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Date November 2016 Marks available 3 Reference code 16N.3.SL.TZ0.15
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Explain Question number 15 Adapted from N/A

Question

Alpha Centauri A and B is a binary star system in the main sequence.

State what is meant by a binary star system.

[1]
a.

(i) Calculate \(\frac{{{b_{\text{A}}}}}{{{b_{\text{B}}}}} = \frac{{{\text{apparent brightness of Alpha Centauri A}}}}{{{\text{apparent brightness of Alpha Centauri B}}}}\).

(ii) The luminosity of the Sun is 3.8 × 1026 W. Calculate the radius of Alpha Centauri A.

[4]
b.

Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.

[2]
c.

Alpha Centauri A is in equilibrium at constant radius. Explain how this equilibrium is maintained.

[3]
d.

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.

[2]
e.

Markscheme

two stars orbiting about a common centre «of mass/gravity»
Do not accept two stars orbiting each other.

a.

i
stars are roughly at the same distance from Earth
OR
d is constant for binaries

\(\frac{{{L_{\rm{A}}}}}{{{L_{\rm{B}}}}} = \frac{{1.5}}{{0.5}} = 3.0\)

Award [2] for a bald correct answer.

 

ii
\(r = \sqrt {\frac{{1.5 \times 3.8 \times {{10}^{26}}}}{{5.67 \times {{10}^{ - 8}} \times 4\pi  \times {{5800}^4}}}} \)

= 8.4 × 10«m»

Award [2] for a bald correct answer.

b.

«A=\(\frac{L}{{\sigma {T^4}}}\)» B and A have similar temperatures

so areas are in ratio of luminosities

«so B radius is less than A»

c.

radiation pressure/force outwards

gravitational pressure/force inwards

forces/pressures balance

d.

Alpha Centauri A within allowable region

some indication of star moving right and up then left and down ending in white dwarf region as indicated

e.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
[N/A]
e.

Syllabus sections

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