What is the approximate relationship governing stellar Luminosity (L) in terms of Mass (M)?
Answer
Luminosity is often cited as proportional to the mass raised to the 3.5 power ($L \propto M^{3.5}$)
The relationship between a star's mass and its energy output, or luminosity, is highly non-linear and aggressive. The text specifies that this relationship is frequently approximated by the equation $L \propto M^{3.5}$. This means that a small increase in mass results in a disproportionately large increase in brightness. For instance, if a star is twice as massive as the Sun, it is not merely twice as bright, but approximately $2^{3.5}$, or about 11.3 times as bright. This steep increase in energy output is the fundamental reason massive stars exhaust their fuel supply so rapidly.
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