Solution (source code)

= Solution

<core-collapse supernovae> follow loss of pressure support in the evolved core of a massive star. <electron> capture and nuclear dissociation contribute to collapse; formation of a hot compact object launches a <shock> that can stall as dissociation and <neutrino> losses drain it. <neutrino> heating and multidimensional fluid motions can revive the <shock>, but some collapses fail to produce a normal bright explosion. The remnant may be a <neutron star> or <black hole>. The <neutrino> burst detected from <SN 1987A> provides direct evidence for the core-collapse <energy> channel: the water-Cherenkov <signal> is a particle-interaction measurement, requiring detector-response and accidental-background checks rather than an optical light-curve inference.<Observation of a Neutrino Burst from the Supernova SN1987A by K. Hirata and others>[pp.1490–1493, burst observation and detector interpretation]{ref}

<Type Ia supernovae> instead involve thermonuclear destruction of a degenerate <carbon-oxygen white dwarf>. They leave expanding ejecta without an ordinary surviving neutron-star core. The ignition channel need not have a unique total <mass> or binary history. Radioactive nickel/cobalt decay powers much of the later luminosity, and empirical light-curve corrections make these events useful distance indicators. Spectral type is not identical to explosion mechanism: hydrogen-rich Type II events are core collapse, but stripped-envelope Ib/c events can also be core collapse despite lacking conspicuous <hydrogen>.

The ejecta first expand nearly freely while swept-up <mass> is small. A strong <shock> heats ambient gas, and once swept-up material dominates, an approximately adiabatic remnant approaches the Sedov-Taylor scaling
$$
\boxed{R_s\propto\left(\frac{Et^2}{\rho_0}\right)^{1/5}.}
$$
Subsequent <radiative cooling> makes a dense shell and ends that energy-conserving approximation. Thermal X-ray lines probe shocked gas and nucleosynthetic ejecta; radio and nonthermal X-rays <trace> <relativistic particles> and <magnetic fields>. <shock> acceleration makes remnants plausible contributors to Galactic <cosmic rays>. Expansion, ambient-density structure, cooling and cosmic-ray <energy> losses complicate <energy> estimates; a bright synchrotron shell alone is not proof of a specific accelerated-particle composition. Supernovae return metals and mechanical <energy> to the <interstellar medium> and therefore connect stellar death to the feedback cycle.