Cosmological Fast Radio Bursts from Binary Neutron Star Mergers
aa r X i v : . [ a s t r o - ph . H E ] N ov PASJ:
Publ. Astron. Soc. Japan , 1– ?? , c (cid:13) Cosmological Fast Radio Bursts from Binary Neutron Star Mergers
Tomonori T
OTANI Department of Astronomy, School of Science, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 Research Center for the Early Universe, School of Science, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033 (Received 2013 July 18; accepted 2013 August 16)
Abstract
Fast radio bursts (FRBs) at cosmological distances have recently been discovered, whose duration is about mil-liseconds. We argue that the observed short duration is difficult to explain by giant flares of soft gamma-ray repeaters,though their event rate and energetics are consistent with FRBs. Here we discuss binary neutron star (NS-NS)mergers as a possible origin of FRBs. The FRB rate is within the plausible range of NS-NS merger rate and itscosmological evolution, while a large fraction of NS-NS mergers must produce observable FRBs. A likely radiationmechanism is coherent radio emission like radio pulsars, by magnetic braking when magnetic fields of neutron starsare synchronized to binary rotation at the time of coalescence. Magnetic fields of the standard strength ( ∼ − G) can explain the observed FRB fluxes, if the conversion efficiency from magnetic braking energy loss to radioemission is similar to that of isolated radio pulsars. Corresponding gamma-ray emission is difficult to detect bycurrent or past gamma-ray burst satellites. Since FRBs tell us the exact time of mergers, a correlated search wouldsignificantly improve the effective sensitivity of gravitational wave detectors.
Key words: stars: neutron — stars: binaries: general — gravitational waves — radio continuum: general
1. Introduction
Thornton et al. (2013) reported a discovery of four enig-matic radio transients emitting Jansky level flux during a fewmilliseconds, called fast radio bursts (FRBs) (see also Lorimeret al. 2007; Keane et al. 2012 for earlier events of possibly thesame population). No repeated events were found, implyingcataclysmic nature. The dispersion measure and the scatteringsignature seen in the exponential tail of their light curves indi-cate that they are located at cosmological distances of redshift z ∼ < ∼ a few msec would place a strongconstraint on possible theoretical scenarios. Giant flares of softgamma-ray repeaters (SGRs) are suggested as a promising can-didate by Popov & Postnov (2007) and Thornton et al. (2013),because of the event rate consistent with that of FRBs (Ofek2007) and sufficient total energy to explain the FRB radio flux(Hurley et al. 2005; Palmer et al. 2005; Terasawa et al. 2005).However, radio emission only within a msec scale duration isnot naturally expected, though the dynamical time of a neu-tron star is about 1 msec. Typical rotation periods of SGRs aremuch longer ( > ∼ −
20 shows a peak width of ∼
100 msec and subsequent modulation of the flux, indicating re-peated energy injections on a time scale longer than 100 msec(Terasawa et al. 2005).Other proposed scenarios for FRBs include interaction ofsupernova shock and neutron star magnetosphere (Egorov &Postnov 2009), annihilating black holes (Keane et al. 2012),collapses of supermassive rotating neutron stars (Falcke &Rezzolla 2013), and binary white dwarf mergers (Kashiyama et al. 2013). In this letter we discuss whether binary neu-tron star (NS-NS) mergers can explain the new results aboutFRBs, with a different picture than those adopted in previ-ous studies about coherent radio emission from NS-NS merg-ers (Lipunov & Panchenko 1996; Hansen & Lutikov 2001;Pshirkov & Postnov 2010; Lutikov 2013).
2. Short Duration Radio Emission from Binary NeutronStar Mergers
Electromagnetic (EM) wave signatures from NS-NS merg-ers have been widely investigated in the literature (e.g.,Metzger & Berger 2012). Two popularly discussed emis-sion mechanisms, i.e., radioactivity of ejected material (Li &Paczy´nski 1998; Metzger et al. 2010; Roberts et al. 2011)and afterglows by energetic outflow interacting with surround-ing medium (Nakar & Piran 2011; Shibata et al. 2011; Piranet al. 2013), predict much longer time scales than msec andhence they are not relevant to FRBs. Rather, coherent ra-dio emission from neutron star magnetosphere like isolated ra-dio pulsars seems more plausible. Hansen & Lyutikov (2001)and Lyutikov (2013) considered pre-merger coherent emissionfrom interacting magnetosphere of a binary consisting of a re-cycled, weak magnetic field neutron star and a slowly rotating,strong field one, before their rotations are synchronized to thebinary period (see also Lipunov & Panchenko 1996). The ra-dio flux predicted by Hansen & Lyutikov (2001) is much lowerthan those of FRBs, even if a very strong magnetic field ( G) is assumed. The flux estimated by Lyutikov (2013) is closerto the FRB flux, but it seems difficult to reconcile the predictedtime evolution ∝ ( − t ) − / with the observed short duration,where − t is the time before a merger whose minimum is ∼ msec.Theoretically it is expected that rotations of neutron stars Totani [Vol. ,are not tidally locked to the binary period until the last stage ofmerger when tidal disruption starts (Bildsten & Cutler 1992).Therefore strong coherent emission by rotation of individualneutron stars in a binary is not expected during gravitationalinspiral. However, at some point in the last stage of a merger,their magnetic field configuration should be synchronized withthe binary rotation, and coherent radio emission is expectedby magnetic braking of a misaligned rotating magnetic dipole,or plasma effect in the magnetosphere, in a similar way to iso-lated radio pulsars. If the synchronization occurs before a com-pletely merged object forms, the radiation would come fromthe original magnetic dipole of a neutron star. Instead, a mag-netic field of a merged object may be responsible for the ra-dio emission, and in this case magnetic field strength may beamplified by differential rotation (Pshirkov & Postnov 2010;Shibata et al. 2011).Because of the strong dependence of the magnetic breakingenergy loss rate on rotation period ( ˙ E ∝ P − ), the luminos-ity should sharply increase with the synchronization of mag-netic fields, and such coherent emission will continue until themerged neutron stars form a black hole (BH). Thus, this ra-diation mechanism seems favorable to explain the msec scaleduration of FRBs. The expected energy loss rate by magneticbraking can be estimated from the standard magnetic dipoleradiation formula, using typical magnetic field strength and ra-dius of a neutron star, but with binary orbital period at the timeof coalescence, i.e., about milliseconds: ˙ E = − . × (cid:18) B . G (cid:19) (cid:18) R
10 km (cid:19) × (cid:18) P . (cid:19) − erg s − . (1)Pshirkov & Postnov (2010) also considered coherent emis-sion by magnetic breaking energy loss, but they considered astrongly amplified magnetic field ( ∼ G) to explain the lu-minosity ( ∼ − erg/s) of short gamma-ray bursts (GRBs)that are much brighter but rarer than FRBs. We show belowthat FRBs can be explained without strong B field amplifi-cation, though a significant fraction of NS-NS merger eventsshould produce FRBs.
3. Rate and Expected Radio Flux
The rate of FRBs is estimated to be . +0 . − . × day − sky − (Thornton et al. 2013), which istranslated into a rate per unit comoving volume of . +1 . − . × yr − Gpc − to the comoving distance D comv =3.3 Gpc corresponding to maximum redshift of z max = 1 . Thisrate is statistically consistent with the “plausible optimisticestimate” of NS-NS mergers, ∼ yr − Gpc − , as reviewedby Abadie et al. (2010). The FRB rate estimated from the fourevents is still statistically highly uncertain. Choosing a slightlylarger value of z max will further reduce the rate in proportionto D − . It should be noted that this comparison does nottake into account the cosmological effects (the cosmologicaltime dilation and merger rate evolution). Increase of themerger rate by a factor of ∼ from z = 0 to 1 is reasonablefrom the cosmic star formation history (Totani 1997; Dominik et al. 2013), which is a bigger effect than the cosmologicaltime dilation that reduces the observed rate by ∝ (1 + z ) − ,making the FRB rate closer to the standard “realistic” estimateof NS-NS mergers ( yr − Gpc − ). Therefore the observedFRB rate is consistent with the NS-NS merger scenario, butthe fraction of NS-NS mergers producing observable FRBsmust be of order unity.The coherent radio emission discussed above may be ob-served from most of the merger events, if the emission is notstrongly beamed. A beaming fraction Ω / (4 π ) of order unity isnot unreasonable given the theoretical uncertainty about beam-ing of pulsar radio emission (e.g., Kalogera et al. 2001), where Ω is the total opening solid angle of radio emission. A di-rect, purely observational estimate based on statistics of associ-ations between pulsars and pulsar-powered nebulae indicates abeaming fraction of ∼
60% for young pulsars (Frail & Moffett1993).Since the physics of coherent radio emission from pulsars ispoorly understood (Lyubarsky 2008), we discuss the expectedradio flux in terms of the ratio ǫ r of the radio luminosity νL ν to the total energy loss rate | ˙ E | . Although there is a large scat-ter of ǫ r for isolated radio pulsars in our Galaxy, we choose atypical value of ǫ r = 10 − (Taylor et al. 1993; Manchester etal. 2005) at the rest-frame frequency corresponding to the ob-served frequency ν obs = 1.4 GHz. Using a luminosity distance D lum to z = 0 . , we get F ν = 1 ν obs ǫ r | ˙ E | πD = 0 . (cid:16) ǫ r − (cid:17) (cid:18) D lum . (cid:19) − × (cid:18) B . G (cid:19) (cid:18) R
10 km (cid:19) (cid:18) P . (cid:19) − Jy . (2)Therefore, the observed FRB fluxes ( ∼ ǫ r ∼ − , ora modest amplification of magnetic field strength to B ∼ G, but a very strong magnetic field such as G is not nec-essary if ǫ r is similar to those for isolated radio pulsars. Ifmagnetic fields of both neutron stars before a merger are muchweaker than G as a result of magnetic field decays, am-plification in a merged object would be required, though decayof magnetic fields in neutron stars is still highly uncertain (e.g.,Mukherjee & Kembhavi 1997).
4. Discussion
Several predictions and implications can easily be derivedfrom the hypothesis proposed here.The NS-NS merger rate must be close to the optimistic (butstill plausible) estimate, which is certainly a good news to grav-itational wave astronomy. The “plausible optimistic estimate”of NS-NS merger rate in Abadie et al. (2010) is still one or-der of magnitude lower than the current upper limit (Abadieet al. 2012), but such a high rate predicts a detection within afew years in the early commissioning phase of the AdvancedLIGO, whose ultimate detection rate would be ∼
400 yr − to ∼
200 Mpc (Abadie et al. 2010; Aasi et al. 2013). Typicalradio flux of FRBs at 200 Mpc would be about 100 Jy, thougha large scatter of radio flux from event to event is expected byvariation of ǫ r , as inferred from radio pulsars. An importanto. ] FRBs from NS-NS mergers 3advantage of FRBs compared with longer time-scale EM sig-nals of NS-NS mergers is that FRBs tell us the exact time ofcoalescence. If a nearby/bright FRB sample is constructed byfuture radio transient surveys, searching for gravitational wavebursts correlated with FRBs would significantly improve theeffective sensitivity of gravitational wave detectors, allowingto detect more distant mergers. Another advantage of FRBsfor gravitational wave astronomy is that they are expected tobe observable for most of NS-NS merger events, in contrast toe.g., short GRBs.If host galaxies are identified for FRBs, they should includeearly type galaxies that are not star forming, while the SGR orsupermassive neutron star scenarios predict only star-forminggalaxies. Since FRBs can be observed to more distant universethan gravitational wave bursts, the cosmological rate evolutionof NS-NS mergers and its relation to host galaxy evolution maybe studied in the future, which would be complementary toshort GRBs (if they are also produced by NS-NS mergers).Detectability of FRBs in other wavelength is also of interest.Pulsed gamma-ray luminosity of pulsars is typically ∼ %of spin-down luminosity (Abdo et al. 2010), and msec du-ration gamma-ray emission from FRBs may be detected byGRB satellites. Assuming ǫ γ /ǫ r = 10 for the gamma-rayband, a typical radio flux of 0.5 Jy at 1.4 GHz is correspond-ing to a gamma-ray flux of νF ν ∼ × − erg cm − s − ,which is much fainter than the typical Swift trigger threshold of ∼ − erg cm − s − in 15–150 keV (Sakamoto et al. 2011).Note that the flux threshold for msec duration bursts shouldbe much higher than this (T. Sakamoto, a private communica-tion). The 50–300 keV flux threshold of BATSE GRBs in the64 msec trigger window is ∼ − erg cm − s − (Fishman etal. 1994), and FRBs of 1 msec duration must be very close ( ∼ Mpc) to be detected by this trigger condition, but the expectedevent rate in such a small volume is extremely small. A searchoptimized for msec duration bursts in the past GRB data maybe interesting.If short GRBs are also produced by NS-NS mergers, theirsmall rate ( ∼
10 yr − Gpc − , Coward et al. 2012) comparedwith FRBs indicates that only a tiny fraction of NS-NS mergerevents produce observable short GRBs. This is possible if shortGRBs are strongly beamed, and/or they are produced by rarerevents such as large mass ratio binaries, mergers resulting in ahypermassive neutron star (HMNS) supported by rotation, orNS-BH/BH-BH mergers (Shibata & Taniguchi 2006; Faber &Rasio 2012). The beaming-corrected estimates of short GRBrate can be as high as ∼ − Gpc − (Coward et al. 2012;Enrico Petrillo et al. 2013), and if this is correct, about 10% ofNS-NS merger events are producing short GRBs to a certaindirection. On the other hand, our hypothesis predicts that mostof short GRBs must be associated with FRBs. The time delayby dispersion is about 1 second at GHz bands, but longer timedelay at lower frequencies may allow to detect FRBs by follow-up searches after short GRBs (Lipunova et al. 1997; Pshirkov& Postnov 2010).Sub-msec scale fine temporal features are difficult to see inthe four events of Thornton et al. (2013), because of dispersivesmearing in the frequency-integrated flux and scattering tailsproduced by propagation in intergalactic medium. Future hightime resolution observations of bright/nearby FRBs may reveal quasi-oscillatory behavior, reflecting binary orbital period orrotation rate of merged objects, though numerical studies arenecessary to make quantitative predictions. The observed shortduration implies that merged neutron stars should promptlyform a black hole on a dynamical time scale. This pictureis consistent with the latest numerical simulations of NS-NSmergers, but a fraction of merger events may form a HMNSthat survives for a time scale longer than milliseconds beforecollapsing into a black hole (Hotokezaka et al. 2011; Faber &Rasio 2012). Such a HMNS may radiate a pulsar-like periodiccoherent emission during its lifetime, and the fraction of suchrelatively long FRBs may give constraints on the mass distri-bution of NS-NS binaries and the equation of state at nucleardensities.The author would like to thank Y. Itoh, K. Kashiyama, N.Kawanaka and T. Sakamoto for useful comments. References
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