A Thorough Search for Short Timescale Periodicity in Four Active Repeating Fast Radio Bursts

Fast Radio Bursts (FRBs) are bright radio transients with millisecond durations which typically occur at extragalactic distances. The association of FRB 20200428 with the Galactic magnetar SGR J1935+2154 strongly indicates that they could originate from neutron stars, which naturally leads to the expectation that periodicity connected with the spinning of magnetars should exist in the activities of repeating FRBs. However, previous studies have failed to find any signatures supporting such a conjecture. Here we perform a thorough search for short timescale periodicity in the four most active repeating sources, i.e. FRBs 20121102A, 20200120E, 20201124A, and 20220912A. Three different methods are employed, including the phase folding algorithm, the H-test and the Lomb-Scargle periodogram. For the three most active repeaters from which more than 1000 bursts have been detected, i.e. FRBs 20121102A, 20201124A, and 20220912A, more in-depth period searches are conducted by considering various burst properties such as the pulse width, peak flux, fluence, and the brightness temperature. No clear periodicity is found in a period range of 0.001--1000 s in all the efforts. Implications of such a null result on the theoretical models of FRBs are discussed.