Question

The rich galaxy cluster Abell 1689 has a redshift z = 0.1832. It contains a large amount of hot gas at a temperature T ≃ 108 K. We observe an emission line due to the n = 2 → 1 transition of Fe XXVI (that is, iron which has lost all but one of its Z = 26 electrons). For a hydrogen-like ion with nuclear charge Z, the energy levels of hydrogen are all multiplied by a factor of Z2.

(a) Calculate the emitted wavelength λe of the photons produced by this transition.

(b) Calculate the observed wavelength λo of these photons when we detect them.

(c) How fast are hydrogen nuclei (protons) in the cluster gas moving at 108 K? Calculate the most likely speed vpeak, and compare it to the orbital velocity of the galaxies, which is about 1200 km s−1.

Answer 1

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