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Date	May 2018	Marks available	1	Reference code	18M.3.SL.TZ2.11
Level	Standard level	Paper	Paper 3	Time zone	2
Command term	Plot	Question number	11	Adapted from	N/A

Question

The following data apply to the star Gacrux.

$\begin{array}{*{20}{l}} {{\text{Radius}}}&{ = 58.5 \times {{10}^9}{\text{ m}}} \\ {{\text{Temperature}}}&{ = 3600{\text{ K}}} \\ {{\text{Distance}}}&{ = 88{\text{ ly}}} \end{array}$

A Hertzsprung–Russell (HR) diagram is shown.

On the HR diagram,

Main sequence stars are in equilibrium under the action of forces. Outline how this equilibrium is achieved.

[2]

A main sequence star P, is 1.3 times the mass of the Sun. Calculate the luminosity of P relative to the Sun.

[1]

The luminosity of the Sun L $_ \odot$ is 3.85 × 10²⁶ W. Determine the luminosity of Gacrux relative to the Sun.

[3]

c.i.

The distance to Gacrux can be determined using stellar parallax. Outline why this method is not suitable for all stars.

[1]

c.ii.

draw the main sequence.

[1]

d.i.

plot the position, using the letter P, of the main sequence star P you calculated in (b).

[1]

d.ii.

plot the position, using the letter G, of Gacrux.

[1]

d.iii.

Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.

[3]

Markscheme

photon/fusion/radiation force/pressure balances gravitational force/pressure

gives both directions correctly (outwards radiation, inwards gravity)

OWTTE

[2 marks]

«L $\propto$ M³⁵ for main sequence»

luminosity of P = 2.5 «luminosity of the Sun»

[1 mark]

L_Gacrux = 5.67 × 10^–8 × 4π × (58.5 × 10⁹)² × 3600⁴

L_Gacrux = 4.1 × 10^–29«W»

$\frac{{{L_{Gacrux}}}}{{{L_ \odot }}}$ «= $\frac{{4.1 \times {{10}^{29}}}}{{3.85 \times {{10}^{26}}}}$ » = 1.1 × 10³

[3 marks]

c.i.

if the star is too far then the parallax angle is too small to be measured

stellar parallax is limited to closer stars

OWTTE

[1 mark]

c.ii.

line or area roughly inside shape shown – judge by eye

Accept straight line or straight area at roughly 45°

[1 mark]

d.i.

P between $1{L_ \odot }$ and ${10^1}{L_ \odot }$ on main sequence drawn

[1 mark]

d.ii.

at ${10^3}{L_ \odot }$ , further to right than 5000 K and to the left of 2500 K (see shaded region)

M18/4/PHYSI/SP3/ENG/TZ2/11.d.iii/M

[1 mark]

d.iii.

ALTERNATIVE 1

Main sequence to red giant

planetary nebula with mass reduction/loss

planetary nebula with mention of remnant mass

white dwarf

ALTERNATIVE 2

Main sequence to red supergiant region

Supernova with mass reduction/loss

Supernova with mention of remnant mass

neutron star

Black hole

OWTTE for both alternatives

[3 marks]

Examiners report

[N/A]

c.i.

[N/A]

c.ii.

[N/A]

d.i.

[N/A]

d.ii.

[N/A]

d.iii.

[N/A]

Syllabus sections

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

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16N.3.SL.TZ0.15e:
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18M.3.SL.TZ1.11c:
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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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plot the position, using the letter G, of Gacrux.
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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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