Show that the luminosity of star X is about 280 times greater than the luminosity of the Sun L.

Determine the ratio $\frac{\text{surface temperature of star X}}{\text{surface temperature of the Sun}}$.

Outline how the parallax angle of a star can be measured.

Show that the distance to star X is 1.6 × 10⁶ AU.

The apparent brightness of the Sun is 1400 Wm^–2. Calculate, in Wm^–2, the apparent brightness of star X.

Label, on the HR diagram, the region of white dwarf stars.

Outline the condition that prevents star D from collapsing further.

Star D emits energy into space in the form of electromagnetic radiation. State the origin of this energy.

Predict the change in luminosity of star D as time increases.

$L_x={5.0}^{3.5}{L}_{\odot }=279.5L_{\odot }$ ✔

Correct working or answer to 4 sig figs required.

$\frac{L_x}{L_{\odot }}=280=\frac{R_x^2}{R_{\odot }^2}\frac{T_x^4}{T_{\odot }^4}$  ✔

$\frac{T_x}{T_{\odot }}«=\sqrt[4]{\frac{280}{{3.2}^2}}»=2.3$  ✔

Award [2] for bald correct answer.

the position of the star is recorded 6 months apart
OR
the radius/diameter of the Earth orbit clearly labelled on a diagram ✔

the parallax is measured from the shift of the star relative to the background of the distant stars ✔

For MP2 accept a correctly labelled parallax angle on a diagram.

Award MP2 only if background distance stars are mentioned.

d = $\frac{1}{0.125}$ = 8.0 «pc» ✔

d = 8.0 × 3.26 × $\frac{9.46\times {10}^{15}}{1.5\times {10}^{11}}$«AU» ✔

«= 1.64 × 10⁶ AU»

ALTERNATIVE 1

$\frac{b_x}{1400}=\frac{\frac{280}{4\pi {\left(1.6\times {10}^6\right)}^2}}{\frac{1}{4\pi {\left(1\right)}^2}}$

OR

$b_x=\frac{279.5}{4\pi \times {\left(1.6\times {10}^6\times 1.5\times {10}^{11}\right)}^2}\text{ and }\frac{L_{\odot }}{4\pi \times {\left(1.5\times {10}^{11}\right)}^2}$   ✔

$b_x=1.5\times {10}^{-7}$«W m^–2»   ✔

ALTERNATIVE 2

$\frac{b_x}{b_{\odot }}=\frac{L_x}{L_{\odot }}\times \left(\frac{d_{\odot }^2}{d_x^2}\right)$ OR $\frac{b_x}{b_{\odot }}=\frac{280}{{\left(1.6\times {10}^6\right)}^2}$ OR $\frac{b_x}{b_{\odot }}=1.094\times {10}^{-10}W{m}^{-2}$  ✔

$b_x=1.09375\times {10}^{-10}\times 1400$  $b_x=1.5\times {10}^{-7}W{m}^{-2}$  ✔

Award [2] for bald correct answer.

Allow ECF from MP1 to MP2

 ✔

Allow any region with L below Sun and left to the main sequence.

an electron degeneracy «pressure develops that opposes gravitation»/reference to Pauli principle ✔

thermal energy/internal energy ✔

«temperature decreases so» luminosity decreases ✔

Star evolution. This question is well designed, with varying degrees of difficulty and a sound capacity to discriminate levels.
(a) The luminosity of the star X was well compared to the luminosity of the Sun by almost all candidates, but the presentation of the work was often poor. The development of direct proportional ratios and the manipulation of equations were often misused.

Star evolution. This question is well designed, with varying degrees of difficulty and a sound capacity to discriminate levels.
In (ii), when conducting the ratio calculations, many omitted the powers in the formulas such as 3.22 and T4.

Measurement of parallax angle was well mastered by most of the candidates, however, some of them omitted to mention the importance of the background stars as a reference. Unit conversion in ii) was also well mastered by most of the candidates.

Unit conversion in ii) was also well mastered by most of the candidates.

Part iii) proved to be very difficult for most of the average candidates with many experiencing difficulties working through the algebraic manipulations required. Many students mixed units or forgot to square the distances.

The region of white dwarfs stars was well labelled on the HR diagram.

Electron degeneracy pressure was well identified by most of the candidates.

The origin of the energy emitted to space from white dwarfs was only well stated by better candidates. Many mentioned different fusion reactions and thus did not recognize that the star had ceased this type of energy production.

The decrease in the luminosity of the dwarf star was well predicted by most of the candidates.