The Hertzsprung–Russell (HR) diagram shows the Sun, a star A and the main sequence.

Using the mass–luminosity relation L ∝ M^3.5, determine the ratio of the mass of star A to the mass of the Sun.

Star A will leave the main sequence and will evolve to become a neutron star. State the

(i) change in star A that marks its departure from the main sequence.

(ii) range of mass of a neutron star.

\(\frac{{{L_{\rm{A}}}}}{{{L_{\rm{S}}}}} = 100 = {\left[ {\frac{{{M_{\rm{A}}}}}{{{M_{\rm{S}}}}}} \right]^{3.5}}\);
\(\left( {\frac{{{M_{\rm{A}}}}}{{{M_{\rm{S}}}}} = {{100}^{1/3.5}} = 3.7} \right) \approx 4\)
Award marks only if a ratio is calculated.

(i) depletion of hydrogen in the core / fusion moves to outer layers;

(ii) 1.4M_Θ<M<3M_Θ; 
Allow between 2M_Θ and 3M_Θ as the upper bound OV limit.

(stellar mass ratio) was well answered, although sometimes the working was poorly presented. Hydrogen depletion was usually not specifically mentioned.

(b)(i) as the cause for a star to leave the main sequence. Many gave unnecessary information about the subsequent path to a neutron star. For (b)(ii) the upper or lower limits for the mass of a neutron star were known, but rarely both. The range 1.4Ms to 2.5Ms or 3Ms was allowed. Often the names of the limits were given, but not the values.