= Solution
\b[Supernovae are explosive stellar events with different energy sources and progenitors; a remnant is the expanding ejecta and shocked environment left afterward.] Their spectra classify the observed event, while explosion mechanisms give a related but distinct physical classification. Lack of <hydrogen> absorption defines TypeI spectroscopically; TypeII shows <hydrogen>. TypeIa typically shows silicon features, while stripped-envelope core-collapse events can be TypeIb or Ic.
In core collapse, an evolved massive star's central core loses support as nuclear processing ceases to supply stable pressure support, <electron captures> reduce <electron> pressure and <photodisintegration> consumes energy. Collapse can form a <neutron star> or <black hole>. A <shock> launched near core bounce loses energy, so a successful explosion requires additional processes, often modeled through <neutrino> heating aided by multidimensional flow; some collapses fail to eject a bright ordinary <supernova>. The compact remnant and <neutrino> emission distinguish this channel physically from a thermonuclear disruption.
TypeIa explosions involve thermonuclear burning of a <carbon-oxygen white dwarf> in a binary-related evolutionary channel. Both near-Chandrasekhar and sub-Chandrasekhar routes are studied; no single progenitor path is forced by the spectral classification alone. Radioactive nickel and cobalt decay can power much of the later optical emission. Empirical light-curve standardization makes these events useful distance indicators, but dust, population differences and calibration must be controlled; they are not intrinsically identical candles.
Initially ejecta may expand nearly freely, with radius $R_s\sim v_{\rm ej}t$, until swept-up external mass becomes dynamically important. The <shock> heats the surrounding gas and a reverse <shock> heats ejecta. For an approximately spherical, adiabatic explosion of fixed energy $E$ into a uniform density $\rho_0$, dimensional analysis gives the Sedov-Taylor stage:
$$
\boxed{R_s=\xi\left(\frac{Et^2}{\rho_0}\right)^{1/5},
\qquad v_s=\frac25\frac{R_s}{t}.}
$$
The dimensionless coefficient $\xi$ depends on the equation of state; no value is needed without specifying that model. For a strong nonrelativistic <shock> in a monatomic gas, an equilibrated post-shock temperature scale is $k_BT\simeq3\mu m_pv_s^2/16$. Collisionless <electron> and ion temperatures may differ.
Later radiative losses can produce a dense cooled shell. Idealized pressure-driven and momentum-conserving snowplough models then have different expansion exponents; the environment and continuing interior pressure determine which description applies. For uniform ambient density and conserved shell <momentum>, $M_{\rm swept}\dot R_s\propto R_s^3\dot R_s$ gives $R_s\propto t^{1/4}$. Real remnants can be asymmetric and encounter nonuniform winds or clouds.
Thermal <X-ray> emission traces shocked <plasma>, optical lines trace cooling gas, and radio synchrotron emission traces relativistic <electrons> and <magnetic fields>. <Shocks> can accelerate <cosmic rays> and alter the energy budget. Ejecta abundances, a surviving compact object, pulsar-powered nebulae and the remnant's dynamics help reconstruct the explosion, but present morphology alone does not uniquely identify the progenitor.
Supernovae enrich the interstellar medium, stir and heat galactic gas and can drive outflows or trigger local compression. Their feedback couples small stellar scales to <galaxy evolution>. Quantifying that effect requires accounting for cooling and the collective environment rather than assigning all explosion energy to a permanently retained galactic reservoir.
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