Repulsion of fallback matter due to central energy source in supernova

The flow of fallback matter being shocked and repelled back by an energy deposition from a central object is discussed using newly found self-similar solutions. We show that there exists a maximum mass-accretion rate if the adiabatic index of the flow is less than or equal to 4/3. Otherwise, we can find a solution with an arbitrarily large accretion rate by appropriately shrinking the energy deposition region. Applying the self-similar solution to supernova fallback, we discuss how the fate of newborn pulsars or magnetars depends on the fallback accretion and their spin-down power. Combining the maximum accretion rate with the condition for the fallback accretion to bury the surface magnetic field into the crust, we argue that supernova fallback with a rate of M _fb ∼ 10−(4-⁶⁾ M s⁻¹ could be the main origin of the diversity of Galactic young neutron stars, i.e., rotation-powered pulsars, magnetars, and central compact objects.