{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figs 1,3,5 from Matthews+ 2022\n",
    "This notebook contains routines for reproducing some of the figures from J. H. Matthews et al. 2022, \"How do magnetic field models affect astrophysical limits on light axion-like particles? An X-ray case study with NGC 1275\". \n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "At the moment, this page is incomplete and minimally documented, but I will gradually add to it. All the plots are missing results from the Gaussian random field models at the moment because I haven't incorporated those models into alpro directly. \n",
    "</div> \n",
    "\n",
    "For limits plots, see the NGC1275 limits page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 1: Pressure Profile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "import numpy as np \n",
    "import alpro \n",
    "import matplotlib.pyplot as plt \n",
    "from alpro.models import unit\n",
    "\n",
    "pressure_conversion = 1.0 / (1000.0 * unit.ev)\n",
    "beta = 100.0\n",
    "\n",
    "def B_from_P_ylim(Ptuple):\n",
    "    B1 = 1e6 * np.sqrt((Ptuple[0] / pressure_conversion / beta)  * 8.0 * np.pi)\n",
    "    B2 = 1e6 * np.sqrt((Ptuple[1] / pressure_conversion / beta)  * 8.0 * np.pi)\n",
    "    return (B1, B2)\n",
    "\n",
    "def beta_func(r, alpha=0.5, beta0=100, r0 = 25.0):\n",
    "    beta = beta0 * (r/r0) ** alpha\n",
    "    return (beta)\n",
    "\n",
    "def make_fig1():\n",
    "\n",
    "    fig, ax2 = plt.subplots()\n",
    "    ax = ax2.twinx()\n",
    "\n",
    "    models = [\"1275a\", \"1275b\"]\n",
    "    label = [\"A\", \"B\"]\n",
    "    color = [\"C3\", \"C0\"]\n",
    "    for i, mod_name in enumerate(models):\n",
    "        s = alpro.Survival(mod_name)\n",
    "        s.init_model()\n",
    "\n",
    "        r = np.logspace(-1,np.log10(2000), 1000)\n",
    "\n",
    "        B = s.cluster.get_B(r)\n",
    "        PB = (B ** 2) / 8.0 / np.pi \n",
    "        ax.plot(r, pressure_conversion * PB * beta, label=\"Reynolds$+$20 Model {}\".format(label[i]), c=color[i], ls=\"-.\", lw=3)\n",
    "\n",
    "        if mod_name == \"1275b\":\n",
    "            s.cluster.plasma_beta = beta_func\n",
    "            s.init_model()\n",
    "            ax2.plot(r, 1e6*s.cluster.get_B(r), ls=\":\", c=\"C0\", label=r\"$B$, $\\beta_{\\rm pl} = 100 (z/25 {\\rm kpc})^{1/2}\")\n",
    "            ax.plot(r, s.cluster.get_B(r), ls=\":\", c=\"C0\", label=r\"$B,\\,\\beta_{\\rm pl} = 100 (z/25\\,{\\rm kpc})^{1/2}$\")\n",
    "\n",
    "\n",
    "    ax.set_ylim(5e-4, 2)\n",
    "    ax2.set_ylim(B_from_P_ylim(ax.get_ylim()))\n",
    "    ax2.set_xlabel(\"$z$~(kpc)\", fontsize=18, labelpad=-2)\n",
    "    ax.set_ylabel(r\"$P_{\\rm th}~{\\rm for}~\\beta_{\\rm pl} = 100~({\\rm keV~cm}^{-3})$\", fontsize=16, labelpad=-2)\n",
    "    ax.legend(fontsize=14, frameon=False, loc=3)\n",
    "    ax2.set_xlim(1,1800)\n",
    "    ax.get_shared_y_axes().join(ax,ax2)\n",
    "\n",
    "    ax2.set_ylabel(r\"$B~(\\mu {\\rm G})$\", fontsize=18, labelpad=-5)\n",
    "    plt.loglog()\n",
    "    \n",
    "alpro.util.set_default_plot_params(tex=True)\n",
    "make_fig1()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 3: Rotation Measures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_rm_models(model_kwargs, rm_reject=False):\n",
    "    N = 200\n",
    "    rm = np.zeros(N)\n",
    "    for i in range(N):\n",
    "        s = setup_model(i, 1e-13 * 1e-9, 1e-13, **model_kwargs)\n",
    "        rm[i] = s.domain.get_rm(cell_centered=False)\n",
    "    return (np.fabs(rm), np.median(np.fabs(rm)))\n",
    "\n",
    "def setup_model(i, g, mass, mod = \"1275b\", lc_scale = True, var_beta = False):\n",
    "    s = alpro.Survival(mod)\n",
    "    s.init_model()\n",
    "    if var_beta:\n",
    "        s.cluster.plasma_beta = beta_func\n",
    "    if lc_scale == False:\n",
    "        s.set_coherence_r0(None)\n",
    "    s.domain.create_box_array(1800.0, i, s.coherence_func, r0=0.0)\n",
    "    s.set_params(g = g, mass = mass)\n",
    "    return (s)\n",
    "\n",
    "ls = [\"-\", \"-\", \"-\", \":\"]\n",
    "colors = [\"C0\", \"C1\", \"C3\", \"k\"]\n",
    "model = [\"1275b\", \"1275b\", \"1275b\", \"1275a\"]\n",
    "labels = [\"1: Cell-based\", r\"2: Cell-based, no $\\Lambda_c$ scaling\", r\"3: Cell-based, variable $\\beta(z)$\", \"R20 Model A\"]\n",
    "var_betas = [False, False, True, False]\n",
    "lc_scales = [True, False, True, True]\n",
    "imods = np.arange(len(ls))\n",
    "bins = np.linspace(0,4e4,100)\n",
    "params = zip(imods, model, var_betas, lc_scales, labels, colors)\n",
    "fig = plt.figure()\n",
    "\n",
    "for imod, mod, var_beta, lc_scale, label, color in params:\n",
    "    model_kwargs = {\"mod\": mod, \"var_beta\": var_beta, \"lc_scale\": lc_scale}\n",
    "\n",
    "    iseed = 0\n",
    "\n",
    "    rms, median = get_rm_models(model_kwargs)\n",
    "    hist, bin_edges = np.histogram(rms, bins=bins)\n",
    "    cdf = np.cumsum(hist) / np.sum(hist)\n",
    "    plt.plot(bin_edges[:-1], cdf, color=color, lw=3, label=labels[imod], ls = ls[imod])\n",
    "    plt.vlines([median], 0, 0.1, color=color, lw=2)\n",
    "    \n",
    "plt.ylabel(\"Cumulative Distribution Function\")\n",
    "plt.xlabel(r\"$|{\\rm RM| (rad~m^{-2}})$\")\n",
    "plt.fill_between([6500,7500], 0, 1, color=\"k\", alpha=0.3, label= \"RM from Taylor$+$ 2006\")\n",
    "plt.ylim(0,1)\n",
    "plt.xlim(0,19000)\n",
    "plt.legend(loc=4, frameon=False)\n",
    "plt.subplots_adjust(hspace=0.05, wspace=0.35, right=0.98)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 5: Magnetic Field Models and survival probabilities\n",
    "This code will reproduce figure 5 from the paper. To avoid a fairly lengthy calculation of the mean survival probability, the code uses precalculated values stored in this repository. \n",
    "\n",
    "| Model | $N$ | $B$-Field  | $\\Lambda_c$ scaling? | $\\beta_{\\rm pl}(z)$                 | Range of scales (kpc) |  Median $|{\\rm RM}|\\,({\\rm rad\\,m^{-2}})$                      | Colour                     |\n",
    "|-------|-----|------------|------|-------------------------------|------------|-------------------------------------------------|-----------|\n",
    "| 1     | 200 | Cell-based | Yes  | constant, 100                | $3.5-10$   | 1915    | Blue      |\n",
    "| 2     | 200 | Cell-based | No   | constant, 100                | $3.5-10$   | 1603    | Orange    |\n",
    "| 3     | 200 | Cell-based | Yes  | $100~\\sqrt{z/25\\,{\\rm kpc}}$ | $3.5-10$   | 2045    | Red       |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = 1e-12 * 1e-9\n",
    "mass = 1e-13\n",
    "from scipy.interpolate import interp1d\n",
    "\n",
    "def set_pgg_axes(ax, xtick, ymin=0.855):\n",
    "    ax.set_xscale(\"log\")\n",
    "    ax.set_xlim(1,10)\n",
    "    ax.set_ylim(ymin,1)\n",
    "    xticks_to_use = [1,2,3,4,6,10]\n",
    "    ax.set_xticks(xticks_to_use)\n",
    "    if xtick:\n",
    "        ax.set_xlabel(\"$E$ (keV)\", fontsize=18)\n",
    "        ax.set_xticklabels([str(i) for i in xticks_to_use])\n",
    "    else:\n",
    "        ax.set_xticklabels([])\n",
    "\n",
    "def get_mean_sd_models(model_kwargs, rm_reject=False):\n",
    "    N = 200\n",
    "    rinterp = np.linspace(0,1800,1801)\n",
    "    Bfine = np.zeros((N,len(rinterp)))\n",
    "    moments = np.zeros((2,len(rinterp)))\n",
    "    for i in range(N):\n",
    "        s = setup_model(i, g, mass, **model_kwargs)\n",
    "        rinterp = np.linspace(0,1800,1801)\n",
    "        interp_func = interp1d(s.domain.rcen, 1e6*s.domain.B, bounds_error=False, fill_value=\"extrapolate\")\n",
    "        Bfine[i,:] = interp_func(rinterp)\n",
    "\n",
    "    moments[0,:] = np.mean(Bfine, axis=0)\n",
    "    moments[1,:] = np.std(Bfine, axis=0)\n",
    "    return moments\n",
    "\n",
    "def plot_model(ax, s, label, color, xtick, moments):\n",
    "    rinterp = np.linspace(0,1800,1801)\n",
    "    ax.step(s.domain.r, 1e6*s.domain.B, label=label, where=\"post\", c=color)\n",
    "    ax.fill_between(rinterp, y1=moments[0,:]-moments[1,:], y2=moments[0,:]+moments[1,:], color=color, alpha=0.3, step=\"mid\")\n",
    "    ax.set_yscale(\"log\")\n",
    "    ax.set_xscale(\"log\")\n",
    "    if xtick:\n",
    "        ax.set_xlabel(\"$z$~(kpc)\", fontsize=18)\n",
    "    ax.legend(fontsize=14, frameon=False, loc=3, handlelength=0.5, handletextpad=0.2)\n",
    "    ax.set_ylabel(r\"$B_\\perp~(\\mu {\\rm G})$\", fontsize=18, labelpad=-2)\n",
    "    ax.set_xlim(10,1800)\n",
    "    ax.set_ylim(2e-2,30)\n",
    "    yticks = [0.1,1,10]\n",
    "    ax.set_yticks(yticks)\n",
    "    ax.set_yticklabels([str(i) for i in yticks])\n",
    "    if xtick == False:\n",
    "        ax.set_xticklabels([])\n",
    "\n",
    "def plot_pgg(ax, s, label, color, xtick):\n",
    "    energies = np.logspace(3,4,1000)\n",
    "    P, _ = s.propagate_with_pruning(s.domain, energies, threshold=0.1, refine=10, required_res=3)\n",
    "    ax.plot(energies/1e3, 1.0 - P, c=color)\n",
    "    set_pgg_axes(ax, xtick, ymin=0.855)\n",
    "    ax.set_ylabel(r\"$P_{\\gamma\\gamma}$\", fontsize=18,  labelpad=-2)\n",
    "\n",
    "def plot_mean(ax, fname, color, xtick):\n",
    "    energies, P, sd = np.genfromtxt(\"../data/{}_13.0_12.0.dat\".format(fname), unpack=True)\n",
    "    ax.plot(energies, P, c=color)\n",
    "    ax.fill_between(energies, y1=P-sd, y2=P+sd, color=color, alpha=0.3)\n",
    "    set_pgg_axes(ax, xtick, ymin=0.855)\n",
    "    ax.set_ylabel(r\"$\\bar{P}_{\\gamma\\gamma,200}$\", fontsize=18, labelpad=-1)\n",
    "\n",
    "\n",
    "var_betas = [False, False, True]\n",
    "lc_scales = [True, False, True]\n",
    "labels = [\"Cell-based\", r\"Cell-based, no $\\Lambda_c$ scaling\", r\"Cell-based, variable $\\beta(z)$\"]\n",
    "iplots = [1, 4, 7]\n",
    "colors = [\"C0\", \"C1\", \"C3\"]\n",
    "xticks = [False, False, True]\n",
    "model = np.arange(len(labels))\n",
    "fnames = [\"cell\", \"cell_noLscaling\", \"cell_varbeta\"]\n",
    "params = zip(model, fnames, var_betas, lc_scales, labels, iplots, colors, xticks)\n",
    "\n",
    "i = 0\n",
    "fig = plt.figure(figsize=(12,12))\n",
    "\n",
    "for imod, fname, var_beta, lc_scale, label, iplot, color, xtick in params:\n",
    "    \n",
    "    # get mean and SD for resampled magnetic field\n",
    "    model_kwargs = {\"mod\": \"1275b\", \"var_beta\": var_beta, \"lc_scale\": lc_scale}\n",
    "    moments = get_mean_sd_models(model_kwargs)\n",
    "    \n",
    "    # initialise individual model\n",
    "    iseed = 0  \n",
    "    s = setup_model(iseed, g, mass, **model_kwargs)\n",
    "    \n",
    "    # make axes to plot\n",
    "    ax1 = fig.add_subplot(5,3,iplot)\n",
    "    ax2 = fig.add_subplot(5,3,iplot+1)\n",
    "    ax3 = fig.add_subplot(5,3,iplot+2)\n",
    "\n",
    "    # plot the magnetic field, pgg, and mean pgg \n",
    "    plot_model(ax1, s, label, color, xtick, moments)\n",
    "    plot_pgg(ax2, s, label, color, xtick)\n",
    "    plot_mean(ax3, fname, color, xtick)\n",
    "plt.subplots_adjust(hspace=0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
