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Date	November 2019	Marks available	1	Reference code	19N.3.SL.TZ0.10
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Calculate	Question number	10	Adapted from	N/A

Question

Eta Cassiopeiae A and B is a binary star system located in the constellation Cassiopeia.

The following data are available.

Apparent brightness of Eta Cassiopeiae A = 1.1 × 10^–9 Wm^–2
Apparent brightness of Eta Cassiopeiae B = 5.4 × 10^–11 Wm^–2
Luminosity of the Sun, $L_{⊙}$ = 3.8 × 10²⁶ W

A Hertzsprung–Russell (HR) diagram is shown.

Distinguish between a constellation and a stellar cluster.

[2]

The peak wavelength of radiation from Eta Cassiopeiae A is 490 nm. Show that the surface temperature of Eta Cassiopeiae A is about 6000 K.

[2]

b(i).

The surface temperature of Eta Cassiopeiae B is 4100 K. Determine the ratio $\frac{radius of the Eta Cassiopeiae A}{radius of the Eta Cassiopeiae B}$ .

[3]

b(ii).

The distance of the Eta Cassiopeiae system from the Earth is 1.8 × 10¹⁷m. Calculate, in terms of $L_{⊙}$ , the luminosity of Eta Cassiopeiae A.

[2]

b(iii).

On the HR diagram, draw the present position of Eta Cassiopeiae A.

[1]

c(i).

State the star type of Eta Cassiopeiae A.

[1]

c(ii).

Calculate the ratio $\frac{mass of Eta Cassiopeiae A}{mass of the Sun}$ .

[1]

c(iii).

Deduce the final evolutionary state of Eta Cassiopeiae A.

[2]

c(iv).

Markscheme

stars in a cluster are gravitationally bound OR in constellation are not ✔

stars in a cluster are the same/similar age OR in constellation are not ✔

stars in a cluster are close in space/the same distance away OR in constellation are not ✔

stars in a cluster originate from same gas cloud OR in constellation do not ✔

stars in a cluster appear much closer in night sky than in a constellation ✔

Notes: Take care to reward only 1 comment from a given marking point for MP1 to MP5.

« $T = \frac{2.9 \times 10^{- 3}}{490 \times 10^{- 9}}$ »

5900 K ✔

NOTE: Answer 6000 K is given in the question.
Answer must be to at least 2 s.f. OR correct working.

b(i).

«from b∝ L∝ R² T⁴»

realization that $R^{2} \propto \frac{b}{T^{4}}$ «for binary stars which are same distance away» ✔

$\frac{R_{A}}{R_{B}} = \sqrt{\frac{(\frac{1.1 \times 10^{- 9}}{5.4 \times 10^{- 11}})}{{(\frac{5900}{4100})}^{4}}}$ ✔

$\frac{R_{A}}{R_{B}} = 2.2$ ✔

NOTE: Award [2] for answer 0.46 from inverted ratio.

b(ii).

«use of $L = 4 π d^{2} b$ »

$L = 4 π \times {(1.8 \times 10^{17})}^{2} \times 1.1 \times 10^{- 9} « = 4.48 \times 10^{26} W »$ ✔

$L = 1.2 L_{⊙}$ ✔

b(iii).

approximately correct position on the main sequence as shown, within highlighted region ✔

c(i).

main sequence star
OR
type F or G star ✔

c(ii).

$\frac{M}{M_{⊙}} = 1 . 2^{\frac{1}{3.5}} = 1.05$ ✔

c(iii).

mass of the «remnant» star $< 1.4 M_{⊙}$ OR Chandrasekhar limit
OR
mass OR luminosity similar to the Sun ✔

the final stage is white dwarf ✔

c(iv).

Examiners report

[N/A]

b(i).

[N/A]

b(ii).

[N/A]

b(iii).

[N/A]

c(i).

[N/A]

c(ii).

[N/A]

c(iii).

[N/A]

c(iv).

Syllabus sections

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

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17N.3.SL.TZ0.12b:
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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.
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Outline why the radius of a white dwarf star reaches a stable value.
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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:
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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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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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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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