Failed and delayed protostellar outflows with high-mass accretion rates

The evolution of protostellar outflows is investigated under different mass accretion rates in the range $\sim10^{-5}-10^{-2} {\rm M}_\odot$ yr$^{-1}$ with three-dimensional magnetohydrodynamic simulations. A powerful outflow always appears in strongly magnetized clouds with $B_0 \gtrsim B_{\rm 0, cr}$ $=10^{-4} (M_{\rm cl}/100 {\rm M}_\odot){\rm G}$, where $M_{\rm cl}$ is the cloud mass. When a cloud has a weaker magnetic field, the outflow does not evolve promptly with a high mass accretion rate. In some cases with moderate magnetic fields $B_0$ slightly smaller than $B_{\rm 0,cr}$, the outflow growth is suppressed or delayed until the infalling envelope dissipates and the ram pressure around the protostellar system is significantly reduced. In such an environment, the outflow begins to grow and reaches a large distance only during the late accretion phase. On the other hand, the protostellar outflow fails to evolve and is finally collapsed by the strong ram pressure when a massive $(\gtrsim 100 {\rm M}_\odot)$ initial cloud is weakly magnetized with $B_0 \lesssim 100 \mu {\rm G}$. The failed outflow creates a toroidal structure that is supported by magnetic pressure and encloses the protostar and disk system. Our results indicate that high-mass stars form only in strongly magnetized clouds, if all high-mass protostars possess a clear outflow. If we would observe either very weak or no outflow around evolved protostars, it means that strong magnetic fields are not necessarily required for high-mass star formation. In any case, we can constrain the high-mass star formation process from observations of outflows.