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Date	May 2019	Marks available	2	Reference code	19M.3.SL.TZ2.13
Level	Standard level	Paper	Paper 3	Time zone	2
Command term	Outline	Question number	13	Adapted from	N/A

Question

The following data are available for the Cepheid variable δ-Cephei.

Peak luminosity = 7.70 × 10²⁹ W

Distance from Earth = 273 pc

Peak wavelength of light = 4.29 × 10^–7 m

Outline the processes that produce the change of luminosity with time of Cepheid variables.

[2]

ai.

Explain how Cepheid variables are used to determine distances.

[2]

aii.

Determine the peak apparent brightness of δ-Cephei as observed from Earth.

[2]

bi.

Calculate the peak surface temperature of δ-Cephei.

[1]

bii.

Astronomers claim to know the properties of distant stars. Outline how astronomers can be certain that their measurement methods yield correct information.

[1]

Markscheme

Cepheid variables expand and contract

Radius increases and decreases

Surface area increases and decreases ✔

Surface temperature decreases then increases✔

Surface becomes transparent then opaque ✔

OWTTE

Do not reward ‘change in luminosity/brightness’ as this is given in the question.

Accept changes in reverse order

ai.

the «peak» luminosity/actual brightness depends on the period

More luminous Cepheid variables have greater period✔

measurements of apparent brightness allow distance determination

Mention of ✔

OWTTE

aii.

$d = « 273 \times 3.26 \times 9.46 \times {10^{15}} =» 8.42 \times {10^{18}}$ «m» ✔

$b = « \frac{L}{{4\pi {d^2}}} = \frac{{7.70 \times {{10}^{29}}}}{{4\pi {{(8.42 \times {{10}^{18}})}^2}}} =» 8.6 \times {10^{ - 10}}$ «Wm^–2» ✔

bi.

« $T = \frac{{2.9 \times {{10}^{ - 3}}}}{{4.29 \times {{10}^{ - 7}}}}$ »

=6800«K» ✔

bii.

Data subject to peer review/checks by others ✔

Compare light from stars with Earth based light sources ✔

measurements are corroborated by different instruments/methods from different teams ✔

OWTTE

Examiners report

The expansion and contraction of Cepheid stars was commonly mentioned. Changes in surface temperature and opacity were less commonly mentioned. A common misconception seems to be that the variation of luminosity is due to a change of the rate of fusion. A few candidates left this question unanswered.

ai.

Many candidates knew that if the luminosity of the Cepheid is known then the absolute brightness can be used to determine distance. But far fewer candidates could link luminosity with the period of the Cepheid star. Many seemed to think that the luminosity of all Cepheids is the same.

aii.

Calculating the brightness of a star from its luminosity was an easy question for most candidates. But quite a few did not convert parsecs into metres especially at SL.

bi.

This simple calculation using Wien’s law was very well answered.

bii.

Many candidates correctly stated that astronomers can use peer review or different methods in checking that the information obtained from stars is correct.

Syllabus sections

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

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18M.3.SL.TZ1.11b.i:
Write down the luminosity of star X (L_X) in terms of the luminosity of the Sun (L_s).
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16N.3.SL.TZ0.16b: Explain why Cephids are used as standard candles.
16N.3.SL.TZ0.15c:
Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.
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18N.3.SL.TZ0.12a.i:
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Outline why the neutron star that is left after the supernova stage does not collapse under the action of gravitation.
19M.3.SL.TZ2.15c:
Outline why the Sun will maintain a constant radius after it becomes a white dwarf.
17N.3.SL.TZ0.12b:
The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25 000 K.
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18N.3.HL.TZ0.18b:
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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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20N.3.HL.TZ0.22a:
Show by calculation that Eta Aquilae A is not on the main sequence.
18M.3.SL.TZ1.11a.i:
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).
19M.3.SL.TZ2.13bii:
Calculate the peak surface temperature of δ-Cephei.
18N.3.SL.TZ0.12b:
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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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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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Estimate the mass of star X (M_X) in terms of the mass of the Sun (M_s).
18M.3.SL.TZ2.11e:
Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.
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Determine the radius of Sirius B in terms of the radius of the Sun.
17N.3.SL.TZ0.12c:
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Show by calculation that Eta Aquilae A is not on the main sequence.
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The Sun and Theta 1 Orionis will eventually leave the main sequence. Compare and contrast the different stages in the evolution of the two stars.
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draw the main sequence.
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Show that the temperature of star X is approximately 10 000 K.
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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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