{ "cells": [ { "cell_type": "markdown", "id": "908287f0", "metadata": { "papermill": { "duration": 0.004008, "end_time": "2026-06-30T01:16:34.336189+00:00", "exception": false, "start_time": "2026-06-30T01:16:34.332181+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": "2026-06-30T01:16:34.343983Z", "iopub.status.busy": "2026-06-30T01:16:34.343777Z", "iopub.status.idle": "2026-06-30T01:16:36.664964Z", "shell.execute_reply": "2026-06-30T01:16:36.663970Z" }, "papermill": { "duration": 2.326047, "end_time": "2026-06-30T01:16:36.665732+00:00", "exception": false, "start_time": "2026-06-30T01:16:34.339685+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": 0.002484, "end_time": "2026-06-30T01:16:36.671257+00:00", "exception": false, "start_time": "2026-06-30T01:16:36.668773+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": "2026-06-30T01:16:36.677690Z", "iopub.status.busy": "2026-06-30T01:16:36.677255Z", "iopub.status.idle": "2026-06-30T01:16:38.552516Z", "shell.execute_reply": "2026-06-30T01:16:38.551640Z" }, "papermill": { "duration": 1.879944, "end_time": "2026-06-30T01:16:38.553728+00:00", "exception": false, "start_time": "2026-06-30T01:16:36.673784+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": 0.002908, "end_time": "2026-06-30T01:16:38.560238+00:00", "exception": false, "start_time": "2026-06-30T01:16:38.557330+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": "2026-06-30T01:16:38.566939Z", "iopub.status.busy": "2026-06-30T01:16:38.566727Z", "iopub.status.idle": "2026-06-30T01:16:41.755166Z", "shell.execute_reply": "2026-06-30T01:16:41.754398Z" }, "papermill": { "duration": 3.193129, "end_time": "2026-06-30T01:16:41.756184+00:00", "exception": false, "start_time": "2026-06-30T01:16:38.563055+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": 0.002646, "end_time": "2026-06-30T01:16:41.764974+00:00", "exception": false, "start_time": "2026-06-30T01:16:41.762328+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": "2026-06-30T01:16:41.771940Z", "iopub.status.busy": "2026-06-30T01:16:41.771695Z", "iopub.status.idle": "2026-06-30T01:16:42.009950Z", "shell.execute_reply": "2026-06-30T01:16:42.008731Z" }, "papermill": { "duration": 0.24299, "end_time": "2026-06-30T01:16:42.010781+00:00", "exception": false, "start_time": "2026-06-30T01:16:41.767791+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": 0.003725, "end_time": "2026-06-30T01:16:42.018561+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.014836+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": "2026-06-30T01:16:42.026049Z", "iopub.status.busy": "2026-06-30T01:16:42.025851Z", "iopub.status.idle": "2026-06-30T01:16:42.286937Z", "shell.execute_reply": "2026-06-30T01:16:42.285880Z" }, "papermill": { "duration": 0.265916, "end_time": "2026-06-30T01:16:42.287658+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.021742+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": 0.003315, "end_time": "2026-06-30T01:16:42.295019+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.291704+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": "2026-06-30T01:16:42.302982Z", "iopub.status.busy": "2026-06-30T01:16:42.302756Z", "iopub.status.idle": "2026-06-30T01:16:42.455827Z", "shell.execute_reply": "2026-06-30T01:16:42.454855Z" }, "papermill": { "duration": 0.158167, "end_time": "2026-06-30T01:16:42.456615+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.298448+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "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": 0.003513, "end_time": "2026-06-30T01:16:42.463823+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.460310+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": 0.003312, "end_time": "2026-06-30T01:16:42.470755+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.467443+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": "2026-06-30T01:16:42.479191Z", "iopub.status.busy": "2026-06-30T01:16:42.478944Z", "iopub.status.idle": "2026-06-30T01:16:42.493070Z", "shell.execute_reply": "2026-06-30T01:16:42.492160Z" }, "papermill": { "duration": 0.019377, "end_time": "2026-06-30T01:16:42.493723+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.474346+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": 0.003491, "end_time": "2026-06-30T01:16:42.501060+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.497569+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": "2026-06-30T01:16:42.509589Z", "iopub.status.busy": "2026-06-30T01:16:42.509381Z", "iopub.status.idle": "2026-06-30T01:16:42.529963Z", "shell.execute_reply": "2026-06-30T01:16:42.529093Z" }, "papermill": { "duration": 0.02578, "end_time": "2026-06-30T01:16:42.530671+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.504891+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": 0.003551, "end_time": "2026-06-30T01:16:42.538140+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.534589+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": "2026-06-30T01:16:42.546611Z", "iopub.status.busy": "2026-06-30T01:16:42.546412Z", "iopub.status.idle": "2026-06-30T01:16:42.553069Z", "shell.execute_reply": "2026-06-30T01:16:42.552129Z" }, "papermill": { "duration": 0.012239, "end_time": "2026-06-30T01:16:42.554147+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.541908+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": 0.003533, "end_time": "2026-06-30T01:16:42.561406+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.557873+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": "2026-06-30T01:16:42.569718Z", "iopub.status.busy": "2026-06-30T01:16:42.569497Z", "iopub.status.idle": "2026-06-30T01:16:42.640441Z", "shell.execute_reply": "2026-06-30T01:16:42.639586Z" }, "papermill": { "duration": 0.076534, "end_time": "2026-06-30T01:16:42.641620+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.565086+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": 0.003535, "end_time": "2026-06-30T01:16:42.649062+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.645527+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": "2026-06-30T01:16:42.657840Z", "iopub.status.busy": "2026-06-30T01:16:42.657620Z", "iopub.status.idle": "2026-06-30T01:16:42.942108Z", "shell.execute_reply": "2026-06-30T01:16:42.941057Z" }, "papermill": { "duration": 0.289986, "end_time": "2026-06-30T01:16:42.942848+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.652862+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": 0.004029, "end_time": "2026-06-30T01:16:42.950984+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.946955+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": "2026-06-30T01:16:42.960162Z", "iopub.status.busy": "2026-06-30T01:16:42.959909Z", "iopub.status.idle": "2026-06-30T01:16:43.337980Z", "shell.execute_reply": "2026-06-30T01:16:43.336746Z" }, "papermill": { "duration": 0.383558, "end_time": "2026-06-30T01:16:43.338622+00:00", "exception": false, "start_time": "2026-06-30T01:16:42.955064+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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": 0.003993, "end_time": "2026-06-30T01:16:43.346934+00:00", "exception": false, "start_time": "2026-06-30T01:16:43.342941+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": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 10.692977, "end_time": "2026-06-30T01:16:44.168124+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": "2026-06-30T01:16:33.475147+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }