  Depending on the value of the accretion rate, black hole accretion is divided
into cold and hot modes. The two modes have distinctly different physics and
correspond to two feedback modes. Most previous feedback works either focus
only on one mode, or the accretion physics is not always properly adopted.
Here, by performing hydrodynamical numerical simulations of AGN feedback in an
elliptical galaxy, we show that including both is important, and gives
different results from including just one or the other. We specifically focus
on the wind and radiation (but neglecting the jet) feedback in the hot mode, to
explore whether this particular mode of feedback can play any important
feedback role. For this aim, we have run two test models. In one model, we
always adopt the cold mode no matter what value the accretion rate is; in
another model, we turn off the AGN once it enters into the hot mode. We have
calculated the AGN light curves, black hole growth, star formation, and AGN
energy duty-cycle; and compared the results with the model in which the two
modes are correctly included. Important differences are found. For example, if
we were to adopt only the cold mode, the total mass of newly formed stars would
become two orders of magnitude smaller, and the fraction of energy ejected
within the high accretion regime (i.e., $L_{\rm BH} > 2\% L_{\rm Edd}$) would
be too small to be consistent with observations. We have also investigated the
respective roles of wind and radiation in the hot mode.
