Why do X-ray binary state transitions show hysteresis?
In plain words
During an outburst a black-hole binary switches from a hard X-ray state to a soft one at a higher brightness than the one at which it switches back, so the state is not set by the feeding rate alone.
Precise statement
In black-hole low-mass X-ray binary outbursts the hard-to-soft transition occurs at $L\sim 0.05\ \text{to}\ 0.5\ L_{\mathrm{Edd}}$, while the soft-to-hard return occurs at $L\sim 0.01\ \text{to}\ 0.04\ L_{\mathrm{Edd}}$. Identify the second parameter besides the accretion rate Mdot (net magnetic flux, history of the inner hot flow, disk evaporation and condensation, inner truncation radius) that produces the loop in the hardness-intensity diagram and the jet quenching at the hard-to-soft transition. Answer: a model whose transition luminosities match the observed distribution across outbursts.
What would settle it
Simulations of a full outburst with evolving accretion rate and magnetic flux that reproduce the hysteresis loop, compared with transition luminosities in a sample of outbursts with known distances and masses.