{ "cells": [ { "cell_type": "markdown", "id": "b1", "metadata": { "papermill": { "duration": 0.005473, "end_time": "2026-05-16T13:59:54.290016+00:00", "exception": false, "start_time": "2026-05-16T13:59:54.284543+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Particle-spray Stream Modeling with streamspraydf\n", "\n", "The particle-spray technique generates tidal streams by \"spraying\" particles\n", "from the Lagrange points of a progenitor cluster as it orbits in a gravitational\n", "potential. Each particle is given a small velocity kick and then integrated forward\n", "in the potential. galpy provides two implementations (described in \n", "[Qian et al. 2022](https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.2339Q/abstract)):\n", "\n", "- `chen24spraydf`: the spray model from [Chen et al. (2024)](https://ui.adsabs.harvard.edu/abs/2025ApJS..276...32C/abstract)\n", "- `fardal15spraydf`: the spray model from [Fardal et al. (2015)](https://ui.adsabs.harvard.edu/abs/2015MNRAS.452..301F/abstract)\n", "\n", "These are faster to set up than `streamdf` and work in any potential." ] }, { "cell_type": "code", "execution_count": 1, "id": "b2", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:54.300617Z", "iopub.status.busy": "2026-05-16T13:59:54.300392Z", "iopub.status.idle": "2026-05-16T13:59:57.036959Z", "shell.execute_reply": "2026-05-16T13:59:57.035952Z" }, "papermill": { "duration": 2.742896, "end_time": "2026-05-16T13:59:57.037762+00:00", "exception": false, "start_time": "2026-05-16T13:59:54.294866+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "from astropy import units as u\n", "from galpy.df import chen24spraydf, fardal15spraydf\n", "from galpy.potential import LogarithmicHaloPotential\n", "from galpy.orbit import Orbit\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "id": "b3", "metadata": { "papermill": { "duration": 0.004415, "end_time": "2026-05-16T13:59:57.047139+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.042724+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Setup\n", "\n", "We set up a potential and a progenitor orbit. The particle-spray classes\n", "only need the potential and the progenitor orbit (no action-angle machinery)." ] }, { "cell_type": "code", "execution_count": 2, "id": "b4", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:57.057429Z", "iopub.status.busy": "2026-05-16T13:59:57.057053Z", "iopub.status.idle": "2026-05-16T13:59:57.061010Z", "shell.execute_reply": "2026-05-16T13:59:57.060103Z" }, "papermill": { "duration": 0.010002, "end_time": "2026-05-16T13:59:57.061693+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.051691+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "lp = LogarithmicHaloPotential(normalize=1.0, q=0.9)\n", "prog = Orbit(\n", " [1.56148083, 0.35081535, -1.15481504, 0.88719443, -0.47713334, 0.12019596],\n", " ro=8.0,\n", " vo=220.0,\n", ")" ] }, { "cell_type": "markdown", "id": "b5", "metadata": { "papermill": { "duration": 0.004291, "end_time": "2026-05-16T13:59:57.070475+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.066184+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Initialize chen24spraydf\n", "\n", "We create a spray model for the leading tail. The key parameters are:\n", "\n", "- `progenitor_mass`: mass of the progenitor in solar masses\n", "- `progenitor`: the progenitor orbit\n", "- `pot`: the gravitational potential\n", "- `tdisrupt`: time since disruption began (in Gyr when using physical units)\n", "- `tail`: which tail to model (`'leading'`, `'trailing'`, or `'both'`)" ] }, { "cell_type": "code", "execution_count": 3, "id": "b6", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:57.080380Z", "iopub.status.busy": "2026-05-16T13:59:57.080211Z", "iopub.status.idle": "2026-05-16T13:59:57.087698Z", "shell.execute_reply": "2026-05-16T13:59:57.086561Z" }, "papermill": { "duration": 0.013403, "end_time": "2026-05-16T13:59:57.088352+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.074949+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "spdf_lead = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"leading\",\n", ")" ] }, { "cell_type": "markdown", "id": "b7", "metadata": { "papermill": { "duration": 0.007016, "end_time": "2026-05-16T13:59:57.100015+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.092999+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Sample stream particles\n", "\n", "The `sample` method generates stream particles by spraying `n` particles\n", "from the progenitor's Lagrange points and integrating them forward." ] }, { "cell_type": "code", "execution_count": 4, "id": "b8", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:57.110408Z", "iopub.status.busy": "2026-05-16T13:59:57.110178Z", "iopub.status.idle": "2026-05-16T13:59:57.574874Z", "shell.execute_reply": "2026-05-16T13:59:57.574072Z" }, "papermill": { "duration": 0.471567, "end_time": "2026-05-16T13:59:57.576229+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.104662+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "numpy.random.seed(1)\n", "lead_stream = spdf_lead.sample(n=500)" ] }, { "cell_type": "markdown", "id": "8296078c", "metadata": { "papermill": { "duration": 0.004464, "end_time": "2026-05-16T13:59:57.585713+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.581249+00:00", "status": "completed" }, "tags": [] }, "source": [ "Let's visualize the sampled stream particles:" ] }, { "cell_type": "code", "execution_count": 5, "id": "b9", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:57.596231Z", "iopub.status.busy": "2026-05-16T13:59:57.595964Z", "iopub.status.idle": "2026-05-16T13:59:57.986919Z", "shell.execute_reply": "2026-05-16T13:59:57.985906Z" }, "papermill": { "duration": 0.397229, "end_time": "2026-05-16T13:59:57.987651+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.590422+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(lead_stream.R(), lead_stream.z(), \"k.\", ms=1)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Leading arm (R, z)\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(lead_stream.R(), lead_stream.vR(), \"k.\", ms=1)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$v_R$\")\n", "plt.title(\"Leading arm (R, vR)\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "b10", "metadata": { "papermill": { "duration": 0.004827, "end_time": "2026-05-16T13:59:57.997507+00:00", "exception": false, "start_time": "2026-05-16T13:59:57.992680+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Leading and trailing arms with tail='both'\n", "\n", "Using `tail='both'` generates both arms in one call. This is more\n", "efficient than creating separate leading and trailing instances." ] }, { "cell_type": "code", "execution_count": 6, "id": "b11", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:58.008235Z", "iopub.status.busy": "2026-05-16T13:59:58.008006Z", "iopub.status.idle": "2026-05-16T13:59:58.924439Z", "shell.execute_reply": "2026-05-16T13:59:58.923640Z" }, "papermill": { "duration": 0.923384, "end_time": "2026-05-16T13:59:58.925743+00:00", "exception": false, "start_time": "2026-05-16T13:59:58.002359+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "numpy.random.seed(1)\n", "spdf_both = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "both_stream = spdf_both.sample(n=1000)" ] }, { "cell_type": "markdown", "id": "a8062c9f", "metadata": { "papermill": { "duration": 0.0046, "end_time": "2026-05-16T13:59:58.935750+00:00", "exception": false, "start_time": "2026-05-16T13:59:58.931150+00:00", "status": "completed" }, "tags": [] }, "source": [ "Plotting both arms in Cartesian coordinates:" ] }, { "cell_type": "code", "execution_count": 7, "id": "b12", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:58.946030Z", "iopub.status.busy": "2026-05-16T13:59:58.945855Z", "iopub.status.idle": "2026-05-16T13:59:59.061882Z", "shell.execute_reply": "2026-05-16T13:59:59.060888Z" }, "papermill": { "duration": 0.122108, "end_time": "2026-05-16T13:59:59.062566+00:00", "exception": false, "start_time": "2026-05-16T13:59:58.940458+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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kxGMvSO3u8Q4dOrjX/f6v08ZypPtdvny5OnfurFdeecVjm6ysrAY/1tlnn62zzz5bM2fO1NKlS5Wenq4XX3xR119/fYPv83hdcsklWrhwodavX69BgwYdddu8vDxVVFTon//8p8dfxfWdCXQ09T3HtWdoVFdXa9iwYce8j+joaF1xxRW64oorVFlZqcsuu0wzZ87U3XffXe9p0GvWrFFRUZFeeeUVnXfeee71O3bsOK7sx9KlSxfV1NTo22+/PeIv0tr38ZYtW9S5c2f3+srKSu3YscP9/R++3X/913953MeWLVs8fh6OpEOHDqqpqdH27ds99nps2bLluL6vY1m+fLkuuOACPfXUUx7r9+3bp7Zt27qXj/TzVbuHJi4uzqvXv3379rrpppt00003qbCwUHa7XTNnzqSA+BkOwcAvHTx4UCtXrlRERIT7EMvFF1+s6upqzZs3z2PbBx98UDabzeM/l+jo6HpPWTxR0dHR9e4yrv0r8PC/+jZu3Kj169cf92Ps3bu3zl/Stb+sTuQwTEPccccdio6O1vXXX689e/bU+fz27dv18MMPS6r/OSguLtbTTz99XI9Z32sXGhqqsWPH6uWXX653j8wvv/zi/rioqMjjcxEREerVq5dM0zzimJr6sldWVmr+/PnHlf1YLr30UoWEhGjGjBl1/vKvfexhw4YpIiJCjzzyiEeep556SsXFxe4zVPr376+kpCQtWLDA433x1ltvafPmzV6dyVL7M/PII494rG/s2X5DQ0PrvKeXLVtW53Th2nlJfv/69+vXT126dNEDDzzg/oPkcLWvf3V1dZ2fz6SkJBmG4fOfHRwbe0DgF9566y33nozCwkItXbpUW7du1V133eUei5CWlqYLLrhAf/nLX7Rz50717dtXK1eu1Ouvv65bbrnF4zh2v3799O6772ru3LkyDEOdOnXSwIEDTzhnv3799I9//EPTp0/XWWedpZiYGKWlpemSSy7RK6+8ojFjxmjkyJHasWOHFixYoF69etX7H+bRPPPMM5o/f77GjBmjLl26qKSkRLm5uYqLi9PFF198wt/D8ejSpYuWLl2qK664Qj179vSYCXXdunVatmyZe56O4cOHKyIiQmlpabrhhhtUWlqq3NxcJSUlaffu3V4/5pFeu9mzZ2v16tUaOHCgHA6HevXqpd9++035+fl699139dtvv7lztGvXTuecc46Sk5O1efNmzZs3TyNHjjzigNrBgwerVatWmjBhgm6++WbZbDY999xzjX5IpWvXrvrLX/6iv/71rzr33HN12WWXKTIyUp988okMw9CsWbOUmJiou+++W9nZ2brooos0atQobdmyRfPnz9dZZ53lHpcSHh6uOXPmaOLEiRoyZIjGjx/vPg23Y8eOuvXWW4+Z54wzztD48eM1f/58FRcXa/DgwVq1apVXc8Qcj0suuUQzZszQxIkTNXjwYH311VdasmSJxx4e6dD7LSEhQQsWLFBsbKyio6M1cOBAderUSU8++aRGjBih3r17a+LEiTrppJP0888/a/Xq1YqLi1NeXp5KSkp08skna9y4cerbt69iYmL07rvv6pNPPlFOTk6jfk9oBL4/8Qb4f/WdhtuiRQvzjDPOMB9//HGPU+5M0zRLSkrMW2+91TQMwwwPDze7detm3n///XW2++6778zzzjvPjIqKMiW5T+usPQ33l19+qTfH4acY1qe0tNS86qqrzISEBFOS+5Tcmpoa8+9//7vZoUMHMzIy0jzzzDPNN954w5wwYUKd03Z1jNMb8/PzzfHjx5unnHKKGRkZaSYlJZmXXHKJuWnTpmM+n0c6DXfZsmUe2+3YsaPe0x2P5N///rfpcDjMjh07mhEREWZsbKx5zjnnmI8++qjHKar//Oc/zT59+pgtWrQwO3bsaM6ZM8dctGhRvadvjhw5st7HOtJrZ5qmuWfPHnPq1KlmSkqKGR4ebrZr184cOnSouXDhQvc2TzzxhHneeeeZbdq0MSMjI80uXbqYt99+u1lcXOzepr7X+6OPPjLPPvtsMyoqyjQMw7zjjjvMFStWmJLM1atXezzH9Z3mW99rfSSLFi0yzzzzTDMyMtJs1aqVOWTIEPOdd97x2GbevHlmjx49zPDwcDM5Odm88cYbzb1799a5r3/84x/u+2rdurWZnp5u/vTTT3WyRUdH15vlwIED5s0332y2adPGjI6ONtPS0sxdu3Z5fRpufa/j79+H5eXlZkZGhtm+fXszKirKPOecc8z169fX2c40TfP11183e/XqZYaFhdV5j3722WfmZZdd5n5tO3ToYF5++eXmqlWrTNM8dDr07bffbvbt29eMjY01o6Ojzb59+5rz58+v93uHtWym6cejpgAAQFBiDAgAAPA5CggAAPA5CggAAPA5CggAAPA5CggAAPA5CggAAPA5JiKrR01NjZxOp2JjY5tsSm8AAIKRaZoqKSmRYRhHvf4QBaQeTqdTKSkpVscAACBg7dq1q84VmA9HAalH7XTNu3btck8DDgAAjs3lciklJeWIlz6oRQGpR+1hl7i4OAoIAAANcKwhDAxCBQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAQAAPkcBAbzkdDqVnZ0tp9NpdRQACHgUEMBLubm5ysvLU25urtVRACDghVkdAAgUDofD418AQMPZTNM0rQ7hb1wul+Lj41VcXKy4uDir4wAAEDC8/R3KIRigETA+BACODwUEaASMDwGA48MYEKARMD4EAI4PY0DqwRgQAAAahjEgAADAb1FAAACAz1FAAACAz1FAAACAz1FAAACAz1FAAB9j0jIAoIAAPsekZQDARGSAzzFpGQAwEVm9mIgMAICGYSIyAADgtygggB9gYCqA5oYCAvgBBqYCaG4YhAr4AQamAmhuGIRaDwahAgDQMAxCBQIc40IABDMKCOCnGBcCIJgxBgTwU4wLARDMGANSD8aAAADQMIwBAQAAfosCAgQBBqwCCDSMAQECmNPpVG5urlwul9auXStJysrKsjgVABwbe0CAAPL7PR21Z8rYbDalpaUxYBVAwGAPCBBAaguHdGhPx+FnyhiGYWU0ADguFBAggPz+1FzDMDjkAiAgcQgGCCC1heP3ezsYhAog0FBAgCDArKkAAg2HYIAgwKypAAINe0CAIPD7QzMckgHg7yggQBDikAwAf0cBAYKQw+FQWlqa0tLS2BMCwC9RQIAgVHtIJi8vTy+//LLS09MpIQD8CgUECGIOh0Nt2rRRUVERh2MA+BUKCBDEDMPQkiVLNHbsWM6QAeBXKCBAkDt8ttQpU6Zo8ODBys/PtzgVgOaOAgI0E7m5uVqyZIk++eQTZWRkWB0HQDPHRGRAM5GWlua+kF1OTo7FaQA0d+wBAZqJ2vKRlpYmu91ucRoAzR17QIBmor7p2p1Op3Jzc+VwOOpc4A4AmhIFBGgmDh+MWisnJ0cvvPCCXC4Xh2UA+BSHYIBmrLCwUEVFRSosLLQ6CoBmhgICNGPbt29XTU2Ntm/fbnUUAM1MwBWQ999/X2lpaTIMQzabTa+99prH503TVGZmptq3b6+oqCgNGzZMW7dutSYs4OfmzZunP/zhD8rKyuKaMQB8KuAKSFlZmfr27avHHnus3s/fd999euSRR7RgwQJt3LhR0dHRSk1NVXl5uY+TAv7Pbrdr9erV2rBhQ52r5zqdTkoJgCYTcINQR4wYoREjRtT7OdM09dBDD+l///d/NXr0aEnSs88+q+TkZL322mu68sorfRkVCBiHnyFTe2ZMSUmJ1qxZI0l1Bq8CwIkKuD0gR7Njxw4VFBRo2LBh7nXx8fEaOHCg1q9ff8Svq6iokMvl8rgBzUntGTKGYSg3N1d5eXkqLS1VbGys0tLSrI4HIAgFVQEpKCiQJCUnJ3usT05Odn+uPrNmzVJ8fLz7lpKS0qQ5AX/mcDjUv39/vfnmmyooKHBPYAYAjSmoCkhD3X333SouLnbfdu3aZXUkwDKGYWjLli0qKipSeXk5V9EF0CSCqoC0a9dOkrRnzx6P9Xv27HF/rj6RkZGKi4vzuAHNWU5OjgYOHKiXX35ZkhiMCqDRBVUB6dSpk9q1a6dVq1a517lcLm3cuFGDBg2yMBkQWGrPjrHb7e4xIYefIQMAJyrgzoIpLS3Vtm3b3Ms7duzQ559/rtatW+uUU07RLbfcor/97W/q1q2bOnXqpHvuuUeGYejSSy+1LjQQwOq7hgwAnCibaZqm1SGOx5o1a3TBBRfUWT9hwgQtXrxYpmkqKytLCxcu1L59+/SHP/xB8+fP16mnnur1Y7hcLsXHx6u4uJjDMcDvcAE7AEfj7e/QgCsgvkABAY4sOztbeXl5SktLY34QAHV4+zs0qMaAAGh6Z599toqKinT22WdbHQVAAKOAADgus2fPVmFhobKzs5Wdna38/HzOkgFw3CggAI5LTk6OBgwYoD59+ujll1/W2LFj9fLLL3OWDIDjEnBnwQCwVu0puk6nU+np6Tpw4IBKSkqYsh3AcWEPCIAGMQxDS5Ys0cknn6zY2FimbAdwXCggABqstoSMHTuWeUIAHBcKCIATUnslXYkp2wF4jwICoFEwZTuA48EgVACNwuFwyOVyqaSkRE6nk1lSARwVe0AANArDMBQXF6c1a9awFwTAMbEHBECj4cJ1ALzFtWDqwbVgAABoGK4FA8BSTqeTs2IAHBEFBECT4KwYAEfDGBAATeLw8SBOp1O5ublyOBycHQNAEmNA6sUYEKBxZWdn6+WXX1abNm20ZMkSSggQxBgDAsBvOBwOtWnTRkVFRRySASCJAgLAB2qvGTN8+HC5XC4GpgKggADwDcMwFBsbq7Vr17IXBACDUAH4zu8nKmNwKtB8UUAA+EztlXNr5wgpKSnRmjVrJMl9RV0AzQOHYAD4XO0cIaZpKi0tjanbgWaIPSAAfO73h2I4DAM0PxQQAD5XeyhGkm677TYtXbpUJSUleuCBByxOBsBXOAQDwFK1cyGapsn1Y4BmhD0gACyVkZEhSbLZbLrjjjv0+uuvy+l06oknnrA4GYCmRAEBYCnDMBQXF6e8vDw5nU7t379fn376qdWxADQxDsEAsJzD4VBaWpoGDRqk0NBQlZWV6bbbbuNQDBDEKCAALFc7KLVjx44KDw/Xtm3b9Nhjj2ngwIHKz8+3Oh6AJkABAeA3MjIy1LdvX0VERKiyslK7d+92jxEBEFwoIAD8hmEYWr58ua655hqdeuqpatWqlX766Sf179+fPSFAkKGAAPArhmGoffv2Ki4ulsvl0vbt2/XZZ5+xJwQIMpwFA8DvOBwOuVwuFRYWatOmTfrtt9/UunVrZWRkKCMjgxlTgSDAHhAAfscwDOXk5Oi5557TlVdeqdDQUK1cuVIvvPCCcnNzrY4HoBGwBwSAX3M4HCopKVFpaamio6O5cB0QJGxm7TzIcHO5XIqPj1dxcbHi4uKsjgMAQMDw9ncoh2AABByuGQMEPgoIgIDhdDp1zTXXqGfPnnruuecYDwIEMMaAAAgYubm5evHFF1VVVaXy8nKlpaVZHQlAA7EHBEDAcDgcSkhIkCTV1NRoyZIl1gYC0GAUEAABwzAMXXbZZQoPD1dERITKysoYCwIEKA7BAAgoWVlZiomJUWFhof75z3+qsrJSJSUleuCBB6yOBuA4sAcEQECpnaTsp59+UmFhofbt26eCggL2hAABhnlA6sE8IID/y8/P1+jRo1VSUqLKykodPHhQXbt21cUXX8x07YCFmAcEQFCz2+16/fXXZbPZdODAAVVVVem7777T888/z+m5QACggAAIWHl5eWrfvr3Cw8MlSSEhISovL9fZZ59tcTIAx0IBARCwHA6HrrjiCuXl5alfv36KiopSaWmpJk6cqIyMDMaEAH6MAgIgYBmGoaysLKWmpur8889XTU2NTNPUvn37uHIu4OcoIACCQu14epvNJtM0VVxcrG7dulmcCsCRUEAABIWMjAz16tVLklReXq79+/frhhtu4DAM4KcoIACCgmEYGjJkiFq1aqXQ0FBJUmlpqS666CJKCOCHKCAAgkZGRob++7//W6NGjXKv+/rrrzV37lwLUwGoDwUEQNCoHZTauXNnhYUdutJESEiI1q1bx14QwM9QQAAEnenTp2vSpEk6/fTTlZSUpF9++UXp6emUEMCPUEAABB3DMLRgwQJdeOGFqqysVGFhoQoKCjgtF/AjFBAAQat2mvb9+/dr79692rp1q2677Tb2hAB+gAICIGhNnz5d8fHxqqqqUmFhoV566SU999xz7AkB/AAFBEDQMgxDo0aNUnh4uEJCQlRTU6P9+/dzrRjAD4RZHQAAmlJmZqaio6O1du1affHFFyorK9Ptt9+uDRs2yOFwyDAMqyMCzZLNrJ2/GG4ul0vx8fEqLi5WXFyc1XEANAKn0ym73a49e/aobdu2Cg8P1/jx45WTk2N1NCCoePs7lEMwAJoFwzB04YUXKiIiQgkJCSopKVFZWZnVsYBmiwICoNlITk5WmzZtFB8fr/DwcC1ZskRXX301Z8UAFmAMCIBmY/r06YqNjVVaWpqGDh2q0tJSvfjii0pOTuZQDOBj7AEB0GzUTtVut9v14osvKjo6WqZp6p133mEvCOBjFBAAzVJqaqpSUlJUU1Ojf//738wNAvgYBQRAs+R0OvXjjz9KkkzT1BNPPKFrrrmGPSGAj1BAADRLubm5qqmpkXSogOzevVsvvfQSe0IAH2EQKoBmyeFwaPfu3Vq7dq0KCgpUXl6uTp06KS0tzepoQLPAHhAAzVLtFXPLy8u1b98+VVZWateuXVq6dKnV0YBmgQICoFlbsGCBTj75ZJ1yyimqqKhQQUGB1ZGAZoECAqBZS01N1a5du9S+fXtVV1dr+fLlWrFihdWxgKBHAQEASfPmzVN4eLgqKio0cuRILV26VNnZ2ZwVAzQRCggASLLb7Ro3bpwkqbq6WldffbUefvhhZkgFmggFBAD+47777lPXrl0lHTo1d+/evVywDmgiFBAA+A/DMJSYmCibzeZe98svv1iYCAheFBAAOMy8efN00kknuUtIXl6e8vPzLU4FBB8KCAAcxm63a+PGjUpISJAkHTx4UNOmTbM2FBCEKCAA8DuGYahz587u5c2bN6t///7sCQEaEQUEAOqxcOFCxcTESJL27dun/Px89oQAjYgCAgD1sNvtSk9PV1RUlMLCwhQSEqK9e/cqIyODuUGARhB0BeTee++VzWbzuPXo0cPqWAACUGZmpgYOHKioqChVV1drx44deuGFF7hiLtAIgvJquL1799a7777rXg4LC8pvE0ATMwxDS5YsUc+ePSVJFRUVioyM5Iq5QCMIyt/MYWFhateundfbV1RUqKKiwr3scrmaIhaAAGQYhl566SWNGDFCpmlq586devDBB9W1a1c5HA4ZhmF1RCAgBd0hGEnaunWrexR7enq6fvzxx6NuP2vWLMXHx7tvKSkpPkoKIBCkpqbq0Ucfdc8NsmzZMj3//PNKT09nPAjQQDbTNE2rQzSmt956S6Wlperevbt2796t7Oxs/fzzz/r6668VGxtb79fUtwckJSVFxcXFiouL81V0AH5uxYoVGjVqlCorKxUaGqqOHTvqmmuuUVZWltXRAL/hcrkUHx9/zN+hQXcIZsSIEe6P+/Tpo4EDB6pDhw566aWXNGnSpHq/JjIyUpGRkb6KCCBAbdiwwf1xdXW1ioqKGA8CNFBQHoI5XEJCgk499VRt27bN6igAApzD4VCbNm0kSTabTaZpaunSpRanAgJT0BeQ0tJSbd++Xe3bt7c6CoAAZxiG3njjDSUkJMg0TblcLhUUFFgdCwhIQVdAbrvtNq1du1Y7d+7UunXrNGbMGIWGhmr8+PFWRwMQBOx2u1588UWFhobKNE0tW7ZMU6ZMYTAqcJyCroD89NNPGj9+vLp3767LL79cbdq00YYNG5SYmGh1NABBYsOGDaqurpYkVVZW6sknn9TAgQO5VgxwHILuLJjG4O0IXgDNk9Pp1ODBg/XDDz+414WEhOi8887T6tWrLUwGWM/b36FBtwcEAJqaYRgaN26cxyzL4eHhuuuuuyxMBQQWCggANMD06dN13XXXqVOnTpIOnZZ72WWX6eqrr2Y8COAFCggANIBhGHriiSdUexS7qqpK+/fv10svvcTF6gAvUEAA4AQsWLDA41BMTEwMk5MBXqCAAMAJSE1NVd++fd3LxcXFWrhwoYWJgMBAAQGAE7Rw4UL17NlTklRTU6Ply5czDgQ4BgoIAJwgu92u5ORk93JRUZFmzJhhYSLA/1FAAKAR5OTkqGXLlu7lF154gYnJgKOggABAI7Db7frggw90+umnKyIiQgcOHNDQoUMpIcARUEAAoJHY7XYNHjxYoaGhqq6uVnFxsUaPHs14EKAeFBAAaETr1q3TgQMHVFNTI9M09fPPP+vOO++0OhbgdyggANCIIiIiZLPZZLPZJEmmaWrlypUWpwL8DwUEABrRwoULNWTIEHcBqcVhGMATBQQAGpHdbtfq1avd14iRDl0dNDs728JUgP+hgABAE3jppZeUkJAgSSovL9crr7zCXhDgMBQQAGgCdrtdq1atUnh4uKRDk5PNnTvX4lSA/6CAAEATsdvt7gvThYeHa926dewFAf6DAgIATSgxMVHR0dFKSEjQ1q1bNW7cOEoIIAoIADSp6OhoxcXFKSUlRWVlZdq0aRMDUgFJYVYHAIBglpGRobi4OHXr1k3XXHONampq9MYbb1gdC7Ace0AAoAkZhqGsrCzl5uaqpqZG0qE5QaZMmcKhGDRrFBAA8IGcnBzFxsa6l3NzczVq1ChKCJotCggA+IDdbtd3332npKQkSVJNTY2++eYbpaenU0LQLFFAAMBHDMPQmDFj3NO0V1ZWateuXcrNzbU4GeB7FBAA8KHJkye7C0hNTY327dsnh8NhcSrA9yggAOBDeXl5Cg0NdS//9ttvysnJ4TAMmh0KCAD4kMPhUEREhHvZNE09//zzHIZBs0MBAQAfqh0HcrjQ0FD3lO1Ac0EBAQAfmzNnjgYNGqTIyEhJUmFhoSZPnsxhGDQrFBAA8DHDMLR8+XIlJiZKkqqrq/XZZ58xRTuaFQoIAFjAMAy9/vrratOmjaRDZ8S89957FqcCfIcCAgAWsdvtOvXUU93LBQUFFqYBfIsCAgAWmjdvnnr06KGYmBg98cQTVscBfIYCAgAWstvt2rx5s9auXat58+ZxkTo0G2FWBwAAHJoh9dNPP9WmTZsUExOjBx54wOpIQJNiDwgA+JGDBw9q/vz5WrFihdVRgCZFAQEAP7Bw4UKFh4dLkg4cOKD09HSLEwFNiwICAH7AbrcrLi7OvVxUVKT8/HwLEwFNiwICAH5ixIgRHssTJ060KAnQ9CggAOAn5syZo5CQ//9vecuWLZwRg6BFAQEAP2EYhh555BH3cnV1NVfJRdCigACAH5k6darefvtttW3bVqGhoVq8eLH69+/PeBAEHQoIAPiZ1NRUtWjRQhUVFdq5c6c+/fRTTZ482epYQKOigACAHxowYIDVEYAmRQEBAD+UmJjoscwZMQg2FBAA8EOmaXosMzU7gg0FBAD8UGxsrMdyQUGBli5dalEaoPFRQADAD02fPl1XX321IiIiJEnl5eWaOnWqxamAxkMBAQA/ZBiGnnvuOV1++eXuycnsdjsTkyFoUEAAwI9FR0e7P167dq26deumPn36MC8IAh4FBAD8WHR0tGpqaiQdmhl1//79+vrrr5WRkWFxMuDEUEAAwI9lZGSoZ8+eHutat26tu+66y6JEQOMIszoAAODIDMPQiBEjFO10apzLpVNMU86SEj2XmanTTz9dhmFYHRFoEAoIAPi5/z35ZMW7XKoxTdkkmZWVsn38sfJuukmXvvaa1fGABuEQDAD4s61b1eq22xRimgqTFKpDfzmGSBqdlydt22ZtPqCBKCAA4M8WLZJps9VZbZNks9mkp57yfSagEVBAAMCf7dwp8z9nwdRhmtLOnT6NAzSW4yogu3btaqocAID6dOwoW8gR/qu22aSOHX0aB2gsx1VAevTooczMTO3fv7+p8gAADnfddbKZpszfrTalQ3tAJk2yIBRw4o6rgLzzzjtasWKFunXrpsWLFzdRJACAW7du0lNPqUbSQUlV/7nVSIfGf3TtamU6oMFs5u+v+eyFZ599Vn/5y1+UlJSkhx56SOeee25TZLOMy+VSfHy8iouLFRcXZ3UcANAfzzxT9s8/V0dJOyUtiYzU1+Xl1oYC6uHt79AGDUL905/+pC1btmjkyJEaMWKExo0bpx07djQ4LADg6K6fPVuZYWG6StKfJTlbtuTCdAhoJ3QWzPDhw3X99dfr1VdfVa9evXTHHXeotLS0sbIBAP5jw4YNioiIcC+XlpZqxowZFiYCTsxxFZAFCxZo0qRJ6tOnj+Lj4zV06FB98MEHmjJlih5++GFt2rRJvXr10qZNm5oqLwA0Sw6HQ5dddpnat2+vVq1a6eDBg/rnP//JXhAErOMqIDNnzlRxcbH+9Kc/afXq1dq3b58+/fRTPfbYY5o8ebLee+89TZkyRddee20TxQWA5skwDHXt2lWGYSglJUUhISHat2+f5s6da3U0oEGO61ow3swDMmnSJN1zzz0NDgQAqJ/D4ZAkbdu2Td9++62qqqpUUlJicSqgYRp9JtSkpCS99957jX23ANDsGYahrKwsSVJ1dbUOHjyoZcuWKT8/3+JkwPFr9AJis9k0ZMiQxr5bAMB/bN68WbUzKOzdu1eTJ0+2OBFw/LgWDAAEmP79+3ucEbN161YGoyLgUEAAIMBkZmbKMAz3ssvlYjAqAg4FBAACjGEYmjlzpsc6JoNEoKGAAEAAys3N9VheuXIlh2EQUCggABCAcnJyFB4e7l6uqKhQdna2srOzKSIICMc1DwgAwD/Y7Xbl5eVp5MiR7lNylyxZoqioKJWUlOiBBx6wOiJwVOwBAYAAlZqaqtGjR8tms0mSysrKtHfvXjXgIueAz1FAACCAderUSaGhoe5l0zSVkZFhYSLAOxQQAAhg06dPV9++fRUScui/886dO1ucCPAOBQQAAphhGFq4cKEGDhyofv36KSoqqs4ZMoA/ooAAQIDLy8tTaWmpJCkmJkZpaWkWJwKOLWgLyGOPPaaOHTuqRYsWGjhwoD7++GOrIwFAk0hLS1NJSYn+/e9/6+OPP9aDDz5odSTgmIKygPzjH//Q9OnTlZWVpfz8fPXt21epqakqLCy0OhoANLq8vDxFRUWptLRU1dXVevnll5kLBH4vKAvI3Llz5XA4NHHiRPXq1UsLFixQy5YttWjRIqujAUCjczgcSk5Odg9EPXDggEaNGkUJgV8LugJSWVmpTz/9VMOGDXOvCwkJ0bBhw7R+/fp6v6aiokIul8vjBgCBwjAMLVmyROPHj3fPjvrFF19o3LhxlBD4raArIL/++quqq6uVnJzssT45OVkFBQX1fs2sWbMUHx/vvqWkpPgiKgA0GsMw9Nxzz+m6665TWFiYqqqq9O2333JGDPxW0BWQhrj77rtVXFzsvu3atcvqSADQIJmZmWrRooUkqbq6Wg6Hw+JEQP2CroC0bdtWoaGh2rNnj8f6PXv2qF27dvV+TWRkpOLi4jxuABCIDMPQpZdeqoiICJ111lk655xztGLFCqtjAXUEXQGJiIhQv379tGrVKve6mpoarVq1SoMGDbIwGQD4xpw5c/TnP/9ZW7du1Q8//KApU6ZYHQmoIyivhjt9+nRNmDBB/fv314ABA/TQQw+prKxMEydOtDoaADS5goIC5eXlqbq6WiEhIbr++uutjgTUYTOD9LKJ8+bN0/3336+CggKdccYZeuSRRzRw4ECvvtblcik+Pl7FxcUcjgEQUJxOpwYOHKiffvrJvS4pKanOYWmgqXj7OzToDsHUmjZtmn744QdVVFRo48aNXpcPAAhkubm5Ki8v91j322+/KT8/36JEQP2C8hAMADRXDodDJSUl2rNnj5YvX67y8nJVVVVp2rRpWrdundXxADcKCAAEEcMw9MADD8jpdMo0TS1btkwHDx5UQkKC1dEAD0F7CAYAmrPc3Fy98847OnjwoEzT1AcffMCsqPArFBAACEK114epVV1drblz51qYCPBEAQGAIGQYhmJiYhQaGqoWLVqooqJCb775JntB4DcoIAAQpObNm6ezzjpLNptNNTU12rZtG9eGgd+ggABAkLLb7UpNTVVIyKH/6k866SSuDQO/QQEBgCDmcDhUVVUlSfrhhx+0Zs0aawMB/0EBAYAgZhiGampq3Mvp6elMSga/QAEBgCB36623eixPmzbNoiTA/6OAAECQ++CDDzyW+/TpY1ES4P9RQAAgyP2+cGRmZlqUBPh/FBAACHKZmZnq2LGjJCksLEzdunXT0qVLrQ2FZo8CAgBBzjAMffTRR0pISFBVVZX279+vG264wepYaOYoIADQDBiGoccee0w2m03SoanZmRUVVqKAAEAz8f7778s0TUnSgQMHdOedd1qcCM0ZBQQAmokvv/zSY/mNN96wKAlAAQGAZmPevHmKiYlxLxcXF3MYBpahgABAM2G325Wenu6+Nkx4eLhycnIsToXmigICAM3ImDFj1KJFC0nSwYMHVVhYaHEiNFcUEABoRmbPnq0DBw5IkkzTrDMuBPAVCggANCM5OTkKCwtzL+/fv9/CNGjOKCAA0IzY7XZdccUV7mWXy2VhGjRnFBAAaGZuvfVWJSQkSJIqKyuVn59vbSA0SxQQAGhm8vLyVFZWJknat2+fRo8ezem48DkKCAA0Mw6HQ1dccYX7bJiCggLNmDHD4lRobiggANDMGIah5557Tt26dZMkVVVVae3atRanQnNDAQGAZqr2wnSStGPHDg7DwKcoIADQTJ1++unujysrK5Wbm2thGjQ3FBAAaKbatWun8PBwSVJERITOPvtsixOhOaGAAEAzNX36dLVq1UqSVFFRoezsbIsToTmhgABAM2UYhlJSUtzLtXODAL5AAQGAZmzmzJkKDQ2VJH311VcWp0FzQgEBgGZsw4YN6tSpk2JiYtS6dWtmRYXPUEAAoBlzOBzq06ePDhw4oK+//lrTpk2zOhKaibBjbwIACFaGYejdd99VdXW1JLlnRwWaGntAAKCZO+ecc9wfb9iwwcIkaE4oIADQzJ1yyinuj7k6LnyFAgIAzVx0dLT74+rqak2ePNnCNGguKCAA0MxlZGQoOTnZvbxz506uC4MmRwEBgGbOMAw988wz7mnZy8rKuC4MmhwFBACgDRs2KCYmRiEhIQoJCeG6MGhyFBAAgBwOh1JSUlRTU6MDBw5wXRg0OQoIAECGYSg6Olo2m002m019+vSxOhKCHAUEACBJysrKUuvWrRUVFaXzzjvP6jgIchQQAICkQ+NAXC6XysrKdOedd1odB0GOAgIAkHRoHEjtpGS//vqrVqxYYXEiBDMKCABA0qFxIC1btpQklZeXa+LEiRYnQjCjgAAA3CIiItwfHzx4kAnJ0GQoIAAAt5kzZyomJkahoaGSxIRkaDJhVgcAAPiPDRs2qFOnToqJidHgwYPlcDisjoQgxR4QAICbw+FQ3759tX37dq1cuVIFBQVWR0KQooAAANwMw9CHH36owsJCffXVV7r22mutjoQgRQEBAHhYsGCBbDabJGnXrl0Wp0GwooAAADykpqaqRYsWkqSKigqL0yBYUUAAAB7y8/Pdp+NyVVw0FQoIAMDDtGnTVFxcLElat26dpkyZwnwgaHQUEACAh8OvhFtRUaFFixZp7ty5FiZCMKKAAAA8ZGZmqlWrVu7lsLAwmaZpYSIEIwoIAMCDYRjq3Lmze/mkk05SRkaGhYkQjCggAIA6Fi5c6J6OnVNx0RQoIACAOux2ux5++GGFhYWpbdu2XBMGjY4CAgCo1/fff6/Y2FiVlJRwOi4aHQUEAFCvwsJC7d27Vy6XS3fccYfVcRBkKCAAgHpt3rzZ/TEXpUNjo4AAAOrVr18/98ddu3a1MAmCEQUEAFCvG264wX1Rus8++8ziNAg2FBAAQL2WLl3q/vjgwYPKz8+3MA2CDQUEAFAv0zQVGRkpSaqqqtLEiRMtToRgQgEBANQrIyNDN910k/vKuD/88IPFiRBMKCAAgHoZhqGcnBz3jKiVlZUWJ0IwoYAAAI6qQ4cOkqSWLVvK6XRanAbBggICADii/Px82Ww2hYWFqbS0VDNmzLA6EoJEmNUBAAD+KyMjQ999951M01RVVZXWr19vdSQECfaAAACOKCcnR61bt3YvMw4EjYUCAgA4Irvdro4dO7qXa8+IAU4UBQQAcFQ9e/Z0f9ylSxcLkyCYUEAAAEeVlJSk8PBw2Ww2LkqHRsMgVADAUWVkZKi0tFRfffWV5s2bZ3UcBAn2gAAAjsowDGVlZWnQoEFaunQpc4GgUQRdAenYsaNsNpvHbfbs2VbHAoCAlp2drXnz5umZZ55Rbm6u1XEQBILyEMyMGTPkcDjcy7GxsRamAYDA9+mnn+rgwYMKDw/3+P8VaKigLCCxsbFq166d19tXVFSooqLCvexyuZoiFgAErP79++vbb79VSUmJvvrqKxmGYXUkBLigOwQjSbNnz1abNm105pln6v7771dVVdVRt581a5bi4+Pdt5SUFB8lBYDAMHnyZJmmqdLSUk2ZMsXqOAgCQbcH5Oabb5bdblfr1q21bt063X333dq9e7fmzp17xK+5++67NX36dPeyy+WihADAYfLy8tSuXTsVFBRo5syZVsdBELCZpmlaHeJY7rrrLs2ZM+eo22zevFk9evSos37RokW64YYbVFpaqsjISK8ez+VyKT4+XsXFxYqLi2tQZgAIJk6nU+np6SooKFC7du20ZMkSDsOgXt7+Dg2IAvLLL7+oqKjoqNt07ty53imCv/nmG5122mn67rvv1L17d68ejwICAHXVlpCioiKNHTtWWVlZVkeCH/L2d2hAHIJJTExUYmJig772888/V0hIiJKSkho5FQA0H06nU7m5ucrJyVFeXh5nwuCEBUQB8db69eu1ceNGXXDBBYqNjdX69et166236uqrr1arVq2sjgcAASsnJ0fPP/+8VqxYoeXLl3P4BScsqM6CiYyM1IsvvqghQ4aod+/emjlzpm699VYtXLjQ6mgAENDKysq0d+9eff7550cd1A94K6j2gNjtdm3YsMHqGAAQdGJiYhQREaGamhqtW7dOTqeTvSA4IUG1BwQA0DSmT5+uKVOmqFevXtq+fTt7QXDCKCAAgGMyDEPTp093n20YACdQws9RQAAAXsnJydH27dvVpUsXZWRkWB0HAY4CAgDwSllZmcrKylRZWWl1FAQBCggAwCvR0dGy2Wz6/vvvdc455yg/P9/qSAhgFBAAgFcyMjJ06aWXav/+/dq9ezeHYXBCKCAAAK8YhqEvvvhCFRUVCgsLU05OjtWREMAoIAAAr/3666+SpLi4ONntdovTIJBRQAAAXnE6nerRo4dCQ0M1depUq+MgwFFAAABeyc3N1UcffaTq6mo9+eSTVsdBgKOAAAC84nA4dMkllyguLk4zZ860Og4CHAUEAOAVwzDUsWNHRUdH69NPP7U6DgIcBQQA4DWbzebxL9BQFBAAgNcuvPBCRUZG6sILL7Q6CgIcBQQA4LXZs2ersLBQs2fPtjoKAhwFBADgtZycHPXs2VMlJSVMxY4TQgEBAHjNbrcrIiJCX375paZNm2Z1HAQwCggAwGtOp1OVlZUKDw9Xnz59rI6DAEYBAQB4LTc3V8XFxYqIiNCYMWOsjoMARgEBAHjN4XCoqqpK5eXlDETFCaGAAACOyx/+8Ae1bdtWd911l9VREMAoIAAAr+Xm5mrVqlWqrq7Whg0brI6DAEYBAQB4LS0tTYZhyDAMpaWlWR0HAYwCAgDwWl5ennbu3KmvvvpKCxcutDoOAhgFBADgNYfDoaioKNXU1OjLL7+0Og4CGAUEAOA1wzD0+uuv66yzzlKfPn3kdDqtjoQARQEBAHjN6XQqLy9PgwcP1qZNm5Sbm2t1JAQoCggAwGu5ubnKy8uTaZpKS0uTw+GwOhICVJjVAQAAgSMtLU1r1qxRenq67Ha71XEQwNgDAgDwWl5enoqKipSRkcH4D5wQCggAwGsOh0MxMTH69ttvNXfuXKvjIIBRQAAAx6WyslJlZWUqKSmxOgoCGAUEAOC1nJwcfffddzJNU7GxsVbHQQBjECoAwGs2m03R0dHq0qWLpk+fbnUcBDD2gAAAvHbhhReqZcuWysrKkmEYVsdBAKOAAAC8Nnv2bBUWFmr27NlWR0GAo4AAALzmcDgUERHBBGQ4YRQQAIDXcnNzVVlZyRTsOGEUEACA13JyctS3b191796dichwQiggAACv2e12paamciE6nDAKCADAa06nUyUlJRoyZAjjQHBCmAcEAOC13NxcrVy5Um3atLE6CgIce0AAAF5zOBxq06aNioqKOASDE0IBAQB4raCgQBUVFRo0aBCHYHBCKCAAAK9lZGToiy++0FdffaXc3FzOhEGDMQYEAOAVp9Op7t27q6KiQn369FFeXp4kKSsry+JkCETsAQEAeCU3N1ebNm1SamqqMjMzlZaWxmEYNBgFBADglbS0NMXGxiotLU2GYXBBOpwQCggAwCt5eXkqKSlRXl6enE6nsrOzGQOCBmMMCADAK7WHWxwOh3JzcxkDghNCAQEAeKX2sIvkWUaAhuAQDADAa7WHXiQxBgQnhD0gAACvOJ1Opaenq6ioSBKHXnBi2AMCAPDK3Llz9e233yomJoZDLzhhFBAAgFdM01RoaKgGDRrEoRecMA7BAAC8kpGRIZvNJtM05XQ6KSE4IewBAQB4xTAMxcbGau3atVwJFyeMAgIA8Nrhs6ECJ4ICAgDw2uGzoQIngjEgAACvMQEZGovNNE3T6hD+xuVyKT4+XsXFxYqLi7M6DgAAAcPb36EcggEAAD5HAQEAAD5HAQEAAD5HAQEAAD5HAQEAAD5HAQEAeM3pdCo7O1tOp9PqKAhwFBAAgNdyc3OVl5fHVOw4YUxEBgDwGhORobEwEVk9mIgMAICGYSIyAECjYvwHGhMFBADgFcZ/oDExBgQA4BXGf6AxMQakHowBAQCgYRgDAgAA/BYFBAAA+BwFBAAA+BwFBAAA+BwFBAAA+FxAFZCZM2dq8ODBatmypRISEurd5scff9TIkSPVsmVLJSUl6fbbb1dVVZVvgwJAkGDyMTSVgCoglZWV+uMf/6gbb7yx3s9XV1dr5MiRqqys1Lp16/TMM89o8eLFyszM9HFSAAgOTD6GphKQ84AsXrxYt9xyi/bt2+ex/q233tIll1wip9Op5ORkSdKCBQt055136pdfflFERIRX9888IABwiNPpVG5urhwOhwzDsDoOAkCznAdk/fr1Ov30093lQ5JSU1Plcrn0zTffHPHrKioq5HK5PG4AAMkwDGVlZVE+0OiCqoAUFBR4lA9J7uWCgoIjft2sWbMUHx/vvqWkpDRpTgAAmjvLC8hdd90lm8121Nt3333XpBnuvvtuFRcXu2+7du1q0scDAKC5s/xidBkZGbr22muPuk3nzp29uq927drp448/9li3Z88e9+eOJDIyUpGRkV49BgAAOHGWF5DExEQlJiY2yn0NGjRIM2fOVGFhoZKSkiRJ77zzjuLi4tSrV69GeQwAAHDiLC8gx+PHH3/Ub7/9ph9//FHV1dX6/PPPJUldu3ZVTEyMhg8frl69eumaa67Rfffdp4KCAv3v//6vpk6dyh4OAAD8iOVjQI5HZmamzjzzTGVlZam0tFRnnnmmzjzzTG3atEmSFBoaqjfeeEOhoaEaNGiQrr76av3pT3/SjBkzLE4OAIGJicjQVAJyHpCmxjwgAHBIdna28vLylJaWpqysLKvjIAB4+zs0oA7BAAB8y+FwePwLNBb2gNSDPSAAADRMs5wJFQAABAYKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8DkKCAAA8LkwqwP4I9M0JUkul8viJAAABJba3521v0uPhAJSj5KSEklSSkqKxUkAAAhMJSUlio+PP+LnbeaxKkozVFNTI6fTqdjYWNlsNqvj+BWXy6WUlBTt2rVLcXFxVscJWjzPvsNz7Rs8z77hD8+zaZoqKSmRYRgKCTnySA/2gNQjJCREJ598stUx/FpcXBz/ifgAz7Pv8Fz7Bs+zb1j9PB9tz0ctBqECAACfo4AAAACfo4DguERGRiorK0uRkZFWRwlqPM++w3PtGzzPvhFIzzODUAEAgM+xBwQAAPgcBQQAAPgcBQQAAPgcBQQAAPgcBQRee+yxx9SxY0e1aNFCAwcO1Mcff2x1pKBz7733ymazedx69OhhdayA9/777ystLU2GYchms+m1117z+LxpmsrMzFT79u0VFRWlYcOGaevWrdaEDXDHeq6vvfbaOu/xiy66yJqwAWzWrFk666yzFBsbq6SkJF166aXasmWLxzbl5eWaOnWq2rRpo5iYGI0dO1Z79uyxKHFdFBB45R//+IemT5+urKws5efnq2/fvkpNTVVhYaHV0YJO7969tXv3bvftww8/tDpSwCsrK1Pfvn312GOP1fv5++67T4888ogWLFigjRs3Kjo6WqmpqSovL/dx0sB3rOdaki666CKP9/gLL7zgw4TBYe3atZo6dao2bNigd955RwcPHtTw4cNVVlbm3ubWW29VXl6eli1bprVr18rpdOqyyy6zMPXvmIAXBgwYYE6dOtW9XF1dbRqGYc6aNcvCVMEnKyvL7Nu3r9Uxgpok89VXX3Uv19TUmO3atTPvv/9+97p9+/aZkZGR5gsvvGBBwuDx++faNE1zwoQJ5ujRoy3JE8wKCwtNSebatWtN0zz0Hg4PDzeXLVvm3mbz5s2mJHP9+vVWxfTAHhAcU2VlpT799FMNGzbMvS4kJETDhg3T+vXrLUwWnLZu3SrDMNS5c2elp6frxx9/tDpSUNuxY4cKCgo83t/x8fEaOHAg7+8msmbNGiUlJal79+668cYbVVRUZHWkgFdcXCxJat26tSTp008/1cGDBz3e1z169NApp5ziN+9rCgiO6ddff1V1dbWSk5M91icnJ6ugoMCiVMFp4MCBWrx4sd5++209/vjj2rFjh84991yVlJRYHS1o1b6HeX/7xkUXXaRnn31Wq1at0pw5c7R27VqNGDFC1dXVVkcLWDU1Nbrlllt0zjnn6LTTTpN06H0dERGhhIQEj2396X3N1XABPzJixAj3x3369NHAgQPVoUMHvfTSS5o0aZKFyYDGceWVV7o/Pv3009WnTx916dJFa9as0dChQy1MFrimTp2qr7/+OuDGi7EHBMfUtm1bhYaG1hk9vWfPHrVr186iVM1DQkKCTj31VG3bts3qKEGr9j3M+9sanTt3Vtu2bXmPN9C0adP0xhtvaPXq1Tr55JPd69u1a6fKykrt27fPY3t/el9TQHBMERER6tevn1atWuVeV1NTo1WrVmnQoEEWJgt+paWl2r59u9q3b291lKDVqVMntWvXzuP97XK5tHHjRt7fPvDTTz+pqKiI9/hxMk1T06ZN06uvvqr33ntPnTp18vh8v379FB4e7vG+3rJli3788Ue/eV9zCAZemT59uiZMmKD+/ftrwIABeuihh1RWVqaJEydaHS2o3HbbbUpLS1OHDh3kdDqVlZWl0NBQjR8/3upoAa20tNTjL+wdO3bo888/V+vWrXXKKafolltu0d/+9jd169ZNnTp10j333CPDMHTppZdaFzpAHe25bt26tbKzszV27Fi1a9dO27dv1x133KGuXbsqNTXVwtSBZ+rUqVq6dKlef/11xcbGusd1xMfHKyoqSvHx8Zo0aZKmT5+u1q1bKy4uTv/93/+tQYMG6eyzz7Y4/X9YfRoOAsejjz5qnnLKKWZERIQ5YMAAc8OGDVZHCjpXXHGF2b59ezMiIsI86aSTzCuuuMLctm2b1bEC3urVq01JdW4TJkwwTfPQqbj33HOPmZycbEZGRppDhw41t2zZYm3oAHW053r//v3m8OHDzcTERDM8PNzs0KGD6XA4zIKCAqtjB5z6nmNJ5tNPP+3e5sCBA+ZNN91ktmrVymzZsqU5ZswYc/fu3daF/h2baZqm72sPAABozhgDAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAgAAfI4CAiAgvPDCC4qKitLu3bvd6yZOnKg+ffqouLjYwmQAGoKL0QEICKZp6owzztB5552nRx99VFlZWVq0aJE2bNigk046yep4AI5TmNUBAMAbNptNM2fO1Lhx49SuXTs9+uij+uCDDygfQIBiDwiAgGK32/XNN99o5cqVGjJkiNVxADQQY0AABIy3335b3333naqrq5WcnGx1HAAngD0gAAJCfn6+zj//fD3xxBNavHix4uLitGzZMqtjAWggxoAA8Hs7d+7UyJEj9ec//1njx49X586dNWjQIOXn58tut1sdD0ADsAcEgF/77bffNHjwYJ1//vlasGCBe/3IkSNVXV2tt99+28J0ABqKAgIAAHyOQagAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDnKCAAAMDn/g/C+prwh1fwfgAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6, 6))\n", "plt.plot(both_stream.x(), both_stream.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=5)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"Both tails in Cartesian coordinates\")\n", "plt.axis(\"equal\");" ] }, { "cell_type": "markdown", "id": "b13", "metadata": { "papermill": { "duration": 0.004844, "end_time": "2026-05-16T13:59:59.072706+00:00", "exception": false, "start_time": "2026-05-16T13:59:59.067862+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Using fardal15spraydf\n", "\n", "`fardal15spraydf` provides an alternative spray model based on\n", "Fardal et al. (2015). The interface is the same." ] }, { "cell_type": "code", "execution_count": 8, "id": "b14", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:59:59.083791Z", "iopub.status.busy": "2026-05-16T13:59:59.083546Z", "iopub.status.idle": "2026-05-16T14:00:00.005057Z", "shell.execute_reply": "2026-05-16T14:00:00.004107Z" }, "papermill": { "duration": 0.928144, "end_time": "2026-05-16T14:00:00.005832+00:00", "exception": false, "start_time": "2026-05-16T13:59:59.077688+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "numpy.random.seed(1)\n", "spdf_fardal = fardal15spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "fardal_stream = spdf_fardal.sample(n=1000)" ] }, { "cell_type": "markdown", "id": "b465061b", "metadata": { "papermill": { "duration": 0.004984, "end_time": "2026-05-16T14:00:00.016193+00:00", "exception": false, "start_time": "2026-05-16T14:00:00.011209+00:00", "status": "completed" }, "tags": [] }, "source": [ "Comparing the two spray models side by side:" ] }, { "cell_type": "code", "execution_count": 9, "id": "b15", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:00.028208Z", "iopub.status.busy": "2026-05-16T14:00:00.027950Z", "iopub.status.idle": "2026-05-16T14:00:00.273194Z", "shell.execute_reply": "2026-05-16T14:00:00.272201Z" }, "papermill": { "duration": 0.252327, "end_time": "2026-05-16T14:00:00.273869+00:00", "exception": false, "start_time": "2026-05-16T14:00:00.021542+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(both_stream.x(), both_stream.y(), \"k.\", ms=1)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"chen24spraydf\")\n", "plt.axis(\"equal\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(fardal_stream.x(), fardal_stream.y(), \"k.\", ms=1)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"fardal15spraydf\")\n", "plt.axis(\"equal\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "eb740819", "metadata": { "papermill": { "duration": 0.005146, "end_time": "2026-05-16T14:00:00.284543+00:00", "exception": false, "start_time": "2026-05-16T14:00:00.279397+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Progenitor self-gravity with progpot\n", "\n", "The `streamspraydf` models can include the progenitor's gravity using the\n", "`progpot` parameter:" ] }, { "cell_type": "code", "execution_count": 10, "id": "bc23e0d2", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:00.296270Z", "iopub.status.busy": "2026-05-16T14:00:00.296018Z", "iopub.status.idle": "2026-05-16T14:00:03.745501Z", "shell.execute_reply": "2026-05-16T14:00:03.744512Z" }, "papermill": { "duration": 3.45636, "end_time": "2026-05-16T14:00:03.746182+00:00", "exception": false, "start_time": "2026-05-16T14:00:00.289822+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "from galpy.potential import PlummerPotential\n", "\n", "progpot = PlummerPotential(2 * 10.0**4.0 * u.Msun, 4.0 * u.pc)\n", "spdf_with_prog = chen24spraydf(\n", " progenitor_mass=2 * 10.0**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", " progpot=progpot,\n", ")\n", "stream_with_prog = spdf_with_prog.sample(n=500)\n", "plt.plot(stream_with_prog.x(), stream_with_prog.z(), \"k.\", ms=1)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"chen24spraydf with progenitor gravity\");" ] }, { "cell_type": "markdown", "id": "60ac321e", "metadata": { "papermill": { "duration": 0.005409, "end_time": "2026-05-16T14:00:03.757289+00:00", "exception": false, "start_time": "2026-05-16T14:00:03.751880+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Time-dependent progenitor mass\n", "\n", "Real cluster progenitors lose mass over their lifetimes. The\n", "`progenitor_mass` argument accepts either a constant (as above) or a\n", "callable `M(t)`. The callable receives the progenitor-time coordinate\n", "`t` — `t=0` is now and `t<0` is the past — and may take/return astropy\n", "`Quantity` values, which are auto-detected.\n", "\n", "Here we compare a constant-mass run to one in which the progenitor mass\n", "declines by a factor of 10 from start of disruption to the present (so\n", "the cluster is more massive in the past and is now nearly dissolved).\n", "Earlier strippings happen at the higher mass and therefore a wider\n", "tidal radius." ] }, { "cell_type": "code", "execution_count": 11, "id": "67eadcc6", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:03.769417Z", "iopub.status.busy": "2026-05-16T14:00:03.769214Z", "iopub.status.idle": "2026-05-16T14:00:05.852599Z", "shell.execute_reply": "2026-05-16T14:00:05.851484Z" }, "papermill": { "duration": 2.090476, "end_time": "2026-05-16T14:00:05.853274+00:00", "exception": false, "start_time": "2026-05-16T14:00:03.762798+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from astropy import units as u\n", "\n", "\n", "def M_declining(t):\n", " # t = Quantity time, t=0 now, t<0 past\n", " # M0 at t=-4.5 Gyr, 0.1*M0 at t=0\n", " return 2e4 * u.Msun * (0.1 - 0.9 * t / (4.5 * u.Gyr))\n", "\n", "\n", "spdf_evol = chen24spraydf(\n", " progenitor_mass=M_declining,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "spdf_const = chen24spraydf(\n", " progenitor_mass=2e4 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "\n", "numpy.random.seed(0)\n", "stream_evol = spdf_evol.sample(n=1000)\n", "numpy.random.seed(0)\n", "stream_const = spdf_const.sample(n=1000)\n", "\n", "plt.figure(figsize=(12, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(stream_const.x(), stream_const.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=5)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"Constant mass\")\n", "plt.axis(\"equal\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(stream_evol.x(), stream_evol.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=5)\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"$y$\")\n", "plt.title(\"Declining mass (1.0 → 0.1 M0)\")\n", "plt.axis(\"equal\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "8f73fc53", "metadata": { "papermill": { "duration": 0.005412, "end_time": "2026-05-16T14:00:05.864590+00:00", "exception": false, "start_time": "2026-05-16T14:00:05.859178+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Integrating sampled orbits\n", "\n", "The `sample` method can return integrated orbits (to the present time) using\n", "`integrate=True`. You can also get the stripping times with `returndt=True`.\n", "The returned `Orbit` object can be further integrated or analyzed:" ] }, { "cell_type": "code", "execution_count": 12, "id": "fc80e237", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:05.876914Z", "iopub.status.busy": "2026-05-16T14:00:05.876721Z", "iopub.status.idle": "2026-05-16T14:00:06.555432Z", "shell.execute_reply": "2026-05-16T14:00:06.554203Z" }, "papermill": { "duration": 0.685748, "end_time": "2026-05-16T14:00:06.556152+00:00", "exception": false, "start_time": "2026-05-16T14:00:05.870404+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "# Sample with integration and stripping times\n", "orbs_integrated, dt = spdf_both.sample(n=500, returndt=True, integrate=True)\n", "\n", "# Integrate the progenitor for context\n", "ts_prog = numpy.linspace(0.0, 3.0, 301)\n", "prog.integrate(ts_prog, lp)\n", "prog.integrate(-ts_prog, lp)\n", "\n", "# Plot the integrated stream with progenitor orbit\n", "prog.plot(d1=\"R\", d2=\"z\", color=\"k\", lw=1)\n", "plt.plot(orbs_integrated.R(), orbs_integrated.z(), \"r.\", ms=1, alpha=0.5)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Integrated stream particles with progenitor orbit\");" ] }, { "cell_type": "markdown", "id": "52865a9f", "metadata": { "papermill": { "duration": 0.005677, "end_time": "2026-05-16T14:00:06.567979+00:00", "exception": false, "start_time": "2026-05-16T14:00:06.562302+00:00", "status": "completed" }, "tags": [] }, "source": [ "You can also obtain the stream points at the time of stripping by using `integrate=False`:" ] }, { "cell_type": "code", "execution_count": 13, "id": "5a650fe8", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:06.581038Z", "iopub.status.busy": "2026-05-16T14:00:06.580794Z", "iopub.status.idle": "2026-05-16T14:00:06.831911Z", "shell.execute_reply": "2026-05-16T14:00:06.830832Z" }, "papermill": { "duration": 0.258737, "end_time": "2026-05-16T14:00:06.832640+00:00", "exception": false, "start_time": "2026-05-16T14:00:06.573903+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "# Sample with integration and stripping times\n", "orbs_not_integrated, dt = spdf_both.sample(n=500, returndt=True, integrate=False)\n", "\n", "# Integrate the progenitor backwards for context\n", "ts_prog = numpy.linspace(0.0, -4.5, 3001) * u.Gyr\n", "prog.integrate(ts_prog, lp)\n", "\n", "# Plot the integrated stream with progenitor orbit\n", "prog.plot(d1=\"R\", d2=\"z\", color=\"k\", lw=1, xrange=[0.0, 32.0], yrange=[-16.0, 16.0])\n", "plt.scatter(\n", " orbs_not_integrated.R(), orbs_not_integrated.z(), c=dt, marker=\"o\", s=20, alpha=0.5\n", ")\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Stream particles at the time of stripping with progenitor orbit\");" ] }, { "cell_type": "markdown", "id": "7ae44cc9", "metadata": { "papermill": { "duration": 0.006193, "end_time": "2026-05-16T14:00:06.845943+00:00", "exception": false, "start_time": "2026-05-16T14:00:06.839750+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Different potential inputs\n", "\n", "When initializing a particle-spray DF, you can also specify a different potential for computing the tidal radius and velocity distribution of the tidal debris, which can be useful when the overall potential contains pieces that are irrelevant for computing the tidal radius and that don’t allow the tidal radius to be computed (using the ``rtpot=`` option). If you want to generate a stream around a moving object, for example, a stream created within a satellite galaxy of the Milky Way, you can specify an orbit for the center of the satellite (``center=``) and the stream will be generated around this center rather than around the center of the total potential (this was used in [Qian et al. 2022](https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.2339Q/abstract)); the center orbit is integrated in ``centerpot``, which can also differ from the potential that stream stars are integrated in (e.g., the stream stars may feel the potential from the satellite itself and/or the satellite could be experiencing dynamical friction which the stream stars do not feel)." ] }, { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.006183, "end_time": "2026-05-16T14:00:06.858509+00:00", "exception": false, "start_time": "2026-05-16T14:00:06.852326+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Smooth stream track from spray samples\n", "\n", "After drawing a set of stream particles with `.sample()`, we can construct a smooth phase-space track through them using `.streamTrack()`. The track is parameterized by an affine curve parameter `tp` along the progenitor's orbit: for the leading arm `tp` runs from `0` (progenitor today) up to a positive `tp_hi`; for the trailing arm `tp` runs from a negative `tp_lo` up to `0`. The exact range is auto-fit from the particle distribution and is much smaller than `tdisrupt` (typically a small fraction of an orbital period).\n", "\n", "At each `tp` the track gives the mean galactocentric phase-space position of the corresponding stream particles, plus a 6×6 covariance that captures the scatter around that mean. The returned object is a `StreamTrack` — or a `StreamTrackPair` with `.leading` / `.trailing` attributes when `tail='both'` — that exposes the same coordinate accessors as `Orbit`: `x`, `y`, `z`, `vx`, `vy`, `vz`, `R`, `vR`, `vT`, `phi`, plus heliocentric (`ra`, `dec`, `dist`, `ll`, `bb`, `pmra`, `pmdec`, `pmll`, `pmbb`, `vlos`).\n", "\n", "Accessors return `NaN` for `tp` values outside the track's valid range (rather than silent cubic-spline extrapolation); use `track.tp_grid()` to see what range is in scope.\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "acae54e37e7d407bbb7b55eff062a284", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:06.872325Z", "iopub.status.busy": "2026-05-16T14:00:06.872137Z", "iopub.status.idle": "2026-05-16T14:00:13.456802Z", "shell.execute_reply": "2026-05-16T14:00:13.455828Z" }, "papermill": { "duration": 6.592731, "end_time": "2026-05-16T14:00:13.457566+00:00", "exception": false, "start_time": "2026-05-16T14:00:06.864835+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(0)\n", "# Build the track for both arms\n", "track = spdf_both.streamTrack(n=3000, tail=\"both\")\n", "# Also draw a particle cloud to overlay\n", "orbs = spdf_both.sample(n=3000)\n", "fig, ax = plt.subplots(figsize=(6, 6))\n", "ax.scatter(orbs.x(), orbs.y(), s=1, alpha=0.2, color=\"0.6\", label=\"samples\")\n", "track.plot(d1=\"x\", d2=\"y\", spread=1, color=\"C0\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "9a63283cbaf04dbcab1f6479b197f3a8", "metadata": { "papermill": { "duration": 0.006517, "end_time": "2026-05-16T14:00:13.471074+00:00", "exception": false, "start_time": "2026-05-16T14:00:13.464557+00:00", "status": "completed" }, "tags": [] }, "source": [ "The shaded band shows a +/- 1 sigma envelope using the projected covariance at each point along the track. Pass `spread=0` to suppress it." ] }, { "cell_type": "code", "execution_count": 15, "id": "8dd0d8092fe74a7c96281538738b07e2", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:13.485171Z", "iopub.status.busy": "2026-05-16T14:00:13.484935Z", "iopub.status.idle": "2026-05-16T14:00:13.633421Z", "shell.execute_reply": "2026-05-16T14:00:13.632450Z" }, "papermill": { "duration": 0.15652, "end_time": "2026-05-16T14:00:13.634182+00:00", "exception": false, "start_time": "2026-05-16T14:00:13.477662+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Heliocentric view: track overlaid on sample (ra, dec)\n", "fig, ax = plt.subplots(figsize=(6, 5))\n", "ax.scatter(orbs.ra(), orbs.dec(), s=1, alpha=0.2, color=\"0.6\")\n", "track.leading.plot(d1=\"ra\", d2=\"dec\", color=\"C0\", label=\"leading\")\n", "track.trailing.plot(d1=\"ra\", d2=\"dec\", color=\"C3\", label=\"trailing\")\n", "ax.set_xlabel(\"RA [deg]\")\n", "ax.set_ylabel(\"Dec [deg]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "72eea5119410473aa328ad9291626812", "metadata": { "papermill": { "duration": 0.006914, "end_time": "2026-05-16T14:00:13.648330+00:00", "exception": false, "start_time": "2026-05-16T14:00:13.641416+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Controlling the smoothness and iteration\n", "\n", "The `smoothing` keyword sets the spline smoothness; `None` (default) picks an automatic Generalized-Cross-Validation (GCV) value from the binned scatter via `scipy.interpolate.make_smoothing_spline` — for galpy's normalized-internal units the GCV optimizer is run on a y-rescaled problem so it is well-behaved at the small absolute scales of the covariance entries. A float scales it; a dict keyed by `'x','y','z','vx','vy','vz'` sets per-coordinate values; an array of length 6 (or 27 with `order=2`) supplies per-spline `s` values directly (e.g. from a previous `track.smoothing_s`).\n", "\n", "`smoothing_factor` (default `1.0`) is a second, simpler knob: it multiplies whatever `s` was selected (by GCV or by the user) by a constant, with `>1` smoother and `<1` rougher. The default GCV usually produces a good fit, but this dial lets you trade bias for variance if you have a particular reason to (e.g. a noisy short-stream sample where you'd rather oversmooth, or a long well-sampled stream where you want every wiggle of the predicted track resolved). See below for an example.\n", "\n", "`niter` runs additional refinement iterations that reassign each particle to the closest point on the current track before refitting. For typical streams, 1-2 iterations suffice." ] }, { "cell_type": "code", "execution_count": 16, "id": "8edb47106e1a46a883d545849b8ab81b", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:13.663323Z", "iopub.status.busy": "2026-05-16T14:00:13.663075Z", "iopub.status.idle": "2026-05-16T14:00:19.218477Z", "shell.execute_reply": "2026-05-16T14:00:19.217468Z" }, "papermill": { "duration": 5.56392, "end_time": "2026-05-16T14:00:19.219151+00:00", "exception": false, "start_time": "2026-05-16T14:00:13.655231+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compare default fit with niter=2 (closest-point reassignment) on a single sample\n", "spdf_both._tail = \"leading\"\n", "tr_default = spdf_both.streamTrack(n=3000, tail=\"leading\")\n", "xv_dt = tr_default.particles # save once, reuse below to skip the resample\n", "tr_iter2 = spdf_both.streamTrack(particles=xv_dt, niter=2)\n", "fig, ax = plt.subplots(figsize=(7, 5))\n", "ax.scatter(orbs.x(), orbs.y(), s=1, alpha=0.2, color=\"0.6\")\n", "tr_default.plot(d1=\"x\", d2=\"y\", color=\"C0\", label=\"default\")\n", "tr_iter2.plot(d1=\"x\", d2=\"y\", color=\"C2\", label=\"niter=2\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "10185d26023b46108eb7d9f57d49d2b3", "metadata": { "papermill": { "duration": 0.007133, "end_time": "2026-05-16T14:00:19.233862+00:00", "exception": false, "start_time": "2026-05-16T14:00:19.226729+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Pulling the 6×6 covariance with `cov()`\n", "\n", "Beyond the mean track, `track.cov(tp, basis=...)` returns the 6×6 covariance of the particle distribution at the requested `tp`. Five output bases are supported: `'galcenrect'` (default; native), `'galcencyl'`, `'sky'` (equatorial), `'galsky'` (Galactic), and `'customsky'` (requires a `custom_sky_transform`). The non-native bases use analytical Jacobians — no finite differences — so the result is a self-consistent transform of the stored galactocentric covariance.\n", "\n", "The diagonal entries can be used directly to draw ±σ bands; the cross-terms encode correlations (e.g. between `pmra` and `pmdec`):\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "8763a12b2bbd4a93a75aff182afb95dc", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:19.249965Z", "iopub.status.busy": "2026-05-16T14:00:19.249745Z", "iopub.status.idle": "2026-05-16T14:00:19.274650Z", "shell.execute_reply": "2026-05-16T14:00:19.273836Z" }, "papermill": { "duration": 0.034019, "end_time": "2026-05-16T14:00:19.275462+00:00", "exception": false, "start_time": "2026-05-16T14:00:19.241443+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tp= 0.000: σ(ra)=0.281 deg, σ(dec)=0.139 deg, σ(dist)=0.043 kpc\n", "tp= 0.303: σ(ra)=0.291 deg, σ(dec)=0.287 deg, σ(dist)=0.044 kpc\n", "tp= 0.606: σ(ra)=0.317 deg, σ(dec)=0.247 deg, σ(dist)=0.046 kpc\n", "tp= 0.909: σ(ra)=0.286 deg, σ(dec)=0.132 deg, σ(dist)=0.049 kpc\n", "tp= 1.212: σ(ra)=0.220 deg, σ(dec)=0.038 deg, σ(dist)=0.055 kpc\n" ] } ], "source": [ "tps = numpy.linspace(*track.leading.tp_grid()[[0, -1]], 5)\n", "for tp in tps:\n", " C = track.leading.cov(tp, basis=\"sky\")\n", " sigma_ra = numpy.sqrt(C[0, 0])\n", " sigma_dec = numpy.sqrt(C[1, 1])\n", " sigma_dist = numpy.sqrt(C[2, 2])\n", " print(\n", " f\"tp={tp:6.3f}: σ(ra)={sigma_ra:.3f} deg, σ(dec)={sigma_dec:.3f} deg, σ(dist)={sigma_dist:.3f} kpc\"\n", " )" ] }, { "cell_type": "markdown", "id": "7623eae2785240b9bd12b16a66d81610", "metadata": { "papermill": { "duration": 0.007156, "end_time": "2026-05-16T14:00:19.290023+00:00", "exception": false, "start_time": "2026-05-16T14:00:19.282867+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Stream-frame plots with `custom_sky_transform`\n", "\n", "For visualizing thin streams, it's often useful to rotate to a frame aligned with the stream itself — a `(φ1, φ2)` system in which the stream lies near `φ2 = 0`. Pass a 3×3 rotation matrix as `custom_sky_transform=` and the track exposes `.phi1`, `.phi2`, `.pmphi1`, `.pmphi2` accessors and `cov(basis='customsky')`. The helper `Orbit.align_to_orbit()` builds such a matrix from the progenitor's angular momentum:\n", "\n", "Calling `Orbit.align_to_orbit()` also stashes the rotation matrix on the orbit itself, so afterwards `prog.phi1(t)`, `prog.phi2(t)`, `prog.pmphi1(t)`, `prog.pmphi2(t)` (and `prog.plot(d1='phi1', d2='phi2')`) work without re-passing `T=`. Below: the same plot but also overlaying the progenitor's orbit in the aligned frame — it traces `phi2 = 0` by construction (the rotation maps the orbital plane onto the equator)." ] }, { "cell_type": "code", "execution_count": 18, "id": "7cdc8c89c7104fffa095e18ddfef8986", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:19.305531Z", "iopub.status.busy": "2026-05-16T14:00:19.305333Z", "iopub.status.idle": "2026-05-16T14:00:23.311742Z", "shell.execute_reply": "2026-05-16T14:00:23.310720Z" }, "papermill": { "duration": 4.015195, "end_time": "2026-05-16T14:00:23.312413+00:00", "exception": false, "start_time": "2026-05-16T14:00:19.297218+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prog = prog() # Need to reset because we integrated it above\n", "T = prog.align_to_orbit()\n", "track_cs = spdf_both.streamTrack(n=3000, tail=\"both\", custom_sky_transform=T)\n", "\n", "# To overlay the progenitor's *orbit* in the aligned frame we have to\n", "# actually integrate it; `prog` is just initial conditions. The\n", "# progenitor sits in the middle of the stream so we integrate both\n", "# forward (to the leading-arm tip) and backward (to the trailing-arm\n", "# tip) — the second integrate() call extends the first rather than\n", "# overwriting it.\n", "tp_lo = float(track_cs.trailing.tp_grid()[0])\n", "tp_hi = float(track_cs.leading.tp_grid()[-1])\n", "prog.integrate(numpy.linspace(0, tp_hi, 201), lp)\n", "prog.integrate(numpy.linspace(0, tp_lo, 201), lp)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 3))\n", "# `prog.align_to_orbit()` stashed the rotation matrix on `prog`, so\n", "# `prog.phi1`/`prog.phi2` work without re-passing T=.\n", "prog.plot(\n", " d1=\"phi1\", d2=\"phi2\", color=\"k\", lw=1.0, ls=\"--\", label=\"progenitor orbit\", gcf=True\n", ")\n", "track_cs.leading.plot(d1=\"phi1\", d2=\"phi2\", color=\"C0\", label=\"leading\")\n", "track_cs.trailing.plot(d1=\"phi1\", d2=\"phi2\", color=\"C3\", label=\"trailing\")\n", "ax.scatter([180.0], [0.0], color=\"k\", s=30, zorder=5, label=\"progenitor (today)\")\n", "ax.set_xlabel(r\"$\\phi_1$ [deg]\")\n", "ax.set_ylabel(r\"$\\phi_2$ [deg]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "ba17f45c", "metadata": { "papermill": { "duration": 0.007373, "end_time": "2026-05-16T14:00:23.327582+00:00", "exception": false, "start_time": "2026-05-16T14:00:23.320209+00:00", "status": "completed" }, "tags": [] }, "source": [ "The `custom_sky_transform` is also exposed as a settable property on the `StreamTrack` (and on `StreamTrackPair`, which broadcasts the assignment to both arms), so you don't have to rebuild the track to look at it in a different frame — or to drop the rotation altogether (set to `None`):" ] }, { "cell_type": "code", "execution_count": 19, "id": "dd826b9d", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:23.343808Z", "iopub.status.busy": "2026-05-16T14:00:23.343565Z", "iopub.status.idle": "2026-05-16T14:00:24.594397Z", "shell.execute_reply": "2026-05-16T14:00:24.593515Z" }, "papermill": { "duration": 1.260226, "end_time": "2026-05-16T14:00:24.595269+00:00", "exception": false, "start_time": "2026-05-16T14:00:23.335043+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "before: None\n", "after : shape (3, 3)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Build the track without a rotation, then attach one after the fact —\n", "# the phi1/phi2 accessors and cov(basis='customsky') light up immediately.\n", "# (track_cs.particles is the both-arm sample from the previous cell; the\n", "# leading-only xv_dt from earlier in the tutorial would be wrong here.)\n", "track_bare = spdf_both.streamTrack(particles=track_cs.particles, tail=\"both\")\n", "print(\"before:\", track_bare.custom_sky_transform)\n", "track_bare.custom_sky_transform = T # broadcasts to both arms of the pair\n", "print(\"after : shape\", track_bare.custom_sky_transform.shape)\n", "\n", "fig, ax = plt.subplots(figsize=(7, 2.5))\n", "track_bare.leading.plot(d1=\"phi1\", d2=\"phi2\", color=\"C0\", label=\"leading\")\n", "track_bare.trailing.plot(d1=\"phi1\", d2=\"phi2\", color=\"C3\", label=\"trailing\")\n", "ax.set_xlabel(r\"$\\phi_1$ [deg]\")\n", "ax.set_ylabel(r\"$\\phi_2$ [deg]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "id": "b118ea5561624da68c537baed56e602f", "metadata": { "papermill": { "duration": 0.007894, "end_time": "2026-05-16T14:00:24.611250+00:00", "exception": false, "start_time": "2026-05-16T14:00:24.603356+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Reusing samples for a smoothing sweep\n", "\n", "The expensive part of `streamTrack` is the orbit-integrated sample (and, on first call, the GCV per-spline `s` selection). The cheap part is the spline fit. To explore smoothing variants without redoing the expensive work, save the particles and pass them back as `particles=` to subsequent calls — only the bin-and-smooth step re-runs.\n", "\n", "There are three reuse handles depending on what object you have in hand:\n", "\n", "* `track.particles` (a single-arm `StreamTrack`) — the `xv` array the fit saw. Pass back as `spdf.streamTrack(particles=..., tail='leading')` (or `'trailing'`).\n", "* `pair.particles` (a `StreamTrackPair` from `tail='both'`) — concatenates the two arms' `xv` arrays in the leading-first order that `streamTrack(tail='both', particles=...)` expects.\n", "* `spdf.sample(tail='both', returndt=False, return_orbit=False, integrate=True)` — pre-sample without building any track at all; returns the same concatenated `xv` array.\n", "\n", "Two further knobs that take the cheap-refit path:\n", "\n", "* `track.smoothing_s` is the per-spline effective `s`. Passing it back as `smoothing=` (with `smoothing_factor=1`) skips the GCV step entirely and re-fits at exactly that smoothness.\n", "* `smoothing_factor=` is the simplest dial: rerun with the same `particles=` and a different multiplier.\n", "\n", "Below: the same `track_cs` sample fit at `smoothing_factor` $\\in \\{0.25, 1, 4\\}$ in the aligned frame, both arms. The factor `0.25` track follows individual bin means and the factor `4` track sands out the corners — the default `1.0` is a balanced fit." ] }, { "cell_type": "code", "execution_count": 20, "id": "938c804e27f84196a10c8828c723f798", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:24.627992Z", "iopub.status.busy": "2026-05-16T14:00:24.627748Z", "iopub.status.idle": "2026-05-16T14:00:27.040707Z", "shell.execute_reply": "2026-05-16T14:00:27.039775Z" }, "papermill": { "duration": 2.422391, "end_time": "2026-05-16T14:00:27.041420+00:00", "exception": false, "start_time": "2026-05-16T14:00:24.619029+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Reuse the both-arms sample from track_cs (built in the previous cell) —\n", "# pair.particles concatenates the two arms in the leading-first order that\n", "# streamTrack(tail='both') expects, so re-fitting only re-runs the splines.\n", "xv_dt = track_cs.particles\n", "tr_cs_rough = spdf_both.streamTrack(\n", " particles=xv_dt, tail=\"both\", custom_sky_transform=T, smoothing_factor=0.25\n", ")\n", "tr_cs_smooth = spdf_both.streamTrack(\n", " particles=xv_dt, tail=\"both\", custom_sky_transform=T, smoothing_factor=4.0\n", ")\n", "fig, ax = plt.subplots(figsize=(8, 3.5))\n", "for arm in (\"leading\", \"trailing\"):\n", " getattr(tr_cs_rough, arm).plot(\n", " d1=\"phi1\",\n", " d2=\"phi2\",\n", " color=\"C3\",\n", " alpha=0.7,\n", " label=\"factor=0.25 (rougher)\" if arm == \"leading\" else None,\n", " )\n", " getattr(track_cs, arm).plot(\n", " d1=\"phi1\",\n", " d2=\"phi2\",\n", " color=\"C0\",\n", " label=\"factor=1.0 (default)\" if arm == \"leading\" else None,\n", " )\n", " getattr(tr_cs_smooth, arm).plot(\n", " d1=\"phi1\",\n", " d2=\"phi2\",\n", " color=\"C2\",\n", " label=\"factor=4.0 (smoother)\" if arm == \"leading\" else None,\n", " )\n", "ax.set_xlabel(r\"$\\phi_1$ [deg]\")\n", "ax.set_ylabel(r\"$\\phi_2$ [deg]\")\n", "ax.legend(loc=\"best\", fontsize=9);" ] }, { "cell_type": "markdown", "id": "1fa33ae5", "metadata": { "papermill": { "duration": 0.007756, "end_time": "2026-05-16T14:00:27.057486+00:00", "exception": false, "start_time": "2026-05-16T14:00:27.049730+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Non-uniform stripping times\n", "\n", "By default, `streamspraydf` draws stripping times uniformly between\n", "`-tdisrupt` and `0`. Real tidal streams, however, are stripped preferentially\n", "near pericenter passages of the progenitor's orbit, where the tidal field\n", "is strongest. The `stripping_pdf=` keyword lets you supply an arbitrary\n", "probability density over the progenitor time axis `t \\in [-t_\\mathrm{disrupt}, 0]`\n", "(`t=0` is the present day, `t<0` the past). Internally the PDF is\n", "converted to a CDF and inverted; samples are drawn via inverse-CDF\n", "transform.\n", "\n", "The PDF need not be normalized. It may accept and return floats,\n", "``numpy`` arrays, or astropy ``Quantity`` (input a time, output a\n", "``1/time``); the detection is the same as for\n", "``AnyAxisymmetricRazorThinDiskPotential``." ] }, { "cell_type": "markdown", "id": "25ad2350", "metadata": { "papermill": { "duration": 0.007662, "end_time": "2026-05-16T14:00:27.073009+00:00", "exception": false, "start_time": "2026-05-16T14:00:27.065347+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Example A: a custom Gaussian stripping window\n", "\n", "Suppose stripping was concentrated around 2.5 Gyr ago, with a width of\n", "0.3 Gyr. We pass a Gaussian PDF in ``Quantity`` form and sample the\n", "stream." ] }, { "cell_type": "code", "execution_count": 21, "id": "96f4819e", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:27.089966Z", "iopub.status.busy": "2026-05-16T14:00:27.089757Z", "iopub.status.idle": "2026-05-16T14:00:27.876925Z", "shell.execute_reply": "2026-05-16T14:00:27.876039Z" }, "papermill": { "duration": 0.796838, "end_time": "2026-05-16T14:00:27.877714+00:00", "exception": false, "start_time": "2026-05-16T14:00:27.080876+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.util import conversion\n", "\n", "ro_, vo_ = 8.0, 220.0\n", "\n", "\n", "def gauss_pdf(t):\n", " return numpy.exp(-0.5 * ((t - (-2.5 * u.Gyr)) / (0.3 * u.Gyr)) ** 2) / u.Gyr\n", "\n", "\n", "spdf_gauss = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " stripping_pdf=gauss_pdf,\n", " tail=\"both\",\n", ")\n", "numpy.random.seed(0)\n", "stream_gauss, dt_gauss = spdf_gauss.sample(n=600, returndt=True)\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.hist(dt_gauss * conversion.time_in_Gyr(vo_, ro_), bins=40, color=\"steelblue\")\n", "plt.xlabel(r\"$\\Delta t$ since stripping [Gyr]\")\n", "plt.ylabel(\"count\")\n", "plt.title(\"Gaussian stripping_pdf\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(stream_gauss.x(), stream_gauss.y(), \"k.\", ms=1)\n", "plt.plot(prog.x(), prog.y(), \"ro\", ms=6)\n", "plt.xlabel(r\"$x$ [kpc]\")\n", "plt.ylabel(r\"$y$ [kpc]\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "453d0ef1", "metadata": { "papermill": { "duration": 0.008169, "end_time": "2026-05-16T14:00:27.894415+00:00", "exception": false, "start_time": "2026-05-16T14:00:27.886246+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Example B: pericenter-driven stripping\n", "\n", "A common physical model is to bunch stripping into Gaussians centered on\n", "each pericenter passage. ``galpy.df.pericenter_stripping_pdf`` builds such\n", "a PDF from the progenitor and potential, given a width ``sigma``. The\n", "returned PDF can be passed straight into ``stripping_pdf=``, and it\n", "exposes a ``.pericenter_times`` attribute listing the pericenter times\n", "in internal units." ] }, { "cell_type": "code", "execution_count": 22, "id": "bd9ebfc1", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T14:00:27.912576Z", "iopub.status.busy": "2026-05-16T14:00:27.912345Z", "iopub.status.idle": "2026-05-16T14:00:29.332762Z", "shell.execute_reply": "2026-05-16T14:00:29.331591Z" }, "papermill": { "duration": 1.430451, "end_time": "2026-05-16T14:00:29.333420+00:00", "exception": false, "start_time": "2026-05-16T14:00:27.902969+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from galpy.df import pericenter_stripping_pdf\n", "from galpy.util import conversion\n", "\n", "ro_, vo_ = 8.0, 220.0\n", "peri_pdf = pericenter_stripping_pdf(\n", " prog, lp, 4.5 * u.Gyr, sigma=50 * u.Myr, ro=ro_, vo=vo_\n", ")\n", "spdf_peri = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " stripping_pdf=peri_pdf,\n", " tail=\"both\",\n", ")\n", "spdf_uniform = chen24spraydf(\n", " progenitor_mass=2 * 10**4.0 * u.Msun,\n", " progenitor=prog,\n", " pot=lp,\n", " tdisrupt=4.5 * u.Gyr,\n", " tail=\"both\",\n", ")\n", "numpy.random.seed(1)\n", "stream_peri, dt_peri = spdf_peri.sample(n=600, returndt=True)\n", "numpy.random.seed(1)\n", "stream_uniform, dt_uniform = spdf_uniform.sample(n=600, returndt=True)\n", "peri_gyr = peri_pdf.pericenter_times * conversion.time_in_Gyr(vo_, ro_)\n", "plt.figure(figsize=(10, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.hist(\n", " dt_uniform * conversion.time_in_Gyr(vo_, ro_),\n", " bins=40,\n", " color=\"0.6\",\n", " alpha=0.6,\n", " label=\"uniform\",\n", ")\n", "plt.hist(\n", " dt_peri * conversion.time_in_Gyr(vo_, ro_),\n", " bins=40,\n", " color=\"C3\",\n", " alpha=0.6,\n", " label=\"pericenter\",\n", ")\n", "for tp in peri_gyr:\n", " plt.axvline(-tp, color=\"k\", lw=0.5, alpha=0.6)\n", "plt.xlabel(r\"$\\Delta t$ since stripping [Gyr]\")\n", "plt.ylabel(\"count\")\n", "plt.legend()\n", "plt.subplot(1, 2, 2)\n", "plt.plot(stream_uniform.x(), stream_uniform.y(), \"k.\", ms=1, alpha=0.4, label=\"uniform\")\n", "plt.plot(stream_peri.x(), stream_peri.y(), \"C3.\", ms=1, alpha=0.6, label=\"pericenter\")\n", "plt.plot(prog.x(), prog.y(), \"yo\", ms=6)\n", "plt.xlabel(r\"$x$ [kpc]\")\n", "plt.ylabel(r\"$y$ [kpc]\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] } ], "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": 36.555937, "end_time": "2026-05-16T14:00:29.958166+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/streams/streamspraydf.ipynb", "output_path": "doc/source/tutorials/streams/streamspraydf.ipynb", "parameters": {}, "start_time": "2026-05-16T13:59:53.402229+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }