A necessary condition for supernova fallback invading newborn neutron-star magnetosphere

We numerically investigate the dynamics of a supernova fallback accretion confronting with a relativistic wind from a newborn neutron star (NS). The time evolution of the accretion shock in the radial direction is basically characterized by the encounter radius of the flow $r_\mathrm{enc}$ and a dimensionless parameter $\zeta \equiv L/\dot M_\mathrm{fb}c^2$, where $L$ is the NS wind luminosity and $\dot M_\mathrm{fb}$ is the fallback mass accretion rate. We find that the critical condition for the fallback matter to reach near the NS surface can be simply described as $\zeta < \zeta_\mathrm{min} \equiv GM_*/c^2r_\mathrm{enc}$ or $r_\mathrm{enc}L/G M_* \dot M_\mathrm{fb} < 1$ independent of the wind Lorentz factor, where $M_*$ is the NS mass. With combining the condition for the fallback matter to bury the surface magnetic field under the NS crust, we discuss the possibility that the trifurcation of NSs into rotation-powered pulsars, central compact objects (CCOs), and magnetars can be induced by supernova fallback.