Gamma decay energy documentation

docs/physics/tardisgamma/decayenergy.ipynb

@@ -0,0 +1,164 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Radioactive Decay Energy\n",
+    "\n",
+    "Within the ejecta of a supernova, the $\\gamma$-rays largely come from the decay of $^{56}Ni$ into $^{56}Co$, which releases a significant amount of energy. \n",
+    "\n",
+    "When $^{56}Ni$ decays into $^{56}Co$ it can release a $\\gamma$-ray at several different transition levels. Each transition level has an energy and an associated probability out of 100 decays. For example, the transition from Energy level 9 to Energy level 7 has an energy of 0.270 Mev and a probability of 36.5 out of 100 decays. To find the total energy per decay you multipliy each energy with its associated probability and add them all up."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from astropy import units as u\n",
+    "from astropy import constants as const"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$1.7202 \\; \\mathrm{meV}$"
+      ],
+      "text/plain": [
+       "<Quantity 1.7202 meV>"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# energies of each transition\n",
+    "t_energies = np.array([0.270, 0.750, 0.480, 1.56, 0.812, 0.158]) * u.meV\n",
+    "# probabilities of each transition\n",
+    "t_prob = np.array([.365, .495, .366, .140, .860, 1.00])\n",
+    "\n",
+    "energy_per_decay = sum(t_energies * t_prob)\n",
+    "energy_per_decay"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "From the above cell, we get the energy per transition of 1.72 MeV. Note that this comes from a simplified scheme of energies and the real total energy per $^{56}Ni$ decay we use is 1.75 MeV. <strong data-cite=\"1994Nadyozhin\">[]</strong> "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The $^{56}Co$ produced from the decay of $^{56}Ni$ is also radioactive and will decay into $^{56}Fe$ and release more $\\gamma$-rays, however this decay is more complicated than the decay of $^{56}Ni$. Whereas $^{56}Ni$ only decays through electron capture, $^{56}Co$ can decay either by electron capture, which occurs for 81 out of 100 cases, or through positron decay, which occurs for 19 out of 100 cases.\n",
+    "\n",
+    "Positron decay produces positrons with a given kinetic energy, that will eventually annihilate with electrons to produce two 0.511 MeV $\\gamma$-rays. The scheme of decays for $^{56}Co$ is slightly more complicated than the $^{56}Ni$ scheme, but to find the total energy per decay, you follow the same process. The total energy per decay from $\\gamma$-rays is 3.61 MeV and the total kinetic energy of positrons is 0.12 MeV"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " The total rate of energy production for a mass of $^{56}Ni$ at a given time is given by the following equation:\n",
+    "\n",
+    "$$\\epsilon = \\frac{M_\\odot}{56m_{u}}\\frac{1}{\\tau_{\\text{Co}}-\\tau_{\\text{Ni}}}[[Q_{\\text{Ni}}(\\frac{\\tau_{\\text{Co}}}{\\tau_{\\text{Ni}}}-1)-Q_{\\text{Co}}]\\exp(-t/\\tau_{\\text{Ni}})+Q_{\\text{Co}}\\exp(-t/\\tau_{\\text{Co}})]\\frac{M_{Ni0}}{M_\\odot}$$\n",
+    "\n",
+    "$M_\\odot$ is a solar mass. $56_{u}$ is 56 atomic mass units. \n",
+    "\n",
+    "$\\tau_{Ni}$ is the lifetime of $^{56}Ni$ which is 8.80 days and $\\tau_{Co}$ is the lifetime of $^{56}Co$ which is 111.3 days. \n",
+    "\n",
+    "$Q_{\\text{Ni}}$ is the energy per decay of $^{56}Ni$ which is 1.75 MeV and $Q_{\\text{Co}}$ is the sum of the energy per decay pf $^{56}Co$ from $\\gamma$-rays and the kinetic energy from positrons which is 3.73 MeV\n",
+    "\n",
+    "If we plug these values into the equation we get the equation:\n",
+    "\n",
+    "$$\\epsilon = (6.45e43\\exp(-t/8.8)+1.45e43\\exp(-t/111.3))\\frac{M_{Ni0}}{M_\\odot} erg/s$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The total energy production rate for 1 solar mass of 56Ni after 10 days is: 3.40e+43 erg / s\n"
+     ]
+    }
+   ],
+   "source": [
+    "#time in days\n",
+    "time = 10 * u.day\n",
+    "#mass of Ni56 in solar masses\n",
+    "m_Ni56 = 1 * const.M_sun\n",
+    "\n",
+    "energy_production_rate = (6.45e43 * np.exp(-time.value/8.8) + 1.45e43 * np.exp(-time.value/111.3)) * (m_Ni56/ const.M_sun).value * u.erg /u.s\n",
+    "\n",
+    "print(f\"The total energy production rate for 1 solar mass of 56Ni after 10 days is: {energy_production_rate:.2e}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The equation for the time-integrated total energy production is:\n",
+    "\n",
+    "$$ E = E_{Ni} + E_{Co} = 1.885e50\\frac{M_{Ni0}}{M_\\odot}ergs$$\n",
+    "\n",
+    "Where $E_{Ni} = 6.22e49 \\frac{M_{Ni0}}{M_\\odot}$ ergs and $E_{Co} = 1.26e50 \\frac{M_{Ni0}}{M_\\odot}$ ergs."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "The total energy production for 1 solar mass of 56Ni is: 1.885e+50 erg\n"
+     ]
+    }
+   ],
+   "source": [
+    "total_energy_production = 1.885e50 * (m_Ni56/const.M_sun).value * u.erg\n",
+    "print(f\"The total energy production for 1 solar mass of 56Ni is: {total_energy_production}\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "tardis",
+   "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": "3.12.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

docs/physics/tardisgamma/index.rst

@@ -10,3 +10,4 @@ Type Ia supernovae produce a large amount of energy from :math:`\gamma`-rays pro
 
 .. toctree::
     packetinitialization
+    decayenergy

docs/tardis.bib

@@ -348,3 +348,18 @@ @ARTICLE{Boyle2017
        adsurl = {https://ui.adsabs.harvard.edu/abs/2017A&A...599A..46B},
       adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
+
+@ARTICLE{1994Nadyozhin,
+       author = {{Nadyozhin}, D.~K.},
+        title = "{The Properties of NI CO Fe Decay}",
+      journal = {\apjs},
+     keywords = {Cobalt Isotopes, Decay, Electron Capture, Gamma Rays, Nickel Isotopes, Nuclear Astrophysics, Nuclear Fusion, Half Life, Iron Isotopes, Neutrinos, Astronomy, ATOMIC DATA, NUCLEAR REACTIONS, NUCLEOSYNTHESIS, ABUNDANCES},
+         year = 1994,
+        month = jun,
+       volume = {92},
+        pages = {527},
+          doi = {10.1086/192008},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/1994ApJS...92..527N},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+