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Date	May 2017	Marks available	1	Reference code	17M.3.SL.TZ1.9
Level	Standard level	Paper	Paper 3	Time zone	1
Command term	Show that	Question number	9	Adapted from	N/A

Question

Theta 1 Orionis is a main sequence star. The following data for Theta 1 Orionis are available.

Luminosity	L = 4 × 10⁵ L $_ \odot$
Radius	R = 13R $_ \odot$
Apparent brightness	b = 4 × 10^–11 b $_ \odot$

where L $_ \odot$ , R $_ \odot$ and b $_ \odot$ are the luminosity, radius and apparent brightness of the Sun.

State what is meant by a main sequence star.

[1]

a.i.

Show that the mass of Theta 1 Orionis is about 40 solar masses.

[1]

a.ii.

The surface temperature of the Sun is about 6000 K. Estimate the surface temperature of Theta 1 Orionis.

[2]

a.iii.

Determine the distance of Theta 1 Orionis in AU.

[2]

a.iv.

Discuss how Theta 1 Orionis does not collapse under its own weight.

[2]

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.

[3]

Markscheme

stars fusing hydrogen «into helium»

[1 mark]

a.i.

$M = {M_ \odot }{\left( {4 \times {{10}^5}} \right)^{\frac{1}{{3.5}}}} = 39.86{M_ \odot }$

« $M \approx 40{M_ \odot }$ »

Accept reverse working.

[1 mark]

a.ii.

$4 \times {10^5} = {13^2} \times \frac{{{T^4}}}{{{{6000}^4}}}$

$T \approx 42\,000$ «K»

Accept use of substituted values into $L = \sigma$ 4 $\pi$ R²T⁴.

Award [2] for a bald correct answer.

[2 marks]

a.iii.

$4 \times {10^{ - 11}} = 4 \times {10^5} \times \frac{{1{\text{A}}{{\text{U}}^2}}}{{{d^2}}}$

$d = 1 \times {10^8}$ «AU»

Accept use of correct values into $b = \frac{L}{{4\pi {d^2}}}$ .

[2 marks]

a.iv.

the gravitation «pressure» is balanced by radiation «pressure»

that is created by the production of energy due to fusion in the core / OWTTE

Award [1 max] if pressure and force is inappropriately mixed in the answer.

Award [1 max] for unexplained "hydrostatic equilibrium is reached".

[2 marks]

the Sun will evolve to become a red giant whereas Theta 1 Orionis will become a red super giant

the Sun will explode as a planetary nebula whereas Theta 1 Orionis will explode as a supernova

the Sun will end up as a white dwarf whereas Theta 1 Orionis as a neutron star/black hole

[3 marks]

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

a.iii.

[N/A]

a.iv.

[N/A]

Syllabus sections

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

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17N.3.SL.TZ0.12e.ii: sketch the expected evolutionary path for Sirius A.
17N.3.SL.TZ0.12d.ii: Identify the star type of Sirius B.
17N.3.SL.TZ0.12e.i: draw the approximate positions of Sirius A, labelled A and Sirius B, labelled B.
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).
17N.3.SL.TZ0.12a: State what is meant by a binary star.
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.
17M.3.SL.TZ2.12c.ii:
Describe how type Ia supernovae could be used to measure the distance to this galaxy.
18N.3.SL.TZ0.12a.i:
Determine the peak wavelength of the radiation emitted by Epsilon Indi.
18N.3.SL.TZ0.12c: Describe how the chemical composition of a star may be determined.
18N.3.SL.TZ0.12a.ii: Using the axis, draw the variation with wavelength of the intensity of the radiation emitted...
18N.3.HL.TZ0.18d: Describe the stages in the evolution of Epsilon Indi from the point when it leaves the main...
18N.3.HL.TZ0.18a.ii: Using the axis, draw the variation with wavelength of the intensity of the radiation emitted...
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19M.3.SL.TZ2.15a: Identify, on the HR diagram, the position of the Sun. Label the position S.
18N.3.HL.TZ0.18a.i:
Determine the peak wavelength of the radiation emitted by Epsilon Indi.
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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.
19M.3.SL.TZ2.15b: Suggest the conditions that will cause the Sun to become a red giant.
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:
A standard Hertzsprung–Russell (HR) diagram is shown.

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(ii): State the star type of Eta Cassiopeiae A.
19N.3.SL.TZ0.10c(iv):
Deduce the final evolutionary state of Eta Cassiopeiae A.
18M.3.SL.TZ1.11b.ii:
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:
Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 ${M_ \odot }$ .
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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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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.
17M.3.SL.TZ2.11c.i:
On the HR diagram in (b), draw a line to indicate the evolutionary path of star X.
18M.3.SL.TZ2.11d.iii:
plot the position, using the letter G, of Gacrux.
17M.3.SL.TZ1.10a.ii:
The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB.
18M.3.SL.TZ1.11b.iii:
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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20N.3.HL.TZ0.22d: Eta Aquilae A is a Cepheid variable. Explain why the brightness of Eta Aquilae A varies.
17N.3.SL.TZ0.12d.i:
Determine the radius of Sirius B in terms of the radius of the Sun.
17N.3.SL.TZ0.12c:
The mass of Sirius B is about the same mass as the Sun. The luminosity of Sirius B is 2.5 % of the luminosity of the Sun. Show, with a calculation, that Sirius B is not a main sequence star.
16N.3.SL.TZ0.16a:
Determine the distance from Earth to the Cepheid star in parsecs. The luminosity of the Sun is 3.8 × 10²⁶W. The average apparent brightness of the Cepheid star is 1.1 × 10^–9W m^–2.
18N.3.HL.TZ0.18c:
The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.
20N.3.SL.TZ0.17a:
Show by calculation that Eta Aquilae A is not on the main sequence.
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17M.3.SL.TZ1.9c:
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.
18M.3.SL.TZ2.11d.i:
draw the main sequence.
17M.3.SL.TZ2.11c.iv:
Determine the region of the electromagnetic spectrum in which the neutron star in (c)(iii) emits most of its energy.
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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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