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Date	November 2020	Marks available	3	Reference code	20N.3.SL.TZ0.17
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Explain	Question number	17	Adapted from	N/A

Question

The data for the star Eta Aquilae A are given in the table.

$L_{⊙}$ is the luminosity of the Sun and $M_{⊙}$ is the mass of the Sun.

Show by calculation that Eta Aquilae A is not on the main sequence.

[2]

Estimate, in $pc$ , the distance to Eta Aquilae A using the parallax angle in the table.

[1]

b(i).

Estimate, in $pc$ , the distance to Eta Aquilae A using the luminosity in the table, given that $L_{⊙} = 3.83 \times 10^{26} W$ .

[3]

b(ii).

Suggest why your answers to (b)(i) and (b)(ii) are different.

[2]

Eta Aquilae A is a Cepheid variable. Explain why the brightness of Eta Aquilae A varies.

[3]

Markscheme

$« \frac{L}{L_{⊙}} = \frac{M^{3.5}}{{M_{⊙}}^{3.5}} = 5 . 70^{3.5} = » 442$ ✓

the luminosity of Eta (2630 $L_{⊙}$ ) is very different «so it is not main sequence» ✓

Allow calculation of $L^{\frac{1}{3.5}}$ to give $M = 9.5 M_{⊙}$ so not main sequence

OWTTE

$d « = \frac{1}{2.36 \times 10^{- 3}} » = 424 « pc »$ ✓

b(i).

Use of $d = \sqrt{\frac{L}{4 πb}}$ ✓

$= \sqrt{\frac{2630 \times 3.83 \times 10^{26}}{4 π \times 7.20 \times 10^{- 10}}}$ ✓

$« = \frac{1.055 \times 10^{19}}{3.26 \times 9.46 \times 10^{15}} » = 342 « pc »$ ✓

Award [3] marks for a bald correct answer between $340$ and $344 « pc »$

b(ii).

parallax angle in milliarc seconds/very small/at the limits of measurement ✓

uncertainties/error in measuring $L$ οr $b$ or $θ$ ✓

values same order of magnitude, so not significantly different ✓

Accept answers where MP1 and MP2 both refer to parallax angle

OWTTE

reference to change in size ✓
reference to change in temperature ✓
reference to periodicity of the process ✓
reference to transparency / opaqueness ✓

Examiners report

[N/A]

b(i).

[N/A]

b(ii).

[N/A]

Syllabus sections

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

Show 55 related questions

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...
18N.3.SL.TZ0.12d: Describe the stages in the evolution of Epsilon Indi from the point when it leaves the main...
19M.3.SL.TZ2.15a: Identify, on the HR diagram, the position of the Sun. Label the position S.
17M.3.SL.TZ1.9a.ii:
Show that the mass of Theta 1 Orionis is about 40 solar masses.
18N.3.HL.TZ0.18a.i:
Determine the peak wavelength of the radiation emitted by Epsilon Indi.
19M.3.SL.TZ2.13aii: Explain how Cepheid variables are used to determine distances.
16N.3.SL.TZ0.15d: Alpha Centauri A is in equilibrium at constant radius. Explain how this equilibrium is...
17M.3.SL.TZ2.11c.ii:
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):
Calculate the ratio $\frac{mass of Eta Cassiopeiae A}{mass of the Sun}$ .
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 $\frac{{{\text{density of star X}}}}{{{\text{density of star Y}}}}$ .
19N.3.SL.TZ0.10c(i): On the HR diagram, draw the present position of Eta Cassiopeiae A.
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 ${M_ \odot }$ .
18M.3.SL.TZ2.11d.ii:
plot the position, using the letter P, of the main sequence star P you calculated in (b).
19N.3.SL.TZ0.10b(i):
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.
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.
19M.3.SL.TZ2.13ai: Outline the processes that produce the change of luminosity with time of Cepheid variables.
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.
18M.3.SL.TZ1.11a.ii:
Show that the temperature of star X is approximately 10 000 K.
21N.1.SL.TZ0.30: Which is correct for a black-body radiator? A. The power it emits from a unit surface area...

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Option D: Astrophysics » Option D: Astrophysics (Core topics)

Option D: Astrophysics

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