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.Comment: 8 pages, 2 figures, accepted for publication in Astron. Astrophy