{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/me-manu/gammaALPs/blob/master/docs/tutorials/rotation_measure_gauss.ipynb)" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "# Calculating the coherence length and rotation measure for Gaussian turbulent field\n", "\n", "This tutorial demonstrates how to the coherence length and rotation measure of a magnetic field with Gaussian turbulence on the example of the Perseus cluster with the central radio galaxy NGC 1275. The assumed B-field environments are the same as in Ajello et al. (2016). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you haven't installed `gammaALPs` already, you can do so using `pip`. Just uncomment the line below:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#!pip install gammaALPs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First some imports:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from gammaALPs.core import Source, ALP, ModuleList\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import time\n", "from scipy.integrate import simps\n", "from scipy.stats import norm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we set the source properties (redshift and sky coordinates), the ALP, and the energy range.\n", "We only need those to init the `ModuleList` later -- we won't actually run the photon-ALP conversion probability calculation here." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "ngc1275 = Source(z=0.017559, ra='03h19m48.1s', dec='+41d30m42s')\n", "alp = ALP(m=1., g=1.)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "ml = ModuleList(alp, ngc1275)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We add the propagation within the intra-cluster Gaussian turbulent field with the same values as in Ajello et al. (2016)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36menvirons.py:\u001b[0;35m 431\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Using inputted chi\n" ] } ], "source": [ "ml.add_propagation(\"ICMGaussTurb\", \n", " 0, # position of module counted from the source. \n", " nsim=10, # number of random B-field realizations\n", " B0=10., # rms of B field in muG\n", " n0=3.9e-2, # normalization of electron density in cm-3\n", " n2=4.05e-3, # second normalization of electron density, see Churazov et al. 2003, Eq. 4 on cm-3\n", " r_abell=500., # extension of the cluster in kpc\n", " r_core=80., # electron density parameter, see Churazov et al. 2003, Eq. 4 in kpc\n", " r_core2=280., # electron density parameter, see Churazov et al. 2003, Eq. 4 in kpc\n", " beta=1.2, # electron density parameter, see Churazov et al. 2003, Eq. 4\n", " beta2=0.58, # electron density parameter, see Churazov et al. 2003, Eq. 4\n", " eta=0.5, # scaling of B-field with electron denstiy\n", " kL=0.18, # maximum turbulence scale in kpc^-1, taken from A2199 cool-core cluster, see Vacca et al. 2012 \n", " kH=9., # minimum turbulence scale, taken from A2199 cool-core cluster, see Vacca et al. 2012\n", " q=-2.80, # turbulence spectral index, taken from A2199 cool-core cluster, see Vacca et al. 2012\n", " seed=0 # random seed for reproducability, set to None for random seed.\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We peek at the transversal magnetic field and the electron density:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, '$r$ (kpc)')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ml.modules[\"ICMGaussTurb\"].r,\n", " ml.modules[\"ICMGaussTurb\"].B * np.sin(ml.modules[\"ICMGaussTurb\"].psi),\n", " lw=1)\n", "plt.plot(ml.modules[\"ICMGaussTurb\"].r,\n", " ml.modules[\"ICMGaussTurb\"].B * np.cos(ml.modules[\"ICMGaussTurb\"].psi),\n", " lw=1, ls = '--') \n", "plt.ylabel('$B$ field ($\\mu$G)')\n", "plt.xlabel('$r$ (kpc)')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, '$r$ (kpc)')" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(ml.modules[\"ICMGaussTurb\"].r,ml.modules[\"ICMGaussTurb\"].nel * 1e-3)\n", "plt.ylabel('$n_\\mathrm{el}$ (cm$^{-3}$)')\n", "plt.xlabel('$r$ (kpc)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spatial correlation and coherence legnth" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `gammaALPs.bfields.Bgaussian` class has methods to calculate the spatial correlation of the magnetic field and the rotation measure. We can access these methods through the the magnetic field model mehtod, which we can access through `ml.modules['ICMGaussTurb'].Bfield_model`. \n", "\n", "The spatial correlation $C(x_3) = \\langle B_\\perp(\\vec{x}) B_\\perp(\\vec{x} + x_3 \\vec{e}_3)\\rangle$ of the transversal magnetic field along the line of sight $z$ is computed like this:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z = np.linspace(0.,50.,1000) # distance in kpc from cluster center\n", "c = ml.modules[\"ICMGaussTurb\"].Bfield_model.spatial_correlation(z) \n", "\n", "plt.plot(z, c / c[0])\n", "plt.xlabel(\"$z$ (kpc)\")\n", "plt.ylabel(\"$C(z) / C(0)$\")\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is turn can be used to calculate the coherence length of the field, \n", "$$ \\Lambda_C = \\frac{1}{C(0)} \\int\\limits_0^\\infty C(z)dz. $$\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coherence length of the field is Lambda_C = 1.492e+00 kpc\n" ] } ], "source": [ "z = np.linspace(0.,1e3,1000) # distance in kpc from cluster center\n", "c = ml.modules[\"ICMGaussTurb\"].Bfield_model.spatial_correlation(z) \n", "\n", "Lambda_c = simps(c, z) / c[0]\n", "\n", "print (\"Coherence length of the field is Lambda_C = {0:.3e} kpc\".format(Lambda_c))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate the rotation measure of the field\n", "\n", "The rotation measure describes the rotation of the polarization vector due to the propagation of an electromagnetic wave through a medium with magnetic field and an electron plasma. \n", "\n", "The change in polarization angle $\\Delta\\phi$ is proportianol to the wavewavelength and the rotation measure $\\mathrm{RM}$ which is given by the integral over the magnetic field parallel to the propagation direction multiplied with the electron density:\n", "\n", "$$ \\mathrm{RM} \\approx 812\\,\\mathrm{rad}\\,\\mathrm{m}^{-2} \\int\\limits_0^z dz' B_{||}(z') n_\\mathrm{el}(z'). $$\n", "\n", "We can calcluate the $\\mathrm{RM}$ through the `ml.modules['ICMGaussTurb'].Bfield_model.rotation_measure` function which computes $B_{||}$ for a requested number `nsim` of random realizations. \n", "In addition to the line of sight we're interested in, we also have to provide the electron density along $z$ and the scaling of the magnetic field with the electron density, i.e. the factor $(n_\\mathrm{el}(z) / n_\\mathrm{el}(z=0)^\\eta$. The latter can be calculated through the `ml.modules[\"ICMGaussTurb\"].nel_model.Bscale` function. \n", "\n", "We calculate the electron density and the scaling:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "n_el = ml.modules[\"ICMGaussTurb\"].nel\n", "Bscale = ml.modules[\"ICMGaussTurb\"].nel_model.Bscale(ml.modules[\"ICMGaussTurb\"].r)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And provide this to the `rotation_measure` function. The loop over the realizations is rather slow, so we calculate the $\\mathrm{RM}$ for only 500 random realizations:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculating RM for 500 realizations took 17.96 seconds\n" ] } ], "source": [ "ml.modules[\"ICMGaussTurb\"].Bfield_model.seed = 0\n", "\n", "t1 = time.time()\n", "nsim=500\n", "rm = ml.modules[\"ICMGaussTurb\"].Bfield_model.rotation_measure(ml.modules[\"ICMGaussTurb\"].r,\n", " n_el=n_el,\n", " Bscale=Bscale,\n", " nsim=nsim)\n", "t2 = time.time()\n", "print(\"Calculating RM for {0:d} realizations took {1:.2f} seconds\".format(nsim, t2 - t1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we plot the histogram of the $\\mathrm{RM}$ values. Since we're assuming a purely turbulent field, we expect a distribution that peaks close to zero and we can compare the spread to the $\\mathrm{RM}$ values reported by Taylor et al. (2006) who found RM values between 6500 and 7500 $\\mathrm{rad}\\,\\mathrm{m}^{-2}$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RM mean +/- sqrt(var) in rad m^-2: 49.62 +/- 2707.52\n" ] }, { "data": { "text/plain": [ "Text(0, 0.5, 'Density')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n, bins, _ = plt.hist(np.sort((rm)), bins=30, density=True, label=\"Simulated RM\")\n", "\n", "mean = np.mean(rm) # mean\n", "var = np.var(rm) # variance\n", "print(\"RM mean +/- sqrt(var) in rad m^-2: {0:.2f} +/- {1:.2f}\".format(mean, np.sqrt(var)))\n", "\n", "plt.plot(bins, norm.pdf(bins, loc=mean, scale=np.sqrt(var)),\n", " lw=2,\n", " label=\"Gaussian Fit\\n$\\mu = {0:.2f}$\\n$\\sigma={1:.2f}$\".format(mean, np.sqrt(var)))\n", "\n", "plt.legend()\n", "plt.gca().tick_params(labelleft=False, left=False, right=False, top=False)\n", "plt.xlabel(\"Rotation Measure (rad m${}^{-2}$)\")\n", "plt.ylabel(\"Density\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With our chosen $B$ field, $\\sigma(\\mathrm{RM}) \\sim 2700 \\,\\mathrm{m}^{-2}$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 4 }