The change in the colour of stars is linked to:

The correct option is Variation in their surface temperature.

Explanation:

The color of a star is primarily determined by its surface temperature, which can be understood through the physics of blackbody radiation and Wien's Displacement Law.

According to Wien's Displacement Law, the wavelength ($\mapsto$_max) at which the radiation emitted by a blackbody peaks is inversely proportional to its absolute temperature (T):

${\lambda }_{\text{max}}\times T=b$

where b is Wien's displacement constant.

Key observations from this law include:

1. Hotter Stars: Stars with higher surface temperatures radiate most of their energy at shorter wavelengths, making them appear blue or blue-white.

2. Cooler Stars: Stars with lower surface temperatures emit peak radiation at longer wavelengths, making them appear red or orange-red.

3. Intermediate Stars: Stars with medium temperatures (like our Sun, at around 5800 K) emit energy predominantly in the middle of the visible spectrum, appearing yellow or white.

Therefore, the variation in the colour of stars is directly linked to the variation in their surface temperature.