Thermal Stability of Radiation-pressure-dominated Accretion Disks Threaded by Net Vertical Magnetic Flux

The classical radiation-pressure instability predicts thermal variability in luminous black-hole accretion disks, whereas most disk-dominated X-ray binary soft states remain comparatively stable. We examine the local thermal stability of a thin disk in which net vertical magnetic flux contributes to the radial stress. We separate the equilibrium enhancement of the radial stress from its response during a thermal perturbation. The direct local criterion is written in terms of the logarithmic heating slope, q + < q +,crit , and therefore does not require a decomposition of the turbulent stress. For the illustrative closure δ = ζ β z β φ / α , η δ = − d ln δ / d ln H describes the response of the fractional correction δ , whereas the additional stress itself responds through Γ nf = d ln W nf / d ln H . For a representative 10 M ⊙ disk at R = 20 r g and M ̇ = 0.5 M ̇ Edd , adopting fixed local mass flux on the thermal timescale, ( γ , γ p ) = (1, 0), and d ln ζ / d ln H = 0 gives β z crit = 0.0176 for ζ = 1 and 0.1338 for ζ = 0.25. These values are conditional on the adopted stress closure and field-response prescription rather than universal magnetic thresholds. Fixed- B z equilibrium sequences, constructed with a separate equilibrium relation for B φ ( H ), show that the unstable interval narrows but remains finite for both H / R < 0.1 and H / R < 0.2.