What exponent approximates the scaling for luminosity (L) based on mass (M) for main sequence stars?
Answer
M^3.5
Astronomers have established the Mass-Luminosity Relation to quantify how a star's energy output relates to its mass while it is on the main sequence, the stable hydrogen-fusing phase. This relationship is not linear but expressed as a power law, where luminosity ($L$) scales with mass ($M$) raised to a specific power ($x$). The commonly accepted approximation for this exponent ($x$) is around 3.5. This substantial power dependence means that even small increases in stellar mass result in enormous, disproportionate increases in the star's luminosity, explaining why the brightest visible stars are rare but overwhelmingly luminous.
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