Gamma-rays from nebulae around binary systems containing energetic rotation powered pulsars

0.25 MB·English

by  W. Bednarek

Mon.Not.R.Astron.Soc.000,1–10(2007) Printed15January2013 (MNLATEXstylefilev2.2)
Gamma-rays from nebulae around binary systems
containing energetic rotation powered pulsars
W. Bednarek1 & J. Sitarek2
3
1Department of Astrophysics, The Universityof L ´od´z, ul. Pomorska 149/153, 90-236 L ´od´z, Poland, [email protected]
1
2IFAE, Edifici Cn., Campus UAB, E-08193 Bellaterra, Spain, [email protected]
0
2

n
Accepted .Received;inoriginalform
a
J

4
ABSTRACT
1
We consider nebulae which are created around binary systems containing rotation

powered pulsars and companion stars with strong stellar winds. It is proposed that
]
E the stellar and pulsar winds have to mix at some distance from the binary system,
H defined by the orbital period of the companion stars and the velocity of the stellar
wind. The mixed pulsar-stellar wind expands with a specific velocity determined by
.
h the pulsar power and the mass loss rate of the companion star. Relativistic particles,
p either from the inner pulsar magnetosphereand/oracceleratedat the shocksbetween
-
o stellar and pulsar winds, are expected to be capturedand isotropizedin the reference
r frame of the mixed wind. Therefore, they can efficiently comptonize stellar radiation
t producing GeV-TeV γ-rays in the inverse Compton process. We calculate the γ-ray
s
a spectra expected in such scenario for the two example binary systems: J1816+4510
[ whichistheredbacktypemillisecondbinaryandLS5039whichissupposedtocontain

energeticpulsar.ItisconcludedthatthesteadyTeVγ-rayemissionfromJ1816+4510
1
v should be on the 100 hr sensitivity limit of the planned Cherenkov Telescope Array,
3 provided that ǫ ∼ 10% of the rotational energy lost by the pulsar is transferred to
5 TeV electrons. On the other hand, the comparison of the predicted steady TeV γ-
9 ray emission, expected from γ-ray binary LS 5039, with the observations of the TeV
2 emission in a low state, reported by the H.E.S.S. Collaboration, allows us to put
1. stringentupper limitonthe productofthepartofthehemisphereinwhichthemixed
0 pulsar-stellarwind is confined,∆mix, andthe energyconversionefficiency, ǫ, fromthe
3 supposedpulsartotheTeVelectronsinjectedinthissystem,∆mix·ǫ<1%.Thislower
1 limit can be understood provided that either the acceleration efficiency of electrons
: is rather low (ǫ ∼ 1%), or the parameters of the stellar wind from the companion
v
star are less extreme than expected, or the injection/accelerationprocess of electrons
i
X occurs highly anisotropically with the predominance towards the companion star.
r
a Key words: binaries: general — pulsars: general — radiation mechanisms: non-
thermal — gamma-rays:theory
1 INTRODUCTION strong winds induced by energy released by the pulsar. In
another type of such binaries, the so-called ”Redback” bi-
narysystems,theenergeticmillisecondpulsarformsabinary
Some binary systems contain rotation powered pulsars
which are energetic enough to prevent accretion of matter system with a low mass ∼0.2 M⊙ star (see Roberts 2011).
Up to now, only one binary system has been discovered in
from stellar winds of companion stars. These pulsars can
theGalaxy tocontain aclassical γ-raypulsaron aclose or-
create strong pulsar winds which collide with the winds of
bit around the massive, Be type,star (i.e. PSR 1259-63/SS
thecompanion stars. Asaresult,ashock structureappears
2883, Johnston et al. 1992, 1994). It has been proposed
within the binary system on which particles can be accel-
thatotherbinarysystemscanalsocontainejectingclassical
erated to relativistic energies. A few types of such binaries
pulsars, e.g. LSI 303 +61 (Maraschi & Treves 1981), Cyg
havebeendiscovereduptonow.Themostfamousisaclass
X-3 (Harding & Gaisser 1990) or LS 5039 (Dubus 2006).
of”BlackWidow”binariesinwhichenergyoutputfromthe
These binaries emit γ-rays in the GeV-TeV energy range,
millisecondpulsarcanevenpartiallyevaporatethecompan-
clearly modulated with the period of the binary system
ion star. The companion stars in these systems are char-
(Albert et al.2009;Aharonian et al.2006).Inthemostpop-
acterised by small masses, below 0.1M⊙, and relatively
∼
(cid:13)c 2007RAS
2 W. Bednarek & J. Sitarek
ularscenario, theseγ-raysareproducedbyrelativistic elec- byρo =Db√η/(1+√η), whereDb is theseparation of the
tronswhichup-scatterstellarradiationintheInverseComp- binary stars. For the example scaling parameters applied
ton process, (e.g. Maraschi & Treves 1981; Tavani& Arons above, the shock should be bound around the pulsar. In
1997; Bednarek 1997). Since the stellar radiation field is the case of binary systems containing energetic millisecond
anisotropic for electrons ejected from the pulsar or acceler- pulsars, the shocks are usually bound around the low mass
atedattheshock,theemissionhastobemodulatedwiththe companion stars due to relatively small power of the stel-
period of the binary system. However, a part of relativistic lar winds in respect to power of the winds around massive
electronsinthepulsarwindcanescapefromthebinarysys- stars.Theseshockstructurescanbemuchmorecomplicated
tem without significant interactions, i.e. those movingclose inthecaseofnon-sphericalstellar windsofmassivestarsof
totheoutwarddirection.Inthecaseoflowmassmillisecond theBetype(seeSierpowska-Bartosik & Bednarek2008).In
pulsarbinaries,mostoftheacceleratedelectronscanescape thislastcasethelocation oftheshockstructurecanchange
radiallyfromthevicinityofthecompanionstar,duetorela- drastically depending on the location of the pulsar within
tivelyweakradiationfield.Fartherfromthebinarysystems, thepolar or equatorial stellar wind.
the winds from the pulsar and the companion star have to
The shock structure tends asymptotically to a cone
mix due to the rotation of the binary system. As a result,
characterised by a half-opening angle ψ = 2.1(1
it is expected that such mixed pulsar-stellar winds move −
η2/5/4)η1/3 rad, where η = min(η,η−1) (see Ball & Dodd
together with some specific velocity determined by the en- m m m
2001; Eichler & Usov 1993). However, due to the rotation
ergyoutputfromthepulsarandthematerialcontentofthe
of the binary system, the cone should be bound at large
stellarwind.Therefore,nebulaearoundbinarysystemscon-
distances from thestars (e.g. Dubus2006, Bosch-Ramon et
tainingrotationpoweredpulsarsshouldhavedifferentstruc-
al. 2012) provided that the velocity of the stellar wind is
turesthannebulaearoundisolatedpulsars.Weproposethat
large in respect to therotational velocity of the companion
suchbinary systemsshouldbesurroundedbynebulaecom-
star. For η > 1 the pulsar wind completely overtakes the
posed of the mixture of the pulsar and stellar winds which
stellarwind,creatingatoruslikestructureintheequatorial
expands with non-relativistic velocity. Relativistic particles
planeofthebinarysystem(see.Fig.1forschematicgeome-
areexpectedtobecapturedandisotropizedinthereference
try).Inthiscase,thepulsarwindcanonlypropagatefreely
frame of this wind.
alongthepolarregionsofthebinarysystem.Intheopposite
In thispaperwe considerradiation processes occurring
caseη<1,thestellarwindovertakesthepulsarwind.How-
insuchnebulae.Wecalculatetheγ-rayspectraproducedby
ever, again in the equatorial region the pulsar wind mixes
relativisticelectronsintheInverseCompton(IC)scattering
with thestellar wind as in thepreviouscase. There are sig-
ofthermalradiationfromthecompanionstar.Incontrastto
nificantdifferencesbetweenthemixedpulsar-stellarwindin
themodulatedγ-rayemissionfromtheinteriorofthebinary
theequatorialregionandthefreelyexpandingpulsarwindin
system, we predict the presence of a steady component of
thepolarregion.Relativisticelectronsareisotropizedinthe
theγ-rayemissionproducedinthenebulaaroundthebinary
referenceframeofarelativelyslowlyexpandingmixedwind.
system. Discovery of such additional component by the fu-
Theseelectrons caninteract efficiently with thethermalra-
tureCherenkovtelescopes(e.g.CherenkovTelescopeArray,
diation from the nearby companion star. Relativistic elec-
CTA,Actis et al.2011)fromthebinariescontainingpulsars
tronsinthepulsarwind,expandinginpolardirections,move
should allow to derive important parameters determining
rectilinear from the binary system. These electrons can be
theacceleration processesinsuchbinariesandpropertiesof
isotropized onlyfaraway from thebinarysystemwherethe
the emission region. The comparison of the predicted high
densityofstellar photonsisalreadyverylow(asinthecase
energy emission with the available observations of the TeV
ofPWNearoundisolated classical pulsars).Theseelectrons
γ-ray emission in the low state from already known γ-ray
are not expected to produce efficiently γ-rays by scattering
binaries should allow to provide additional constraints on
stellar radiation. They finally scatter the Microwave Back-
the acceleration efficiency of particles occurring around the
ground Radiation and the infrared radiation in the Galaxy
rotation powered pulsars in the binary systems.
producing extended γ-ray sources which are more difficult
to detect with the Cherenkov telescopes. If the parameter
η is lower than unity, then the equatorial regions of the bi-
2 NEBULAE AROUND BINARY SYSTEMS narysystemaredominatedbythemixedpulsar-stellarwind
but thepolar regions are dominated by thestellar wind. In
Aswehaveoutlinedaboveweconsiderspecifictypeofnebu-
thiscaseall electrons in thepulsar wind areexpectedtobe
laearoundbinarysystemscontainingrotationpoweredpul-
isotropized at some distance from the binary system.
sars and companion stars with substantial mass loss rate.
In fact, in such type of binaries a double shock structure We calculate thefactor which determines a part of the
appearsalready within thebinarysystem incollision of the hemisphere (the solid angle divided by 4π) in which the
pulsar and stellar winds. Its parameters are determined by mixedpulsar-stellarwind(thetoroidalstructureintheplane
the energy loss rate of the pulsar and the power of the of the binary system, see Fig. 1) is confined. This factor is
stellar wind. In the case of spherical winds, the distance calculated fortheknownvalueofthehalfopeningangle,ψ,
of the shock from the star is defined by the parameter, of the shock created within the binary system in collisions
η=(Lpul/c)/M˙wvw 0.05L36/(M−7v8) (Girard & Willson of these two winds. This part of the hemisphere is equal to
≈
1987), where the pulsar wind power is L = 1036L ∆ = ∆Ω /4π = (1 cosψ), where ∆Ω is the solid
pul 36 mix mix mix
erg/s, the stellar wind mass loss rate is M˙w = 10−7M−7 angle in which the mixe−d pulsar-stellar wind is confined.
M⊙/yr and its velocity is vw = 108v8 cm/s. The closest, Both winds are expected to mix completely at the distance
radial distance of the shock from the pulsar is then given fromthebinarysystemwhichdependonthevelocityofthe
(cid:13)c 2007RAS,MNRAS000,1–10
Gamma-rays from nebulae around binary systems containing pulsars 3
pulsar wind
mixed
mixed mixed stellar
pNulSsar Db ρo starstellar Dmix swtweilnaedrn− nvpeublusalar wpstueinllsldaarr ndpulsar wind swstteailnrladr NS wstainrd pulsar wind ellar wind spwtueilnlsldaarr
wind wind wi st
ellar pulsar wind
st
D D
mix mix
Figure 1.Schematic representation (nottoscale) ofthevicinityofthebinarysystem containing anenergetic pulsarandacompanion
star (seen fromthe reference frame of the pulsar). The top view (i.e. from the pole of the binary system) is shown on the left and the
backview(fromthesideofthebinaryplane)isshownontheright.Ontheleft:Thedottedlineshowstheorbitofthestar.Thepulsar
createsenergeticwindwhichcollideswiththestellarwind.Asaresult,adoubleshockstructureiscreated(markedbythedashedcurve).
Thestellar(pulsar)windcreatesacometarytailwhichinteractswiththepulsar(stellar)wind.Atsomedistancefromthebinarysystem
(signedby Dmix)both windsmixtogether. The mixedstellar-pulsarwindpropagates withthe commonvelocity estimated fromEq.3.
Relativistic particles accelerated by the pulsar move rectilinear in the pulsar wind up to the shock structure. In this region many of
them are not able to interact with the stellar radiation due to the small interaction angles. However, in the mixed stellar-pulsar wind
theyareisotropized.Theystarttoloseefficientlyenergyoncomptonizationofthestellarradiation.Moreoversomeparticlescanbealso
accelerated at the shock between the pulsar and stellar winds in the Fermi acceleration process. On the right: This same picture but
viewedfromtheplaneofthebinarysystemforthecaseoftheparameterη>1.Inthiscasethepulsarwindcanescapefreelyonlyalong
thepolarregionsofthe binarysystem.Thestellarandpulsarwindshave tomixatthedistance Dmix intheregionoftheplaneofthe
binarysystem.
stellar windandtherotational periodofthebinarysystem, that the magnetic field in themixed wind is determined by
themagnetic field in thestellar wind. It has a dipole struc-
D τ v 8.6 1012τ v cm, (1)
mix≈ orb w ≈ × d 8 tureonlyveryclosetothestellarsurface.Fartherout,ithas
wheretheperiodofthebinarysystemisτ =1τ days.In aradialstructureandfinallyreachesatoroidalstructuredue
orb d
theaboveformulaweassumedthatthestellarwindvelocity to the rotation of the star (for details see Usov & Melrose
is much greater than orbital velocity of the star which is 1992). The magnetic field strength with the toroidal struc-
usually the case for the considered binaries. As a result of turecanbeapproximatedasafunctionofthedistancefrom
themixingprocess,thepulsarwindbecomesuploadedwith thestar by thefollowing formula,
the stellar wind matter. The mixture of both winds starts
B(D) 0.01B R /D G, (4)
tomovetogetherwiththecommonvelocity,wenv,estimated ≈ 2 11 13
from the energy conservation, assuming that the transition between the region of the
L +L =M˙w2 /2, (2) toroidal and the radial magnetic field occurs at the dis-
pul sw env
tance of 10 stellar radii (where the radius of the star
where Lsw = M˙wvw2/2 is the kinetic power of the stellar is R⋆ =10∼11R11 cm). In this formula, the surface magnetic
wind.Hereweneglect theenergyloss of thebulkmotion of fieldofthestarisB =100B G,andthedistancefromthe
⋆ 2
themixedwindsontheisotropizationofthedirectionofthe star is expressed as D=1013D cm.
13
particles in it. If the stellar wind power dominates over the We assume that relativistic electrons are captured by
pulsar wind power, then wenv vw. In the opposite case, the wind (and advected with the wind) if their Larmor
≈
radius, R , is lower than the characteristic distance scale
L
wenv =q2Lpul/M˙ ≈5.4×108(L36/M−7)1/2 cm/s, (3) g3ive1n09bEy the/Bd(iDstanc)ecmfro<mDthe,mwhaessrieveEs=ta1rE, i.e. TReLV≈is
resulting in a non-relativistic bulk motion of the mixed × TeV mix mix TeV
theenergyofanelectron,andB(D )(measuredinGauss)
winds for the assumed aboveexample parameters. mix
isthelocalmagneticfieldstrengthinthemixedwind.Based
Relativistic electrons accelerated in the inner binary
on this condition, we concludethat electrons with energies,
system, either by the pulsar itself or on the shock formed
in the pulsar and stellar winds collision, are immersed in
E <30B TeV, (5)
2
the mixed stellar-pulsar wind. We estimate the maximum
energies of the electrons for which they are captured and should be captured in themixed stellar-pulsar wind.
confined by the mixed wind magnetic field. It is assumed Electrons, captured in the magnetic field of the mixed
(cid:13)c 2007RAS,MNRAS000,1–10
4 W. Bednarek & J. Sitarek
stellar-pulsar wind, are isotropized in the reference frame Forexample,inthecaseoftheeccentricitynotfarfromunity
of the relatively slow wind. They lose energy on the syn- the distance, D , differs significantly for the periastron
mix
chrotron radiation and on the IC scattering of the stellar and apastron passages. These distances can be estimated
radiation. The importance of the synchrotron energy losses from, Dper τ v , for the periastron passage and from
canbeevaluatedbycomparingthesynchrotroncoolingtime Dapo mτix ∼v pfeorrwthe apastron, where τ and τ are
mix ∼ apo w per apo
scale with the advection time scale with the velocity of the thetimescalesdescribingthepassageofthecompactobject
winds. The advection time scale can be estimated from, through a half of the orbit centered on the periastron and
apastron, respectively. In such eccentric binaries, nebulae
τ =D/w =105D /w s, (6)
adv env 13 8 should have the shape corresponding to the shape of the
where v = 108w cm/s, and the synchrotron time scale orbit of thecompanion stars.
env 8
from, In the present paper we outline only qualitatively the
scenario describing the process and properties of the mix-
τ =E /E˙ 290/(B2E) s, (7)
syn e syn ≈ ing of stellar and pulsar winds and concentrate on the ex-
whereE˙ =(4/3)cU σ E2/m2 3.5 10−3B2E2 TeV/s, pectedhighenergyradiationproducedinsuchscenario.The
syn B T e e ≈ ×
m = 511keV and electron energy E is expressed in TeV. details of the mixing process of the winds are very compli-
e
By comparing Eq.6 and 7, we get thelimit on theelectron cated.However,thefirstresultsofhydrodynamicnumerical
energy above which the synchrotron energy loss time scale simulations of collisions of stellar winds are consistent with
is shorter than the advection time scale, generalfeaturesofthescenariodescribedinthissection(see
e.g. Pittard 2009, Lamberts et al. 2012).
Esyn 29w D /(B R )2 TeV. (8)
adv ≈ 8 13 2 11
This critical electron energy is equal to E
e
≈
130τdv8(L36/M−7)1/2/(B2R11)2 TeV, for the mixture 3 NEBULAE AROUND SPECIFIC BINARY
distance of the winds given by Eq. 1 and the velocity of SYSTEMS
themixed wind given by Eq. 3. We conclude that electrons
with TeV energies are not able to lose efficiently energy on As an example, we estimate the parameters of nebulae
the synchrotron process during their advection with the around a few binary systems containing (or expected to
mixed pulsar-stellar wind. However, at larger energies the contain) energetic pulsars, i.e. classical radio pulsar PSR
synchrotron energy losses should betaken into account. 1259-63, millisecond pulsar B1957+20 in the Black Widow
Relativistic electrons, after isotropization by the mag- type binary system, millisecond pulsar J1816+4510 in the
netic field in themixed pulsar-stellar wind, should lose effi- Redback type binary system, and supposed classical pulsar
ciently energy also on the IC scattering of the stellar radi- in the binary system LS 5039 belonging to the class of the
ation. We estimate the optical depth for the IC scattering TeV γ-ray binaries. The basic parameters of these binaries,
processintheThomsonregimeforelectronsatthedistance collected or proposed in different works, are summarised in
of D on, Table 1.
mix
Considered above binary systems are expected to be
τIC/T =n⋆σTc(Dmix/wenv)≈4.7T43R121/(τdv8w8), (9) surrounded by nebulae with quite different parameters. We
estimatethebasicparametersofthesenebulaebasedonthe
where the density of stellar photons is n = 2.75
⋆
109T3(R /(τ v )2 cm−3,andD /w isthecharacteri×s- formulae derived in Sect. 2 (see Table 2). The best con-
4 11 d 8 mix env
ditions for γ-ray production seems to be provided by the
tic time scale spend byelectrons at the distance D from
mix
binary system of the redback type, containing millisecond
the binary system. Note that the scattering in the Thom-
pulsar J1816+4510, and thesupposed pulsar within the bi-
son regime is valid only for electrons with energies below
m2c4/3k T 100/T GeV.However,inthecaseofLS5039, nary system LS 5039 from which already GeV and TeV γ-
e B ∼ 4 rayemissionhasbeendetected.Theobservedemissionfrom
theopticaldepthforthe TeVelectronsshouldbestillclose
∼ LS 5039 is modulated with the binary period. Therefore,
to unity, keeping in mind that the Klein-Nishina cross sec-
it is expected to be originated within the binary system.
tion drops inversely proportional with the electron energy.
We propose that additional steady γ-ray emission compo-
We conclude that electrons with TeV energies should ef-
nentshouldbealsoproducedinthenebulasurroundingthis
ficiently lose energy on the IC scattering of stellar radia-
system provided that it contains energetic pulsar. We cal-
tionafterbeingisotropizedinthepulsar-stellarwindnebula.
culatethesteadyγ-rayfluxesfromthenebulaesurrounding
However,inthemassivebinarysystemsoftheLS5039type,
two binary systems mentioned above selecting them as the
electrons, moving rectilinear in the pulsar wind in the out-
best candidates for production of observable steady γ-ray
ward direction from the companion star, are not expected
emission in the surrounding nebulae, i.e. those containing
tolosesignificantlyenergyalreadyinthebinarysystemdue
millisecond pulsar J1816+4510 and LS 5039.
to the small scattering angles between electrons and stellar
photons. The γ-rays produced at the distance D from
mix
the star should escape from stellar radiation field without
3.1 J1816+4510
significant absorption (e.g. see thescaling formula given by
Eq.26inBednarek(2009)fortheopticaldepthsinthestel- The millisecond pulsar J1816+4510, with the period of 3.2
lar radiation field). ms, was recently discovered in the survey as a part of the
The nebulae formed by the mixed pulsar-stellar winds Green Bank North Celestial Cap (Stovall et al. 2012). This
can have very complicated structures in the case of binary pulsar is in the binary system with the low mass compan-
systems in which the wind of the companion star is non- ion (mass below 0.16M⊙) having an orbital period of 8.7
spherically-symmetric or the orbit has a large eccentricity. hrs. The distance to this binary has been estimated on 2.4
(cid:13)c 2007RAS,MNRAS000,1–10
Gamma-rays from nebulae around binary systems containing pulsars 5
Table 1.Basicparametersofstarsandpulsarsinbinarysystems:theradiusofthecompanionstarR⋆,itssurfacetemperatureT⋆,the
masslossrate,M˙,andthevelocity,vw,ofthestellarwind,themagneticfieldstrengthsatthesurfaceofthestarB⋆,thebinaryorbital
periodτorb andthespindownluminosityoftheobserved(orsupposed)pulsarLpul.
Name R⋆ (cm) T⋆ (K) M˙ (M⊙/yr) vw (km/s) B⋆ (G)(?) τorb (days) Lpul (erg/s)
B1259-63 4.2×1011 2.7×104 2×10−7 2×103 102−103 1236.7 8.3×1035
B1957+20 1011 8×103 3×10−10 7×102 1−103 0.38 7.5×1034
J1816+4510 7×1010 2×104 3×10−10 7×102 1−103 0.36 5×1034
LS5039 6.5×1011 3.9×104 2.6×10−7 2.4×103 102−103 3.9 1037
kpc, based on the dispersion measure (Kaplan et al. 2012). on the acceleration rate of relativistic electrons in terms of
The pulsed γ-ray emission from J1816+4510 has been also ourmodel.
detectedbyFermi,implyinganenergyconversionefficiency For this binary system, the shock structure bends
of 25% from the pulsar’s spin down luminosity into γ- around the pulsar, η 0.08 (see Table 2). This means that
∼ ∼
rays. The pulsations have two peaks separated by 0.5 in thewholepulsarwindisovertakenbythestellar wind.The
∼
phase. The γ-ray spectrum is measured between 0.5 GeV mixed pulsar-stellar wind propagate only in a part of the
and 5 GeV. The spectrum is flat. It can be described by a sphere. Electrons are expected to be accelerated to several
purepowerlawwithaphotonindex 2.20 0.07orapower TeVforthelikelysurfacemagneticfieldstrengthofthecom-
− ±
law with an index of 2.0 0.1 and an exponential cut-off panionstar.Theopticaldepthforelectronsintheradiation
− ±
at 7.5 4.0GeV (Kaplan et al. 2012). The companion star fieldofthecompanionstar(intheThomsonregime)isvery
±
has a radius of 0.1R⊙ and the surface temperature in the large (of the order of 100) at the distance of Dmix. Thus,
∼
range 1.8 2.1 104 K (Kaplan et al. 2012). We have se- efficientproductionofγ-raysisexpectedevenfromelectrons
− ×
lected thisbinaryasoneoftheinterestingexamplesforour withenergiesoftheorderofseveralTeV,whichalreadyscat-
fartheranalysisduetothelargespindownluminosityofthe terstellar radiation in theKlein-Nishina regime.
pulsar, 5 1034 ergs−1 andaveryhotcompanion,which
∼ ×
is unusualfor theRedback typemillisecond binary system.
The likely parameters of this binary system allows us
4 RELATIVISTIC PARTICLES IN NEBULAE
toestimate theshapeoftheshock inthisbinarydefinedby
the parameter η. For η 1.2 the shock almost divide the Weassumethatrelativisticparticlesinthenebulasurround-
∼
volume of the binary in two equal parts. For such geome- ing binary system are directly injected from the pulsar in-
try, the mixed wind dominates almost at the whole sphere ner magnetosphere (close to mono-energetic case) or they
around the binary system, i.e. ∆mix 1. The energies of are accelerated in the shocks created in pulsar-stellar wind
∼
electrons accelerated in this system can reach TeV energies collisions. The Lorentz factors of the mono-energetic parti-
(see Table 2) for the intermediate magnetic field strengths cles, γpul, areusually considered to beof theorder of afew
e
from therange mentionedin Table1. Theacceleration pro- times 10(4−6). It is expected that a significant part of these
cessoftheseelectrons willbeconsidered inamoredetailin particles, those injected in the outward direction from the
thenextsection.Alsotheopticaldepthsforelectronsatthe companionstar,escapetothesurroundingnebulaandreach
distance of Dmix are in this case of the order of a few see thedistanceofDmix.Weestimatethemaximumenergiesof
Table 2). particleswhichcanbeacceleratedattheturbulentregionat
the distance of D by comparing their acceleration time
mix
scale and their advection time scale from the shock region
3.2 LS 5039
given by Eq. 6. The acceleration time scale is given by,
LS 5039 is a well known binary system containing O type τacc =Ee/P˙acc 100ETeV/(χ−3B) s, (10)
massivestarandacompactobjectontheorbitwithaperiod ≈
of3.9days(Casares et al.2005).Thedistancetothesystem whereP˙acc =χcE/RL andRL istheLarmorradiusofparti-
is2.9 0.8kpc(Casares et al.2012).ThevicinityofLS5039 cles.Theaccelerationprocessisparametrisedinthiscaseby
shows±radiomorphologywhichindicatesapresenceofanen- theaccelerationefficiencyχ=10−3χ−3 whichisassumedto
ergetic pulsar in this system (Moldon et al. 2012) as earlier beoftheorderof (wenv/c)2.ApplyingEq.4,weestimate
∼
suggested by Dubus (2006). This binary system has been the maximum energies of electrons due to their advection
detectedintheTeVγ-rays(Aharonian et al.2005)andalso from theacceleration region on,
saitstGenetVemeniesrsgioiensmboydFuelramteid(wAibthdotheetoarlb.i2t0a0l9p)e,rsiohdowoifntghepebri-- Eamdavx≈10χ−3B2R11/w8 TeV. (11)
narysystem.TheGeVandTeVγ-raylightcurvesareclearly Themaximumenergiesofparticles,acceleratedattheshock
anticorrelated.Theγ-rayspectrumextendsupto 20TeV at the distance of D , can be additionally constrained by
mix
∼
indicatingthepresenceofmulti-TeVparticleswithinthisbi- their energy losses. Therefore, we compare the acceleration
nary system. The spectral slope changes dramatically with timescale of particles with theirenergy loss timescale. For
theorbital phasebetween -1.85 and -2.53 (Aharonian et al. theradiationenergylosstimescalesofelectronsinthevicin-
2006). We have selected this binary due to relatively small ityofthestars(synchrotronandICprocesses),thestandard
eccentricity (e 0.35) and the well measured modulated formulae(Blumenthal & Gould1970)areapplied.Thecom-
∼
TeV γ-ray emission which should allow to put constraints parison of the acceleration and the synchrotron energy loss
(cid:13)c 2007RAS,MNRAS000,1–10
6 W. Bednarek & J. Sitarek
Table2.Parametersofthenebulaearoundbinarysystemsandenergiesofparticleswhichproduceγ-rays:theparameterηdefiningthe
shock structure, the partof the hemisphere, ∆mix, inwhichthe mixed windisconfined, the windmixingdistance Dmix, the magnetic
fieldBmix atDmix,andthebulkspeedofthemixedwindwenv,theaccelerationefficiencyofelectronsχ=10−3χ−3,theopticaldepth
for IC scattering of stellar photons τ , and the electron acceleration limit due to advection, Emax, and synchrotron Emax energy
IC/T adv adv
losses.
Name η ∆mix Dmix (cm) Bmix (G) wenv (cm/s) χ−3 τIC/T Esmyanx (TeV) Eamdavx (TeV)
B1259-63 0.01 0.09 2×1016 2×10−5−2×10−4 3.5×108 0.14 0.4 47-150 1.7-17
B1957+20 1.8 0.82 2.3×1012 4.4×10−4−0.4 2.7×109 8.1 0.4 17-460 0.1−85
J1816+4510 1.2 0.95 2×1012 4×10−4−0.4 2.2×109 5.4 3.4 12-410 0.05-50
LS5039 0.08 0.32 8×1013 8×10−3−8×10−2 1.1×109 1.3 110 7-24 7.7-77
time scales gives us the maximum energies of electrons due energy on hadronic processes. These protons mainly escape
to thesynchrotron energy losses, from the binary system and contribute to the galactic cos-
micrays.Notethatthestellarwind(andalsomixedpulsar-
Esmyanx≈19(χ−3D13/B2R11)1/2 TeV. (12) stellar wind) can be quite inhomogeneous. However, rela-
Themaximum energies dueto theInverseCompton energy tivistic protons have to be very efficiently captured within
losses (in theThomson regime) are given by, the regions with density effectively enhanced by a factor of
105−6, in respect to average densities estimated above for
EImCa/xT ≈0.4(χ−3B2D13/R11)1/2/T42 TeV. (13) t∼heconsideredbinaries,inordertoprovidetheirefficientin-
teractionwith thematter.Suchefficientcapturingseemsto
We stress that this second limit is only important in the
beratherunlikelyinthestellarwindssincethefillingfactor
Thomson regime, i.e. for electrons with energies < 100/T
4 of the stellar wind with such dense regions should be very
GeV. For larger energies, due to the falling of the Klein-
low.
Nishinacross-section, thelimit isrelaxed.Thevaluesofthe
maximumenergies ofelectrons duetotheirescapewith the
expansion of the nebula and due to the synchrotron energy
5 GAMMA-RAY PRODUCTION IN NEBULAE
losses are shown for the considered binary systems in Ta-
ble.2.Weconcludethatelectronscan beaccelerated toen-
Wecalculatetheγ-rayspectraproducedbyrelativisticelec-
ergiesestimatedbythelowervaluebetweenEmaxandEmax.
syn adv tronswithin thenebulaein theInverseCompton scattering
Notethatthesemaximumenergiesareclosetothosevalues
of the stellar radiation and the Microwave Background Ra-
expected for electrons injected from the inner pulsar mag-
diation.Weassumethatrelativisticelectronsareisotropized
netosphere.Sinceitisnotclearwhichmechanismaccelerate
inthemixedpulsar-stellarwindatthedistancesaboveD .
mix
electron in the vicinity of the binary system, we consider
Themaximumenergiesoftheelectronsareconsideredinthe
twolimitingcases:(1)electronsareinjectedintothenebula
range which is consistent with the estimations reported in
surrounding the binary system with a power law spectrum
thelast twocolumnsinTable2.Theelectronsarecaptured
extending between Emin = m γpul and Emax, or (2) they
e e e e by the magnetic field of the mixed winds and move grad-
are injected with monoenergetic energies Emin.
e ually with the velocity of these winds. We also include the
Relativistichadronsarealsoexpectedtobeaccelerated
synchrotron energy losses of the electrons in the magnetic
in such nebulae. The maximum energies of these hadrons
field of the winds with the values equal to B at the dis-
mix
should be also limitted by their advection from the nebula.
tance D . This magnetic field drops with the distance,
mix
Sothen,theyaregivenbythesameformulaasforelectrons
D, from the binary system as 1/D. For example, in the
(Eq. 11). We estimate the optical depth for the interaction case of J1816+4510, we apply∝the value B = 10−2 G.
mix
of these relativistic hadrons with the matter of the mixed
Forthisvalue,theenergy density of stellar radiation at the
pulsar-stellarwind.Itisassumedthathadronsarecaptured
distanceD overcomestheenergydensityofthemagnetic
mix
by the magnetic field of the mixed wind above D . They
mix fieldbyafactorof 200.Therefore,thesynchrotronenergy
are advected with the velocity of the wind w . In such a ∼
env losses can only start to be important at energies above a
case theoptical depthis equal to
few hundred GeV, where the IC emission is suppressed by
τ = ∞ n σ c dD 3 10−3 M−7 , (14) the Klein-Nishina cross-section provided that we consider
pp ZDmix H ppwenv ≈ × w82D13 the upper range of the magnetic fields (equal to ∼ 0.4G,
seeTable2).Therelativeimportanceofthesynchrotronen-
cwmhe−r3e insHth=e dMe˙n/s(i4tyπDof2wtehnevmmpa)tt≈er 3in×th1e07mMi−x7e/d(Dpu123lswa8r)- eLrSgy50lo3s9seissisnimreilsaprecttottohathteesItCimeanteerdgyfolorsJse1s8,1i6n+t4h5e10ca.sTehoef
stellar wind as a function of the distance from the star, surface temperature of the companion star in LS 5039 is a
σ =3 10−26 cm2 is the cross section for proton-proton factor of two higher but the distance of the mixing region
pp
×
interaction, and m is theproton mass. For theparameters fromthestar(inunitsofstellarradius)isafactorof4larger.
p
of the binary systems considered above (see Tables 1 and Therefore the radiation field in the case of both sources at
2), the optical depths for hadronic interactions are clearly the distance D are comparable. Note however, that the
mix
lower than unity. Therefore, we conclude that relativistic time scale for theIC scattering is a factor of 40 larger for
∼
hadrons are not able to findenough target mass within the LS 5039 which affects the optical depth for electrons (see
considerednebulaearoundbinarysystemstoefficientlylose D and τ in Table 2).
mix IC/T
(cid:13)c 2007RAS,MNRAS000,1–10
Gamma-rays from nebulae around binary systems containing pulsars 7
-2) m -9 PSR J1816+4510 -9 LS5039
c
-1s -10 -10
g
E / er -11 -11
d
N/ -12 -12
d
2E
g( -13 -13
o
l
-14 -14
-15 -15
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5
-2) m -9 PSR J1816+4510 -9 LS5039
c
-1s -10 -10
g
E / er -11 -11
d
N/ -12 -12
d
2E
g( -13 -13
o
l
-14 -14
-15 -15
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5
-2) m -9 PSR J1816+4510 -9 LS5039
-1cs -10 -10
g
er -11 -11
E /
N/d -12 -12
d
2E -13 -13
g(
o
l
-14 -14
-15 -15
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5
log(E / GeV) log(E / GeV)
Figure 2. γ-ray SEDs expected from the nebula surrounding the Redback millisecond binary system J1816+4510 (on the left) and
the binary system LS 5039 supposed to contain a classical pulsar (on the right). The upper panels show the results for monoenergetic
injectionofelectrons withenergy:102 GeV(dotted), 103 GeV(dashed), and104 GeV(solid).Themiddlepanelsshowtheresultsfora
power-lawinjectionwithspectralindexof−2.1betweenEmin=10GeVandEmax=3×102 GeV(dotted), 3×103 GeV(dashed),and
3×104GeV(solid).Thebottompanelsshowtheresultsforapower-lawinjectionwithspectralindexof−3inenergyranges:10−3×102
GeV (forJ1816+4510) and 100−3×103 GeV (for LS 5039) (dotted), 10−3×103 GeV (for J1816+4510) and10−3×104 GeV (for
LS5039)(dashed),10−3×104 GeV(forJ1816+4510) and100−3×104 GeV(forLS5039)(solid).Itisassumedthat∆mix·ǫ=10%
ofthepulsarwindpowerisconvertedtorelativisticelectrons.InthecaseofJ1816+4510 mostoftherelativisticelectrons inthepulsar
wind escapes from the binary system but in the case of LS 5039 only a part of the electrons in the wind, estimated on ∆bin ∼ 0.2,
IC
can escape from the binary system. For the comparison, the 100 hr differential sensitivity of MAGIC (Aleksi´cetal. 2012) and CTA
(Bernl¨ohretal. 2012) are also marked by the gray solid and dotted curve respectively. Full and empty data circles show the SED of
LS 5039 measured by H.E.S.S. in 2 different orbital phases (Aharonianetal. 2006) and the average spectrum from 30 months of the
observationswithFermi-LATisshownwithtriangles(Hadasch2012).Thethinblacklineintheleftpanelsshowthespectralfittothe
Fermi-LATobservations ofJ1816+4510 (Kaplanetal.2012).
We apply the Monte Carlo method in order to obtain Those two binary systems, J1816+4510 and LS 5039,
the γ-ray spectra produced by electrons which IC scatter areselectedformoredetailedcalculations. Theyseemtobe
stellar photons. These electrons are advected from the bi- the best candidates for the production of detectable γ-ray
nary system with the velocity of the mixed pulsar-stellar fluxesfromthenebulaeduetotheluminousstellarcompan-
windw .Theturbulentmagneticfieldinthemixedpulsar- ions and relatively compact nebulae. We assume that rela-
env
stellar wind isotropizes the directions of electrons. There- tivistic electrons take ǫ = 10% of the rotational power lost
fore,inthereferenceframeofelectronsthestellarradiation by the pulsars. In the case of the monoenergetic injection
from the companion star is isotropic. We take into account of electrons from the pulsar magnetosphere in the binary
that electrons propagate in the stellar radiation field and systemLS5039, onlyelectrons,movingwithinthesolid an-
the magnetic field which decrease with the distance from gle directed outward from the companion star, ∆Ωbin, can
IC
the binary system. The γ-ray spectra are calculated apply- escape from the inner region of the binary system without
ingtheformulaefortheICspectrainthegeneralcase from significant energy losses on the IC process. These electrons
Blumenthal & Gould (1970). escapeintheoutwarddirection(inrespecttothestar)since
(cid:13)c 2007RAS,MNRAS000,1–10
8 W. Bednarek & J. Sitarek
they move in the highly anisotropic stellar radiation field. termined by the value of the parameter η. For the value of
Basedonthepreviouscalculationsoftheradiationprocesses η, calculated for the supposed shock structure in LS 5039,
withinthebinarysystemLS5039(Bednarek2006),weesti- ∆ is larger than required above (see Table 2). In fact,
mix
matethispartofthehemisphereon∆bin =∆Ωbin/4π 0.2. differentphenomenacaneffecttheestimated valueof∆ .
IC IC ∼ mix
Thus, only 20% of the relativistic electrons escape without At first, the value of η might be much larger than 0.08,
∼
significant energy losses to the outer regions of the binary i.e the stellar wind may not effectively confine the pulsar
system LS 5039. This additional factor has been included wind. In fact the winds around Be type massive stars are
in our calculations for LS 5039. In the case of J1816+4510, expected to be aspherical with the dense and slow equato-
electrons moving rectilinear through the binary system do rial wind and the fast and rare poloidal wind. If the pulsar
not lose efficiently energy on the IC process due to lower is mainly immersed in the poloidal wind, than the shock
surface temperature and smaller radius of the companion structuremightevenbendaroundthestar(seecalculations
star. Therefore, we assume ∆bin 1 for J1816+4510. in Sierpowska-Bartosik & Bednarek 2008), i.e. the value of
IC ∼
The γ-ray spectra, expected from the nebulae around η islarger thanunity.Insuchcaseonlyapartofthepulsar
these two binary systems, are shown in Fig. 2 for the case wind can mix with the stellar wind. Second, the electrons
of the monoenergetic spectrum of electrons (upper figures) couldbeinjected anisotropically from thepulsaroracceler-
and the power law spectra of electrons which were ejected ated anisotropically in the pulsar wind. In fact, the pulsar
with the spectral indices equal to 2.1 (middle figures) and winds are expected to be highly anisotropic with the dom-
3 (bottom figures). The parameters defining these spectra inantequatorialcomponent(e.g.Bogovalov & Khangoulian
arereportedinthefigurecaption.Themaximumenergiesof 2002;Volpi et al.2008).Suchasphericalpulsarwindwillin-
electronsareconsistentwiththelimitsderivedforthecaseof troduce significant complications to the discussed scenario.
dominant synchrotron energy losses oradvection timescale More energy in relativistic electrons will be directed to the
with themixed winds (Table 2). equatorial regions of the binary system resulting in much
The γ-ray spectra, expected at the observer, are com- largereffectivevalueofη (evenlargerthanunity).However
pared with the sensitivity of the present generation (e.g. the solid angle, in which mixed stellar-pulsar wind is con-
MAGIC) and future (Cherenkov Telescope Array, CTA) fined,willbecomelower. Simpleestimations, whichbaseon
imagingatmosphericCherenkovtelescopes(IACTs).Detec- theformulaeinSect.2,showthattheincreaseofsignificant
tion of the considered here TeV γ-ray emission from the effectivepowerofthewindintheequatorialdirectionresults
Redback millisecond binary J1816+4510 with the present inmorepowertransferredintheformofrelativisticelectrons
instruments is unlikely. However, with a deep exposure of to the nebula. However, in such a case a significant part of
100 hr, such emission could be detected by CTA as long as theparticles,acceleratedbythepulsartowardsthecompan-
the energy conversion efficiency, ǫ, is at least 10%. The γ- ionstar,couldnotbeabletoescapefromthebinarysystem
rayspectrumobtainedfromtheFermi-LATobservationsof due to efficient IC interactions with the stellar radiation.
that source does not constrain the product of part of the Therefore, the final effect of the anisotropic pulsar wind on
hemisphere subtracted by the mixed wind and the energy the energy transferred to nebula in the form of relativistic
conversion efficiency for this source, i.e. ∆ ǫ. particlesisdifficulttoestimatewithoutmoredetailedcalcu-
mix
·
The γ-ray spectra expected from the LS 5039 are 2 lations.Thethirdpossibilityisthatmoreelectronscouldbe
∼
ordersofmagnitudeabovetheexpectedsensitivityofCTA. accelerated in the general direction towards the companion
Withtheassumedenergyconversionefficiencyfromthepul- star.Thismighthappenin thecaseofasignificant collima-
sar to relativistic electrons (10%), such emission should be tion of the relativistic particles in the pulsar winds by the
clearly detected even by thepresently operating Cherenkov shockstructure(e.g.seeDubuset al.2010;Bogovalov et al.
telescopes.TheTeVemission observedfromLS5039bythe 2008. Then, electrons lose efficiently energy on IC process
H.E.S.S.telescopesismodulatedwiththeorbitalperiod.On before they manage to escape into themixed wind region.
the other hand, the emission expected from the presented We conclude that the derived limits on the parameter
here model should contribute as a constant component in ∆mix ǫ,determiningthehighenergyemissionfromtheneb-
·
thewholeemission ofthesystem.Therefore,wecanusethe ulaaround LS5039, indicate on eitherdifferent parameters
low state observed by H.E.S.S. telescopes to constrain the ofthestellarwindthanusuallyexpectedintheliterature,or
parameters which determine the energy transferred to the ontheimportanceofanisotropicstellarandpulsarwinds,or
TeV electrons which escape from the binary system. This on theanisotropic injection/acceleration of relativistic elec-
power depends on the product of a part of the hemisphere trons within the binary system.
inwhichthemixedstellar-pulsarwindisconfined,∆ and
mix
the energy conversion efficiency, ǫ. Derived upper limits on
∆ ǫ are reported in Table. 3 for different spectra of
mix · 6 CONCLUSIONS
electrons in the case of LS 5039. For the broad range of
themodelparameters, ∆mix ǫisseverelyconstrained tobe We considered nebulae around binary systems which con-
·
1%. tainrotationpoweredpulsarsandhotcompanionstarswith
≪
Itisbelievedthattheenergyconversionefficiencyfrom a relatively large mass loss rate. Such nebulae differ signifi-
thepulsar to relativistic electrons, in theinnerpulsar mag- cantlyfromthepulsarwindnebulaearoundisolatedrotation
netosphere and in the shock acceleration scenario, is of the powered pulsars since a part of (or whole) the pulsar wind
orderof10%.Then,thepartofthehemisphereinwhichthe becomesloaded withthemassfromthecompanion star.As
mixed wind is confined should be also below ∆ 10%. aresult,thepulsarwindrelativisticplasmaslowsdownand
mix
∼
AsshowninSect.2,thisfactordependsonthehalfopening mixeswiththematterofthestellarwind.Themixedpulsar-
angle of the shock within the binary system which is de- stellar wind moves from the binary system in the outward
(cid:13)c 2007RAS,MNRAS000,1–10
Gamma-rays from nebulae around binary systems containing pulsars 9
Table 3. The upper limits on the product of the part of the hemisphere overtaken by the mixed pulsar-stellar wind (∆mix) and the
energy conversion efficiency (ǫ) from the pulsar to relativistic electrons for the binary system LS 5039 obtained from comparison with
H.E.S.S.andFermi-LATspectralmeasurements
Monoenergetic Power-law,α=−2.6 Power-law,α=−3
Emax [GeV] 102 103 104 102.5 103.5 104.5 103.5 104.5 104.5
Emin [GeV] 102 103 104 10 10 10 100 10 100
∆mix·ǫ <0.3% <0.05% <0.03% <0.3% <0.3% <0.2% <0.4% <0.3% <0.4%
direction with a reduced velocity determined by the power panion star and lose efficiently energy already within the
of thepulsar wind and themass of thestellar wind. Wear- binary system.
guethatthedistanceatwhichthesetwowindshavetomix It seems that the TeV γ-ray binary containing classi-
completelyisdeterminedbytheorbitalperiodofthebinary cal radio pulsar PSR B1259-63 should be also a good can-
system. This mixing process can concern the whole pulsar didate source for the application of the above considered
wind(forη<1thestellarwindpressuredominatesoverthe model. However, this pulsar is on a very elongated orbit
pulsar wind pressure) or only a part of the pulsar wind for around the companion star. Therefore, the nebula around
η >1. In the latter case, the rest of the pulsar wind (along this binary system is expected to have complicated, non-
polar regions of thebinary system) expandsfreely interact- spherically symmetricshape.Inthispaperweprovidedcal-
ingwiththeinterstellarmediumatlargedistancesfromthe culationsonlyforthebinarysystemswhich areexpectedto
binary system as observed in nebulae around isolated pul- produce nebulae which can be more or less approximated
sars. by a symmetric shape. The more complicated case of the
nebula around binary system, such as that containing PSR
Due to the efficient mixing, relativistic electrons are B1259-63, will be discussed in detail in a future paper.
isotropized in the reference frame of the mixed wind rela-
tively close to the binary system. Therefore, they can effi-
ciently comptonize thermal radiation from the companion
ACKNOWLEDGMENTS
star.Thisisin contrarytothenebulaearoundisolated pul-
sarswheretheinnerpartof thenebulaisnon-radiativedue This work is supported by the grants from the Polish
to thealmost radial motion of the plasma from thepulsar. MNiSzWthroughtheNCNNo.2011/01/B/ST9/00411 and
through theNCBiR No. ERA-NET-ASPERA/01/10.
We calculate the γ-ray spectra produced by leptons in
the IC scattering process in the case of the mono-energetic
particles(leavingthelightcylinderradiusofthepulsar)and
REFERENCES
in the case of the power law spectra of leptons formed as
a result of re-acceleration at the shocks produced in the Abdo,A.A. et al. 2009 ApJ 706, L56
pulsar-stellar wind collisions. Note that this γ-ray emission Actis, M. et al. 2011 Exp.Astron. 32, 193
shouldbesteady,i.e.independentonthephaseofthebinary Aharonian, F., et al. 2005, Science, 309, 746
system. As an example, we show the γ-ray spectra for the Aharonian, F.A. et al. 2006 A&A460, 743
supposed pulsar in the binary system LS 5039 and for the Albert, J., et al. 2009, ApJ, 693, 303
recentlydiscoveredRedbacktypemillisecondbinarysystem Aleksi´c, J., et al., 2012, Astropart. Phys., 35, 435
J1816+4510, containingrelatively hot companion star. It is Ball, L, Dodd, J. 2001 PASA 18, 98
foundthatifelectronstakeapartofthepulsarwindenergy Bednarek, W. 1997 A&A 322, 523
loss rate defined by the product of the part of the hemi- Bednarek, W. 2006 MNRAS368, 579
sphere,inwhichthemixedpulsar-stellarwindexpands,and Bednarek, W. 2009 A&A 495, 919
fortheaccelerationefficiencyofelectrons∆Ωǫequalto10%, Bernlo¨hr, K., et al. 2012, arXiv:1210.3503
·
than the TeV γ-ray emission from the millisecond binary Blumenthal, G.R., Gould, R.J. RvMP 42, 237
system is comparable to the sensitivity of the Cherenkov Bogovalov, S.V. et al. 2008 MNRAS 387, 63
Telescope Array (CTA). However, in the case of LS 5039, Bogovalov,S.V.,Khangoulian,D.V.2002MNRAS336,L53
electrons with such value of ∆Ω ǫ should produce γ-ray Bosch-Ramon, V. et al. 2012 A&A 544, 59
·
emission on the level clearly above the sensitivity of both Casares, J. et al. 2005 MNRAS364, 899
the present Cherenkov telescopes and CTA. By comparing Casares, J. et al. 2012, in preparation
theγ-rayspectra predictedfor LS5039 with theTeVγ-ray Dubus,G. 2006 A&A 456, 801
emission in the low state established by the H.E.S.S. tele- Dubus,G. et al. 2010 MNRAS404, L55
scopes, and with the average Fermi-LAT observations, we Eichler, D., Usov,V. 1993 ApJ402, 271
put strong limits on ∆ ǫ < 1%. Such low limit suggest Hadasch, D. 2012, IJMP, Conf. Ser. 8, 61
mix
·
that either the parameters of the stellar wind are less ex- Harding, A.K., Gaisser, T.K. 1990 ApJ 358, 561
treme than considered up to now in the literature or the Girard, T., Willson, L.A. 1987 A&A183, 247
injection of electrons from the inner pulsar magnetosphere Johnston, S. et al. 1992, MNRAS255, 401
and/or accelerated at the shock is highly anisotropic. Most Johnston, S. et al. 1994, MNRAS268, 430
of relativistic electrons might be directed towards the com- Kaplan, D.L. et al. 2012 ApJ753, 174
(cid:13)c 2007RAS,MNRAS000,1–10
10 W. Bednarek & J. Sitarek
A. Lamberts, A. et al. 2012 A&A 546, 60
Maraschi, L., & Treves, A. 1981, MNRAS,194, 1
Moldon, J, Ribo, M., Paredes, J.M. 2012, A&A, in press
(arXiv:1209.6073)
Pittard, J.M. 2009 MNRAS396, 1743
Roberts, M.S.E. 2011, in Proc. Radio pulsars: An astro-
physical key to unlock secrets of the Universe, AIP, v.
1357, p. 127-130 (arXiv:1103.0819)
Sierpowska-Bartosik, A.,Bednarek,W.2008MNRAS385,
2279
Stovall, K. et al. 2012, in preparation
Tavani, M., Arons, J. ApJ477, 439
Usov, V.V., Melrose, D.B. 1992 ApJ395, 575
Volpi, D. et al. 2008 A&A 485, 337
(cid:13)c 2007RAS,MNRAS000,1–10