Testing a reduced model of transient inner-disk dynamics in magnetically arrested black-hole accretion
Abstract
Abstract Transient disruption and re-formation of the inner disk in magnetically arrested (MAD) black-hole accretion is followed reliably only by general-relativistic magnetohydrodynamic (GRMHD) simulation, at a cost that precludes systematic surveys. Whether a low-cost reduced description carries independent predictive content is therefore a practical question. We study a minimal reaction–diffusion closure for a bounded connectivity order parameter and ask what of its output is not already contained in its input. Four null tests show that the collapse–recovery timescale ratio tracks the prescribed asymmetry of the driver across three decades, varies threefold with the recovery-threshold convention, and yields an amplitude scaling steepened 2.4-fold by two boundary-saturated points; timescale matching therefore cannot validate such a closure. In its place we drive the closure with the horizon magnetic flux measured in a GRMHD run, fit the kinetic coefficients once on a training window, and require the predicted inner-region connectivity on a disjoint window to beat the closure’s own memoryless limit at equal parameter count. Phase-randomised surrogates supply the null, with the whole fitting procedure repeated for each. On an empirically identified stationary interval of one axisymmetric MAD run the closure attains an out-of-sample skill of 0.53, with p = 0.002 against 500 refitted surrogates, stable under movement of the train/test split and of the aggregation radius; on…
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