  We study the effects of optically thin radiative cooling on the structure of
radiatively inefficient accretion flows (RIAFs). The flow structure is
geometrically thick, and independent of the gas density and cooling, if the
cooling time is longer than the viscous timescale (i.e., $t_{\rm cool} \gtrsim
t_{\rm visc}$). For higher densities, the gas can cool before it can accrete
and forms the standard geometrically thin, optically thick Shakura-Sunyaev
disk. For usual cooling processes (such as bremsstrahlung), we expect an inner
hot flow and an outer thin disk. For a short cooling time the accretion flow
separates into two phases: a radiatively inefficient hot coronal phase and a
cold thin disk. We argue that there is an upper limit on the density of the hot
corona corresponding to a critical value of $t_{\rm cool}/t_{\rm ff} (\sim
10-100)$, the ratio of the cooling time and the free-fall time. Based on our
simulations, we have developed a model for transients observed in black hole
X-ray binaries (XRBs). An XRB in a quiescent hot RIAF state can transition to a
cold black-body dominated state because of an increase in the mass accretion
rate. The transition from a thin disk to a RIAF happens because of mass
exhaustion due to accretion; the transition happens when the cooling time
becomes longer than the viscous time at inner radii. Since the viscous
timescale for a geometrically thin disk is quite long, the high-soft state is
expected to be long-lived. The different timescales in black hole transients
correspond to different physical processes such as viscous evolution, cooling,
and free-fall. Our model captures the overall features of observed state
transitions in XRBs.
