{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GWs from bosons around black holes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import gwaxion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Black holes and bosons\n",
    "\n",
    "Let's create a black-hole--boson system starting from a given BH mass ($M = 50 M_\\odot$), initial dimensionless BH spin ($\\chi=0.9$) and a fine structure constant ($\\alpha = 0.2$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "bhb = gwaxion.BlackHoleBoson.from_parameters(m_bh=50, alpha=0.2, chi_bh=0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the code assumes the boson is a scalar, but we could have specified a different spin-weight via the argument `spin`. Let's now print some properties of the system.\n",
    "\n",
    "First, the BHB system contains a **black-hole** (`BlackHole`) with the following properties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The initial black-hole has a mass of 50.0 MSUN (9.9e+31 kg).\n",
      "It also has a dimensionless spin of chi=0.90, which corresponds to an angular momentum J=2.0e+45 Js, and Kerr parameter a=6.6e+04 m.\n",
      "The outer radius is 1.1e+05 m, with a horizon angular frequency of 1272.1 rad/s.\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nThe initial black-hole has a mass of %.1f MSUN (%.1e kg).\"\n",
    "      % (bhb.bh.mass_msun, bhb.bh.mass))\n",
    "print(\"It also has a dimensionless spin of chi=%.2f, which corresponds to an \"\n",
    "      \"angular momentum J=%.1e Js, and Kerr parameter a=%.1e m.\"\n",
    "      % (bhb.bh.chi, bhb.bh.angular_momentum, bhb.bh.a))\n",
    "print(\"The outer radius is %.1e m, with a horizon angular frequency of %.1f rad/s.\"\n",
    "      % (bhb.bh.rp, bhb.bh.omega_horizon))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Had we wanted to, we could have created a standalone black-hole by doing `bh = physics.BlackHole(50, chi=0.9, msun=True)`.\n",
    "\n",
    "The BHB system also contains a **boson** (in this case, a scalar):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The boson has a rest-mass of 1e-48 kg, which corresponds to an energy of 5.3e-13 eV. Its spin is 0.\n"
     ]
    }
   ],
   "source": [
    "print(\"The boson has a rest-mass of %1.e kg, which corresponds to an energy of \"\n",
    "      \"%.1e eV. Its spin is %i.\" % \n",
    "      (bhb.boson.mass, bhb.boson.energy_ev, bhb.boson.spin))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Together, the black-hole--boson system has a finestructure constant given by the ratio of the gravitational radius ($r_g=GM/c^2$) to the boson's reduced Compton wavelength [$\\lambda_C = \\hbar / (\\mu c)$]. In this case this is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20000000000000004"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bhb.alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which is what we requested when we constructed the BHB system in the first place."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Energy levels\n",
    "\n",
    "Let's compute the growth rate for a bunch of energy levels with quantum numbers $(l, m, n_r)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(l, m, nr, growth rate in Hz)\n",
      "----------------------------\n",
      "(0, 0, 0, -1.5e+00)\n",
      "(0, 0, 1, -1.9e-01)\n",
      "(0, 0, 2, -5.5e-02)\n",
      "(1, 0, 0, -1.3e-05)\n",
      "(1, 0, 1, -4.5e-06)\n",
      "(1, 0, 2, -2.0e-06)\n",
      "(1, 1, 0, 4.2e-06)\n",
      "(1, 1, 1, 1.5e-06)\n",
      "(1, 1, 2, 6.5e-07)\n",
      "(2, 0, 0, -4.9e-12)\n",
      "(2, 0, 1, -2.9e-12)\n",
      "(2, 0, 2, -1.7e-12)\n",
      "(2, 1, 0, 1.3e-12)\n",
      "(2, 1, 1, 7.5e-13)\n",
      "(2, 1, 2, 4.4e-13)\n",
      "(2, 2, 0, 7.0e-11)\n",
      "(2, 2, 1, 4.2e-11)\n",
      "(2, 2, 2, 2.5e-11)\n"
     ]
    }
   ],
   "source": [
    "print(\"(l, m, nr, growth rate in Hz)\")\n",
    "print(\"----------------------------\")\n",
    "for l in range(0, 3):\n",
    "    for m in range(0, l+1):\n",
    "        for nr in range(0, 3):\n",
    "            print(\"(%i, %i, %i, %.1e)\" % (l, m, nr, bhb.level_omega_im(l, m, nr)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly the $l=m=1$ mode grows very fast. We could have also directly checked whether the $m=1$ mode satisfies the superradiant condition $\\mu < m \\Omega$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bhb.is_superradiant(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also directly ask for the fastest growing level:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1, 0, 4.174052907537487e-06)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bhb.max_growth_rate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The energy of a given level is given by $E_n = E_0(1-\\frac{\\alpha^2}{2n^2})$, where $E_0=mc^2$ and $n$ is the principal quantum number. For the $l=1, n_r=0$ level this is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.32e-13 eV\n"
     ]
    }
   ],
   "source": [
    "l, nr = (1, 0)\n",
    "print(\"%.2e eV\" % bhb.level_energy(l + nr + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clouds\n",
    "\n",
    "We can now add a cloud to our BHB system to populate the largest growing level:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "cloud = bhb.best_cloud()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The system now has one cloud with $(l=1, m=1, n_r=0)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(1, 1, 0): <gwaxion.physics.BosonCloud at 0x7fe4ecad3310>}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bhb.clouds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could have equivalently added this cloud by doing `bhb.cloud(1, 1, 0)` which would retrieve (or create) the desired cloud, but using `bhb.best_cloud()` we don't have to know the quantum numbers of the best cloud a priori.\n",
    "\n",
    "Let's print some properties of the cloud:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "After superradiant growth, the cloud has mass 3.3 MSUN (6.5e+30 kg).\n",
      "This is 6.6%  of the original BH mass.\n"
     ]
    }
   ],
   "source": [
    "mass_fraction = cloud.mass / cloud.bhb_initial.bh.mass\n",
    "print(\"\\nAfter superradiant growth, the cloud has mass %.1f MSUN (%.1e kg).\"\n",
    "      % (cloud.mass_msun, cloud.mass))\n",
    "print(\"This is %.1f%%  of the original BH mass.\" % (mass_fraction*100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the cloud object contains a pointer to the original BlackHoleBoson system under `cloud.bhb_initial`. It also has a similar object for the black hole that remains after superradiant growth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mass and spin of the final black hole are: (46.7 MSUN, 0.65)\n"
     ]
    }
   ],
   "source": [
    "print(\"The mass and spin of the final black hole are: (%.1f MSUN, %.2f)\"\\\n",
    "      % (cloud.bhb_final.bh.mass_msun, cloud.bhb_final.bh.chi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gravitational waves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the superradiant stage is over, the cloud will emit GWs at a frequency of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "257.28 Hz\n"
     ]
    }
   ],
   "source": [
    "print(\"%.2f Hz\" % cloud.fgw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also easily obtain the corresponding waveform, Eqs. (39) and (40) in Brito et al. (2017):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe4ecb152d0>"
      ]
     },
     "execution_count": 15,
     "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": [
    "# Create a waveform and plot it\n",
    "hp, hc = cloud.gw().hp, cloud.gw().hc\n",
    "inclination = np.pi/4\n",
    "time = np.arange(0, 0.05, 1E-4)\n",
    "\n",
    "plot(time, hp(inclination, 0, time), label=r'$+$', color='dodgerblue', lw=2, alpha=0.7)\n",
    "plot(time, hc(inclination, 0, time), label=r'$\\times$', color='darkorange', lw=2, alpha=0.7)\n",
    "xlabel(\"Time (s)\");\n",
    "ylabel(r\"$h(t)$\");\n",
    "title(\"GWs from BH (%.f MSUN) and scalar (%.1e eV)\"\n",
    "          % (cloud.bhb_final.bh.mass_msun, cloud.bhb_final.boson.energy_ev));\n",
    "legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This folds in all the proper spheroidal harmonics and numerical factors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "gwaxion",
   "language": "python",
   "name": "gwaxion"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}