Constraining the FRB Central Engine from Flux Variations of Persistent Radio Sources: FRB 20240114A as the First Attempt

Some repeating fast radio bursts (FRBs) are associated with persistent radio sources (PRSs), likely driven by the long-term activity of a central engine. We investigate FRB 20240114A-currently the most active repeating FRB-to explore the link between its burst activity and the flux variability of its associated PRS. We model electrons responsible for FRB emission being continuously injected from a central magnetar into its magnetar wind nebula (MWN), where synchrotron radiation produces the PRS. Comparing our model with the latest PRS spectra and flux variations, we constrain the physical properties of the FRB source. We find that the total energy injected into the MWN during FAST observations from January to August 2024 is about 10 48,, consistent with the magnetic energy budget of a magnetar with an internal magnetic field of about 10 16, G. The bulk Lorentz factor of the FRB-emitting plasma is mildly constrained to 10 cubed, and FRB 20240114A is inferred to be powered by a young magnetar aged about 10 - 20, yr. These results show that the PRS flux variability effectively probes FRB emission properties. We predict that while PRS luminosity increases rapidly with enhanced FRB activity, it will slowly fade over decades via adiabatic cooling after FRB activity ceases. Energetics suggest that the hyper-active phase observed in FRB 20240114A (burst rate about 700, hr-1) is a rare state with a duty cycle of 10-2, which is broadly consistent with its detection rate in current FRB-PRS samples.