Optical depths for gamma-rays in the radiation field of a star heated by external X-ray source in LMXBs: Application to Her X-1 and Sco X-1

0.33 MB·English

by  W. Bednarek

Astronomy&Astrophysicsmanuscriptno.aa13391 (cid:13)c ESO2010
January29,2010
Optical depths for gamma-rays in the radiation field of a star
heated by external X-ray source in LMXBs
Application to Her X-1 and Sco X-1
W.Bednarek&J.Pabich
DepartmentofAstrophysics,UniversityofŁo´dz´,90-236Ło´dz´,ul.Pomorska149/153,Poland
e-mail:[email protected]
0
Received;accepted
1
0
ABSTRACT
2

n ThesurfaceofalowmassstarinsideacompactlowmassX-raybinarysystem(LMXB)canbeheatedbytheexternalX-raysource
a whichmayappear duetotheaccretionprocessontoacompanion compact object (aneutronstaror ablackhole).Asaresult,the
J surfacetemperatureofthestarcanbecomesignificantlyhigherthanitisinthenormalstateresultingfromthermonuclearburning.We

9 wonderwhetherhighenergyelectronsandgamma-rays,injectedwithinthebinarysystem,canefficientlyinteractwiththisenhanced
2 radiation field. To decide this, we calculate the optical depths for the gamma-ray photons in the radiation field of such irradiated
starasafunctionofthephaseofthebinarysystem.Basedonthesecalculations,weconcludethatcompactlowmassX-raybinary

] systemsmayalsobecomesourcesofhighenergygamma-rayssinceconditionsforinteractionofelectronsandγ-raysarequitesimilar
E totheseonesobservedwithinthehighmassTeVγ-raybinariessuchasLS5039andLSI303+61.However,duetodifferencesin
H thesoftradiationfield,theexpectedγ-raylightcurvescansignificantlydifferbetweenlowmassandhighmassX-raybinaries.Asan
example,weapplysuchcalculationstotwowellknownLMXBs:HerX-1andScoX-1.Itisconcludedthatelectronsacceleratedto
.
h highenergiesinsidethesebinariesshouldfindenoughsoftphotontargetfromthecompanionstarforefficientγ-rayproduction.
p
- Key words. gamma-rays: theory –radiationmechanisms: non-thermal –binarysystems: close: –binary systems: individual: Her
o X-1,ScoX-1–neutronstars
r
t
s
a
1. Introduction atedintheshockwavescreatedinthestreamofmatterexpelled
[
from the inner part of the accretion disk (a jet) (e.g. Levinson
1 RecentlyTeVγ-rayshavebeenobservedfromafewmassiveX- & Blandford 1996, Georganopoulos et al. 2002, Romero et
v ray binaries (e.g. Aharonian et al. 2005a, Albert et al. 2006). al. 2002) or at the border in which accreting matter is stopped
5 Up to now such γ-ray emission has not been reported from bytherotatingneutronstarmagnetosphere(Bednarek2009a,b).
8 the low mass X-ray binaries (see e.g. observations of SS 433,
ThesecondscenariocanalsooccurinthecaseoflowmassX-ray
3 Aharonianetal.2005b),whichareveryluminousX-raysources
binaries.Therefore,itispossiblethataccelerationofparticlesto
5 (L ∼1036−39ergs−1,seethecatalogofLMXBLiuetal.2007).
X TeVenergiesshouldalsooccurwithinthelowmassX-raybina-
1. However,theclassofLMXBsasawholehasnotbeenmonitored ries. Note that TeV γ-ray emission is observed from variety of
0 intensively by the modern Cherenkov telescopes up to now. In cosmic sources (jets of active galaxies, vicinity of pulsars, su-
0 this paper we try to argue that very compact LMXBs are also
pernovaremnants,clustersofstars)whichsignificantlydifferin
1 promissingtargetsforTeVγ-rayastronomy.
structureandphysicalparameters.Sothen,evenifparametersof
: LMXBs likely contain a neutron star which accretes mat-
v objectsresponsibleforaccelerationofparticleswithinHMXBs
i ter from a companion star. Sometimes X-ray emission shows and LMXBs may differ significantly, this does not exclude ac-
X also pulsations with the rotational period of the neutron
celerationofparticlestoTeVenergiesinLMXBs.Howeverthe
r star(Nagase1989,Karino2007).SomeLMXBsshowalso op- efficiencyofparticleaccelerationmaydiffer.Themainpurpose
a
ticalmodulationwiththeperiodofthebinarysystemwhichcan
of searching for γ-ray emission from LMXBs with the present
beinterpretedasaresultofexternalheatingofthestellarsurface
andfutureCherenkovtelescopes(e.g.CTA)willbetoputlight
bytheX-raysource(e.g.HerX-1,ScoX-1).
onthisbasicquestion.Theaimofthispaperistoshowwhatare
The mechanism for particle acceleration and γ-ray produc-
themostfavourableconditionsfordetectionofTeVγ-raysignal
tion in the massive TeV γ-ray binaries is not at present clear.
fromtheclassofverycompactLMXBs.
Two general scenarios are considered. In the first one, ener-
getic pulsar creates relativistic wind which collides with the Efficientγ-rayproductionwithinmassivebinarieslikelyoc-
strong wind of the massive star creating a shock wave (e.g. curs due to the comptonization by relativistic electrons of the
Maraschi&Treves1981,Vestrand& Eichler1982,Harding& soft radiation produced by the massive star. Such strong radi-
Gaisser1990,Tavani&Arons1997,Kirketal.1999).Electrons ation is not present inside the low mass binaries where a nor-
can be accelerated up to the TeV energies in the shock accel- malstar has characteristicsurface temperaturebelow ∼ 104 K.
erationscenarioorinthenotwellknownmechanismoccurring Therefore,in general,efficientTeV γ-ray productionis notex-
inthepulsarwind.Inthesecondscenario,acompactobjectac- pectedthere.However,inverycompactLMXBs,alowmassstar
cretes matter from the massive star. Electrons can be acceler- canbe extensivelyheatedby theX-raysourceproduceddueto
2 W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs
ontothe stellar surface (see Fig. 1).Simple considerationsturn
outtothetemperatureprofileonthestellarsurfaceofthetype,
1/4
L cosβ/4πσ R2
X−ray αγ Eγ T(z)=T⋆4 + z2+X(cid:18)H− qR2⋆S−B z⊙2(cid:19)12/4
P
≈7.3×104 L38cosβ  K, (1)
α φ γ z2+(cid:18)H− qR2⋆−z2(cid:19)2
H where distances are defined in Fig. 1, L = 1038L erg s−1 is
X 38
R theluminosityoftheX-raysource,σ istheStefan-Boltzmann
SB
constant,β=π−µ−ν,cosµ=z/R ,tanν= H− R2 −z2 /z,
⋆ ⋆
(cid:18) q (cid:19)
and R is the stellar radius. The distances H, R, R , and z are
T(z) ⋆ ⋆
expressedinunitsoftheSolarradiusR =7×1010cm.Thevalue
z ⊙
ofzcanchangeintherangefrom0toz =R H2−R2/H.
max ⋆ ⋆
Star q
φ Thedistributionoftemperatureonthesurfaceofsuchirradi-
atedstarseenbytheexternalobserverlocatedatdifferentplaces
outside the star is shown in Fig. 2. Two effects determine this
soft radiationfield at a specific place:(a) the distance, R, from
thestellarsurfacedeterminesthesolidangleinterceptedbythe
Fig.1.Schematicpictureofthegeometricalsituationconsidered star;(b)theangle,α,atwhichthehotregionisseen(measured
inthepaper.γ-rayphotonwithenergyE isinjectedfromaplace in respect to the direction defined by the X-ray source and the
γ
atthedistanceR fromthecenterofthe staranda directionde- star). Note, that for reasonable parameters of the low mass X-
finedbytheangleαandφ.γ-raypropagatesattheanglesα and ray binary system (e.g. L = 1038 erg s−1, and H = 2R ), the
γ X ⋆
φ .ThestarisirradiatedbyapointX-raysource(withthelumi- surfacetemperaturecanincreaseduetoirradiationofthestarup
γ
nosityL )whichisatthedistanceH.Asaresultofirradiation, toafew104K.Thisiscomparabletothesurfacetemperatureof
X
atemperaturegradientappearsonthestellarsurface(T(z))with themassivestarswithinthehighmassX-raybinaries.Therefore,
themaximumvalueattheclosestpointtotheX-raysource. weexpectthattheopticaldepthsforTeVγ-raysinthesoftradi-
ationofsuchirradiatedlowmassstarscanalsoreachsubstantial
values,exceedingunityinsomecases.
accretionofmatterontocompanioncompactobject.Asaresult, Since the γ-ray photon injected at a specific place sees the
some parts of the stellar surface can reach temperaturecompa- hotpartofthestaratdifferentangles,thesoftradiationfieldseen
rabletothoseobservedinthecaseofhighmassstars(i.e.afew bytheγ-rayphotonchangessignificantlyduringitspropagation
104 K). Thissoftradiationprovidesenoughtargetforrelativis- inthevicinityofthestar(duetothechangeoftheviewingangle
ticelectrons,acceleratedinsidesuchcompactlowmassbinaries, and the distance from the stellar surface). In Fig. 2 we show
forproductionofTeVγ-rays.Inthispaperwecalculatetheop- the example radiation field from the stellar surface as seen by
ticaldepthsforγ-rayphotonsintheradiationfieldofirradiated the γ-ray photonat differentpropagationdistances L assuming
lowmassstarinordertocheckwhetherγ-rayproductioninsuch thattheprimaryγ-rayisinjectedattheX-raysource.Notethat,
systemscanoccurefficientandwhetherproducedγ-rayscanes- forthepropagationanglesα > 90o(seeFig.1),thesolidangle
γ
cape from the vicinity of the star. Note, that the cross sections subtractedbythestaratfirstincreasessincetheγ-rayapproaches
forγ-rayproductionintheinverseComptonscattering(ICS)and thestellarsurface.Forsmallanglesα ,thesolidanglesubtracted
γ
γ-rayabsorptionin collisionwithsoftphotonsarecomparable. by the star continuouslydropswith the γ-ray propagationpath
Therefore,directionswithin the binarysystem in which signif- andthehotregionbecomeslessvisible.
icant absorption of γ-rays can occur should also correspondto
directionsofefficientγ-rayproductioninICSprocess.
3. Theopticaldepthsforgamma-rays
Theopticaldepthsforγ-rayphotonsinjectedatanarbitrarydis-
2. Softradiationfromirradiatedstar
tance from the surface of the star in the case of its fixed sur-
TheX-rayemissionproducedinthevicinityofacompactsource face temperature were calculated for the first time in the gen-
insomecloselowmassX-raybinariescanreachthevaluesof∼ eral case by Bednarek (1997,2000).In respect to previous cal-
1036−39ergs−1.ApartofthisX-rayemissioncanilluminatethe culations (e.g. Moskalenko et al. 1993), Bednarek took also
surfaceofacompanionstar.Asaresult,thesurfacetemperature into account dimensions of the star, which allows their appli-
risessignificantly.Wecalculatethetemperatureprofileontothe cationtoverycompactbinariessuchase.g.CygX-3.Suchcal-
surface of such irradiated star by a point X-ray source located culations are necessary in the case of the IC e± pair cascades
at the distance, H, from the center of the star. We assume that developing within the massive binaries since in principle sec-
all X-ray emission absorbed by the stellar surface is irradiated ondary e± pairs and γ-rays can appear everywhere within the
as a black body emission with characteristic temperature T(z), binary.Theycanalsofallontothesurfaceofthecompanionstar.
wherez is the distance measuredfromthe directiondefinedby Theopticaldepthsforγ-rayscalculatedintheradiationfieldof
the center of the star and the X-ray source and a specific point the star withspecific parameterscan beeasily re-scaledforthe
W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs 3
Fig.2.Theradiationfieldseenbyγ-rayphotonatitsdifferentlocationsalongthedirectionofpropagationL.Thisradiationisdue
totheirradiationbyexternalX-raysourcewithluminosity1038ergs−1 locatedatthedistanceH =2R fromthecenterofthestar.
⋆
γ-raysarealsoinjectedatthedistanceH =2R butatdifferentanglesα =45o(upperpanel),90o(middlepanel),and120o(bottom
⋆ γ
panel)inrespecttothelinedefinedbytheinjectionpointandthecenterofthestar.ThepropagationdistanceisequaltoL=0(left),
R (left-middle),3R (right-middle),and5R (right).ThestarhastheradiusR =R equaltotheradiusoftheSunandthesurface
⋆ ⋆ ⋆ ⋆ ⊙
temperatureT =6000K.Thegreyscaledenotestherangeoftemperaturestartingfrom7.5×104K(white)to6×103K(black).
⋆
casesofmassivestarswithothersurfacetemperaturesandradii nuclear burning. However, in the presence of a nearby strong
(Bednarek 2009a). For example, γ-ray photons with energies, X-raysource,thesurfacetemperatureofastarcansignificantly
Eo, propagatingat specific distance D from the star, and in di- increaseduetotheirradiationprocess(seesection2).Therefore,
γ
rection (defined by the angle α), approaching close to the star relativisticelectronsinjectednotfarfromthesurfaceofthelow
with specific parameters (T and R ) are related to the optical mass star in a compactX-ray binary can also suffer strong en-
o o
depths around arbitrary stars with T and R in the following ergy losses on the ICS process. Primary γ-rays and secondary
⋆ ⋆
way, cascadeγ-rayscan beefficientlyabsorbedinthis softradiation
Eo field.Inordertocheckwhethersuchprocessesmaybecomeim-
τ( γ,T ,R ,D,α)=S3S τ(Eo,T ,R ,D,α) (2) portant,wecalculatetheopticaldepthsforγ-raysinsuchmore
S ⋆ ⋆ T R γ o o
T complicatedscenariofollowingthestandardprescription,
where S = T /T , S = R /R , and the distance D is mea-
T ⋆ o R ⋆ o
suredin stellar radii. Theseγ-ray opticaldepthshavebeen fre-
τ= dl dǫdΩn(l,ǫ,Ω)σ (ǫ,θ)(1−cosθ), (3)
quentlydiscussed in the contextof the massive stars inside the Z Z γγ
ℓ
highmassX-raybinariesrecentlydetectedintheTeVγ-rays(see
e.g.Bo¨ttcher&Dermer2005,Bednarek2006a,Dubus2006). wheren(l,ǫ,Ω)isthedifferentialdensityofsoftphotonswithen-
Hereweareinterestedinamorecomplicatedscenariowhich ergyǫwhicharrivefromthelowmassstarinsidethesolidangle
can be appropriate for the low mass X-ray binary systems. In Ωtoinstantaneouslocationoftheγ-rayphotonatthepropaga-
LMXBs the companion stars produce relatively weak soft ra- tion distance l, σ is the e± pair productioncross section, and
γγ
diation field due to its low surface temperature resulting from θistheanglebetweenthemomentumvectorsofthegamma-ray
4 W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs
Fig.3.Theopticaldepthsforγ-raysintheradiationfieldcreatedbyalowmassstarirradiatedbyexternalX-raysource.Itisassumed
thattheX-raysourceisatthedistanceH =2R (upperpanel)fromthecenterofthestar.Theγ-raysareinjectedatdifferentdistances
⋆
fromthestar(seeFig.1):R = 1.5R (leftfigure),2R (middle),and3R (right),andtheanglesα = 0o andφ = 0o.γ-rayphoton
⋆ ⋆ ⋆
movesatdifferentangleα = 30o(solid),60o(dashed),90o(dot-dashed),and120o(dotted).Theopticaldepthsforotherdistances
γ
oftheX-raysourceandinjectionplacesofγ-rays,H = 1.5R andR = 1.5R andH = 3R andR = 3R ,areshowninthebottom
⋆ ⋆ ⋆ ⋆
panelontheleftandrightfigures,respectively.Theparametersofthestarinthebinarysystemare:T =6000K,R =R =7×1010
⋆ ⋆ ⊙
cm.
andsoftphoton.ℓ denotesthepathalongpropagationdirection dependonlylinearlywiththisdistance.DuetothecloserX-ray
ofthegamma-rayphotoninthesoftradiationfield. source,thesurfaceisheatedtohighertemperature.
Weinvestigatetheopticaldepthsforγ-raysasafunctionof InFig.4,weshowhowtheopticaldepthsdependonthean-
their energiesand other free parametersdescribing the geome- gle α (which is the angle between the direction defined by the
tryofthepicture,suchastheinjectiondistanceRandtheangle location of the X-ray source and the center of the star and the
α (see Fig. 1). The low mass stars with differentradii and sur- injection place of γ-raysand the center of the star, see Fig. 1).
facetemperaturesareconsidered.Forthepurposeoftheexample Suchsituationmaycorrespondtothecaseofinjectionofγ-rays
calculations,theX-rayluminosityofthecompactobject(aneu- from differentplaces of the jet launched from the compactob-
tron star) is fixed on LX = 1038 erg s−1. The optical depths as ject.Note,thatforlargeranglesαthehottestregiononthestellar
a functionof γ-ray photonenergyfor selected injection angles surfaceisalsoseenunderlargerangles.Therefore,theeffective
anddistancesfromthecompanionstarareshowninFig.3.The radiation field from the stellar surface seen from the injection
calculationsshowthattheopticaldepthsaresignificantforsome placeoftheγ-raydropssignificantly.Asaconsequencetheop-
rangeofinvestigatedenergiesofγ-rayphotons.Theyareclearly tical depthsfor γ-ray photonsare lower (comparee.g. Figs. 4a
above unity provided that γ-rays are injected within R ∼ 2R⋆ and4c).
from the center of the star at a partof the hemispherecontain-
ing the star. Note that the optical depthsincrease also for stars
withlowerradiiinthecaseofsimilarcompactnessofthebinary In summary,we concludethat the opticaldepthsforγ-rays
system (expressedas the ratio of the injection distance and the canalsoexceedunityinthecase ofverycompactlowmassX-
radiusof the star).Thisis due to thefactthatirradiatingX-ray ray binary systems. Therefore, we predict that these LMXBs
sourceisclosertothestellarsurfaceinsuchcases.Notethatthe can become sources of GeV-TeV γ-rays as in the case of high
amountof powersuppliedto thestellar surfacefromthe X-ray mass X-raybinaries, providedthatthe accelerationmechanism
sourceincreasesasasquareofitsdistancebuttheopticaldepths ofelectronstoTeVenergiesstillworks.
W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs 5
Fig.4. As in Fig. 3 but for the X-ray source at the distance H = 2R , injection distance of γ-rays from the star R = 1.5R and
⋆ ⋆
differentangles of the injection place α = 10o (left figure), 20o (middle), and 30o (right). γ-ray photon movesat different angle
α =1o(triple-dot-dashedcurve),31o(solid),61o(dashed),91o(dot-dashed),and121o(dotted).
γ
Theexampleγ-rayopticaldepthlightcurvesarecalculated
fortherangeoftheinclinationanglesofthebinarysystem and
specific energies of γ-ray photons injected in the direction to-
wards the observer. The results for the X-ray source on a cir-
Obs cular orbitwith the radiusRb = 2R⋆ andthe injectionplace of
γ-rays also at the X-ray source are shown in Fig. 6. Note the
characteristic optical depth light curvesin the case of the non-
α
eclipsingsystemswiththeinclinationanglesdifferentthanzero.
90o −α Insuchcase,theopticaldepthsreachthemaximumwhentheX-
raysource(andalsoγ-raysource)isbehindthestar(inrespectto
theobserver).Theopticaldepthsatthepeakofthemaximumare
largerforlargerinclinationanglesofthebinarysystem.Forthe
star
considered parameters of the binary system, the optical depths
are above unity at least for some range of phases close to the
β phaseΦ =0.5.Inthecaseoftheeclipsingbinariestheobserver
shouldseetwopeaksintheopticaldepthlightcurveduetothe
Φ eclipse of the X-ray and γ-ray source by the star. Note, that at
the phases at which the γ-ray optical depth light curves reach
themaximum,thehot,irradiatedpartofthestellarsurfaceisnot
wellvisible.Therefore,itisnaturaltoexpectunticorrelationbe-
tween the maximum of γ-ray light curve and the maximum in
X−ray
theopticallightcurvefromsuchlowmassbinarysystems.This
prediction might be useful in order to increase the probability
Fig.5.Thegeometricalsituationconsideredinthecaseofacom-
ofthedetectionoftheGeV-TeVγ-raysignalfromthecompact
pactX-raysourceonanorbitaroundalowmassstar.TheX-ray
X-rayluminousLMXBs.
sourceirradiatesthestellarsurfaceheatingittotemperaturesig-
nificantly above that one due to nuclear burning. The observer
Since the assumed orbit of the X-ray source (and γ-ray
seestheheatedstellarsurfaceattheangleβmeasuredinrespect
source) is circular, the light curve looks symmetric. This light
to the direction defined by the X-ray source and the star. The
curvecanbesignificantlymodifiedwhenthedistanceoftheX-
systemisinclinedattheangleαinrespecttotheobserver.The
raysourcechangeswiththephaseofthebinary.Inordertohave
X-raysourceandtheγ-raysourcearelocatedatthephaseΦin
impressionabouttheinfluenceoftheellipticityoftheorbit,we
respecttotheplaneoftheobserver.
calculate the optical depth light curves for other distances of
the X-ray and γ-ray sources from the star. In Fig. 7, we inves-
tigate the optical depths for the orbits of the X-ray source in
4. Gamma-rayopticaldepthlightcurves
the range R = 2− 3R and distances of the γ-rays source in
b ⋆
We investigatealso howthe γ-rayopticaldepthscanchangein the range R = 1.5−3R . Note significant change of the opti-
⋆
the case ofa lowmass compactbinarysystem in whichthe X- caldepthswiththesetwobasicparametersR andR.However,
b
ray sourceis on the circularorbitaroundthe solar typestar. In forthewholerangeoftheseparameters,theopticaldepthsareal-
thiscasetheangleβbetweenthedirectiontowardstheobserver waysaboveunityforsomerangeofphases.Therefore,weexpect
and the direction defined by the X-ray source and the star can thatintensiveabsorption(andalsoproduction)ofγ-rayphotons
changesignificantlydependingontheinclinationangleαofthe mightoccurinthecaseofcompactlowmassX-raybinarysys-
binarysystem.βisdeterminedinthiscasebythephaseΦofthe tems. Howeverin therealistic case, thespectrumof γ-raypho-
X-raysource(forgeometricalsituationseeFig.5). tons should be formed in the complicated cascade process due
6 W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs
to a highlyanisotropicsoftradiationcreatedby suchirradiated
star.Thiscascadescenariowillbeclearlymorecomplicatedthan
considereduptonowfortheγ-rayproductioninsidethemassive
binarysystems(seee.g.earlyresultsbyBednarek2000).
Forcomparison,wealsoshowtheγ-raylightcurvesforthe
caseofstellarmasscompanionwhichisinthegiantphase(other
parametersofthebinaryasinFig.7b).Duetolargerdistanceof
theX-raysourcefromthesurface,theopticaldepthsareclearly
lowerthaninthecase ofthebinarysystemwiththesolarmass
star on the Main Sequence. However, still for small range of
phasesandrelativelylargeinclinationanglesofthe binarysys-
tem,theopticaldepthsovercomeunity.Therefore,insomegeo-
metricalsituationsalsothesemoregeometricallyextendedbina-
ries(i.e.withlongerorbitalperiods)canprovideconditionsfor
efficientproductionofGeV-TeVγ-rays.
Calculatedhereγ-rayopticaldepthlightcurvesallowusto
conclude that the largest fluxes of GeV γ-rays should be ex-
pectedinthephaseswheretheopticaldepthsare clearlyabove
unity. In such cases the cascading effects degradea part of the
primaryγ-rayspectrumintheTeVenergyrangeduetoefficient
cascading.Ontheotherhand,thelargestfluxesofTeVγ-raysare
expectedinphaseswheretheopticaldepthsareclosetounity.In
suchcase, primaryTeVγ-raysareefficientlyproducedandnot
severelyabsorbedintheICe± paircascades.Basedontheanal-
ysis of Figs. 6 and 7, we expect the largest fluxes of the GeV
γ-rayswhen the X-ray source (a compactobject) is behindthe
normalstar(excepttheeclipsingbinaries).Thelargestfluxesof
theTeVγ-raysareexpectedfortheintermediatephases,i.e.just
beforeandafterthelargestfluxesofGeVγ-rays.
5. TheexamplecasesofLMXBs
As an example, we show the γ-ray optical depth light curves
fortwoLMXBsystemswhichshowopticalmodulationwiththe
binary system period. This modulation is interpreted as due to
the irradiation of the companionstar by the X-ray source (e.g.
Milgrom1976).Theyhavebeenreportedinthepastasapossible
TeV-PeVγ-raysources.
5.1.HerX-1
ThefamousLMXB,HerX-1,ischaracterisedbytheX-raylumi-
nosityL =6×1037ergs−1(Whiteetal.1983).Thecompanion
x
star has the radius R = 3.86R , the mass M = 2M with a
⋆ ⊙ ⋆ ⊙
neutron star on an orbit with the radius R = 8.61R . The in-
b ⊙
clinationof the binarysystem has beenestimated on α = 80+8
−5
degreesanditsorbitalperiodis1.7days(Nagase1989).
HerX-1hasbeenclaimedinthepastasapulsedTeVγ-ray
source bythe WhippleCollaboration(e.g.Gorhamet al. 1986,
Fig.6.Thedependenceoftheγ-rayopticaldepthsinthethermal
Lamb et al. 1988).However, later analysis have not confirmed
radiationoftheirradiatedstarasafunctionofthephaseofthebi-
these reports (Reynolds et al. 1991). The modern Cherenkov
narysystem.Thephaseismeasuredfromthesituationinwhich
telescope collaborations have not reported any observations of
theX-raysourceisinfrontofthestar(inrespecttotheobserver).
thissourcerecently.
Specificfiguresshowtheγ-rayopticaldepthlightcurvesforse-
We have calculated the γ-ray optical depth light curves for
lectedenergiesofγ-rayphotonsequalto:33GeV(a),100GeV
theparametersofHerX-1.Itisassumedthatthesourceofpri-
(b),330GeV(c),1TeV(d),and3.3TeV(e).Thelightcurvesfor
maryγ-rays(producedby acceleratedelectrons)is close to the
differentinclinationanglesofthe binarysystem are shownfor:
X-raysource.TheresultsareshowninFig.8forselectedener-
α = 0o (triple-dotdashedcurve),30o (solid),45o (dashed),60o
giesofγ-rayphotons.Itisclearthattheopticaldepthsaregreater
(dashed), and 89o (dot-dashed).The thin dotted line marks the
thanunityforsomerelativelysmallrangeofphasesinthecase
opticaldepthequalto unity.Theparametersofthe star arefol-
ofγ-rayswithenergiesintherangeE =0.1−1TeV.Theoptical
lowing:R = R anditssurfacetemperatureT = 6000K.The γ
⋆ ⊙ ⋆ depthscanreachthemaximumvaluesτ∼3.Therefore,thepos-
orbitof the X-ray source is circular with the radiusR = 2R .
b ⋆ sible cascadingeffects haveto be taken into accountwhencal-
Theγ-raysareinjectedfromthevicinityoftheX-raysource.
culatingdetailedγ-rayspectrumescapingtowardstheobserver.
W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs 7
However,theprimaryγ-rayspectrumshouldnotbeverysever- vationsturnstoratherintermediateinclinationangles(Fomalont
allydegradedattheTeVγ-rayenergiesasexpectedinthecaseof et al. 2001,Steeghys & Casares 2002) which is applied in this
massivebinarysystemssuchasLS5039orLSI61303.Wepre- paper. The present lack of strong modulation of UV emission
dictthatthe largestfluxesof GeV-TeVγ-raysshouldappearin mightbeunderstoodassumingthatsignificantpartofthehotre-
therangeofphasesjustbeforeandaftertheeclipseoftheX-ray gion on the stellar surface is shadowed by the large accretion
sourcebythecompanionstar,i.e.intheranges:Φ∼0.35−0.45 diskin thissystem.Note,thatthe outerradiusofthisaccretion
and0.55−0.65.Notethatzerophasecorrespondstothe situa- diskhasbeenestimatedon∼ 6×1010 cm (Vrtileketal. 1991)
tionwheretheX-raycompactsourceisinfrontofthecompanion whichiscomparabletotheseparationofstarsinthisbinary.
star.Moreover,thisγ-rayemissionshouldbeunticorrelatedwith
theopticalemissioncomingfromapartofthestellarsurfaceir-
6. DiscussionandConclusion
radiated by the X-ray source. In fact, evidences of the optical
modulation with the period of the binary system Her X-1 has WeshowedthattheopticaldepthsforTeVγ-rays,injectedinside
beenclearlydetectedinthepast. theLMXBsclosetothesurfaceofthecompanionstarsirradiated
Fortheinjectionplaceofprimaryγ-rayswhichsignificantly bytheX-raysources,arelargerthanunityforspecificlocations
differfromthelocationoftheX-raysource(e.g.fartherfromthe oftheobserver.Itiseasytoshowthatduetosimilarcrosssec-
X-ray source along the jet or at the shock structure),the phase tionfortheγ−γ→e± absorptionprocessandthecrosssection
patternsoftheγ-rayopticaldepthsshouldofcoursechangeac- fortheICSprocessofsoftphotonsbyrelativisticelectrons,also
cordingly. the optical depths for electrons on these same stellar radiation
shouldhavesimilarvalues.Therefore,itisexpectedthatthepro-
ductionandcascadingofγ-rayscanbeefficientintheLMXBsin
5.2.ScoX-1
whichthecompanionstariseffectivelyheatedbythecloseX-ray
The second binary system, Sco X-1, has significantly different source.However,theopticaldepthsinthecaseofirradiatedlow
parameters from Her X-1. It contains a low mass star, M = massstarsaregenerallylowerthantheopticaldepthsexpectedin
⋆
0.5M , and a neutron star (Liu et al. 2007). Sco X-1 belongs theHMXBsdetectedintheTeVγ-rays(suchasLS5039orLSI
⊙
to the class of Z sources with three states of X-ray emission 303+61,e.g.Bednarek2006a).Sothen,thecascadingeffectsin
characterised by the luminosities L = (4−12)×1037 erg s−1 the LMXBsshouldnotoccurso efficientlyas itwas shownfor
x
(Hasinger& vanderKlis 1989).Theaccretiondiskaroundthe those sources (Bednarek 2006b, 2007, Sierpowska-Bartosik &
neutronstarinthisbinarysystemlaunchesajet.Therefore,the Torres2007,2009).Duetothese substantialopticaldepths,we
object belongs also to the class of microquasars. The inclina- expectthat the GeV-TeVγ-ray emission can be also efficiently
tionangleofthebinarysystemhasbeenestimatedintherange: producedwithincompactLMXBs in which the compactX-ray
α = 44o ±6o (Fomalontet al. 2001).The period of the binary sourcestronglyirradiatescompanionstarprovidedthatelectrons
systemis18,9hrs(Gottliebetal.1975).Inourcalculationswe areacceleratedtoTeVenergiesalsoinsideLMXBs.Themech-
applytheradiusofthecompanionstarR = 1R (evolvedsub- anism of particle acceleration inside LMXBs can either differ
⋆ ⊙
giant,Steeghys&Casares2002),theradiusofthebinarysystem fromthatoneoperatingwithintheHMXBsorcanbequitesim-
R =2.14r =1.5×1011cm,theinclinationofthebinarysystem ilar.Infact,theTeVγ-raysareobservedfromdifferenttypesof
b ⊙
α=44o,andthepoweroftheX-raysource1038ergs−1. sources(e.g.jetsofAGNs,vicinityofpulsars,orshocksofsu-
ScoX-1hasbeenalsoclaimedasaTeV-PeVγ-rayssourcein pernovaremnants).Therefore,differentconditionsaroundcom-
the80-tiesbutwiththelowsignificance(e.g.Brazieretal.1990, pact objects in HMXBs and LMXBs can also turn to accelera-
Tonwaretal.1991).Alsotheseresultshavenotbeenconfirmed tionofparticlestoTeVenergies.Ontheotherhand,TeVγ-ray
bylatterobservations. emissioninsideLMXBsmaybeproducedinsimilarscenariosas
AsforHerX-1,theγ-rayopticallightcurveshavebeencal- proposedforHMXBs (e.g.accretingneutronstar scenariopro-
culatedasafunctionofenergyofγ-rayphotons.Note,thatSco posedrecentlybyBednarek2009b).However,aswehaveshown
X-1 is more compact binary system than Her X-1. Therefore, above the TeV γ-ray emission from LMXBs should be limited
therangeofphases,forwhichtheγ-rayopticaldepthsareabove tospecificnarrowrangeofphaseswhichareexpectedtobedif-
unity, is significantly broader. Also, the absolute values of the ferentfromtherangeofphasesobservedintheHMXBsdueto
opticaldepthsarelarger.Sothen,weexpectmuchstrongermod- differences in the soft radiation field (see considered example
ification of the escaping γ-ray spectra by IC e± pair cascading casesofHerX-1andScoX-1).
effects.Duetothesereasons,theTeVγ-rayemissioncanbesev- Basedontheresultsofcalculationsoftheopticaldepthsand
erallyattenuatedforthephasescloseto∼0.5andtheTeVγ-ray asimpleapplicationofthelawofgravity,wecanenvisagewhich
light curve may show two minima, first due to inefficient pro- LMXBsareexpectedtobepotentialGeV-TeVγ-raysources.We
ductionintheregioncloseto∼0.0phaseandtheseconddueto concludethatinthecaseofthesolartypestarintheevolutionary
strongabsorptionintheregionclosetothephase∼ 0.5.Incon- phaseontheMainSequence(R⋆ = R⊙ and M⋆ = M⊙)andthe
trast,theGeVγ-raylightshouldshowonebroadmaximumcen- orbitwith the radiusRb < 3R⋆, the γ-rayshavea chanceto be
teredonthephase0.5.Theseconclusionsarederivedassuming efficientlyabsorbedwhichmeansalsotheirefficientproduction
the circular orbit of the compact object around the companion inICprocessbyelectrons.Thiswilloccurprovidedthatthepe-
star.Themoredetailedanalysisisatpresentnotpossibledueto riodofthebinarysystemisshorterthanP ∼ 17R3/2M−1/2 hrs,
b ⋆ ⋆
thelackofinformationonthedetailsoftheorbitofthecompact whereR andM areinthesolarunits.NotethatmanyLMXBs
⋆ ⋆
objectinScoX-1(i.e.ellipticity,phaseofperiastron). havetheorbitalperiodswithinthislimit(Liuetal.2007).
It isnotclearat presentwhetherthecompanionstar in Sco Based on the analysis of the optical depth light curves we
X-1 is really efficiently irradiated by the X-ray source. Early concludethattheemissionpatternsofescapingγ-raysfromthe
calculations by Milgrom (1976) suggest that irradiation is im- lowmassbinarysystemstronglydependonitsinclinationangle.
portantandconsistentwithobservationalresultsatthattime.In Wepredictthatinthesimplestconsideredmodelofapointlike
these calculations relatively small inclination angles has been source of primary γ-rays on a circular orbit around irradiated
considered (up to i ∼ 6o). The analysis of more recent obser- lowmassstar,theobserverlocatedat:
8 W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs
– Smallinclinationangles:detectssignificantGeV-TeVγ-ray locationoftheγ-raysourceisclearlyconsistentwiththedimen-
emissiononlyfromverycompactbinariesinwhichthecom- sionsofthebinarysystem.
pactobjectisatthedistanceoflessthan2stellarradiifrom Based on similar estimations it is possible to show that the
thecompanionstar(comparethetriple-dotdashedlineswith radiation field from the inner part of the accretion disk around
thethindottedlinesinFigs.6and7).Inthiscasethemodu- the neutron star may not preventescape of γ-ray photonseven
lationoftheUVemissionfromanirradiatedcompanionstar if they are created within or close to this region. For example,
withtheperiodofthebinarysystemmaybesignificantlyre- in the case of Her X-1 the inner disk temperature is estimated
ducedsincethehottestpartsofthestellarsurfacearenotwell intherange∼ (1.8−2.5×104)K(Sazonov2009)andthedisk
visible. inner radius is at the distance of the order of a few ∼ 108 cm
– Intermediateinclinationangles:detectsasinglepulseofγ- from the neutron star (Ghosh & Lamb 1979). We estimate the
rayemissionwiththemaximumcorrespondingtothephases mean free path for γ-rays propagating in such radiation on ∼
whenthe X-raysourceisbehindthecompanionstar. Inthe 5 × 109 cm. This is clearly larger than dimension of the disk
casetheobservershoulddetectsignificantmodulationofthe innerradius.Therefore,γ-rayscanescapefromtheinnerpartof
UVemissionfromthestellarsurfacemodulatedwiththepe- theaccretiondiskwithoutsignificantabsorption.Note,thatthe
riodofthebinarysystem. regionofparticleaccelerationmaybelocatedatsomedistance
– Largeinclinationanglesandeclipsingbinaries:detectstwo fromthehotneutronstarsurfaceandtheinneraccretiondiskbut
narrow pulses of γ-rays just before and after the eclipse of still inside the binary systems. For example, there are models
theX-raysourcebythecompanionstar.Inthiscasethemod- whichproposeaccelerationofparticleswithinthejetswhichare
ulationoftheUVemissionshouldbeclearlyobservedbutin observedinthecaseofsomeLMXBs(e.g.ScoX-1).
somecasescanbealsostronglysuppressedduetotheobscu- We can envisage realistic situation in which the absorption
rationof thehottestpartsonthe stellar surfacebythe large ofTeVγ-raysintheradiationoftheX-raysourcecanbesafely
accretiondisk. neglected.Forexample,inthecaseofHerX-1,theX-raysource
canbeproducedontheneutronstarsurfaceduetoaccretionof
The γ-ray emission features from LMXBs can differ from matter. However, the acceleration of electrons (and production
those observed in HMXBs. The differences are due to the fact oftheprimaryγ-rays)canoccurclosetoorinaveryturbulent,
thatingeneraltheopticaldepthsforγ-raysintheradiationfield magnetized region at the inner accretion disk radius where the
of irradiated stars in LMXBs are lower in respect to these cal- pressureoftheaccretingmatterisbalancedbystronglymagne-
culated in the case of HMXBs. We want to mention that the tizedrotatingneutronstarmagnetosphere(thesurfacemagnetic
specific binary system may in fact differ significantly from the fieldofHerX-1isestimatedon2.9×1012G,e.g.Karino2007).
simplified picture discussed in this paper. The main geometri- Then, the inner radius of the accretion disk in Her X-1 is ex-
cal complications can be introduced by the inhomogeneousir- pectedatthedistanceofafew108 cmfromtheneutronstar.In
radiationofthestarbyX-raysource(anisotropicX-raysource) thecaseofScoX-1productionofγ-rayscanoccurinsideapart
and the elliptic orbit of the X-ray source around the compan- of the jet at some distance from the neutron star and the inner
ionstar.Moreover,ouranalysisbaseontheassumptionthatthe diskbutstillinsidethebinarysystem.
possible cascade initiated by primary electrons and γ-rays de-
velopmono-directionallythroughthebinarysystem.Infact,the Acknowledgements. This work is supported by the Polish MNiSzW grant N
structureofthemagneticfieldofthestarcaninfluencethepaths N203390834.
of secondary cascade e± pairs. As a result, the escaping sec-
ondary γ-rays can form complicated structures on the sky (see
References
Sierpowska&Bednarek2005).
Someone can wonder whether absorption of γ-rays should Aharonian,F.etal.2005aScience309,746
Aharonian,F.etal.2005bA&A439,635
notoccurefficientlyintheradiationfieldoftheX-raysourceon
Albert,J.etal.2006Science312,1771
thesurfaceoftheaccretingneutronstar.Weshowbelowthatthis
Bednarek,W.2000A&A363,646
isnotthecaseprovidedthatγ-raysareinjectedatsomereason- Bednarek,W.2006aMNRAS368,579
abledistancefromtheX-raysource.Assumingthecharacteris- Bednarek,W.2006bMNRAS371,1737
ticdimensionoftheX-raysourceequalto∼ 105 cm(theorder Bednarek,W.2007A&A464,259
Bednarek,W.2009aA&A495,919
ofthepolarcapontheneutronstarsurface)andtheluminosity
Bednarek,W.2009bMNRAS397,1420
ofthe X-raysource1038 ergs−1, we estimate the characteristic Bo¨ttcher,M.,Dermer,C.D.2005ApJ634,81
temperature of the X-ray source on T ≈ 6×107L1/4R−1/2 K, Brazier,K.T.S.etal.1990A&A232,383
X 38 5 Dubus,G.2006A&A451,9
whereR = 105R cmisthecharacteristicdimensionoftheX-
x 5 Fomalont,E.B.,Geldzahler,B.J.,Bradshaw,C.F.2001ApJ512,L121
raysource.Note,thatforsimplicityweassumedtheblackbody Georganopoulos,M.,Aharonian,F.A.,Kirk,J.G.2002A&A388,L25
typeemissionfromtheX-raysource.Weestimatethedistance, Gorham,P.W.etal.1986ApJ308,L11
D, from such X-ray source at which the optical depths in the Ghosh,P.,Lamb,F.1979ApJ234,296
Gottlieb,E.W.,Wright,E.L.,Lillier,W.1975ApJ195,L33
radiation of such X-ray source become lower than unity from
Harding,A.K.,Gaisser,T.K.1990ApJ358,561
τ = Dσγγ→e±nx, where σγ−γ→e± is the cross section fore± pair Hasinger,G.,vanderKlis,M.1989A&A225,79
creationinγ−γcollision,n ≈20T3(R /D)2cm−3isdensityof Karino,S.2007PASJ59,961
x x
X-rayphotonsatthedistanceD.Applyingthatthecrosssection Kirk,J.G.,Ball,L.,Skjaeraasen,O.1999APh10,31
Lamb,R.C.etal.1988ApJ328,L13
for γ−γ collision is inversely proportionalto energy of γ-ray
Levinson,A.,Blandford,R.1996ApJ456,L29
photon,we estimate that the optical depth becomes lower than Liu,Q.Z.etal.2007A&A469,807
unityfordistanceslargerthanD∼108cmandenergiesofγ-rays Maraschi,L.,Treves,A.1981MNRAS194,1
above∼ 10 GeV. Note moreoverthat most of the γ-raysmove Milgrom,M.1976ApJ208,191
Moskalenko,I.V.,Karakuła,S.,Tkaczyk,W.1993,MNRAS260,681
in the outward direction in respect to the location of the X-ray
Nagase,F.1989PASJ41,1
source. Thus, the geometricaleffects can additionally decrease
Reynolds,P.T.etal.1991ApJ382,640
the optical depths in the X-rays. This estimate on the possible Romero,G.E.,KaufmanBernadoM.M.,Mirabel,F.2002A&A393,61
W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs 9
Sierpowska,A.,Bednarek,W.2005MNRAS356,711
Sierpowska-Bartosik,A.,Torres,D.2007ApJ671,145
Sierpowska-Bartosik,A.,Torres,D.2009ApJ693,1462
Tavani,M.,Arons,J.1997ApJ477,439
Tonwar, S.C., Gopalakrishnan, N.V., Gupta, S.K., Rajeev, M.R., Sreekantan,
B.V.,Srivatsan,R.1991PRL67,2248
Sazonov,A.N.2009,arXiv:0912.0706
Steeghys,D.,Casares,J.2002ApJ568,273
Vestrand,W.T.,Eichler,D.1982ApJ261,251
Vrtilek, S.D., Penninx, W., Raymond, J.C., Verbunt, F., Hertz, P., Wood, K.,
Lewin,W.H.,Mitsuda,K.1991ApJ376,278
White,N.E.,Swank,J.H.,Holt,S.S.1983ApJ270,711
Fig.7.AsinFig.6butfordifferentdistancesoftheX-raysource
fromthestar(R )anddifferentinjectionplacesofγ-rayphotons
b
(R):R = 2R andR = 1.5R (a),R = 2R andR = 2R (b),
b ⋆ ⋆ b ⋆ ⋆
R = 3R and R = 3R (c), and R = 3R and R = 2R (d).
b ⋆ ⋆ b ⋆ ⋆
Thecase ofthe solarmassstarin thegiantphaseisconsidered
(R =100R andT =3000K)forR =2R andR=2R (see
⋆ ⊙ ⋆ b ⋆ ⋆
figure e). It is assumed that γ-ray injection place is always on
thelinedefinedbytheX-raysourceandthestar.Theenergiesof
γ-rayphotonshavebeenfixedon330GeV.
10 W.Bednarek&J.Pabich:Opticaldepthsforgamma-raysinLMXBs
Fig.8. The γ-ray opticaldepth lightcurvesfor two binary sys-
tems with the parametersmentioned in the main text: Her X-1
(upper figure) and Sco X-1 (bottom). Specific curves show re-
sults for different energies of γ-ray photons: 100 GeV (triple-
dot-dashed curve), 330 GeV (solid), 1 TeV (dashed), and 3.3
TeV (dot-dashed). It is assumed that the injection place of the
γ-raysisatthelocationoftheX-raysource.