The Fast Radio Burst Luminosity Function and Death Line in the Low-twist Magnetar Model

Abstract

We explore the burst energy distribution of fast radio bursts (FRBs) in the low-twist magnetar model of Wadiasingh & Timokhin (2019). Motivated by the power-law fluence distributions of FRB 121102, we propose an elementary model for the FRB luminosity function of individual repeaters with an inversion protocol which directly relates the power-law distribution index of magnetar short burst fluences to that for FRBs. The protocol indicates the FRB energy scales virtually linearly with crust/field dislocation amplitude, if magnetar short bursts prevail in the magnetoelastic regime. Charge starvation in the magnetosphere during bursts (required in WT19) for individual repeaters implies the predicted burst fluence distribution is narrow, < ∼ 3 decades for yielding strains and oscillation frequencies feasible in magnetar crusts. Requiring magnetic confinement and charge starvation, we obtain a death line for FRBs which segregates magnetars from the normal pulsar population, suggesting only the former will host FRBs. We convolve the burst energy distribution for individual magnetars to define the distribution of luminosities in evolved magnetar populations. The broken power-law luminosity function's low energy character depends on the population model, while the high energy index traces that of individual repeaters. Independent of the evolved population, the broken power-law isotropic-equivalent energy/luminosity function peaks at ∼ 10 38 − 10 40 erg with a sharp low-energy cutoff at < ∼ 10 37 erg. Lastly, we consider the local fluence distribution of FRBs, and find that it can constrain the subset of FRB-producing magnetar progenitors. Our model suggests that improvements in sensitivity may reveal flattening of the global FRB fluence distribution and saturation in FRB rates. 1/7 c and ε CR,pp ∝ ρ 1/2 c . There also exist regimes between B ∼ 10 13 − 10 14 G where the splitting length may be shorter than the pair length, owing to the dependence of splitting amplitude integrals M σ on B (for details, see Hu et al. 2019). A more complete study of pair cascades with splitting for FRB models is deferred to the future.

Multi-dimensional population modelling using frbpoppy: Magnetars can produce the observed fast radio burst sky

“…The flat nature of the parameter space seen in our Monte Carlo simulation indicates the range of values allowed is far wider than our choice of model input. This result is in contrast with results from Wadiasingh et al (2020), who argued for a narrow energy band, but it is in line with with the recent detections of FRBlike bursts originating from the magnetar SGR 1935+2154 that span many orders of magnitude (see e.g. The CHIME/FRB Collaboration et al 2020;Kirsten et al 2020).…”

Implications of a Fast Radio Burst from a Galactic Magnetar

“…An alternative possibility is that the repetition rate increases significantly with the periodicity (Wadiasingh et al 2020). In this case, the periodicity of 180916 (and its high activity relative to SGR 1935+2154) may be ascribed to an extremely long period magnetar (Beniamini et al 2020).…”

“…In the low-twist models (Wadiasingh & Timokhin 2019;Wadiasingh et al 2020), magnetic field dislocations and oscillations in the NS surface can lead to pair cascades, assuming that the background charge density is sufficiently Figure 5. Two-component magnetar population consisting of (i) ordinary magnetars fixed to properties of SGR 1935+2154and extrapolated as a function of the luminosity function slope γ and (ii) a magnetar population whose activity rate (parameterized via the internal magnetic field) and birth rate (a fraction f CCSN of the CCSN rate) are allowed to vary (the value of γ is identical to both populations).…”

Periodicity in recurrent fast radio bursts and the origin of ultralong period magnetars

“…The approximate estimates for the pulsar death line are shown by dashed and dot-dashed lines (respectively cases I' and III' from (Zhang et al 2000)). Finally, the 'death line' for FRB creation in the low twist model (Wadiasingh et al 2020) (hereafter W20) is depicted by a dotted line. Allowed sources lie above the line.…”