  We analytically study the dynamical and thermal properties of the
optically-thin gases at the parsec-scale when they are spherically accreted
onto low luminous active galactic nuclei (LLAGNs). The falling gases are
irradiated by the central X-ray radiation with the Compton temperature of
5--15$\times10^7$ K. The radiative heating/cooling and the bulge stellar
potential in galaxies are taken into account. We analyze the effect of
accretion rate, luminosity, gas temperature, and Compton temperature on steady
solutions of dynamical and thermal properties. The steady solutions are
obviously different from Bondi solution. Compared to our models, the Bondi
model underestimates the accretion rate. We give the boundary between thermal
stability and instability. The boundary is significantly affected by Compton
temperature. When Compton temperature is higher, the falling gases tend to
become thermally unstable. When thermal instability takes place in the
irradiated gases, the gases become two phases (i.e. hot gases and cool gases)
and the hot gases may become outflows. This effect may reduce the accretion
rates.
