A "Cosmic Comb" Model of Fast Radio Bursts

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by  Bing Zhang

PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
A “COSMIC COMB” MODEL OF FAST RADIO BURSTS
Bing Zhang
DepartmentofPhysicsandAstronomy,UniversityofNevadaLasVegas,NV89154,USA
ABSTRACT
Recent observations of fast radio bursts (FRBs) indicate a perplexing, inconsistent picture. We
proposeaunifiedscenariotointerpretdiverseFRBsobserved. Aregularpulsar,otherwiseunnoticeable
7 atacosmologicaldistance,mayproduceabrightFRBifitsmagnetosphereissuddenly“combed”bya
1 nearby,strongplasmastreamtowardstheanti-streamdirection. IftheEarthistothenightsideofthe
0
stream,thecombedmagneticsheathwouldsweepacrossthedirectionofEarthandmakeadetectable
2
FRB. The streamcouldbe an AGN flare,a GRB or supernova blastwave,a tidal disruptionevent, or

b evena stellarflare. Since it is the energyfluxreceivedby the pulsar ratherthanthe luminosityof the
e stream origin that defines the properties of the FRB, this model predicts a variety of counterparts of
F FRBs, including a possible connectionbetween FRB 150418andan AGN flare,a possible connection
between FRB 131104 and a weak GRB, a steady radio nebula associated with the repeating FRB
2
121102,and probably no bright counterparts for some FRBs.

] Subject headings: pulsar – radio continuum – radiation mechanism: non-thermal
E
H
1. INTRODUCTION 2014, 2016a; Wang et al. 2016) cannot interpret the re-
.
h peating FRB 121102. The previously favored super-
The origin of fast radio bursts (FRBs) remains a
p giant-pulse model (in analogy to nanoshots from the
mystery after one decade of observations (Lorimer et al.
- Crab pulsar) (Cordes & Wasserman 2016; Connor et al.
o 2007; Thornton et al. 2013; Petroff et al. 2015a;
2016) invokesnearby galaxynotat the cosmologicaldis-
r Champion et al. 2016; Masui et al. 2015; Keane et al.
t 2016; Spitler et al. 2016; DeLaunay et al. 2016; tances and therefore are challenged by the fact that
s
the repeater is located in a host galaxy at redshift
a Chatterjee et al. 2017). The distance scale of FRBs
[ is finally settled to the cosmological range (∼ Gpc) z =0.193(Tendulkar et al.2017)(butseeKatz2016a,b).
Themagnetargiantflaremodel(Popov & Postnov2010;
thanks to multi-wavelength follow-up observations that
2 Kulkarni et al. 2014; Katz 2016c) is in apparent con-
nail down the host galaxy of the repeating source
v flict with the non-detection of bright radio pulse from
that produced FRB 121102 (Chatterjee et al. 2017;
4 the SGR 1806-20 giant flare (Tendulkar et al. 2016).
Marcote et al. 2017; Tendulkar et al. 2017).
9
Other repeating models (e.g. Dai et al. 2016a; Gu et al.
0 The collected data for FRBs so far are however per-
2016) invoke specific physical conditions. These mod-
4 plexing and inconsistent. 1. Whereas the source of FRB
els also cannot account for the apparent association
0 121102 clearly repeats (Spitler et al. 2016; Scholz et al.
of FRB 131104 with the gamma-ray transient Swift
. 2016), other FRBs so far have not been observed to re-
1 J0644.5-5111 (DeLaunay et al. 2016). Models invoking
peat, despite dedicated follow-up observations for some
0 more energetic magnetars as the source of FRBs have
of them (Petroff et al. 2015b); 2. In the error circle of
7 been proposed (Zhang 2014; Murase et al. 2016a; Piro
FRB150418,abrightfadingradiosourcewasdiscovered
1 2016;Murase et al.2016b;Gao & Zhang2017;Dai et al.
in a galaxy at redshift z = 0.492, which was claimed
: 2016b; Metzger et al. 2017). However, in order to ac-
v as the afterglow of the FRB (Keane et al. 2016; Zhang
i 2016b). However, the radio source re-brightened later, count for both the repeater and the putative association
X of a GRB for FRB 131104(DeLaunay et al. 2016), both
leading to the suggestion that the radio source is a co-
r incident background AGN not associated with the FRB catastrophic and repeating mechanisms are needed.
a Here we propose an alternative mechanism to pro-
(Williams & Berger 2016). However, the chance proba-
duce FRBs, which may give a unified interpretation of
bility to have such a highly variable AGN in the field of
all FRBs observed so far. This model invokes an in-
view of the FRB and to have a bright flare follow the
teractionbetween an astrophysicalplasma stream and a
FRB is low (Li & Zhang 2016; Johnston et al. 2017); 3.
foreground regular pulsar. The pulsar is otherwise non-
DeLaunay et al. (2016) discovered a sub-threshold long
detectable at the cosmological distance, but may pro-
GRB that was spatially and temporally associated with
duce an FRB as observed by an Earth observer when
FRB 131104 (Ravi et al. 2015); 4. The repeating bursts
the plasma stream with significant ram pressure combs
from the FRB 121102 source are not associated with
themagnetospheretowardstheanti-streamdirectionand
bright transient counterparts in other wavelengths, but
sweeps the direction of Earth.
the repeaterisratherassociatedwithasteadybrightra-
dio source (Chatterjee et al. 2017; Marcote et al. 2017;
2. THEMODEL
Tendulkar et al. 2017).
Many FRB models have been proposed so far. How- The condition for a cosmic comb is that the ram pres-
ever, no model can explain all the above observa- sure of the stream is greater than the magnetic pressure
tional facts. The catastrophic models (e.g. Totani 2013; of the pulsar magnetosphere. For a most general ex-
Kashiyama et al. 2013; Falcke & Rezzolla 2014; Zhang pression, we write the ram pressure in the relativistic
form. The energy-momentum tensor of a perfect fluid is
2 Zhang
given by Tµν = (ρc2+e+p)uµuν +pgµν, where gµν is for a continuous wind (where M˙ is the wind mass loss
the metric tensor, uµ =γ(1,β ,β ,β )is the dimension- rate). One can see that cosmic comb condition can be
x y z
less4-velocity,(β ,β ,β )isthedimensionless3-velocity satisfied for a variety of systems if the pulsar is close
x y z
vector with amplitude β = v/c, γ = (1−β2)−1/2 is the enoughto the source. For typical parameters,the “hori-
Lorentzfactor,ρ,e,andp=(γˆ−1)earethemassdensity, zon”ofacosmiccombisoftheorderof0.1pc. However,
internalenergydensity,andpressureofthe fluid,respec- noticing the sensitive dependence of magnetic pressure
tively,γˆistheadiabaticindex,andcisspeedoflight. For onP andB,thehorizoncaneasilyreach∼pcforslower
a fluid with co-moving mass density ρ , internal energy and weaker-field pulsars.
0
density e andpressure p, the lab-frameenergy density is If the cosmic comb condition is satisfied, when the
T00 = γ2(ρ c2+e+p)−p = γ2ρ c2 +(γˆγ2 −γˆ+1)e. plasma stream suddenly arrives, the pulsar magneto-
0 0
Subtracting the rest mass energy density one canobtain sphere is combed towards the anti-stream direction in a
the rampressure. The condition for a cosmic comb then durationof∼Rsh/v ∼(3s)Rsh,10β−1,whereRsh ∼RLC
reads is the distance of the sheath from the pulsar (Fig.1, in
analogywiththeEarthmagnetosphere). Thestrongram
B2
(γ2−1)ρ c2+(γˆγ2−γˆ+1)e> . (1) pressure of the stream may trigger magnetic reconnec-
0
8π tions, which would quickly accelerate particles to rela-
For a non-relativistic (γ2 −1 ≃ β2), cold (e ≃ 0) flow, tivisticspeeds withinatime scalemuchshorterthanthe
combingtimescale. Therelativisticparticlesmovealong
this is reduced to the familiar form of
the magnetic field lines and flow out from the sheath to
ρv2 > B2. (2) produce coherent radio emission. During the combing
8π process, the sheath very quickly sweeps a near-2π hemi-
sphere solid angle. If the electrons (or electron-positron
The magnetosphere of a pulsar is enclosed within the
light cylinder with radius R = c/Ω = cP/2π ∼ pairs) in the sheath move with a Lorentz factor γe, then
LC
(4.8×109cm)P,whereΩandP aretheangularfrequency the emission beam angle of the sheath would be 1/γe,
which is usually much smaller than the physical open-
and period of the pulsar, respectively. The magneto-
ing angle of the sheath. If the distance range overwhich
sphereofapulsarissignificantlymodifiediftherampres-
emission into the characteristic radio band of the tele-
sure exceeds the magnetic pressure at the light cylinder,
B ∼B (R /R)−3,whereR∼106 cmistheradiusof scope(e.g. GHzrange)issmall,anobserveratarandom
LC s LC directioninthe“night”sideofthehemispherewouldde-
the neutron star, and a dipolar magnetic configuration
tect the signal in a duration
has been assumed. The right hand side of Eqs.(1) and
(2) is therefore R
∆t∼ sh ≃(3.3 ms)R β−1γ−1. (7)
B2 B2 ΩR 6 vγe sh,10 −1 e,3
LC = s ≃(3.4 erg cm−3) B2 P−6, (3)
8π 8π c s,12 This is consistent with the millisecond durations of the
(cid:18) (cid:19) observed FRBs if γ &103 is satisfied.
e
where the median values of surface magnetic field B =
s The coherent radio emission mechanism is not speci-
1012 G and period P = 1 s for Galactic radio pulsars
fied. One interesting estimate is that with the nominal
have been adopted (throughout the paper, the conven-
parameters, the curvature radiation frequency is
tion Q = 10nQ is adopted in cgs units). Noticing the
n
strong dependence on Bs and especially on P, one can ν = 3 cγ3 ≃(7.2×108 Hz) ρ−1γ3 , (8)
conclude that cosmic combs more easily happen in slow 4πρ e 10 e,3
and low-field pulsars.
which falls into the range of FRB detection frequency
ForarelativisticblastwavesuchasaGRBafterglowor
a relativisticAGN flare,since e≫ρ c2 andγˆ ≃4/3due (the curvature radius ρ∼Rsh has been assumed). If the
0
combingprocessmayallowparticlestoemitinphase(the
to relativistic shock heating, the left hand side of Eq.(1)
antennamechanism), brightcoherentradioemissioncan
can be simplified as
begenerated. Alternatively,acyclotroninstabilitymech-
4γ2e≃ 4γ3n m c2 ≃(2.0 erg cm−3) γ3n (4) anism,aswasproposedtointerpretpulsarradioemission
3 3 ISM p 1 ISM,0 (Kazbegi et al. 1991), may operate near the light cylin-
for a nominal value γ = 10 and n = 1 cm−3, where der region to power the FRB. A sheath-origin coherent
e=(γ−1)n m c2. Foranon-reIlSaMtivisticoutflowsuch emissionhasbeenintroducedto interpretradioemission
ISM p ofPulsarBinthedoublepulsarsystem(Lyutikov2004).
as a supernova explosion, a quasi-isotropiccompact star
Here we assume that the combing process can produce
mergerejecta,oraquasi-isotropictidaldisruptionejecta,
brightcoherentradioemissiondetectablefromcosmolog-
the left hand side of Eq.(2) can be expressed as
ical distances, and encourage a full investigation of the
∆Mv2 ∆M coherent mechanism of such a process in detail.
ρv2 = =(14.2 erg cm−3) β2 r−2∆−1
4πr2∆ (cid:18)M⊙ (cid:19) −1 17 16 3. CASESTUDIES
(5)
foranimpulsiveexplosion(where∆M istheejectamass, This model canexplain the puzzling properties of sev-
∆ is the thickness ofthe shell, r is the distance from the eral FRBs in a unified way:
center of explosion, and v is the speed of the ejecta), or FRB150418: Keane et al.(2016)discoveredabright
radio source starting from 2 hours after the FRB. The
M˙ v M˙ source dimmed in the next two observational epochs at
ρv2 = 4πr2 =(1.5 erg cm−3) M⊙ yr−1!β−1r1−72 (6) 6 and 8 days after the FRB, respectively, and reached
A cosmic comb model of FRBs 3
there might be γ-ray emission already 7 seconds before
the FRB according to the data. Furthermore, the Swift
BATwasnotpointingtowardthesourcedirectionbefore
−7 seconds with respect to the FRB (DeLaunay et al.
2016). So it is likely that the FRB occurred during the
process of a long-duration GRB. If so, known models
are difficult to interpret the FRB. In the cosmic comb
model,onerequiresthatapulsarislocatedatadistance
r > γ2c(7 s) ∼ 2×1016 cmγ2 away from the central
2.5
engine in the direction of the jet (or at a closer distance
if the line of sight is mis-aligned from the pulsar-engine
direction). Consideringapossiblestarformingregionfor
a long GRB or a possible globular cluster for a NS-NS
or NS-BH merger event, the chance probability to have
a foreground pulsar from the GRB may not be small.
The repeater (FRB 121102): The repeater is lo-
Figure 1. A cartoon picture of a cosmic comb. An FRB is pro- cated in a star-forming dwarf galaxy at z = 0.193
ducedinthesheathregion,whichsweepsthelineofsightduringa (Tendulkar et al. 2017). The source is associated with
shortperiodoftimedefinedbyEq.(7).
a radio source (Marcote et al. 2017), which is offset
from the center of the galaxy (Tendulkar et al. 2017).
a quiescent level with a steady flux. Williams & Berger
A plausible scenario might be that the source of the
(2016) discovered that the source re-brightened to the
FRB, likely a rapidly spinning magnetar, is at the cen-
level of the original detection flux more than 300 days
ter of the radio source and pumping energy to power a
later, suggesting that the radio source is an AGN rather
nebula (e.g. Yang et al. 2016; Murase et al. 2016a; Piro
than the afterglow of the FRB. Long term monitor-
2016; Metzger et al. 2017). However, this model pre-
ing of the source (Johnston et al. 2017) suggested that
dicts an observable evolution of DM over the year time
the source is usually not in the high state. A Monte
scale (Piro 2016; Metzger et al. 2017; Yang et al. 2017),
Carlo simulation suggests that the random probability
which is marginally inconsistent with the non-detection
of having the FRB to occur almost during the peak flux
time of the AGN activity is very low, i.e. 10−3−10−4 ofDM evolutionofthe repeating FRBs. Within the cos-
mic comb scenario proposed in this paper, the repeat-
(Li & Zhang2016). InsteadofattributingtheAGNflare
ing bursts may originate from a foregroundpulsar being
toanindependenteventfromtheFRB,weinterpretFRB
episodically combed by an unsteady flow from a young
150418 as emission from a combed pulsar by the AGN
flare1. ApredictionisthatFRB150418mayrepeatdur- supernova remnant. If the condition (1) is marginally
satisfied, the pulsar may relax to its normal magne-
ing another bright flare from the same AGN. However,
tospheric configuration after a particular combing, but
notallflaresmaytriggeradditionalFRBsfromthesame
may be combed again and again when clumps with a
pulsar. This is because at the close distance (< 0.1 pc)
higher ram pressure reach the pulsar magnetosphere re-
from the super-massive black hole, the pulsar must be
gion repeatedly. The pulsar is therefore observed to
undergoing orbital motion, so that there are occasions
emit FRBs repeatedly. For a remnant with a finite
when the geometry does not work for the cosmic comb
width ∆ and speed v, the repeating phase may last for
signal to be detectable from Earth. Within this picture,
the galaxy at z = 0.492 is indeed associated with FRB ∆/v = 107 s∆16v9−1. Since the repeater has been ob-
150418,asissupportedbythemeasuredDMoftheFRB served to repeat in a multi-year time scale, the remnant
(Keane et al. 2016). maybecontinuouslyenergizedbyacentralengine,likely
FRB 131104: DeLaunay et al. (2016) discovered a a rapidly rotating neutronstar. Since the FRB source is
sub-threshold, putative GRB that coincides with FRB aforegroundpulsarfromthecentralsource,theDMevo-
131104 both in spatial position and in time. A radio lutioncouldbemuchweakerdependingonthegeometry,
afterglow was not detected (Shannon & Ravi 2016), but consistentwiththedata. Thereisnodirectobservational
the non-detection is consistent with the afterglow model evidence of ram pressure variation within a supernova
if the ambient density is low (as expected from the NS- remnant. However,for a nebular poweredby continuous
NS or NS-BH merger models) or the shock microphysics energy injection from a central engine (which is not the
parameters are low (Murase et al. 2016b; Gao & Zhang source of FRBs in the cosmic comb model), variation of
2017;Dai et al.2016b). Thepossiblemechanismstopro- rampressureofthestreamisexpected. Foramarginally
duce an FRB associated with a GRB include collapse satisfied comb condition envisaged here, a variation of
of a supra-massive millisecond magnetar to a black hole ram pressure by a factor of a few would suffice to make
(Zhang2014),whichrequiresthattheFRBappearsnear a repeating FRB source as observed.
the end of an extended X-ray plateau; or a pre-merger Other FRBs: Nocounterpartshavebeenclaimedfor
electromagnetic processes (Zhang 2016a,b; Wang et al. other FRBs. Within the cosmic comb model, the ram
2016),whichrequiresthattheFRBleadsthe burst. The pressureoftheplasmastreamessentiallydependsonthe
latter scenario may be argued to marginally match the energy flux of the stream source. For example, a flare
data (Dai et al. 2016b; Gao & Zhang 2017). However, fromacompanionstar(similartoacoronamassejection
eventoftheSun)mayprovideacomparablerampressure
1OthermechanismstoconnectanFRBwithanAGNhavebeen to a pulsar as the blastwave of a more distant GRB or
also suggested in the literature (e.g. Romeroetal. 2016; Zhang supernova. As a result, one does not necessarily expect
2017).
4 Zhang
that all FRBs are associated with bright counterparts. tions of FRBs all reveal associations with bright radio
It is possible that a fraction of FRBs may be associated nebulae, it would suggest a new-born millisecond mag-
with GRBs, supernovae, AGN flares, or tidal disruption netar as the source of FRBs (e.g. Murase et al. 2016a;
events, while other FRBs may be combed by a stellar Metzger et al. 2017), an FRB coincident with a gravita-
flare of a companion star so that no bright counterpart tional wave (GW) signal due to a neutron star - neu-
is detectable. tronstar(NS-NS),neutronstar-blackhole(NS-BH),or
black hole - black hole (BH-BH) merger would suggest
4. DISCUSSION a direct connection between the FRB and the merger
We have proposed a scenario of FRBs that may in- (Totani 2013; Zhang 2016a; Wang et al. 2016)3; and an
terpret the perplexing, inconsistent FRB phenomenol- FRB coincident with the disappearance of an extended
ogywithinaunifiedframework. Themagnetosphereofa plateau emission would suggest the ejection of a magne-
slow,low-fieldpulsarmaybecombedbyacosmicplasma tosphere during the collapse of a supra-massive neutron
stream towards the direction of the Earth to make an star(“blitzar”)asthe mechanismof FRBs (Zhang 2014;
FRB. The stream may originate from an explosion (a Falcke & Rezzolla 2014).
supernova, a GRB, or a neutron star merger event), an
AGNflare,atidaldisruptionevent,orevenastellarflare
I thank Sarah Burk-Spolaor, Zi-Gao Dai, Yuan-Pei
from a binary companion of the pulsar.
TheeventratedensityofFRBsisestimatedasρ˙ ≃ Yang, and an anonymous referee for helpful com-
FRB ments. This work is partially supported by NASA
(5.7 × 103 Gpc−3 yr−1)(D /3.4 Gpc)−3(N˙ /2500) ,
z FRB NNX15AK85G and NNX14AF85G.
whereN˙ ∼2500day−1isthenumberofFRBsperdayall
skywiththecurrenttelescopesensitivity,andthetypical
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