fferent typically by $3-4$ orders of magnitude, we increase the radial cell size $\Delta
r$ with the fixed size ratio $\Delta r_i/\Delta r_{i-1}$ $(>1)$. We set $\Delta r_1 = 0.1 R_{\mathrm{in}}$ at the inner boundary. The grids in the angular direction are homogeneously distributed over $0<\theta<90^\circ$, and thus the grid size is $\Delta\theta =
90^\circ/N_\theta$.

We have tested the convergence of the numerical results by varying the grid numbers or inner boundary radius (see Appendix \[sec:res\_check\]). We follow the evolution over the duration $t_{\mathrm{end}}$, until the accretion reaches a steady state in Di and Ddn runs, or until $\dot{M}$ reaches almost constant in the other runs.

Results {#sec:result}
=======

Structures of flows {#sec:structure}
-------------------

. \[tab:d-model\]

  run    subgrid radiation type   $\theta_{\mathrm{inflow}}(r_{\mathrm{B}})$$^{a}$   $\dot{M}/\dot{M}_{\mathrm{B}}$$^{d}$
  ----- ------------------------ -------------------------------------------------- --------------------------------------
  Di           isotropic                             ...$^{b}$                                   $0.17\%^{e}$
  Ddn             disc                               ...$^{c}$                                   $0.13\%^{e}$
  Dds       disc $+$ shadow                          $40^\circ$                                   $59\%^{f}$

  : Summary of the results in Sec. \[sec:structure\]

\

NOTES. $^{a}$opening angle of equatorial neutral inflow region at $r_{\mathrm{B}}$ (see text); $^{b}$no equatorial neutral region; $^{c}$equatorial neutral region does not reach $R_{\mathrm{in}}$; $^{d}$accretion rate normalized by Bondi one; $^{e}$averaged between $t=4\times 10^5{\,\mathrm{yr}}$ and $5\times 10^5{\,\mathrm{yr}}$; $^{f}$evaluated at the end of simulation.

In this section, we perform the simulations of “D-series”, in order to see how the flow structure changes with different directional dependences of the radiation fields. The basic results for these cases are summarized in