Fast Radio Bursts' emission mechanism: implication from localization

TL;DR

This paper argues that the localization of a repeating fast radio burst at approximately 1 Gpc rules out models based on rotationally-powered pulsar emissions, suggesting alternative mechanisms.

Contribution

It provides evidence that rules out certain pulsar-based models for FRB emission based on localization data.

Findings

Localization at ~1 Gpc excludes young pulsar emission models.

Supports alternative, non-rotational mechanisms for FRB origins.

Refines understanding of possible FRB progenitors.

Abstract

We argue that the localization of the Repeating FRB at $\sim 1$ Gpc excludes rotationally-powered type of radio emission (e.g., analogues of Crab's giant pulses coming from very young energetic pulsars) as the origin of FRBs.

Equations

$$L_{FRB}=4\pi D^2(\nu F_{\nu })\approx 10^{42}{F}_{1\mathrm{Jy}}{D}_{\mathrm{Gpc}}^2{\mathrm{erg}\mathrm{s}}^{-1},$$

$$B_{eq}=\sqrt{8\pi }\frac{\sqrt{\nu F_{\nu }}D}{c^{3/2}\tau }=3\times 10^8{\tau }_{-3}^{-1}\mathrm{G}.$$

$$T_b\approx \frac{2\pi D^2{F}_{\nu }}{{\nu }^2{\tau }^2}\frac{\Delta \Omega }{4\pi }\approx 5\times 10^{35}\mathrm{K}$$

$$a=\frac{eE}{m_{e}c\omega }\approx 10^5\gg 1$$

$$a_B=\frac{eE}{m_{e}c{\omega }_B}\approx 1$$

$$\frac{L_{FRB}}{L_{GP}}\approx 2.5\times 10^5$$

$$\left(\frac{B_{FRB}}{B_{Crab}}\right){\left(\frac{P_{FRB}}{P_{Crab}}\right)}^{-2}\approx 500$$

$$\nu F_{\nu }=\eta \frac{L_{sd}}{4\pi D^2},$$

$${\tau }_{SD}=\eta \frac{\pi I_{NS}}{2D^2\nu F_{\nu }{P}_{min}^2}\approx 600\eta \mathrm{yrs}$$

Full text

1 Introduction

Fast radio bursts (FRBs, Lorimer et al., 2007; Keane et al., 2012; Thornton et al., 2013; Kulkarni et al., 2014; Spitler et al., 2014, 2016) are recently identified type of transient radio emission. The recent localization of the host galaxy of the repeating Fast Radio Burst 121102 (the Repeating FRB below) by Chatterjee et al. (2017) establishes sources of FRBs as cosmological (and not only extragalactic) objects. The host galaxy is located at the distance $D\sim 1$ Gpc.

The power and the (upper limit on the intrinsic) duration of FRBs require neutron star-like energy densities of the magnetic field in the emission region (Lyutikov et al., 2016a). In the case of FRB 121102, the instantaneous (isotropic-equivalent) luminosity $L_{FRB}$ is

[TABLE]

where $F_{\nu}$ flux in Jansky and $\nu$ is the observation frequency. Taking the duration of the bursts $\tau\approx 1$ msec $\equiv\tau_{-3}$ as indication of the emission size, the equipartition magnetic field energy density at the source is

[TABLE]

(For a beamed motion of the emitting plasma a similar magnetic field would be required to collimate the beam.) As the estimate (2) is the lower estimate on the magnetic field at the source, this narrows down the location of the emission region to magnetospheres of neutron stars.

The brightness temperature

[TABLE]

clearly implies a coherent mechanism.

In addition, the estimate of the wave intensity parameter

[TABLE]

where $E=\sqrt{L_{FRB}/(c^{3}\tau^{2})}$ is the typical electric field in the wave at the emission site and $\omega=2\pi\nu$ is the observed frequency (Luan & Goldreich, 2014), require presence of strong magnetic field with $\omega_{B}\gg\omega$, so that the correct definition of the intensity parameter (4) is (Lyutikov et al., 2016a)

[TABLE]

where $\omega_{B}=eB/(m_{e}c)$ is the corresponding cyclotron frequency.

Thus, magnetospheres of neutron stars are the most promising loci of the FRBs emission generation (Popov & Postnov, 2010; Pen & Connor, 2015; Cordes & Wasserman, 2016; Lyutikov et al., 2016a). Identification of FRBs with neutron star and the repetitiveness as evidence against catastrophic events (collapse, coalescence, etc.), leave two possible types of the production of radio emission: (i) hypothetical radio emission accompanying giant flares in magnetars (Lyutikov, 2002; Popov & Postnov, 2010; Lyubarsky, 2014; Keane et al., 2012; Pen & Connor, 2015; Katz, 2016); (ii) Giant pulses (GPs) analogues emitted by young pulsars (Lundgren et al., 1995; Soglasnov et al., 2004; Popov & Stappers, 2007), see discussions by Lyutikov et al. (2016a); Cordes & Wasserman (2016); Connor et al. (2016). These two possibilities rely on different source of energies for FRBs: strong magnetic fields in case of magnetars and the rotational energy in case of GPs.

2 Not Giant Pulses from young energetic pulsars

Lyutikov et al. (2016a) argued that if the FRBs are analogues of giant pulses (GPs) but coming from young (ages tens to hundreds years) pulsars with Crab-like magnetic field, then the required initial periods need to be in a few msec range - a reasonable assumption for $D\leq$ few hundreds Mpc. Identification of the FRB host with a galaxy at $D=1$ Gpc makes this possibility unlikely, as we discuss next.

For Crab pulsar the peak GP fluxes $F_{\nu}$ exceed Mega-Jansky (Hankins et al., 2003; Soglasnov, 2007). The observed fluxes from the Repeating FRB were in the hundreds milliJy range. Thus, it is required that the intrinsic GP power at the FRB source is

[TABLE]

Scaling the FRB power with the spin-down power (we note that this is not the case for the bulk of the pulsar population Manchester et al., 2005) then puts constraints on the magnetic field and the spin period of the FRB source:

[TABLE]

($B$ and $P$ are corresponding surface magnetic fields and periods). Thus, a Crab-like pulsar needs to spin at $1.5$ msec, while a magnetar-like neutron star with quantum magnetic field on the surface needs to spin at $\sim$ 5 msec. Though these are physically allowed values, as we show below the corresponding spin-down time is very short, contradicting the observed constancy of the Repeating FRB over the few years of observations.

One possible caveat is that the FRB source can have higher efficiency in converting spin-down power into radiation than Crab’s GPs (for Crab the instantaneous efficiency can reach $10^{-2}$). Parametrizing the observed flux as

[TABLE]

where $L_{sd}$ is the spin-down luminosity an $\eta\leq 1$ is the conversion efficiency. The conversion efficiency $\eta$ is smaller than unity since the energy associated with an FRB should originate in the magnetospheres of NSs (and not, *e.g., *in the crust - this would involve much longer time scales, $\sim 100$ msec - the shear time scale through the crust). Also, pulsar glitches do not produce any considerable perturbation to the magnetosphere. There is no way to “store” more energy in the magnetosphere.

The longest possible spin-down time is then

[TABLE]

for $F_{\nu}=1$ Jy and the minimal period of $P_{min}=1$ msec. (For a given FRB luminosity $L_{FRB}$, scaled with spin-down power, the longest spin-down time is for shortest periods and, correspondingly, smallest magnetic fields). The longest possible spin-down time scale (9) is barely consistent with constant value of the properties of the Repeating FRB over the period of few years - that would require an unrealistically high conversion efficiency $\eta\rightarrow 1$.

Another constraint comes from the constant values of the dispersion measure (DM) over few years (Chatterjee et al., 2017). For the Repeating FRB approximately half of the DM contribution comes from the local plasma, $DM_{loc}\sim 300$. Since, as we argued above, the typical time scale of the source is very short, a SN remnant should still be present. If DM is associated with an expanding SN shell, then it should sharply decrease with time, $DM\propto t^{-2}$ (Lyutikov et al., 2016a; Piro, 2016). Since no DM changes are seen, this further excludes young rotationally-powered pulsars as FRB sources.

3 Discussion

The location of the Repeating FRB at $\sim$ 1 Gpc (an order of magnitude further away than what was a fiducial model in Lyutikov et al., 2016a), combined with a very steady value of DM, virtually excludes FRBs as analogues of Crab giant pulses. The allowed parameter region is very narrow: only an extremely efficient conversion of the rotational energy into radio waves, $\eta\approx 1$, combined with millisecond period at birth and a very specific range of ages $100$ yrs $<t$ $<500$ yrs (the lower limit come from the requirement of nearly constant DM, while the upper limit comes from the spin-down age, Eq. (9)) can account for fluxes, duration, distance to FRB and the constant value of DM.

The alternative model – hypothetical generation of high brightness coherent radio emission during the initial stages of magnetar flares (e.g., * Lyutikov, 2003) – is only marginally better suited to explain FRBs. Briefly, we expect that during the initial explosive stages of the current sheet formation in magnetar magnetospheres  the inductive electric fields accelerate particles (somewhat similar to acceleration mechanism discussed by Lyutikov et al., 2016b), producing distributions unstable to generation of coherent emission. The peak luminosity of the flare from SGR $1806-20$ was $10^{47}$ erg s-1* Palmer et al. (2005). Thus, efficiency of $\sim 10^{-5}$ between radio and $X$-rays is sufficient to power an FRB. But the corresponding signal from a magnetar at 10 $kpc$ would produce an FRB in the Giga-Jansky range. This may contradict the non-detection of the SGR $1806-20$ flare by Parkes (Tendulkar et al., 2016). We encourage an observational campaign to detect possible radio burst contemporaneous with magnetar bursts and flares. Another puzzling property of FRBs within the frameworks of both models is a very high and constant in time local DM.

I would like to thank members of McGill Space Institute (in particular Victoria Kaspi and Shriharsh Tendulkar), Ue-Li Pen and Sergey Popov for discussions.

This work was supported by NSF grant AST-1306672 and DoE grant DE-SC0016369.