 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/2012/s26/3/2/solution

Massive young stars emit ionizing ultraviolet radiation that creates H II regions. Recombination and radiative cascades produce H-alpha emission, including the

n = 3 \to 2

transition. Shocks or other ionizing sources can also produce it, but disk star-forming gas is the natural interpretation for an extended spiral-galaxy rotation measurement.

The systemic redshift and inclination of an intrinsically circular thin disk are

z = \frac{689.1 - 656.3}{656.3} ≃ 0.04998, cos i = \frac{7.5}{30} = \frac{1}{4}, i ≃ 75.5 2^{\circ} .

The rotation-induced half-width is

(689.7 - 688.5) /2 = 0.6 nm

. Divide by the systemic observed wavelength to remove the common redshift factor before applying the small-velocity Doppler shift:

v_{los} = c \frac{0.6}{689.1} ≃ 261.0 km s^{- 1}, v_{m a x} = \frac{v _{los}}{sin i} ≃ 269.6 km s^{- 1} .

The circular-orbit and thin-disk assumptions neglect intrinsic thickness, warps and noncircular gas motion.

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