{ "cells": [ { "cell_type": "markdown", "id": "908287f0", "metadata": { "papermill": { "duration": 0.003533, "end_time": "2026-05-16T13:49:42.391238+00:00", "exception": false, "start_time": "2026-05-16T13:49:42.387705+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Dissipative Forces\n", "\n", "galpy supports velocity-dependent (dissipative) forces that can be combined\n", "with regular gravitational potentials for orbit integration. These are\n", "implemented as subclasses of `DissipativeForce`.\n", "\n", "
\n", "\n", "**Warning**\n", "\n", "Dissipative forces only work in 3D orbit integration.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "id": "8a1aaa82", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:42.398278Z", "iopub.status.busy": "2026-05-16T13:49:42.398022Z", "iopub.status.idle": "2026-05-16T13:49:44.818035Z", "shell.execute_reply": "2026-05-16T13:49:44.817143Z" }, "papermill": { "duration": 2.42487, "end_time": "2026-05-16T13:49:44.819070+00:00", "exception": false, "start_time": "2026-05-16T13:49:42.394200+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "from matplotlib import pyplot as plt\n", "from galpy import potential\n", "from galpy.potential import (\n", " MWPotential2014,\n", " LogarithmicHaloPotential,\n", " ChandrasekharDynamicalFrictionForce,\n", ")\n", "from galpy.orbit import Orbit\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "id": "7f11f1f7", "metadata": { "papermill": { "duration": 0.002708, "end_time": "2026-05-16T13:49:44.825008+00:00", "exception": false, "start_time": "2026-05-16T13:49:44.822300+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Chandrasekhar Dynamical Friction\n", "\n", "`ChandrasekharDynamicalFrictionForce` implements the classical Chandrasekhar\n", "dynamical-friction formula. It requires a background potential (whose density\n", "is used to compute the local density) and the mass of the sinking object." ] }, { "cell_type": "code", "execution_count": 2, "id": "26705d0d", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:44.831737Z", "iopub.status.busy": "2026-05-16T13:49:44.831382Z", "iopub.status.idle": "2026-05-16T13:49:46.871845Z", "shell.execute_reply": "2026-05-16T13:49:46.870843Z" }, "papermill": { "duration": 2.044696, "end_time": "2026-05-16T13:49:46.872544+00:00", "exception": false, "start_time": "2026-05-16T13:49:44.827848+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "from astropy import units as u\n", "\n", "# Logarithmic halo as the host\n", "lp = LogarithmicHaloPotential(normalize=1.0, q=1.0)\n", "\n", "# Dynamical friction from a satellite of mass 5e10 Msun\n", "cdf = ChandrasekharDynamicalFrictionForce(\n", " GMs=0.5, # satellite mass in natural units (fraction of v_0^2 * R_0)\n", " rhm=0.125, # half-mass radius of the satellite\n", " dens=lp, # background density from this potential\n", ")\n", "\n", "print(type(cdf))" ] }, { "cell_type": "markdown", "id": "405af62b", "metadata": { "papermill": { "duration": 0.002787, "end_time": "2026-05-16T13:49:46.878490+00:00", "exception": false, "start_time": "2026-05-16T13:49:46.875703+00:00", "status": "completed" }, "tags": [] }, "source": [ "Now integrate an orbit with and without dynamical friction to see the effect:" ] }, { "cell_type": "code", "execution_count": 3, "id": "107fca23", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:46.885284Z", "iopub.status.busy": "2026-05-16T13:49:46.885049Z", "iopub.status.idle": "2026-05-16T13:49:50.414301Z", "shell.execute_reply": "2026-05-16T13:49:50.413314Z" }, "papermill": { "duration": 3.533818, "end_time": "2026-05-16T13:49:50.415218+00:00", "exception": false, "start_time": "2026-05-16T13:49:46.881400+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator dopr54_c instead)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: Orbit integration with ChandrasekharDynamicalFrictionForce entered domain where r < minr and ChandrasekharDynamicalFrictionForce is turned off; initialize ChandrasekharDynamicalFrictionForce with a smaller minr to avoid this if you wish (but note that you want to turn it off close to the center for an object that sinks all the way to r=0, to avoid numerical instabilities)\n" ] } ], "source": [ "# Integrate an orbit with and without dynamical friction\n", "o_nodf = Orbit([1.5, 0.1, 0.8, 0.0, 0.0, 0.0])\n", "o_df = Orbit([1.5, 0.1, 0.8, 0.0, 0.0, 0.0])\n", "\n", "ts = numpy.linspace(0.0, 30.0, 10001)\n", "\n", "# Without friction\n", "o_nodf.integrate(ts, lp)\n", "# With friction: combine potential + dissipative force\n", "o_df.integrate(ts, lp + cdf)" ] }, { "cell_type": "markdown", "id": "20333514", "metadata": { "papermill": { "duration": 0.002922, "end_time": "2026-05-16T13:49:50.421539+00:00", "exception": false, "start_time": "2026-05-16T13:49:50.418617+00:00", "status": "completed" }, "tags": [] }, "source": [ "Compare the orbital radius over time:" ] }, { "cell_type": "code", "execution_count": 4, "id": "674528e5", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:50.428792Z", "iopub.status.busy": "2026-05-16T13:49:50.428577Z", "iopub.status.idle": "2026-05-16T13:49:50.656096Z", "shell.execute_reply": "2026-05-16T13:49:50.654920Z" }, "papermill": { "duration": 0.232411, "end_time": "2026-05-16T13:49:50.656970+00:00", "exception": false, "start_time": "2026-05-16T13:49:50.424559+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compare the orbital radius over time\n", "plt.plot(ts, o_nodf.R(ts), label=\"No friction\")\n", "plt.plot(ts, o_df.R(ts), label=\"With dynamical friction\")\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$R / R_0$\")\n", "plt.legend()\n", "plt.title(\"Effect of dynamical friction on orbital decay\");" ] }, { "cell_type": "markdown", "id": "26aa94e5", "metadata": { "papermill": { "duration": 0.003625, "end_time": "2026-05-16T13:49:50.664053+00:00", "exception": false, "start_time": "2026-05-16T13:49:50.660428+00:00", "status": "completed" }, "tags": [] }, "source": [ "The orbit in the x-y plane clearly shows the inspiral with friction:" ] }, { "cell_type": "code", "execution_count": 5, "id": "96ab429e", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:50.671471Z", "iopub.status.busy": "2026-05-16T13:49:50.671275Z", "iopub.status.idle": "2026-05-16T13:49:50.946514Z", "shell.execute_reply": "2026-05-16T13:49:50.945395Z" }, "papermill": { "duration": 0.279961, "end_time": "2026-05-16T13:49:50.947249+00:00", "exception": false, "start_time": "2026-05-16T13:49:50.667288+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the orbit in x-y\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n", "axes[0].plot(o_nodf.x(ts), o_nodf.y(ts))\n", "axes[0].set_title(\"No friction\")\n", "axes[0].set_xlabel(\"x\")\n", "axes[0].set_ylabel(\"y\")\n", "axes[0].set_aspect(\"equal\")\n", "axes[1].plot(o_df.x(ts), o_df.y(ts))\n", "axes[1].set_title(\"With dynamical friction\")\n", "axes[1].set_xlabel(\"x\")\n", "axes[1].set_ylabel(\"y\")\n", "axes[1].set_aspect(\"equal\")\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "id": "4c927323", "metadata": { "papermill": { "duration": 0.003502, "end_time": "2026-05-16T13:49:50.954647+00:00", "exception": false, "start_time": "2026-05-16T13:49:50.951145+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Energy dissipation\n", "\n", "We can verify that dynamical friction removes energy from the orbit:" ] }, { "cell_type": "code", "execution_count": 6, "id": "cf3664cd", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:50.963162Z", "iopub.status.busy": "2026-05-16T13:49:50.962917Z", "iopub.status.idle": "2026-05-16T13:49:51.116094Z", "shell.execute_reply": "2026-05-16T13:49:51.115019Z" }, "papermill": { "duration": 0.158481, "end_time": "2026-05-16T13:49:51.116831+00:00", "exception": false, "start_time": "2026-05-16T13:49:50.958350+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ts, o_nodf.E(ts, pot=lp), label=\"No friction\")\n", "plt.plot(ts, o_df.E(ts, pot=lp), label=\"With friction\")\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$E$\")\n", "plt.legend()\n", "plt.title(\"Energy evolution\");" ] }, { "cell_type": "markdown", "id": "464d1092", "metadata": { "papermill": { "duration": 0.006485, "end_time": "2026-05-16T13:49:51.127359+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.120874+00:00", "status": "completed" }, "tags": [] }, "source": [ "## NonInertialFrameForce\n", "\n", "galpy also provides `NonInertialFrameForce` for integrating orbits in\n", "non-inertial (e.g., rotating or accelerating) reference frames. This is\n", "covered in detail in the [Integration and Plotting](../orbits/integration_and_plotting.ipynb)\n", "tutorial, since it is most naturally used in the context of orbit integration.\n", "\n", "Key points:\n", "- It adds fictitious forces (Coriolis, centrifugal, etc.)\n", "- Specified via `Omega` (rotation) and/or `a0` (linear acceleration)\n", "- 3D only, like all dissipative forces\n", "\n", "For basic potential usage, see the [Introduction to Potentials](introduction.ipynb)." ] }, { "cell_type": "markdown", "id": "a3b883cf", "metadata": { "papermill": { "duration": 0.003635, "end_time": "2026-05-16T13:49:51.134932+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.131297+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Example: Schwarzschild precession of the S2 orbit around Sgr A*\n", "\n", "The S2 star orbits the supermassive black hole Sgr A* at the Galactic Center on a highly eccentric orbit with a 16-year period. The [GRAVITY Collaboration (2020)](https://arxiv.org/abs/2004.07187) detected the **Schwarzschild precession** of S2's orbit -- the relativistic precession of the pericenter due to the GR correction to the Kepler potential. Here we reproduce this calculation using galpy by adding the first-order GR correction, which is a velocity-dependent force, to a `KeplerPotential` (note that it is not dissipative, just velocity-dependent).\n", "\n", "We use [rebound](https://rebound.readthedocs.io/) to convert S2's orbital elements (semi-major axis, eccentricity, inclination, argument of pericenter, longitude of ascending node, time of pericenter) to a Cartesian position and velocity that can initialize a galpy `Orbit`." ] }, { "cell_type": "code", "execution_count": 7, "id": "76841d19", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:51.143804Z", "iopub.status.busy": "2026-05-16T13:49:51.143566Z", "iopub.status.idle": "2026-05-16T13:49:51.157379Z", "shell.execute_reply": "2026-05-16T13:49:51.156447Z" }, "papermill": { "duration": 0.019311, "end_time": "2026-05-16T13:49:51.158065+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.138754+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "S2 semi-major axis = 1031.3 AU, e = 0.885\n" ] } ], "source": [ "import rebound\n", "import astropy.units as u\n", "from astropy.constants import c as c_si\n", "from galpy.potential import KeplerPotential\n", "from galpy.potential.DissipativeForce import DissipativeForce\n", "\n", "c_kms = c_si.to_value(u.km / u.s)\n", "\n", "# Sgr A* parameters\n", "R0 = 8246.7 * u.pc\n", "vo = 220.0 * u.km / u.s\n", "MSgrA = 4.261e6 * u.Msun\n", "\n", "# Set up a rebound simulation with S2's orbital elements (GRAVITY Collaboration 2020)\n", "sim = rebound.Simulation()\n", "sim.units = (\"AU\", \"yr\", \"Msun\")\n", "sim.add(m=MSgrA.to_value(u.Msun)) # Sgr A*\n", "sim.add(\n", " m=0.0,\n", " a=(125.058 * u.mas * R0).to_value(u.AU, equivalencies=u.dimensionless_angles()),\n", " e=0.884649,\n", " inc=(134.567 * u.deg).to_value(u.rad),\n", " omega=(66.263 * u.deg).to_value(u.rad),\n", " Omega=(228.171 * u.deg).to_value(u.rad),\n", " T=(8.37900 * u.yr).to_value(u.yr) - 0.35653101, # time since 2010's apocenter\n", ")\n", "print(f\"S2 semi-major axis = {sim.particles[1].a:.1f} AU, e = {sim.particles[1].e:.3f}\")" ] }, { "cell_type": "markdown", "id": "5e81a175", "metadata": { "papermill": { "duration": 0.003722, "end_time": "2026-05-16T13:49:51.165809+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.162087+00:00", "status": "completed" }, "tags": [] }, "source": [ "Initialize a galpy `Orbit` from the rebound Cartesian position and velocity, then integrate it in a `KeplerPotential` representing Sgr A*:" ] }, { "cell_type": "code", "execution_count": 8, "id": "193a4bd9", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:51.174705Z", "iopub.status.busy": "2026-05-16T13:49:51.174486Z", "iopub.status.idle": "2026-05-16T13:49:51.198738Z", "shell.execute_reply": "2026-05-16T13:49:51.197780Z" }, "papermill": { "duration": 0.029721, "end_time": "2026-05-16T13:49:51.199446+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.169725+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "pt = sim.particles[1]\n", "# Sgr A* at the Galactic Center as the reference point\n", "ogc = Orbit([0.0, 0.0, 0.0, 0.0, 0.0, 0.0], ro=R0, vo=vo)\n", "ra_gc, dec_gc = ogc.ra(), ogc.dec() # degrees (floats)\n", "\n", "\n", "# Convert rebound Cartesian to (RA, Dec, dist, pmRA, pmDec, vlos) offsets\n", "def make_s2_orbit():\n", " return Orbit(\n", " [\n", " ra_gc * u.deg\n", " + (pt.y * u.AU / R0).to(u.deg, equivalencies=u.dimensionless_angles()),\n", " dec_gc * u.deg\n", " + (pt.x * u.AU / R0).to(u.deg, equivalencies=u.dimensionless_angles()),\n", " ogc.dist() * u.kpc + pt.z * u.AU,\n", " ogc.pmra() * u.mas / u.yr\n", " + (pt.vy * u.AU / u.yr / R0).to(\n", " u.mas / u.yr, equivalencies=u.dimensionless_angles()\n", " ),\n", " ogc.pmdec() * u.mas / u.yr\n", " + (pt.vx * u.AU / u.yr / R0).to(\n", " u.mas / u.yr, equivalencies=u.dimensionless_angles()\n", " ),\n", " ogc.vlos() * u.km / u.s + pt.vz * u.AU / u.yr,\n", " ],\n", " radec=True,\n", " ro=R0,\n", " vo=vo,\n", " )\n", "\n", "\n", "kp = KeplerPotential(amp=MSgrA, ro=R0)\n", "times = numpy.linspace(0.0, 4.0 * 16.0455, 1001) * u.yr # 4 orbital periods\n", "\n", "o = make_s2_orbit()\n", "o.integrate(times, kp)" ] }, { "cell_type": "markdown", "id": "b48ac1a9", "metadata": { "papermill": { "duration": 0.003959, "end_time": "2026-05-16T13:49:51.207694+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.203735+00:00", "status": "completed" }, "tags": [] }, "source": [ "To compute the Schwarzschild precession we implement the leading-order GR correction as a `DissipativeForce` (which is the galpy class for velocity-dependent forces):\n", "\n", "$$\n", "\\vec{a}_{\\mathrm{SP}} = f_{\\mathrm{SP}}\\,\\frac{GM}{c^2 r^2}\\left[\\left(2(\\gamma+\\beta)\\,\\frac{GM}{r} - \\gamma\\,v^2\\right)\\frac{\\vec{r}}{r} + 2(1+\\gamma)\\,v_r\\,\\vec{v}\\right].\n", "$$\n", "\n", "The factor $f_{\\mathrm{SP}}$ is the \"GR factor\" used by GRAVITY Collaboration (2020) -- $f_{\\mathrm{SP}} = 1$ corresponds to standard GR. The PPN parameters $\\gamma$ and $\\beta$ default to their GR values ($\\gamma = \\beta = 1$)." ] }, { "cell_type": "code", "execution_count": 9, "id": "7c923cf1", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:51.217026Z", "iopub.status.busy": "2026-05-16T13:49:51.216777Z", "iopub.status.idle": "2026-05-16T13:49:51.223915Z", "shell.execute_reply": "2026-05-16T13:49:51.222829Z" }, "papermill": { "duration": 0.012788, "end_time": "2026-05-16T13:49:51.224556+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.211768+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "class SchwarzschildPrecessionForce(DissipativeForce):\n", " def __init__(self, amp=1.0, fsp=1.0, gamma=1.0, beta=1.0, ro=None, vo=None):\n", " DissipativeForce.__init__(self, amp=amp, ro=ro, vo=vo, amp_units=\"mass\")\n", " self._fsp = fsp\n", " self._gamma = gamma\n", " self._beta = beta\n", "\n", " def _force_firstterm(self, r, v):\n", " return (\n", " 1.0\n", " / (c_kms / self._vo) ** 2\n", " / r**3\n", " * (2.0 * (self._gamma + self._beta) * self._amp / r - self._gamma * v**2)\n", " )\n", "\n", " def _force_secondterm(self, r, vr):\n", " return 2.0 * (1.0 + self._gamma) / (c_kms / self._vo) ** 2 / r**2 * vr\n", "\n", " def _Rforce(self, R, z, phi=0.0, t=0.0, v=None):\n", " r = numpy.sqrt(R**2 + z**2)\n", " vr = R / r * v[0] + z / r * v[2]\n", " vmag = numpy.sqrt(v[0] ** 2 + v[1] ** 2 + v[2] ** 2)\n", " return self._fsp * (\n", " self._force_firstterm(r, vmag) * R + self._force_secondterm(r, vr) * v[0]\n", " )\n", "\n", " def _zforce(self, R, z, phi=0.0, t=0.0, v=None):\n", " r = numpy.sqrt(R**2 + z**2)\n", " vr = R / r * v[0] + z / r * v[2]\n", " vmag = numpy.sqrt(v[0] ** 2 + v[1] ** 2 + v[2] ** 2)\n", " return self._fsp * (\n", " self._force_firstterm(r, vmag) * z + self._force_secondterm(r, vr) * v[2]\n", " )\n", "\n", " def _phitorque(self, R, z, phi=0.0, t=0.0, v=None):\n", " r = numpy.sqrt(R**2 + z**2)\n", " vr = R / r * v[0] + z / r * v[2]\n", " return self._fsp * (self._force_secondterm(r, vr) * v[1] * R)" ] }, { "cell_type": "markdown", "id": "302fa038", "metadata": { "papermill": { "duration": 0.003973, "end_time": "2026-05-16T13:49:51.232889+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.228916+00:00", "status": "completed" }, "tags": [] }, "source": [ "To make the precession clearly visible over just a few orbits, we exaggerate it with $f_{\\mathrm{SP}} = 5$. We integrate the same initial conditions in the Kepler potential plus the precession force and compare:" ] }, { "cell_type": "code", "execution_count": 10, "id": "72caae1b", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:51.242377Z", "iopub.status.busy": "2026-05-16T13:49:51.242149Z", "iopub.status.idle": "2026-05-16T13:49:51.322088Z", "shell.execute_reply": "2026-05-16T13:49:51.321154Z" }, "papermill": { "duration": 0.086244, "end_time": "2026-05-16T13:49:51.323195+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.236951+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "galpyWarning: Cannot use C integration because some of the potentials are not implemented in C (using leapfrog instead)\n", "galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator odeint instead)\n" ] } ], "source": [ "sp = SchwarzschildPrecessionForce(amp=MSgrA, ro=R0, fsp=5.0)\n", "\n", "osp = make_s2_orbit()\n", "osp.integrate(times, kp + sp)" ] }, { "cell_type": "markdown", "id": "86c4bde0", "metadata": { "papermill": { "duration": 0.004007, "end_time": "2026-05-16T13:49:51.331448+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.327441+00:00", "status": "completed" }, "tags": [] }, "source": [ "Plot the orbit as $\\Delta\\mathrm{Dec}$ vs. $\\Delta\\mathrm{RA}$ relative to Sgr A*. The Newtonian Kepler orbit is a closed ellipse, while the GR orbit precesses, tracing out a rosette:" ] }, { "cell_type": "code", "execution_count": 11, "id": "3fab95f7", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:51.340634Z", "iopub.status.busy": "2026-05-16T13:49:51.340407Z", "iopub.status.idle": "2026-05-16T13:49:51.631014Z", "shell.execute_reply": "2026-05-16T13:49:51.629906Z" }, "papermill": { "duration": 0.296187, "end_time": "2026-05-16T13:49:51.631770+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.335583+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(5, 10))\n", "o.plot(\n", " d1=f\"(ra-{ra_gc})*3600\",\n", " d2=f\"(dec-{dec_gc})*3600\",\n", " xlabel=r\"$\\Delta\\mathrm{RA}\\,(\\mathrm{arcsec})$\",\n", " ylabel=r\"$\\Delta\\mathrm{Dec}\\,(\\mathrm{arcsec})$\",\n", " label=\"Newtonian (Kepler)\",\n", " gcf=True,\n", ")\n", "osp.plot(\n", " d1=f\"(ra-{ra_gc})*3600\",\n", " d2=f\"(dec-{dec_gc})*3600\",\n", " overplot=True,\n", " label=r\"With GR precession ($f_{\\mathrm{SP}}=5$)\",\n", ")\n", "plt.plot([0], [0], \"k+\", ms=15, label=\"Sgr A*\")\n", "plt.xlim(0.075, -0.095)\n", "plt.ylim(-0.03, 0.21)\n", "plt.legend(fontsize=10);" ] }, { "cell_type": "markdown", "id": "0997abdd", "metadata": { "papermill": { "duration": 0.004341, "end_time": "2026-05-16T13:49:51.640736+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.636395+00:00", "status": "completed" }, "tags": [] }, "source": [ "The pericenter advances by a few degrees per orbit, exactly the relativistic effect detected by GRAVITY Collaboration (2020). With the actual GR value $f_{\\mathrm{SP}} = 1$ the precession is five times smaller -- still measurable with high-precision astrometry, but harder to see in a plot of just a few orbits.\n", "\n", "Finally, let's check that when setting $\\beta = 2(1+\\gamma) = 4$ for $\\gamma = 1$ we get zero precession (a useful sanity check on the PPN form of the precession formula):" ] }, { "cell_type": "code", "execution_count": 12, "id": "2d6beea1", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:49:51.650163Z", "iopub.status.busy": "2026-05-16T13:49:51.649945Z", "iopub.status.idle": "2026-05-16T13:49:52.032302Z", "shell.execute_reply": "2026-05-16T13:49:52.031221Z" }, "papermill": { "duration": 0.388029, "end_time": "2026-05-16T13:49:52.032987+00:00", "exception": false, "start_time": "2026-05-16T13:49:51.644958+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spzero = SchwarzschildPrecessionForce(amp=MSgrA, ro=R0, fsp=1.0, beta=4.0, gamma=1.0)\n", "ozero = make_s2_orbit()\n", "ozero.integrate(times, kp + spzero)\n", "\n", "plt.figure(figsize=(5, 10))\n", "o.plot(\n", " d1=f\"(ra-{ra_gc})*3600\",\n", " d2=f\"(dec-{dec_gc})*3600\",\n", " xlabel=r\"$\\Delta\\mathrm{RA}\\,(\\mathrm{arcsec})$\",\n", " ylabel=r\"$\\Delta\\mathrm{Dec}\\,(\\mathrm{arcsec})$\",\n", " label=\"Newtonian (Kepler)\",\n", " gcf=True,\n", ")\n", "osp.plot(\n", " d1=f\"(ra-{ra_gc})*3600\",\n", " d2=f\"(dec-{dec_gc})*3600\",\n", " overplot=True,\n", " label=r\"With GR precession ($f_{\\mathrm{SP}}=5$)\",\n", ")\n", "ozero.plot(\n", " d1=f\"(ra-{ra_gc})*3600\",\n", " d2=f\"(dec-{dec_gc})*3600\",\n", " overplot=True,\n", " ls=\"--\",\n", " label=r\"PPN: $\\beta=2(1+\\gamma)$, no precession\",\n", ")\n", "plt.plot([0], [0], \"k+\", ms=15, label=\"Sgr A*\")\n", "plt.xlim(0.075, -0.095)\n", "plt.ylim(-0.03, 0.21)\n", "plt.legend(fontsize=9);" ] }, { "cell_type": "markdown", "id": "a3f008ce", "metadata": { "papermill": { "duration": 0.004485, "end_time": "2026-05-16T13:49:52.042414+00:00", "exception": false, "start_time": "2026-05-16T13:49:52.037929+00:00", "status": "completed" }, "tags": [] }, "source": [ "As expected, the dashed PPN curve traces the same closed ellipse as the Newtonian orbit -- the choice $\\beta = 2(1+\\gamma)$ exactly cancels the pericenter precession." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": 11.263335, "end_time": "2026-05-16T13:49:52.763507+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/potentials/dissipative.ipynb", "output_path": "doc/source/tutorials/potentials/dissipative.ipynb", "parameters": {}, "start_time": "2026-05-16T13:49:41.500172+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }