{
"cells": [
{
"cell_type": "markdown",
"id": "a1",
"metadata": {
"papermill": {
"duration": 0.004107,
"end_time": "2026-05-16T13:58:00.716422+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:00.712315+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": "2026-05-16T13:58:00.724313Z",
"iopub.status.busy": "2026-05-16T13:58:00.724052Z",
"iopub.status.idle": "2026-05-16T13:58:03.460057Z",
"shell.execute_reply": "2026-05-16T13:58:03.459131Z"
},
"papermill": {
"duration": 2.740962,
"end_time": "2026-05-16T13:58:03.460818+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:00.719856+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": 0.003058,
"end_time": "2026-05-16T13:58:03.467450+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:03.464392+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": 0.003057,
"end_time": "2026-05-16T13:58:03.473729+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:03.470672+00:00",
"status": "completed"
},
"tags": []
},
"source": [
"## Initialize streamdf"
]
},
{
"cell_type": "markdown",
"id": "6f08cd87",
"metadata": {
"papermill": {
"duration": 0.003076,
"end_time": "2026-05-16T13:58:03.480065+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:03.476989+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": "2026-05-16T13:58:03.487618Z",
"iopub.status.busy": "2026-05-16T13:58:03.487295Z",
"iopub.status.idle": "2026-05-16T13:58:03.491601Z",
"shell.execute_reply": "2026-05-16T13:58:03.490627Z"
},
"papermill": {
"duration": 0.00897,
"end_time": "2026-05-16T13:58:03.492255+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:03.483285+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": 0.003107,
"end_time": "2026-05-16T13:58:03.498679+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:03.495572+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": "2026-05-16T13:58:03.506082Z",
"iopub.status.busy": "2026-05-16T13:58:03.505882Z",
"iopub.status.idle": "2026-05-16T13:58:09.864804Z",
"shell.execute_reply": "2026-05-16T13:58:09.863981Z"
},
"papermill": {
"duration": 6.363825,
"end_time": "2026-05-16T13:58:09.865790+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:03.501965+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": 0.003281,
"end_time": "2026-05-16T13:58:09.872817+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:09.869536+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": "2026-05-16T13:58:09.880818Z",
"iopub.status.busy": "2026-05-16T13:58:09.880612Z",
"iopub.status.idle": "2026-05-16T13:58:10.109192Z",
"shell.execute_reply": "2026-05-16T13:58:10.108077Z"
},
"papermill": {
"duration": 0.233544,
"end_time": "2026-05-16T13:58:10.109828+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:09.876284+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
""
]
},
"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": 0.003354,
"end_time": "2026-05-16T13:58:10.117002+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.113648+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": "2026-05-16T13:58:10.127913Z",
"iopub.status.busy": "2026-05-16T13:58:10.127715Z",
"iopub.status.idle": "2026-05-16T13:58:10.134403Z",
"shell.execute_reply": "2026-05-16T13:58:10.133431Z"
},
"papermill": {
"duration": 0.014461,
"end_time": "2026-05-16T13:58:10.135005+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.120544+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"type: StreamTrack\n",
"ll (deg) : [160.96266762 200.33106506 221.71399911 234.64875218 244.02402589]\n",
"bb (deg) : [56.81288729 41.40802881 21.00715844 5.10575318 -5.81364365]\n",
"dist (kpc) : [ 8.34973111 7.92760519 8.89589981 10.7603418 12.98833547]\n",
"vlos (km/s): [-117.9274023 85.75097646 255.29006974 342.5453684 374.56839459]\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": "2026-05-16T13:58:10.143357Z",
"iopub.status.busy": "2026-05-16T13:58:10.143142Z",
"iopub.status.idle": "2026-05-16T13:58:10.148403Z",
"shell.execute_reply": "2026-05-16T13:58:10.147623Z"
},
"papermill": {
"duration": 0.010445,
"end_time": "2026-05-16T13:58:10.149205+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.138760+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": "2026-05-16T13:58:10.157790Z",
"iopub.status.busy": "2026-05-16T13:58:10.157599Z",
"iopub.status.idle": "2026-05-16T13:58:10.653644Z",
"shell.execute_reply": "2026-05-16T13:58:10.652449Z"
},
"papermill": {
"duration": 0.501478,
"end_time": "2026-05-16T13:58:10.654377+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.152899+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": 0.003792,
"end_time": "2026-05-16T13:58:10.662460+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.658668+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": 0.003791,
"end_time": "2026-05-16T13:58:10.670185+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.666394+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": "2026-05-16T13:58:10.678879Z",
"iopub.status.busy": "2026-05-16T13:58:10.678669Z",
"iopub.status.idle": "2026-05-16T13:58:10.691173Z",
"shell.execute_reply": "2026-05-16T13:58:10.690340Z"
},
"papermill": {
"duration": 0.017977,
"end_time": "2026-05-16T13:58:10.692031+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.674054+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Stream length (radians): 93.48282256049195\n",
"Stream length (physical kpc): 12.31150295587134\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": 0.003866,
"end_time": "2026-05-16T13:58:10.699916+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.696050+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": "2026-05-16T13:58:10.708746Z",
"iopub.status.busy": "2026-05-16T13:58:10.708576Z",
"iopub.status.idle": "2026-05-16T13:58:11.466937Z",
"shell.execute_reply": "2026-05-16T13:58:11.465957Z"
},
"papermill": {
"duration": 0.763731,
"end_time": "2026-05-16T13:58:11.467745+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:10.704014+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",
"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": 0.00412,
"end_time": "2026-05-16T13:58:11.476440+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:11.472320+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": "2026-05-16T13:58:11.486210Z",
"iopub.status.busy": "2026-05-16T13:58:11.485942Z",
"iopub.status.idle": "2026-05-16T13:58:37.010521Z",
"shell.execute_reply": "2026-05-16T13:58:37.009400Z"
},
"papermill": {
"duration": 25.530475,
"end_time": "2026-05-16T13:58:37.011193+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:11.480718+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": 0.004311,
"end_time": "2026-05-16T13:58:37.020392+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:37.016081+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": "2026-05-16T13:58:37.030433Z",
"iopub.status.busy": "2026-05-16T13:58:37.030228Z",
"iopub.status.idle": "2026-05-16T13:58:37.932702Z",
"shell.execute_reply": "2026-05-16T13:58:37.931746Z"
},
"papermill": {
"duration": 0.909011,
"end_time": "2026-05-16T13:58:37.933841+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:37.024830+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Frequency eigenvalue ratio (isotropic): 34.44969734444917\n",
"Frequency eigenvalue ratio (model): 29.625559518503955\n",
"Misalignment (rad): -0.00864416358230713\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": 0.004374,
"end_time": "2026-05-16T13:58:37.943060+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:37.938686+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": "2026-05-16T13:58:37.953196Z",
"iopub.status.busy": "2026-05-16T13:58:37.952969Z",
"iopub.status.idle": "2026-05-16T13:58:38.423065Z",
"shell.execute_reply": "2026-05-16T13:58:38.422001Z"
},
"papermill": {
"duration": 0.476134,
"end_time": "2026-05-16T13:58:38.423783+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:37.947649+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 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": 0.004778,
"end_time": "2026-05-16T13:58:38.433775+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:38.428997+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": "2026-05-16T13:58:38.444375Z",
"iopub.status.busy": "2026-05-16T13:58:38.444182Z",
"iopub.status.idle": "2026-05-16T13:58:38.651379Z",
"shell.execute_reply": "2026-05-16T13:58:38.650448Z"
},
"papermill": {
"duration": 0.213609,
"end_time": "2026-05-16T13:58:38.652193+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:38.438584+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",
"# 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": "2026-05-16T13:58:38.662203+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:38.657418+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": "2026-05-16T13:58:38.673310Z",
"iopub.status.busy": "2026-05-16T13:58:38.673121Z",
"iopub.status.idle": "2026-05-16T13:58:38.679223Z",
"shell.execute_reply": "2026-05-16T13:58:38.678247Z"
},
"papermill": {
"duration": 0.012655,
"end_time": "2026-05-16T13:58:38.679828+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:38.667173+00:00",
"status": "completed"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"log PDF at progenitor: [-8.49066974]\n",
"log PDF near stream track: [-152.00787863]\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": 0.004817,
"end_time": "2026-05-16T13:58:38.689942+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:38.685125+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": "2026-05-16T13:58:38.701019Z",
"iopub.status.busy": "2026-05-16T13:58:38.700808Z",
"iopub.status.idle": "2026-05-16T13:59:51.043208Z",
"shell.execute_reply": "2026-05-16T13:59:51.041940Z"
},
"papermill": {
"duration": 72.354389,
"end_time": "2026-05-16T13:59:51.049374+00:00",
"exception": false,
"start_time": "2026-05-16T13:58:38.694985+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": "3.13.13"
},
"papermill": {
"default_parameters": {},
"duration": 111.834836,
"end_time": "2026-05-16T13:59:51.671905+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": "2026-05-16T13:57:59.837069+00:00",
"version": "2.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}