Defining properties: rapid increase in absolute magnitude of supernovae;…

The idea

A supernova is identified by a rapid increase in absolute magnitude, meaning its intrinsic brightness rises sharply as the star's core collapses and the outer layers are ejected. The absolute magnitude becomes much more negative over days, so the event can outshine a galaxy. A neutron star is the collapsed core, composed mainly of neutrons with some protons and electrons, with a density comparable to an atomic nucleus, around 10¹⁷ kg m⁻³. A black hole forms when the escape velocity from the collapsed core exceeds the speed of light c, so even light cannot escape. The escape velocity is v_esc = √(2GM/r); setting v_esc > c gives a Schwarzschild radius r_s = 2GM/c². For a 10 M☉ black hole, r_s is about 30 km.

What earns the marks

• State that a supernova shows a rapid increase in absolute magnitude, meaning the absolute magnitude becomes more negative over a short time.
• Explain that the rapid brightening is caused by the collapse of the core and the resulting ejection of outer layers, producing a huge increase in luminosity.
• Describe a neutron star as composed mainly of neutrons, with some protons and electrons, at nuclear density around 10¹⁷ kg m⁻³.
• Derive or use v_esc = √(2GM/r) and set v_esc > c to define a black hole.
• Rearrange to r_s = 2GM/c² and interpret r_s as the Schwarzschild radius or event horizon.
• Compare densities: a neutron star is about 10¹⁷ kg m⁻³, whereas a black hole's mass is concentrated within its event horizon.

Common mistakes and how to put them right

• Confusing absolute magnitude with apparent magnitude.

  Put it right by defining absolute magnitude as the brightness the star would have at 10 pc.

• Thinking a neutron star is made only of neutrons.

  Put it right by stating the composition includes neutrons, protons and electrons.

• Using v_esc = c as the condition for a black hole instead of v_esc > c.

  Put it right by writing v_esc > c and then r_s = 2GM/c².

• Forgetting to square c in r_s = 2GM/c².

  Put it right by writing c² in the denominator.

Exam tips

• When defining a supernova, link the rapid increase in absolute magnitude to the collapse and ejection process, not just to a brightening.
• For neutron stars, quote a typical density such as 10¹⁷ kg m⁻³ and state the main composition.
• For black holes, start from the escape velocity equation and show the inequality v_esc > c before rearranging to r_s = 2GM/c².
• Use consistent units: G = 6.67 × 10⁻¹¹ N m² kg⁻², c = 3.00 × 10⁸ m s⁻¹, and masses in kg.