Fast Radio Bursts' emission mechanism: implication from localization

I Introduction

Fast radio bursts (Lorimer et al. 2007; Keane et al. 2012; Thornton et al. 2013; Kulkarni et al. 2014; Spitler et al. 2014; Spitler et al. 2016, FRBs,) 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

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

(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.

In addition, the estimate of the wave intensity parameter

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)

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.

II 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

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

($B$ 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

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

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.

III Discussion

The location of the Repeating FRB at $\sim$ 1 Gpc (Lyutikov et al. 2016a, an order of magnitude further away than what was a fiducial model in ), 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 (Lyutikov 2003, e.g., ) – 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 (Lyutikov et al. 2016b, somewhat similar to acceleration mechanism discussed by), 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.

References