Practise › Questions › The HR diagram and stellar evolution
The HR diagram and stellar evolution questions
Plot absolute magnitude against spectral class and stars fall into the main sequence, the giants and the white dwarfs rather than spreading out at random. Following a star off the main sequence gives the rest of the topic: red giants, white dwarfs, supernovae, neutron stars and black holes.
19 original questions · 60 marks · the hr diagram and stellar evolution notes · Astrophysics
On this topic the library is tagged for AQA, Edexcel, OCR A.
Every question here is written for this library rather than taken from a past paper. Write your answer out before opening a mark scheme: the schemes award marks point by point, and the marks are easier to see when you have something of your own to compare against.
State the quantities plotted on the two axes of a Hertzsprung-Russell diagram, including the direction each axis runs and its typical range.
Mark scheme
Absolute magnitude on the vertical axis, from about +15 at the bottom to −10 at the top, brighter upward on a reversed scale (1); temperature on the horizontal axis from about 50 000 K down to 2500 K left to right (1), often labelled instead by spectral class O B A F G K M. (If luminosity is plotted instead of magnitude, it increases upward normally on a log scale; only the temperature and magnitude scales run backwards.) (1)Name the three populated regions of the HR diagram and state where each sits.
Mark scheme
The main sequence, a diagonal band from hot-bright (top left) to cool-dim (bottom right) (1); the red giants, above it on the cool side (1); and the white dwarfs, below it on the hot side (1).State what a star on the main sequence is doing, and where the Sun sits on the diagram.
Mark scheme
It is fusing hydrogen in its core, the long stable phase of a star's life (1). The Sun sits partway down the main sequence, class G, absolute magnitude about +4.8 (1).State the Chandrasekhar limit, and what happens to a stellar core more massive than it.
Mark scheme
About 1.4 solar masses, the greatest mass electron degeneracy pressure can support as a white dwarf (1). A heavier core collapses further, to a neutron star or a black hole (1).State two properties of a neutron star.
Mark scheme
Any two of the following, one mark each (2): composed almost entirely of neutrons; massof order one to two solar masses; radius of order 10 km; density comparable with that of an atomic nucleus.State what supports a white dwarf against gravitational collapse, and what energy source it has left.
Mark scheme
Electron degeneracy pressure, the quantum refusal of electrons to be squeezed into the same state (1). None: fusion has ended, so it only radiates its stored thermal energy, cooling and fading (1).Describe the future evolution of the Sun as a path on the HR diagram, naming each stage and the physical change that drives it.
Mark scheme
When core hydrogen runs low, fusion moves to a shell (1), the outer layers swell and the surface cools: the Sun leaves the main sequence and moves up and to the right, becoming a red giant (1). It then sheds its outer layers; the exposed core drops down and to the left as a white dwarf, no longer fusing (1), and slowly cools and fades (1).A red giant is cooler than the Sun yet far more luminous. Explain, using Stefan's law, how both can be true.
Mark scheme
P = σAT4: its lower temperature cuts the power per unit area (1), but its enormously larger surface area more than compensates (1). High luminosity at low temperature forces a huge radius, which is exactly what the giant region of the diagram encodes (1).A type Ia supernova peaks at apparent magnitude 18.2. Taking the peak absolute magnitude of a type Ia to be −19.3, calculate the distance to its host galaxy.
A neutron star has mass 3.0 × 1030 kg and radius 12 km. Calculate its density.
Describe the formation of a star, from a cloud of gas and dust to its arrival on the main sequence.
An X-ray source is identified as a black hole with a Schwarzschild radius of 30 km. Determine its mass in solar masses. G = 6.67 × 10−11 N m2 kg−2, c = 3.0 × 108 m s−1, solar mass = 1.99 × 1030 kg.
The escape velocity from a spherical mass M of radius r is √(2GM/r). Show that setting the escape velocity equal to the speed of light leads to the expression Rs ≈ 2GM/c2 for the Schwarzschild radius.
Calculate the Schwarzschild radius of a black hole of six solar masses (solar mass 1.99 × 1030 kg), and state what the radius represents.
Explain why type Ia supernovae can be used as standard candles, and what surprising conclusion their use led to in the late 1990s.
Describe the shape of the light curve of a type Ia supernova, and name a transient event that instead accompanies the death of a massive star.
A type Ia supernova detonates in a galaxy 40 Mpc away. An astronomy society's telescope can record objects brighter than apparent magnitude +15. Taking the peak absolute magnitude of a type Ia to be −19.3, deduce whether the society could record the supernova at its peak.
A star of twenty solar masses leaves the main sequence. Describe fully its subsequent evolution and its possible final states, explaining why its fate differs from the Sun's.
The Schwarzschild radius of one solar mass is about 3.0 km. A supermassive black hole at the centre of a galaxy has a mass of 2 × 109 solar masses. Calculate its Schwarzschild radius and compare it with the Earth-Sun distance, 1.5 × 1011 m.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
Practise the hr diagram and stellar evolution one question at a time
The player marks nothing for you. It shows one question, waits, then shows the scheme so you can mark yourself, and brings a question back sooner when it went badly.