Low-Dipole-Field Magnetars: Burst Activity Below the Quantum Critical Field and the Case for Hidden Internal Strength

Several sources burst like magnetars while spinning down like ordinary pulsars. Their dipole fields sit at or below the quantum critical value, some of them an order of magnitude under it, yet their burst energies are unmistakably magnetar-like. The tension is quantitative: a dipole-strength reservoir is too small, so the energy must be stored where spin-down cannot see it. 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: n low field sources 2; lowest B G 6.10e+12; sources below BQ 2; dipole reservoir lowest erg 6.20e+42; interior 30x reservoir lowest erg 5.58e+45. 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.