A Bayesian Framework for Constraining Magnetar Magnetic Fields from Repeating FRB Statistics

Abstract: Fast radio bursts (FRBs) are widely considered to be associated with magnetars, motivated by the detection of an FRB-like radio burst from the Galactic magnetar SGR~1935+2154. However, constraining the magnetic field strength of extragalactic FRB sources remains challenging. In this work, we develop a Bayesian framework that models FRB time--energy sequences as a marked point process, combining burst waiting-time statistics with energy distributions to quantify the magnetic field strengths required to sustain the observed bursting activity under the magnetar powered scenario. Applying this method to a sample of repeating FRBs, we derive constraints on their magnetic fields by incorporating an empirical prior on the radio emission efficiency calibrated from the Galactic event. Under a conservative assumption for the activity duty cycle, most sources require magnetic energy reservoirs consistent with magnetar strength fields, with characteristic field strengths of order $10<sup>{13}$--$10<sup>{15}$ G, although the constraints remain sensitive to the poorly known efficiency and duty-cycle parameters. FRB~20200120E provides an interesting case with a substantially lower field requirement, highlighting the importance of source environment and evolutionary history in interpreting FRB activity. Our framework provides a statistical approach for connecting transient burst properties with magnetic energy reservoirs, with potential applications to FRBs and other magnetically powered transients.