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Date May 2018 Marks available 2 Reference code 18M.3.SL.TZ2.11
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term Outline 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.

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

[1]
b.

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]
e.

Markscheme

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

gives both directions correctly (outwards radiation, inwards gravity)

 

OWTTE

[2 marks]

a.

«L \( \propto \) M35 for main sequence»

luminosity of P = 2.5 «luminosity of the Sun»

[1 mark]

b.

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

LGacrux = 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

OR

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°

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

[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

OR

planetary nebula with mention of remnant mass

 

white dwarf

 

ALTERNATIVE 2

Main sequence to red supergiant region

 

Supernova with mass reduction/loss

OR

Supernova with mention of remnant mass

 

neutron star

OR

Black hole

 

OWTTE for both alternatives

[3 marks]

e.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
d.i.
[N/A]
d.ii.
[N/A]
d.iii.
[N/A]
e.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.1 – Stellar quantities
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