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The evolution of protostellar outflows is investigated under different massaccretion rates in the range $\sim10^{-5}-10^{-2} {\rm M}_\odot$ yr$^{-1}$ withthree-dimensional magnetohydrodynamic simulations. A powerful outflow alwaysappears 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 thecloud mass. When a cloud has a weaker magnetic field, the outflow does notevolve promptly with a high mass accretion rate. In some cases with moderatemagnetic fields $B_0$ slightly smaller than $B_{\rm 0,cr}$, the outflow growthis suppressed or delayed until the infalling envelope dissipates and the rampressure around the protostellar system is significantly reduced. In such anenvironment, the outflow begins to grow and reaches a large distance onlyduring the late accretion phase. On the other hand, the protostellar outflowfails to evolve and is finally collapsed by the strong ram pressure when amassive $(\gtrsim 100 {\rm M}_\odot)$ initial cloud is weakly magnetized with$B_0 \lesssim 100 \mu {\rm G}$. The failed outflow creates a toroidal structurethat is supported by magnetic pressure and encloses the protostar and disksystem. Our results indicate that high-mass stars form only in stronglymagnetized clouds, if all high-mass protostars possess a clear outflow. If wewould observe either very weak or no outflow around evolved protostars, itmeans that strong magnetic fields are not necessarily required for high-massstar formation. In any case, we can constrain the high-mass star formationprocess from observations of outflows.

Failed and delayed protostellar outflows with high mass accretion rates