{ "cells": [ { "cell_type": "markdown", "id": "7fb27b941602401d91542211134fc71a", "metadata": { "papermill": { "duration": 0.004146, "end_time": "2026-05-16T13:45:01.974022+00:00", "exception": false, "start_time": "2026-05-16T13:45:01.969876+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Spherical Distribution Functions\n", "\n", "galpy includes several distribution functions for spherical systems, both\n", "isotropic and anisotropic. These DFs are tied to a specific spherical potential\n", "and can be used to compute properties of the system or to generate samples. \n", "galpy contains a number of specific isotropic and anisotropic DFs, \n", "but it also includes a general classes for computing the DF of any spherical system \n", "using Eddington's formula for isotropic systems and similar formulas for anisotropic systems\n", "with constant anisotropy or anisotropy of the Osipkov-Merritt type. See [galaxiesbook.org](https://galaxiesbook.org/chapters/I-04.-Equilibria-of-Collisionless-Stellar-Systems_6-Spherical-distribution-functions.html) for more details on these DFs and the underlying theory." ] }, { "cell_type": "code", "execution_count": 1, "id": "acae54e37e7d407bbb7b55eff062a284", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:01.982217Z", "iopub.status.busy": "2026-05-16T13:45:01.981959Z", "iopub.status.idle": "2026-05-16T13:45:03.122928Z", "shell.execute_reply": "2026-05-16T13:45:03.122070Z" }, "papermill": { "duration": 1.146642, "end_time": "2026-05-16T13:45:03.124217+00:00", "exception": false, "start_time": "2026-05-16T13:45:01.977575+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "from galpy.util.quadpack import AccuracyWarning\n", "import warnings\n", "\n", "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)\n", "warnings.filterwarnings(\"ignore\", category=AccuracyWarning)" ] }, { "cell_type": "markdown", "id": "9a63283cbaf04dbcab1f6479b197f3a8", "metadata": { "papermill": { "duration": 0.003281, "end_time": "2026-05-16T13:45:03.131255+00:00", "exception": false, "start_time": "2026-05-16T13:45:03.127974+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Isotropic Hernquist DF\n", "\n", "The `isotropicHernquistdf` is initialized from a `HernquistPotential` instance.\n", "The DF is a function of energy only, $f(E)$, corresponding to an isotropic\n", "velocity distribution." ] }, { "cell_type": "code", "execution_count": 2, "id": "8dd0d8092fe74a7c96281538738b07e2", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:03.139049Z", "iopub.status.busy": "2026-05-16T13:45:03.138758Z", "iopub.status.idle": "2026-05-16T13:45:04.749269Z", "shell.execute_reply": "2026-05-16T13:45:04.748225Z" }, "papermill": { "duration": 1.615461, "end_time": "2026-05-16T13:45:04.750071+00:00", "exception": false, "start_time": "2026-05-16T13:45:03.134610+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "from galpy.potential import HernquistPotential\n", "from galpy.df import isotropicHernquistdf\n", "\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfh = isotropicHernquistdf(pot=hp)" ] }, { "cell_type": "markdown", "id": "72eea5119410473aa328ad9291626812", "metadata": { "papermill": { "duration": 0.003128, "end_time": "2026-05-16T13:45:04.756743+00:00", "exception": false, "start_time": "2026-05-16T13:45:04.753615+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Evaluating the DF as a function of energy\n", "\n", "The DF can be evaluated at a given (relative) energy $E$. The relative energy\n", "is defined as $E = \\Psi(r) - \\frac{1}{2}v^2$ where $\\Psi = -\\Phi$ is the\n", "relative potential:" ] }, { "cell_type": "code", "execution_count": 3, "id": "8edb47106e1a46a883d545849b8ab81b", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:04.764527Z", "iopub.status.busy": "2026-05-16T13:45:04.764151Z", "iopub.status.idle": "2026-05-16T13:45:05.077376Z", "shell.execute_reply": "2026-05-16T13:45:05.076401Z" }, "papermill": { "duration": 0.318062, "end_time": "2026-05-16T13:45:05.078061+00:00", "exception": false, "start_time": "2026-05-16T13:45:04.759999+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Evaluate at several energies\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "# Scale by Phi(0) to get the DF as a function of energy\n", "phi0 = hp(0.0, 0.0, use_physical=False)\n", "fE = numpy.array([dfh.fE(E * phi0) for E in Es])\n", "plt.semilogy(Es, fE)\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$f(E)$\")\n", "plt.title(\"Isotropic Hernquist DF\");" ] }, { "cell_type": "markdown", "id": "10185d26023b46108eb7d9f57d49d2b3", "metadata": { "papermill": { "duration": 0.003326, "end_time": "2026-05-16T13:45:05.085212+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.081886+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Sampling positions and velocities\n", "\n", "The `sample` method draws random phase-space points from the DF.\n", "By default it returns an `Orbit` object:" ] }, { "cell_type": "code", "execution_count": 4, "id": "8763a12b2bbd4a93a75aff182afb95dc", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:05.093065Z", "iopub.status.busy": "2026-05-16T13:45:05.092835Z", "iopub.status.idle": "2026-05-16T13:45:05.113786Z", "shell.execute_reply": "2026-05-16T13:45:05.112752Z" }, "papermill": { "duration": 0.025804, "end_time": "2026-05-16T13:45:05.114463+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.088659+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Type: \n", "Number of orbits: 5000\n" ] } ], "source": [ "numpy.random.seed(1)\n", "samples = dfh.sample(n=5000)\n", "print(\"Type:\", type(samples))\n", "print(\"Number of orbits:\", len(samples))" ] }, { "cell_type": "markdown", "id": "664873cf", "metadata": { "papermill": { "duration": 0.003338, "end_time": "2026-05-16T13:45:05.121367+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.118029+00:00", "status": "completed" }, "tags": [] }, "source": [ "Let's plot the spatial distribution of the sampled orbits:" ] }, { "cell_type": "code", "execution_count": 5, "id": "7623eae2785240b9bd12b16a66d81610", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:05.129224Z", "iopub.status.busy": "2026-05-16T13:45:05.129000Z", "iopub.status.idle": "2026-05-16T13:45:05.269099Z", "shell.execute_reply": "2026-05-16T13:45:05.267953Z" }, "papermill": { "duration": 0.145328, "end_time": "2026-05-16T13:45:05.270183+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.124855+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the spatial distribution\n", "Rs = samples.R()\n", "zs = samples.z()\n", "plt.scatter(Rs, zs, s=1, alpha=0.3)\n", "plt.xlabel(r\"$R$\")\n", "plt.ylabel(r\"$z$\")\n", "plt.title(\"Sampled positions from isotropic Hernquist DF\")\n", "plt.xlim(0, 15)\n", "plt.ylim(-15, 15);" ] }, { "cell_type": "markdown", "id": "7cdc8c89c7104fffa095e18ddfef8986", "metadata": { "papermill": { "duration": 0.003632, "end_time": "2026-05-16T13:45:05.277924+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.274292+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Velocity dispersion profile\n", "\n", "We can compare the velocity dispersion profile of the samples to the\n", "analytical prediction. The `sigmar` method computes $\\sigma_r(r)$:" ] }, { "cell_type": "code", "execution_count": 6, "id": "b118ea5561624da68c537baed56e602f", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:05.288946Z", "iopub.status.busy": "2026-05-16T13:45:05.288738Z", "iopub.status.idle": "2026-05-16T13:45:05.494367Z", "shell.execute_reply": "2026-05-16T13:45:05.493496Z" }, "papermill": { "duration": 0.211002, "end_time": "2026-05-16T13:45:05.495213+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.284211+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Analytical velocity dispersion\n", "rs = numpy.linspace(0.1, 10.0, 50)\n", "sigmar = numpy.array([dfh.sigmar(r) for r in rs])\n", "\n", "# Velocity dispersion from samples\n", "r_samples = samples.r()\n", "vr_samples = (\n", " samples.x() * samples.vx() + samples.y() * samples.vy() + samples.z() * samples.vz()\n", ") / r_samples\n", "\n", "# Bin the samples\n", "rbins = numpy.linspace(0.1, 10.0, 11)\n", "rmid = 0.5 * (rbins[:-1] + rbins[1:])\n", "sig_binned = numpy.zeros(len(rmid))\n", "for i in range(len(rmid)):\n", " mask = (r_samples >= rbins[i]) & (r_samples < rbins[i + 1])\n", " if numpy.sum(mask) > 2:\n", " sig_binned[i] = numpy.std(vr_samples[mask])\n", "\n", "plt.plot(rs, sigmar, label=\"Analytical\")\n", "plt.plot(rmid, sig_binned, \"o\", label=\"Samples\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(r\"$\\sigma_r(r)$\")\n", "plt.legend()\n", "plt.title(\"Velocity dispersion profile\");" ] }, { "cell_type": "markdown", "id": "72511469", "metadata": { "papermill": { "duration": 0.003854, "end_time": "2026-05-16T13:45:05.503272+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.499418+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Jeans equation tools\n", "\n", "galpy also provides tools for computing velocity moments from the Jeans equation\n", "in `galpy.df.jeans`. These are useful for comparing with DF-based calculations\n", "and for quick estimates when a full DF is not needed.\n", "\n", "The main functions are:\n", "- `jeans.sigmar(pot, r)`: radial velocity dispersion $\\sigma_r(r)$\n", "- `jeans.sigmalos(pot, R)`: line-of-sight velocity dispersion $\\sigma_\\mathrm{los}(R)$\n", "\n", "Both of these functions allow the user to specify the anisotropy profile $\\beta(r)$, which is defined as\n", "$\\beta(r) = 1 - \\frac{\\sigma_\\theta^2 + \\sigma_\\phi^2}{2\\sigma_r^2}$ as well as the tracer density profile $\\nu(r)$, which is needed to solve the Jeans equation. By default, `beta` is set to 0 (isotropic) and `nu` is set to the density profile of the potential." ] }, { "cell_type": "code", "execution_count": 7, "id": "ad85600f", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:45:05.512185Z", "iopub.status.busy": "2026-05-16T13:45:05.511888Z", "iopub.status.idle": "2026-05-16T13:46:18.031337Z", "shell.execute_reply": "2026-05-16T13:46:18.030409Z" }, "papermill": { "duration": 72.528656, "end_time": "2026-05-16T13:46:18.035899+00:00", "exception": false, "start_time": "2026-05-16T13:45:05.507243+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 jeans\n", "\n", "# Compute radial velocity dispersion from the Jeans equation\n", "rs_jeans = numpy.linspace(0.1, 10.0, 50)\n", "sigmar_jeans = numpy.array([jeans.sigmar(hp, r, use_physical=False) for r in rs_jeans])\n", "\n", "# Compute for constant beta=0.3\n", "sigmar_jeans_b03 = numpy.array(\n", " [jeans.sigmar(hp, r, beta=0.3, use_physical=False) for r in rs_jeans]\n", ")\n", "\n", "# Compute for Osipkov-Merritt-style beta(r) = r^2/(r^2 + ra^2)\n", "beta_om = lambda r: r**2 / (r**2 + 1.4**2)\n", "sigmar_jeans_om = numpy.array(\n", " [jeans.sigmar(hp, r, beta=beta_om, use_physical=False) for r in rs_jeans]\n", ")\n", "\n", "# Compute line-of-sight velocity dispersion\n", "sigmalos_jeans = numpy.array(\n", " [jeans.sigmalos(hp, R, use_physical=False) for R in rs_jeans]\n", ")\n", "sigmalos_jeans_b03 = numpy.array(\n", " [jeans.sigmalos(hp, R, beta=0.3, use_physical=False) for R in rs_jeans]\n", ")\n", "sigmalos_jeans_om = numpy.array(\n", " [jeans.sigmalos(hp, R, beta=beta_om, use_physical=False) for R in rs_jeans]\n", ")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "axes[0].plot(rs_jeans, sigmar_jeans, label=r\"Isotropic ($\\beta=0$)\")\n", "axes[0].plot(rs_jeans, sigmar_jeans_b03, label=r\"Constant $\\beta=0.3$\")\n", "axes[0].plot(rs_jeans, sigmar_jeans_om, \"--\", label=r\"OM ($r_a=1.4$)\")\n", "axes[0].set_xlabel(r\"$r$\")\n", "axes[0].set_ylabel(r\"$\\sigma_r(r)$\")\n", "axes[0].set_title(\"Jeans equation: radial velocity dispersion\")\n", "axes[0].legend()\n", "\n", "axes[1].plot(rs_jeans, sigmalos_jeans, label=r\"Isotropic ($\\beta=0$)\")\n", "axes[1].plot(rs_jeans, sigmalos_jeans_b03, label=r\"Constant $\\beta=0.3$\")\n", "axes[1].plot(rs_jeans, sigmalos_jeans_om, \"--\", label=r\"OM ($r_a=1.4$)\")\n", "axes[1].set_xlabel(r\"$R$\")\n", "axes[1].set_ylabel(r\"$\\sigma_\\mathrm{los}(R)$\")\n", "axes[1].set_title(\"Jeans equation: line-of-sight velocity dispersion\")\n", "axes[1].legend()\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "938c804e27f84196a10c8828c723f798", "metadata": { "papermill": { "duration": 0.004083, "end_time": "2026-05-16T13:46:18.044396+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.040313+00:00", "status": "completed" }, "tags": [] }, "source": [ "## King DF\n", "\n", "The King DF models a tidally-truncated, lowered-isothermal distribution.\n", "It is initialized with the dimensionless central potential $W_0$, total mass, and\n", "tidal radius:" ] }, { "cell_type": "code", "execution_count": 8, "id": "504fb2a444614c0babb325280ed9130a", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:18.053957Z", "iopub.status.busy": "2026-05-16T13:46:18.053738Z", "iopub.status.idle": "2026-05-16T13:46:18.302463Z", "shell.execute_reply": "2026-05-16T13:46:18.301559Z" }, "papermill": { "duration": 0.254551, "end_time": "2026-05-16T13:46:18.303188+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.048637+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "numpy.random.seed(1)\n", "from galpy.df import kingdf\n", "\n", "kdf = kingdf(W0=3.0, M=1.0, rt=1.5)\n", "\n", "# Sample from the King model\n", "king_samples = kdf.sample(n=5000)\n", "r_king = king_samples.r()\n", "plt.hist(r_king, bins=30, density=True, label=\"Samples\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(\"Density\")\n", "plt.title(\"King model radial distribution (W0=3)\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "74bb50cf", "metadata": { "papermill": { "duration": 0.004401, "end_time": "2026-05-16T13:46:18.312393+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.307992+00:00", "status": "completed" }, "tags": [] }, "source": [ "We can compare the sampled radial distribution with the theoretical King density\n", "profile. The King DF provides a `dens(r)` method that returns the density at a\n", "given radius. To compare with the histogram of radii, we need to weight by the\n", "volume element $4\\pi r^2$:" ] }, { "cell_type": "code", "execution_count": 9, "id": "ed1c1963", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:18.322407Z", "iopub.status.busy": "2026-05-16T13:46:18.322204Z", "iopub.status.idle": "2026-05-16T13:46:18.510143Z", "shell.execute_reply": "2026-05-16T13:46:18.508884Z" }, "papermill": { "duration": 0.193993, "end_time": "2026-05-16T13:46:18.510871+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.316878+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Theoretical King density profile weighted by volume element\n", "r_theory = numpy.linspace(0.01, 1.49, 200)\n", "rho_theory = numpy.array([kdf.dens(r) for r in r_theory])\n", "# The histogram shows the PDF of radii, which is proportional to rho(r) * 4*pi*r^2\n", "radial_pdf = rho_theory * 4.0 * numpy.pi * r_theory**2\n", "# Normalize to integrate to 1 (since histogram is density=True)\n", "from scipy import integrate\n", "\n", "radial_pdf /= integrate.trapezoid(radial_pdf, r_theory)\n", "\n", "plt.hist(r_king, bins=30, density=True, alpha=0.5, label=\"Samples\")\n", "plt.plot(r_theory, radial_pdf, \"r-\", lw=2, label=\"Theoretical King profile\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(\"PDF\")\n", "plt.title(\"King model: samples vs. theoretical radial distribution\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "0654d7d6", "metadata": { "papermill": { "duration": 0.004584, "end_time": "2026-05-16T13:46:18.520514+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.515930+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Differential energy distribution\n", "\n", "galpy can also compute the differential energy distribution $N(E)$, which is the number of stars per unit energy. This is related to the DF by integrating over phase space at fixed energy:" ] }, { "cell_type": "code", "execution_count": 10, "id": "da7366cc", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:18.531140Z", "iopub.status.busy": "2026-05-16T13:46:18.530906Z", "iopub.status.idle": "2026-05-16T13:46:18.937788Z", "shell.execute_reply": "2026-05-16T13:46:18.936953Z" }, "papermill": { "duration": 0.413247, "end_time": "2026-05-16T13:46:18.938515+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.525268+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfh = isotropicHernquistdf(pot=hp)\n", "\n", "from galpy.potential import NFWPotential, PlummerPotential\n", "from galpy.df import isotropicNFWdf, isotropicPlummerdf\n", "\n", "nfp = NFWPotential(amp=1.0, a=1.0)\n", "dfnfw = isotropicNFWdf(pot=nfp)\n", "pp = PlummerPotential(amp=1.0, b=1.0)\n", "dfplummer = isotropicPlummerdf(pot=pp)\n", "\n", "# Evaluate at several energies\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "# Scale by Phi(0) to get the DF as a function of energy\n", "phi0_hp = hp(0.0, 0.0, use_physical=False)\n", "dMdE_hp = numpy.array([dfh.dMdE(E * phi0_hp) for E in Es])\n", "phi0_nfw = nfp(0.0, 0.0, use_physical=False)\n", "dMdE_nfw = numpy.array([dfnfw.dMdE(E * phi0_nfw) for E in Es])\n", "phi0_plummer = pp(0.0, 0.0, use_physical=False)\n", "dMdE_plummer = numpy.array([dfplummer.dMdE(E * phi0_plummer) for E in Es])\n", "plt.semilogy(Es, dMdE_hp, label=\"Hernquist\")\n", "plt.semilogy(Es, dMdE_nfw, label=\"NFW\")\n", "plt.semilogy(Es, dMdE_plummer, label=\"Plummer\")\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$dM/dE$\")\n", "plt.title(\"Isotropic DFs\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "c98e8906", "metadata": { "papermill": { "duration": 0.004709, "end_time": "2026-05-16T13:46:18.948318+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.943609+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Using the Eddington inversion\n", "\n", "The ``eddingtondf`` class can be used to compute the isotropic DF for any spherical potential using Eddington's formula. This is useful for potentials that do not have an analytical DF, for comparing with the analytical DFs of specific potentials, or for computing the DFs of tracers in a given potential, e.g., a Hernquist population in an NFW potential. We give an example of the latter here:" ] }, { "cell_type": "code", "execution_count": 11, "id": "15c62173", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:18.959001Z", "iopub.status.busy": "2026-05-16T13:46:18.958795Z", "iopub.status.idle": "2026-05-16T13:46:19.348701Z", "shell.execute_reply": "2026-05-16T13:46:19.347719Z" }, "papermill": { "duration": 0.396243, "end_time": "2026-05-16T13:46:19.349398+00:00", "exception": false, "start_time": "2026-05-16T13:46:18.953155+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 eddingtondf\n", "\n", "nfp = NFWPotential(amp=1.0, a=1.0)\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "df_edd = eddingtondf(pot=nfp, denspot=hp)\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "phi0_nfw = nfp(0.0, 0.0, use_physical=False)\n", "dMdE_edd = numpy.array([df_edd.dMdE(E * phi0_nfw) for E in Es])\n", "plt.semilogy(Es, dMdE_edd, label=\"Eddington inversion\")\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$dM/dE$\")\n", "plt.title(\"Isotropic DF from Eddington inversion\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "59bbdb311c014d738909a11f9e486628", "metadata": { "papermill": { "duration": 0.00492, "end_time": "2026-05-16T13:46:19.359751+00:00", "exception": false, "start_time": "2026-05-16T13:46:19.354831+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Anisotropic DFs\n", "\n", "galpy includes anisotropic DFs for spherical systems.\n", "\n", "### Constant-beta Hernquist DF\n", "\n", "The `constantbetaHernquistdf` implements a Hernquist DF with constant velocity\n", "anisotropy parameter $\\beta$. Unlike the isotropic case ($\\beta=0$), this DF\n", "has different radial and tangential velocity dispersions. The anisotropy\n", "parameter is defined as $\\beta = 1 - \\sigma_t^2 / (2\\sigma_r^2)$, so\n", "$\\beta > 0$ corresponds to radially-biased orbits and $\\beta < 0$ to\n", "tangentially-biased orbits." ] }, { "cell_type": "code", "execution_count": 12, "id": "b43b363d81ae4b689946ece5c682cd59", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:19.370969Z", "iopub.status.busy": "2026-05-16T13:46:19.370774Z", "iopub.status.idle": "2026-05-16T13:46:19.882498Z", "shell.execute_reply": "2026-05-16T13:46:19.881538Z" }, "papermill": { "duration": 0.518397, "end_time": "2026-05-16T13:46:19.883317+00:00", "exception": false, "start_time": "2026-05-16T13:46:19.364920+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", "from galpy.df import constantbetaHernquistdf\n", "\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfb = constantbetaHernquistdf(pot=hp, beta=0.3)\n", "\n", "# Sample and compute the velocity anisotropy from samples\n", "samples_b = dfb.sample(n=10000)\n", "r_b = samples_b.r()\n", "vr_b = samples_b.vr()\n", "vt2_b = samples_b.vx() ** 2 + samples_b.vy() ** 2 + samples_b.vz() ** 2 - vr_b**2\n", "\n", "# Compare analytical sigma_r with isotropic and Jeans equation\n", "rs = numpy.linspace(0.3, 8.0, 30)\n", "sigmar_beta = numpy.array([dfb.sigmar(r) for r in rs])\n", "sigmar_iso = numpy.array([dfh.sigmar(r) for r in rs])\n", "sigmar_jeans_beta = numpy.array(\n", " [jeans.sigmar(hp, r, beta=0.3, use_physical=False) for r in rs]\n", ")\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "# Left panel: velocity dispersion comparison\n", "axes[0].plot(rs, sigmar_iso, label=r\"Isotropic ($\\beta=0$)\")\n", "axes[0].plot(rs, sigmar_beta, label=r\"Constant $\\beta=0.3$ (DF)\")\n", "axes[0].plot(rs, sigmar_jeans_beta, \"--\", label=r\"Jeans ($\\beta=0.3$)\")\n", "axes[0].set_xlabel(r\"$r$\")\n", "axes[0].set_ylabel(r\"$\\sigma_r(r)$\")\n", "axes[0].legend()\n", "axes[0].set_title(\"Radial velocity dispersion\")\n", "\n", "# Right panel: measured anisotropy from samples\n", "rbins = numpy.linspace(0.3, 8.0, 12)\n", "rmid = 0.5 * (rbins[:-1] + rbins[1:])\n", "beta_measured = numpy.zeros(len(rmid))\n", "for i in range(len(rmid)):\n", " mask = (r_b >= rbins[i]) & (r_b < rbins[i + 1])\n", " if numpy.sum(mask) > 10:\n", " sig_r2 = numpy.var(vr_b[mask])\n", " sig_t2 = numpy.mean(vt2_b[mask])\n", " beta_measured[i] = 1.0 - sig_t2 / (2.0 * sig_r2)\n", "\n", "axes[1].axhline(0.3, color=\"r\", ls=\"--\", label=r\"Input $\\beta=0.3$\")\n", "axes[1].plot(rmid, beta_measured, \"o\", label=\"Measured from samples\")\n", "axes[1].set_xlabel(r\"$r$\")\n", "axes[1].set_ylabel(r\"$\\beta(r)$\")\n", "axes[1].legend()\n", "axes[1].set_title(\"Velocity anisotropy profile\")\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "8a65eabff63a45729fe45fb5ade58bdc", "metadata": { "papermill": { "duration": 0.005144, "end_time": "2026-05-16T13:46:19.894274+00:00", "exception": false, "start_time": "2026-05-16T13:46:19.889130+00:00", "status": "completed" }, "tags": [] }, "source": [ "### Osipkov-Merritt Hernquist DF\n", "\n", "The Osipkov-Merritt DF is a widely used model for radially-anisotropic\n", "spherical systems. The velocity anisotropy varies with radius as\n", "$\\beta(r) = r^2/(r^2 + r_a^2)$, where $r_a$ is the anisotropy radius.\n", "This means the system is nearly isotropic at the center ($r \\ll r_a$)\n", "and becomes increasingly radially anisotropic at large radii ($r \\gg r_a$,\n", "$\\beta \\to 1$). Smaller values of $r_a$ lead to stronger overall anisotropy." ] }, { "cell_type": "code", "execution_count": 13, "id": "c3933fab20d04ec698c2621248eb3be0", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:19.905809Z", "iopub.status.busy": "2026-05-16T13:46:19.905590Z", "iopub.status.idle": "2026-05-16T13:46:20.592732Z", "shell.execute_reply": "2026-05-16T13:46:20.591636Z" }, "papermill": { "duration": 0.693913, "end_time": "2026-05-16T13:46:20.593441+00:00", "exception": false, "start_time": "2026-05-16T13:46:19.899528+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 osipkovmerrittHernquistdf\n", "\n", "dfom = osipkovmerrittHernquistdf(pot=hp, ra=1.4)\n", "\n", "# Compare velocity dispersion profiles: DF vs. Jeans equation\n", "rs = numpy.linspace(0.3, 8.0, 30)\n", "sig_iso = numpy.array([dfh.sigmar(r) for r in rs])\n", "sig_om = numpy.array([dfom.sigmar(r) for r in rs])\n", "\n", "# Jeans equation prediction with the OM beta profile\n", "beta_om = lambda r: r**2 / (r**2 + 1.4**2)\n", "sigmar_jeans_om = numpy.array(\n", " [jeans.sigmar(hp, r, beta=beta_om, use_physical=False) for r in rs]\n", ")\n", "\n", "plt.plot(rs, sig_iso, label=\"Isotropic (DF)\")\n", "plt.plot(rs, sig_om, label=\"Osipkov-Merritt (DF, $r_a=1.4$)\")\n", "plt.plot(rs, sigmar_jeans_om, \"k--\", label=\"Jeans equation (OM $\\\\beta$)\")\n", "plt.xlabel(r\"$r$\")\n", "plt.ylabel(r\"$\\sigma_r(r)$\")\n", "plt.legend()\n", "plt.title(\"Comparing isotropic, Osipkov-Merritt, and Jeans predictions\");" ] }, { "cell_type": "markdown", "id": "1908e31c", "metadata": { "papermill": { "duration": 0.005346, "end_time": "2026-05-16T13:46:20.604579+00:00", "exception": false, "start_time": "2026-05-16T13:46:20.599233+00:00", "status": "completed" }, "tags": [] }, "source": [ "For all anisotropic DFs, the sampling and evaluation methods work similarly to the isotropic case, but the velocity distribution will reflect the specified anisotropy.\n", "\n", "We can also compute the differential energy distribution for anisotropic DFs, which will differ from the isotropic case due to the different velocity structure." ] }, { "cell_type": "code", "execution_count": 14, "id": "296e26da", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:46:20.616725Z", "iopub.status.busy": "2026-05-16T13:46:20.616475Z", "iopub.status.idle": "2026-05-16T13:47:41.768827Z", "shell.execute_reply": "2026-05-16T13:47:41.767822Z" }, "papermill": { "duration": 81.165089, "end_time": "2026-05-16T13:47:41.775123+00:00", "exception": false, "start_time": "2026-05-16T13:46:20.610034+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hp = HernquistPotential(amp=2.0, a=1.3)\n", "dfh = isotropicHernquistdf(pot=hp)\n", "dfh_constantbeta = constantbetaHernquistdf(pot=hp, beta=0.5)\n", "dfh_ombeta = osipkovmerrittHernquistdf(pot=hp, ra=1.4)\n", "# Evaluate at several energies\n", "Es = numpy.linspace(0.01, 0.99, 50)\n", "# Scale by Phi(0) to get the DF as a function of energy\n", "phi0_hp = hp(0.0, 0.0, use_physical=False)\n", "dMdE_hp = numpy.array([dfh.dMdE(E * phi0_hp) for E in Es])\n", "dMdE_constantbeta = numpy.array([dfh_constantbeta.dMdE(E * phi0_hp) for E in Es])\n", "dMdE_ombeta = numpy.array([dfh_ombeta.dMdE(E * phi0_hp) for E in Es])\n", "plt.semilogy(Es, dMdE_hp, label=\"Isotropic\")\n", "plt.semilogy(Es, dMdE_constantbeta, label=\"Constant beta\")\n", "plt.semilogy(Es, dMdE_ombeta, label=\"Osipkov-Merritt\")\n", "plt.xlabel(r\"$E / \\Phi(0)$\")\n", "plt.ylabel(r\"$dM/dE$\")\n", "plt.title(\"Anisotropic DFs\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "0a5f7b62", "metadata": { "papermill": { "duration": 0.005636, "end_time": "2026-05-16T13:47:41.786613+00:00", "exception": false, "start_time": "2026-05-16T13:47:41.780977+00:00", "status": "completed" }, "tags": [] }, "source": [ "General formulas for computing constant-ansisotropy and Osipkov-Merritt DFs for any spherical potential are also implemented in the `constantbetadf` and `osipkovmerrittdf` classes, which can be used to compute the DF for any spherical potential with the specified anisotropy profile. For example, again embedding a Hernquist population in an NFW potential, we can compute the constant-beta and Osipkov-Merritt DFs for this system as follows and sample the different DFs to compare their velocity distributions:" ] }, { "cell_type": "code", "execution_count": 15, "id": "42a09c9e", "metadata": { "execution": { "iopub.execute_input": "2026-05-16T13:47:41.799186Z", "iopub.status.busy": "2026-05-16T13:47:41.798950Z", "iopub.status.idle": "2026-05-16T13:47:51.861037Z", "shell.execute_reply": "2026-05-16T13:47:51.859947Z" }, "papermill": { "duration": 10.069344, "end_time": "2026-05-16T13:47:51.861732+00:00", "exception": false, "start_time": "2026-05-16T13:47:41.792388+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 constantbetadf, osipkovmerrittdf\n", "\n", "r0 = 2.0\n", "n_samples = 8000\n", "numpy.random.seed(1)\n", "\n", "nfp = NFWPotential(amp=1.0, a=1.0)\n", "hp = HernquistPotential(amp=2.0, a=1.3)\n", "df_edd = eddingtondf(pot=nfp, denspot=hp)\n", "# Use half-integer beta, for which the numerics are much faster\n", "df_constb = constantbetadf(pot=nfp, denspot=hp, twobeta=1)\n", "df_constb_low = constantbetadf(pot=nfp, denspot=hp, twobeta=-1)\n", "df_omb = osipkovmerrittdf(pot=nfp, denspot=hp, ra=1.4)\n", "\n", "samples_edd = df_edd.sample(n=n_samples, R=r0, z=0.0)\n", "samples_constb = df_constb.sample(n=n_samples, R=r0, z=0.0)\n", "samples_constb_low = df_constb_low.sample(n=n_samples, R=r0, z=0.0)\n", "samples_omb = df_omb.sample(n=n_samples, R=r0, z=0.0)\n", "\n", "vr_edd = samples_edd.vr()\n", "vr_constb = samples_constb.vr()\n", "vr_constb_low = samples_constb_low.vr()\n", "vr_omb = samples_omb.vr()\n", "\n", "vt_edd = numpy.sqrt(samples_edd.vT() ** 2 + samples_edd.vtheta() ** 2)\n", "vt_constb = numpy.sqrt(samples_constb.vT() ** 2 + samples_constb.vtheta() ** 2)\n", "vt_constb_low = numpy.sqrt(\n", " samples_constb_low.vT() ** 2 + samples_constb_low.vtheta() ** 2\n", ")\n", "vt_omb = numpy.sqrt(samples_omb.vT() ** 2 + samples_omb.vtheta() ** 2)\n", "\n", "fig_vel, ax_vel = plt.subplots(1, 2, figsize=(12, 4))\n", "\n", "ax_vel[0].hist(\n", " vr_edd, bins=31, density=True, histtype=\"step\", lw=2, label=\"Eddington (isotropic)\"\n", ")\n", "ax_vel[0].hist(\n", " vr_constb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=0.5$\",\n", ")\n", "ax_vel[0].hist(\n", " vr_constb_low,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=-0.5$\",\n", ")\n", "ax_vel[0].hist(\n", " vr_omb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Osipkov-Merritt ($r_a=1.4$)\",\n", ")\n", "ax_vel[0].set_xlabel(r\"$v_r$\")\n", "ax_vel[0].set_ylabel(\"PDF\")\n", "ax_vel[0].set_title(rf\"Radial velocities at $r={r0}$\")\n", "ax_vel[0].legend()\n", "\n", "ax_vel[1].hist(\n", " vt_edd, bins=31, density=True, histtype=\"step\", lw=2, label=\"Eddington (isotropic)\"\n", ")\n", "ax_vel[1].hist(\n", " vt_constb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=0.5$\",\n", ")\n", "ax_vel[1].hist(\n", " vt_constb_low,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Constant $\\beta=-0.5$\",\n", ")\n", "ax_vel[1].hist(\n", " vt_omb,\n", " bins=31,\n", " density=True,\n", " histtype=\"step\",\n", " lw=2,\n", " label=r\"Osipkov-Merritt ($r_a=1.4$)\",\n", ")\n", "ax_vel[1].set_xlabel(r\"$v_t$\")\n", "ax_vel[1].set_ylabel(\"PDF\")\n", "ax_vel[1].set_title(rf\"Tangential speeds at $r={r0}$\")\n", "ax_vel[1].legend()\n", "\n", "fig_vel.tight_layout();" ] }, { "cell_type": "markdown", "id": "073bcf0b", "metadata": { "papermill": { "duration": 0.005775, "end_time": "2026-05-16T13:47:51.873741+00:00", "exception": false, "start_time": "2026-05-16T13:47:51.867966+00:00", "status": "completed" }, "tags": [] }, "source": [ "Note that the calculation of constant-anisotropy DFs in this way requires the [jax](https://github.com/google/jax) library to be installed, as it relies on automatic differentiation to compute the necessary derivatives of the potential and density profiles. The Osipkov-Merritt DFs can be computed without ``jax``. Both can be quite slow." ] } ], "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": 171.490989, "end_time": "2026-05-16T13:47:52.595968+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/distribution_functions/spherical_dfs.ipynb", "output_path": "doc/source/tutorials/distribution_functions/spherical_dfs.ipynb", "parameters": {}, "start_time": "2026-05-16T13:45:01.104979+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }