Main sequence stars are in equilibrium under the action of forces. Outline how this equilibrium is achieved.

A main sequence star P, is 1.3 times the mass of the Sun. Calculate the luminosity of P relative to the Sun.

The luminosity of the Sun L\(_ \odot \) is 3.85 × 10²⁶ W. Determine the luminosity of Gacrux relative to the Sun.

The distance to Gacrux can be determined using stellar parallax. Outline why this method is not suitable for all stars.

draw the main sequence.

plot the position, using the letter P, of the main sequence star P you calculated in (b).

plot the position, using the letter G, of Gacrux.

Discuss, with reference to its change in mass, the evolution of star P from the main sequence until its final stable phase.

photon/fusion/radiation force/pressure balances gravitational force/pressure

gives both directions correctly (outwards radiation, inwards gravity)

OWTTE

[2 marks]

«L \( \propto \) M³⁵ for main sequence»

luminosity of P = 2.5 «luminosity of the Sun»

[1 mark]

L_Gacrux = 5.67 × 10^–8 × 4π × (58.5 × 10⁹)² × 3600⁴

L_Gacrux = 4.1 × 10^–29 «W»

\(\frac{{{L_{Gacrux}}}}{{{L_ \odot }}}\) «= \(\frac{{4.1 \times {{10}^{29}}}}{{3.85 \times {{10}^{26}}}}\)» = 1.1 × 10³

[3 marks]

if the star is too far then the parallax angle is too small to be measured

OR

stellar parallax is limited to closer stars

OWTTE

[1 mark]

line or area roughly inside shape shown – judge by eye

Accept straight line or straight area at roughly 45°

[1 mark]

P between \(1{L_ \odot }\) and \({10^1}{L_ \odot }\) on main sequence drawn

[1 mark]

at \({10^3}{L_ \odot }\), further to right than 5000 K and to the left of 2500 K (see shaded region)

[1 mark]

ALTERNATIVE 1

Main sequence to red giant

planetary nebula with mass reduction/loss

OR

planetary nebula with mention of remnant mass

white dwarf

ALTERNATIVE 2

Main sequence to red supergiant region

Supernova with mass reduction/loss

OR

Supernova with mention of remnant mass

neutron star

OR

Black hole

OWTTE for both alternatives

[3 marks]