Hysteresis in spectral state transitions - a challenge for theoretical   modeling
  Many low-mass X-ray binaries show both hard and soft spectral states. For several sources the transitions between these states have been observed, mostly from the soft to the hard state during a luminosity decrease. In a few cases also the transition from the hard to the soft state was observed, coincident with an increase of the luminosity. Surprisingly this luminosity was not the same as the one during a following change back to the hard state. The values differed by a factor of about 3 to 5. We present a model for this hysteresis in the light curves of low-mass X-ray binaries (sources with neutron stars or black holes). We show that the different amount of Compton cooling or heating acting on the accretion disk corona at the time of the transition causes this switch in the accretion mode at different mass accretion rates and therefore different luminosities. The inner disk during the soft state provides a certain amount of Compton cooling which is either not present or much less if the inner region is filled with a hot advection-dominated accretion flow (ADAF) that radiates a hard spectrum. 
E. Meyer-Hofmeister, B.F. Liu, F. Meyer (MPA Garching)