Best-fit SCD and template for Bartels et al disk MSPs

msp_disk.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute best-fit source count and spatial template of Galactic MSPs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to Bartels et al (1805.11097), using their log-normal luminosity function and Lorimer disk spatial distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"/Users/smsharma/PycharmProjects/Lensing-PowerSpectra/\")\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from tqdm import *\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pylab as pylab\n",
    "from cycler import cycler\n",
    "import palettable\n",
    "from scipy.integrate import quad\n",
    "from scipy.interpolate import interp1d\n",
    "import healpy as hp\n",
    "\n",
    "from theory.units import *\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Source counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Class to calculate source counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SourceCountMSP:\n",
    "    def __init__(self, dNdL, dFdE, dNdV, E_1_0=100 * MeV, E_2_0=100 * GeV, dNdL_kwargs={}, dNdV_kwargs={}):\n",
    "        \"\"\"\n",
    "        Compute MSP source count distributions. Normalization is arbitrary! Need to sensibly normalize later.\n",
    "        \n",
    "        :param dNdL: Luminosity function of MSPs\n",
    "        :param dFdE: Function specifying photon flux spectrum of MSPs\n",
    "        :param dNdV: Function specifying spatial distribution of MSPs from Galactic center\n",
    "        :param E_1_0: Lower limit of energy range in which luminosity function is specified (usually 0.1 GeV in the literature)\n",
    "        :param E_2_0: Upper limit of energy range in which luminosity function is specified (usually 100 GeV in the literature)\n",
    "        :param r_deg_mask: Radial mask in degrees\n",
    "        :param b_deg_mask: Latitude mask in degrees\n",
    "        :param dNdL_kwargs: Keyword arguments that feed into specified luminosity function\n",
    "        :param dNdV_kwargs: Keyword arguments that feed into specified spatial density distribution\n",
    "        \"\"\"\n",
    "        \n",
    "        self.dNdL = dNdL\n",
    "        self.dFdE = dFdE\n",
    "        self.dNdV = dNdV\n",
    "                \n",
    "        self.dNdL_kwargs = dNdL_kwargs\n",
    "        self.dNdV_kwargs = dNdV_kwargs\n",
    "\n",
    "        # Pre-compute some useful integrals to speed up code\n",
    "        self.E_integ = quad(lambda E: E * dFdE(E), E_1_0, E_2_0)[0]  # Integrated energy flux in range luminosity function is specified in\n",
    "        self.F_integ = quad(lambda E: dFdE(E), E_1_0, E_2_0)[0]  # Integrated photon flux in range luminosity function is specified in\n",
    "\n",
    "    def dNdF(self, F_gamma, E_1=20 * MeV, E_2=20 * GeV):\n",
    "        \"\"\" \n",
    "        Differential source counts function\n",
    "        \n",
    "        :param F_gamma: Photon flux at which SCD evaluated\n",
    "        :param E_1: Lower limit of energy range\n",
    "        :param E_2: Upper limit of energy range\n",
    "        \"\"\"    \n",
    "        \n",
    "        # 1 / \\delta F factor. Make sure output stable to this choice!\n",
    "        dF_gamma = 1e-2 * F_gamma\n",
    "        \n",
    "        # Integrate (by approximating as sum) in spherical coordinates from us as origin\n",
    "        # WARNING: checked stability to integration gridding, but ideally should run higher resolution still\n",
    "        phi_integ_ary = np.linspace(0, 2. * np.pi, 50)\n",
    "        theta_integ_ary = np.linspace(0, np.deg2rad(40), 30)  # Choose smaller area to capture most of the flux, for speed\n",
    "        D_l_integ_ary = np.linspace(4 * kpc, 20 * kpc, 30)  # Choose a line-of-sight range to capture most of the flux\n",
    "\n",
    "        integ = 0\n",
    "        \n",
    "        for D_l in D_l_integ_ary:\n",
    "            for theta in theta_integ_ary:\n",
    "                for phi in phi_integ_ary:\n",
    "                        \n",
    "                    # Calculate distance from GC\n",
    "                    D_r = np.sqrt(D_l ** 2 + Rsun ** 2 - 2 * D_l * Rsun * np.cos(theta))\n",
    "                    \n",
    "                    # Get cylindrical coordinates using some triggg\n",
    "                    R = np.sqrt((D_l * np.cos(theta) - Rsun) ** 2 + (D_l * np.sin(theta) * np.cos(phi)) ** 2)\n",
    "                    z = D_l * np.sin(theta) * np.sin(phi)\n",
    "                    \n",
    "                    if np.abs(z) > 5 * kpc: continue\n",
    "\n",
    "                    # Luminosity range to integrate over\n",
    "                    Lgamma_min = self.L_gamma(self.Fp_gamma(F_gamma, E_1, E_2), D_l)\n",
    "                    Lgamma_max = self.L_gamma(self.Fp_gamma(F_gamma + dF_gamma, E_1, E_2), D_l)\n",
    "                    \n",
    "                    # Luminosity integral is over a small range so don't need many subdivisions\n",
    "                    L_gamma_integ_ary = np.linspace(Lgamma_min, Lgamma_max, 4)\n",
    "\n",
    "                    # Integration measure\n",
    "                    measure = (L_gamma_integ_ary[1] - L_gamma_integ_ary[0]) * (theta_integ_ary[1] - theta_integ_ary[0]) * (D_l_integ_ary[1] - D_l_integ_ary[0])  * (phi_integ_ary[1] - phi_integ_ary[0])\n",
    "\n",
    "                    for L_gamma in L_gamma_integ_ary:\n",
    "                        \n",
    "                        # Spherical integration element\n",
    "                        integ += measure * (1 / dF_gamma / (4 * np.pi) * np.sin(theta) * self.dNdL(L_gamma, **self.dNdL_kwargs) * D_l ** 2 * self.dNdV(R, z, **self.dNdV_kwargs))\n",
    "\n",
    "        return integ\n",
    "\n",
    "    def Fp_gamma(self, F_gamma, E_1, E_2):\n",
    "        \"\"\" Stretch flux F_gamma into a given range (between E_1_0 and E_2_0) from value between energies E_1 and E_2\n",
    "        \"\"\"\n",
    "        return F_gamma * self.F_integ / quad(lambda E: self.dFdE(E), E_1, E_2)[0]\n",
    "\n",
    "    def L_gamma(self, F_gamma, D_l):\n",
    "        \"\"\" \n",
    "        Return luminosity flux given photon flux. First get energy flux, then \n",
    "        convert to luminosity flux with L = 4 * pi * D_l^2 * (energy flux)\n",
    "        \n",
    "        :param F_gamma: Photon flux\n",
    "        :param D_l: Line-of-sight distance \n",
    "            \n",
    "        \"\"\"\n",
    "        return 4 * np.pi * D_l ** 2 * (F_gamma / self.F_integ * self.E_integ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models of luminosity function, energy spectrum and spatial distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MSP luminosity function\n",
    "\n",
    "def dNdL_gamma_lognormal(L_gamma, L_0, sigma_L, L_min=10 ** 30 * erg / Sec, L_max=10 ** 37 * erg / Sec, ln=False):\n",
    "    \"\"\" Log-normal luminosity function parameterization\n",
    "        Eq. (5d) of Bartels et al (1805.11097)\n",
    "    \"\"\"\n",
    "    if L_gamma < L_min or L_gamma > L_max: \n",
    "        return 0\n",
    "    else:\n",
    "        if not ln:\n",
    "            return np.log10(np.e) / (sigma_L * np.sqrt(2 * np.pi) * L_gamma) * np.exp(-(np.log10(L_gamma) - np.log10(L_0)) ** 2 / (2 * sigma_L ** 2))\n",
    "        else: \n",
    "            return (sigma_L * np.sqrt(2 * np.pi) * L_gamma) * np.exp(-(np.log(L_gamma) - np.log(L_0)) ** 2 / (2 * sigma_L ** 2))    \n",
    "\n",
    "# MSP spatial density distribition\n",
    "\n",
    "def rho_V_Lorimer(R, z, zs=0.63 * kpc, B = 2.75, C=5.94):\n",
    "    \"\"\" Spatial number density according to Lorimer disk profile (unnormalized)\n",
    "        Eq. (6) of Bartels et al (1805.11097), after removing constant terms\n",
    "    \"\"\"\n",
    "    return (R / Rsun) ** B * np.exp(-C * ((R - Rsun) / Rsun)) * np.exp(-np.abs(z) / zs)\n",
    "\n",
    "# MSP energy spectrum\n",
    "\n",
    "def dFdE(E, alpha=-1.57, E_cut=3.78 * GeV):\n",
    "    \"\"\" MSP energy specrtum from Cholis et al (1407.5583)\n",
    "    \"\"\"\n",
    "    return E ** alpha / E_cut ** (1 + alpha) * np.exp(-E / E_cut)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute source counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_bins_ary = np.logspace(-14, -7, 50) * Centimeter ** -2 * Sec ** -1\n",
    "dF_ary = F_bins_ary[1:] - F_bins_ary[:-1]\n",
    "F_centers_ary = 10 ** ((np.log10(F_bins_ary[1:]) + np.log10(F_bins_ary[:-1])) / 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## MSP distribution parameters from Bartels et al\n",
    "\n",
    "# Best-fit lognormal LF from  from Table 3 of Bartels et al (1805.11097)\n",
    "L_0 = 10 ** 32.61 * erg / Sec\n",
    "sigma_L = 0.63\n",
    "\n",
    "# Best-fit Lorimer spatial disk profile parameters, from Table 3 of Bartels et al (1805.11097)\n",
    "zs = 0.63 * kpc\n",
    "B = 2.75\n",
    "C = 5.94\n",
    "\n",
    "# Total number of sources from Table 3 of Bartels et al (1805.11097)\n",
    "N_MSP = 10 ** 4.12 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Compute MSP SCD\n",
    "\n",
    "SC = SourceCountMSP(dNdL_gamma_lognormal, dFdE, rho_V_Lorimer, \n",
    "                    dNdL_kwargs={'L_0':L_0, 'sigma_L':sigma_L, 'ln':False},\n",
    "                    dNdV_kwargs={'zs':zs, 'B':B, 'C':C})\n",
    "dNdF_ary = [SC.dNdF(F, 2 * GeV, 20 * GeV) for F in tqdm_notebook(F_centers_ary)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calibrate, plot and save"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "deg = 180 / np.pi\n",
    "sr = 4 * np.pi\n",
    "srdeg2 = sr * deg**2  # (180/np.pi)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_bins_plot_ary = F_bins_ary / (Centimeter ** -2 * Sec ** -1)\n",
    "dF_plot_ary = F_bins_plot_ary[1:] - F_bins_plot_ary[:-1]\n",
    "F_centers_plot_ary = 10 ** ((np.log10(F_bins_plot_ary[1:]) + np.log10(F_bins_plot_ary[:-1])) / 2.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calibrate amplitude of SCD using total number of sources, which is provided\n",
    "calib = N_MSP / np.sum(dF_plot_ary * dNdF_ary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Bartels et al. (2018) MSP population')"
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     "execution_count": 18,
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     "output_type": "execute_result"
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    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 418.909x314.182 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plot\n",
    "\n",
    "# Plot limits\n",
    "max_lim = np.log10(np.max(F_centers_plot_ary ** 2 * (calib * np.array(dNdF_ary)) / srdeg2)) + 1\n",
    "min_lim = np.log10(np.max(F_centers_plot_ary ** 2 * (calib * np.array(dNdF_ary)) / srdeg2)) - 4\n",
    "\n",
    "# Plot\n",
    "plt.plot(F_centers_plot_ary, F_centers_plot_ary ** 2 * (calib * np.array(dNdF_ary)) / srdeg2, color='forestgreen', ls='--')\n",
    "\n",
    "plt.xlabel(\"$F$ [ph\\,cm$^{-2}$\\,s$^{-1}$]\")\n",
    "plt.ylabel(\"$F^2\\,dN/dF$ [ph\\,cm$^{-2}$\\,s$^{-1}$\\,deg$^{-2}$]\")\n",
    "\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "\n",
    "plt.ylim(10 ** min_lim, 10 ** max_lim)\n",
    "\n",
    "plt.title(\"Bartels et al. (2018) MSP population\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez(\"dNdF_MSP_Bartels.npz\",\n",
    "        F_centers_ary=F_centers_plot_ary,\n",
    "        dNdF_ary=(calib * np.array(dNdF_ary)) / srdeg2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Spatial distribution template"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mod(dividends, divisor):\n",
    "    \"\"\" Return dividends (array) mod divisor (double)\n",
    "        Stolen from Nick\n",
    "    \"\"\"\n",
    "\n",
    "    output = np.zeros(len(dividends))\n",
    "\n",
    "    for i in range(len(dividends)): \n",
    "        output[i] = dividends[i]\n",
    "        done=False\n",
    "        while (not done):\n",
    "            if output[i] >= divisor:\n",
    "                output[i] -= divisor\n",
    "            elif output[i] < 0.:\n",
    "                output[i] += divisor\n",
    "            else:\n",
    "                done=True\n",
    "\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "nside = 256\n",
    "npix = hp.nside2npix(nside)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get lon/lat array\n",
    "\n",
    "theta_ary, phi_ary = hp.pix2ang(nside, np.arange(npix))\n",
    "\n",
    "b_ary = np.pi / 2. - theta_ary\n",
    "l_ary = mod(phi_ary + np.pi, 2. * np.pi) - np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "def R_z_GC(s, b, l):\n",
    "    \"\"\" Convert lon/lat to cylindrical coordinates\n",
    "    \n",
    "        :param s: distance from Earth [kpc]\n",
    "        :param b: latitude in galactic coordinates [rad]\n",
    "        :param l: longitude in galactic coordinates [rad]\n",
    "        :returns: distance from GC [kpc]\n",
    "    \"\"\"\n",
    "    R = np.sqrt(s ** 2 - 2 * s * Rsun * np.cos(l) + Rsun ** 2)\n",
    "    z = s * np.tan(b)\n",
    "    return R, z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rho_V_Lorimer_lonlat(s, b, l):\n",
    "    \"\"\" Lorimer density, this time in lot/lat\n",
    "    \"\"\"\n",
    "\n",
    "    R, z = R_z_GC(s, b, l)\n",
    "    return rho_V_Lorimer(R, z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def L_integ_Lorimer(b, l):\n",
    "    \"\"\" Line-of-sight integral (discrete sum) for Lorimer disk profile\n",
    "    \"\"\"\n",
    "    s_ary = np.linspace(0, 100, 2000) * kpc  # Integration range\n",
    "    return np.sum(rho_V_Lorimer_lonlat(s_ary, b, l))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "260d67ce7f2343058e5787d663aaf21e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=786432), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Loop over pixels and create disk template by doing los integrals of Lorimer profile\n",
    "\n",
    "disk_template = np.zeros(npix)\n",
    "\n",
    "for p in tqdm_notebook(range(npix)):\n",
    "    disk_template[p] = L_integ_Lorimer(b_ary[p], l_ary[p])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "disk_template_norm = disk_template / np.mean(disk_template)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 612x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hp.mollview((hp.ud_grade(disk_template_norm, 128)), min=0, max=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save(\"temp_lorimer_disk_Bartels.npy\", hp.ud_grade(disk_template_norm, 128))"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}