Comparison between the BH accretion timescale and the cavity evolution timescale, and the corresponding reduced BH mass accretion rate. Top rows show t _acc/(t _cav + t _ref) and bottom rows show ﹩{\dot{M}}_{\mathrm{BH},\mathrm{red}}/{\dot{M}}_{\mathrm{Edd}}﹩. Three columns show the s = 0.2, 0.5, and 0.8 cases with m _BH = 10M _⊙, respectively. In the top-middle panel, the magenta, red, and green lines represent the same boundaries as in Figure 1; the yellow, orange, brown lines, and left regions represent the boundaries of ﹩{r}_{\mathrm{obd}}\leqslant {r}_{\mathrm{tr}}﹩, r _obd ≤ r _rad−gas, and r _obd ≤ r _es−ff, respectively; the cyan line and above region represent the boundary of ﹩{t}_{\mathrm{acc}}\leqslant {t}_{\mathrm{bre}}﹩.