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Date	November 2017	Marks available	2	Reference code	17N.3.SL.TZ0.12
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show	Question number	12	Adapted from	N/A

Question

Sirius is a binary star. It is composed of two stars, Sirius A and Sirius B. Sirius A is a main sequence star.

The Sun’s surface temperature is about 5800 K.

The image shows a Hertzsprung–Russell (HR) diagram.

The mass of Sirius A is twice the mass of the Sun. Using the Hertzsprung–Russell (HR) diagram,

State what is meant by a binary star.

[1]

a.

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.

[1]

b.

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.

[2]

c.

Determine the radius of Sirius B in terms of the radius of the Sun.

[2]

d.i.

Identify the star type of Sirius B.

[1]

d.ii.

draw the approximate positions of Sirius A, labelled A and Sirius B, labelled B.

[1]

e.i.

sketch the expected evolutionary path for Sirius A.

[1]

e.ii.

Markscheme

two stars orbiting a common centre «of mass»

Do not accept “stars which orbit each other”

a.

« $\lambda$ x T = 2.9 x 10^–3»

T = $\frac{{2.9 \times {{10}^{ - 3}}}}{{115 \times {{10}^{ - 9}}}}$ = 25217 «K»

b.

use of the mass-luminosity relationship or ${\left( {\frac{{{M_{{\text{Sirius}}}}}}{{{M_{{\text{Sun}}}}}}} \right)^{3.5}}$ = 1

if Sirius B is on the main sequence then $\left( {\frac{{{L_{\,{\text{Sirius}}\,{\text{B}}}}}}{{L{\,_{{\text{Sun}}}}}}} \right)$ = 1 «which it is not»

Conclusion is given, justification must be stated

Allow reverse argument beginning with luminosity

c.

$\left( {\frac{{{L_{\,{\text{Sirius}}\,{\text{B}}}}}}{{L{\,_{{\text{Sun}}}}}}} \right)$ = 0.025

r _Sirius = « $\sqrt {0.025 \times {{\left( {\frac{{5800}}{{25000}}} \right)}^4}}$ =» 0.0085 r _Sun

d.i.

white dwarf

d.ii.

Sirius A on the main sequence above and to the left of the Sun AND Sirius B on white dwarf area as shown

Both positions must be labelled

Allow the position anywhere within the limits shown.

e.i.

arrow goes up and right and then loops to white dwarf area

e.ii.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.i.

[N/A]

d.ii.

[N/A]

e.i.

[N/A]

e.ii.

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.SL.TZ0.17d: Eta Aquilae A is a Cepheid variable. Explain why the brightness of Eta Aquilae A varies.
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.
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