{ "cells": [ { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.004337, "end_time": "2026-06-30T01:11:08.834376+00:00", "exception": false, "start_time": "2026-06-30T01:11:08.830039+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": "2026-06-30T01:11:08.842217Z", "iopub.status.busy": "2026-06-30T01:11:08.842014Z", "iopub.status.idle": "2026-06-30T01:11:09.211131Z", "shell.execute_reply": "2026-06-30T01:11:09.210123Z" }, "papermill": { "duration": 0.374265, "end_time": "2026-06-30T01:11:09.212251+00:00", "exception": false, "start_time": "2026-06-30T01:11:08.837986+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": 0.003331, "end_time": "2026-06-30T01:11:09.219479+00:00", "exception": false, "start_time": "2026-06-30T01:11:09.216148+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": "2026-06-30T01:11:09.226813Z", "iopub.status.busy": "2026-06-30T01:11:09.226505Z", "iopub.status.idle": "2026-06-30T01:11:11.132547Z", "shell.execute_reply": "2026-06-30T01:11:11.131743Z" }, "papermill": { "duration": 1.910833, "end_time": "2026-06-30T01:11:11.133272+00:00", "exception": false, "start_time": "2026-06-30T01:11:09.222439+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": 0.002692, "end_time": "2026-06-30T01:11:11.138975+00:00", "exception": false, "start_time": "2026-06-30T01:11:11.136283+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": "2026-06-30T01:11:11.149131Z", "iopub.status.busy": "2026-06-30T01:11:11.148752Z", "iopub.status.idle": "2026-06-30T01:11:11.664103Z", "shell.execute_reply": "2026-06-30T01:11:11.663249Z" }, "papermill": { "duration": 0.523365, "end_time": "2026-06-30T01:11:11.665123+00:00", "exception": false, "start_time": "2026-06-30T01:11:11.141758+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": 0.003266, "end_time": "2026-06-30T01:11:11.672091+00:00", "exception": false, "start_time": "2026-06-30T01:11:11.668825+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": "2026-06-30T01:11:11.678791Z", "iopub.status.busy": "2026-06-30T01:11:11.678578Z", "iopub.status.idle": "2026-06-30T01:11:11.683500Z", "shell.execute_reply": "2026-06-30T01:11:11.682914Z" }, "papermill": { "duration": 0.009243, "end_time": "2026-06-30T01:11:11.684185+00:00", "exception": false, "start_time": "2026-06-30T01:11:11.674942+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": 0.002684, "end_time": "2026-06-30T01:11:11.691940+00:00", "exception": false, "start_time": "2026-06-30T01:11:11.689256+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": "2026-06-30T01:11:11.698716Z", "iopub.status.busy": "2026-06-30T01:11:11.698523Z", "iopub.status.idle": "2026-06-30T01:11:12.103081Z", "shell.execute_reply": "2026-06-30T01:11:12.102366Z" }, "papermill": { "duration": 0.409337, "end_time": "2026-06-30T01:11:12.104036+00:00", "exception": false, "start_time": "2026-06-30T01:11:11.694699+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): 0.023214249869379366\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": 0.002786, "end_time": "2026-06-30T01:11:12.110161+00:00", "exception": false, "start_time": "2026-06-30T01:11:12.107375+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": "2026-06-30T01:11:12.117135Z", "iopub.status.busy": "2026-06-30T01:11:12.116941Z", "iopub.status.idle": "2026-06-30T01:11:13.911281Z", "shell.execute_reply": "2026-06-30T01:11:13.909913Z" }, "papermill": { "duration": 1.798836, "end_time": "2026-06-30T01:11:13.911910+00:00", "exception": false, "start_time": "2026-06-30T01:11:12.113074+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " at (R=1, z=0): 0.03406689383453625\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): 0.0017174864094052277\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": 0.002996, "end_time": "2026-06-30T01:11:13.918140+00:00", "exception": false, "start_time": "2026-06-30T01:11:13.915144+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": "2026-06-30T01:11:13.925271Z", "iopub.status.busy": "2026-06-30T01:11:13.925018Z", "iopub.status.idle": "2026-06-30T01:11:20.266461Z", "shell.execute_reply": "2026-06-30T01:11:20.265524Z" }, "papermill": { "duration": 6.346336, "end_time": "2026-06-30T01:11:20.267517+00:00", "exception": false, "start_time": "2026-06-30T01:11:13.921181+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": 0.003239, "end_time": "2026-06-30T01:11:20.274300+00:00", "exception": false, "start_time": "2026-06-30T01:11:20.271061+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": "2026-06-30T01:11:20.282086Z", "iopub.status.busy": "2026-06-30T01:11:20.281827Z", "iopub.status.idle": "2026-06-30T01:11:20.857152Z", "shell.execute_reply": "2026-06-30T01:11:20.856524Z" }, "papermill": { "duration": 0.581242, "end_time": "2026-06-30T01:11:20.858870+00:00", "exception": false, "start_time": "2026-06-30T01:11:20.277628+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": 0.003222, "end_time": "2026-06-30T01:11:20.865821+00:00", "exception": false, "start_time": "2026-06-30T01:11:20.862599+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": "2026-06-30T01:11:20.873361Z", "iopub.status.busy": "2026-06-30T01:11:20.873132Z", "iopub.status.idle": "2026-06-30T01:11:22.634194Z", "shell.execute_reply": "2026-06-30T01:11:22.633061Z" }, "papermill": { "duration": 1.765769, "end_time": "2026-06-30T01:11:22.634919+00:00", "exception": false, "start_time": "2026-06-30T01:11:20.869150+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": 0.00343, "end_time": "2026-06-30T01:11:22.642240+00:00", "exception": false, "start_time": "2026-06-30T01:11:22.638810+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": "2026-06-30T01:11:22.650339Z", "iopub.status.busy": "2026-06-30T01:11:22.650100Z", "iopub.status.idle": "2026-06-30T01:11:22.877888Z", "shell.execute_reply": "2026-06-30T01:11:22.877485Z" }, "papermill": { "duration": 0.234244, "end_time": "2026-06-30T01:11:22.879988+00:00", "exception": false, "start_time": "2026-06-30T01:11:22.645744+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: 1.1913934874850225 (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": 0.003617, "end_time": "2026-06-30T01:11:22.887537+00:00", "exception": false, "start_time": "2026-06-30T01:11:22.883920+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": "2026-06-30T01:11:22.896123Z", "iopub.status.busy": "2026-06-30T01:11:22.895883Z", "iopub.status.idle": "2026-06-30T01:11:23.908416Z", "shell.execute_reply": "2026-06-30T01:11:23.907231Z" }, "papermill": { "duration": 1.017615, "end_time": "2026-06-30T01:11:23.909022+00:00", "exception": false, "start_time": "2026-06-30T01:11:22.891407+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "meanvR(1, 0): 0.0\n", "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": 0.003776, "end_time": "2026-06-30T01:11:23.916863+00:00", "exception": false, "start_time": "2026-06-30T01:11:23.913087+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": "2026-06-30T01:11:23.925476Z", "iopub.status.busy": "2026-06-30T01:11:23.925215Z", "iopub.status.idle": "2026-06-30T01:11:24.119838Z", "shell.execute_reply": "2026-06-30T01:11:24.119250Z" }, "papermill": { "duration": 0.200571, "end_time": "2026-06-30T01:11:24.121171+00:00", "exception": false, "start_time": "2026-06-30T01:11:23.920600+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): 0.10314272868452166 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": 0.003717, "end_time": "2026-06-30T01:11:24.128968+00:00", "exception": false, "start_time": "2026-06-30T01:11:24.125251+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": "2026-06-30T01:11:24.137415Z", "iopub.status.busy": "2026-06-30T01:11:24.137207Z", "iopub.status.idle": "2026-06-30T01:11:35.556471Z", "shell.execute_reply": "2026-06-30T01:11:35.555636Z" }, "papermill": { "duration": 11.424374, "end_time": "2026-06-30T01:11:35.557121+00:00", "exception": false, "start_time": "2026-06-30T01:11:24.132747+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rs = numpy.linspace(0.5, 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": 0.004048, "end_time": "2026-06-30T01:11:35.566535+00:00", "exception": false, "start_time": "2026-06-30T01:11:35.562487+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": "2026-06-30T01:11:35.575472Z", "iopub.status.busy": "2026-06-30T01:11:35.575272Z", "iopub.status.idle": "2026-06-30T01:11:36.979535Z", "shell.execute_reply": "2026-06-30T01:11:36.978562Z" }, "papermill": { "duration": 1.410026, "end_time": "2026-06-30T01:11:36.980589+00:00", "exception": false, "start_time": "2026-06-30T01:11:35.570563+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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LVDfl/tbaOnTocMdfWoMGDUJISAgmT56MBx98EKNGjcLIkSOb/Muuro9LU86NiYnB999/j3PnzqFv375Neu3G0s0qujnY6AwePBg7d+7EtWvXEBISoj8eHR1tcF7Hjh0BaENhQ+HmwIEDeOyxx1BQUIDevXvD09MTMpkMKpWq3mUcmuLXX3+Fu7s7SkpKcPjwYUREROD999+/7bz33nuvxa9lbN9//z3efvttTJ06Fe+++67BY0uWLGny8+m+l+ua+q1SqW4b00emw3BDRjFz5kx88803eP3111FUVIQZM2bUed7Ro0fxwgsv4K233sIbb7yhP3748GHs3LlT/8tcp66BtLoF6ur668jV1RUlJSV3rPfWQZ3AXz+YdOt8/PDDD/j444/x448/GkxrXbZsGY4dO3ZbrY2RkZGB++67Dy4uLtiyZYtBHRUVFQC0a6UcPHjwtmvj4uIghLjj+28MXcuQLtwsXrwY586dw5o1a/Tn9OjRA4B2IG9WVhbuv/9+g/FIdWlJbe7u7khISMA333yDbdu24dlnn0VpaSnuuecerFixAr6+vnd8X3K5XN9q0xgN1al7L3K5vM7PdUvWc9E9d10fE92xm9ebUSgUtw0evvXrtS4qlQpTpkxBjx49kJycbPDL1cvLq1lfw7e6ebZUamoqhgwZgnHjxuHw4cMGkwQsZcyNzq5du/D0009j8ODBWLFihcGAfqB5Y250Sz9kZ2ff1mqYlZV1W6skmQ7DDRnFkCFDEBYWhg8//BCjR49GcHBwnecdOHAAAPDUU08ZHK9v9sKtP3CAv/5iTU1NRYcOHQweS01NbdIvt4bs378fHh4et63XUV+td1JaWorx48ejoKAAe/bsMfirHNAO3gSAv/3tbw12xei6KlJSUm577MqVK42qJSwsDK6urkhKSkJ+fj7+9a9/Yc6cOXU2w586dQpubm6Nmtaraw1LSUlBt27d9Merq6uRnp6uf4/18fT0xPz58zF//nzU1NTg559/xvTp0/Hvf/8bn332WZ1fDze70+O3auhjqHsv/v7+qKioQGVlpUE3VV3XNvb1dc9d17Tmy5cvQ6FQ1Ps91BQXL15EdnY2Fi5caBBsMjIyUFxcbHBuUz92dQkJCcEnn3yCBx98EP/973/xyiuv6B9bsGCBwSre9QkNDTX5dO/k5GRMnjwZHTp0wK+//qrvnr7Z7NmzG/X9dPMgZF1L4MmTJzFs2DD9OUqlEmfPnsWUKVOM9A7oThhuyGhee+01bNiwAbNnz673HF3zeXp6uv6vmMrKSnz11VeNfp177rkHLi4u+N///ofhw4frj2/evBm5ublGCzf+/v4oLy9Hfn6+/jlzcnKwevXqJj9XTU0Npk6dijNnzmD9+vV1dofcc889CAwMxAcffICxY8feNt38+vXrCAoKgo+PD0aMGIGVK1fi9ddf1/+ln5OTg99//71R9cjlckRGRuL06dN4/fXXoVAoDFYPvlliYiIiIyMb9ctv4sSJWLBgAZYsWYJPP/1Uf/zbb7+9YytBTk4O2rRpox9fZWdnh2nTpmHu3LnIzs4GoG3VcHZ2blTrXGP88ccfyMrK0o8FqaiowLJlyzBkyBB9d5huBtquXbswfvx4ANrWEt3MrZv5+Pg0qraoqCiEhYVh6dKlmDt3rj54ZGdn48cff8S9997bqGned3Lz99vN3n333duWXtB9jbf0Yztt2jR88MEHePfddzFr1iz9OCFzjLnZuHEjfH19G1w/KTs7G/feey/kcjm2bNlSb4tgc8bc9O/fHxEREfjuu+/w3HPPQaFQAABWrFiByspKPPHEE018R9RcDDdkNDNmzKi3O0pn4sSJ6Ny5M6ZPn44FCxZAo9FgxYoVmD59OuLj4xv1Ot7e3vjyyy/xxBNPQK1WY/z48UhNTUViYiKGDx9utH2knnrqKXz++ee45557MGfOHBQUFGDFihWYM2cOXn/99SY917Jly7Bt2zbce++9kMlkty3oFhcXBxcXF2zYsAETJkxA37598dhjjyEgIABpaWnYuXMnPD09sW7dOgDAl19+iWHDhmHIkCGYPXs2VCoVfvzxR8yYMQMfffRRo2qKiorCsmXLcPToUSxevLje1XMTExP1Y3TupHPnzli4cCFeeeUVlJaWYsSIEUhKSkJOTo5BS05djh49ihdffFHfjSKTybBhwwZUVFRg7ty5+vNGjhyJNWvWoFu3bvD29tavc9McM2bMwNSpUzFlyhQ4OTnh66+/RllZmUHYHj9+PKKjo/Hkk0/itddeg52dHdavX4/p06fjH//4h8HzjR49Gp9//jk+//xzBAcH69e5uZVcLsf333+Pe+65B8OGDcOTTz6JqqoqfPrpp/Dx8cEXX3zRrPdzK19fXzz66KN4//33IZPJ0KlTJ2zZsgVBQUG3hYghQ4bA2dkZr7/+Oh588EE4ODg0eZ0bnXfeeQdjx47F+++/r18GoLljbs6fP4/z588D0K5bpVQqb1vjSGfSpEkYPnw49uzZU+/zLViwANeuXcP8+fORnJyM5ORk/WM3dzE1Z8wNoP1eHzVqFO6991489thjSElJwcKFC/HCCy/cNkWcTIfhhprF29sbcXFxt3Wt3KpHjx6Ii4vTN+e7ubnhxIkT+OKLL7B37174+vriyy+/hL+/P/bt22fQzTRkyBD9Wia3mjlzJrp27YqVK1fq16dYs2YNRowYYTCOoq7tFwYMGFDnD+zOnTsb1NqpUyecPn0aS5YswbZt29CxY0ds2LABubm5OHHihMFia6NGjTL4q/TW7RcCAgIQFxcHAHWudzNhwgTIZDLExMTg4sWLWLVqFY4fP45jx44hJCQEr776qsEvye7du+P06dNYvHgxdu/ejU6dOmH16tU4deoULl++XGcz+63uu+8+3LhxA76+vrd1E94sMTGxwda4Wy1YsADR0dFYu3Yttm7dimHDhmHhwoV4+eWXDQLUrdsv3H///YiOjsbq1auxe/du/cfjiy++MBi4vXz5cixevBjbtm2DUqnUr3PTq1cv/cf4Vrduv2Bvb4+4uDgMGzYMf//73/HFF18gJSUFY8eOxZw5cwxeTyaTYceOHfj888+xf/9+tG/fHv/73/+Ql5eHuLg4g6+DN998EwEBAThy5Ah27dqFTp06YcSIEXVuvzBo0CAkJyfju+++w549e6BQKPDiiy/i8ccfN1jUsL73pfuaulNL5bJlyxAbG4t9+/bh6tWrmDx5MqZOnYrS0lKDVofg4GDs2LEDq1atwo8//gi1Wt3gOjfdunWrd/uMu+++G/PmzUNaWhpUKpW+Na45EhMT9dtZhIeHIzw8XP89pPvcA9CvYTR48OAGn69nz56Ii4vD5cuXb+v+6tq1a4sW8QO0A7/PnDmDpUuX4tdff4WnpyfWr1+Pe++9t0XPS00jE8YYUUZkATQaDdq1a4exY8fetkgXNY9arYabmxv2799/2+w0IkuyfPlyvPTSS0hNTa1zwgC1LtwVnKxSXbter127Fjk5OZg4caL5C7JR586d069+TGTJKisr8fHHHzPYEAC23JCV+u233/D+++/jgQcegJ+fH44fP47FixcjLi4O69atM8rMD9LO8EpLS0PPnj2lLoWIqNEYbshqHTlyBBs3bsTVq1fh6emJu+++G5MmTbrjppZERGTbGG6IiIjIpvBPXCIiIrIpDDdERERkU1rlOjcajQY3btyAu7s7B54SERFZCSEESktLERgY2OD4ylYZbm7cuGGUfVuIiIjI/NLT0w0W27xVqww3utU/09PT61xdk4iIiCxPSUkJgoODDVbxrkurDDe6rigPDw+GGyIiIitzpyElHFBMRERENoXhhoiIiGwKww0RERHZFIYbIiIisikMN0RERGRTGG6IiIjIpjDcEBERkU1huCEiIiKbwnBDRERENoXhhoiIiGwKww0RERHZFIYbIiIisikMN0RERGRTWuWu4EREtubwlXy8syUZxZUquNjbwdlBARcHBTp4u+DvY7vC181R6hKJzIbhhojIitWoNfhs12V8vusShLj98UNX8nHoSj6+f2IAQnxdzV8gkQQYboiIrFRmcSVeWJuIY6kFAIAH+wVjWv9gVKnUqKhWo0ypwsfbLyKtoAIPLD6Ib2f2R98ObSSumsj0GG6IiKzQ/ku5eH5NAgorVHBztMM7k3ohLirotvOGdmmLJ78/jtMZxZi+9Ag+f6gvxvTwl6BiIvPhgGIiIiuTXlCBZ384icIKFSKCPLFp3tA6gw0AtHV3xNpZAzGia1tUqTR4ZuUJrDuRbuaKicyL4YaIyIqoNQLzfzqFMmUNoju2wfpnB6HTHcbSuDjYYemMfnhoQDA0Anjj17PILqkyU8VE5sdwQ0RkRZbuT8GxqwVwdVDgv9Oi4GinaNR1dgo5Fk6KQHTHNqhUqfHBtgsmrpRIOgw3RERWIvlGCT76UxtK/nV/T3TwcWnS9TKZDK/f1wMA8PPJDCRlFBu9RiJLwHBDRGQFqlRqvPRjIlRqgTE9/DG1X/tmPU9UsBcmRgVCCODtTckQdc0fJ7JyDDdERFbgw20XcCG7FL5uDlj0QARkMlmzn2vBuG5wspfj2NUCbD2TZcQqiSwDww0RkYVLSCvENwdSAQDvTY5s8WrDgV7OmHVXKABg4R/nUKVSt7hGIkvCcENEZOE+2XEJAPBA3yCM6m6cNWpmD+8Mfw9HpBdUYvmhq0Z5TiJLwXBDRGTBTqUXYe/FXCjkMrw4Ktxoz+viYIeXx3YDAHyx6zLyypRGe24iqTHcEBFZsM93XQYAxEUFNnl21J080CcIPQM9UKaswboTGUZ9biIpMdwQEVmoszeKseNcNmQyYO6ILkZ/frlchscGdQIArItP58wpshkMN0REFuqL2lab+yIDEdrWzSSvcW9kOzjbK5CSW46TaUUmeQ0ic2O4ISKyQBezS/FH7TTteSON32qj4+Zoh3siAgAA6+PZNUW2geGGiMgC6Vpt7ukVgHB/d5O+1tToYADAplM3UFnNaeFk/RhuiIgszJXcMvx++gYA4DkTttroxIR4o30bZ5Qqa7DtLBf1I+vHcENEZGEW774CIYDR3f3QM9DT5K8nl8swJVq7ncO6+HSTvx6RqTHcEBFZkMLyavx+SttqY4oZUvWZ3Fcbbg5dyUdGYYXZXpfIFBhuiIgsyC8J11Gt1qBnoAf6dGhjttcN9nbBoM4+EALYcPK62V6XyBQYboiILIQQAj8e13YL/b/+wWZ/fd1O4+vjM6DRcM0bsl4MN0REFiIxvQgXskvhaCfHhKggs7/+uF4BcHO0Q1pBBY5fLTD76xMZi53UBZw6dQqHDh2CnZ0dBg8ejJ49ezZ4/h9//IH4+HiDY35+fpg1a5YpyyQiMjldq834iHbwdLY3++u7ONhhfEQ7/HgiHeviMxDT2cfsNRAZg2QtN0IIjBkzBjNnzkRSUhIOHjyI/v3744033mjwul9//RWrVq1CVVWV/qZUcsM3IrJuZcoa/FY7kPhBCbqkdCbXzpranpyNGrVGsjqIWkKylhshBF555RWMHj1afywuLg4PPPAApk+fjm7dutV7bc+ePfGf//zHHGUSEZnF5tM3UFGtRoivKwaEeEtWR3THNvB0tkdxpQqnMooQ3VG6WoiaS7KWG7lcbhBsAGDw4MEAgNTU1AavTU9Px8cff4xvv/0W586dM1mNRETmsra2S+rB/sGQyWSS1aGQyzAszBcAsOdCrmR1ELWERQ0o/umnn2Bvb4++ffs2eJ5SqcTVq1exZcsWREVF4c0337zj+SUlJQY3IiJLcSGrFAlpRbCTy/BAX/MPJL5VbFc/AAw3ZL0kH1Csc+LECbzyyiv417/+BX9//3rPmzdvHr766iv9/Y0bN2LSpEkYM2YMhgwZUuc1ixYtwltvvWX0momIjEE3kHhUdz/4uTtJXA0wPLwtACDpejFyS5Vo6+4ocUVETWMRLTdJSUkYN24cHn/8cfzzn/9s8NxbZ1NNnDgR7dq1w+7du+u95tVXX0VxcbH+lp7O5cWJyDIoa9TYkKDdjfv/9e8gcTVabd0d0SvIAwCw7yJbb8j6SB5uzpw5g5EjR2Lq1Kn44osvmvUccrkcZWVl9T7u6OgIDw8PgxsRkSXYeS4HRRUqBHg44a7aFhNLEBte2zXFcENWSNJwc/bsWYwcORJTpkzB4sWL6xxEt3nzZnz99dcAALVajdOnTxs8vmXLFly/fh2xsbHmKJmIyKg2n84EAMT1CYRCLt1A4lsN76oNWvsv5ULN1YrJykg25qaiogKjRo2CTCZDYGAg3nnnHf1j9913H6KiogAAv/zyC44cOYJZs2ZBCIGnn34a/v7+6NmzJ9LS0vDzzz/jhRdewLhx4yR6J0REzVOurMHO89kAgPsjAyWuxlCfYC94ONmhqEKFxPQiRHc03z5XRC0l6YDip556CgBuW4RPrVbr/3/fffehd+/eAAA7OzscOXIE27dvR0JCAkJCQvCPf/zjjqsaExFZol3nc1Cl0qCjjwt6BlpWd7mdQo5hYW2xOSkTey/kMNyQVZEJIVpde2NJSQk8PT1RXFzM8TdEJJnZK+Ox9WwW5sSGYsG4+hculcpPJ9KxYP1pRLb3xG/PDZW6HKJG//6WfEAxEVFrVKaswe4LOQCA8ZHtJK6mbrG1A5xPZxQjr4zb3JD1YLghIpLAznPZUNZo0NnXFT3aWWYLsp+Hk742Tgkna8JwQ0QkAd0sqfGR7STdbuFOYmtnTXG1YrImDDdERGZWWqXSrx9jqV1SOrqtGPZxSjhZEYYbIiIz23kuB9U1GoS2dUVXf3epy2lQ3w5ecK+dEn4qo0jqcogaheGGiMjMNum7pAItuksK0E4JHxzqAwA4mlIgcTVEjcNwQ0RkRiVVKv3g3PssvEtKp38nbwBA/DWGG7IODDdERGa0/Ww2qtUahPm5IdzCu6R0dAv4nbhWCA3H3ZAVYLghIjKjzUl/zZKyFj0DPeFkL0dRhQopefVvUkxkKRhuiIjMpFxZgwOX8gAA90ZYT7hxsJOjd3svAMDxq4XSFkPUCAw3RERmsv9SLqrV2r2kwvzcpC6nSXTjbk4w3JAVYLghIjKTHee02y2M7u5v8bOkbhXdSTfuhoOKyfIx3BARmYFaI7DrvDbcjOruJ3E1Tde3QxvIZMC1/ArklFZJXQ5RgxhuiIjMICGtEAXl1fBwstN38VgTT2d7/YKD8eyaIgvHcENEZAa6LqkR3fxgr7DOH739Ov01JZzIklnndxgRkZXZcS4bADCqu7/ElTTfX4OKOe6GLBvDDRGRiV3NK8flnDLYyWUYHt5W6nKaTbeY39kbJaiorpG4GqL6MdwQEZmYrtUmprM3PJ3tJa6m+YK8nNHO0wk1GoHE9CKpyyGqF8MNEZGJ6bukullvlxQAyGQyfesNBxWTJWO4ISIyoeIKlX5V39FWPN5GRzfu5jgHFZMFY7ghIjKhPRdzoNYIdPV3RwcfF6nLaTFdy03CtUKouYkmWSiGGyIiE9qerJslZX0L99WlW4A73BztUKqswYWsUqnLIaoTww0RkYlU12iw90IuAGB0D+vvkgIAO4UcfTp4AQDiuRUDWSiGGyIiEzl+tQClyhr4ujkgqnZXbVvQr2Ptejccd0MWiuGGiMhEdtfuJRXb1Q9yuXVtlNkQ3UrF8Qw3ZKEYboiITGTvRW2XVGxX6124ry69gjwBABmFlSgsr5a4GqLbMdwQEZnA9aJKXMopg1wGDOtiW+HG09kenWpnfp25USxxNUS3Y7ghIjKBPRe0XVJ9O7SBp4v1rkpcH13rzekMhhuyPAw3REQmoJslZc17STUksr023Jy5znBDlofhhojIyKprNDh4OQ+AdjCxLdK13CQx3JAFYrghIjKy+GuFKK9Ww9fNAT0DPaQuxyQ4qJgsGcMNEZGR7bmoHW9zV1hbm5oCfjMPp78GFbP1hiwNww0RkZHpx9vY2BTwW0XULkzIcEOWhuGGiMiIsoqrcD6rFDIZMCzMxsNNkLbLLYkzpsjCMNwQERnR3touqd7tveDt6iBxNabFQcVkqRhuiIiMSLcqsa1OAb+ZLtxcL6pEAQcVkwVhuCEiMpIatQb7L+mmgNt+uPFwskeIrysAtt6QZWG4ISIykoT0IpRW1aCNiz0ibWgX8IboWm+4mB9ZEoYbIiIj0W25MCysLRQ2OgX8VpG6cTccVEwWhOGGiMhIbHUX8IZwUDFZIoYbIiIjyC9T4sz1EgDA0DBfiasxn56108E5qJgsCcMNEZERHKjdS6p7Ow/4uTtJXI35eDjZozMHFZOFYbghIjIC3Sypu1pRq42Ovmsqo0jaQohqMdwQEbWQEAIHasNNa+qS0onguBuyMAw3REQtdDmnDFklVXC0k6N/J2+pyzG7v6aDl0hcCZEWww0RUQvtq221GRDiDSd7hcTVmF+vmwYV55cpJa6GiOGGiKjFDlzSTgEf1gq7pADAnYOKycIw3BARtYCyRo0jKQUAbH8X8Ib0rO2aOpdZKnElRAw3REQtEn+tEJUqNXzdHNEtwF3qciSje+/nszjuhqTHcENE1AK6WVLDwnwhk7WOLRfq0r2dNtycy2S4IelJGm6Sk5Px9NNPo2fPnujduzfmzp2LrKysO163evVqxMTEoFOnTrj//vtx5swZM1RLRHS7/TeFm9asezvtoOIrueVQ1qglroZaO8nCjVqtxoMPPoiBAwdi3bp1+Pbbb3HmzBmMGjUKlZWV9V63fv16zJw5E08//TQ2b94MX19fxMbGIicnx4zVExEBBeXVOHNDO4B2aJfWHW4CPJzg6WwPtUbgck6Z1OVQKydZuFEoFDh9+jSefPJJ9OjRA/369cO3336L5ORkHD16tN7r/vOf/+Cxxx7DU089hZ49e2Lp0qWQy+VYsmSJGasnIgIOXs6DENrxJn4erWfLhbrIZLK/xt1wUDFJTNJuqVv7p5VK7foIDg4OdZ5fUlKCU6dOYcyYMfpjdnZ2GDVqFPbt22e6QomI6rC/lU8Bv5Wua4qDiklqdlIXoCOEwP/93/8hPDwc/fv3r/Oc69evAwD8/f0Njvv7+yMxMbHe51YqlfrgBGhDEhFRS9y85UJrngJ+s78GFbPlhqRlMbOlFixYgH379uHHH3+Evb19necIIQBoW2tuZmdnB7W6/gFsixYtgqenp/4WHBxsvMKJqFW6kluOG8VVcLCTY0BI69tyoS7dAthyQ5bBIsLNa6+9hv/973/YunUroqKi6j2vbVvtX0d5eXkGx3Nzc+Hn51fvda+++iqKi4v1t/T0dKPUTUStl25V4v6d2rTKLRfqEu7vDpkMyCurRm4pt2Eg6Ugebt544w189tln2Lp1KwYNGtTguW3btkWnTp1w4MABg+P79+/HgAED6r3O0dERHh4eBjciopY4cLl2F/Au7JLScXZQIMRHuw0DW29ISpKGm7feeguffPIJtm7disGDB9d5zvz58xEbG6u//9xzz+Gbb75BfHw81Go1Pv74Y2RkZGDWrFlmqpqIWjuVWnPTlgscTHwz3aBiLuZHUpJsQHFBQQHefPNNODk54YEHHjB47OOPP8b06dMBAMXFxQbdUH/729+QnZ2Nu+66CxqNBm3btsX69evRrVs3s9ZPRK3X6YwilClr4OVijx7t2BJ8s24B7ticlMnp4CQpycJNmzZtkJmZWedjnp6e+v9//PHHUKlU+vsymQzvv/8+Fi5ciNLSUnh5ebXqJc+JyPwOXMoHAAwJ9YVczp8/N+uma7nJYrgh6UgWbmQyGQICAu54Xn3jY+zs7NCmTRtjl0VEdEcHLmsHEw9p5asS10W3kN/lnFKo1BrYKyQf2kmtEL/qiIiaoExZg4S0IgAcb1OX9m2c4e5oB5Va4Eout2EgaTDcEBE1wbHUfNRoBDp4uyDY20XqciyOTCZDt3bchoGkxXBDRNQE+vE27JKql24xv3OcDk4SYbghImoC3Xib1r4LeEPYckNSY7ghImqknJIqXMwug0wGDA71kboci8W1bkhqDDdERI108Ip2za1egZ5o4+ogcTWWq6u/tuUmp1SJ/DJuw0Dmx3BDRNRI+2t3Aed4m4a5Otqho492sPUFrndDEmC4ISJqBCEEDur3k2K4uRPdejdczI+kwHBDRNQIV3LLkF2ihIOdHP06cQHRO+G4G5ISww0RUSMcqO2SGtDJG072ComrsXz66eAMNyQBhhsiokY4cJnjbZrir20YyqDWCImrodaG4YaI6A5Uag2OpBQAAIZ04RTwxgj2doGjnRzKGg3SCyqkLodaGYYbIqI7OJ1RhDJlDbxc7NEz0FPqcqyCQi5DFz83AMCFbA4qJvNiuCEiugPdlguDQ32gkMskrsZ66Na7ucRwQ2bGcENEdAcHOd6mWcJqw83FbO4OTubFcENE1IByZQ1OphUC4Po2TdU1QNstdZEtN2RmDDdERA04llqAGo1A+zbO6ODtInU5ViXMT9tyk5JbDpVaI3E11Jow3BARNUA3BXxYmC9kMo63aYogL2e4OChQrdbgWn651OVQK8JwQ0TUAI63aT65XMZxNyQJhhsionrklFbhfO3eSINDGW6aI9yP427I/BhuiIjqcfiKdgp4z0APeLs6SFyNdQrXt9ww3JD5MNwQEdVDt58UZ0k1X3gAu6XI/BhuiIjqIITgeBsjCPfXdktdzSuHskYtcTXUWjDcEBHVITWvHDeKq+CgkKN/J2+py7FaAR5OcHe0Q41GIDWPM6bIPBhuiIjqoGu1ie7YBs4OComrsV4ymYxdU2R2DDdERHXQrW8zNIxdUi2l65riHlNkLgw3RES3UGsEDtXOlOJ4m5bTrVR8IYvhhsyD4YaI6BZJ14tRWlUDdyc7RAR5Sl2O1eta2y11KYfdUmQeDDdERLfQjbcZ1NkHCjm3XGipsNpuqWv55ahSccYUmR7DDRHRLfZfygWg3U+KWq6tmyO8XOyhEcBltt6QGTDcEBHdpKK6BvHXCgEAQ8PaSlyNbZDJZPqVii/lcNwNmR7DDRHRTY6mFkClFgjyckYnHxepy7EZuhlTnA5O5sBwQ0R0k4O1Wy4MC/OFTMbxNsai32OKM6bIDBhuiIhucoBbLpiEPtywW4rMgOGGiKhWTmkVzmeVQiZjuDE2XbhJL6hEubJG4mrI1jHcEBHV0k0B7xnoAW9XB4mrsS3erg7wdXMEwBlTZHoMN0REtfbXjrcZ2oWzpEzhr0HF7Joi02K4ISICIITQt9wMZZeUSYT5acMNW27I1BhuiIig/YWbXaKEo50c/Tq1kbocmxTmz20YyDwYboiI8FeX1IAQbzjZKySuxjbpWm64kB+ZGsMNERH+mgLOLinT0bXcZBRWoqKaM6bIdBhuiKjVU6k1OJKSD4BTwE3J29UBPq4OEAJIyS2XuhyyYQw3RNTqJaQVoaJaDR9XB/Ro5yF1OTatC7umyAwYboio1TtQuwv44C6+kMu55YIphdVOB7/EPabIhBhuiKjV268fb+MjcSW2L8yvdhsGhhsyIYYbImrViitVOJVeBAAYGsbF+0ztr7Vu2C1FpsNwQ0St2qHLedAIILStK4K8nKUux+Z1qe2WSiuoQJVKLXE1ZKsYboioVdtXu77NMLbamEVbN0d4OttDwxlTZEIMN0TUagkhsO+idjDx8HCGG3OQyWRczI9Mzk7qAgAgKSkJFy5cwPDhw9G2bcM/YBISEnDlyhWDY56enhgzZowpSyQiG5SaV47rRZVwUMgR09lb6nJajTB/d5y4Vsg9pshkJA03u3fvxuuvv47MzEykpKRg9+7diI2NbfCa//3vf9i0aRMGDhyoP9ahQweGGyJqMl2rTb9ObeDiYBF/67UK+pYbzpgiE5H0u7mwsBCLFi1CSEgIgoODG33dwIEDsX79ehNWRkStwX6Ot5GEfq0bdkuRiUgabh544AEAQEZGRpOuKy4uxpYtW+Dp6YmIiAh4eHBFUSJqmuoaDQ7XbrlwVzi3XDAn3Vo3V/MrUF2jgYMdh3+ScVnlV1R8fDw++eQTzJo1Cx07dsTKlSsbPF+pVKKkpMTgRkStW/y1QlRUq+Hr5oDuAfwDyZz8PRzh7mgHtUbgaj5nTJHxWV24mTZtGjIyMvDnn3/i7Nmz+Oc//4knn3wSZ86cqfeaRYsWwdPTU39rShcYEdmm/bVbLgwLa8stF8xMJpPp17vhuBsyhWaFm/T0dGzatAkrV67Eb7/9hpSUFGPXVa+RI0fCxcVFf3/+/Pnw8PDAH3/8Ue81r776KoqLi/W39PR0c5RKRBZsnz7csEtKCpwOTqbU6DE3VVVV+Pbbb/HVV1/pW0kcHBxQXV0NAAgLC8OsWbPwzDPPwN3d3TTV1kEmk8Hd3R05OTn1nuPo6AhHR0ez1UREli2/TIkz17Xd00MZbiShG3fDlhsyhUa13Bw9ehQ9evTA999/j6eeegoJCQmorKyEUqmEUqnEmTNn8NJLL+G3335Dt27d8OeffxqtwPj4eGzfvh0AoNFokJeXZ/B4QkICrl27hn79+hntNYnIth2o3SizezsP+Lk7SVxN69SFM6bIhBrVclNQUIDvvvuuzjVoHBwc0LNnT/Ts2RPPPvssTpw4gdTU1Ea9+LVr13D8+HEUFBQAAPbu3Yu8vDz06NEDPXr0AAAsWbIER44cwZkzZ6BWqzF06FBMmDABPXv2RFpaGj799FOMHTsWU6ZMaeRbJqLWbt9Fbbi5i602ktF1S6XmlUOl1sBeYXVDQMmCNSrc3HPPPXUeP3HiBLKzszF+/Hj9sX79+jW6FSU1NRVr164FAEyePBlJSUlISkrCtGnT9OGmX79++qne9vb2OH78OJYtW4Y9e/agTZs2WLp0KSZNmtSo1yMiEkLoBxPfxS0XJBPo6QwXBwUqqtW4ll+BLrVhh8gYWrTOzZkzZ7Bnzx6DcNMUsbGxd1yRePbs2Qb33d3d8fzzzzfr9YiILmSXIqdUCSd7OaI7tpG6nFZLLtfuMXUqoxiXc0oZbsio2A5IRK2KbsuFmBAfONkrJK6mdevCQcVkIi1eoXjLli2YOXMm+vfvj/79+6N3796cmUREFmvPBW24ie3KLimp/bUNA8MNGVeLW24GDBiAMWPG4NKlS3jxxRfh7++P/v3745tvvjFGfURERlOmrMHxq9oJDLFd/SSuhnSDii9mc8YUGVeLW258fX3x8MMP4+GHHwYA1NTU4MyZM6isrGxxcURExnToch5UaoGOPi4I8XWVupxWT7fWTUpeOdQaAQVXiiYjaVG46dKlC4qKigyf0M4OUVFRLXlaIiKT2FM73mY4Z0lZhPZtnOFkL0eVSoO0ggoGTjKaJndLLV68WL+dwdChQ/Hiiy+aoCwiIuMSQmAvx9tYFLlcpp8ldYldU2RETQ43Q4cOxY4dOxAaGor//ve/+u0XiIgs2eWcMlwvqoSDnRyDOnPxPkuh34aBg4rJiJocbiIjI3Hs2DEsXrwYixcvRteuXbFq1SoIIUxRHxGRUehmScWEeMPZgVPALQVbbsgUmjVbSiaTYdq0aUhOTsbf//53zJ8/H9HR0fo9oIiILM3ei7ouKc6SsiTh/my5IeNr0VRwe3t7zJ07F5cvX8aECRMwceJEvPfee8aqjYjIKMqVNTiWqpsCzvE2lkQ3HfxyThnUGvYAkHE0a7ZUdnY2kpOT9bdz584hOTkZFRUVyM3NNXaNREQtcvhKPqrVGgR7O6MzZ+RYlGBvFzjayaGs0SCjsAIdffj5oZZrcrj55JNP8NJLLwEA2rdvj4iICPTv3x9PPPEEIiIi0L17d6MXSUTUEnsu5gAAYsP9IJNxLRVLopDLENrWDcmZJbiUXcZwQ0bR5HBz9913Y9++fYiIiICXl5cJSiIiMh4hBLdcsHBh/rXhJqcMo3v4S10O2YAmh5sePXqYog4iIpO4kluOjMJKOCjkGBTqI3U5VIcwzpgiI2vUgOKkpCQUFhY26gnLysoQHx/foqKIiIxlzwVtl9SAEG+4OLR4xxkygTDOmCIja1S4uXTpErp27YpXXnkFZ8+erfOc8+fP4/XXX0dYWBhOnDhh1CKJiJrrryng7JKyVDfPmNJwxhQZQaP+jHnggQfQvXt3vPnmm4iKioKnpyfCwsLg6emJ0tJSXLp0Cfn5+bj33nuxadMmREdHm7puIqI7KlfW4GgKp4Bbug7eLnBQyFGpUuN6USWCvV2kLomsXKPbaLt3744ff/wRWVlZ2LFjh76rysPDA0899RTGjBmD9u3bm7JWIqImOXA5D9VqDTp4uyC0rZvU5VA97BRydG7rivNZpbiUU8pwQy3W5A7ogIAAPPLII6aohYjIqHad0463GdWdU8AtXZi/uzbcZJdhZDfOmKKWadbouqysLCxfvhwZGRnw8/PD2LFjERMTY+zaiIiaTaMR2Hm+Ntzwl6XF0427uZjNQcXUck3efiErKwuRkZH47LPPcOnSJaxduxaDBw/G3XffjaysLFPUSETUZEnXi5FXpoSrgwIDQrylLofuINxfN6iY08Gp5ZocbrZs2YKgoCCkpqZi27ZtSE5OxsWLF+Hr64sRI0agsrLSFHUSETWJrtXmrvC2cLBr0TZ6ZAZd/P6aDi4EZ0xRyzT5O14ul2Pw4MFwdHTUHwsNDcXq1asRGBiINWvWGLVAIqLm2HU+GwAwqju7pKxBRx8X2CtkqKhW40ZxldTlkJVrcri55557cPjw4TpbaGJjY5GSkmKUwoiImiuruApnrpdAJuMUcGthr5Cjs69u3A27pqhlmhxuTp8+DS8vL8TGxmLPnj364xUVFfjjjz8QFRVlxPKIiJpuV22XVFSwF3zdHO9wNlmKLrpxNxxUTC3U5HBTVVWFoqIinDp1CiNGjECbNm0QFRWFoKAgKBQK9O3bl/2lRCQpfZdUNz+JK6Gm0O8xxUHF1EJNDjf3338/Tp48idLSUpw6dQqffvopRo4ciT59+iA5ORmhoaHw8vLC0KFD8eOPP5qiZiKielWp1DhwOQ8Ax9tYm/DaPaY4HZxaqtm7yNnb2yMyMhKRkZGYMWOG/nhaWhoSExORmJgIjUZjlCKJiBrr0JU8VKk0CPR0QrcAd6nLoSa4eY8pIQQXXqRmM/oWuR06dECHDh0wYcIEYz81EdEd7axdlXgkVyW2Oh19XGEnl6FMWYOskiq083SWuiSyUlz8gYhshhBCP5iYqxJbHwc7OUJ8XQGwa4pahuGGiGzGucxSZBZXwdlegUGhPlKXQ80QVjtj6mIWBxVT8zHcEJHN2HFOO0tqSBcfONkrJK6GmuOvQcUMN9R8DDdEZDP+TNbub3d3jwCJK6Hm6spwQ0bAcENENiGjsAJnrpdALgNGdef6NtYqPOCv6eAaDddMo+ZhuCEim7A9Wdsl1a+TN3y4KrHV6ujtAgc7OSpVamQUciNmah6GGyKyCX+e1Yabu3twlpQ1s1PI0aWtdlDxBXZNUTMx3BCR1Sssr8axqwUAgLE9Od7G2nUN4LgbahmGGyKyejvP50CtEejezgPB3i5Sl0MtpJsxdYHTwamZGG6IyOr9eVY3S4pdUraga0DtWjdsuaFmYrghIqtWWa3Gvku5AIC7ezLc2AJdy82V3DKo1NyjkJqO4YaIrNq+S7moUmkQ5OWMHu08pC6HjCDIyxmuDgqo1AJX88qlLoesEMMNEVk13SypsT0DuFGmjZDJZPr1bjhjipqD4YaIrFaNWoOd52ungLNLyqboVyrmoGJqBoYbIrJax64WoKhChTYu9ujXsY3U5ZAR6WdMseWGmoHhhoislq5LanR3f9gp+OPMlnS9aRsGoqbiTwMiskpCCP2WC3dz4T6bo2u5uZpfjiqVWuJqyNow3BCRVUpML8L1okq4OCgwLMxX6nLIyHzdHODt6gAhgMs5bL2hpmG4ISKrtCUpEwAwqrs/nOwVEldDxiaTyRDuX7vHFAcVUxMx3BCR1RFCYEuSdlXi8RHtJK6GTEU/Y4qDiqmJGG6IyOrouqRcHRSI7dpW6nLIRLjWDTWX5OEmISEBs2fPRmxsLBITExt1zdGjR/HYY49h3LhxePnll5Gbm2vaIonIoui6pEayS8qmca0bai5Jw82bb76Jxx9/HIGBgdi7dy+KiorueM2BAwcwbNgwtG3bFk8//TTi4+MxZMgQlJdziW6i1oBdUq1HWG24uVFchZIqlcTVkDWRNNzMmzcPiYmJeOKJJxp9zT//+U/ExcXhww8/xOTJk/Hbb78hMzMTS5cuNWGlRGQp2CXVeng626OdpxMA4BK7pqgJJA03Pj4+TTq/oqICBw4cwIQJE/TH3NzcMHr0aPz555/GLo+ILBBnSbUu+pWKszgdnBpP8jE3TZGRkQGNRoOgoCCD40FBQbh27Vq91ymVSpSUlBjciMj63NwldS+7pFqFv1YqZssNNZ5VhZvq6moAgLOzs8FxFxcX/WN1WbRoETw9PfW34OBgk9ZJRKbBLqnW56+WG4YbajyrCjdt2mg3xsvPzzc4np+fr3+sLq+++iqKi4v1t/T0dJPWSUSmwS6p1kc3Y+p8VgmEEBJXQ9bCqsJNUFAQ/Pz8cPLkSYPjx48fR58+feq9ztHRER4eHgY3IrIu7JJqncL83aCQy1BYoUJ2iVLqcshKWHy4+eCDD/D444/r78+cORPffPMNsrO1G+b9/vvvSEpKwsyZMyWqkIjMgV1SrZOTvQKdfV0BAOcyOV6SGkfScLN161bExsZi6tSpAIAXX3wRsbGxWL58uf6cCxcu4Pjx4/r7b775JqKiotClSxdERkZi2rRp+PjjjzFo0CBzl09EZvT7KXZJtVY9ArWt7ckMN9RIdlK+eFRUFN58883bjnfq1En//5dfftlgdpOzszN+++03pKSkIDs7G127doW3t7cZqiUiqdSoNfjt1A0AQFxUoMTVkLl1b+eBXxNvMNxQo0kabgICAhAQENDgOV27dq3zeOfOndG5c2dTlEVEFubQlXzklSnRxsUed4WzS6q16d5O23Jz7gbDDTWOxY+5ISLamHAdAHBfZCDsFfyx1dr0qA03qfnlqKiukbgasgb8KUFEFq2iugbbzmpnSU3swy6p1qituyN83RwhBNe7ocZhuCEii7Y9ORvl1WoEezujb4f617Mi28ZBxdQUDDdEZNF+TdQOJJ4YFQSZTCZxNSSV7u20i/lxOjg1BsMNEVms/DIl9l7MBQDERQXd4WyyZbpxN8kcVEyNwHBDRBZrc1Im1BqBiCBPdPFzk7ockpAu3JzPKoVGw20YqGEMN0RksX6pnSU1sQ9bbVq7EF9XONjJUVGtRlpBhdTlkIVjuCEii3QtvxwJaUWQy4D7e3MvqdbOTiFHtwDtuBsOKqY7YbghIou0MUE7kHhIF1/4uTtJXA1Zgu4BtYv5MdzQHTDcEJHFEULg18TaLikOJKZauhlTHFRMd8JwQ0QWJ/5aIVLyyuFsr8DYXg1v0UKtR49ATwBsuaE7Y7ghIovz04l0AMD4yHZwc5R0CzyyIN1qW25uFFehqKJa4mrIkjHcEJFFKVPWYNPpTADAtH7BEldDlsTDyR7B3s4AOKiYGsZwQ0QWZcvpTFRUqxHi64r+nbjdAhn6a1Ax95ii+jHcEJFF+bG2S2pqv/bcboFu050rFVMjMNwQkcW4nFOG+GuFUMhlmNK3vdTlkAXSbaDJQcXUEIYbIrIY62pbbWLD28LPg2vb0O102zBcyilFdY1G4mrIUjHcEJFFUKk1+Pmkdm2bqRxITPVo38YZ7o52UKkFruSWSV0OWSiGGyKyCLvP5yCvTAlfNweM6u4ndTlkoWQyGcfd0B0x3BCRRfjpRAYAYFKfINgr+KOJ6tczSBtukq4XS1wJWSr+BCEiyeWUVGH3hRwAXNuG7qx3ey8AwKmMIknrIMvFcENEklt/MgNqjUCfDl4I83eXuhyycJHttdswJN8ogUrNQcV0O4YbIpKUWiOw6kgaAOChAR0kroasQScfV7g72UFZo8GFLC7mR7djuCEiSe0+n4PrRZXwdLbHhN6BUpdDVkAulyEiSNt6w3E3VBeGGyKS1Ioj1wAA0/q1h5O9QuJqyFpE1o67Oc1xN1QHhhsikkxqXjn2XcyFTAY8MrCj1OWQFeldO+7mVDpbbuh2DDdEJJkfaltthoe3RUcfV4mrIWsSGewFALiQXYoqlVraYsjiMNwQkSQqq9X67RZmDGKrDTVNoKcTfN0coNYInOVifnQLhhsiksRvp66jpKoGwd7OGB7OFYmpaWQyGcfdUL0YbojI7IQQWHFY2yX1SExHKOQyiSsia6Rb7+Z0BsfdkCGGGyIyu5NpRTh7owSOdnKuSEzNxpWKqT4MN0RkdisPXwUA3N87EG1cHaQthqyWruUmJbccJVUqiashS8JwQ0RmlVNShS1JWQA4kJhaxsfNEUFezgCAM1zMj27CcENEZrXs0FVUqzXo17GNfkAoUXNx3A3VheGGiMymTFmDVbVr28y6q7PE1ZAt4IwpqgvDDRGZzY/H01FSVYPOvq4Y3d1f6nLIBnClYqoLww0RmUWNWoPvDqQCAJ4a1hlyTv8mI+hVG26uF1Uiv0wpcTVkKRhuiMgsNidl4npRJXxcHfBA3yCpyyEb4eFkj85ttVt3cNwN6TDcEJHJCSGwdH8KAOCxwZ24+zcZFde7oVsx3BCRyR2+ko8z10vgZC/n7t9kdJwxRbdiuCEik/u6ttVmWr9geHPRPjIy3YypU+lFEEJIWwxZBIYbIjKpC1ml2HMhF3IZ8OTQEKnLIRvUK8gDDnZy5JdXIyWvXOpyyAIw3BCRSS3ecxkAMK5XADr6uEpcDdkiRzsFompbb46nFkhbDFkEhhsiMpnLOWX47dQNAMCc2C4SV0O2bECINwDg2FWGG2K4ISIT+nzXJQgB3N3DH72CPKUuh2xY/9pwc5zhhsBwQ0QmcnOrzfOjwiSuhmxd3w5ekMuA9IJKZBZXSl0OSYzhhohMgq02ZE7uTvboEegBADjGcTetHsMNERnd5Zwy/M5WGzKz/p3YNUVaDDdEZHRf7LoEjQDGsNWGzChGN+4mtVDiSkhqdlIXAAClpaXIz89HUFAQ7O3tGzw3OzsbhYWGX7iOjo4ICeH6GUSW4OaxNi+w1YbMqF9ty82F7FIUVVTDy4ULRrZWkrbc1NTU4JlnnoGvry8GDBgAf39/rFq1qsFr/vWvf2HAgAGYOHGi/vbCCy+YqWIiuhO22pBUfN0c9ZtoHr/K1pvWTNKWm3fffRe//PILkpKSEB4eju+++w6PPfYYIiIiEBkZWe91d999N9avX2/GSomoMc5lluBXttqQhAZ08kZKbjmOXy3AmB7+UpdDEpG05eZ///sfnnrqKYSHhwMAnnjiCXTp0gVLly5t8DohBNLS0lBczE3SiCzJwi3nIAQwPrIdW21IEvrF/DhjqlWTLNxkZWUhIyMDAwcONDg+aNAgxMfHN3jthg0bMHDgQPj7+yMyMhIHDx40ZalE1Aj7LuZi/6U82CtkeGVsN6nLoVZKN2PqzPViVFTXSFwNSUWycJOfnw8A8PX1NTju6+uLvLy8eq8bMmQILl68iBs3bqCoqAgDBw7E+PHjkZGRUe81SqUSJSUlBjciMh61RmDhlnMAgEcHdkIHHxeJK6LWqn0bZ7TzdEKNRiAxrUjqckgikoUbhUIBAKiurjY4rlQqYWdX/1CgRx99FGFh2r58JycnfPHFF1Cr1diwYUO91yxatAienp76W3BwsBHeARHpbDiZgfNZpXB3ssO8kdxDiqQjk8n0rTdH2TXVakkWboKCgiCTyZCZmWlwPCsrC+3bt2/08zg4OCAgIABpaWn1nvPqq6+iuLhYf0tPT2923URkqLJajY/+vAgAmDeyC9q4cvotSWsA95lq9SQLN+7u7oiOjsbWrVv1x6qrq7Fjxw7Exsbqj2VlZSE1NRWAdiBxTY1hH2p6ejquXr2qH5RcF0dHR3h4eBjciMg4vjuYiqySKgR5OWPGoE5Sl0OkDzcJaUVQqTUSV0NSkHS21FtvvYVVq1bho48+wqFDhzB9+nQ4OTlh9uzZ+nNee+013H///QAAlUqFAQMGYMWKFYiPj8cvv/yCe++9F6GhoXj44YelehtErVZemRJL9lwBACwY1xVO9gqJKyICurR1g5eLPSpVapy5zlm1rZGk4ebee+/Fxo0bsW3bNjz77LNwcnLCgQMH4O3trT+nXbt26Ny5MwBtF9SaNWtw4MABzJ49G0uWLMG0adMQHx8PV1dXqd4GUav14bYLKFPWICLIE/dHBkpdDhEAQC7/a9zNoSv5EldDUpAJIYTURZhbSUkJPD09UVxczC4qomaKv1aIyUsOAQDWzR6k/2VCZAlWHr6K1389iwGdvPHT7EFSl0NG0tjf39w4k4iarEatwWsbzwAApka3Z7AhixPb1Q8AEJ9WiOJKlcTVkLkx3BBRky0/dBXnMkvg5WKPV+/tLnU5RLcJ9nZBFz83qDUCBy7Vv3Ya2SaGGyJqkqziKvx3u3bq9yvjusGbU7/JQsWGtwUA7L6QI3ElZG4MN0TUJG9vSkZ5tRp9O3jhwX5cEJMs14hu2q6pvRdzodG0uuGlrRrDDRE12t6LudiclAm5DPjPxAjI5TKpSyKqV79ObeDqoEBuqRLJmdx2pzVhuCGiRqmorsEbv2oHEc8cHIIegZxpSJbN0U6BwV20+xfuPs+uqdaE4YaIGuW9P87jWn4FAjyc8NKYMKnLIWqUEbWzpvZczJW4EjInhhsiuqODl/Pw/eFrAID3p0TC3cle4oqIGie2q3ZQcUJaIQrLq+9wNtkKhhsialBJlQovrzsFAHhkYAfcVTsDhcgaBHo5o6u/OzQC2HeJrTetBcMNETXo7d+TcaO4Ch19XPDqPVzThqxPbDdtIN9zgeGmtWC4IaJ67UjOxrr4DMhkwIdTe8PV0U7qkoiaTDfuhlPCWw+GGyKqU0F5Nf5vQxIAYNawztxigaxWdMc2cHe0Q0F5NU5zl/BWgeGGiG6j0Qi8vO4U8sqUCPd3w0tjwqUuiajZ7BVyDA3jlPDWhOGGiG7z1b4r2Hk+Bw52cvz3wSg42SukLomoRfRTwrkVQ6vAcENEBg5fyceH2y4AAN6O64megZ4SV0TUcrFd20ImA05lFCO9oELqcsjEGG6ISC+npArz1iRAI4Ap0e0xjXtHkY3w83DCkFBt19QvCdclroZMjeGGiAAANWoNnluTgLwyJboFuOPtuF6Qybh3FNmOiX2CAAAbE65DCM6asmUMN0QEAPjwz4s4lloAN0c7LH64L5wdOM6GbMu4XgFwspcjJa8cpzI4a8qWMdwQETaczMBXe68AAN6bHInObd0krojI+Nwc7XB3jwAA2tYbsl0MN0St3OEr+Xjl59MAgNnDQzE+sp3EFRGZzqS+2q6p30/dgEqtkbgaMhWGG6JW7HJOGZ5ZeQIqtcD4yHZYMLar1CURmdSwLr7wdXNAfnk19nOvKZvFcEPUSuWVKfH48mMoqapB3w5e+Ghqb8jlHEBMts1OIcf9vQMBABtOsmvKVjHcELVCVSo1nl5xAukFlejg7YKlM/pxoT5qNR7o0x4AsD05G6VVKomrIVNguCFqZZQ1asxZdRIJaUXwdLbHssf7w8fNUeqyiMymV5AHQtu6QlmjwR9nsqQuh0yA4YaoFVGpNXhudQJ2nc+Bk70cXz8ajVDOjKJWRiaT4YG+2tYbzpqyTQw3RK1EjVqDF9YmYHtyNhzs5Fg6ox9iOvtIXRaRJCbUjrs5nJKPzOJKiashY2O4IWoF1BqBl346hS1JWXBQyPG/R6MxLKyt1GURSSbY2wUDQrwhBLD2WLrU5ZCRMdwQ2bgatQZ/X3cKv5+6ATu5DF8+3Fe/QzJRa/bowI4AgO8PX0W5skbiasiYGG6IbFhltRrPrIzHLwnXoZDL8PlDfTCmh7/UZRFZhHsj2qGTjwuKKlRYcyxN6nLIiBhuiGxUQXk1pn9zBDvP58DRTo4lD/fFPRFcfZhIRyGXYfbwUADA0v0pUNaoJa6IjIXhhsgGZRRWYMpXh/TTvVc9FYO7ewZIXRaRxZnUNwj+Ho7ILlHiFy7qZzMYbohszJnrxXhg8SGk5JYj0NMJ62cPQr9O3lKXRWSRHO0UeHpYZwDAV3uvQK0REldExsBwQ2RD1sdnYPKSQ8gpVaKrvzt+njMYYf7uUpdFZNEeGtABXi72uJpfgS1JmVKXQ0bAcENkA6prNHhtYxL+vu4UlDUajOzmh59mD0I7T2epSyOyeK6Odpg5uBMAYPGeKxCCrTfWjuGGyMplFlfiwa8P44cjaZDJgJdGh+ObGf3g6WwvdWlEVmPm4E5wcVDgXGYJ9lzkbuHWjuGGyIptPZOJ8Z8dQEJaETyc7PDdY/3xwugw7u5N1EReLg54OKYDAODznZfYemPlGG6IrFBxhQovrk3A7B9OoqC8Gj3aeeD3eUMxohsX5yNqrqeGdYaTvRwn04rw43GuWmzNGG6IrMyeCzm4+5O92Jh4A3IZMHdEKH6ZOxgdfVylLo3Iqvl7OGH+mK4AgHc2n0NWcZXEFVFzMdwQWYnskiq89GMiZi47juwSJTr7uuLnZwfj5bHd4GinkLo8IpvwxNAQ9A72QqmyBq9tTGL3lJViuCGycNU1Gny19wpGfrgHvyRch0ymHfy4+flh6NOhjdTlEdkUhVyGD6ZEwl4hw45zOfj9NKeGWyM7qQsgoroJIbDnQi7e3pSMlLxyAEBUsBfemtATvYO9pC2OyIaF+7vjuRFh+O+Oi3jzt7MYEuoDHzdHqcuiJmC4IbIwQggcuJyH/26/iJNpRQAAXzdH/N893fBAnyDOhCIyg2djQ/HHmUyczyrFW78n47OH+khdEjUBww2RhRBC4HBKPv67/SKOXy0EADjayfHY4E54bmQXeDhx3Roic3Gwk+P9KZGY+OVB/HbqBkZ288PEPkFSl0WNxHBDJLHqGg22JGVi2cFUnMooBqD9wfpwTAc8OzwUfh5OEldI1DpFtvfCs7Gh+HL3Ffx93Sl4ONthZDd/qcuiRmC4IZJIbqkSq4+m4Yej15BbqgSgDTUP9Q/Gs7FdEODJUEMktfljuuJ6YSU2Jt7A7B9OYvnj/TE41FfqsugOGG6IzKhKpcbOcznYcDIDey7m6ncg9vdwxKMDO+KhAR04cJHIgsjlMnwwtTfKq9XYnpyNp78/gR+eiuFMRQsnE61wEn9JSQk8PT1RXFwMDw8PqcshG1ddo8HR1HxsScrEptOZKK2q0T/Wt4MXZg4JwT29AmCv4MoMRJaqSqXGk98fx8HL+fB0tsePzwxEtwD+/jC3xv7+ZrhhuCETKKlSYe+FXPyZnI09F3IMAk2gpxMm9Q3CpD7t0cXPTcIqiagpypU1ePTbozhZu5fb2xN7IS6Kg4zNieGmAQw3ZGxVKjXirxXi0JU8HLqSj9MZxfouJ0A7lXt0dz/ERQUhJsSb07mJrFRxhQqPLz+mX6bhvsh2+M/EXvBycZC2sFaC4aYBDDfUEkIIXC+qREJaERLTtbek68WortEYnNe5rSvu7hGAMT380SfYi4GGyEbUqDX4cvcVfLbrEtQaAX8PR3wwpTfuCm8rdWk2z2rCTWZmJn744QdkZ2cjIiIC06dPh719w+t5NOeamzHcUGNVVNfgSk45zmeV4HxWqfbfzFLkl1ffdq6/hyOGhPpiUKgPBnfxRZCXswQVE5G5nEovwks/JSIlV7uC+LAwX8wc3AkjuvrxjxkTsYpwc/HiRQwePBgDBgxATEwMVq1ahaCgIOzYsQMKRd0bATbnmlsx3JCORiOQV6ZERlElbhRV4nphJa7mVyA1rwxX8yqQVVL3rsB2chm6t/NAnw5eiAr2Qp8ObdDJxwUyGX+gEbUmldVqvPvHOaw4cg2636YdfVwwY1AnTO4bxO4qI7OKcDNp0iQUFhZi9+7dkMlkyMjIQGhoKJYuXYoZM2YY7ZpbMdzYLiEEKlVqlFTWoLhShYLyahRWVGv/La9GbpkSOSVK5JRWIbtEidxSJarVmgaf09vVAV393dGtnTu6B3igWzt3hPu7w8meO3ETkVZ6QQVWHrmGtcfSUFI7gUAmA3q080BMiA8GdvbGgBBvhp0Wsvhwo1Kp4O7ujs8++wyzZs3SHx87dizc3Nzw888/G+WaujDcGI8QAhoBaITQ3jSAWv9/AXXtrcbgXw1UaoEatYBKo9H+q9agWq1BdY0GKrUGSpUGyhoNlDVqVNdoUKlSo1KlRlW19t+KajXKlTUoV6pRXl2DcmUNSqtqUFKlgkrdtC9puQwI8HBCoJczgto4o4O3C0J8XfU3/jAiosaqqK7BLwnXsfLwNZzPKr3tcV83BwR7u6Cjtws6eLvA39MJns728HS2h5ezAzyc7eBkr4CjnRyOdgo42MmhYBeXXmN/f0u2iF9aWhqUSiVCQkIMjnfu3BkHDx402jUAoFQqoVQq9fdLSkpaUHn97v/8ALLr6cZoqbp+Xd8eS28/S3eO0N8Xt50phPa4qH1A4K/7QgACovYc7f814q9QY6kUchk8ne3RxsUe3q4OaOOivbV1d4SfhyP83B3R1t0J/h6O8Pdw4hozRGQULg52eDimIx6O6YickiocSS3A0ZR8HEnJx5XccuSVVSOvrBoJtbOtGkMu0/5MU8hlUMhkkMtlkMtkkMkAGaD//1+0d+rqJTdnTPp93lD4S7R9jGThprKyEgDg7u5ucNzDwwMVFRVGuwYAFi1ahLfeeqsl5TZKfpkSOaXKO5/YyshlgJ1cDrlc+6+dQgY7uRz2Cu03q4NCDnuFHPZ2Mu2/CvlNf7nI4WAnh7O9QntzUMCp9v9ujnZwdbSDq6P2/+5O9vBwtoOHkz1cHBQc/0JEkvLzcMKE3oGY0DsQgHb9q7T8CqQVaG/X8iuQV6ZEcaUKJZUq/b/KGg1qbvrrUSMAjVo0uVVaahoJ5ytJFm7c3LSLlxUVFRkcLywsrLepqTnXAMCrr76Kv/3tb/r7JSUlCA4ObkbVDVv+xACo7jB+oz6yZubpW39/6+7f/Hy3nWNw/K+ELwMgk8lq/9U+h/75ZNq/Dgz+Wqj960Euq71OBihk2sCiO66QyxgyiIgAeDjZo1eQJ3oFed7x3JrarvoqlQY1ag3UQtuVrxHa7v2bW9xvDhH61vpG5ApRZ5+A8fi4SreVjGThpkOHDnBzc8O5c+cwbtw4/fFz586hR48eRrsGABwdHeHoaPoPcri/+51PIiIiugM7hRx2Cjk45K95JBtoIJfLMXXqVCxfvlzf3ZSYmIhDhw7hwQcf1J+3evVqLFy4sEnXEBERUesl6VTwnJwcxMbGAgCioqKwdetWTJo0Cd9++63+nKeeegpHjhzBmTNnGn3NnXC2FBERkfWx+KngOkqlEtu2bdOvNjxw4ECDx3fv3o2srCw89NBDjb7mThhuiIiIrI/VhBspMNwQERFZn8b+/ubiHkRERGRTGG6IiIjIpjDcEBERkU1huCEiIiKbwnBDRERENoXhhoiIiGwKww0RERHZFIYbIiIisikMN0RERGRTJNsVXEq6RZlLSkokroSIiIgaS/d7+06bK7TKcFNaWgoACA4OlrgSIiIiaqrS0lJ4enrW+3ir3FtKo9Hgxo0bcHd3h0wmM9rzlpSUIDg4GOnp6a1izyq+X9vX2t4z369t4/u1fkIIlJaWIjAwEHJ5/SNrWmXLjVwuR/v27U32/B4eHjbzhdQYfL+2r7W9Z75f28b3a90aarHR4YBiIiIisikMN0RERGRTGG6MyNHREf/617/g6OgodSlmwfdr+1rbe+b7tW18v61HqxxQTERERLaLLTdERERkUxhuiIiIyKYw3BAREZFNYbhpgrS0NDz77LOIjY3F9OnTceTIEZNcYykKCgrw8ssvY8SIEZg8eTK2bt3a4PlCCPz888949NFHMXr0aDz77LM4d+6cmaptuYqKCvz73//GyJEjcf/992P16tWNvrayshL3338/Bg4ciOLiYhNWaTw1NTX49NNPcffdd2Ps2LH48ssvodFo7njduXPn8Oyzz2LEiBGYM2cOrl+/boZqjWP58uUYP348Ro8ejXfffRdKpbLB8wsKCvDWW29h/PjxGDNmDF588UWkpqaaqdqWEUJg+/btmDp1KgYOHIjMzMxGXffrr79i4sSJGDFiBF599VWr+XoGgCNHjmDmzJkYOHAgTp48ecfz8/Pz8c4772D8+PGIi4vDBx98gIqKCjNUahxnzpzBc889h4EDB2Lz5s1NunbXrl0YOHAgXnnlFRNVJzFBjZKbmysCAwPFxIkTxebNm8X8+fOFg4ODOHLkiFGvsRRKpVJERESIYcOGid9++00sXLhQKBQKsWHDhnqvef7558WUKVPEihUrxPbt28WsWbOEo6OjOH78uBkrb76xY8eKHj16iJ9//lksXrxYODs7i//+97+NunbWrFmiV69eAoDIzc01baFGMmvWLNGuXTuxevVqsXLlStG2bVvxwgsvNHjNjh07hLOzs5g3b57YtWuXWL58uRg5cqR5Cm6hf//738LDw0N88803Yt26dSI0NFRMnjy5wWv69u0r+vbtKzZu3Ci2bdsm7rvvPuHn5ydycnLMVHXzPfLII2LUqFHiH//4hwAgUlNT73jNihUrhL29vfjoo4/Er7/+Kvr16ycGDBggampqTF9wC/3jH/8QAwYMEO+++64AIHbv3t3g+TU1NaJTp07itddeE5s3bxbr1q0TPXr0EEOHDhUqlco8RbfA119/LXr27Ck+/fRToVAoxLJlyxp9bU5OjujYsaMIDw8XcXFxJqtRSgw3jfTGG2+IgIAAUV1drT82duxYMW7cOKNeYym+++474eDgIPLz8/XHnnnmGdGtW7d6ryktLb3tWP/+/cXjjz9ukhqNadeuXQKASEpK0h9btGiR8PT0FFVVVQ1eu27dOhERESHWr19vNeHmypUrQiaTid9//11/bM2aNUKhUIjr16/XeU11dbVo3769mD17tsHxyspKk9ZqDCUlJcLZ2VksWbJEf2z//v0CgDhx4kSd11y7dk0AEDt27NAfy83NFQDEr7/+avKaW6qoqEgI8df7vFO40Wg0on379uKVV17RH0tLSxMymUysX7/elKUahe79pqenNyrcCCFEWVmZwf1Tp04JAOLgwYOmKNGoiouL9f9vSrjRaDRi3Lhx4v333xdxcXE2G27YLdVIO3fuxLhx42Bvb68/FhcXh927d0OtVhvtGkuxc+dODB48GN7e3vpjcXFxOH/+fL3dEG5ubnUeq66uNlmdxrJz50507NgRvXr10h+Li4tDcXExTpw4Ue91V69exbx587B69WqrWkti165dsLe3x913360/dv/990Oj0WD37t11XrNnzx5kZGRgzpw5BsednJxMWqsxHDx4UN91qDNkyBD4+Phgx44ddV4TEBCA9u3b49ChQ/pjBw4cgKOjIyIjI01ec0s1Zon6m124cAEZGRkGH6Pg4GD06dOn3o+RJWnq+wUAV1dXg/u6n2HW8DOrudspfPTRR1AqlZg/f76RK7IsDDeNdO3aNQQGBhocCwwMhFKpRHZ2ttGusRT11a57rDEOHjyIvXv3YuLEicYuz+iuXbuGoKAgg2N3er81NTWYPn06/u///s8gFFmDa9euwdfXFw4ODvpjrq6u8PT0rPf9Jicnw8nJCdXV1Zg2bRpGjx6NF198ERkZGeYqu9muXbsGmUyGgIAA/TGZTIZ27drV+34dHBywd+9e/PzzzwgNDUXPnj0xd+5c7Nq1C506dTJT5eaj+zjU9X3f2O95a/fOO++gXbt2GDBggNSlmMTx48fx4YcfYsWKFQ1uOmkLbPvdGZFKpbrtL3NnZ2f9Y8a6xlK0tPaUlBRMmTIFjzzyCKZMmWKSGo2pOe/3tddeg4eHB55//nmT12dsdb1fQPue63u/VVVV0Gg0mDFjBiZNmoSXX34ZV65cQXR0NHJyckxdcouoVCrY2dlBoVAYHG/o/Wo0GrzwwgtQKBT48MMP8dFHHyE6OhqzZ89GUVGRGao2L93Hoa7vA0v/eWUMn332GVauXImVK1fCxcVF6nKMrqSkBA899BA+//xzk24cbSla5a7gzeHt7Y2CggKDY/n5+frHjHWNpWiodh8fnwavvXr1KkaOHImhQ4fi22+/NVmNxuTt7Y3z588bHLvT+/3+++/h6emJQYMGAYD+F964cePwxBNP3NZ9Y0nq+vwC2vdc3/v19vZGdXU13n//fYwfPx4AcNddd8Hf3x9r16616JDn7e0NlUqFsrIyg+7Tht7v9u3bsWnTJly6dAldunQBAIwYMQKBgYH4+uuvsWDBArPUbi66n0kFBQUGrTf5+flo27atVGWZxddff42XX34ZP/30E0aNGiV1OSaxf/9+pKWl4aOPPsJHH30EALh48SIAYODAgVi/fr1NhR6Gm0bq27cvjh8/bnDs6NGj6NKlC9zd3Y12jaXo27cvvv/+ewghIJPJAGhrd3V1RVhYWL3XXbt2DSNGjEC/fv2wZs0a2NlZx5dY37598d133xn88jt69CgAICoqqs5rNm/ebNA3f/DgQfz973/HO++8gx49epi85pbo27cviouLcenSJf3nMzExEdXV1ejTp0+d1/Tr1w+AYbeFs7MzvLy8UFhYaPqiW6Bv374AtM3yI0aMAADk5OTg6tWr9b5fXfi7+f06OjrCx8enzmBo7Xr16gV7e3scP35c382qUqmQkJBgu9OFAXzzzTeYN28e1qxZYxVd6M01ZMgQ7Nu3z+CY7vP63nvv2V6AlXpEs7XYtWuXkMvlYtu2bUII7WwTHx8fsWjRIv0527dvFzExMfoZRo25xlJduHBB2NnZiaVLlwohhMjLyxOhoaHimWee0Z9z5swZERMTI86cOSOE0M6sCAkJEZMnT7aKqZQ3KygoEF5eXuKf//ynEEI7A2jQoEFi7Nix+nPy8/NFTEyM2L59e53P8fvvv1vNbCmVSiVCQ0PFI488IjQajVCr1eKBBx4Q3bt3F2q1Wn/eXXfdJVasWKG/379/f/H000/rz/n111+FTCYT+/fvN/t7aKrBgweL0aNH62cvPvfcc8Lf399gxsyUKVPEhx9+KIQQIiUlRTg4OBh8v27evFnIZDKxadMm8xbfAg3Nlpo3b56YP3++/v706dNFRESEfibOhx9+KJycnERaWpq5ym2xhmZLLVy4UEyfPl1//9tvvxUODg7i559/NmOFxlffbKlly5aJESNG1HudLc+WYrhpgg8++EA4OTmJ8PBw4ejoKGbMmGHwS3zNmjUCgMjMzGz0NZbshx9+EO7u7iI0NFS4uLiIsWPHipKSEv3jhw8fFgDE4cOHhRBCTJ06VQAQ0dHRIiYmRn978sknpXoLTbJ9+3bh5+cnOnToIDw9PUX//v0NpkVnZmYKAGLNmjV1Xm9N4UYIIRITE0Xnzp2Fv7+/aNu2rQgLCxNnz541OMfR0dHgl3tKSoqIiooS7dq1E926dRMeHh7i888/N3fpzZKamioiIyOFt7e3CAoKEoGBgeLAgQMG54SGhoq5c+fq769atUr4+vqKjh07iq5duwoXFxfx1ltvmbv0Zlm6dKmIiYkRPXr0EABEVFSUiImJMQhmo0aNEuPHj9ffLygoELGxscLNzU2EhIQILy+vBte2siSbNm0SMTExok+fPgKA6N69u4iJidH/gSaEEE8++aTo2bOnEEKIwsJCIZfLRZs2bQx+XsXExFjFVP/4+Hh9vQBE586dRUxMjPj3v/+tP+ftt98Wrq6u9T6HLYcb7greRMXFxUhJSUG7du0MZl4A2r7pS5cuITo62mD6d0PXWLqKigpcvHgR3t7e6NChg8FjZWVlOHPmDHr16gU3NzdcvHixzuZ6d3d39OzZ01wlt4hKpcK5c+fg4uKiH2dx82Px8fEICwurc5xGUVERzp8/j379+llNd5xGo8G5c+cgk8nQvXt3fRekzrFjx9C+ffvbZtBcunQJKpUKoaGhVjUFHtCOM1Aqlejevfttn6fExER4eXkZzIZSqVS4du0aqqurERISoh9obukyMjLqnMkWGhqq74I4d+4c5HI5unbtanBOamoqiouL0a1bN6uY6g8Aubm5uHLlym3H27dvrx9LkpKSgrKyMkRGRqKmpqbeZR5u/hhZqpKSEiQnJ992vG3btggNDQUAXL9+HTdu3ED//v3rfA7dmJvw8HDTFSoRhhsiIiKyKZwKTkRERDaF4YaIiIhsCsMNERER2RSGGyIiIrIpDDdERERkUxhuiIiIyKYw3BAREZFNYbghIiIim8JwQ0RERDaF4YaIrNITTzyB7777zuBYdXU1JkyYgB07dkhUFRFZAoYbIrJKJSUl+PPPPw2Offnll0hOTsbw4cMlqoqILAHDDRFZpYiICJw7d05/v7i4GO+88w4WLlxosHEtEbU+1rF1MRHRLSIiIrBo0SKo1WooFAq899576Ny5M6ZOnYrc3FzMmzfvtmtkMhmWL19udTuZE1HTMNwQkVWKiIiAUqlESkoKXF1d8emnn2LTpk2QyWRQKBSYOHEiAGDhwoWIi4tDz549YWdnx2BD1ArIhBBC6iKIiJpKo9HA3d0dq1evxubNm3H9+nVs3rz5tvOCgoKQkJAAPz8/CaokIimw5YaIrJJcLkePHj2wYcMGrF27FidOnLjtnOvXr8Pe3p7BhqiV4YBiIrJaERERWLFiBaZPn46IiIjbHj927Bj69+8vQWVEJCW23BCR1XrjjTcwY8YMREZG1vn48ePHMWDAADNXRURSY8sNEVmtTp06ITY2Ft7e3nU+fvz4cbbcELVCHFBMRDZr06ZNGDVqFJydnaUuhYjMiOGGiIiIbAq7pYiIiMimMNwQERGRTWG4ISIiIpvCcENEREQ2heGGiIiIbArDDREREdkUhhsiIiKyKQw3REREZFMYboiIiMimMNwQERGRTfn/UxmZfd7ubGsAAAAASUVORK5CYII=", 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" ] }, "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": 0.00422, "end_time": "2026-06-30T01:11:36.989432+00:00", "exception": false, "start_time": "2026-06-30T01:11:36.985212+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": "2026-06-30T01:11:36.999273Z", "iopub.status.busy": "2026-06-30T01:11:36.999039Z", "iopub.status.idle": "2026-06-30T01:11:40.367938Z", "shell.execute_reply": "2026-06-30T01:11:40.366784Z" }, "papermill": { "duration": 3.374867, "end_time": "2026-06-30T01:11:40.368608+00:00", "exception": false, "start_time": "2026-06-30T01:11:36.993741+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": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 33.121512, "end_time": "2026-06-30T01:11:41.091300+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": "2026-06-30T01:11:07.969788+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }