How is the mass-luminosity relationship mathematically quantified for main-sequence stars?
Answer
$L \propto M^\alpha$
The mass-luminosity relationship governing stars on the main sequence is expressed not linearly, but as a power law quantified by the equation $L \propto M^\alpha$. In this relationship, $L$ represents the star's luminosity, $M$ represents its mass, and $\alpha$ is a specific exponent that describes the sensitivity of luminosity to mass changes. This power law indicates that even small changes in mass lead to very large, non-linear changes in the star's energy output, which is the primary factor distinguishing the brightness of stars with similar chemical compositions.
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