Energy and waiting time distributions of FRB 121102 observed by FAST

Abstract

The energy and waiting time distributions are important properties to understand the physical mechanism of repeating fast radio bursts (FRBs). Recently, Five-hundredmeter Aperture Spherical radio Telescope (FAST) detected the largest sample of FRB 121102, containing 1652 bursts. The energy distribution at high-energy range (> 10 38 erg) can be fitted with a single power-law function with an index of −1.86. However, the distribution at low-energy range deviates from the power-law function. The energy distributions of high-energy bursts at different epochs are inconsistent. We find the power-law index of −1.70 for early bursts and −2.60 for later bursts. For bursts observed in a single day, a linear repetition pattern is found. We use the Weibull function to fit the waiting time distribution. The shape parameter k = 0.72 +0.01 −0.02 and the event rate r = 734.47 +29.04 −27.58 day −1 are derived. If the waiting times with δ t < 28 s are excluded, the burst behavior can be described by a Poisson process. The best-fitting values of k are slightly different for low-energy and high-energy bursts. The event rates change significantly across the observing time, while the shape parameters k vary slightly in different days.

The Sources of Apparently Non-Repeating FRB

“…This is sufficient, given the assumptions (most significantly, the energy distribution of the bursts), to exclude the constant rate hypothesis with a confidence level > 97%. Zhang et al (2021) suggest α = 1.7 in one subset of their data and α = 2.6 in another subset. The lower value would imply (for the Parkes data) T 2 ≈ 1000 h, T 2 /T1 ≈ 115 and rejection of the constant rate hypothesis at a confidence level ≈ 97%; the higher value of α would increase T 2 /T1 to 10 4 and rejection to a confidence level > 99% 2 .…”

“…When different observing systems have differing sensitivities, T2 is replaced by an effective T 2 = T2(F2/F1) −α , where F2 and F1 are the detection thresholds, fluxes or fluences, of the two systems and the distribution function of the source signals is assumed to be ∝ F −α ; for FRB α ≈ 1.85 (Zhang et al 2021) is plausible, although it appears to be variable. With this scaling, the 720 hours of lower sensitivity observations of Bannister et al (2019) have T 2 ≈ 70 h while their 11 h of higher sensitivity observations have T 2 ≈ 1500 h, implying T 2 /T1 ≈ 170.…”

“…If the distribution function of the source signal strength F (flux or fluence) is ∝ F −α , the actual duration T2 of the second observation is replaced by an effective T 2 = T2(F2/F1) −α , where F2 and F1 are the detection thresholds, fluxes or fluences, of the second and discovery observing systems respectively. Zhang et al (2021) fitted α ≈ 1.85 to their entire dataset for the repeating FRB 121102. They also divided their data into two subsets, finding α = 1.7 in one and α = 2.6 in the other.…”