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Date	May 2019	Marks available	1	Reference code	19M.3.SL.TZ2.15
Level	Standard level	Paper	Paper 3	Time zone	2
Command term	Outline	Question number	15	Adapted from	N/A

Question

The Hertzsprung-Russell (HR) diagram shows several star types. The luminosity of the Sun is L_☉.

Identify, on the HR diagram, the position of the Sun. Label the position S.

[1]

Suggest the conditions that will cause the Sun to become a red giant.

[3]

Outline why the Sun will maintain a constant radius after it becomes a white dwarf.

[1]

During its evolution, the Sun is likely to be a red giant of surface temperature 3000 K and luminosity 10⁴ L_☉. Later it is likely to be a white dwarf of surface temperature 10 000 K and luminosity 10-4 L_☉. Calculate the $\frac{{{\text{radius of the Sun as a white dwarf}}}}{{{\text{radius of the Sun as a red giant}}}}$ .

[2]

Markscheme

the letter S should be in the region of the shaded area ✔

the fusion of hydrogen in the core eventually stops

core contracts ✔

the hydrogen in a layer around the core will begin to fuse ✔

Sun expands AND the surface cools ✔

helium fusion begins in the core ✔

Sun becomes more luminous/brighter✔

Ignore any mention of the evolution past the red giant stage

electron degeneracy <<prevents further compression>> ✔

Ignore mention of the Chandrasekhar limit.

Award [0] for answer mentioning radiation pressure or fusion reactions.

Examiners report

Locating the Sun’s position on the HR diagram was correctly done by most candidates, although a few were unsure of the surface temperature of the Sun.

The evolution of a main sequence star to the red giant region is reasonably well understood. However many struggled to find three different facts to describe the changes. Answers were often too vague, when writing about a change in temperature or size of a star, the candidates are expected to mention whether they are referring to the core or the surface/outer layer. A surprising number of candidates wrote that the Sun must be less than eight solar masses.

The mention of electron degeneracy pressure was fairly common, but incorrect answers were even more common at SL.

Calculating the ratio of the radius of a white dwarf to a red giant star was done quite well by most candidates. However quite a few candidates made POT errors or forgot to take the final square root.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.2 – Stellar characteristics and stellar evolution

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Show that the mass of Theta 1 Orionis is about 40 solar masses.
18N.3.HL.TZ0.18a.i:
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17N.3.SL.TZ0.12b:
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18N.3.HL.TZ0.18b:
Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 ${M_ \odot }$ .
16N.3.SL.TZ0.15e:
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Using the HR diagram, draw the present position of Alpha Centauri A and its expected evolutionary path.
18M.3.SL.TZ1.11c:
Star X is likely to evolve into a stable white dwarf star.

Outline why the radius of a white dwarf star reaches a stable value.
19N.3.SL.TZ0.10c(iii):
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Show by calculation that Eta Aquilae A is not on the main sequence.
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Suggest, using the graphs, why star X is most likely to be a main sequence star.
17M.3.SL.TZ2.11b:
The Hertzsprung–Russell (HR) diagram shows two main sequence stars X and Y and includes lines of constant radius. R is the radius of the Sun.

Using the mass–luminosity relation and information from the graph, determine the ratio $\frac{{{\text{density of star X}}}}{{{\text{density of star Y}}}}$ .
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19N.3.SL.TZ0.10c(iv):
Deduce the final evolutionary state of Eta Cassiopeiae A.
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Determine the radius of star X (R_X) in terms of the radius of the Sun (R_s).
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plot the position, using the letter P, of the main sequence star P you calculated in (b).
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17M.3.SL.TZ2.11c.i:
On the HR diagram in (b), draw a line to indicate the evolutionary path of star X.
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plot the position, using the letter G, of Gacrux.
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The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB.
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draw the main sequence.
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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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