I know that in some types of supernovae, the cause of the increased luminosity is the radioactive decay of certain elements ejected during the explosion, so a question came to my mind. If the ejected material carrying the isotopes that decay to give the electromagnetic radiation is expelled at velocity of say 5% the speed of light, and given the fact that some supernovae stay extremely luminous for more than 4 weeks, then by that time the radioactive isotopes will have traveled more than 30 billion kilometers from the exploded star. So, does that mean a supernova at 4 weeks can be expected to look like a star with a radius of 30 billion kilometers and luminosity of $10^8$-$10^9$ times the solar luminosity ? Or I am getting the idea of the radioactive decay as the source of the supernova luminosity wrong ?
-
$\begingroup$ @KyleKanos, yes. But what confuses me is whether the radioactive decay is the only source of luminosity, because I still feel like (without knowing how to prove it) that the core itself is very luminous. I mean, are the supernova remnants the only luminous part of the supernova ? because sooner or later this remnant shell will have expanded so much that it is almost transparent, so isn't the core a source of luminosity too at least in the first few days ? $\endgroup$– Abanob EbrahimSep 1, 2014 at 7:45
-
1$\begingroup$ @AbanobEbrahim: There may be no remnant, at all, if the core of the supernova collapses into a black hole! And even if it doesn't, the remnant is a very small, very dense object. There is simply not enough surface area to emit a significant amount of radiation in comparison to the bulk of the expanding shell. The initial radiation burst from the supernova is, of course, enormous and some of that energy is carried off by neutrinos, which can leave the core and the shell. $\endgroup$– CuriousOneSep 1, 2014 at 11:00
-
1$\begingroup$ @CuriousOne Well if a pulsar forms then the radiation jets will light up their particular area, and whatever remnants they hit. As another note, in pair instability supernovae there is no remnant at all, as the star is completely disrupted. $\endgroup$– zibadawa timmySep 1, 2014 at 16:42
1 Answer
Your math does check out: \begin{align} r&=vt \\ &=0.05\cdot2.9979\times10^{10}\frac{cm}s\cdot4\cdot604800\,s\\ &=3.63\times10^{15}\,cm\\ &=36.3\times10^9\,km\\ &=0.012\,pc \end{align}
When a supernova explodes, it enters the free expansion phase, it's position is linear in time ($r=vt$, as used above). It stays in this phase for a few hundred years (depends heavily on the ambient density); assuming 200 years, then $$ r_{fe}=9.45\times10^{18}\,cm=3\,pc $$
After this point, the Supernova Remnant (technically speaking, SNe is the explosion while SNR is the result of the material after said explosion) continues expanding, though at a reduced rate (because it has swept-up ambient material this entire time, building up a thick shell of thickness $w\sim0.1\,pc$) for many thousands of years.
SNe theory says a normal Type Ia produces about $0.5\,M_\odot$ of nickel-56 which then decays to an excited state of cobalt-56, which then emits an X-ray photon: \begin{align} \,^{56}{\rm Ni}+e^-&\to\,^{56}{\rm Co}^*+\nu_e \\ \,^{56}{\rm Co}^*&\to\,^{56}{\rm Co}+\gamma \end{align} The cobalt-56 (lifetime around 100 days) then decays to iron-56 which also decays with some X-ray photons. Until SN 2014J, we had only observed the iron-56 decay line due to the fact that the lifetime of the above reaction is about 9 days and the ejecta are opaque to these lines due to Compton scattering in this same time-frame. SN 2014J provided $\gamma$-ray and X-ray emissions due to the cobalt-56, proving the theory correct.
Note that the shell remains very thick during this whole time. Wikipedia provides an image of SN 1006 (exploded in the year 1006, so it's now 1008 years old) that shows the expansion of the shell:
This shell is measured to be between 0.04 and 0.2 pc, which are roughly $1.2\cdot10^{12}$ km and $6.2\cdot10^{12}$ km thick, which is just shy of 1 lightyear. And after all this time, it is strong in radio, X-ray & $\gamma$-ray emissions (from this site):
