{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hierarchical analysis figures for GW190521 Implications paper\n", "\n", "This notebook generates figures 11 and 12 for GW190521 Implications paper\n", "__Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521__ avaliable\n", "through [ApjL](), [DCC](https://dcc.ligo.org/LIGO-P2000021/public) and [arXiv](https://arxiv.org/abs/2007.xxxx).\n", "\n", "The data used in this notebook can be downloaded from the public DCC page [LIGO-P2000158](https://dcc.ligo.org/P2000158/public).\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "# generic imports\n", "import numpy as np\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "from scipy import stats\n", "from scipy.integrate import trapz\n", "import json\n", "import os\n", "import corner\n", "import seaborn as sns\n", "\n", "# suppress ignorable warnings\n", "import warnings\n", "warnings.simplefilter('ignore', category=UserWarning)\n", "\n", "# ligo-specific imports\n", "import bilby # https://pypi.org/project/bilby/" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# set up color map, fonts, etc\n", "color_array = sns.color_palette(\"colorblind\", n_colors=10, desat=.7)\n", "cmap = sns.color_palette(\"RdBu_r\", 26).as_hex()\n", "cmap = cmap[:-1]\n", "\n", "params = {\n", " # latex\n", " 'text.usetex': True,\n", " # fonts\n", " 'font.family': 'serif', \n", "\n", " # figure and axes\n", " 'figure.figsize': (14,7),\n", " 'figure.titlesize': 35, \n", " 'axes.grid': False, \n", " 'axes.titlesize':20,\n", " #'axes.labelweight': 'bold', \n", " 'axes.labelsize': 40,\n", "\n", " # tick markers\n", " 'xtick.direction': 'in', \n", " 'ytick.direction': 'in', \n", " 'xtick.labelsize': 16,\n", " 'ytick.labelsize': 16, \n", " 'xtick.major.size': 10.0,\n", " 'ytick.major.size': 10.0,\n", " 'xtick.minor.size': 3.0,\n", " 'ytick.minor.size': 3.0,\n", "\n", " # legend\n", " 'legend.fontsize': 20,\n", " 'legend.frameon': False,\n", " #'legend.framealpha':1.0,\n", "\n", " # colors\n", " 'image.cmap': 'viridis',\n", "\n", " # saving figures\n", " 'savefig.dpi': 300\n", " }\n", "\n", "plt.rcParams.update(params)\n", "plt.rcParams['font.serif'] = ['Computer Modern', 'Times New Roman']\n", "plt.rcParams['font.family'] = ['serif', 'STIXGeneral']\n", "plt.rcParams['savefig.bbox'] = 'tight'\n", "plt.rcParams['text.latex.preamble'] = [r'\\usepackage{amsmath}'] #for \\text command\n", "plt.rcParams.update({'font.size': 22})" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "#---------------------\n", "# plotting functions\n", "#---------------------\n", "\n", "def set_ticks(data,axes):\n", " fontsize=14\n", " N = len(data.T)\n", " cols = np.array([i + N*np.array(range(N)) for i in range(N) ])\n", " for ii,col in enumerate(cols):\n", " tick_labels, major_ticks, minor_ticks = get_ticks(data.T[ii])\n", "\n", " for jj in range(ii,N):\n", " axes[col[jj]].set_xticks(major_ticks)\n", " #axes[col[jj]].set_xticks(minor_ticks,minor=True)\n", " if jj == N-1: axes[col[jj]].set_xticklabels(tick_labels,fontsize=fontsize)\n", " \n", " for ii, row in enumerate(cols.T[1:]):\n", " tick_labels, major_ticks, minor_ticks = get_ticks(data.T[ii+1])\n", " for jj in range(ii+1):\n", " #print(jj)\n", " axes[row[jj]].set_yticks(major_ticks)\n", " #axes[row[jj]].set_yticks(minor_ticks,minor=True)\n", " if jj==0: axes[row[jj]].set_yticklabels(tick_labels,fontsize=fontsize)\n", "\n", "\n", "def get_ticks(d):\n", " min_tick = int(round(min(d)))-1\n", " max_tick = int(round(max(d)))+1\n", " \n", " major_ticks = list(range(min_tick,max_tick))\n", " \n", " if len(major_ticks)>10:\n", " major_ticks = [major_ticks[i] for i in range(len(major_ticks)) if i % 3 == 0]\n", "\n", " elif len(major_ticks)>7:\n", " major_ticks = [major_ticks[i] for i in range(len(major_ticks)) if i % 2 == 0]\n", " \n", " tick_labels = ['$10^{'+str(tick)+'}$' for tick in major_ticks]\n", " minor_ticks=[]\n", " for tick in major_ticks:\n", " minor_ticks.extend([np.log10(i*10**tick) for i in range(2,10)])\n", " \n", " return tick_labels, major_ticks, minor_ticks\n", "\n", "\n", "def getCL(Z,CL):\n", " zf = Z.flatten()\n", " zsort = np.argsort(zf)[::-1]\n", " levels=[]\n", " for cl in CL:\n", " zsum = 0\n", " zlast = 0\n", " j=0\n", " while zsum/np.sum(zf)<=CL:\n", " max_i = zsort[j]\n", " j+=1\n", " zlast=zf[max_i]\n", " zsum+=zf[max_i]\n", " levels.append(zlast)\n", " return levels " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Relative Rates Plot" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#Load in result files\n", "rdir = 'GW190521_Implications_figure_data/hierarchical_data/'\n", "result = bilby.core.result.read_in_result(rdir+'gwtc1_plus_NRSur/gauss_result.json')\n", "result_no = bilby.core.result.read_in_result(rdir+'gwtc1_plus_no_zero_spin_NRSur/gauss_result.json')\n", "gamma1_5 = result.posterior['branching_ratio_1_5'].values\n", "gamma2 = result.posterior['branching_ratio_2'].values\n", "delta_chi = result.posterior['delta_chi'].values\n", "gamma1_5_no = result_no.posterior['branching_ratio_1_5'].values\n", "gamma2_no = result_no.posterior['branching_ratio_2'].values\n", "\n", "#For non-zero-spin runs, delta_chi is zero, which will mess up the plot ranges. \n", "#Load in the with-zero-spin posterior, we'll delete those lines later\n", "delta_chi_no = result.posterior.sample(len(gamma2_no),replace=True)['delta_chi'].values\n", "\n", "#We want to plot in log\n", "data = np.array([np.log10(delta_chi),np.log10(gamma1_5), np.log10(gamma2)]).T\n", "data_no = np.array([np.log10(delta_chi_no),np.log10(gamma1_5_no), np.log10(gamma2_no),]).T\n", "\n", "labels = [r'$\\lambda_{0}$',r'$\\frac{\\mathcal{R}_{1g+2g}}{\\mathcal{R}_{1g+1g}}$',r'$\\frac{\\mathcal{R}_{2g+2g}}{\\mathcal{R}_{1g+1g}}$']\n", "labels_no = [r'$\\lambda_{0}$',r'$\\frac{\\mathcal{R}_{1g+2g}}{\\mathcal{R}_{1g+1g}}$',r'$\\frac{\\mathcal{R}_{2g+2g}}{\\mathcal{R}_{1g+1g}}$']\n", "\n", "plot_parameter_keys = ['branching_ratio_1_5','branching_ratio_2']\n", "\n", "kwargs = dict(labels=labels,\n", " bins=50, smooth=0.9, label_kwargs=dict(fontsize=30),\n", " title_kwargs=dict(fontsize=20), color='#0072C1',\n", " truth_color='tab:orange', quantiles=None,\n", " levels=(1 - np.exp(-0.5), 1 - np.exp(-2), 1 - np.exp(-9 / 2.)),\n", " plot_density=False, plot_datapoints=True, fill_contours=True,\n", " max_n_ticks=5)\n", "#Plot with-zero-spin results\n", "fig = corner.corner(data, **kwargs,hist_kwargs=dict(density=True,label='With zero-spin'))\n", "kwargs['color'] = color_array[1]\n", "kwargs['labels'] = labels_no\n", "#Plot without-zero-spin results\n", "no =corner.corner(data_no,**kwargs,hist_kwargs=dict(density=True,label='Without zero-spin'),fig=fig)\n", "\n", "#Delete all points associated with without-zero-spin delta_chi\n", "axes = fig.get_axes()\n", "axes[3].lines[1].remove()\n", "for coll in axes[3].collections[-8:]:\n", " coll.remove()\n", "axes[6].lines[1].remove()\n", "for coll in axes[6].collections[-8:]:\n", " coll.remove()\n", "axes[0].patches[1].remove()\n", "#Manually set ticks\n", "set_ticks(data,axes)\n", "\n", "lines=[]\n", "#Create legend\n", "lines.append(matplotlib.lines.Line2D([0], [0], color='#0072C1'))\n", "lines.append(matplotlib.lines.Line2D([0], [0], color=color_array[1]))\n", "labels = ['With zero-spin channel','Without zero-spin channel']\n", "axes[1].legend(lines,labels,loc=2)\n", "\n", "#Set plot limits\n", "dchi_min = -2.75\n", "dchi_max = 0\n", "r15_min = -4.5\n", "r15_max = 0\n", "r2_min = -9.5\n", "r2_max = 0\n", "#dchi\n", "axes[0].set_xlim(dchi_min,dchi_max)\n", "axes[3].set_xlim(dchi_min,dchi_max)\n", "axes[6].set_xlim(dchi_min,dchi_max)\n", "#r15\n", "axes[3].set_ylim(r15_min,r15_max)\n", "axes[4].set_xlim(r15_min,r15_max)\n", "axes[7].set_xlim(r15_min,r15_max)\n", "\n", "axes[6].set_ylim(r2_min,r2_max)\n", "axes[7].set_ylim(r2_min,r2_max)\n", "axes[8].set_xlim(r2_min,r2_max)\n", "\n", "axes[4].set_ylim(0,1.5)\n", "axes[8].set_ylim(0,0.75)\n", "\n", "axes\n", "\n", "fig.set_figheight(9)\n", "fig.set_figwidth(9)\n", "filename = 'GW190521_Implications_Figures_pdf/relative_rates.pdf'\n", "fig.savefig(filename,dpi=200)\n", "fig.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayes Factors Plot\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Norm = 0.9940999327900775\n" ] } ], "source": [ "# process BF vs m,a with contours - NRSur\n", "\n", "event = 'GW190521'\n", "result = 'gwtc1_plus_no_zero_spin_NRSur'\n", "#Load PE samples\n", "with open(os.path.join(rdir,result,'full_pe_samples.json'),'r') as f:\n", " posteriors = json.load(f)\n", " \n", "posterior = posteriors[event][-1]['final_samples']\n", "m_post = posterior['mass_1']\n", "a_post = posterior['a_1']\n", "ma_post = [m_post,a_post]\n", "\n", "#Create 2D KDE over M1, A1\n", "kde_post = stats.gaussian_kde(ma_post)\n", "\n", "#load ppds\n", "with open(os.path.join(rdir,result,'gauss_ppds.json'),'r') as f:\n", " ppds = json.load(f)\n", "\n", "#Create grid to evaluate kdes on\n", "a1s = a2s = ppds['a1s']\n", "m1s = ppds['m1s']\n", "M,A = np.meshgrid(m1s,a1s)\n", " \n", "#Evaluate GW190521 M1,A1 kde and get 90% contours\n", "Zpost = np.reshape(kde_post(np.vstack([M.ravel(),A.ravel()])).T, M.shape)\n", "levels90=getCL(Zpost,[0.9])\n", "levels68=getCL(Zpost,[0.68])\n", "\n", "#Avoid taking log10(0)\n", "ppd1g, ppd15g, ppd2g = [np.array(ppds[key]['a1m1']) +1e-30 for key in ('1G','1.5G','2G')]\n", "#Check everything's normalized\n", "print('Norm =',trapz(trapz(ppd2g,m1s),a1s))\n", "#Take log10 of Bayes Factor\n", "Z = np.log10(ppd2g/ppd1g)\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Norm = 0.9924994979927636\n" ] } ], "source": [ "# process BF vs m,a with contours - Phenom\n", "\n", "event = 'GW190521'\n", "result = 'gwtc1_plus_no_zero_spin_IMRPv3HM'\n", "#load ppds\n", "with open(os.path.join(rdir,result,'gauss_ppds.json'),'r') as f:\n", " ppds = json.load(f)\n", "\n", "#Create grid to evaluate kdes on\n", "a1s = a2s = ppds['a1s']\n", "m1s = ppds['m1s']\n", "M,A = np.meshgrid(m1s,a1s)\n", "\n", "#Avoid taking log10(0)\n", "ppd1g, ppd15g, ppd2g = [np.array(ppds[key]['a1m1']) +1e-30 for key in ('1G','1.5G','2G')]\n", "#Check everything's normalized\n", "print('Norm =',trapz(trapz(ppd2g,m1s),a1s))\n", "#Take log10 of Bayes Factor\n", "Z = np.log10(ppd2g/ppd1g)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# make the BF figure with both NRSur and Phenom\n", "\n", "plt.figure(figsize=(10,8))\n", "ax = plt.subplot(1,1,1)\n", "lines = []\n", "colors=[\"#7570b3\", \"#d95f02\"]\n", "labels = ['NRSur PHM', 'Phenom PHM']\n", "results = ['gwtc1_plus_no_zero_spin_NRSur','gwtc1_plus_no_zero_spin_IMRPv3HM']\n", "color_dict = dict(zip(results,colors))\n", "label_dict = dict(zip(results,labels))\n", "lw=3\n", "\n", "for result in results:\n", " with open(os.path.join(rdir,result,'full_pe_samples.json'),'r') as f:\n", " posteriors = json.load(f)\n", " \n", " posterior = posteriors[event][-1]['final_samples']\n", " m_post = posterior['mass_1']\n", " a_post = posterior['a_1']\n", " ma_post = [m_post,a_post]\n", "\n", " #Create 2D KDE over M1, A1\n", " kde_post = stats.gaussian_kde(ma_post)\n", " Zpost = np.reshape(kde_post(np.vstack([M.ravel(),A.ravel()])).T, M.shape)\n", " levels90=getCL(Zpost,[0.9])\n", " levels68=getCL(Zpost,[0.68])\n", "\n", " CS = ax.contour(M,A,Zpost,levels=levels90,colors= color_dict[result],linewidths=lw,zorder=2)\n", " CS68 = ax.contour(M,A,Zpost,levels=levels68,colors=color_dict[result],linestyles='--',linewidths=lw,zorder=2)\n", "\n", " #Create legend\n", " lines.append(matplotlib.lines.Line2D([0], [0], color=color_dict[result]))\n", "\n", "ax.legend(lines,labels, loc=2,fontsize=18) \n", "contour= ax.contourf(m1s,a1s,Z, vmin=-24, levels=np.arange(-25,27,2),colors=cmap)\n", "ax.set_xlabel('$m_1 (M_{\\odot})$', fontsize=22)\n", "ax.set_ylabel('$\\chi_1$',fontsize=22)\n", "cb = plt.colorbar(contour,orientation='horizontal', ticks=list(range(-24,26,4)))\n", "cb.set_label(label=r\"$\\log_{10} \\left[\\frac{P(m_1,\\chi_1|xg+2g)}{P(m_1,\\chi_1|1g+1g)} \\right] $\",fontsize=26)\n", "ax.set_xlim([30,160])\n", "\n", "filename = 'GW190521_Implications_Figures_pdf/hierarchical_bayes_factor.pdf'\n", "plt.savefig(filename,dpi=200)\n", "fig.show()" ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }