Solved: Sirius is a binary star. It is composed of two stars, Sirius A and Sirius Sirius... [IB Physics]

Question

SLPaper 3

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

State what is meant by a binary star.

[1]

Verified

Solution

two stars orbiting a common centre «of mass» ✔

Do not accept "stars which orbit each other"

The peak spectral line of Sirius B has a measured wavelength of 115 nm. Show that the surface temperature of Sirius B is about 25000 K.

[1]

Verified

Solution

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

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]

Verified

Solution

use of the mass-luminosity relationship or $(\frac{M_{sirius}}{M_{Sun}})^{3.5}=1$ ✔ if Sirius B is on the main sequence then $(\frac{L_{sirius}}{L_{sun}})=1$ «which it is not» ✔

Conclusion is given, justification must be stated Allow reverse argument beginning with luminosity

The Sun's surface temperature is about 5800 K. Determine the radius of Sirius B.

[2]

Verified

Solution

i. $\frac{M_{sirius}}{M_{sun}}=2.02$ ✔ $M_{sirius}=2.02 \times 2 \times 10^{30}=4.04 \times 10^{30}$ «kg» ✔

Identify the star type of Sirius B.

[1]

Verified

Solution

i. $\frac{M_{sirius}}{M_{sun}}=2.02$ ✔ $M_{sirius}=2.02 \times 2 \times 10^{30}=4.04 \times 10^{30}$ «kg» ✔

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,

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

(ii) sketch the expected evolutionary path for Sirius A.

[2]

Verified

Solution

ii. white dwarf ✔

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

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