Why do radiation-dominated accretion disks appear thermally stable?
In plain words
Theory from the 1970s predicts that disks held up mostly by the pressure of light should heat up and fall apart unstably, yet many bright disks look steady.
Precise statement
Standard alpha disks in which radiation pressure exceeds gas pressure, with stress proportional to total pressure, are thermally and viscously unstable (Lightman-Eardley), predicting limit cycles; most X-ray binaries in the soft state at $L \sim 0.1 \text{ to } 0.5\,L_{\mathrm{Edd}}$ show stable disk emission, with GRS 1915+105 and a few others as exceptions. Determine the stabilizing physics (magnetic pressure support, opacity effects, stress scaling with gas pressure). Answer: a mechanism and stability criterion matching which sources vary and which do not.
What would settle it
Radiation-MHD simulations predicting stability boundaries that match the observed luminosity at which limit-cycle variability appears.