2020ApJ...892..135W

While the radiation mechanism of fast radio bursts (FRBs) is unknown, coherent curvature radiation and synchrotron maser are promising candidates. We find that both radiation mechanisms work for a neutron star (NS) central engine with B≳10¹² G, while for a synchrotron maser, the central engine can also be an accreting black hole (BH) with B≳10¹² G and a white dwarf (WD) with B∼10⁸–10⁹ G. We study the electromagnetic counterparts associated with such central engines, i.e., nebulae for repeating FRBs and afterglows for nonrepeating FRBs. In general, the energy spectrum and flux density of the counterpart depend strongly on its size and total injected energy. We apply the calculation to the nebula of FRB 121102 and find that the persistent radio counterpart requires the average energy injection rate into the nebula to be between 2.7×10³⁹ergs^–1 and 1.5×10⁴⁴ergs^–1, and the minimum injected energy to be 6.0×10⁴⁷erg in around 7 yr. Consequently, we find that for FRB 121102 and its nebula: (1) WD and accretion BH central engines are disfavored; (2) a rotation-powered NS central engine works when 1.2×10¹²G≲B≲7.8×10¹⁴G with initial period P< 180 ms, but the radio emission must be more efficient than that in typical giant pulses of radio pulsars; and (3) a magnetic-powered NS central engine works when its internal magnetic field B≳10¹⁶ G. We also find that the radio-emitting electrons in the nebula could produce a significant rotation measure (RM), but cannot account for the entire observed RM of FRB 121102.