Testing the Young Neutron Star Scenario with Persistent Radio Emission Associated with FRB 121102

Recently a repeating fast radio burst (FRB) 121102 has been confirmed to be an extragalactic event and a persistent radio counterpart has been identified. While other possibilities are not ruled out, the emission properties are broadly consistent with Murase et al. (2016) that theoretically proposed quasi-steady radio emission as a counterpart of both FRBs and pulsar-driven supernovae. Here we constrain the model parameters of such a young neutron star scenario for FRB 121102. If the associated supernova has a conventional ejecta mass of $M_{\rm ej}\gtrsim{\rm a \ few}\ M_\odot$, a neutron star with an age of $t_{\rm age} \sim 10-100 \ \rm yrs$, an initial spin period of $P_{i} \lesssim$ a few ms, and a dipole magnetic field of $B_{\rm dip} \lesssim {\rm a \ few} \times 10^{13} \ \rm G$ can be compatible with the observations. However, in this case, the magnetically-powered scenario may be favored as an FRB energy source because of the efficiency problem in the rotation-powered scenario. On the other hand, if the associated supernova is an ultra-stripped one or the neutron star is born by the accretion-induced collapse with $M_{\rm ej} \sim 0.1 \ M_\odot$, a younger neutron star with $t_{\rm age} \sim 1-10$ yrs can be the persistent radio source and might produce FRBs with the spin-down power. These possibilities can be distinguished by the decline rate of the quasi-steady radio counterpart.