Axion_Halo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import integrate\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_soliton = 1.45#kpc\n",
    "rho_soliton = 2.42e9#SM*kpc−3\n",
    "rho_NFW = 0.037*rho_soliton\n",
    "r_s = 0.39#kpc\n",
    "m_axion = 2.44e-22#eV\n",
    "G = 4.302e-6#kpc/SM(km/s)^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rho_reps(r,rho_sol,m_a):\n",
    "    rsol = ((rho_sol/(2.42e9))*(m_a/1.0e-22)**2.)**(-0.25)\n",
    "    d = (1. + (r/rsol)**2.)**8.\n",
    "    return 1/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rho_rmayor(r,rho_sol,m_a,eps,r_s):\n",
    "    rsol = ((rho_sol/(2.42e9))*(m_a/1.0e-22)**2.)**(-0.25)\n",
    "    r_eps = rsol*np.sqrt(eps**(-1./8.) - 1.)\n",
    "    delta_NFW = eps*(r_eps/r_s**3.)*(r_s + r_eps)**2.\n",
    "    d = (r/r_s**3.)*(r_s + r)**2.\n",
    "    return delta_NFW/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = np.linspace(0.,15.,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.45246598658288756 [0.01       0.11473684 0.21947368 0.32421053 0.42894737 0.53368421\n",
      " 0.63842105 0.74315789 0.84789474 0.95263158 1.05736842 1.16210526\n",
      " 1.26684211 1.37157895 1.47631579 1.58105263 1.68578947 1.79052632\n",
      " 1.89526316 2.        ]\n"
     ]
    }
   ],
   "source": [
    "rsol_1 = ((0.037*rho_soliton/(2.42e9))*(m_axion/1.0e-22)**2.)**(-0.25)\n",
    "r_eps_1 = rsol_1*np.sqrt(0.48**(-1./8.) - 1.)\n",
    "r_1 = np.linspace(0.01,2,20)\n",
    "r_2 = np.linspace(0.01,20.,90)\n",
    "print r_eps_1,r_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'r')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#plt.plot(r,rho_sol*0.037*rho_reps(r,rho_sol=0.037*rho_sol,m_a=m_axion))\n",
    "#plt.plot(r,rho_sol*0.037*rho_rmayor(r,rho_sol=0.037*rho_sol,m_a=m_axion,eps=0.48,r_s=0.39))\n",
    "plt.plot(r_2,rho_soliton*0.037*rho_rmayor(r_2,rho_sol=0.037*rho_soliton,m_a=m_axion,eps=0.48,r_s=0.39))\n",
    "plt.plot(r_1,rho_soliton*0.037*rho_reps(r_1,rho_sol=0.037*rho_soliton,m_a=m_axion))\n",
    "plt.yscale('log')\n",
    "plt.xscale('log')\n",
    "plt.ylabel(r'$\\rho(r)$')\n",
    "plt.xlabel('r')\n",
    "#plt.xlim(0,2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "rsol_2 = ((0.057*rho_soliton/(2.42e9))*(m_axion/1.0e-22)**2.)**(-0.25)\n",
    "r_eps_2 = rsol_2*np.sqrt(0.464**(-1./8.) - 1.)\n",
    "r_1_2 = np.linspace(0.,r_eps_2,10)\n",
    "r_2_2 = np.linspace(r_eps_2,20.,90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'r')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.plot(r_2_2,rho_soliton*0.057*rho_rmayor(r_2_2,rho_sol=0.057*rho_soliton,m_a=m_axion,eps=0.464,r_s=0.57))\n",
    "plt.plot(r_1_2,rho_soliton*0.057*rho_reps(r_1_2,rho_sol=0.057*rho_soliton,m_a=m_axion))\n",
    "plt.yscale('log')\n",
    "plt.ylabel(r'$\\rho(r)$')\n",
    "plt.xlabel('r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vc_rmayor(r,eps,r_s,m_a,rho_sol):\n",
    "    rsol = ((rho_sol/(2.42e9))*(m_a/10.0e-22)**2.)**(-0.25)\n",
    "    r_eps = rsol*np.sqrt(eps**(-1./8.) - 1.)\n",
    "    delta_NFW = eps*(r_eps/r_s**3.)*((r_s+r_eps))**2.\n",
    "    t = np.log(r+r_s) - np.log(r_eps+r_s) + r_s/(r+r_s) - r_s/(r_eps+r_s)\n",
    "    return 4.*np.pi*G*rho_sol*delta_NFW*r_s**3.*t/r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vc_rminor(r,m_a,rho_sol,eps):\n",
    "    rsol = ((rho_sol/(2.42e9))*(m_a/10.0e-22)**2.)**(-0.25)\n",
    "    r_eps = rsol*np.sqrt(eps**(-1./8.) - 1.)\n",
    "    t = 3465.*rsol*r_eps**13. + 23100.*r_eps**11.*rsol**3. + 65373.*r_eps**9.*rsol**5. + 101376.*r_eps**7.*rsol**7. + 92323.*r_eps**5.*rsol**9. + 48580.*r_eps**3.*rsol**11. - 3465.*r_eps*rsol**13. + 3465.*(r_eps**2. + rsol**2.)**7.*np.arctan(r_eps/rsol)\n",
    "    d = 215040.*r*(r_eps**2. + rsol**2.)**7.\n",
    "    return 4.*np.pi*G*rho_sol*rsol**3.*t/d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/atalia/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1189d5590>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.plot(r_1,np.sqrt(vc_rminor(r_1,m_a=m_axion,rho_sol=0.037*rho_soliton,eps=0.48)))\n",
    "plt.plot(r_2,np.sqrt(vc_rmayor(r_2,eps=0.48,r_s=0.39,m_a=m_axion,rho_sol=0.037*rho_soliton)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/atalia/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in divide\n",
      "  \n",
      "/Users/atalia/miniconda2/lib/python2.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118967850>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.plot(r_1_2,np.sqrt(vc_rminor(r_1_2,m_a=m_axion,rho_sol=0.037*rho_soliton,eps=0.48)))\n",
    "plt.plot(r_2_2,np.sqrt(vc_rmayor(r_2_2,eps=0.464,r_s=0.57,m_a=m_axion,rho_sol=0.057*rho_soliton)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.0e-22==10.0**(-22)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}