Supernovae and Compact Objects

A sufficiently massive star can build a core whose fusion no longer supplies enough outward support. Collapse and the associated explosion produce a core-collapse supernova. A neutron star is an extremely compact remnant made predominantly of neutrons, with a density of order nuclear density. More massive collapsing cores can form black holes.

The event horizon is a boundary from inside which light cannot escape to distant observers. The Newtonian escape-speed argument motivates the Schwarzschild expression, although a full account requires general relativity. Supermassive black holes are found at many galactic centres. Some collapsing massive stars power intense gamma-ray bursts; avoid claiming every supernova produces one.

A type Ia supernova involves a thermonuclear explosion of a white dwarf and is distinct from massive-star core collapse. Its luminosity rises rapidly to a peak and then declines over weeks and months. The absolute magnitude becomes much more negative near peak: “brighter” means a numerical decrease in magnitude.

After calibrating differences between their light curves, type Ia supernovae provide an estimate of intrinsic peak luminosity or absolute magnitude. Compare that with observed flux or apparent magnitude to infer distance. Standard candles are calibrated objects, not an assumption that every supernova has exactly identical output.

Compare energy outputs by multiplying a sustained luminosity by duration. Distinguish a burst’s power from its total energy: a very short burst can have enormous power without radiating at that power for years.

Distant type Ia supernovae appear fainter than expected in a simple decelerating-expansion model, indicating larger distances. Combined with redshift observations this supports accelerated expansion. Dark energy is a name for the inferred cause within cosmological models; its physical nature is not settled. Account for extinction and calibration before treating faintness as cosmological evidence.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.