How does a star's mass relate to its luminosity ($L$)?
Answer
Luminosity is extraordinarily sensitive to mass, approximated by $L propto M^{3.5}$
The relationship between a star's mass ($M$) and its luminosity ($L$) on the main sequence is highly non-linear and extremely sensitive. A small increase in mass results in a disproportionately large increase in energy output. For stars on the main sequence, this relationship is often mathematically approximated by the formula where luminosity is proportional to the mass raised to the power of 3.5 ($L propto M^{3.5}$). This exponential increase in luminosity is the physical mechanism driving the short lives of massive stars, as it mandates a much faster rate of fuel consumption compared to less massive stars.
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