We find a new two-temperature hot branch of equilibrium solutions for stationary accretion disks around black holes. In units of Eddington accretion rate defined as $10L_{\rm Edd}/c^2$, the accretion rates to which these solutions correspond are within the range $\dot{m}_1 \la \dot{m} \la 1$, here $\dot{m}_1$ is the critical rate of advecti$. In these solutions, the energy loss rate of the ions by Coulomb energy transfer between the ions and electrons is larger than the viscously heating rate and it is the advective heating together with the viscous dissipation that balances the Coulomb cooling of ions. When $\dot{m}_1 \la \dot{m} \la \dot{m}_2$, where $\dot{m}_2 \sim 5 \dot{m}_1 < 1$, the accretion flow remains hot throughout the disk. When $\dot{m}_2 \la \dot{m}\la 1$, Coulomb interaction will cool the inner region of the disk within a certain radius ($r_{\rm tr} \sim$ several -- tens of Schwarzschild radii or larger depending on the accretion rate and the outer boundary condition) and the disk will collapse onto the equatorial plane and form an optically thick cold annulus. Compared to ADAF, these hot solutions are much more luminous because of the high accretion rate and efficiency, therefore, we name them luminous hot accretion disks.

12 pages, 6 figures, uses mn.sty, the final version accepted by MNRAS, discussion extended to emphasize the difference between ADAF and my model