 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s26/3/4/solution

Use an explicit Tully-Fisher-type scaling

L \propto v_{m a x}^{4}

for comparable spiral populations and photometric band. Relative to the preceding galaxy,

L_{2} \sim 1 0^{10} (100/282)^{4} L_{⊙} \sim 1.6 \times 1 0^{8} L_{⊙} .

The exponent and normalization are empirical and have scatter; one galaxy alone does not establish the relation. Different stellar populations, inclination errors and extinction change the photometric inference.

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