Field-Decay Heating and Persistent X-Ray Luminosity: Required Decay Times for the Magnetar Catalogue

Magnetars shine in quiescence at luminosities that rotation alone cannot explain. The standard remedy is heat released as the internal field decays, but the remedy is usually invoked qualitatively. Dividing each star reservoir by its measured persistent luminosity turns the invocation into a number: the time the field would need to last if decay alone paid the bill. Working from published values for the sources concerned, this paper computes the relevant quantities under one stated set of conventions and compares them source by source. Headline results: longest required decay time source CXOU J164710.2-455216; longest required decay time yr 5.28e+06; shortest required decay time yr 3.27e+02; sources Lx above Edot 11; median Lx over decay power 0.387. The comparisons are budget statements: they establish whether the energies, stresses, powers and timescales involved are mutually consistent, and by what margin. Every number quoted is produced by the deposited compute.py script from the stated inputs, and the full per-source record is deposited as results.json alongside the text.