{ "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/photon_dispersion.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Photon-photon dispersion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial shows how to include photon-photon dispersion off of background photon fields in the ALP-photon propagation calculation. The relevance of photon dispersion for ALP calculations is discussed in [Dobrynina 2015](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.083003). A background field adds to the dispersive part of the refractive index of the propagation medium $n = 1+\\chi$. [Dobrynina 2015](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.083003) show that at $z=0$, $\\chi_{CMB} = 5.11\\times10^{-43}$. Dispersion off the CMB is included by default, but other values of $\\chi$ can be included manually." ] }, { "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 import what we will need:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "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 astropy import constants as c\n", "from matplotlib.patheffects import withStroke\n", "from astropy import units as u\n", "import time\n", "from scipy.interpolate import RectBivariateSpline as RBSpline\n", "\n", "effect = dict(path_effects=[withStroke(foreground=\"w\", linewidth=2)]) # used for plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\chi$ is included in the code as a 2D spline function in energy and propagation distance. This means that the points at which $\\chi$ is calculated at do not need to be exactly the same as the points used for the magnetic field. It is also possible to include $\\chi$ as an array of size `(1)` if you want a constant value, or size `(len(EGeV),len(r))`, if you have calculated $\\chi$ in the exact magnetic field domains you will be using." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\chi$ function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will create a fake $\\chi$ function which changes with distance and energy, and then see its effects on mixing in different environments." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "EGeV = np.logspace(-5.,6.,1000)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "chiCMB = transfer.chiCMB" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.0962922355799666e-43" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chiCMB" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$r$ will be in pc for the jets and kpc for the clusters and GMF." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "rs = np.logspace(-2,5,200)\n", "chis = 1.e9 * rs[np.newaxis,:]**-3 * chiCMB * EGeV[:,np.newaxis]**(1.5) + chiCMB" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'r [pc or kpc] or z')" ] }, "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(rs,chis[0,:])\n", "plt.loglog(rs,chis[500,:])\n", "plt.loglog(rs,chis[-1,:])\n", "plt.ylabel(r'$\\chi$')\n", "plt.xlabel('r [pc or kpc] or z')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our $\\chi$ changes with both energy and distance." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'r [pc or kpc]')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ee, rr = np.meshgrid(EGeV,rs,indexing='ij')\n", "plt.pcolormesh(ee,rr,np.log10(chis),cmap=plt.get_cmap('coolwarm'),\n", " shading='auto')\n", "plt.colorbar(label=r\"log($\\chi$)\")\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.xlabel('E [GeV]')\n", "plt.ylabel('r [pc or kpc]')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the spline function:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "chispl = RBSpline(EGeV,rs,chis,kx=1,ky=1,s=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can test it for a source. We will use 3C454.3 (see the individual environment tutorials for more details on each of the environments)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "src = Source(z=0.859 , ra='22h53m57.7s', dec='+16d08m54s', bLorentz=60.) # 3C454.3" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "pin = np.diag((1.,1.,0.)) * 0.5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's test the `\"Jet\"` class:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "ml = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)\n", "ml_chi = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# other jet\n", "gamma_min = 18." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Add the same jet module to each, including $\\chi$ with the `chi` keyword for the second one." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36menvirons.py:\u001b[0;35m 758\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Assuming equipartion at r0: n0(r0) = 6.307e-01 cm^-3\n", "\u001b[0;36menvirons.py:\u001b[0;35m 767\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Using inputted chi\n", "\u001b[0;36menvirons.py:\u001b[0;35m 758\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Assuming equipartion at r0: n0(r0) = 6.307e-01 cm^-3\n", "\u001b[0;36menvirons.py:\u001b[0;35m 764\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Using interpolated chi\n" ] } ], "source": [ "ml.add_propagation(\"Jet\", \n", " 0, # position of module counted from the source. \n", " B0=0.32, # Jet field at r = R0 in G \n", " r0=1., # distance from BH where B = B0 in pc\n", " rgam=3.19e17 * u.cm.to('pc'), # distance of gamma-ray emitting region to BH\n", " alpha=-1., # exponent of toroidal mangetic field (default: -1.)\n", " psi=np.pi/4., # Angle between one photon polarization state and B field. \n", " # Assumed constant over entire jet. \n", " helical=True, # if True, use helical magnetic-field model from Clausen-Brown et al. (2011). \n", " # In this case, the psi kwarg is treated is as the phi angle \n", " # of the photon trajectory in the cylindrical jet coordinate system\n", " equipartition=True, # if true, assume equipartition between electrons and the B field. \n", " # This will overwrite the exponent of electron density beta = 2 * alpha \n", " # and set n0 given the minimum electron lorentz factor set with gamma_min\n", " gamma_min=gamma_min, # minimum lorentz factor of emitting electrons, only used if equipartition=True\n", " gamma_max=np.exp(10.) * gamma_min, # maximum lorentz factor of emitting electrons,\n", " # only used if equipartition=True\n", " Rjet= 40., # maximum jet length in pc (default: 1000.)\n", " n0=1e4, # normalization of electron density, overwritten if equipartition=True\n", " beta=-2. # power-law index of electron density, overwritten if equipartition=True\n", " )\n", "ml_chi.add_propagation(\"Jet\", \n", " 0, # position of module counted from the source. \n", " B0=0.32, # Jet field at r = R0 in G \n", " r0=1., # distance from BH where B = B0 in pc\n", " rgam=3.19e17 * u.cm.to('pc'), # distance of gamma-ray emitting region to BH\n", " alpha=-1., # exponent of toroidal mangetic field (default: -1.)\n", " psi=np.pi/4., # Angle between one photon polarization state and B field. \n", " # Assumed constant over entire jet. \n", " helical=True, # if True, use helical magnetic-field model from Clausen-Brown et al. (2011). \n", " # In this case, the psi kwarg is treated is as the phi angle \n", " # of the photon trajectory in the cylindrical jet coordinate system\n", " equipartition=True, # if true, assume equipartition between electrons and the B field. \n", " # This will overwrite the exponent of electron density beta = 2 * alpha \n", " # and set n0 given the minimum electron lorentz factor set with gamma_min\n", " gamma_min=gamma_min, # minimum lorentz factor of emitting electrons, only used if equipartition=True\n", " gamma_max=np.exp(10.) * gamma_min, # maximum lorentz factor of emitting electrons,\n", " # only used if equipartition=True\n", " Rjet= 40., # maximum jet length in pc (default: 1000.)\n", " n0=1e4, # normalization of electron density, overwritten if equipartition=True\n", " beta=-2., # power-law index of electron density, overwritten if equipartition=True\n", " chi=chispl \n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pick a mass and coupling where there is some mixing, and run the calculation for each." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "ml.alp.m = 100.\n", "ml.alp.g = 0.3\n", "\n", "ml_chi.alp.m = 100.\n", "ml_chi.alp.g = 0.3" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\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;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m: Running Module 0: \n" ] } ], "source": [ "px, py, pa = ml.run()\n", "pgg = px + py \n", "\n", "px_c, py_c, pa_c = ml_chi.run()\n", "pgg_chi = px_c + py_c " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for p in pgg: \n", " plt.plot(ml.EGeV, p, label=r'$\\chi_{CMB}$')\n", " \n", "for p_c in pgg_chi: \n", " plt.plot(ml_chi.EGeV, p_c, label=r'$\\chi$-spline')\n", "\n", "plt.grid(True, lw = 0.2)\n", "plt.grid(True, which = 'minor', axis = 'y', lw = 0.2)\n", "\n", "plt.xlabel('Energy (GeV)')\n", "plt.ylabel(r'Photon survival probability')\n", "\n", "plt.gca().set_xscale('log')\n", "plt.annotate(r'$m_a = {0:.1f}\\,\\mathrm{{neV}}, g_{{a\\gamma}}'\n", " r' = {1:.2f} \\times 10^{{-11}}\\,\\mathrm{{GeV}}^{{-1}}$'.format(ml.alp.m,ml.alp.g),\n", " xy=(0.05,0.1),\n", " size='large',\n", " xycoords='axes fraction',\n", " ha='left',\n", " **effect)\n", "plt.legend(loc='upper left')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $P_{\\gamma\\gamma}$'s are quite different between the two cases. $\\chi$ affects the mixing by lowering the high critical energy, $E_{crit}^{high}$, and so oftern reduces mixing at very high energies." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cluster" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's look at a cluster magnetic field, `\"ICMGaussTurb\"`. We can use the same $\\chi$ array in $(E,r)$ but this time $r$ will be in kpc instead of pc." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "# cluster\n", "ml = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)\n", "ml_chi = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36menvirons.py:\u001b[0;35m 431\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Using inputted chi\n", "\u001b[0;36menvirons.py:\u001b[0;35m 428\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Using interpolated chi\n" ] } ], "source": [ "ml.add_propagation(\"ICMGaussTurb\", \n", " 0, # position of module counted from the source. \n", " nsim=1, # number of random B-field realizations\n", " B0=10., # rms of B field\n", " n0=39., # normalization of electron density\n", " n2=4.05, # second normalization of electron density, see Churazov et al. 2003, Eq. 4\n", " r_abell=500., # extension of the cluster\n", " r_core=80., # electron density parameter, see Churazov et al. 2003, Eq. 4\n", " r_core2=280., # electron density parameter, see Churazov et al. 2003, Eq. 4\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", " )\n", "ml_chi.add_propagation(\"ICMGaussTurb\", \n", " 0, # position of module counted from the source. \n", " nsim=1, # number of random B-field realizations\n", " B0=10., # rms of B field\n", " n0=39., # normalization of electron density\n", " n2=4.05, # second normalization of electron density, see Churazov et al. 2003, Eq. 4\n", " r_abell=500., # extension of the cluster\n", " r_core=80., # electron density parameter, see Churazov et al. 2003, Eq. 4\n", " r_core2=280., # electron density parameter, see Churazov et al. 2003, Eq. 4\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", " chi = chispl\n", " )" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "ml.alp.m = 10.\n", "ml.alp.g = 0.7\n", "\n", "ml_chi.alp.m = 10.\n", "ml_chi.alp.g = 0.7" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n" ] } ], "source": [ "px, py, pa = ml.run()\n", "pgg = px + py \n", "\n", "px_c, py_c, pa_c = ml_chi.run()\n", "pgg_chi = px_c + py_c " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for pi,p in enumerate(pgg): \n", " if pi==0:\n", " plt.plot(ml.EGeV, p, color=plt.cm.tab10(0.), alpha = 0.7, label=r'$\\chi_{CMB}$')\n", " else:\n", " plt.plot(ml.EGeV, p, color=plt.cm.tab10(0.),alpha = 0.1)\n", " \n", "for pi_c,p_c in enumerate(pgg_chi): \n", " if pi_c==0:\n", " plt.plot(ml_chi.EGeV, p_c, color=plt.cm.tab10(1), alpha = 0.7, label=r'$\\chi$-spline')\n", " else:\n", " plt.plot(ml_chi.EGeV, p_c, color=plt.cm.tab10(1),alpha = 0.1)\n", "\n", "plt.grid(True, lw = 0.2)\n", "plt.grid(True, which = 'minor', axis = 'y', lw = 0.2)\n", "\n", "plt.xlabel('Energy (GeV)')\n", "plt.ylabel(r'Photon survival probability')\n", "\n", "plt.gca().set_xscale('log')\n", "plt.annotate(r'$m_a = {0:.1f}\\,\\mathrm{{neV}}, g_{{a\\gamma}}'\n", " r' = {1:.2f} \\times 10^{{-11}}\\,\\mathrm{{GeV}}^{{-1}}$'.format(ml.alp.m,ml.alp.g),\n", " xy=(0.05,0.1),\n", " size='large',\n", " xycoords='axes fraction',\n", " ha='left',\n", " **effect)\n", "plt.legend(loc='upper left')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, including $\\chi$ lowers the highest energy at which there is strong mixing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## GMF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the GMF:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "# GMF\n", "ml = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)\n", "ml_chi = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36menvirons.py:\u001b[0;35m1196\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Using inputted chi\n", "\u001b[0;36menvirons.py:\u001b[0;35m1193\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Using interpolated chi\n" ] } ], "source": [ "ml.add_propagation(\"GMF\", \n", " 0, \n", " model='jansson12')\n", "ml_chi.add_propagation(\"GMF\",\n", " 0, \n", " model='jansson12',\n", " chi = chispl)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "ml.alp.m = 1.\n", "ml.alp.g = 3.\n", "\n", "ml_chi.alp.m = 1.\n", "ml_chi.alp.g = 3." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n" ] } ], "source": [ "px, py, pa = ml.run()\n", "pgg = px + py \n", "\n", "px_c, py_c, pa_c = ml_chi.run()\n", "pgg_chi = px_c + py_c " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for p in pgg: \n", " plt.plot(ml.EGeV, p, label=r'$\\chi_{CMB}$')\n", " \n", "for p_c in pgg_chi: \n", " plt.plot(ml_chi.EGeV, p_c, label=r'$\\chi$-spline')\n", "\n", "plt.grid(True, lw = 0.2)\n", "plt.grid(True, which = 'minor', axis = 'y', lw = 0.2)\n", "\n", "plt.xlabel('Energy (GeV)')\n", "plt.ylabel(r'Photon survival probability')\n", "\n", "plt.gca().set_xscale('log')\n", "plt.annotate(r'$m_a = {0:.1f}\\,\\mathrm{{neV}}, g_{{a\\gamma}}'\n", " r' = {1:.2f} \\times 10^{{-11}}\\,\\mathrm{{GeV}}^{{-1}}$'.format(ml.alp.m,ml.alp.g),\n", " xy=(0.05,0.1),\n", " size='large',\n", " xycoords='axes fraction',\n", " ha='left',\n", " **effect)\n", "plt.legend(loc='upper left')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The effect is the same." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## IGMF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mixing in the IGMF is slightly different. Far from pair-produciton energies, $\\chi \\propto \\rho$ where $\\rho$ is the energy density of the background field. The energy density of the CMB evolves with redshift as $\\rho \\propto T^4 \\propto (1+z)^4$. Therefore, by default, mixing in the IGMF doesn't use a constant value of $\\chi_{CMB}$, but rather uses $\\chi(z)=\\chi_{CMB}(1+z)^4$ where $\\chi_{CMB} = 5.11\\times10^{-43}$ as mentioned above and is calculated at $z=0$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also possible to manually include a spline function for $\\chi$ in the IGMF, but now the spline needs to be in energy and redshift instead of energy and distance:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "zs = np.logspace(-1,np.log10(1.5),200)\n", "chispl_z = RBSpline(EGeV,zs,chis,kx=1,ky=1,s=0)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "# IGMF\n", "ml = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)\n", "ml_chi = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)\n", "ml_chiz = ModuleList(ALP(m=1., g=2.), src, pin=pin, EGeV=EGeV, seed = 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For comparison we will also include a constant value of $\\chi_{CMB}$. Any environment will accept a single value of chi in the form of `chi=np.array([chi])`." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36menvirons.py:\u001b[0;35m 109\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Using inputted chi\n", "\u001b[0;36menvirons.py:\u001b[0;35m 107\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Using interpolated chi\n" ] } ], "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", " chi = np.array([chiCMB])\n", " )\n", "ml_chi.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", " chi = chispl_z\n", " )\n", "ml_chiz.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": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "ml.alp.m = 0.1\n", "ml.alp.g = 3.\n", "\n", "ml_chi.alp.m = 0.1\n", "ml_chi.alp.g = 3.\n", "\n", "ml_chiz.alp.m = 0.1\n", "ml_chiz.alp.g = 3." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n", "\u001b[0;36m core.py:\u001b[0;35m 658\u001b[0;0m --- \u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36m\u001b[1;36mINFO\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m\u001b[1;0m: Running Module 0: \n" ] } ], "source": [ "px, py, pa = ml.run()\n", "pgg = px + py \n", "\n", "px_c, py_c, pa_c = ml_chi.run()\n", "pgg_chi = px_c + py_c \n", "\n", "px_cz, py_cz, pa_cz = ml_chiz.run()\n", "pgg_chiz = px_cz + py_cz " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for p in pgg: \n", " plt.plot(ml.EGeV, p, label=r'$\\chi_{CMB}$')\n", " \n", "for p_cz in pgg_chiz: \n", " plt.plot(ml_chiz.EGeV, p_cz, label=r'$\\chi_{CMB} (1+z)^4$')\n", "\n", "for p_c in pgg_chi: \n", " plt.plot(ml_chi.EGeV, p_c, label=r'$\\chi$-spline')\n", " \n", "plt.grid(True, lw = 0.2)\n", "plt.grid(True, which = 'minor', axis = 'y', lw = 0.2)\n", "\n", "plt.xlabel('Energy (GeV)')\n", "plt.ylabel(r'Photon survival probability')\n", "\n", "plt.gca().set_xscale('log')\n", "plt.annotate(r'$m_a = {0:.1f}\\,\\mathrm{{neV}}, g_{{a\\gamma}}'\n", " r' = {1:.2f} \\times 10^{{-11}}\\,\\mathrm{{GeV}}^{{-1}}$'.format(ml.alp.m,ml.alp.g),\n", " xy=(0.05,0.1),\n", " size='large',\n", " xycoords='axes fraction',\n", " ha='left',\n", " **effect)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All three are different." ] }, { "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 }