{ "cells": [ { "cell_type": "markdown", "id": "a1", "metadata": { "papermill": { "duration": 0.004522, "end_time": "2026-06-30T01:24:26.571575+00:00", "exception": false, "start_time": "2026-06-30T01:24:26.567053+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Stream Modeling with streamdf\n", "\n", "galpy's `streamdf` class models tidal streams using action-angle coordinates.\n", "The basic idea is that stream stars were stripped from a progenitor at different\n", "times and therefore have slightly different orbital frequencies. Over time, this\n", "frequency spread causes them to spread out along the orbit, forming a stream.\n", "`streamdf` predicts the stream track on the sky, the density along the stream,\n", "and allows sampling of stream stars." ] }, { "cell_type": "code", "execution_count": 1, "id": "a2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:26.580290Z", "iopub.status.busy": "2026-06-30T01:24:26.580047Z", "iopub.status.idle": "2026-06-30T01:24:29.310359Z", "shell.execute_reply": "2026-06-30T01:24:29.309440Z" }, "papermill": { "duration": 2.735746, "end_time": "2026-06-30T01:24:29.311283+00:00", "exception": false, "start_time": "2026-06-30T01:24:26.575537+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "from galpy.df import streamdf\n", "from galpy.orbit import Orbit\n", "from galpy.potential import LogarithmicHaloPotential\n", "from galpy.actionAngle import actionAngleIsochroneApprox\n", "from galpy.util import conversion\n", "from astropy import units\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "id": "streamdf-physical-picture", "metadata": { "papermill": { "duration": 0.002922, "end_time": "2026-06-30T01:24:29.317485+00:00", "exception": false, "start_time": "2026-06-30T01:24:29.314563+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Physical picture behind `streamdf`\n", "\n", "`streamdf` is based on a simple action-angle picture of tidal stripping.\n", "As an example, the movie below shows the disruption of a cluster on a GD-1-like\n", "orbit around the Milky Way from [Bovy (2014)](http://adsabs.harvard.edu/abs/2014ApJ...795...95B).\n", "The blue curve is the progenitor orbit and the black points are stripped stars.\n", "\n", "\n", "\n", "Once stars are stripped from the progenitor in a static host potential, their\n", "actions are approximately conserved, but they have slightly different orbital\n", "frequencies from the progenitor and from one another. Those small frequency\n", "offsets accumulate into angle offsets that grow roughly linearly with time,\n", "which is why the debris stretches into a long, thin stream. Because the debris\n", "occupies a distribution in actions and frequencies, the stream track is in\n", "general not the same as the progenitor orbit. The next movie shows the debris in\n", "action space: stars in the stream settle onto nearly fixed actions once they are\n", "stripped, while stars still bound to the cluster do not.\n", "\n", "\n", "\n", "Angle offsets then grow approximately linearly with time, which is what stretches\n", "the debris into a stream.\n", "\n", "\n", "\n", "Finally, the frequency-angle structure along the stream explains why streams are\n", "not exactly orbits: stars removed with larger frequency offsets run away faster,\n", "so different parts of the stream trace slightly different effective orbits.\n", "\n", "\n", "\n", "Later in this notebook,\n", "`freqEigvalRatio` measures how nearly one-dimensional the debris is,\n", "`misalignment` measures how well the stream aligns with the progenitor\n", "frequency direction, and `plotCompareTrackAAModel` checks that the computed\n", "track is self-consistent in frequency-angle space." ] }, { "cell_type": "markdown", "id": "a5", "metadata": { "papermill": { "duration": 0.002774, "end_time": "2026-06-30T01:24:29.323270+00:00", "exception": false, "start_time": "2026-06-30T01:24:29.320496+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Initialize streamdf" ] }, { "cell_type": "markdown", "id": "6f08cd87", "metadata": { "papermill": { "duration": 0.00277, "end_time": "2026-06-30T01:24:29.328910+00:00", "exception": false, "start_time": "2026-06-30T01:24:29.326140+00:00", "status": "completed" }, "tags": [] }, "source": [ "We need three ingredients to initialize a `streamdf` instance:\n", "\n", "1. A gravitational potential\n", "2. An action-angle calculator for that potential\n", "3. A progenitor orbit\n", "\n", "As an example, we will use the a simple flattened logarithmic potential, the `actionAngleIsochroneApprox` method for computing actions, and a progenitor orbit with a pericenter of 14 kpc and an apocenter of 26 kpc." ] }, { "cell_type": "code", "execution_count": 2, "id": "656f032a", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:29.339348Z", "iopub.status.busy": "2026-06-30T01:24:29.338838Z", "iopub.status.idle": "2026-06-30T01:24:29.343645Z", "shell.execute_reply": "2026-06-30T01:24:29.342823Z" }, "papermill": { "duration": 0.012965, "end_time": "2026-06-30T01:24:29.344773+00:00", "exception": false, "start_time": "2026-06-30T01:24:29.331808+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "lp = LogarithmicHaloPotential(normalize=1.0, q=0.9)\n", "aAIA = actionAngleIsochroneApprox(pot=lp, b=0.8)\n", "obs = Orbit([1.56148083, 0.35081535, -1.15481504, 0.88719443, -0.47713334, 0.12019596])" ] }, { "cell_type": "markdown", "id": "1de7a4e5", "metadata": { "papermill": { "duration": 0.003035, "end_time": "2026-06-30T01:24:29.351122+00:00", "exception": false, "start_time": "2026-06-30T01:24:29.348087+00:00", "status": "completed" }, "tags": [] }, "source": [ "\n", "Now we initialize the `streamdf` model. The key parameters are:\n", "\n", "- `sigv`: the velocity dispersion of the progenitor\n", "- `progenitor`: the progenitor orbit\n", "- `pot`: the gravitational potential\n", "- `aA`: the action-angle instance\n", "- `leading`: whether to model the leading (`True`) or trailing (`False`) arm\n", "- `tdisrupt`: the time since disruption began" ] }, { "cell_type": "code", "execution_count": 3, "id": "a6", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:29.358656Z", "iopub.status.busy": "2026-06-30T01:24:29.358441Z", "iopub.status.idle": "2026-06-30T01:24:36.529823Z", "shell.execute_reply": "2026-06-30T01:24:36.528938Z" }, "papermill": { "duration": 7.176682, "end_time": "2026-06-30T01:24:36.530918+00:00", "exception": false, "start_time": "2026-06-30T01:24:29.354236+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: In versions >1.3, the output unit of streamdf.misalignment has been changed to radian (from degree before)\n" ] } ], "source": [ "sigv = 0.365 * units.km / units.s\n", "sdf = streamdf(\n", " sigv,\n", " progenitor=obs,\n", " pot=lp,\n", " aA=aAIA,\n", " leading=True,\n", " nTrackChunks=11,\n", " tdisrupt=4.5 * units.Gyr,\n", ")" ] }, { "cell_type": "markdown", "id": "a7", "metadata": { "papermill": { "duration": 0.003343, "end_time": "2026-06-30T01:24:36.538316+00:00", "exception": false, "start_time": "2026-06-30T01:24:36.534973+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Plot the stream track\n", "\n", "We can visualize the predicted stream track and the progenitor's orbit." ] }, { "cell_type": "code", "execution_count": 4, "id": "a8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:36.545602Z", "iopub.status.busy": "2026-06-30T01:24:36.545397Z", "iopub.status.idle": "2026-06-30T01:24:36.766459Z", "shell.execute_reply": "2026-06-30T01:24:36.765400Z" }, "papermill": { "duration": 0.22566, "end_time": "2026-06-30T01:24:36.767131+00:00", "exception": false, "start_time": "2026-06-30T01:24:36.541471+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sdf.plotTrack(\n", " d1=\"r\",\n", " d2=\"z\",\n", " interp=True,\n", " color=\"b\",\n", " spread=2,\n", " overplot=False,\n", " lw=2.0,\n", " scaleToPhysical=True,\n", ")\n", "sdf.plotProgenitor(\n", " d1=\"r\", d2=\"z\", color=\"r\", overplot=True, ls=\"--\", scaleToPhysical=True\n", ")\n", "plt.xlabel(r\"$R\\,(\\mathrm{kpc})$\")\n", "plt.ylabel(r\"$Z\\,(\\mathrm{kpc})$\");" ] }, { "cell_type": "markdown", "id": "f5017cd9", "metadata": { "papermill": { "duration": 0.003481, "end_time": "2026-06-30T01:24:36.774928+00:00", "exception": false, "start_time": "2026-06-30T01:24:36.771447+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Unified `StreamTrack` interface\n", "\n", "galpy's `StreamTrack` class is a smooth phase-space track container that's\n", "shared across all stream DFs. `streamspraydf` returns one from\n", "`streamspraydf.streamTrack()` (fit to sampled particles); `streamdf` returns the\n", "same kind of object from `streamdf.streamTrack()`, built directly from the\n", "analytically computed action-angle track — no particle fitting required.\n", "\n", "The `StreamTrack` exposes a richer accessor set than `plotTrack`: sky / Galactic /\n", "custom-frame coordinates with proper-motion accessors, plus a `cov(basis=...)`\n", "method that returns the 6×6 phase-space covariance in any of `galcenrect`,\n", "`galcencyl`, `sky`, `galsky`, or `customsky` bases via analytical Jacobian\n", "transforms." ] }, { "cell_type": "code", "execution_count": 5, "id": "57d791b8", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:36.783117Z", "iopub.status.busy": "2026-06-30T01:24:36.782914Z", "iopub.status.idle": "2026-06-30T01:24:36.789407Z", "shell.execute_reply": "2026-06-30T01:24:36.787943Z" }, "papermill": { "duration": 0.011712, "end_time": "2026-06-30T01:24:36.790077+00:00", "exception": false, "start_time": "2026-06-30T01:24:36.778365+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "type: StreamTrack\n", "ll (deg) : [160.96266863 200.33106012 221.71397966 234.64878143 244.02404764]\n", "bb (deg) : [56.81288692 41.40803055 21.00716228 5.1057252 -5.8136726 ]\n", "dist (kpc) : [ 8.34973129 7.92760554 8.89590065 10.76034701 12.98834319]\n", "vlos (km/s): [-117.92739814 85.75094286 255.28989604 342.54550621 374.56841591]\n" ] } ], "source": [ "track = sdf.streamTrack()\n", "print(\"type:\", type(track).__name__)\n", "\n", "# Sample accessors at five tps spanning the stream (LB axes in deg / kpc / km/s / mas/yr).\n", "tps = numpy.linspace(0.0, sdf._deltaAngleTrack * 0.9, 5)\n", "print(\"ll (deg) :\", track.ll(tps, use_physical=False))\n", "print(\"bb (deg) :\", track.bb(tps, use_physical=False))\n", "print(\"dist (kpc) :\", track.dist(tps, use_physical=False))\n", "print(\"vlos (km/s):\", track.vlos(tps, use_physical=False))" ] }, { "cell_type": "code", "execution_count": 6, "id": "61bf9049", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:36.798334Z", "iopub.status.busy": "2026-06-30T01:24:36.798109Z", "iopub.status.idle": "2026-06-30T01:24:36.803372Z", "shell.execute_reply": "2026-06-30T01:24:36.802567Z" }, "papermill": { "duration": 0.010355, "end_time": "2026-06-30T01:24:36.804100+00:00", "exception": false, "start_time": "2026-06-30T01:24:36.793745+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigma(ll) = 0.465 deg\n", "sigma(bb) = 0.299 deg\n", "sigma(dist) = 0.0351 kpc\n", "sigma(pmll) = 0.0365 mas/yr\n", "sigma(pmbb) = 0.0209 mas/yr\n", "sigma(vlos) = 1.2 km/s\n" ] } ], "source": [ "# 6x6 covariance in the (l, b, dist, pmll, pmbb, vlos) Galactic-sky basis at one tp,\n", "# in physical units (deg / kpc / mas/yr / km/s). With ``use_physical=True`` the\n", "# Jacobian is run against the stored ``ro=8 kpc`` and ``vo=220 km/s``.\n", "C = track.cov(0.5, basis=\"galsky\", use_physical=True)\n", "sigmas = numpy.sqrt(numpy.diag(C))\n", "for name, unit, s in zip(\n", " [\"ll\", \"bb\", \"dist\", \"pmll\", \"pmbb\", \"vlos\"],\n", " [\"deg\", \"deg\", \"kpc\", \"mas/yr\", \"mas/yr\", \"km/s\"],\n", " sigmas,\n", "):\n", " print(f\"sigma({name}) = {s:.3g} {unit}\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "e8589665", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:36.812300Z", "iopub.status.busy": "2026-06-30T01:24:36.812078Z", "iopub.status.idle": "2026-06-30T01:24:37.262425Z", "shell.execute_reply": "2026-06-30T01:24:37.261648Z" }, "papermill": { "duration": 0.455794, "end_time": "2026-06-30T01:24:37.263598+00:00", "exception": false, "start_time": "2026-06-30T01:24:36.807804+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# StreamTrack.plot draws the same kind of figure as streamdf.plotTrack and\n", "# accepts every accessor name as an axis label, including sky bases. Overlay\n", "# both on a single set of axes for comparison.\n", "sdf.plotTrack(d1=\"ll\", d2=\"bb\", spread=1, color=\"b\", lw=2.0)\n", "track.plot(d1=\"ll\", d2=\"bb\", spread=1, color=\"r\", ls=\"--\", lw=2.0)\n", "plt.title(\"streamdf.plotTrack (blue) + StreamTrack.plot (red dashed)\");" ] }, { "cell_type": "markdown", "id": "f7da4090", "metadata": { "papermill": { "duration": 0.004209, "end_time": "2026-06-30T01:24:37.272605+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.268396+00:00", "status": "completed" }, "tags": [] }, "source": [ "The `custom_sky_transform` argument to `streamdf` (a 3×3 rotation from equatorial\n", "coordinates to a custom $(\\phi_1, \\phi_2)$ sky frame) is forwarded to the\n", "`StreamTrack`, enabling its `phi1`, `phi2`, `pmphi1`, and `pmphi2` accessors. A\n", "convenience helper, `Orbit.align_to_orbit`, builds a rotation matrix that aligns\n", "$\\phi_1$ with the progenitor's track.\n", "\n", "For sky covariance bands, the cov attached to the streamTrack is the **local**\n", "perpendicular cov (parallel-angle variance = `sigangledAngle**2`), matching the\n", "streamspraydf streamTrack convention. The legacy `_allErrCovsXY` keeps its\n", "likelihood-marginal semantics (parallel-angle variance = 1 rad², needed by\n", "`gaussApprox`) and is what `plotTrack(spread=...)` uses via a 2D minor-eigenvalue\n", "projection. Both pipelines agree exactly at the chunk grid and report the same\n", "perpendicular width; between chunks the eigen-slerp interpolation\n", "(`plotTrack`) and entry-wise linear interpolation (`StreamTrack.plot`) can\n", "differ at the percent level." ] }, { "cell_type": "markdown", "id": "a9", "metadata": { "papermill": { "duration": 0.003509, "end_time": "2026-06-30T01:24:37.279904+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.276395+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Stream length and width\n", "\n", "We can compute the stream length (the angular extent along the stream)\n", "and the width (the spread perpendicular to the stream track)." ] }, { "cell_type": "code", "execution_count": 8, "id": "a10", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:37.288410Z", "iopub.status.busy": "2026-06-30T01:24:37.288186Z", "iopub.status.idle": "2026-06-30T01:24:37.300021Z", "shell.execute_reply": "2026-06-30T01:24:37.298988Z" }, "papermill": { "duration": 0.016934, "end_time": "2026-06-30T01:24:37.300645+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.283711+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Stream length (radians): 93.48285485852354\n", "Stream length (physical kpc): 12.311511040223106\n" ] } ], "source": [ "print(\"Stream length (radians):\", sdf.length(ang=True))\n", "print(\"Stream length (physical kpc):\", sdf.length(phys=True))" ] }, { "cell_type": "markdown", "id": "a11", "metadata": { "papermill": { "duration": 0.003829, "end_time": "2026-06-30T01:24:37.308455+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.304626+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Sample from the stream\n", "\n", "We can draw random samples of stars from the stream distribution function." ] }, { "cell_type": "code", "execution_count": 9, "id": "a12", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:37.317115Z", "iopub.status.busy": "2026-06-30T01:24:37.316905Z", "iopub.status.idle": "2026-06-30T01:24:37.927004Z", "shell.execute_reply": "2026-06-30T01:24:37.925937Z" }, "papermill": { "duration": 0.615417, "end_time": "2026-06-30T01:24:37.927719+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.312302+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", "RvR = sdf.sample(n=1000)\n", "plt.figure(figsize=(8, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(RvR[0] * 8.0, RvR[3] * 8.0, \"k.\", ms=2)\n", "plt.xlabel(r\"$R\\,(\\mathrm{kpc})$\")\n", "plt.ylabel(r\"$Z\\,(\\mathrm{kpc})$\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(RvR[0] * 8.0, RvR[1] * 220.0, \"k.\", ms=2)\n", "plt.xlabel(r\"$R\\,(\\mathrm{kpc})$\")\n", "plt.ylabel(r\"$v_R\\,(\\mathrm{km s}^{-1})$\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "a13", "metadata": { "papermill": { "duration": 0.003765, "end_time": "2026-06-30T01:24:37.935547+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.931782+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Predict observables with callMarg\n", "\n", "`streamdf` can also compute marginalized predictions for observables.\n", "For example, the predicted distribution of distance at a given angle\n", "along the stream, marginalizing over all other phase-space dimensions.\n", "Dimensions set to `None` are marginalized over.\n", "\n", "For plotting these marginalized distributions, it is useful to start with\n", "a Gaussian approximation to the result, which can be obtained using the `gaussianApprox` method. This gives us a mean and covariance for the distribution of observables at each point along the stream, which we can use to set the range and scale of our plots. We can then use `callMarg` to compute the actual marginalized distribution and compare it to the Gaussian approximation:" ] }, { "cell_type": "code", "execution_count": 10, "id": "a14", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:24:37.944977Z", "iopub.status.busy": "2026-06-30T01:24:37.944757Z", "iopub.status.idle": "2026-06-30T01:25:03.113315Z", "shell.execute_reply": "2026-06-30T01:25:03.112260Z" }, "papermill": { "duration": 25.174278, "end_time": "2026-06-30T01:25:03.113981+00:00", "exception": false, "start_time": "2026-06-30T01:24:37.939703+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "meanp, varp = sdf.gaussApprox([None, None, 2.0 / 8.0, None, None, None])\n", "xs = numpy.linspace(\n", " meanp[0] - 3 * numpy.sqrt(varp[0, 0]), meanp[0] + 3 * numpy.sqrt(varp[0, 0]), 51\n", ")\n", "logps = numpy.array([sdf.callMarg([x, None, 2.0 / 8.0, None, None, None]) for x in xs])\n", "ps = numpy.exp(logps)\n", "ps /= numpy.sum(ps) * (xs[1] - xs[0]) * 8.0\n", "plt.plot(xs * 8.0, ps, label=\"Marginalized distribution\")\n", "plt.plot(\n", " xs * 8.0,\n", " 1.0\n", " / numpy.sqrt(2.0 * numpy.pi)\n", " / numpy.sqrt(varp[0, 0])\n", " / 8.0\n", " * numpy.exp(-0.5 * (xs - meanp[0]) ** 2.0 / varp[0, 0]),\n", " label=\"Gaussian approximation\",\n", ")\n", "plt.xlabel(r\"$X\\,(\\mathrm{kpc})$\")\n", "plt.ylabel(r\"$p(X)$\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "4ffd107c", "metadata": { "papermill": { "duration": 0.00399, "end_time": "2026-06-30T01:25:03.122413+00:00", "exception": false, "start_time": "2026-06-30T01:25:03.118423+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Checking track accuracy\n", "\n", "To verify that the stream track is calculated accurately, use\n", "`plotCompareTrackAAModel` (the track in frequency-angle space should\n", "match the points calculated from the track's phase-space positions).\n", "Also check the eigenvalue ratio and misalignment:" ] }, { "cell_type": "code", "execution_count": 11, "id": "30c1fcc5", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:25:03.131937Z", "iopub.status.busy": "2026-06-30T01:25:03.131542Z", "iopub.status.idle": "2026-06-30T01:25:04.122470Z", "shell.execute_reply": "2026-06-30T01:25:04.121327Z" }, "papermill": { "duration": 0.996668, "end_time": "2026-06-30T01:25:04.123180+00:00", "exception": false, "start_time": "2026-06-30T01:25:03.126512+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Frequency eigenvalue ratio (isotropic): 34.449740915155836\n", "Frequency eigenvalue ratio (model): 29.625569108953943\n", "Misalignment (rad): -0.008644139914229854\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Eigenvalue ratio: a large value means a ~1D stream will form\n", "print(\"Frequency eigenvalue ratio (isotropic):\", sdf.freqEigvalRatio(isotropic=True))\n", "print(\"Frequency eigenvalue ratio (model):\", sdf.freqEigvalRatio())\n", "\n", "# Misalignment between progenitor frequency vector and mean stream frequency\n", "print(\"Misalignment (rad):\", sdf.misalignment())\n", "\n", "sdf.plotCompareTrackAAModel()" ] }, { "cell_type": "markdown", "id": "0444d5e2", "metadata": { "papermill": { "duration": 0.004568, "end_time": "2026-06-30T01:25:04.133290+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.128722+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Mock stream data in observable coordinates\n", "\n", "We can generate mock data directly in Galactic coordinates (l, b, distance,\n", "proper motions, line-of-sight velocity):" ] }, { "cell_type": "code", "execution_count": 12, "id": "47a2ac43", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:25:04.142900Z", "iopub.status.busy": "2026-06-30T01:25:04.142698Z", "iopub.status.idle": "2026-06-30T01:25:04.550845Z", "shell.execute_reply": "2026-06-30T01:25:04.549870Z" }, "papermill": { "duration": 0.414017, "end_time": "2026-06-30T01:25:04.551572+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.137555+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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CYrEgNzdXzrhNRM4xoCAi8hPSHVSz2eztqhAFHGkp5nbt2gEAwsLC5HkVRqMRaWlpCAkJQVpampdrSuR7vBpQVFdXY8WKFRg1ahS6dOnitJF0pYwzOTk5GDJkCBITEzF+/Hjs2bPH09UnImpTTGZH1PoWLVoErVaL22+/HTExMdBoNIiPj8fy5cths9mQm5vr7SoS+RyvBhQZGRn45JNP8MADD+D48eOorq52q0xDq1atwvTp0zFz5kysXbsWHTt2xKhRo3DixInW+BhERG2CyeyIWp/0d2Y2m2G1WhEVFYUdO3bIr4eHh3PFJ6IGvBpQPP/881i5ciVGjhzZojINPfvss5g2bRpmzJiBAQMG4I033oBSqUR2drYnqk1E1Oa4dCVR25J6BIUQsNlsAOqGQVVUVCAjI4N/k0T1eDWgUCov/PaulKmvrKwMO3fuxA033CBvCwkJwZgxY/D99983u45ERL7AaDTCYrHAaDR6uypEQUHqqSgsLJS3RUZGyv/m3yTR/wTcpOwjR44AADp37uywvXPnzjh69GiT+1VVVaGsrMzhQUTkKzh/gsg7kpKS5P9mZmZCo9EAAHQ6Hf8mif6/gMtDIeXpCwlx/GghISFyl6UzCxcuxIIFC1q1bkRE7tLr9Zw7QeQFW7ZscXgu9Uzk5eUBqJvrCYB/nxTUAq6HIj4+HgBw8uRJh+3FxcXo1KlTk/vNnz8fpaWl8qOoqKhV60lERET+R+otBACr1Qqr1YqMjAx5PgXnVlAwCsiAIjExET/88IPD9o0bN+Lqq69ucr/w8HBER0c7PIiIiIjqk+ZWZGZmQq1WQ6FQoLKyEhaLBenp6cjIyODcCgo6ARFQzJ07F6NGjZKfp6enY+nSpdi2bRtsNhteeuklHD58GA888ID3KklEREQBQ6/XIz4+HkIIREREQKFQwGazoby8XJ5bwd4KChZeDShWrlyJLl26YNCgQQCASZMmoUuXLnjxxRebVaa0tNRhiNMjjzyCmTNnYuTIkYiMjMTLL7+MVatW4dJLL22jT0ZERESBThr+lJmZKW+rra1FQUEBgLobnOytoGCgENIsZi84d+4cSktLG22PjIyUl2ZzpUxZWRlqamoQFxfnUKa2thbl5eWIjY2FQqFoVt3KysoQExOD0tJSDn8iIq8xmUwwGo0wGAxtNumT1786PA/UHO3bt0dFRQUUCgWmTJmClStXwm63AwBSU1ORk5Pj5RoSua651z+vBhS+jA0JEfmCxMREWCwWaLVa+a5na+P1rw7PAzWHyWRCeno6bDYblEqlHEwAgEajQUlJiRdrR9Q8zb3+BcQcCiKiQMX8E0T+Qa/XIysrC1qtFhEREU7LcE4FBSr2UDSBd6aIKFjx+leH54HclZaWhuXLlwMAVCoVsrKyoNfrvdLjSOQO9lAQEREReZHZbAbgGEyYTCYUFxdDqVRCp9N5uYZEnsWAgoiIiMiDpKGKUjAB1GXYrqiogN1ulwMOokDBgIKIiIjIg6Tkd/VXZtPpdPKKk8XFxZxHQQGFAQURERFRKzObzZCmrVZUVCAjI8PLNSLyHAYURERERK3MYDBAo9E0Oy8WkT9gQEFERETUyvR6PUpKSrB48eJG2bWJ/F2ItytAREREFCz0en2bZb0naivsoSAiIiLyAWlpaQgJCUFaWpq3q0LULAwoiIiIiLykfvbs3Nxc2Gw25ObmertaRM3CgIKIyAfV/5FBRIErIyMDFosFGRkZSElJgUqlwsCBA/n3T36FAQURkQ8yGo2wWCwwGo3ergoRtYHy8nLk5uYiJSUFxcXF/Psnv8KAgojIh0g9EzqdDlqtFgaDwdtVIqJWlJmZCa1WC5vNBpvNhuXLl/Pvn/wOAwoiIh8i9UyYzeZGmXaJKPBIWbUnT54sb8vLy0NBQQG+//57TtImv8CAgojIR6SlpaGwsBBqtZp3JomCTE5ODjQajfzcZDJh+fLlcq9FXFwc0tLSOLeCfJJCSHngyUFZWRliYmJQWlqK6Ohob1eHiIJASEgIbDYbVCoVamtrvVYPXv/q8DxQWzOZTDAajTAYDHJvZX0qlQo2mw1arRYFBQXeqSQFheZe/9hDQUTkI6QVXlJSUrxdFb/x5ZdfYsqUKXjvvfcavXbgwAE8/vjjmD59OhYtWoSzZ896oYZErpOGP+n1ehgMBmg0GqjVaoSGhkKpVCIhIQEqlQo6nc7bVSVywICCiMhH5OTkoLa2Fjk5Od6uil/4888/cf/99+Prr7/G9u3bHV7Lz8/HwIEDcfToUQwePBjLli3DyJEjUV1d7aXaEjWPXq9HVFQUKioqYLfbYbfbUVhYCJvNBrPZ7O3qETlgQEFERH7Hbrfjrrvuwrx589CtW7dGrxsMBowYMQLvv/8+5syZg/Xr12Pv3r14++23vVBbIvcYDAZotVoMHDhQ3qZUKmEwGJirhnwKAwoiIh9gMpkQFxeHuLg4/kBwQWZmJiIiIpCent7otaqqKnz11Ve488475W0dO3bEddddh7Vr17ZlNYlaRBoCVVxcLG+LjY2FXq9nrhryKQwoiIh8gNFohNVqhdVq5Q+EC/jxxx+RnZ3dZG9DYWEhamtr0bNnT4ftWq0Whw4davK4VVVVKCsrc3gQ+QKDwQC1Wg2FQoHy8nLExcUxVwX5FAYUREQ+QJqAqdFo+APhPE6dOoW0tDQsWbIEnTt3dlqmsrISABAZGemwPTIyUn7NmYULFyImJkZ+9OjRw3MVJ2oBvV6P+Ph4CCFQU1MDq9XKXDXkUxhQEBH5AL1ej5KSEpSUlPAHwnksX74cpaWlWLZsGaZMmYIpU6bAYrFg3bp1mDJlCux2O2JiYgAAVqvVYd+SkhLExsY2eez58+ejtLRUfhQVFbXmRyFqlvqrPtW/8cC5FOQLQrxdASIiIlfdcMMNDsm/AGDTpk3o06cPJk6cCIVCgR49eiA2NhZ79uzBzTffLJfbvXs3Lr/88iaPHR4ejvDw8FarO1FL6PV6h5sN0ryr06dPw263IyMjQ85hwZsS1NZ8IqA4d+4cjh8/ji5duiAiIsJpmcrKSpw+fRqdOnWCUnn+jpWSkhKUl5c7bAsLC3O6EggREfmPiy++GBdffLHDNqPRiL59+2LKlCnytrS0NLz55pvQ6/WIjo7GDz/8gJ9//hnPPfdcW1eZqFVI864kp06dcpiDxeCC2pJXhzz9/vvvePjhh6HVatGrVy9s2rSpURm73Y6//e1viI2NxSWXXIJu3bph1apV5z1uRkYGBgwYgFGjRsmPe++9t7U+BhGR2zhcoXVkZmaiQ4cO6N+/P8aOHYsbb7wR8+bNw5gxY7xdNSKPkIZASTdZhRBy0rvZs2fDYrEgIyPDy7WkYOHVgGLNmjXQarX46quvmizzr3/9C8uWLcPWrVtx+vRpPP3000hNTcUvv/xy3mPfdNNNKCgokB95eXmerj4RUYtx6ceWe/755zFt2jSHbbGxsTCbzcjNzcWsWbOQn5+P559/3ks1JPI8ad7Va6+9Ji/okJKSgtzcXAghANTNI+LNCmoLXg0oHn74Yfz9739Hhw4dmiyzePFizJgxA5dddhkUCgVmz56NxMREvPHGGxc8/okTJ3Du3DlPVpmIyKOkxFVc2cl9ycnJDom/JEqlEjqdDrfddhsuuugiL9SMqPXVX9DBbDbDZrM5vM6bFdQWfHqVpxMnTqCwsBA6nc5h+zXXXIMtW7acd9+PP/4Yl156KWJiYnD11VdfsDwRkTdIias4zpmI3FF/2KR0gyIpKQkKhQJqtZo3K6hN+HRAIWWGjIuLc9jesWNHh6yRDQ0ZMgQ7d+6Uk0T169cPycnJ+PPPP5vchwmNiMgbOIeCiFqi/rBJ6QbFli1bsHjxYsTHx3u7ehQkfDqgkCYa1dbWOmyvqamBSqVqcr97771XXhowMjISS5YsQXV1NT766KMm92FCIyLyBs6hIKKWaGrYJK8t1JZ8OqDo3r07AODYsWMO248dO4aEhASXjxMREYGuXbuioKCgyTJMaERE3sA5FETUEk0Nm5RWgSouLkZcXBzS0tLYG0qtxqcDiqioKAwaNMhhhaaamhp89dVXuPbaa+VtJSUlOHr0qPzcbrc7HOfo0aOwWCzo06dPk+8VHh6O6OhohwcRUWvjHAoiai2lpaWoqKiA1WrF8uXLuZQstRq3EttZLBZs3LgRhw8fBgD06NEDI0aMQM+ePZt1nDNnzuDkyZNyD8SxY8dQUFCA2NhYxMbGAgCefvpp3HHHHbjqqqswbNgwLFq0CCqVCrNmzZKP8/jjj2PTpk3Ys2cPqqqqMHLkSMydOxcDBgxAYWEhMjIy0LNnT9x9993ufFwiIiIiv2I0Ghut+ATUJQpOTExk0jvyqGb1UKxatQo6nQ6JiYmYNWsWXn/9dbz++ut48MEHodVqMXz48PPOU2joiy++wKhRozBlyhS5y3/UqFF455135DITJkzAihUrsHLlSqSmpqKqqgrff/89OnbsKJfp2LGjPAQqPDwcS5cuxeeff44pU6Zg4cKFuOmmm7Bt2zZERUU15+MSERER+aWGK2R26NBBnn/KuRXkaQohZT+5gJEjR+LEiRO47777MG7cOPTr1w8KhQJAXXbGX3/9FZ9//jnefvttdO7cGd99912rVry1lZWVISYmBqWlpRz+REQeZzKZYDQaffIuIa9/dXgeyJ8lJibCYrE4fU2tVmPRokU+d+0h39Hc65/LAcX777+Pu+66S155qSl2ux3Lli3D1KlTXauxj2JDQkStSWrstVrteReM8AZe/+rwPJA/k25a6HQ65ObmOgx/UqlUjVbQJKqvudc/l4c8TZ069YLBBFC31Ku/BxNERK2NqzsRUWuSFnzIyclBVlYWNBoNQkNDoVQqkZCQgJCQEKSlpXm7mhQgXO6haKikpKRRwjln2/wV70wRUbDi9a8OzwMFEqlXVKVSwW63Q/r5p9FokJmZyeFP5KDVeijqW7JkCZ544olG25944gm88cYb7hySiChoMDs2EbU1g8EAlUoFm82G+veSrVYrl5KlFnOrh6JPnz7YsGEDevXq5bD9999/x80334zffvvNYxX0Ft6ZIqLW4svzJwBe/yQ8DxRoTCYT5syZ0yhfl0ajQUlJiZdqRb6oTXoojh496vTgMTExKCwsdOeQRERBg/MniMgb9Hq9nOdLIq3YyUza1BJuBRRXXHEF3nvvvUbb3333XVx22WUtrhQRUSBjdmwi8pbMzExoNBqo1Wqo1WoAdcOeVq5cyfwU5Da3MmU//fTTmDhxIrZs2YKRI0dCCIHvv/8eH374IT777DNP15GIiIiIPECv18s3M+Li4lBRUQGgbinZ2NhYlJeXw2Qy8YYHNYtbAcUtt9yCzz//HM899xwee+wxKBQKDBw4EP/9738xduxYT9eRiIiIiFpRaGgoSktLYbPZkJ6eDgAMKshlbi8bG+g4GY+IghWvf3V4HijQmUwmzJ07F+fOnUPDn4OcqB3c2mRStuTAgQNYvXo1Vq9ejQMHDrTkUERERETUhvR6PeLj4xsFExIucU2uciugKC4uxrhx49C3b1/cfvvtuP3229G3b1/ceuutOHnypKfrSEREREStwGAwOEzSVqlUAIDy8nJkZGRwoja5xK2AYubMmSguLsaWLVtQWVmJyspKbNmyBcePH8cDDzzg6ToSEfk93ukjIl+k1+tRUlKCs2fP4uzZs/L2mpoaAOAS1+QSt+ZQqNVq7N69G3369HHYfvDgQVxxxRXyigH+jGNniciTfD2ZXX28/tXheaBglJaWhhUrVgAApkyZgpycHC/XiLyhTeZQdOrUCe3bt2+0PTIyEp07d3bnkEREAU0aViAtyUhE5ItycnLQoUMHCCGwYsUKxMXFwWQysZeVzsutgCItLQ0PPfQQrFarvM1qteKhhx5CamqqxypHROTP6jfAer0eUVFRsFqtHI9MRH5BCCFfs4xGI+dTUJPcCijWr1+PVatWoVu3bhgwYAD69++Pbt26YdWqVVi/fj2GDh0qP4iIglXDBthgMHA8MhH5vIbZtMvLy6HT6Xj9oia5NYfi2Wefdbnsk08+2dzD+wSOnSWiljKZTDAajTAYDH6VIIrXvzo8D0T/m/+lUqkwcOBA7NixAykpKZxbEeCae/1zK6Cw2+1QKp13bpw5cwaRkZHNPaTPYUNCRMGK1786PA9EdTdG0tPTYbPZ5G0qlQq1tbVerBW1tjaZlC2lZG/ozJkzuOmmm9w5JBFRQOOERiLyR3q9HllZWQ7bBg4cyOsZOXAroPjiiy/w1FNPOWwrLy/HjTfe6BDBEhFRHU5oJCJ/pdfrkZqaCoVCAQDYtWsXLBYLMjIyvFwz8hVuT8p+44038MorrwD4XzAhhEBeXp5HK0hEFAg4IZuI/JXJZILZbIY0Sr66uhoAUFlZyZ4KAuDmHAoAyM/Px+jRo/Hcc8/hgw8+gEKhwLp16xAVFeXpOnoFx84SUbBqretfSUkJdu/ejVOnTiEmJgYDBgzw6dxFbAeI6kgTs+vTaDQA6tIG+EPCTmqeNplDAQBXXnklPvvsMzzyyCNQKpX44osvAiaYICIiz6itrcW7776LYcOGoVOnThg9ejQmTZqEMWPGoEuXLhg0aBBMJhMqKyu9XVUiaoLUw5qUlOSwvbS0FADg5r1pCiAu91A0lVPi4MGD6Nq1q0Pm7E2bNnmmdl7EO1NE1BL+umQs4Lnr344dO3DXXXcBAO666y5ce+21uPTSSxETE4Py8nIcOHAA33//PZYvX45Tp07hnXfewbXXXuupj9FibAeIGjOZTJg7dy4qKioctmdnZ/vdtY6a1mrLxgZD7on62JAQUUtIQwT8cSiAp65/q1evhlKpxLhx4y5Y9rvvvsPhw4flAMQXsB0gci4kJKTRIjwajQZRUVF+eROFGmuTPBSetnv3bvz222+49tprER8f3+h1IQS2bt2K48eP47LLLkNiYuIFj+nOPvWxISGilmAPhf/jeSBybvDgwdi6dSuUSiXsdjsUCgU6dOjA+RQBpNXmUHz00UculRNCuFz2m2++wfDhwzFx4kTceeed+OWXXxqVKSsrw4gRI3Drrbdi0aJFGDBgwAV7QNzZh4jIk/R6PQwGA4xGI1dAIaKAUlxcDOB/cyfatWuHzMxMrmQXxFwOKF544QUMGjQIS5YswdGjRxu9XlhYiKysLAwcOBAvvPCCS8c8deoUFi5ciO+++67JMk8++SSOHz+OvXv34ptvvsF///tfZGZm4uuvv/boPkREnsbcE//zxhtvIDEx0emjd+/eGDhwIGbPno3CwkJvV5WILkCapN2uXTsAQEREhMPrTOQZfFwOKDZt2oS///3vWLx4MRISEtC1a1dceeWV+Mtf/oLOnTtDq9Vi6dKlmDt3rsuTsidNmoQRI0Y0+boQAh988AHuv/9+xMbGAgCuvfZaDB48GB988IHH9iEiag06nQ4qlQo6nc7bVfE6nU4HjUaD0NBQTJs2DfPnz8eMGTMQFRUFhUKB1NRUbNu2DaNHj8bZs2e9XV0iOg+9Xo+CggIsWrQIGo0GlZWVmD17NiwWC+bMmYOMjAzeTAkyIa4WVCgUmDp1KqZOnYpff/0VP/74I4qKiqBQKNC9e3cMHz4c/fr182jlDh8+jFOnTuGKK65w2H7FFVcgPz/fY/sAQFVVFaqqquTnZWVlbtebiAgA8vLyYLPZmPATQE1NDc6dO4f8/HyHVQEff/xxjBgxAldeeSXmzp2LIUOG4OOPP8bUqVO9WFsicoVer0dGRobDik92ux0AOPwpyLgcUNTXv39/9O/f39N1aURa37hDhw4O2+Pi4nD69GmP7QMACxcuxIIFC9yvLBERNWnr1q0YOXKkQzABAKGhoRg7dix+/vlnjB07FjfddBN+//13L9WSiDzh9OnTSE5O9rsFKch9bie2awvh4eEA0Git4zNnzjQar9eSfQBg/vz5KC0tlR9FRUUtqToRBTlp7LBGo0FmZqaXa+N97dq1ww8//NAogV1tbS2+/vprqNVqAMDx48fRq1evCx5v27ZtWLhwITIyMpCTk4Pq6upGZf7880/861//wqOPPop3330XNTU1nvkwRCTLzMyESqUCAKhUKnnlp9zcXM6lCCI+HVD06NEDISEhjSbpFRYWonfv3h7bB6gLRKKjox0eRETuMhqNsFqtiIqK4l06ABMmTEB1dTWuuuoqGI1GvPfee3jxxRcxdOhQ/P7777jrrrtw+PBhbNq0Cbfddtt5j/X3v/8df/vb31BZWYmIiAg8++yzuOqqq+QeagDYv38/Lr/8cnzzzTeIiopCZmYmxo4d22jtfCJqGb1ej6ysLGi1WmRlZWHQoEEAgIEDB3JhimAifEBRUZEAIL755ptGr91www3i5ptvlp+fPHlStGvXTixevFjetnXrVrF+/fpm7XMhpaWlAoAoLS1t5qchomCVnZ0tNBqN0Gg0IjU1VWi1WpGdne3tajVba13/iouLxaOPPir69+8vYmNjxSWXXCJmzZolDh8+LIQQora2VtTU1FzwOPv373d4XlJSIlQqlVi2bJm8beLEieLaa68VdrtdCFHXzoSFhYl3333X5fqyHSBqPq1WKwDI1z9/vQ4Gu+Ze/7ya2M5isWDLli2wWq148MEH8cwzz2DAgAEOczS2b9+OESNGICUlBcOGDcMbb7yBmpoabN68WR7eNGPGDGzatAl79uxxeZ8LYUIjImouKTs2AL9O7uRv1z+LxYJevXph3bp1SE5ORk1NDaKiovDqq6/igQcekMslJycjMjLS5VxJ/nYeiHyBlNQzPj4eO3bsQEpKCkaOHOm3iT6DVasltnPGZrO1aK7BH3/8gRUrVmD9+vW4/fbbsXv3bqxYsUIODABg0KBB2LZtGzp06IDvvvsOt99+OzZu3OgQGCQlJWHs2LHN2oeIyNMMBgM0Gg00Gg1XN2nC559/jieeeEL+UX/48GHs3Lmz2cfZu3cv0tPTcc899+CGG27A888/j+TkZAB1Q1yrqqoazcXo3bs3Dhw40OQxq6qqUFZW5vAgouaRlpTdvn07bDYbVq5cKQ99Sk9P53yKAOXWKk8VFRV45JFH8M4776CqqkrOlDh16lTMmzcPl19+uUvHGTVqFEaNGnXBcpdeeileeumlJl93Fu1eaB8iotYQFRXFu3BNuPfee7FmzRrExcWhuroat99+O9q1a4c777wT27dvR2RkpMvHat++PS699FKcPHkSP//8M7766ivo9XpERUXh3LlzAOr+X9QXHR3daMGO+rjaH5HnREREoKKiAiqVSs6sbbPZYDQaeX0MQG71UDz11FPYuXMn1q9f77D9jjvuwDPPPOOJehER+R1OQGza5s2bsWHDBvz2228Ow5Di4uKg0+mwcuXKZh2vZ8+eSE9PxzPPPIOff/4Z+fn5ePnllwFADkwaLhV+6tSp83bdc7U/Is9ZtGgRtFotQkND5UBeoVCw9zZAuRVQfPjhh3jvvfcwcuRIh+3XXHMNvvzyS49UjIjI3zAzdtPy8/Nxyy23IC4uDgqFwuG1Xr16tSj3RHR0NC655BLs378fQF2wERkZib179zqU27t373lzKHG1PyLPkYY+1V+y34vTdqmVuRVQnDhxAt26dQMAh4ahpqaGS/IRUdD67LPPYLPZ8Nlnn3m7Kj4nPDwcVqvV6Wu7du1Cp06dXDpOdXU1vvvuO4dtBw8exPbt23HVVVcBAJRKJe68806888478vCn/Px8mM1mTJ48uQWfgoiaKzk52eG3IudRBCa3AorLLrsMGzZsAOAYUJhMJvmCTkQUbKSkbQ2Tt1Hdj4r169fj22+/ldsNm82GV155BWvWrMH48eNdOo5CoYDRaMTQoUNx3333YdKkSbjyyisxfvx4zJo1Sy5nNBpRU1ODq666Cmlpabjuuuswffp0l9+HiDzDbDZDCAGNRgOVSiXPo6DA4tak7AULFuCuu+5Ceno6AOC1117DF198gXXr1iEvL8+jFSQi8heTJ09Gbm4uUlJSvF0Vn9O1a1e8/vrruPnmm6FSqRAWFobs7GxUV1dj8eLF6NOnj0vHCQ0Nxbp167Br1y7s2LED7du3xwsvvICLLrrIoVynTp2wY8cO5OXl4fjx4/jrX/+KoUOHtsZHI6LzMBgM8pKxb775JrZu3Yr4+HhvV4s8zO08FF999RWee+45bN26FXa7HYMGDcLTTz+NMWPGeLqOXsH1x4koWLXm9e/48eNYs2YNjhw5gri4ONxyyy2Nlnf1FWwHiDwrJCQENpsNKpUKtbW13q4OnUdzr39eTWzny9iQEJGrpEROgbJcLK9/dXgeiDxr8ODB2Lp1K3r27AmFQgGdTgez2Rww185A0mYBRUlJCeLi4i64zV+xISGiC5ECifLyclitVr/Ojl2fp65/P/74I9atW+dS2eHDh+PGG290+71aA9sBIs9KTEyExWKBUqmE3W6XtwfKtTOQNPf659YciiVLlmD79u1YsmSJw/YnnngCSUlJmDlzpjuHJSLyK1LeCaVSyezYThw9ehSbNm2Snx84cACFhYXo1asXEhIScPz4cRw4cABdunRBz549vVhTImptJpMJ5eXl0Gg0KC0tdXiNS237P7dWeXrhhRecNpzz5s3Diy++2OJKERH5A4PBAIVCAbvd3iiJGgF33nknNmzYgA0bNiAnJwcAsG7dOhw6dAgbN27E/v378dNPPyE0NBTXXXedl2tLRK3JaDTCarUiKirKoXcCqFsJivybWwHF0aNHnXZ/xMTEoLCwsMWVIiLydSaTCRkZGfJzu93OpRDP49tvv8W1117baFjT0KFDMWXKFJeHRhGRfzIYDNBqtTAYDJgyZYq8XalUory8HCaTCSaTCYmJicxT4YfcCiiuuOIKvPfee422v/vuu7jssstaXCkiIl8n3W0TQkChUHDI0wWcPHkSp06dcvqa1WrFyZMn27hGRNSWpMzZer0eOTk5yM7OhlarRWxsLKxWK9LT05GRkQGLxcKbM37IrTkUTz/9NCZOnIgtW7Zg5MiREELg+++/x4cffsgMsUQUFHQ6HSwWCwDgqquuwpYtW7xcI982duxY/P3vf8eTTz6JBx98EN26dUNxcTE++OADvPvuu/jxxx+9XUUiakPSqk5z584FUJfo8syZM1CpVJxT4YfcXuUpLy8Pzz33HLZv3w6FQoGBAwciIyMDY8eO9XQdvYKrexDR+UirlQAIuDXVW+v6t2bNGvz1r391WM2la9euePHFF5GWluax9/EUtgNErSsuLg5Wq7XRdq765H1tssoTACQnJyM5Odnd3YmI/JbJZEJxcTEAQKFQMDO2i8aPH48bb7wRv/zyC44cOYIuXbpgwIABiIiI8HbViMhHSPkpyL8wsV0TeGeKiJpSv3ciNDQU1dXVXq6RZ/H6V4fngah1SYtbVFZWoqKiQt7OHgrva+71z61J2X/++SemTp2K3r17IzY2ttGDiCiQ1Z98XVNT48Wa+LZPPvkEn376qUtlv/zyS7z77rutWyEi8il6vR4lJSU4e/YskpKSADiu+kT+w60hT/fffz9OnjyJ+fPno0OHDp6uExGRzwsLC0N1dbXcCFJjffr0wT333AODwYCpU6di5MiR6Nu3L2JiYlBeXo4DBw7g+++/x7Jly1BZWYl33nnH21UmIi+pP4xUWvUJ+N/kbfJtbg15ioqKwr59+5CQkNAadfIJ7OomoqZIEwk1Gg1KSkq8XR2P8+T1z2azITc3F4sXL8ZPP/0Em80mv6ZQKJCUlIQHH3wQU6dORVhYWEur7lFsB4jajslkgtFohE6nQ25uLmw2G4c+eVGbTMqOj49HeHi4O7sSEVEQUalUSE1NRWpqKsrKyvDLL7/g1KlTiI6ORv/+/aHRaLxdRSLyAXq93qE3YuXKlSguLobJZGIvhR9waw7FPffcg3/+858Od5qIiIJFcnIylEolKisrOc63GaKjozFs2DDcfPPNGD58OIMJInIqLy8PdrsdFRUVSE9P53XWD7gVUHz++ed49dVX0a1bNwwZMgRDhw51eBARBTKz2Sw3dszoSkTUemw2G4xGI0wmExITExlc+Ci3hjxNnDgREydO9HBViIh8W/0xvuXl5QAcV3wiIqKWy8zMlK+1ZrMZBoMBRqMRFosFRqORQ6B8kFsBxZNPPunpehAR+byMjAxYrVaUl5cH5GRsIiJf0HA+hcRoNPImjo9yO1M2EREREVFbaCrIIN/gdkDxxx9/YM2aNSgsLERtba3Day+//HJL60VE5HOkbnjeIXNPbW0t1q5diz/++AOdOnXCddddhy5duni7WkTko6RhpgaDQQ4m0tLSkJubi5SUFOTk5Hi5hiRxK6DIy8vDpEmTMHDgQPz4448YM2YMdu3aheLiYowePdrTdcQvv/yCr776CqdPn8bQoUMxduzY85b/9NNPsWnTJodtXbp0wcMPP+zxuhER0YWdO3cOI0aMwO7du6HVavHnn3+isrISM2fOxKJFi9CuXTtvV5GIfIyzeRNSjorc3FwGFD7ErVWeMjIy8Oqrr+KHH34AAGzYsAGFhYW46667cMkll3i0gv/5z38wePBg7N69G+fOncPMmTNx3333nXefL774AmvXrkVsbKz8iIqK8mi9iCh4pKWlQaVSYfbs2XLjRs2zevVqlJSU4NChQ9i/fz/KysqwYcMG7N69G5MmTYIbOVaJKMAZDAZotVq5VzgtLU1OWTBw4EBvVo0acCtTtlqtxokTJxAZGYmQkBCcOXMGEREROHr0KAYOHIjjx497pHJlZWXo2LEjXn75ZcyePRsAcOTIEfTp0wdr1qzBDTfc4HQ/vV6PkydPYtWqVS16b2ZIJSIACAkJkRsxlUqFrKysgB7L2xrXvyVLlmDnzp1YvHixw/ba2loMGTIE8+fPxx133OGR9/IUtgNEvsFkMsmLYkiYRbt1Nff651YPxblz5xAZGQmgbijR77//DgBycOEphw4dQk1NjUNui4SEBPTs2fOCwUJBQQH+7//+D6+88gq2bdvmsToRUfBJSUmBUqmEWq0O+GDCk+rPr0tOTsaOHTsazbkLCQnBhAkTkJ+f38a1IyJ/0TCYUKvVnMvmY9wKKOq76aaboNfrsXTpUtx9990eTWzXp08fhIWF4bvvvpO3WSwWWCwW7Nu377z7hoeHo7KyEtu3b4dOp8Ojjz563vJVVVUoKytzeBARAUBOTg5sNhvOnj3LYKIZXnnlFSQkJOCWW27B0qVLERsbizvuuANFRUVyGSEEzGYz+vXr58WaEpG/0Gg0mDBhgpzsjnyDW0OeVqxYgSlTpgAATp06hb/+9a/46aefcOmll+I///kPevXq5bEKZmVlYe7cuZgwYQI6duyI9evXo3379ggLC8OWLVuc7nPw4EFcdNFF8vO8vDzceOON+OabbzBq1Cin+zzzzDNYsGBBo+3s6iYKXvUT2UnJlYIhoPDUUJ9jx47h66+/xo4dO5Cfn4/8/HycPHkSoaGhGDRoELp3745ffvkF3bp1w5o1a6BWqz34KVqOQ56IfIN0LS4vL4fVaoVSqYTdbodGo2FOoFbS3OufWwGFyWRqslE932vu2r9/PzZu3Ihz587h5ptvxsMPP4yqqirk5eW5fIzu3bvjgQcewNNPP+309aqqKlRVVcnPy8rK0KNHDzYkREEsMTERFotFfh4sjVdr/pA+fPgw8vPzHYKMP/74A4888ghefPFFj75XSzGgIPItzuZSqNVqREREIDMzMyhu+LSVNgkoFApFkytynO81T6ipqUHXrl2Rnp6OZ555xuX9unbtinvvvRfPPfecS+XZkBCRyWRCenq6PCGbAUXrvV95eTkSEhJa/b2ag+0Ake9peKNHwknantUmk7KbUlRUBI1G48lDYufOnbDb7fLzRYsWobq6GjNnzpS3ffzxx3Iyvdra2kY5KD766CMcO3YMY8aM8WjdiCjwxcTEIDQ0FEqlEsnJyd6uTkCKjo72uWCCiHyTwWCARqNBWFiYw/by8nLOqfCiZvVQXHnllQDqfuT/5S9/cXjNbrejoKAA48ePx7JlyzxWwbfeeguvvfYarrnmGvz222/4+eefsXz5ctx4441ymRkzZmDTpk3Ys2cPbDYbxowZA6VSiQEDBqCwsBB5eXl49NFH8eyzz7r8vrwzRUQN74QFyx0wXv/q8DwQ+a7612dpdEywXKPbQnOvf83KlH333XcDqAsopH9LQkNDkZiYiFtuuaU5h7yg++67D0OHDsU333yDIUOGYPny5Y16QW6//XYMGzYMQN0a8d9++y3MZjN27NiBYcOG4d///jd69+7t0XoRUeAzGAzykCeVSsVlComIfITBYEBGRgaAumWppYUzyDvcmkPxzjvvYPr06a1QHd/BO1NEwUtaUURqnKR/B8uEP17/6vA8EFGwapM5FBMmTMBbb70lP1++fDmSkpIwefLkoJiwSESBzWg0wmKxwGg0Qq/Xo6CgIGiCCSIif2EymZCYmIi0tDQkJiZyDoUXuRVQPP7441AoFACA4uJizJgxA6NHj8aJEycumECOiMjXGQwGaLVadp8TEfkw6ebP8uXL5ZtA5B1uBRSrV6/GrbfeCgBYt24dhg8fjn/961947733sG7dOo9WkIioLdUf7sReCSIi32UwGKBU1v2UVSgU0Ol07KnwErcCinPnzsm5Jr7++mvccMMNAIDY2FhUVFR4rnZERG2s/nAnIiLyXXq9HrGxsQCADh06wGw28/rtJW4FFEOGDMHcuXPx3nvvYdWqVRg3bhwAYOvWrRg8eLBHK0hE1JY43ImIyH9kZmZCq9UiMzMTOp0OSqUSxcXFnFfRxtxa5Wn//v24//77YbFYkJ6ejnnz5gEAbrzxRsybNw/XXXedxyva1ri6B1Hw4DAnR7z+1eF5IPIv9XNTqFQq2Gw25qZwU3Ovf24FFMGADQlR8JAaITY8dXj9q8PzQORfTCYTMjIyUFlZCQCIiIhAZmYmbxS5oU2WjSUiCiQGgwEajQbl5eXsHici8lN6vR6ZmZmoqqpCRUUFSktLvV2loOFyD8Vll10GANizZ4/876bs2bOn5TXzMt6ZIgou7KX4H3+4/m3btg1msxkhISG45pprcMUVVzQqU1paio8//hjHjx/H5Zdfjptvvlle8twV/nAeiMhRXFwcrFarw7bU1FTk5OR4qUb+qbnXvxBXDzxjxgyn/yYi8ncmkwnl5eUICwtDYWEh0tLS2Pj4KLvdjjFjxuDMmTMYNmwYKioq8Oijj+Jvf/sbnnvuOblcYWEhhg8fjoSEBCQlJeE///kPrr76anz88cfNCiqIyP/l5ubymt7KOIeiCbwzRRQ8wsLCUFNTIz9XqVSora31Yo28y5evf0IIfPfddxg1apS8bfXq1ZgwYQJ+/fVX9OvXD0DdHclDhw7hxx9/REhICPbv34/+/ftj+fLluPPOO116L18+D0TknLTIRnFxsUMqg7CwMLzyyiucT+EizqEgImqmhsFESkqKF2tD56NQKByCCaBuKXMA8lA1m82Gzz77DFOnTkVISF1HfN++fTFy5EisWrWqLatLRG1Mr9ejoKAAixYtgkqlkrdXV1dj9uzZiIuL41y5VuDykKeLLrrI5YMePHjQrcoQEbUlaUUQSWhoKKqrq71YI3LHihUrEBYWhkGDBgGoG+507tw5XHzxxQ7lLr74YmzevLnJ41RVVaGqqkp+XlZW1joVJqJWJ/VEzJo1S94mhIDVakV6erpDGWo5lwOK+kmefv/9d7z44ou4/fbb5UR2W7ZswUcffYRHH33U87UkImoFRqNRnrynVCrx6quverlG1FybN2+GwWDAggUL0LlzZwDAmTNnAAAxMTEOZWNjY+XXnFm4cCEWLFjQepUlojYlBQwZGRkOE7VtNhuMRiMDCg9ya1J2cnIy3nrrLUydOtWhzHvvvYdly5Z5rnZERK1Ip9PJSZDI/+Tn5+Pmm2/GzJkzHW56RUZGAkCjJSNPnz4tv+bM/Pnz8cgjj8jPy8rK0KNHDw/Xmojakl6vh16vl1d/UqvViI+Pd7hmUMu5NYdi8+bNmDBhQqPtEydOxM8//9ziShERtRaTyYTExESYTCaYzWZ5u91uh9Fo9GLNqDl27dqF66+/HqmpqY16lnr06IF27drhwIEDDtsPHDiASy65pMljhoeHIzo62uFBRIEhMzMTWq0WixYtQkFBAXsnPMytgKJdu3bYsGFDo+0bNmxAu3btWlwpIqLWYjQaYbFYYDQaYTAYoNVqkZqaCq1WyztWfmL37t0YM2YMpkyZgqysrEavh4SEYMKECXj//ffl1br279+P77//HrfffntbV5eIfIA0WZuBROtwechTfY8++ijuvvtuTJ8+HYMHD4YQAlu3bsU777zjsA44EZGvMRgMMBqN0Ol0yMjIQGVlJfLy8pCZmcmGxg9UVFRgzJgxUCqV6NixI5555hn5tVtvvVWemP3888/jmmuuwciRI5GUlISPP/4Y48ePd3nJWCIKTNKysjqdDmazGQaDgdd+D3A7D8Wnn36Kf//73/j1118BAP3798cjjzzidCiUP+L640SBy2QyYc6cObDb7fI2Zsj+H1++/lVUVOCFF15w+lr9gAKom0Px0UcfyZmyb7nlFmbKJgpyiYmJDnPn1Go1zp4968Ua+abmXv+Y2K4JbEiIApc0OQ+oy2vQoUMH9lDUw+tfHZ4HosDT8IaSUqmEzWbzcq18T3Ovf24NeSIi8meVlZXyv6dMmYKcnBwv1oaIiNpS/XvpkydP9mJNAgczZRNR0JBWeKofUOTm5jJrKhFRkDAajXJAkZqayhtKHsKAgoiChrTCU/25E1KCIyIiCnwGgwEqlQoAsGLFCqhUKqSlpXm5Vv6PAQURBQ2dTufwPCkpicvFEhEFEb1ej6ysLCgUCgghYLfbsXz5cgYVLcSAgoiChpTITqVSITs7G1u2bOG65EREQUav1zda8W3lypVy0lNqPgYURBTwpLkTOp0OWq0WWVlZDCKIiILY5MmToVAooFKpoFAoYLfbYbFYkJGR4e2q+SWfX+XJbrfj/fffR15eHk6fPo2hQ4fikUceQWRk5Hn327x5MxYvXiyvPz5v3jzEx8e3Ua2JyJdIcycAMNcEEREhJydHnpBdfylxco/P91DMnDkTTzzxBMaMGYMHH3wQP/74I8aMGYPa2tom9/nhhx8wYsQIxMfHY+bMmdi2bRuuueYaJi4hClLSzQQhBBITE5GWlsaubSIigslkwqlTpwDU5SXKzMz0co38k08ntjt+/Di6dOmCjz76CJMmTQJQlyW1a9euyMrKwtSpU53ud+2116JTp0748MMPAQBnzpxB165d8c9//hMPP/ywS+/NhEZEgcFkMmHWrFlOX2N2bOd4/avD80AU+Or3Tmg0GpSUlHi5Rr6hudc/n+6hOHHiBACgZ8+e8ja1Wo2OHTviiy++cLpPRUUFfvjhB9x6663ytsjISFx//fVYv35961aYiHxO/SVhk5KS5OUCVSoVV3ciIiLZ6dOnudqTm3w6oOjbty/i4+Px5ptvyklIvvrqK/zxxx9N3lU8fPgw7HY7EhISHLYnJCTIY6idqaqqQllZmcODiPyfTqeDSqVCUlISiouLkZKSwonZREQEAMjMzIRWq5UnZq9YsYJDYt3g05Oyw8PDsWLFCtxzzz1Yt24dNBoNKisrMXr0aJSXlzvdp7q6GgDQrl07h+1qtVp+zZmFCxdiwYIFnqs8EfkEs9kMm82GHTt2wGazAeDEbCIiqqPX66HX6xEWFoaamhoIIWCxWJCeni6/Thfm0z0UAHDdddfh0KFDWLt2LV5//XXs2rULCoUCXbt2dVq+Q4cOANBoDFxJSYn8mjPz589HaWmp/CgqKvLchyCiNiUtEzt48GAUFhZCrVbLPRMc5kRERA2FhoY6PLfZbA5DZun8fLqHQhIWFoYBAwYAqBvfZjab8fzzzzstm5CQgE6dOmH79u0YN26cvH3Lli0YNmxYk+8RHh6O8PBwz1aciLxCWiZWGuZYWVkpLw9IRETUUEREBCoqKuTnnGfXPD7fQ/Hpp5/KvQ3V1dWYM2cOunTpgnvvvVcu869//cvh+fTp07F06VIcP34cALBmzRrs3r0b06dPb9O6E5F3GAwGefI1UNdQEBERNUWaS5Gamuowz07q8eacivPz+R6K6OhoDB48GB07dkRBQQESExPx5ZdfOiS2++2337Blyxb5+TPPPIO9e/fioosuQq9evXDgwAG89NJL5+2hIKLA8f3330MIgdDQUERFRXFdcSIiOi9pLkVDUo+30WjkfIrz8PmA4rrrrsO+ffuwe/duxMbGok+fPo3KPPbYYw6rMrVr1w6rV6/GoUOHcPz4cVxyySXQaDRtWW0i8qLc3FzY7XbY7XZkZmayESAiomYxmUwwGo3Q6XQAwOFPF+DTie28iQmNiPyPyWRCRkYGysvLUVNTA4DJ69zB618dngei4JWYmAiLxSIv5jF37lxUVlZi8uTJQTEnL6AS2xERNYfRaITVakVNTQ0UCgUUCgWKi4s59pWIiJrFYDDIwYTRaERFRQXsdjtyc3O9XTWfxICCiAKGTqeTAwkhBIQQqKio4NJ/RETULHq9Xu7dLi4ulrcPHDjQSzXybT4/h4KIyFVmsxlCCHnOVGVlJSIiIjj2lYiI3CL1TkgOHTrkxdr4LvZQEFFAMJlMKC4uhlKpRHJyMkpKSnD27FmUlJRwUjYREbnFYDBwYR8XMKAgooBQf4yr2Wz2dnWIiCgA6PV6lJSUIDs7G1qtlsuQN4EBBREFBOkukkaj4RAnIiLyKGlOBXu8nWNAQUQBQ0pixws+ERF5kslkQlxcHOLi4rhyoBMMKIjIL5lMJiQmJsoX9vrZTImIiDxJWpbcarVi1qxZSEtL83aVfAoDCiLyS1IAMWfOHMTFxUGn08lrhhMREXlSw8nZK1ascLipFewYUBCRXzIYDFAqlbDb7bBarTCbzRzfSkRErUKanJ2UlAQACA0NhcViQXp6OoMKMKAgIj8mhAAAKBQK9kwQEVGrk5LcRUZGQqVSwWazcagtGFAQkZ8yGo1yQDFlyhT2TBARUaszGAzQarVITk5GTEwMVxb8/xhQEJHfkZLYSZh3goiI2oK0fGxeXp48SfvNN98M+hWgGFAQkd+RktgBdcOdysvLg/YiTkRE3rV161Y5uAjW4U8MKIjIr5hMJpSXl0OhUMjbgvkiTkREbc9ZxuxgHv4U4u0KEBE1R0ZGBqxWK9RqNeLj46HT6WA2m4P2Ik5ERN6hUCjkuXw9e/Z0uNEVbNhDQUQ+r2ESOwCIiIhAQUEBcnJyuFwsERG1qfoLgwDAkSNHYLFYkJGREZT5KRhQEJHPk5LYzZ49G1arFWFhYQAQdBdsIiLyDVKiO7VaDY1Gg5SUFGi1WgCAxWIJumG4DCiIyOcZDAaoVCr5blB1dTXnTRARkdfo9XpkZmYiIiICADBy5EgUFBQgOTkZSqUSxcXFQXXTiwEFEfk8vV6PlJQU+blKpQrqyW9EROR9RqNRXt1JyphtNptht9tRUVERVDe9GFAQkU+qP2/CZDIhNzdXfs1msyEqKorzJoiIyGukYU9KpVLOmC31pCuVyqC66aUQ9WeUkKysrAwxMTEoLS1FdHS0t6tDFHQSExNhsVgcxqRKlEolXnvtNQYUrYTXvzo8D0TkCpPJBKPRCIPBgFmzZsnb/fkndnOvf+yhICKfZDAYoNVqYTAY5H+npqZCq9UymCAIIbBhwwZkZWXhyJEjTstUVVVhzZo1WLp0KTZv3tzGNSSiYCFlz9br9UhKSgIA+b/OVikMROyhaALvTBH5lvp3gBhMtC5fv/599tlneOyxx9ChQwf8/PPP+OabbzBq1CiHMidOnJC3/eUvf0FeXh4mTZqEpUuXuvw+vn4eiMi3mUwmpKenw2azQavVoqCgwNtVcllzr39MbEdEPk0KJMrLy+WVnRhQBLf27dtj7dq1aNeuHXr06OG0jMFgQGhoKDZt2oR27dohPz8fV111FSZMmIDx48e3cY2JKBgZjUbYbDaoVKqAn0/BIU9E5JOkbuKMjAx5/oQ0BIqC2/XXX4+LL764ydftdjtWrVqF6dOno127dgCAK6+8EjqdDitXrmyrahJRkJOG62ZlZQX8jTCfDyjKysrw8MMPo2/fvoiPj8dVV12FN95447z7PPzww4iMjHR4XH311W1UYyLyBCmZHVAXSGRmZjIjNrmkqKgI5eXl6Nevn8P2fv364ddff21yv6qqKpSVlTk8iIjcVX9uRaDz+YDiwQcfxLp167Bs2TL8+uuvePjhhzF79myHJSQbqqysxA033IBjx47Jj++++64Na01ELSXd2UlOTvZ2VcjPlJeXAwBiY2Mdtnfo0OG8QcLChQsRExMjP5oaTkVE5AqTyYS4uDjExcUF/KRsnw8ofvrpJ6SmpmLw4MGIj4/H1KlT0b9/f/z000/n3U+lUjn0UEjd3kTkH6Q7O2azGRaLJagSBFHLSNd7KbCQlJWVQa1WN7nf/PnzUVpaKj+KiopatZ5EFNjqJ74L9DbM5wOK2267DWvWrMGRI0cghMDXX3+NQ4cO4dZbbz3vfhs2bECnTp1w8cUX47777sOff/7ZRjUmopZouMRe/eVjiVzRs2dPhIWF4Y8//nDYfujQofPOvQgPD0d0dLTDg4jIXVLiO41GE/BtmM8HFIsWLULfvn3RvXt3hIWF4aabbkJWVhZGjx7d5D49evRAdnY28vPzkZOTg99//x3Dhw/HmTNnmtyHY2eJ2p6z9bmlSdgZGRkAgmsMKnlGaGgobrrpJuTk5MiJpQ4fPoxvv/32gjejiIg8Ra/XIzMzE1FRUQACOyeFz+ehmDFjBn788Ue89dZb6NOnD9avX48HHngAK1eudHnpv5MnTyIhIQGvvfYaZsyY4bTMM888gwULFjTazvXHiVpPXFwcrFYrACAsLAw1NTXyD0CFQoHFixczkPACX8+/sG/fPmzYsAGnT5/GU089hb/+9a+4+OKLcfXVV8sLcPz222/Q6XQYOnQohgwZgg8++AAJCQn48ssvERLi2orpvn4eiMj3JSYmwmKxQKvVAoD8b1/PSRFQmbKtVivefPNNLFiwAMOGDUOnTp1w9913Y+LEiXjxxRddPk7Hjh3Rs2dP7N+/v8kyHDtL1LbS0tLkYAIAqqurUf/+hhAi4MeckntKS0uxb98+HDt2DHPmzIHNZsO+fftw8uRJucwll1yCPXv24Nprr0VpaSmeeOIJrF+/3uVggojIE+oP25WGQJWXlwdcL4VfXFnDwsIaPW9Ox8qZM2dw5MgRdOrUqcky4eHhCA8Pd7uORNQ8Ta3UFhoaitDQUERERAT8mFNyz5AhQzBkyJALluvatSvmzZvXBjUiInJNaWkpbDZbwCVp9ekeCo1GA51Oh+eeew4FBQWw2+3YsGEDPvzwQ4fhTunp6XI3d1VVFaZOnYpff/0VNpsNRUVFuPvuuxEeHo60tDRvfRQiaiAlJQUqlQqpqalITU2V/11dXY2zZ8+ipKQkoC62REQUfKScSkajMaAzZ/t0QAHU3cXs1asXBg4ciIiICEyfPh3z5s3D3Llz5TKVlZWoqKgAUNfTMG7cONx9991o3749/vKXv0AIgZ9++gndunXz1scgCmrOJqKNHDkS3bt3BwCYzWZkZWUhJyfHW1UkIiLyuIZDngI1c7bPT8qur7a21un416qqKtjt9ka5JqQo0B2cjEfkOfUnpUkT0aQJ2QqFAkIIqNVqxMfHw2AwBNyF1t/w+leH54GIglVATcpuqKnJdOHh4U4T17kbTBCR55hMJpSXlze5Drd0T6OyspIJ7IiIiPyQXwUUROR/pEyhUVFRcs+DNPRJqay7BKlUKkyePJkJ7IiIiPwQAwoialXSmFGdTofExERotVrMmjULVqsVsbGx8njSnJwcJrAjIqKgEUiJ7vxqDkVb4thZIs+S5lHUl52dzQDCB/H6V4fngYhak7P5hb4ioOdQEJF/MZlMiIuLQ/v27XH06FEolUooFApvV4uIiMirLjS/0N8woPAwk8mE9u3bQ6lUMu8FBb2MjAxYrVZUVFSgpqZGXo1NWjCBE7CJiCgYOZtf6M8YUHiY0WhERUUFhBAOmYClcXJpaWkO/w2EcXNEF9KwVyIrK4sTsImIKGjVz08RCDiHognujp01mUyYO3cuzp07hylTpsiJuhquuS/RaDQoKSlp8lhGo5Hr8pNfqf+9BSD/W+qtON93nnwD5w7U4XkgomDFORReptfrcfbsWdjt9iaz/p5vDHn9Gf/107UT+YO0tDTMmjVL/t7q9XrodDrMmTNHHiuamZnp7WoSERH5jIajWPxx9AoDijaQlpaGU6dOyb0T9XsoGv64qh9EBFp3GAW++sP8pGViV6xYAbvdjpqamoAZK0pEROQp0m+/3Nxcv72RzICiDeTm5kIIAYVCAa1WC7VaDaBuuFPDH1f1gwi9Xs91+ckvpKWlISQkBAkJCVCpVEhKSpIvjO3atYNSqYRarWZwTERE1IBOp4NKpcLAgQP99kYyA4o2kJKSImcCLigowKJFi6DVap0O/WAQQf4oNzcXNpsNR44cQW1tLQ4dOgSbzQalUolFixbBZrPh7Nmz/F4TERE1YDabYbPZUFxcDIPBAKPR6HfDnhhQtDKTyQSz2SxnAgbcDxoCKaMi+b/6Yz6lYXwJCQkOZWJjYxlEEBERnUf90SkZGRmwWCyYM2eOX/3eY0DRypo7sbph0NDUJO1AmMBD/k266C1fvhx2ux0AUFhYiLi4OPTu3RsqlQrJycleriUREZFvc3aj2W63+9VcCgYUrcyVidXS+PO0tLRGAYj0oy0jI8PhWA0n8KSnpzOooDZVWVnpdLvVasWOHTtgs9mQl5fHgJeIiMhFmZmZ0Gg0fpdBmwFFK3NleJM0/nzFihXy0prSCjlN/WgzGAzQaDQIDw+HQqGAzWbzq0iW/JfUO1ZVVSVvS01NRXZ2tnwRTElJgVarBQC/XbGCiIioren1epSUlMj5mvzlphwDCh8gTdpu166dnIbdbDbDYrEgIiJCnsBdv/dCr9cjKioKFRUV6NChg9+uCkD+R/oe2mw2AHV5VXJychwugjk5OSgoKEBmZia/m0RERC7y13xkDCh8QE5ODmpra7Fo0SJoNBoUFxejuLhYTgIm9XA0HD4lPa9fpiFO5CZPkb5LOp0OWq0WPXv2BABcddVVTe7DVcuIiIhc57f5yAQ5VVpaKgCI0tLSNn1frVYrAAgAQqvVXrB8dna20Gg0QqPRiOzsbHmbVquV/+vqsRruSyTJzs4WKpVKAJC/b0qlUn7O70xg8db1z9fwPBBRW/OV32HNvf4phKiXtplkZWVliImJQWlpKaKjo9vsfU0mEzIyMgDUTcy50J3dxMREWCwWAIBarUZERAROnToFIQQ0Go1cLjk5GWazWU6Yd6HjabVaFBQUtPwDkV+Tvo/Sd8oZKQM8vzOBw1vXP1/D80BEvkAa/nSh33Ce1NzrH4c8+Zj649Bd+dLodDr535WVlbBarRBCQKVSAahbcQeAy+nc/ap7jVqd0WiUv1NNkb5v/M4QERF5nj/MpWBA4efMZjMAyJm4pVV2srKy5AmxlZWVctbiC/3o45j34NZwzo3BYIBarYZCoWhUtmfPng7fN35niIiIPM8fbvZyyFMT/KWr25VusLi4OFitVmg0GnkZsubsT8FD+q6o1WrEx8c75DyRhjZJOMQpcPnL9a+18TwQUbDikKcg40qPQnJycpNZi8/XjcYVogJfw4zrUt6TyspKOWGiTqeDSqWS5+X4Y8IdIiIiaj0MKIKA2WyGzWaTh0fVz8ztrBtN+pEpZek+XxZuBh3+TQooV65cCYvFgtraWqhUKgwaNAgqlUr+3mRlZclLFDdnjg8RERF5jq/+7uKQpyYEUld3w2FNISEhsNlsUKlUqK2tdSg7ePBgbN26FUDdqlFVVVWw2WxNDm/hqlD+R/o+6HQ6fPTRR6iuroZSqYTdbnco17NnTxw5cgQpKSnIycnxUm3JGwLp+tcSPA9E5Gva6ndXwA55slqt+P3333Hu3DmX9zl9+jQOHjyI6urqVqyZ72s4LErKzJ2SktKorBRMAEBERIR8Z7qp4S1SD4dOp5MjZl+NnoNZ/f8nUs/T8uXLHf42pJXBJIWFhQ49W0REROQ9JpMJR48eBQDEx8d7uTYNeDwThof99ttvYsiQISIyMlL07t1bREREiPvuu09UV1c3uU9NTY247777RFhYmOjatauIiYkR7777brPeN1gTGiUlJQkAIjQ09LxJVbKzs4VarRZKpVKkpqbKCfSUSqVQKBQCgFCpVF5PzBLonCXAqZ/sUPp/o9Fo5P8/+P+JE+s/UlNT5WOFhobK3wFfSK5DbS9Yr38N8TwQkS+pn/xY+o3VWu10c69/Ph9QXHvttWLUqFHi7NmzQgghfv31VxEZGSlefvnlJvdZsGCB6NSpkzh48KAQQoh3331XKJVKsWPHDpfflw1JnYZfVum59ANV+pFaP3Ny/YerGbrJPc4yoTe84AAQarW60f+b0NBQoVKpHIKJ7Oxsn8nSSd7D618dngci8iVN3cxtjd9azb3++fyQp8OHD2PkyJFQq9UAgH79+qFXr14oKipqcp/XX38dM2fORJ8+fQAA99xzD/r27YulS5e2SZ0DScNVoKTnQN0cC6VSiYiICDn5mVqthkajQWpqqsNQqdYYBsWhVc7XpjYYDNBoNFCr1QgPD3fImC5RKpW44447EBMTg88++wxz5syRJ+ADYC4SIiIiH6PX63H27FnYbDbk5OT4Vn4Kj4c0HvbGG2+I7t27i1WrVoktW7aIzMxM0bVrV/Hbb785Lf/nn38KAGL16tUO2++9914xdOhQl9+Xd6bqNLxbnZqaKhQKhVCr1Q7b8P/vems0Gqf7tkYU3ZqRuT9r2IvUsEcJ9XounD04VI14/avD80BEwSrgeijuvPNODBs2DNOmTUNKSgoyMzNhMBjQt29fp+WlxG1xcXEO2+Pi4nDy5Mkm36eqqgplZWUOD2o8odtsNkMIgYqKCrnXouGkXannYO7cubBYLMjIyJBzGeh0OocyLeld8KnIvBU09xw1XO4XqOtFKioqQu/evR0mXdtsNvnf9XuVpKVineUlISIiInKqdeOblrvmmmtEcnKyKC8vF0IIsXfvXhEXFycWLVrktPy+ffsEAPHNN984bH/ooYdEv379mnyff/zjH07v1vLOlKP6E37rz6vQaDRCrVbLr6HeBGCNRiP3Jkj/lsqc7264P47l92SdnfXASMeXxk4mJSUJlUol/xf/f76ENDEeDXodpP9PYWFhQqFQiNTU1FarP/kv3pmvw/NARMEqoCZlHzlyRAAQn3/+ucP2GTNmiKuvvtrpPuXl5UKhUIicnByH7XfccYcYO3Zsk+9VWVkpSktL5UdRUREbkmZqGDRIP3pTU1PlQEOaHKxWq+UfwE0NWWp4vIY/cp0FNxfS2j+YPTUMq6nPJh2/qSFL9VfZqv9ISkpioEAu4w/pOjwPRBSsAmrIU0xMDBQKRaOhSsXFxejQoYP8/OjRozh48CAAIDIyEoMHD8Z///tf+fWqqips2LABo0ePbvK9wsPDER0d7fCg5pGGIGVmZqKgoAA5OTkoKChAXl4erFYrKisrUVlZCeDCOS5MJhPKy8uhVqtx+vRppxm7MzIyYLVaYbVaLzhEp+FwoNYa0lN/GFZLhnUZjUZYrVaUlpbi+++/R1xcHOLi4qDT6aDVauVcIpKkpCRotVrExsZC1MtVqVQqoVarsW3btlb93ERERBTEWje+abm7775bdOvWTSxfvlxs3rxZ/POf/xQKhUKsWrVKLnP//feLAQMGyM/XrVsnVCqVMBqN4rvvvhMTJ04UCQkJ4tSpUy6/L+9MeUZ2drZ8x1waAiUNv2k4fMeVO/H17/xLw6YUCsV577zXnzSuVqudLoPrrA7OPouzfZvap7m9FfXrUn8Z3obnQBqm5Kzu2dnZDuUb/ps9FOQKXv/q8DwQka9rrZEXATXkSYi6oUgvvfSSSE5OFklJSeL2228XX3zxhUOZp59+WkycONFh27p168RNN90kBg0aJKZNmyb++OOPZr0vGxLPqB8YNPzR3jBocDZXQEq05+wHcVM/8Bu+T/0f1dIqVA1XQjpfHRomh5PK1B+S5Wx4UmpqqtM8D01pOPdEmgvRMKBQKpVOz7FUr4aJ7Zo7LIyI1786PA9E5Otaa8XLgAsovIUNiWec74e0K70D9YOOpo5R/wd9/R/kSqVSZGdni9TUVKFUKh2WupXKSj0WrvSSNJzL4SzJn/R6/URyWq32gp/DWZ0aLvVav5eFieioNQXK9c9mswmz2Sw++eQTceDAgWbvHyjngYgCF3sofBwbEt/Q1B+Ksx/z0g/x0NDQRj/wGx6j/uTw+qRehaSkpPPe5W/4g17qTZDK1g8ApDLS0K+mhmjV79GQ3kOj0ThMsq4fTLTGHQkiIQLj+nf69GkxdOhQ0a1bN3H99dcLtVotHn/88WYdIxDOAxEFB08HFgwoPIQNiW+rP9yo/vK0QgiHH/T1U9PX78mQAoqGP+6lYzUMSBoOiWr4g75+gNIwyJE07LUQwjGAkQKH+skBhRBO35+9EtSaAuH6N2fOHNG3b19x+vRpIYQQGzduFADEhg0bXD5GIJwHIgoO9X+XeOI3AgMKD2FD4tvON+Sn4Q9wachT/Tv9CoVCfl7/Lr/Uu6FUKoVWqxU9e/Z0mLsgBQxJSUkOw6jqD7Nylk1cCOeTyJ0t/9owoGj4eYlam79f/+x2u4iNjRXPP/+8w/arr75aTJ8+3eXj+Pt5IKLgUf93gidGMTCg8BA2JP7N2R+Wsx/uDX+kN5zH0HAytLPVk6Sgpf7Ec2cTvOsn/5PeU9qvZ8+eToMQIm/w9+tfYWGhACDWrl3rsP3+++8XV111VZP7MR8REQUCb/RQ+HQeCiJ36fV6FBQUQK/Xw2AwQKPRQKPRIDU1Vf63lC8DgJwvIjMzE1qtFhEREbBYLA7HtNvtUCqV0Gg0SElJkY9jMBiQk5ODrKwsmM1mOVeETqeTjyvllaiqqnLIm5GTk4Pa2looFAoIIRAfHw+9Xt/Wp4sooJSWlgIANBqNw/a4uDicPn26yf0WLlyImJgY+dGjR4/WrCYRUauo/xuorTCgoICn1+tRUlKCkpIS5OTkyP+W/tCMRqOcOA8ACgoK5MAiNTXV4b+vvfbaBY9jNptRUFAAs9ksJ5OTEt6lpKQ4TeZXPyEeEbVMeHg4AODMmTMO28+cOYOIiIgm95s/fz5KS0vlR1FRUavWk4ioNbUkwW5zKYSol1aXZGVlZYiJiUFpaSmzZgc4k8mE9PR02Gw2aLVaudfCneNIwYNer2/0nMhf+Pv1r6qqCpGRkViyZAnuu+8+efu4ceOgVCqxevVql47j7+eBiIJbYmIiLBaLW79tmnv9Yw8FBT29Xo+srKwW9xA07GL0RpcjEdX1UIwZMwYffvihvO3kyZP4+uuvccstt3ixZkREbactRz+wh6IJvDNFRMEqEK5/+fn5GD58OG677TYMGzYMS5cuhUKhgNlslodEXUggnAciInewh4KIiILelVdeie3bt6Nr167YvHkz0tLS8P3337scTBARketCvF0BIiKi1tC3b1+88MIL3q4GEVHAYw8FERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jYntmiCEAFCXepyIKJhI1z3pOhis2A4QUbBqbjvAgKIJ5eXlAIAePXp4uSZERN5RXl6OmJgYb1fDa9gOEFGwc7UdUIhgvwXVBLvdjqNHjyIqKgoKhcJpmbKyMvTo0QNFRUWIjo5u4xr6F54r1/FcuYbnyXXNPVdCCJSXl6Nbt25QKoN3ZCzbAc/iuXIdz5VreJ5c19rtAHsomqBUKtG9e3eXykZHR/OL7CKeK9fxXLmG58l1zTlXwdwzIWE70Dp4rlzHc+UanifXtVY7ELy3noiIiIiIqMUYUBARERERkdsYULRAeHg4/vGPfyA8PNzbVfF5PFeu47lyDc+T63iuWg/Pret4rlzHc+UanifXtfa54qRsIiIiIiJyG3soiIiIiIjIbQwoiIiIiIjIbQwoiIiIiIjIbQwomnD48GH88MMPOHPmTJNlamtrsXv3blgslibLFBQUYOvWrec9jr/btWsXtmzZ0uTrFRUV2L17N/bs2YNz5845LWOz2bBr1y7s3r0bdru9tarqVUePHsXOnTvl7LvOlJWVYevWrSgsLGxRGX9ms9mwd+9eHDhwALW1tW6XAYCioiJs3boVZWVlrVVdrzp79izy8/Nx9OjRC5Y9dOgQfvjhB5SWljZ6zW63Y8+ePdi5cydsNltrVNUvsR1wHdsB17AdcA3bAdf5TDsgyIHZbBa33nqr6NixowAgtmzZ4rTcsmXLRMeOHcVFF10k+vfvL2655RZx+vRp+fUzZ86Im266SbRv315ccsklQq1Wi6VLl7bVx2gTS5YsEZdffrmIjY0VCQkJTsu88sorIioqSvTv319ceumlIjo6WmRnZzuU2b59u9BqtSIhIUF06dJF9OnTR+zevbstPkKbyMvLEwMHDhRdu3YVV1xxhVCr1eKxxx5rVO61114T7dq1E5deeqlQq9ViwoQJoqKiotll/Nmzzz4rOnfuLPr16ycSExNFQkKCWLNmTbPLnDt3TkyaNEk+V+3atROvvvpqW36UVnXkyBExdepUERMTI6688koRGxsrRowYISwWS5PlO3fuLACIb775xuG1X375RVx00UWiS5cuIiEhQfTs2bPJ616wYDvgOrYDrmE74Dq2A67xtXaAAUUDS5YsEZ988onYs2dPkw3JunXrhFKpFMuXL5e3ffHFF+LAgQPy8/T0dNG7d29RXFwshBDi/fffF0qlMqAukI899pjYuXOnWLhwodOG5PfffxcAxNtvvy1vy8rKEgqFQhw5ckQIIUR1dbXo3bu3mDZtmhBCCLvdLu68805x6aWXCpvN1hYfo9UtXrxY7NixQ37+888/i4iICPHmm2/K27Zs2SIUCoX4+OOPhRBC/Pnnn6J79+4ODY4rZfxZbW2tyMjIECUlJfK2f/zjH0KtVos///zT5TJCCGEwGET37t3F0aNHhRBCfPLJJwKA2LRpUxt9mtZlNpvF+++/L2pra4UQQpSVlYlrrrlGjB49ulFZm80mRo8eLR5//PFGDYnNZhMDBgwQd9xxh7Db7UIIIaZNmya0Wq2oqqpqk8/ii9gOuI7tgGvYDriG7YDrfK0dYEDRhL179zbZkAwePFhMmjSpyX1rampEdHS0ePHFFx229+rVS8ydO9fjdfW2phqSzZs3CwBi37598rYdO3YIAGLXrl1CCCHWr18vAIiDBw/KZfLz8wUAsXHjxtavvJcMHz5c3HvvvfLz2bNni8suu8yhzDPPPCM6duwo/4G7UibQHDt2TAAQa9eubVaZzp07i2eeecah3GWXXSYefPDBVqurt5lMJhEeHt7ou7BgwQIxbtw48ccffzRqSMxmswAg8vPz5W0HDx4UAMS6devaquo+i+2A69gONB/bAdewHXCdN9sBzqFoptLSUmzduhXjx49HaWkptm3bhuPHjzuUOXToEMrKynDVVVc5bB88eDB27NjRltX1qsGDB+OOO+7ArFmz8Pnnn2P16tWYM2cO7rnnHlx++eUAgB07diAmJgZ9+vSR9/vLX/6CsLCwgD1XZ8+exd69e3HRRRfJ23bs2NHo+3L11Vfj5MmTOHz4sMtlAo00Jrv+9+NCZY4ePYrjx487PVeB+p0C6s5D7969oVAo5G0//PADXn/9dbz55ptO99mxYwdCQkJwxRVXyNv69OkDjUYT0OeqpdgOuI7tgHNsB1zHdsB13mwHGFA007FjxyCEwObNm3HJJZdg5syZ6NOnD8aPHy9P+LFarQCAuLg4h33j4uLk14KBQqHArFmzYLFY8Nhjj+Gxxx7DyZMnMWPGDLmM1WptdJ6AwD5Xc+bMQUhICB544AF5m7PzID2XzoMrZQLJyZMn8dBDDyElJQWXXHKJy2WC8e8vLy8Pb7/9Np566il5m9VqxV133YU33ngDnTp1crqf1WqFRqNxaHyAwD5XnsB2wHVsB5xjO+AatgOu83Y7wICimUJDQwEA3377LX799Vds374dv//+O3bt2oWMjAyHMpWVlQ77njt3DmFhYW1bYS/atWsXxo4di8zMTOzduxe//fYbDAYDrr/+evz2228A6s5Vw/MEBO65mj9/Pj755BOsXr0aHTt2lLc7Ow/SSijSeXClTKAoLS3FjTfeiC5dumDp0qXNKhNsf3+bNm3CnXfeifnz5yM1NVXe/uijj+Kiiy5CVFQUfvjhB2zduhUAsHv3bvz6668Agu/vz1PYDriO7UBjbAdcw3bAdb7QDjCgaKaEhASEhIQgJSUFGo0GANC5c2dMnDgRGzduBABotVoAwJEjRxz2PXLkCHr27Nm2FfaidevWISYmBlOmTJG33XvvvQgJCUFeXh6AunN18uRJVFdXy2XOnj2L0tLSgDtXTz75JF577TV88cUXuPrqqx1e02q1Tr8vCoUCPXr0cLlMICgrK8PYsWOhUqnwxRdfICoqqlllevToAaVSGRR/f5s3b0ZycjJmz56NZ5991uG1mJgYVFVVwWAwwGAw4PnnnwcAvP7663j33XcB1H2nysrKHJawrK6uRnFxccCdK09iO+A6tgOO2A64hu2A63ymHWjh/I+Adb7JeNdff724//77HbZNmjRJXH/99fLzK6+80mGyldVqFeHh4WLJkiWtV2kvaWoy3ptvvilCQ0MdllEsLi4WSqVS5OTkCCGEOHTokFAoFOKzzz6Ty+Tk5AiVSiWvzBAInnrqKREVFSV+/PFHp6+//PLLIioqSpw5c0belpKSIoYNG9asMv6utLRUDBkyRFx99dUO35vmlhk+fLi488475ednzpwRUVFRYtGiRa1Sb2/4+eefRUxMjJg3b55L5Z1Nxjt27JgICQkRy5Ytk7etXr1aKBQKhwmywYrtgOvYDlwY2wHXsB1wnS+1AwwoGjh69KjYuHGjWLZsmQAgli5dKjZu3CgOHz4sl9m8ebOIjIwUzz77rMjLyxNPPvmkUKlUIi8vTy7z3//+V6hUKvGPf/xDfPrpp2LEiBGif//+4ty5c974WK1i9+7dYuPGjUKv14v4+HixceNGsXHjRvkzWq1W0b17dzFy5Ejx6aefik8++UTodDrRq1cvUVpaKh9n1qxZokuXLuK9994Tb7/9toiLixOPPPKItz6Wxz3//PNCoVCI559/Xj5HGzduFHv27JHLnDlzRlx88cVizJgx4tNPPxXz588XISEh4uuvv25WGX9WXV0tdDqd6NSpk/j8888dztWxY8dcLiOEEN9++60IDQ0VBoNBfPbZZ+L6668Xffr0EeXl5d76eB61Z88eERsbK66//nqHc7Bx40ZRU1PjdB9nDYkQdct+xsXFibfeeku8//77omvXruKBBx5og0/hu9gOuI7tgGvYDriG7YDrfK0dUAghhPsdLYHn448/xksvvdRoe3p6ukOX7fbt2/Hqq6/i8OHDSExMhF6vR1JSksM+33zzDUwmE0pKSjBw4EA8/vjjDuMl/d3f//53p5lRV65ciYSEBADAiRMn8PLLL2PXrl1QKBS48sor8be//c3hPNhsNmRnZ2Pt2rVQKBS49dZb8cADD0CpDIwReQ899JDTlRKGDh2KF198UX5+4sQJGI1G7Ny5E506dcLs2bMxYsQIh31cKeOvSktLccsttzh9zWAwYNy4cS6Vkfz444947bXXcPz4cVx++eUwGAzo0qVLq9S9rX3++ecwGo1OX1u7di1iYmIabT927BjuuOMO/Oc//8HAgQPl7Xa7HUuXLsVnn30Gu92Om2++GbNmzUJISEir1d/XsR1wHdsB17AdcA3bAdf5WjvAgIKIiIiIiNwWGKE/ERERERF5BQMKIiIiIiJyGwMKIiIiIiJyGwMKIiIiIiJyGwMKIiIiIiJyGwMKIiIiIiJyGwMKIiIiIiJyGwMKIg+YOXMmXn/99SZfr6qqwtixY/HHH380WWb//v1ISkrCmTNnPFav0tJSjB49GidPnvTYMYmIqDG2AxTMGFAQecBHH32EDh06NPn6Sy+9BLVajV69ejVZpqKiAtu2bUNtba3H6hUTE4MBAwbgySef9NgxiYioMbYDFMwYUBC1kMViwalTpxzS2NdXVVWFf//730hPT2/jmtWZNWsW3n77bZw4ccIr709EFOjYDlCwY0BB1EL5+fmIiopCnz59nL7++eefw2azYcyYMQ7b9+/fj7vuugujRo3C7NmzceTIkUb7/vHHH5gzZw5GjBiBSZMmIScnx+H1c+fO4amnnsKIESMwefJkrF27FlOmTEFubq5cZsCAAejduzeWL1/ugU9LREQNsR2gYMeAgqiF8vPzccUVV0ChUDh9/dtvv8XgwYMdXj99+jSGDx8Om82GJ598En369EFqaqrDfgcPHsTgwYMRFRWFf/7zn7jzzjvxxBNPYOHChXKZGTNmYNmyZXj44Ydx1113Yd68efjkk08a3YUaNmwYvv76aw9+aiIikrAdoGAX4u0KEPm7/Pz8Jru5AeDQoUPo3r27w7asrCxER0cjJycHSqUS119/PY4fP45//etfcpmnnnoKEyZMgNFolLdFR0djypQpMBgM+P3337F8+XL88MMP0Ol0AIDevXvj8ssvb1SH7t274+eff27pRyUiIifYDlCwY0BB1EL5+fkYN25ck69XVVUhLCzMYdvWrVsxevRoKJX/6yS84YYbHBqSb7/9FhERERg6dCiEEBBC4Ny5czhz5gwOHz6MHTt2IDw8XG5EAOCyyy5D586dG9UhIiIClZWVLfmYRETUBLYDFOwYUBC1QGlpKQoKCs57Z6pz586Nlus7c+YMtFqtw7b27ds7PD979iymTZuGO+64o9ExO3XqhDNnzkCtVjd6reFxAODkyZPo0qXLeT8LERE1H9sBIgYURC2Sn5+PkJAQDBgwoMkygwcPxuLFix229e7dG/v27XPYtnfvXofnF198MY4dO4akpCSnx+3duzesViuKi4sRHx8PoK6Bcjapb8eOHRg6dKhLn4mIiFzHdoCIk7KJWiQ/Px/9+vVDeHh4k2UmTJiAQ4cOoaCgQN523333YcOGDdiwYQMAoLi4GC+++KLDfn/961/xwQcf4NNPP5W3HT16VJ6MN3z4cFx00UV48sknIYQAAPzf//0fqqqqHI5TXl6OzZs347bbbmvJRyUiIifYDhAxoCBqkQtNxAOAXr16Yfz48XjrrbfkbUOHDsWCBQtw88034+KLL8Yll1yCESNGOOw3bdo0vPDCC7j33nuRkJCAXr16YejQofLEPpVKhffeew9r1qxB165dkZCQgL1796J79+4ICflf5+PKlStx6aWX4pprrvHgJyciIoDtABEAKIQU0hJRs+3fvx+RkZHo1q3becv99ttvGDlyJPbt2+eQSdVqteL48ePo06cPbDYbfvnlFwwcOBAqlUouU1NTg4MHD6J9+/bo2bNno2PX1NRg//796NatGyIjIxEbG4vly5fj1ltvRW1tLfr164fXX38do0eP9twHJyIiAGwHiAAGFERtZt++fejSpQtiY2M9dsx169ahX79+SExMhN1uxxNPPIHs7GwUFRUhOjoaFRUVOHjwIK644gqPvScREbmH7QAFKk7KJmojl156qceP2aVLF9xwww1QKBSwWq1o3749Pv30U0RHRwMA1Go1GxEiIh/BdoACFXsoiAJAQUEBVCoVunfv3mSmViIiClxsB8ibGFAQEREREZHbuMoTERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG5jQEFERERERG57f8B4IexgFqGqQEAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "# Sample in (l, b, dist, pmll, pmbb, vlos) coordinates\n", "lb = sdf.sample(n=500, lb=True)\n", "plt.figure(figsize=(8, 4))\n", "plt.subplot(1, 2, 1)\n", "plt.plot(lb[0], lb[2], \"k.\", ms=2)\n", "plt.xlabel(r\"$l$ (deg)\")\n", "plt.ylabel(r\"distance (kpc)\")\n", "plt.subplot(1, 2, 2)\n", "plt.plot(lb[0], lb[1], \"k.\", ms=2)\n", "plt.xlabel(r\"$l$ (deg)\")\n", "plt.ylabel(r\"$b$ (deg)\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "b45e8a44", "metadata": { "papermill": { "duration": 0.004469, "end_time": "2026-06-30T01:25:04.561041+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.556572+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Frequency-angle sampling\n", "\n", "We can also sample in frequency-angle coordinates, which returns frequency\n", "vectors, angle vectors, and stripping times:" ] }, { "cell_type": "code", "execution_count": 13, "id": "34cf821c", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:25:04.571409Z", "iopub.status.busy": "2026-06-30T01:25:04.571138Z", "iopub.status.idle": "2026-06-30T01:25:04.757623Z", "shell.execute_reply": "2026-06-30T01:25:04.756534Z" }, "papermill": { "duration": 0.192879, "end_time": "2026-06-30T01:25:04.758566+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.565687+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", "# Returns (frequencies [3,N], angles [3,N], stripping_time [N])\n", "mockaA = sdf.sample(n=500, returnaAdt=True)\n", "plt.plot(mockaA[0][0], mockaA[0][2], \"k.\", ms=2)\n", "plt.xlabel(r\"$\\Omega_R$\")\n", "plt.ylabel(r\"$\\Omega_Z$\")\n", "plt.title(\"Frequency space\");" ] }, { "cell_type": "markdown", "id": "788a36e2", "metadata": { "papermill": { "duration": 0.004785, "end_time": "2026-06-30T01:25:04.769430+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.764645+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Full PDF evaluation\n", "\n", "The stream PDF (log probability of a phase-space position) can be evaluated directly:" ] }, { "cell_type": "code", "execution_count": 14, "id": "3a156cc0", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:25:04.779927Z", "iopub.status.busy": "2026-06-30T01:25:04.779709Z", "iopub.status.idle": "2026-06-30T01:25:04.786076Z", "shell.execute_reply": "2026-06-30T01:25:04.785273Z" }, "papermill": { "duration": 0.012533, "end_time": "2026-06-30T01:25:04.786721+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.774188+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log PDF at progenitor: [-8.49075355]\n", "log PDF near stream track: [-152.00755895]\n", "log PDF far from stream: [-inf]\n" ] } ], "source": [ "# Evaluate log PDF at the progenitor location\n", "logpdf = sdf(obs.R(), obs.vR(), obs.vT(), obs.z(), obs.vz(), obs.phi())\n", "print(\"log PDF at progenitor:\", logpdf)\n", "\n", "# Evaluate at a point near the stream track (small offset in R)\n", "logpdf_near = sdf(\n", " obs.R() + 0.01, obs.vR(), obs.vT(), obs.z(), obs.vz(), obs.phi() + 0.05\n", ")\n", "print(\"log PDF near stream track:\", logpdf_near)\n", "\n", "# A point far from the stream has -inf probability\n", "logpdf_far = sdf(obs.R() - 0.5, obs.vR(), obs.vT(), obs.z() + 0.5, obs.vz(), obs.phi())\n", "print(\"log PDF far from stream:\", logpdf_far)" ] }, { "cell_type": "markdown", "id": "0f4ee576", "metadata": { "papermill": { "duration": 0.004853, "end_time": "2026-06-30T01:25:04.797143+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.792290+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Modeling gaps in streams: streamgapdf\n", "\n", "galpy also contains `streamgapdf`, a subclass of `streamdf` for modeling the\n", "effect of impacts from dark-matter subhalos on streams (see [Sanders, Bovy, & Erkal\n", "2016](https://ui.adsabs.harvard.edu/abs/2016MNRAS.457.3817S/abstract)). It shares many methods with `streamdf` but additionally takes parameters\n", "specifying the impact (impact parameter, velocity, location, time, and subhalo\n", "mass/structure). This allows one to model gaps and density variations along\n", "streams caused by subhalo encounters.\n", "\n", "Let's set up a basic `streamgapdf` example following the Sanders et al. paper:" ] }, { "cell_type": "code", "execution_count": 15, "id": "4a504cac", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:25:04.808100Z", "iopub.status.busy": "2026-06-30T01:25:04.807903Z", "iopub.status.idle": "2026-06-30T01:26:32.125203Z", "shell.execute_reply": "2026-06-30T01:26:32.124198Z" }, "papermill": { "duration": 87.328575, "end_time": "2026-06-30T01:26:32.130697+00:00", "exception": false, "start_time": "2026-06-30T01:25:04.802122+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 streamgapdf\n", "\n", "lp = LogarithmicHaloPotential(normalize=1.0, q=0.9)\n", "aAI = actionAngleIsochroneApprox(pot=lp, b=0.8)\n", "prog_unp_peri = Orbit(\n", " [\n", " 2.6556151742081835,\n", " 0.2183747276300308,\n", " 0.67876510797240575,\n", " -2.0143395648974671,\n", " -0.3273737682604374,\n", " 0.24218273922966019,\n", " ]\n", ")\n", "sigv = 0.365 * (10.0 / 2.0) ** (1.0 / 3.0) * units.km / units.s\n", "tdisrupt = 10.88 * units.Gyr\n", "\n", "# Impact parameters: time of impact, location along stream, impact parameter,\n", "# velocity of the subhalo, and subhalo mass (as a Plummer sphere)\n", "GM = 10.0**8.0 * units.Msun\n", "rs = 0.625 * units.kpc\n", "impactb = 0.0\n", "subhalovel = numpy.array([6.82200571, 132.7700529, 149.4174464]) * units.km / units.s\n", "timpact = 0.88 * units.Gyr\n", "impact_angle = -1.34\n", "\n", "sdf = streamdf(\n", " sigv,\n", " progenitor=prog_unp_peri,\n", " pot=lp,\n", " aA=aAI,\n", " leading=False,\n", " nTrackChunks=26,\n", " nTrackIterations=1,\n", " sigMeanOffset=4.5,\n", " tdisrupt=tdisrupt,\n", ")\n", "\n", "sdf_gap = streamgapdf(\n", " sigv,\n", " progenitor=prog_unp_peri,\n", " pot=lp,\n", " aA=aAI,\n", " leading=False,\n", " nTrackChunks=26,\n", " nTrackIterations=1,\n", " sigMeanOffset=4.5,\n", " tdisrupt=tdisrupt,\n", " impactb=impactb,\n", " subhalovel=subhalovel,\n", " timpact=timpact,\n", " impact_angle=impact_angle,\n", " GM=GM,\n", " rs=rs,\n", ")\n", "\n", "# Compare density along the stream with and without the gap\n", "stream_length_deg = sdf.length(ang=True)\n", "dangle = numpy.linspace(0.0, numpy.radians(stream_length_deg), 51)\n", "dens_nogap = numpy.array([sdf.density_par(da) for da in dangle])\n", "dens_gap = numpy.array([sdf_gap.density_par(da) for da in dangle])\n", "\n", "plt.plot(dangle, dens_nogap / numpy.max(dens_nogap), label=\"No gap (streamdf)\")\n", "plt.plot(dangle, dens_gap / numpy.max(dens_gap), label=\"With gap (streamgapdf)\")\n", "plt.xlabel(r\"$\\Delta\\theta$ along stream (rad)\")\n", "plt.ylabel(\"Normalized density\")\n", "plt.legend()\n", "plt.title(\"Stream density: effect of a subhalo impact\");" ] } ], "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": 127.144456, "end_time": "2026-06-30T01:26:32.853264+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/streams/streamdf.ipynb", "output_path": "doc/source/tutorials/streams/streamdf.ipynb", "parameters": {}, "start_time": "2026-06-30T01:24:25.708808+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }