HSC Exam Practice

Sample response. Type Ia: Progenitor is a white dwarf in a binary system that accretes mass from its companion until it exceeds the Chandrasekhar limit (~1.4 M⊙). The explosion is a thermonuclear runaway — carbon ignites explosively throughout the entire star. No remnant is left; the white dwarf is completely destroyed. Type II (core collapse): Progenitor is a massive star (>8 M⊙) that has built an iron core. The iron core collapses in less than a second when it exceeds the Chandrasekhar limit; neutron degeneracy pressure halts the collapse and a shock wave ejects the envelope. The remnant is a neutron star (if <3 M⊙) or a black hole (>3 M⊙).

Marking notes. 1 mark per correct feature for each type (3 each): progenitor, mechanism, remnant.

Sample response. Neutron degeneracy pressure is a quantum mechanical effect arising from the Pauli exclusion principle applied to neutrons: no two neutrons can occupy the same quantum state, creating a pressure that resists compression [1]. This pressure supports the neutron star against gravitational collapse without the need for thermal energy [1]. The Tolman-Oppenheimer-Volkoff (TOV) limit (~3 M⊙) is the maximum mass a neutron star can have before even neutron degeneracy pressure is overwhelmed by gravity, causing collapse to a black hole [1].

Marking notes. 1 mark for each: definition of neutron degeneracy pressure (Pauli/quantum); role in support (no thermal energy needed); TOV limit with correct value and implication.

Sample response. A standard candle is an object whose intrinsic luminosity is known, so its distance can be calculated from its apparent brightness [1]. Type Ia supernovae are standard candles because they always explode at the same mass (Chandrasekhar limit), producing a consistent peak luminosity, allowing distance to be calculated [1]. When researchers measured Type Ia SNe at high redshifts in 1998, they found them fainter than expected for a decelerating universe, implying they were farther away — evidence that the expansion of the universe is accelerating (driven by dark energy) [1].

Sample response. \(M = 1.4 \times 2.0\times10^{30} = 2.8\times10^{30}\) kg [½]; \(R = 12\times10^3 = 1.2\times10^4\) m; \(V = \tfrac{4}{3}\pi(1.2\times10^4)^3 = 7.24\times10^{12}\) m³ [1]; \(\rho = 2.8\times10^{30}/7.24\times10^{12} \approx 3.9\times10^{17}\) kg/m³ [1].

Marking notes. 1 mark for correct mass in kg; 1 mark for volume calculation; 1 mark for correct density (accept 3.5–4.0×10¹⁷ kg/m³).

Sample response. A pulsar is a rapidly rotating neutron star with a strong magnetic field that emits beams of electromagnetic radiation (typically radio waves) from its magnetic poles [1]. As the star rotates, the beam sweeps across Earth periodically, like a lighthouse, producing regular radio pulses [1]. Neutron stars rotate rapidly because of conservation of angular momentum: as the massive star’s core (roughly Earth-sized) collapses to a neutron star radius (~10 km), the enormous reduction in radius causes a corresponding increase in rotation rate [1].

Sample response (a). Can be produced by stellar fusion: Sr = No; Au = No; U = No. r-process product: Sr = Yes; Au = Yes; U = Yes. [1 for all fusion = No; 1 for all r-process = Yes]

Sample response (b). Strontium has Z = 38, which is heavier than iron (Z = 26). Fusion beyond iron is endothermic (requires energy input) because the resulting nuclei have lower binding energy per nucleon than iron [1]. Therefore, strontium cannot be produced by nuclear fusion in stellar cores [1]. The detection of strontium in the kilonova spectrum indicates it was produced by the r-process — rapid neutron capture in the extreme neutron flux of the merger debris, which built up strontium nuclei faster than they could beta-decay. This is direct observational evidence that neutron star mergers are a site of r-process nucleosynthesis [1].

Sample response (c). A kilonova is a luminous transient produced when two neutron stars merge and eject neutron-rich debris [1]. It is powered by the radioactive decay of freshly synthesised r-process nuclei in the ejected material, which heats the ejecta over hours to days. Unlike a Type Ia supernova (thermonuclear) or Type II (core collapse), there is no thermonuclear runaway or core bounce; the energy comes entirely from r-process nuclear decay [1].

Sample response. Core-collapse supernovae (Type II) are produced when a massive star (>8 M⊙) builds an iron core that exceeds the Chandrasekhar limit. Gamma-ray photons cause photodisintegration of iron nuclei, absorbing energy and accelerating collapse. At nuclear densities, neutron degeneracy pressure halts the collapse (TOV limit ~3 M⊙), and the resulting shock — revived by neutrino heating — ejects the stellar envelope at ~10,000 km/s. The r-process can occur in the neutrino-driven wind from the proto-neutron star, producing heavy elements. [2: mechanism with photodisintegration, neutron degeneracy, neutrino driven shock + r-process site] Neutron star mergers provide a complementary r-process site. When two neutron stars in a binary inspiral and merge, the tidal disruption ejects neutron-rich material at extreme neutron densities (~10²&sup0; n/cm³). Nuclei capture neutrons rapidly, building r-process products far from stability that then beta-decay to stable heavy isotopes such as gold, platinum, and uranium. [1: NS merger mechanism + r-process] The neutron star density is extraordinarily high: for M = 1.4 M⊙ = 2.8×10³&sup0; kg and R = 12 km = 1.2×10&sup4; m, \(\rho = M/\tfrac{4}{3}\pi R^3 \approx 3.9\times10^{17}\) kg/m³, comparable to atomic nuclear density. This extreme density means neutrons are packed as densely as in individual nuclei, explaining why the merger ejecta provides the necessary neutron flux for r-process. [1: density calculation with result and link to r-process conditions] The GW170817 event (2017) provided the first direct evidence that neutron star mergers are a major r-process site. Gravitational waves confirmed the neutron star merger, the accompanying kilonova produced heavy element spectral signatures (including strontium), and this confirmed that a substantial mass of r-process material (>10−² M⊙) was synthesised in a single event. [2: GW170817 significance, kilonova, heavy element evidence] Both sites (supernovae and NS mergers) likely contribute to the cosmic r-process inventory. Supernovae may be more important for early r-process enrichment (they occur soon after massive stars form), while NS mergers contribute disproportionately to the heaviest elements. [1: both sites and complementary roles] The evidence is strong but not complete; a limitation is that it is difficult to decompose the observed cosmic r-process abundances into contributions from each site, and the rate and yield of each remains uncertain. [1: evaluative conclusion / limitation]

Marking criteria (8 marks). 1 = core-collapse mechanism (photodisintegration, neutron degeneracy, shock); 1 = neutrino role or r-process in SN environment; 1 = NS merger tidal disruption → r-process conditions; 1 = density calculation correct (M in kg, formula, answer ~3.5–4.0×10¹⁷ kg/m³); 1 = density linked to nuclear conditions for r-process; 1 = GW170817 observation described (kilonova, heavy element signatures); 1 = significance of GW170817 assessed (confirmation of NS mergers as r-process site); 1 = evaluative synthesis (both sites, limitation, or uncertainty acknowledged).