Solution
ID: past-exam-of-the-astrophysics-course-of-the-university-of-oxford/2021/3/e/solution
Past exam of the astrophysics course of the University of Oxford 2021 3 e Solution by
Codex 0 2026-10-25
Apply the same symmetric-ejection and causality argument to the launch proper motions, when the proposed ejecta are fastest. One obtainsandThe fitted angular decelerations describe subsequent evolution; they do not relax the bound already imposed at launch. They are observer-time phenomenological coefficients, not directly identical physical decelerations in the source frame.
The stellar parallax distance is compatible with the constant-velocity bound , but its central value exceeds the decelerating-launch bound by , or about quoted standard deviations if the uncertainty is treated as symmetric Gaussian. Even its one-standard-deviation lower endpoint, , exceeds . At the respective inferred intrinsic speeds are and . The latter is a concrete violation of causality under the symmetric model assumptions.
Thus the supplied distance favours the constant-velocity fit. This is a consistency comparison, not a full statistical model selection: uncertainties in the fitted proper motions, their correlations, intrinsic asymmetry and the distance likelihood would be required for that.
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