## Velocity dispersion profiles\n", "\n", "We can also compute the velocity dispersion profiles as a function of radius:" ] }, { "cell_type": "code", "execution_count": 9, "id": "4dd4641cc4064e0191573fe9c69df29b", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:40.683528Z", "iopub.status.busy": "2026-05-16T13:44:40.683090Z", "iopub.status.idle": "2026-05-16T13:44:42.326128Z", "shell.execute_reply": "2026-05-16T13:44:42.325229Z" }, "papermill": { "duration": 1.648381, "end_time": "2026-05-16T13:44:42.326835+00:00", "exception": false, "start_time": "2026-05-16T13:44:40.678454+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigR2 = numpy.array([qdf.sigmaR2(R, 0.0) for R in Rs])\n", "sigT2 = numpy.array([qdf.sigmaT2(R, 0.0) for R in Rs])\n", "plt.plot(Rs, numpy.sqrt(sigR2), label=r\"$\\sigma_R$\")\n", "plt.plot(Rs, numpy.sqrt(sigT2), label=r\"$\\sigma_T$\")\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$\\sigma$\")\n", "plt.legend()\n", "plt.title(\"Velocity dispersion profiles\");" ] }, { "cell_type": "markdown", "id": "7a902d78", "metadata": { "papermill": { "duration": 0.003936, "end_time": "2026-05-16T13:44:42.334945+00:00", "exception": false, "start_time": "2026-05-16T13:44:42.331009+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Estimating scale lengths\n", "\n", "We can estimate the actual scale lengths of the DF (which differ slightly from\n", "the input parameters):" ] }, { "cell_type": "code", "execution_count": 10, "id": "c1c9c320", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:42.343524Z", "iopub.status.busy": "2026-05-16T13:44:42.343340Z", "iopub.status.idle": "2026-05-16T13:44:42.555683Z", "shell.execute_reply": "2026-05-16T13:44:42.555021Z" }, "papermill": { "duration": 0.217947, "end_time": "2026-05-16T13:44:42.556763+00:00", "exception": false, "start_time": "2026-05-16T13:44:42.338816+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated radial scale length hr: 0.32908013715579104 (input: 0.333)\n", "Estimated sigma_R scale length hsr: 1.191393519002444 (input: 1.0)\n", "Estimated sigma_z scale length hsz: 1.0506910721558342 (input: 1.0)\n" ] } ], "source": [ "print(\"Estimated radial scale length hr:\", qdf.estimate_hr(1.0), \"(input: 0.333)\")\n", "print(\"Estimated sigma_R scale length hsr:\", qdf.estimate_hsr(1.0), \"(input: 1.0)\")\n", "print(\"Estimated sigma_z scale length hsz:\", qdf.estimate_hsz(1.0), \"(input: 1.0)\")" ] }, { "cell_type": "markdown", "id": "b9cc50cf", "metadata": { "papermill": { "duration": 0.003792, "end_time": "2026-05-16T13:44:42.565354+00:00", "exception": false, "start_time": "2026-05-16T13:44:42.561562+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Mean velocities\n", "\n", "Mean velocities can also be computed as a function of radius:" ] }, { "cell_type": "code", "execution_count": 11, "id": "20c215fb", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:42.574563Z", "iopub.status.busy": "2026-05-16T13:44:42.574347Z", "iopub.status.idle": "2026-05-16T13:44:43.520232Z", "shell.execute_reply": "2026-05-16T13:44:43.519244Z" }, "papermill": { "duration": 0.951754, "end_time": "2026-05-16T13:44:43.521243+00:00", "exception": false, "start_time": "2026-05-16T13:44:42.569489+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "meanvR(1, 0): 0.0\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "meanvz(1, 0): 0.0\n", "meanvT(1, 0): 0.9198834638078105\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Mean radial velocity is zero for an axisymmetric potential\n", "print(\"meanvR(1, 0):\", qdf.meanvR(1.0, 0.0))\n", "# Mean vertical velocity is also zero\n", "print(\"meanvz(1, 0):\", qdf.meanvz(1.0, 0.0))\n", "# Mean tangential velocity shows asymmetric drift\n", "print(\"meanvT(1, 0):\", qdf.meanvT(1.0, 0.0))\n", "\n", "# meanvT decreases with height above the plane\n", "zs = numpy.linspace(0.0, 0.25, 21)\n", "mvts = numpy.array([qdf.meanvT(1.0, z) for z in zs])\n", "plt.plot(zs, mvts)\n", "plt.xlabel(r\"$z$\")\n", "plt.ylabel(r\"$\\langle v_T \\rangle$\")\n", "plt.title(\"Mean rotational velocity vs. height\");" ] }, { "cell_type": "markdown", "id": "b5f41944", "metadata": { "papermill": { "duration": 0.004074, "end_time": "2026-05-16T13:44:43.529934+00:00", "exception": false, "start_time": "2026-05-16T13:44:43.525860+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Velocity ellipsoid tilt\n", "\n", "The tilt of the velocity ellipsoid is zero when using the adiabatic approximation\n", "(because it assumes decoupled planar and vertical motions). The Staeckel\n", "approximation captures the coupling better:" ] }, { "cell_type": "code", "execution_count": 12, "id": "aedf81cc", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:43.539194Z", "iopub.status.busy": "2026-05-16T13:44:43.538972Z", "iopub.status.idle": "2026-05-16T13:44:43.739123Z", "shell.execute_reply": "2026-05-16T13:44:43.738575Z" }, "papermill": { "duration": 0.206786, "end_time": "2026-05-16T13:44:43.740957+00:00", "exception": false, "start_time": "2026-05-16T13:44:43.534171+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tilt (adiabatic) at (1, 0.125): 0.0 rad\n", "Tilt (Staeckel) at (1, 0.125): 0.10314272868452165 rad\n", " = 5.9 degrees\n" ] } ], "source": [ "from galpy.actionAngle import actionAngleStaeckel\n", "\n", "# Staeckel-based action-angle calculator\n", "aAS = actionAngleStaeckel(pot=MWPotential2014, delta=0.45, c=True)\n", "qdfS = quasiisothermaldf(\n", " 1.0 / 3.0,\n", " 0.2,\n", " 0.1,\n", " 1.0,\n", " 1.0,\n", " pot=MWPotential2014,\n", " aA=aAS,\n", " cutcounter=True,\n", ")\n", "\n", "# Tilt is zero for adiabatic approximation:\n", "print(\"Tilt (adiabatic) at (1, 0.125):\", qdf.tilt(1.0, 0.125), \"rad\")\n", "# Non-zero for Staeckel:\n", "print(\"Tilt (Staeckel) at (1, 0.125):\", qdfS.tilt(1.0, 0.125), \"rad\")\n", "print(\" = {:.1f} degrees\".format(qdfS.tilt(1.0, 0.125) * 180.0 / numpy.pi))" ] }, { "cell_type": "markdown", "id": "69f5e313", "metadata": { "papermill": { "duration": 0.004027, "end_time": "2026-05-16T13:44:43.749742+00:00", "exception": false, "start_time": "2026-05-16T13:44:43.745715+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Surface density radial profile\n", "\n", "Compare the surface density from the adiabatic and Staeckel approximations\n", "to a pure exponential:" ] }, { "cell_type": "code", "execution_count": 13, "id": "2563f814", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:43.759175Z", "iopub.status.busy": "2026-05-16T13:44:43.758856Z", "iopub.status.idle": "2026-05-16T13:44:54.310376Z", "shell.execute_reply": "2026-05-16T13:44:54.309243Z" }, "papermill": { "duration": 10.557093, "end_time": "2026-05-16T13:44:54.311080+00:00", "exception": false, "start_time": "2026-05-16T13:44:43.753987+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rs = numpy.linspace(0.5, 1.5, 21)\n", "surfr = numpy.array([qdf.surfacemass_z(r) for r in rs])\n", "surfrS = numpy.array([qdfS.surfacemass_z(r) for r in rs])\n", "plt.semilogy(rs, surfr / surfr[10], label=\"Adiabatic\")\n", "plt.semilogy(rs, surfrS / surfrS[10], label=\"Staeckel\")\n", "plt.semilogy(\n", " rs, numpy.exp(-(rs - 1.0) / (1.0 / 3.0)), \"--\", label=\"Exponential (hr=1/3)\"\n", ")\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$\\Sigma(R) / \\Sigma(R_0)$\")\n", "plt.legend()\n", "plt.title(\"Surface density radial profile\");" ] }, { "cell_type": "markdown", "id": "0583ebfb", "metadata": { "papermill": { "duration": 0.004387, "end_time": "2026-05-16T13:44:54.320470+00:00", "exception": false, "start_time": "2026-05-16T13:44:54.316083+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Marginalized velocity probabilities\n", "\n", "The DF provides marginalized velocity probabilities `pvT`, `pvR`, `pvz`,\n", "`pvRvT`, `pvRvz`, and `pvTvz`. These are multiplied by the density\n", "(so marginalizing over remaining velocity components gives the density)." ] }, { "cell_type": "code", "execution_count": 14, "id": "7f337ae4", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:54.330503Z", "iopub.status.busy": "2026-05-16T13:44:54.330314Z", "iopub.status.idle": "2026-05-16T13:44:55.653484Z", "shell.execute_reply": "2026-05-16T13:44:55.652595Z" }, "papermill": { "duration": 1.329356, "end_time": "2026-05-16T13:44:55.654315+00:00", "exception": false, "start_time": "2026-05-16T13:44:54.324959+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Marginalized vT distribution at R=1, z=0\n", "vts = numpy.linspace(0.0, 1.5, 101)\n", "pvt = numpy.array([qdfS.pvT(vt, 1.0, 0.0) for vt in vts])\n", "plt.plot(vts, pvt / numpy.sum(pvt) / (vts[1] - vts[0]))\n", "plt.xlabel(r\"$v_T$\")\n", "plt.ylabel(r\"$p(v_T)$\")\n", "plt.title(\"Marginalized $v_T$ distribution at R=1, z=0\");" ] }, { "cell_type": "markdown", "id": "96c66def", "metadata": { "papermill": { "duration": 0.004563, "end_time": "2026-05-16T13:44:55.663876+00:00", "exception": false, "start_time": "2026-05-16T13:44:55.659313+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Sampling velocities\n", "\n", "We can sample velocities at a given location using `sampleV`:" ] }, { "cell_type": "code", "execution_count": 15, "id": "7a28786a", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:44:55.674226Z", "iopub.status.busy": "2026-05-16T13:44:55.674010Z", "iopub.status.idle": "2026-05-16T13:44:58.804678Z", "shell.execute_reply": "2026-05-16T13:44:58.803718Z" }, "papermill": { "duration": 3.136799, "end_time": "2026-05-16T13:44:58.805422+00:00", "exception": false, "start_time": "2026-05-16T13:44:55.668623+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: -6.244277\n", " Iterations: 1\n", " Function evaluations: 13\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "vs = qdfS.sampleV(1.0, 0.0, n=10000)\n", "# Compare sampled vT distribution to the marginalized pvT\n", "plt.hist(\n", " vs[:, 1], density=True, histtype=\"step\", bins=101, range=[0.0, 1.5], label=\"Sampled\"\n", ")\n", "plt.plot(vts, pvt / numpy.sum(pvt) / (vts[1] - vts[0]), \"r-\", label=\"pvT\")\n", "plt.xlabel(r\"$v_T$\")\n", "plt.ylabel(r\"$p(v_T)$\")\n", "plt.legend()\n", "plt.title(\"Sampled vs. marginalized $v_T$ at (R=1, z=0)\");" ] } ], "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": "3.13.13" }, "papermill": { "default_parameters": {}, "duration": 31.15503, "end_time": "2026-05-16T13:44:59.427400+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/distribution_functions/disk_df_3d.ipynb", "output_path": "doc/source/tutorials/distribution_functions/disk_df_3d.ipynb", "parameters": {}, "start_time": "2026-05-16T13:44:28.272370+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }