Luminous hot accretion flows: thermal equilibrium curve and thermal stability

In a previous paper, we presented the global solution of a new accretion flow model, namely luminous hot accretion flows (LHAFs). In this {\em Letter}, we first show the corresponding thermal equilibrium curve of LHAFs in the mass accretion rate vs. surface density diagram. Then we examine its thermal stability again local perturbations. We find that LHAFs are thermally unstable when thermal conduction is neglected. However, when the accretion rate is not very large, the timescale of the growth of perturbations is longer than the accretion timescale, therefore the instability has no dynamical effect on the accretion flow. When the accretion rate is large, the perturbations can grow very fast at a certain radius. As a result, some cold clumps may form and the accretion flow will become multi-phase.