SI units of stellar luminosity from the Stefan-Boltzmann law

Steps:

• Luminosity L is the total power radiated by the star, with SI unit watt (W).
• W = J/s, and joule J = kg m² s⁻², so W = kg m² s⁻³.
• The given formula L = 4π r² T⁴ omits the Stefan-Boltzmann constant σ (units kg s⁻³ K⁻⁴).
• Including σ, [L] = [r²] [σ T⁴] = m² · (kg s⁻³ K⁻⁴ · K⁴) = kg m² s⁻³; the odd T units likely indicate a non-standard scaling but do not alter L's definition.

Why A is correct:

• A matches the base SI units for power, the physical definition of luminosity.

Why the others are wrong:

• B: Units of energy (J = kg m² s⁻²), not rate of energy output.
• C: Units of power per length (W/m = kg m s⁻³), irrelevant for total stellar luminosity.
• D: Units of power per length per time (W/(m s) = kg m s⁻⁴), not applicable.

Final answer: A