The reason for the darkness of sunspots.

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Chapter 12, Problem 6TY

To determine

The reason for the darkness of sunspots.

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Describe what the Sun would look like from Earth if the entire photosphere were the same temperature as a sunspot.

If a sunspot has a temperature of 4,270 K and the average solar photosphere has a temperature of 5,780 K, how many times more energy is emitted in 1 second from a square meter of the photosphere compared to a square meter of the sunspot? (Hint: Use the Stefan-Boltzmann law, E = σT4 (J/s/m2) where E is the energy, σ is a proportionality constant equal to 5.67 ✕ 10−8 J/s/m2/K4, and T is the temperature in kelvins.)

a) At solar maximum sunspots might cover up to 0.4% of the total area of the Sun. If the sunspots have a temperature of 3800 K and the surrounding photosphere has a temperature of 6000 K, calculate the fractional change (as a percentage) in the luminosity due to the presence of the sunspots. b) A star of the same stellar class as the Sun is observed regularly over many years, and a time series of its bolometric apparent magnitude is collected. What would be the signal in this time series which indicated that the star had a magnetic dynamo similar to the Sun? Briefly describe two or three possible sources of other signals which could confuse the interpretation of the data.