diff --git a/docs/physics/tardisgamma/decayenergy.ipynb b/docs/physics/tardisgamma/decayenergy.ipynb new file mode 100644 index 00000000000..c1e1e0ff3b3 --- /dev/null +++ b/docs/physics/tardisgamma/decayenergy.ipynb @@ -0,0 +1,160 @@ +{ + "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": 2, + "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": [ + "" + ] + }, + "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. [] " + ] + }, + { + "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": 12, + "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/(8.8*u.day)) + 1.45e43 * np.exp(-time/(111.3*u.day))) * (m_Ni56/ const.M_sun) * 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": "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) * u.erg\n", + "print(f\"The total energy production for 1 solar mass of 56Ni is: {total_energy_production}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} diff --git a/docs/physics/tardisgamma/index.rst b/docs/physics/tardisgamma/index.rst index a67b089ba77..96601cf5a6e 100644 --- a/docs/physics/tardisgamma/index.rst +++ b/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 \ No newline at end of file diff --git a/docs/tardis.bib b/docs/tardis.bib index c324fb30456..2f54a9550ee 100644 --- a/docs/tardis.bib +++ b/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} +} +