If a sunspot appears one-third as bright as the surrounding photosphere,and the average temperature of the photosphere is 5800 K,what is the temperature of the gas in this sunspot?

Question

Quizplus · Accepted Answer

Brightness is proportional to temperature to the fourth power (brightness ∝ T⁴) according to the Stefan-Boltzmann law. If the sunspot appears one-third as bright, it means it has one-third the temperature to the fourth power compared to the photosphere. Therefore, (T_sunspot/T_photosphere)⁴ = 1/3, which gives T_sunspot = T_photosphere * (1/3)^(1/4) = 4400 K (rounded to the nearest hundred).

If a Sunspot Appears One-Third as Bright as the Surrounding