A repeating fast radio burst (FRB), FRB 20180916B (hereafter FRB 180916), was reported to have a 16.35-day period. This period might be related to a precession period. In this paper, we investigate two precession models to explain the periodic activity of FRB 180916. In both models, the radio emission of FRB 180916 is produced by a precessing jet. For the first disk-driven jet precession model, an extremely low viscous parameter (i.e., the dimensionless viscosity parameter α ≲ 10−8) is required to explain the precession of FRB 180916, which implies its implausibility. For the second tidal-force-driven jet precession model, we consider that a compact binary consists of a neutron star/black hole and a white dwarf; the white dwarf fills its Roche lobe, and mass transfer occurs. Due to the misalignment between the disk and orbital plane, the tidal force of the white dwarf can drive jet precession. We show that the relevant precession periods are several days to hundreds of days, depending on the specific accretion rates and component masses. The duration of FRB 180916 generation in the binary with extremely high accretion rate will be several thousand years.

According to the number of detected bursts, fast radio bursts (FRBs) can be classified into two categories, i.e., one-off FRBs and repeating ones. We make a statistical comparison of these two categories based on the first FRB catalog of the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project. Using the Anderson–Darling, Kolmogorov–Smirnov, and Energy statistic tests, we find significant statistical differences (p-value < 0.001) in the burst properties between the one-off FRBs and the repeating ones. More specifically, after controlling for distance, we find that the peak luminosities of one-off FRBs are, on average, higher than the repeating ones; the pulse temporal widths of repeating FRBs are, on average, longer than the one-off ones. The differences indicate that these two categories could have distinct physical origins. Moreover, we discuss the subpopulations of FRBs and provide statistical evidence to support the existence of subpopulations in one-off FRBs and in repeating ones.

Ultraluminous X-ray bursts (ULXBs) are ultraluminous X-ray flares with a fast rise (∼1 minute) and a slow decay (∼1 hour), which are commonly observed in extragalactic globular clusters. Most ULXBs are observational one-off bursts, whereas five flares from the same source in NGC 5128 were discovered by Irwin et al. In this article, we propose a neutron star (NS)–white dwarf (WD) binary model with super-Eddington accretion rates to explain the repeating behavior of the ULXB source in NGC 5128. With an eccentric orbit, the mass transfer occurs at the periastron where the WD fills its Roche lobe. The ultraluminous X-ray flares can be produced by the accretion column around the NS magnetic poles. On the other hand, some repeating fast radio bursts (FRBs) were also found in extragalactic globular clusters. Repeating ULXBs and repeating FRBs are the most violent bursts in the X-ray and radio bands, respectively. We propose a possible association between the repeating ULXBs and the repeating FRBs. Such an association is worth further investigation by follow-up observations on nearby extragalactic globular clusters.

We revisit the eccentric neutron star (NS)–white dwarf (WD) binary model for the periodic activity of fast radio burst (FRB) sources, by including the effects of gravitational-wave (GW) radiation. In this model, the WD fills its Roche lobe at the periastron and mass transfer occurs from the WD to the NS. The accreted materials can be fragmented and arrive at the NS episodically, resulting in multiple bursts through curvature radiation. Consequently, the WD may be kicked away owing to the conservation of angular momentum. To initiate the next mass transfer, the WD has to refill its Roche lobe through GW radiation. In this scenario, whether the periodic activity can show up relies on three timescales, i.e., the orbital period P orb, the timescale T GW for the Roche lobe to be refilled, and the time span T frag for all the episodic events corresponding to each mass-transfer process. Only when the two conditions T GW ≲ P orb and T frag < P orb are both satisfied, the periodic activity will manifest itself and the period should be equal to P orb. In this spirit, the periodic activity is more likely to show up for relatively long periods (P orb ≳ several days). Thus, it is reasonable that FRBs 180916 and 121102, the only two sources having been claimed to manifest periodic activity, both correspond to relatively long periods.