{ "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/mixing_IGMF.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Mixing in the intergalactic magnetic field (IGMF)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial demonstrates photon-ALP mixing in the IGMF. The propagation also includes absorption in the extragalactic background light (EBL). The absorption is modeled through the `OptDepth` class of the `ebltable` python package. The implementation closely follows De Angelis et al. (2011).\n", "The tutorial also shows how one can easily change the ALP parameters and rerun the calculations." ] }, { "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": [ "We start with the typical imports:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [], "source": [ "from gammaALPs.core import Source, ALP, ModuleList\n", "from gammaALPs.base import environs, transfer\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from ebltable.tau_from_model import OptDepth\n", "from astropy import constants as c" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's assume some generic source. Only the redshift will matter, as we won't include the mixing in the GMF." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "src = Source(z=0.341, ra=0., dec=0.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's init the module, only with mixing in the IGMF. We assume an unpolarized beam." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [] }, "outputs": [], "source": [ "EGeV = np.logspace(1., 5., 200)\n", "pin = np.diag((1.,1.,0.)) * 0.5\n", "\n", "ml = ModuleList(ALP(m = 1., g = 6.), src, pin=pin, EGeV=EGeV, seed=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we add the propagation in the IGMF with a B-field strength of $10^{-9}$G and coherence length of 1 Mpc (both strength and coherence length are given at $z=0$) and a constant electron density of the intergalactic medium of $10^{-7}\\,\\mathrm{cm}^{-3}$. We only calculate the mixing in one random realization (`nsim=1`)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "ml.add_propagation(\"IGMF\", \n", " 0, # position of module counted from the source. \n", " nsim=1, # number of random B-field realizations\n", " B0=1e-3, # B field strength in micro Gauss at z = 0\n", " n0=1e-7, # normalization of electron density in cm^-3 at z = 0\n", " L0=1e3, # coherence (cell) length in kpc at z = 0\n", " eblmodel='dominguez' # EBL model\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we step through some ALP masses and calculate the mixing probability" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [] }, "outputs": [], "source": [ "malp = np.array([0.001,0.01, 1., 10.])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we initialize the arrays that will store the results" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "tags": [] }, "outputs": [], "source": [ "px = np.zeros((malp.shape[0], EGeV.shape[0]))\n", "py = np.zeros((malp.shape[0], EGeV.shape[0]))\n", "pa = np.zeros((malp.shape[0], EGeV.shape[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And calculate the case without photon-ALP mixing, i.e., EBL absorption only:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [] }, "outputs": [], "source": [ "tau = ml.modules[\"IGMFCell\"].t.opt_depth(ml.source.z, ml.EGeV / 1e3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The case with ALPs is computed in a loop over the considered ALP masses." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [] }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 0: \n", "/Users/mey/Python/gammaALPs/gammaALPs/base/transfer.py:799: UserWarning: Not all values of linear polarization are real values!\n", " warnings.warn(\"Not all values of linear polarization are real values!\")\n", "/Users/mey/Python/gammaALPs/gammaALPs/base/transfer.py:802: UserWarning: Not all values of circular polarization are real values!\n", " warnings.warn(\"Not all values of circular polarization are real values!\")\n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 0: \n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 0: \n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36mINFO\u001b[1;0m: Running Module 0: \n" ] } ], "source": [ "for i, mi in enumerate(malp):\n", " ml.alp.m = mi\n", " px[i], py[i], pa[i] = ml.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we plot the results for the different ALP masses and the no-ALP case." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Photon survial probability')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ls = ['-','--','-.']\n", "\n", "for i, mi in enumerate(malp):\n", " plt.loglog(EGeV, px[i] + py[i], \n", " label='$m = {0:.3f}$ neV'.format(mi),\n", " ls=ls[i % len(ls)])\n", " \n", "plt.loglog(ml.EGeV, np.exp(-tau),\n", " label='EBL absorption only',\n", " color='k',\n", " ls=':')\n", "\n", "plt.legend()\n", "plt.gca().set_ylim(1e-3,1.1)\n", "plt.xlabel('Energy (GeV)')\n", "plt.ylabel('Photon survial probability')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You notice that with increasing mass the oscillations are shifted towards higher energies as the critical energy increases. For the lowest two masses, the curves are identical. The reason is that the difference between the plasma frequency becomes very small (and the difference $|m_a^2 - \\omega_\\mathrm{pl}^2|$ is what enters the critical energy).\n", "\n", "You also see that at low energies the attenuation becomes stronger, whereas it decreased at higher energies. The reason is that as more and more photons are attenuated in the interaction with EBL photons, the component of ALPs reconverting into photons close to Earth becomes more and more visible." ] } ], "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 }