  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.
