Suppose a Cepheid oscillates from an initial state 1 to a state 2 where its radius has decreased 10 percent, and its temperature has increased 10 percent compared with the values at state 1. How do the luminosities at states 1 and 2 compare?

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Quizplus · Accepted Answer

The luminosity of a star is directly related to both its radius and temperature. Specifically, luminosity $L$ is proportional to the radius $R$ squared and the temperature $T$ to the fourth power ($L \propto R^2T^4$). A 10 percent decrease in radius ($R^2$ term decreases) and a 10 percent increase in temperature ($T^4$ term increases) would result in an overall increase in luminosity due to the more significant impact of the temperature's fourth power increase compared to the square of the radius decrease. Therefore, the luminosity is greater at position 2.

Suppose a Cepheid Oscillates from an Initial State 1 to a State