Gravitational self-lensing of Fast Radio Bursts in neutron star magnetospheres: II. Applications to strong repeaters and the CHIME population

Abstract

Paper I in this series introduced a model in which seed radio bursts produced by a hotspot anchored in the magnetosphere of a highly-magnetic neutron star (NS) are greatly amplified by strong gravitational self-lensing and thus give rise to Fast Radio Bursts (FRBs). Key features of the FRB population such as the observed dichotomy between repeating and non-repeating sources, their large luminosities and the high-energy power-law distribution of their bursts naturally arise in the model from the amplification dependence on the relative orientation of the rotation axis with respect to the hotspot and the line of sight. Here we compare the model predictions with Five-hundred-meter Aperture Spherical radio Telescope (FAST) data from repeaters and with the general population of FRBs. We find that the burst energy distribution from FRB 20121102A can be explained by assuming two antipodal hotspots in the NS magnetosphere, both producing seed bursts with the same log-normal energy distribution. This scenario implies a well-aligned system geometry, with the rotation axis, line of sight, and hotspot sites separated by $\lesssim 2$°. Similar constraints are found for FRB 20201124A and FRB 20220912A, and weaker ones for FRB 20190520B, owing to its smaller burst sample. We also show that precession of the NS rotation axis can explain the time evolution of the burst energy distribution from FRB 20121102A as well as its temporary disappearance. In application to a cosmological population of randomly-oriented sources the model predicts distance and fluence distributions of FRBs in good agreement with those from a completeness-selected subsample of the first CHIME/FRB catalogue, provided the energy distribution of seed bursts spans a range of ${\sim10^{35}-10^{38}}$ erg.

Figures (8)

• Figure 1: Sketch of the possible geometry for FRB 20121102A. The hotspots trace two circumferences during their rotation with the NS (in red), one closer to the observer (green, dashed), the other one on the opposite side of the NS (green, solid). In the further circumference, the angle from the caustic line to the rotation axis, $i$ (in red), and the emission colatitude, $\xi$ (in blue), are indicated, their size exaggerated for visual clarity.
• Figure 2: The expected energy distribution of bursts from FRB 20121102A (green solid curve) in the configuration described in Sect. \ref{['ssec:dod']}, vs. the observed energy distribution li21. The configuration has $i=1.3$°, $\xi = 1.35$°, plus a small jittering of the emission colatitude with semi-amplitude $\delta \xi =0.5$°. The emitting spots have linear size $\ell = 150$ m and are located at $R=50 R_g$. A constant event rate is assumed, while the seed log-normal has a peak (mode) value of $E_0 = 5.5\times 10^{37}$ erg and $\sigma =1/2$. The dashed red vertical line indicates the FAST 90% completeness threshold li21.
• Figure 3: Left: Energy distribution of bursts from FRB 20201124A (histogram; data from both 2021 observational campaigns published in zhangetal22 and xu22) compared with the two emission components expected from our model as described in Sect. \ref{['ssec:ven']} (green solid curve). Right: Same as left panel, but for the bursts from FRB 20220912A observed between MJD 59880 and 59936 Zhang2023; see the discussion in Sect. \ref{['ssec:2209']}.
• Figure 4: The expected energy distribution of bursts from FRB 20190520B in the configuration described in Sect. \ref{['ssec:dic']} (green solid curve) versus the energy distribution of observed bursts (histogram; data published in niu22 and Cao25). The 90% completeness threshold is indicated by the red vertical line.
• Figure 5: Comparison of the observed energy distribution (solid line) of bursts from FRB 20121102A when divided by date in three groups li21 with the expected energy distribution from our model (dashed line) integrating over the respective phases in the precession cycle.