A model for the repeating FRB 121102 in the AGN scenario
Florencia L. Vieyro, Gustavo E. Romero, Valentí Bosch-Ramon, Benito Marcote, María V. del Valle
aa r X i v : . [ a s t r o - ph . H E ] A p r Astronomy & Astrophysics manuscript no. 30556˙Vieyro c (cid:13)
ESO 2018September 27, 2018
A model for the repeating FRB 121102 in the AGN scenario
F. L. Vieyro , , G. E. Romero , , V. Bosch-Ramon , B. Marcote , and M. V. del Valle Departament de F´ısica Qu`antica i Astrof´ısica, Institut de Ci`encies del Cosmos (ICCUB), Universitat de Barcelona,IEEC-UB, Mart´ı i Franqu`es 1, E08028 Barcelona, Spain Instituto Argentino de Radioastronom´ıa (IAR, CCT La Plata, CONICET; CICPBA), C.C.5, (1984) Villa Elisa,Buenos Aires, Argentina Facultad de Ciencias Astron´omicas y Geof´ısicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900, LaPlata, Argentina Joint Institute for VLBI ERIC, Postbus 2, 7990 AA Dwingeloo, The Netherlands Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, GermanyPreprint online version: September 27, 2018
ABSTRACT
Context.
Fast radio bursts, or FRBs, are transient sources of unknown origin. Recent radio and optical observations haveprovided strong evidence for an extragalactic origin of the phenomenon and the precise localization of the repeatingFRB 121102. Observations using the Karl G. Jansky Very Large Array (VLA) and very-long-baseline interferometry(VLBI) have revealed the existence of a continuum non-thermal radio source consistent with the location of the burstsin a dwarf galaxy. All these new data rule out several models that were previously proposed, and impose stringentconstraints to new models.
Aims.
We aim to model FRB 121102 in light of the new observational results in the active galactic nucleus (AGN)scenario.
Methods.
We propose a model for repeating FRBs in which a non-steady relativistic e ± -beam, accelerated by animpulsive magnetohydrodynamic (MHD)-driven mechanism, interacts with a cloud at the centre of a star-forming dwarfgalaxy. The interaction generates regions of high electrostatic field called cavitons in the plasma cloud. Turbulence isalso produced in the beam. These processes, plus particle isotropization, the interaction scale, and light retardationeffects, provide the necessary ingredients for short-lived, bright coherent radiation bursts. Results.
The mechanism studied in this work explains the general properties of FRB 121102, and may also be appliedto other repetitive FRBs.
Conclusions.
Coherent emission from electrons and positrons accelerated in cavitons provides a plausible explanation ofFRBs.
Key words.
Radio continuum: general - Galaxies: dwarf - Galaxies: jets - Radiation mechanisms: non-thermal
1. Introduction
Fast radio bursts (FRBs) are bright transient flashes ofcosmic origin with durations of a few milliseconds de-tected at radio wavelengths. They were discovered byLorimer et al. (2007) and found to exhibit large disper-sion measures (DM). These dispersions are in excess of thecontribution expected from the electron distribution of ourGalaxy, hence suggesting an extragalactic, cosmological ori-gin. Most of the eighteen known bursts have been detectedso far with the Parkes radio telescope (e.g. Thornton et al.2013, Petroff et al. 2016). Only a couple of them were foundwith the Arecibo and Green Bank telescopes (Spitler et al.2014, 2016, Masui et al. 2015).The physical origin of FRBs remains a mystery. The pu-tative extragalactic distances and the extremely rapid vari-ability imply brightness temperatures largely beyond theCompton limit for incoherent synchrotron radiation (e.g.Katz 2014). Thus a coherent origin of the radiation seemscertain. Models proposed so far can be divided into those ofcatastrophic nature, in which the source does not survive
Send offprint requests to : F. L. Vieyroe-mail: [email protected] the production of the burst, and those that can repeat. Anon-unique FRB population is possible, with different typesof sources, as is the case with the gamma-ray bursts (seeKatz 2016b, for a review).The unambiguous identification of the counterparts ofFRBs at other wavelengths is a very difficult task because ofthe extremely short life span of the events at radio frequen-cies, their appearance from random directions in the sky,and the large uncertainties in the determination of theirprecise positions. A huge step towards the clarification ofthe origin and nature of these happenings was the recent di-rect localization of an FRB and its host by Chatterjee et al.(2017). These authors achieved the sub-arc second localiza-tion of FRB 121102, the only known repeating FRB, usinghigh-time-resolution radio interferometric observations thatdirectly imaged the bursts. They found that FRB 121102originates very close to a faint and persistent radio sourcewith a continuum spectrum consistent with non-thermalemission and a faint optical counterpart. This latter opti-cal source has been identified by Tendulkar et al. (2017) asa low-metallicity, star-forming, dwarf galaxy at a redshiftof z = 0 . were provided by Marcote et al. (2017) through very-long-baseline radio interferometric observations. Marcote et al.were able to simultaneously detect and localize both, thebursts and the persistent radio source, on milliarcsecondscales. The bursts are found to be consistent with the loca-tion of the persistent radio source within a projected linearseparation of less than 40 pc, 12 mas angular separation,at 95% confidence, and thus both are likely related. Theunambiguous association of FRB 121102 with persistentradio and optical counterparts, along with the identifica-tion of its host galaxy, impose, for the first time, very strictconstraints upon theoretical models for FRBs, beyond thegeneral limits imposed by variability timescales and energybudgets.Romero et al. (2016) show that under certain condi-tions, a turbulent plasma hit by a relativistic jet can emitshort bursts consistent with the ones observed in FRBs.In this paper we apply the latter model to FRB 121102,based on the idea that the multiple observed bursts are theresult of coherent phenomena excited in turbulent plasmaby the interaction of a sporadic relativistic e ± -beam or jet,which originates from a putative somewhat massive blackhole in the central region of the observed dwarf galaxy andambient material. Our model can account for the differentproperties known so far for FRB 121102 and can be testedthrough observations of other repetitive FRBs. In what fol-lows we first detail the known features of FRB 121102 andits host that are relevant for the involved physics (Sect. 2),then we describe our model (Sect. 3) and its application toFRB 121102 (Sect. 4), and we finally offer some discussionand our conclusions (Sects. 5 and 6).
2. Main facts about FRB 121102
Fast radio burst 121102 is the only known source of itsclass that presents repeated bursts with consistent DMand sky localization (Spitler et al. 2014, 2016, Scholz et al.2016). This implies that the source is not annihilated bythe production mechanism of the bursts. Most of the in-dividual bursts have peak flux densities in the range 0 . . . × ergs − at 1.7 GHz. Its associated brightness temperature is ap-proximately 2 . × K, meaning more than twenty threeorders of magnitude above the Compton limit, clearly indi-cating that the emission is coherent.The radio observations reported by Chatterjee et al.(2017) and Marcote et al. (2017) show a compact sourcewith a persistent emission of approximately 180 µ Jy at1.7 GHz, implying a radio luminosity of approximately3 × erg s − , with a bandwidth of 128 MHz. No signifi-cant, short-term changes in the flux density occur after the arrival of the bursts. Its 1–10-GHz radio spectrum is flat,with an index of α = − . ± . S ν ∝ ν α . The projectedlinear diameter of the persistent radio source is measuredto be less than 0.7 pc at 5.0 GHz, and it is found to bespatially coincident with the FRB 121102 location withina projected distance of 40 pc. This kind of a close prox-imity strongly suggests that there is a direct physical linkbetween the bursts and the persistent source. The observedproperties of the persistent source cannot be explained bya stellar or intermediate black hole, either in a binary sys-tem or not, a regular supernova remnant (SNR), or a pulsarwind nebula such as the Crab (see Marcote et al. 2017, fora detailed discussion).There is a 5- σ X-ray upper limit in the 0.5-10 keVband for the radio source of L X ≤ . × erg s − (Chatterjee et al. 2017). Hence, the ratio of the radio tothe X-ray flux is log R X > − .
4, consistent with those ob-served in low-luminosity AGNs (Paragi et al. 2012).The host galaxy of the bursts and the persistent radiosource is a dwarf star-forming galaxy with a diameter of lessthan 4 kpc and a high star-forming rate of 0 . ⊙ yr − .The stellar mass of the galaxy is estimated to be in therange 4–7 × M ⊙ . Current evidence supports the ideathat the supermassive black hole-to-galaxy mass ratio lieswithin 0 . − .
05 (Targett et al. 2012); there are few ex-ceptions for which this ratio can be as high as 0 .
15 (e.g.van den Bosch et al. 2012). Therefore, the presence of a su-permassive black hole with mass M BH > M ⊙ in the hostgalaxy of FRB 121102 is unlikely, because it would alreadyhave a mass larger than, or of the order of, the total stellarmass of the galaxy. This leads to an estimation of the massof the putative black hole of M BH ∼ –10 M ⊙ .
3. Model and emission mechanism
A model for FRB 121102 should be capable of accountingfor the fast bursts, their plurality, and the compactness ofthe continuum radio source. In addition, in the context ofan AGN, the model should account for the modest energybudget inferred from the moderate M BH -range allowed, andthe stringent X-ray upper limit. A young supernova rem-nant powered by a strongly magnetized and rotating neu-tron star faces at least three major problems: the constantDM observed in the bursts from 2012 to 2016, the lack ofchange of the radio flux due to rapid expansion expected inall very young SNRs, and finally the absence of an X-raycounterpart that in the case of a pulsar-powered remnant isunavoidable (see, e.g. Waxman 2017). We favour, instead, amodel based on interactions between a relativistic (magne-tized) e ± -jet launched by a moderately massive black holewith material in the centre of the host galaxy. We assumed that the galaxy where FRB 121102 occurshosts a low luminosity active galactic nucleus (AGN), assuggested by Chatterjee et al. (2017). Accretion onto thecentral black hole results in the launching of a relativisticjet, which we assume takes place in an episodic fashion. Thisdiscontinuous jet may not be resolvable at radio frequen-cies; the outflow may become smooth on pc-scales, however,and be responsible for the observed persistent radio sourceof size < . hand, the sporadic jet can interact with material accumu-lated on its way while jet activity was off. For example,at spatial scales of approximately 10 cm from a centralblack hole of M BH ∼ M ⊙ (see below), clouds movingat approximately Keplerian velocities could fill the channelopened by a previous jet on day timescales.The interaction between an episodic ejection with acloud can take place without a cloud penetration phase intothe jet. In fact, avoiding this kind of a phase is required,because it would last much longer than the actual FRB du-ration for any reasonable parameter choice. Another condi-tion for the interaction is that the cloud boundaries or edgesmust be sharp enough for a quick jet-cloud effective inter-action. In principle, the thermal or the ram pressure of theenvironment confining the cloud can provide this sharpen-ing. For the same reason, the jet-leading edge should be alsosharp, whereas the magnetic field should be weak enoughso as to avoid rapid e ± -beam isotropization. These two con-ditions can naturally occur in the scenario adopted here.A standard ejection mechanism in AGNs is the produc-tion of magnetized jets from accreting rotating black holes(Blandford & Znajek 1977), in which the innermost regionsof jets consist of strongly magnetized, relativistic e ± -beams.No significant presence of protons is expected at the baseof this kind of a jet, although barions are thought to be en-trained farther out ( see, e.g. Perucho 2014, and referencestherein).The different ejections of the intermittent jet shouldhave a configuration akin to that of a relativistic ejec-tion driven by an impulsive magnetohydrodynamic (MHD)mechanism, meaning a weakly magnetized thin leading shellmoving with a high Lorentz factor driven by strong mag-netic pressure gradients, followed by the strongly magne-tized jet bulk (Komissarov 2011, Granot et al. 2011). Thiskind of impulsive MHD acceleration mechanism allows theejecta to achieve higher bulk Lorentz factors, γ ≥ e ± -beam. Thus, the electron and beam Lorentz fac-tors can be considered equal in the laboratory frame (LF), γ . When this ultra-relativistic jet-leading edge reaches thetarget cloud, electrons propagate in a straight line untilelectric and magnetic fields cause a significant deflection.This stage, in which electrons move in quasi-straight tra-jectories within the cloud, presents suitable conditions forhighly beamed, strong coherent emission, as long as theparticles’ mean free path is not too short (see below). The penetration of a relativistic e ± -beam into a densertarget plasma results in the formation of concentrationsof electrostatic plasma waves called cavitons. The elec-trons crossing this caviton-filled region produce the co-herent emission (see Sec. 3.2.2). This emission is stronglybeamed towards the observer if the line of sight coincideswith the electron direction of motion.When an electron crosses a caviton, it emits a pulse ofBremsstrahlung-like radiation within a solid angle of ap-proximately 1 /γ in its direction of motion, such as the observer direction of motion. This yields a beaming factorfor the radiation of approximately γ . When particle de-flection is included, however, the beaming factor towardsthe initial electron direction gets reduced. For instance, as-suming an uniform magnetic field B , the average beamingfactor along a distance covered by the electron equal to itsgyro-radius ( r g = γm e c /qB ) yields a factor approximately γ instead of γ . It should be noted that r g is the electronmean free path in the case of an uniform B -field.In addition to relativistic geometric beaming, light re-tardation effects also strongly enhance the radiation lumi-nosity in the electron direction of motion, because the ap-parent time in which electrons radiate is shortened by afactor of 1 / γ with respect to the LF. In our scenario,this factor does not need to be averaged along the electrontrajectory. The reason for this is that most of the radia-tion towards the observer is actually produced before theelectron is deflected by an angle & /γ .Both effects, the averaged beaming and the light retar-dation, lead to an enhancement of the apparent luminositywhen looking at the beam on axis by a factor approximately γ compared to the LF luminosity. It should be noted thatthe factor γ is actually a lower limit. This is due to theassumption of an uniform B -field, which produces the elec-tron strongest possible deflection. In the case of negligibleelectron deflection, the apparent luminosity would be en-hanced by δ ≈ γ , where δ D is the Doppler factor. Thisis because the beaming factor would be constant along thestraight electron trajectory, and of the order of γ . Collective effects lead to coherent radiation, enhancing theemitted power (Weatherall & Benford 1991). For a uniformjet, the emission between any two electrons scattered by acaviton will not present any phase coherence. If, on thecontrary, the jet presents density fluctuations that are cor-related, then the radiation can be coherent, and thereforestrongly enhanced. This correlation in the density fluctua-tions is the result of turbulence generated by the couplingbetween the background plasma and the beam: electronsfrom the beam perturb the plasma, producing the two-stream instability, then cavitons form, and beam-electronbunching is also generated (Weatherall & Benford 1991).Turbulence development should not significantly affect thecold nature of the beam as long as the turbulence-associatedelectron velocities do not themselves become relativistic inthe flow frame. Caviton formation takes place on very shorttimescales, ≪ The residual magnetic field dragged along by the jet-leadingthin shell eventually deflects the energetic electrons prop-agating through the target plasma. The interpenetrationof the jet-leading thin shell with the target cloud leads tothe formation of a contact layer between both, the regionin which the coherent emission is produced, in which elec- For this very same reason, the effective beaming factor is ∼ γ rather than ∼ γ , for source statistics purposes. 3ieyro, Romero, Bosch-Ramon, et al.: Model of a repeating fast radio burst trons tend to isotropize. This layer is approximately at restin the LF, and a strong enhancement of the perpendicular B -component ( B ⊥ ) dragged by the beam is expected there.For this reason, it seems natural to assume that the meanfree path of the electrons in the interpenetration region willbe approximately r g , with B ∼ B ⊥ . On the other hand,the electrostatic field E inside the cavitons, expected tobe randomly oriented, will induce pitch-angle diffusion tothe emitting electrons. The value of E cannot be too high,because the mean free path of electrons should be largerthan the caviton size, meaning r g > D , if the mechanismis to work. More precisely, r g ≫ D if pitch-angle diffusionis realized. For the same reason, the magnetic field in thebeam cannot be too high, and a similar constraint appliesto the cloud magnetic field, the geometry of which may bebetween a strongly ordered B -field and the chaotically ori-ented E -field. It is also worth noting that, even if the elec-tron mean free path in the interpenetration region is > D ,it should also be long enough as to ensure that the emittingvolume is sufficiently large to produce the observed fluxes.The time required for particle isotropization in the beamis δt iso & r g /c . After this time, the perturbation originatedby the jet-cloud interaction can affect the incoming elec-trons even before it reaches the cloud, isotropizing themand the electromagnetic fields they carry. At this stage, theisotropized electrons may still interact with cavitons aroundthe jet-cloud contact discontinuity through some level ofjet-cloud interpenetration. However, the related coherentemissivity is strongly reduced by a factor of & /γ (seeSect. 3.2.1). Moreover, as the bulk of the jet, which is moremagnetized than its leading edge, reaches the cloud, the ex-pected higher magnetic field filling the region can stop thecoherent radiation completely by making the electron meanfree paths smaller than the cavitons. We conclude then that δt iso determines the duration of the coherent emission phasefor electrons from the jet-leading thin shell interacting si-multaneously with the cloud, such that δt obs ∼ & δt iso . Despite δt iso playing a major role in the FRB scenario pro-posed here, it seems likely that the cloud will present anirregular surface. Assuming that ∆ r is the relevant irreg-ularity scale of the target cloud, the ultra-relativistic thinshell must cover a distance ∆ r in a time δt cross ≈ ∆ r/c inthe LF for full interaction. Unless B is extremely low, it willbe the case in our scenario that δt iso ≪ r could determine the event duration. This implies that,for the observer, δt obs ≈ δt cross / γ ≈ ∆ r/ cγ . r j / cγ ,where ∆ r ≈ r j is the largest effective irregularity scale,and light retardation effects have been taken into account,meaning: δt obs ≈ δt cross / γ . Therefore, unless the mag-netic field is very low, it is the case that δt iso /c ≪ & M BH / M ⊙ ) s. Even if the jet ejection lasts for ≫ The spectrum of the coherent emission presents two maincomponents, a line at the plasma frequency ω e , and a broad-band tail that inherits the power-law behaviour of the den-sity fluctuation spectrum of the e ± -beam. The existence ofthis type of emission is well known from controlled plasmaexperiments (e.g. Kato et al. 1983, Masuzaki et al. 1991,Benford & Weatherall 1992, Ando et al. 1999).The broad-band component of the spectrum extendsfrom the plasma frequency to ω max = 2 γ c/D , which isthe highest frequency emitted by electrons with Lorentzfactor γ being scattered by cavitons of size D . The size D of the cavitons induced in the plasma by the rela-tivistic e ± -beam can be estimated as approximately 15 λ D (Weatherall & Benford 1991), where λ D is the Debye lengthof the plasma, such that λ D = 6 . p T c /n c cm, with [ T c ] =K and [ n c ] = cm − .For a e ± -beam interacting with a denser target plasma,the required condition for collective emission is q = n b /n c ≥ .
01, with n b and n c being the beam and tar-get densities, respectively. The radiated power per elec-tron in the LF in the form of coherent emission is givenby (Weatherall & Benford 1991): P e = E σ T c π n b πD π f " (cid:18) ∆ n b n b (cid:19) .
24 ln (cid:18) γ cDω p (cid:19) , (1)where σ T is the Thomson cross-section, ∆ n b /n b is thefluctuation-to-mean-density ratio of the relativistic elec-trons, and f is the fraction of the cloud volume that is filledwith cavitons, for which we adopted f = 0 . n b πD /
3, is the num-ber of electrons inside a caviton, and it is known as thecoherence factor (Weatherall & Benford 1991).The first term in Eq. (1) represents the power emitted atthe plasma frequency, whereas the second term is the poweremitted in the tail of the spectrum. Emission at the plasmafrequency is likely to be absorbed (Weatherall & Benford1991), hence the relevant term is the one associated with thebroad-band emission. It is natural for a density fluctuationspectrum with power-law behaviour to arise as the result ofturbulence in the plasma, for example a Kolmogorov spec-trum has an index α = − /
3. Density fluctuations show alarge range of variation, and can reach values of order unity,meaning ∆ n b /n b ∼ νP ν ∝ ν α +1 , and the power emitted in the broad-band com-ponent is comparable to the power emitted at the line, withmost of the former being radiated in the low-frequency partof the power-law spectrum. Thus, although the radiationproduced at the plasma frequency may be easily absorbedby the emitting plasma, the radiation at slightly higher fre-quencies has a comparable luminosity. The total power P t issimply the power emitted per particle times the number ofrelativistic electrons inside the region filled with cavitons.
4. Application to FRB 121102
In the following, we consider a cloud with an irregular sur-face with irregularity scale ∆ r ≈ r j and total jet-interactionsection π r (see Fig. 1). As explained in Sect. 3.2, ∆ r and, consequently, r j are constrained by the duration of the event: ∆ r ≈ r j ≈ × (cid:16) γ (cid:17) cm . (2)Assuming a half-opening angle of a few degrees, this kindof an r j -value would correspond to approximately 10 R G ∼ cm for a 10 M ⊙ black hole, where R G = GM/c . Blackhole Jet Cavitons Cloud (cid:1) R e Observer
Fig. 1.
Schematic representation of the model.The coherent emission is broad-band, extending fromthe plasma frequency ω e up to ω max = 2 γ c/D . The ob-served frequency of 1 . ω e / π < . < ω max / π . The first condition, ω e / π < . n c ≤ × cm − , where thesubscript c indicates the region where cavitons form.Because the emission radiated at the plasma frequencywill likely be absorbed, we adopted a lower value of theplasma density, n c = 10 cm − . With this choice, thepeak of the emission is at ν = 900 MHz. If one adopts aKolmogorov spectrum for the turbulence, νP ν ∝ ν − / , theluminosity at the observed frequency will be approximately70% of the luminosity of the peak.It is worth mentioning that calculations in the weakturbulence regime suggest that ambient plasma might also,in principle, produce an attenuation of the coherent sig-nal by Raman scattering (e.g. Levinson & Blandford 1995).However, experiments show that these effects are sup-pressed in the strong turbulence case, where there is no the-ory available (Benford & Lesch 1998, Romero et al. 2016).For the coherent emission to escape, free-free absorptionshould be also minor within the cloud. Adopting 6 × cmfor the cloud size and n c = 10 cm − , the cloud is opticallythin as long as its (pre-interaction) temperature is & K;in principle this is possible because the virial temperatureat 10 R G is approximately 10 K.The second condition, 1 . < ω max / π , results in: γ p T c /n c ≥ . , (3)with [ T c ] = K and [ n c ] = cm − . The impact of the jet canheat the cloud up to a temperature of T c = qm e c γ/k B .For the adopted n c -value, and a density ratio of q = 1, T c = 6 × K; this T c -value together with the adoptedone for n c fulfils Eq. (3). Cavitons formed in a plasma withthese characteristics have a size of D ∼
800 cm; the numberof electrons inside cavitons results in 2 × . The obtainedvalue for D is similar to the values found in particle-in-cell(PIC) numerical simulations (e.g. Beall et al. 2010). It isworth recalling that coherent emission is only possible if r g is larger than the size of cavitons, as discussed in Sect.3.2.3.The jet power can be obtained from the jet particledensity in the LF at the interaction location, n j , through the relation: γn j m e c ≈ L j πr c . (4)Using the radius jet constrained by the event duration givenby Eq. 2, Eq. (4) yields a jet power L j ∼ × erg s − .When electrons enter the cloud, they strongly radiatetowards the observer until they isotropize, which occurs ona time δt iso & r g /c ∼ × − γ/B s. Assuming that themagnetic energy density is a fraction ξ of the jet kineticenergy density, the magnetic field in the LF can be obtainedfrom: B , eq π = 12 ξL j πr . (5)At the interaction location, this yields an equipartition field(i.e. ξ = 1) of B j , eq ∼ ξ <
1) in the interactingshell, as explained in Sect. 3.1; in particular, we consider B = 5 × − B j , eq .To obtain E in Eq. (1), we imposed the condition thatthe pitch-angle diffusion timescale, given by t diff = λ E Dc , (6)with λ E = γm e c /eE , should be longer than δt iso = r g /c ,as discussed in Sect. 3.2.3). This results in E ∼
45 G,yielding W = E / πn c k B T c ∼ − , which is within therange values obtained in numerical simulations (Henri et al.2011).Typically, δt iso << δt cross , and therefore not all elec-trons will radiate simultaneously. By the time the jet-leading edge has crossed all of the cloud irregular surface,the electrons that interacted first are already isotropizedand their coherent emission has been suppressed. To derivethe observer luminosity, the LF luminosity (Eq. 1) must becorrected by a factor of δt iso /δt cross to account for a smallersimultaneously emitting volume. In addition, to account forlight retardation effects, another factor t cross /t obs must beconsidered. All this renders a factor of δt iso /δt obs that forthe adopted values of ∆ r and B is & × − . In addi-tion to t iso /t obs , Doppler boosting must be considered toobtain the observer luminosity, as explained in Sect. 3.2;this results in: L obs ≈ γ (cid:16) P e N e (cid:17) δt iso δt obs , (7)where N e is the number of electrons in the volume of theemitting region, meaning approximately π r r g .Using the adopted parameter values, the predicted FRBobserver luminosity is approximately 3 × erg s − , com-parable to the luminosity of burst B -values, ∆ r < r g , inwhich case δt iso and not δt cross would determine δt obs . Thiswould correspond to a plane jet-cloud interface, in whichcase no weighting by δt iso δt obs should be applied.Another possibility that cannot be ruled out is thatthe transition region between the unisotropized, mean-ing unshocked, and the isotropized, meaning shocked,beam could be the coherent emitter (Weatherall & Benford An alternative to the scenario presented here, in which theFRBs occur at the onset of a jet’s ejections, is that of a jetchanging its direction (see Katz 2016a). Occasionally, thiswandering jet would intercept a cloud while pointing tothe observed and then producing an FRB. In that case, thetimescale of the event will be the time needed by the jetto change direction by 1 /γ rad while it is interacting withthe cloud. This situation resembles that of a lighthouse,in which the event duration is not affected by causalityconstraints.A lighthouse effect combined with coherent emissionfrom jet-target interactions cannot in principle be dis-carded, and dispenses us with the need to assume a dis-continuous jet with a sharp leading edge interacting withan irregular target. On the other hand, a modest magneticfield and a high Lorentz factor are still required. In fact,most of the details of the model given in Sect. 3 still holdin this alternative scenario, but now the crossing and theobserver timescales are the same.Nevertheless, there is drawback in the lighthouse sce-nario. The change in direction by 1 /γ rad of the emittingelectrons in just 1 ms requires that the properties of theleading thin shell substantially change along the jet axison a spatial scale of approximately 1 ms · c ∼ × cm,which is ≪ r j . This kind of a jet configuration is in princi-ple possible but requires the flow to be very cold, meaninga Mach number ≫ /γ . Otherwise, electrons will tend tohomogenize their properties on these small scales, and thevery short-scale jet-bending coherence will be lost. In addi-tion, the fast changes in direction require angular velocitiesof approximately 10 (100 /γ ) rad s − , which may not befeasible for a jet-launching engine that has already a size & M BH / M ⊙ ) light-second.The constraints mentioned can be relaxed for smallercentral engines and thus smaller black hole masses, al-though smaller black holes imply tighter energy limits. Ifthe source were super-Eddington, for example similar toSS 433, the energetics might fulfil the minimum require-ments (Katz 1980, 2016a, Kaufman Bernad´o et al. 2002),but this kind of a scenario requires a dedicated study.
5. Discussion
We propose that FRB 121102 and similar events are theresult of coherent radio emission produced by a relativis-tic, turbulent e ± -beam interacting with plasma cavitons.An advantage of this mechanism is that it might oper-ate in different scenarios involving relativistic jets. For in-stance, Romero et al. (2016) discuss possible settings in-volving long gamma-ray bursts and mini-jets produced bymagnetic reconnection inside a larger outflow. Even single-event FRB may be explained in the basic framework of the In the model discussed in Katz (2016a) the jet does notnecessarily intercept a cloud; in this case, the jet might sweepthrough the existing medium or the radiation might be producedinternally in the jet. proposed model as long as the recurrence time of the eventsis very long, depending on sensible factors such as beamorientation, Lorentz factor, propagation length within theplasma, and the interaction scale. Here, we investigate themechanism in the context of an extragalactic episodic jet in-teracting with the environment, to check whether the modelcan account for FRB 121102 in light of new observationalevidence. In what follows we further comment on a numberof important assumptions of the model.
The proposed scenario requires episodic jet launching.Episodic ejections are known to take place in several as-trophysical sources. The hydrogen ionization instability isresponsible for switches between periods of outburst andquiescence in dwarf novae. The state transition observed innumerous X-ray binaries is also proof of a variable accretionregime (e.g. Done et al. 2007). In fact, multiple variabilitytimescales are common for the radiation associated withgalactic and extragalactic jets. Non-steady jet productionmay be behind this variability and therefore render it asomewhat natural phenomenon, at least at the relativelysmall spatial scales relevant in our scenario, meaning ap-proximately 10 R G . At larger scales this sporadic jet ac-tivity does not affect the persistent radio source. As indicated, strongly magnetized sporadic ejections can beefficiently accelerated by a MHD-driven impulsive mech-anism to high bulk Lorentz factors such as γ ≥ . γ .
40 (Jorstad et al. 2005), and thehigher Lorentz factors invoked to explain the rapid TeV-variability observed in blazars (e.g. Barkov et al. 2012). Inthis context, the short timescale flares observed at TeV en-ergies would be associated with variable emission from theseshells, whereas the radio data would be associated with theemission from a larger scale, smoother flow with a lowerLorentz factor (Lyutikov & Lister 2010, Komissarov 2011).
Clouds from the AGN broad-line region (BLR) present den-sities of 10 − cm − at distances of 10 − R G to the central black hole (Peterson 2006, Risaliti et al.2011). The presence of material for jet interaction mightbe also related to the accretion phenomenon itself (e.g.Blandford & Begelman 1999, Begelman 2012). In our model, the observed continuum flat-spectrum radiosource would correspond to the synchrotron radiation of thejet, which is the result of the averaged intermittent ejec-tions. The synchrotron luminosity expected at radio wave-lengths for a jet with L j = 3 × erg s − can be roughlyestimated as (e.g. Bosch-Ramon 2015): L ( ∼ . ≈ η NT L j δ γ t esc t syn , (8)where η NT is the non-thermal-to-total energy density ratioin the emitter, δ D is the Doppler factor, and t esc and t syn are the electron escape and cooling times, respectively. Asdiscussed in Sect. 3.2.1, for a highly relativistic jet point-ing towards the observer, δ D ∼ γ . The jet magnetic fieldcan be estimated assuming again a certain value for theequipartition fraction ξ , not necessarily the same as in theFRB-emitting region. From all this, plus adopting a jet dis-tance to the black hole of z ∼ /γ = 0 . /γ ) rad, one obtains: L ( ∼ . ≈ × erg s − (cid:16) η NT − (cid:17)(cid:16) γ (cid:17) (cid:16) ξ − (cid:17) / . (9)This luminosity is well above the persistent radio lumi-nosity mentioned in Sect. 2, indicating that the scenariounder typical assumptions is consistent from the energeticpoint of view even when considering duty cycles of jet ac-tivity . The stellar mass of the galaxy is in the range 4–7 × M ⊙ (Tendulkar et al. 2017). Little is known about the ex-istence of massive black holes in these kinds of small galax-ies. If we extrapolate from the scaling relation given byReines & Volonteri (2015), determined in the range 10 ≤ M stellar / M ⊙ ≤ , we obtain a black hole mass of ap-proximately 10 M ⊙ , within the allowed range (see Sect. 2).Although most of the estimations of the masses for blackholes in the centre of galaxies are above 10 M ⊙ , there isevidence of the presence of black holes with masses of ap-proximately 10 M ⊙ in some AGNs (Papadakis 2004). Ifthis kind of a black hole accretes at 1% of the Eddingtonrate, its luminosity would be approximately 10 erg s − , avalue comparable to the one adopted in our model, and ofthe order of the X-ray upper limit. FRBs present an additional challenge concerning polar-ization. There is no evidence of polarized emission fromthe repeater FRB 121102 (Scholz et al. 2016); however,FRB 150807 presented linear polarization (Ravi & Lasky2014), whereas a high degree of circular polarization wasmeasured in FRB 140514 (Petroff et al. 2015). The radia-tion mechanism proposed in this work might produce linearpolarization in the presence of a magnetic field, whereas in-trinsic circular polarization is not expected (Benford 1992).
An analysis of the multi-wavelength non-thermal emissionassociated with the mechanism discussed for FRB 121102is under way and will be presented elsewhere. We can putforward however a general framework in which the cloudimpacted by the jet and the shock in the jet itself may lead to efficient particle acceleration, and to high-energyemission that could be detectable very briefly, seconds tominutes, if the beam is fast enough, even for modest en-ergetic budgets (see, e.g. Barkov et al. 2012, Bosch-Ramon2015).
6. Conclusions
The model proposed in this work, based on a mechanism ofcoherent emission in beam-excited plasma cavitons, is ableto explain the diverse properties of FRBs: the extragalacticorigin, the energy budget, the high brightness temperature,the repetitions with no apparent periodicity, and the coun-terparts and upper flux limits obtained in different wave-lengths. The very short duration of the events is explainedby the dynamical timescale of the process corrected by lightretardation effects, although the isotropization timescale ofthe beam particles plays also an important role, and maydetermine the event duration for very low magnetic fields.
Acknowledgments
The authors are grateful to Jordi Miralda-Escud´e forhis very useful comments and suggestions. This workwas supported by the Argentine Agency CONICET (PIP2014-00338) and the Spanish Ministerio de Econom´ıay Competitividad (MINECO/FEDER, UE) under grantsAYA2013-47447-C3-1-P and AYA2016-76012-C3-1-P withpartial support by the European Regional DevelopmentFund (ERDF/FEDER), MDM-2014-0369 of ICCUB(Unidad de Excelencia ‘Mar´ıa de Maeztu’), and the CatalanDEC grant 2014 SGR 86. V.B.R. also acknowledges finan-cial support from MINECO and European Social Fundsthrough a Ram´on y Cajal fellowship. This research has beensupported by the Marie Curie Career Integration Grant321520. M.V.d.V acknowledges support from the Alexandervon Humboldt Foundation.
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