(ii) Gomeisa has a radius four times that of the Sun. Use the data in (c) to show that the ratio

\[\frac{{{\rm{luminosity of Gomeisa}}}}{{{\rm{luminosity of Sun}}}}\]

is about 200.

(iii) Assuming the value of n in the mass–luminosity equation to be 3.5, calculate

\[\frac{{{\rm{mass of Gomeisa}}}}{{{\rm{mass of Sun}}}}\]

(iv) Outline, with reference to the Chandrasekhar limit, the likely eventual fate of Gomeisa.

On the HR diagram above, sketch the likely evolutionary path of Luyten’s star.

(i) \(2.9 =  - 0.7 + 51{\rm{g}}\left( {\frac{d}{{10}}} \right)\);
\(\frac{d}{{10}} = {10^{\frac{{3.6}}{5}}}\);
52(pc);
Award [2 max] ECF if magnitudes are reversed giving 1.9 (pc).
Award [2 max] if data for Lutyen’s star is used and no credit for the distance of 4 (pc) has already been given in (c)(i).
Award [3] for a bald correct answer.

(ii) \(\frac{{{L_{\rm{G}}}}}{{{L_{\rm{S}}}}} = {\left[ {\frac{{{R_{\rm{G}}}}}{{{R_{\rm{S}}}}}} \right]^2}{\left[ {\frac{{{T_{\rm{G}}}}}{{{T_{\rm{S}}}}}} \right]^4}\);
\( = {4^2} \times {\left[ {\frac{{11000}}{{5800}}} \right]^4}\);
=210; (must see this answer to better than 1 significant figure)
Approximate answer of 200 is given in the question so correct steps in the working are required to award any marks.

(iii) \(\frac{{{m_{\rm{G}}}}}{{{m_{\rm{S}}}}} = {\left[ {\frac{{{L_{\rm{G}}}}}{{{L_{\rm{S}}}}}} \right]^{\frac{1}{{3.5}}}}\) / OWTTE;
allow values in the range of 4.3 to 4.6; [2]
Allow ECF from (d)(ii).
Award [2] for a bald correct answer.

(iv) mentions value of (Chandrasekhar limit) 1.4 solar masses;
if (remnant) mass of G is greater than the Chandrasekhar limit, it would become a neutron star; { (ignore any reference to a black hole)
if (remnant) mass of G is less than the Chandrasekhar limit, it would become a white dwarf;
Do not award both second and third marking points.
Award second or third marking point for the general idea, consistent with any value used for Chandrasekhar limit.
Allow ECF from (d)(iii).
For masses of G, from (d)(iii), which are over 8 solar masses, allow reference to a black hole as eventual fate.

any anticlockwise path that goes above and right of the Sun and passes through/ends below and left of the Sun;