Final answer:
Both Rigel and Sirius B are of spectral class B8, indicating similar temperatures. However, a star's temperature also affects its luminosity. Without exact temperatures, we cannot determine which star has a higher surface temperature based on spectral class and luminosity differences alone.
Step-by-step explanation:
The question regards the surface temperature of stars and their luminosity, mainly within the field of astrophysics. Since both Rigel and Sirius B are of spectral class B8, they have similar temperatures based on their spectral classification. However, surface temperature is not solely determined by spectral class; luminosity plays a key role as well. The luminosity of a star is proportional to the fourth power of its surface temperature and the square of its radius, as described by the formula L = 4πR²σT´, where L is luminosity, R is radius, T is surface temperature, and σ is the Stefan-Boltzmann constant.
Star B in the provided information has a surface temperature twice that of Star A, leading to it being significantly more luminous, due to the relation between temperature and luminosity. Although direct comparison between Rigel and Sirius B is not provided, based on the same spectral class and large disparity in luminosity, we can infer Rigel has a larger radius than Sirius B. Therefore, despite the same spectral class, the higher luminosity of Rigel suggests it might have a greater surface temperature or a much larger radius. Since a white dwarf like Sirius B is known for its high temperature but low luminosity due to a small size, and a star like Rigel is a blue supergiant with a much larger size, it's likely they have similar temperatures but vastly different sizes.
To clearly determine which star has the greater surface temperature, we must rely on their spectral class and known properties: Sirius B is a white dwarf, implying it is extremely hot despite its low luminosity, and Rigel, being a blue supergiant, is also very hot but has a much greater size contributing to its brightness. Without precise temperature measurements for both stars, we cannot conclusively determine which has the greater surface temperature based solely on the given information.