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/2018/s26/3/b/solution

A K-star-like integrated spectrum indicates that old or intermediate-age cool stars, often luminous red giants, dominate the observed optical/near-infrared light. It suggests little ongoing formation of very luminous hot O and B stars. It does not imply that every star is K type: faint low-mass dwarfs and remnants can contribute substantial mass while contributing little light.
Using the reference wavelength printed in the problem,
The low-redshift Hubble estimate is
Peculiar velocities and the distinction between luminosity and angular-diameter distance introduce percent-level or larger corrections to this simple estimate. The numerical result intentionally uses the supplied calcium reference rather than replacing it with a different tabulated line wavelength.

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