GLAST testing of a pulsar model matching H.E.S.S. observations of LS 5039

0.65 MB·English

by  Agnieszka Sierpowska-Bartosik

DRAFTVERSIONFEBRUARY2,2008
PreprinttypesetusingLATEXstyleemulateapjv.12/14/05
GLAST TESTINGOFA PULSAR MODEL MATCHING H.E.S.S. OBSERVATIONS OFLS5039
AGNIESZKASIERPOWSKA-BARTOSIK1&DIEGOF.TORRES2,1
DraftversionFebruary2,2008
ABSTRACT
LS5039isoneofahandfulofX-raybinariesthathavebeenrecentlydetectedathigh-energyγ-rays,inthis
case, bytheHigh-EnergyStereoscopyArray(H.E.S.S.). Thenatureofthissystemisunknown: bothablack
holeandapulsarhavebeeninvokedaspossiblecompactobjectcompanions. Hereweworkwithamodelof
the high energy phenomenologyof the system in which it is assumed that the companion object is a pulsar
8 rotating around an O6.5V star in the ∼ 3.9 days orbit. The model assumes two differentsets of power-law
0 spectralparametersoftheinteractingprimaryleptonscorrespondingtothetwoorbitalphaseintervalsdefined
0 byH.E.S.S.ashavingdifferentgamma-rayspectraandvery-high-energy(VHE)cutoffs.WeshowtheH.E.S.S.
2
phenomenologyiscompletelyexplainedbythismodel.Wepresentpredictionsforphotonswithlowerenergies

n (forE >1GeV),subjecttotestintheforthcomingmonthswiththeGLASTsatellite. WefindthatGLASTis
a abletojudgeonthismodelwithinoneyear.
J
Subjectheadings:X-raybinaries(individualLS5039),γ-rays:observations,γ-rays:theory
9

] 1. INTRODUCTION the orbit and indicate that the new modelcan nicely explain
h
the H.E.S.S. observations. We then present predictions for
p TheGamma-rayLargeAreaSpaceTelescope(GLAST)is
the flux and spectrum as functionof phase for photonswith
- thenextgenerationγ-rayobservatorydueforlaunchinMay
o lowerenergies,whereH.E.S.S.isnotsensitivebutGLASTis.
2008. Its primary instrument is the Large Area Telescope
r LS 5039 is near the galactic center and has two other γ-ray
t (LAT), which will measure γ-ray flux and spectra from 100
s MeVto ∼100GeV. LATis thesuccessorofthe EGRETex- sourcesnearby,aswellasasignificantgalacticdiffuseback-
a ground:itisnotaneasytargetforGLAST(seeDubois2006).
[ perimentthat flew onboardthe Compton satellite. LAT will
have better angular resolution, greater effective area, wider Inordertostudyorbitalvariability,theneedtointegratelong

1 fieldofview,andbroaderenergycoveragethanEGRET.De- timeintervalsandmakeharderenergycutstobringthesignal
v veloping predictions for the GLAST energy domain upon abovebackgroundwasreported.
7
which to test models of LS 5039 is then timely and worth
8 2. THEPULSARMODELWITHORBITALVARIABILITYINTHE
exploring.
4 INTERACTINGPRIMARYSPECTRUM
Inthepreviouswork(Sierpowska-Bartosik&Torres2007,
1 The main features of the model are described by
wherewereferthereaderforreferences),undertheassump-
.
1 tionthatLS5039iscomposedbyapulsarrotatingaroundan Sierpowska-Bartosik&Torres(2007). ForLS5039’sparam-
0 O6.5Vstar in the ∼ 3.9 daysorbit, we presentedthe results etersthestarwinddominatesovertheputativepulsar’s,anda
8 ofatheoreticalmodelingofthehighenergyphenomenology shockwrapsaroundthe latter. We assume thenthat the vol-
0 observedbyH.E.S.S.3 Themaindifferencebetweenthepre- umeofthesystemisshock-separatedasaresultofthecolli-
: sionbetweenthepulsarandthemassivestarwinds. Between
v vious model and the current one is that the former assumed
thepulsarandtheshock,insidethepulsarwindzone(PWZ),
i aconstantspectrumdescribingtheinteractingparticlesalong
X relativisticleptonsareassumedtobefrozeninthemagnetized
the orbit, whereas now it is let to vary. The previousmodel
r (including detailed account of the system geometry, Klein- pulsarwindwhichpropagatesradiallyfromthepulsar.Inthis
a PWZ,wecomputeKlein-NishinaICcascadesagainstthermal
NishinainverseCompton(IC),γγabsorption,andcascading)
wasabletodescribereasonablywelltherichdetailsfoundin radiationfromthemassivestar. Secondaryγ-raysmoveinto
themassivestarwindregionandwhereassomeescapethebi-
thesystem,bothfluxandspectrum-wise.However,almostthe
completespectralenergydistributionatsuperiorconjunction, nary system, others get absorbed due to γγ process. These
cascadesarefollowedbymeansofaMonteCarloprocedure.
as well as other features of the observedorbital variation of
We have computed geometric dependences upon the opaci-
the H.E.S.S. energyspectra, remained to be consistently ex-
tiesto theseprocesses. Forclosebinaries, theradiationfield
plained. Withmodelsthatdonotentirelymatchtheobserved
ofhotmassivestars(typeO,BeorWR,havingtypicalsurface
dataatthehighestenergies,thestudyoflowerenergypredic-
tionslackstestingpower(strictlyspeaking,thesemodelsare temperaturesintherangeTs ∼104−105Kandlineardimen-
already ruled out by H.E.S.S. observations). Here, we ana- sionRs ∼10R⊙)dominatesalongthewholeorbitoverother
possiblefields(e.g.,themagneticfieldorthethermalfieldof
lyze and motivate the description of the VHE data allowing
the neutron star). This thermal radiation field is anisotropic
for a variable spectrum of interacting primary leptons along
fore+e− injectedclose to the pulsar(theradiationsourceis
1InstitutdeCie`nciesdel’Espai(IEEC-CSIC),CampusUAB,TorreC5, misplacedwithrespecttotheelectroninjectionplace).
2aplanta,08193Barcelona,Spain.Email:[email protected] We assume that the injected power in relativistic leptons,
2Institucio´CatalanadeRecercaiEstudisAvanc¸ats(ICREA).Email:dtor- which initiate the cascading processes, is a fraction of the
[email protected]γ-rayflux–consistentwiththeorbital spin-down luminosity, LSD. We particularize on the sim-
plest case in which leptons are described, after being repro-
timescale asdetermined byCasares etal. (2005)–andfastvariability dis-
playedontopofthisperiodicbehavior,bothinfluxandspectrum(Aharonian cessed by losses which dominance can be a function of or-
etal.2006). bitalphase,byapower-lawinenergythatmaybeconstant(as
2 A. SIERPOWSKA-BARTOSIK & D.F. TORRES
inSierpowska-Bartosik&Torres2007)orvaryalongtheor- teractingpopulationremainsthe same. Giventhatthe losses
bit. Here,wefocusonthecaseinwhichtwodifferentpower- dominancealongLS5039’sorbitcanbeafunctionofphase,
laws are assumed for the interacting lepton population, cor- and in addition that also the opacity to pair production is
respondingto the two orbitalintervalsproposedbyH.E.S.S. phase dependent, it seems natural to assume that in approx-
aroundinferior(0.45<φ≤0.90)andsuperior(φ≤0.45and imating the distribution of the interacting lepton population
φ > 0.90)conjunction(INFCandSUPC).Table1showsthe withapower-law,ithasadifferentindexalongthetwobroad-
modelparameterschosen. In bothcases we assume a nomi- phaseintervalswhichqualitativeobservedfeaturesdifferthe
nalvalueforLSD = 1037 ergs−1, andEmax=50TeV. Note most. In this context, the distinction between electron spec-
thatLSDandthefractionofitthatisconvertedintorelativistic traatINFCandSUPCshouldbeunderstoodasanaverageof
leptons(β) are obviouslyrelated. The position of the shock a smoother phase-dependence of the electron primary spec-
(which defines the size of the PWZ where we compute the trum,whatcouldinturnbetestedwithfuturequalityofdata
cascades) is defined by the parameter η = LSD/(M˙ Vwc), ifmorecomplexmodelingisavailable.
where the wind velocity, Vw, dependson the radial distance
fromthemassivestar,andM˙ isthestarmass-lossrate. Then, 3. MATCHINGOFH.E.S.S.RESULTSANDPREDICTIONSFOR
GLAST
M˙ Vw andLSD arealsoconnected. Differentsetsofparame-
Fig. 1 shows the results of our model, both flux and
ters(e.g.,asmallerLSD withahigherβ)givesimilarresults.
spectrum-wise, compared with corresponding H.E.S.S. data
This is the consequenceof a mild dependencewith η of the
(obtained from Aharonian et al. 2006). The spectra for LS
distancefromthepulsartotheshock.Inthemodelspresented
here, only a small fraction (∼1%) of the pulsar’s LSD ends 5039ispresentedintwobroadorbitalphaseintervalsaround
INFCandSUPC.Eachoftheexperimentaldatapointsrepre-
upinrelativisticleptons.Thisisconsistentwithionscarrying
sentsatypicaltimespanof28min.Thecorrespondingphases
muchofthewindluminosity.
for apastron, periastron, INFC, and SUPC are marked. Two
Oncethepulsarinjectsrelativisticleptons(whatcoulditself
periods are shown. To ease the comparison with our earlier
be subject to orbital variability), or alternatively, a close-to-
resultusingaconstantspectrumofinteractingparticlesalong
the-pulsarshockacceleratesaprimarypopulationassumedto
theorbit(Sierpowska-Bartosik& Torres2007)we includeit
beisotropicinthepulsarrestframe(e.g.,Kirketal.1999),the
(withafinergridding)alsointheseplots.
interactingleptonpopulationarisesfromtheequilibriumbe-
H.E.S.S.hasalsoprovidedtheevolutionofthenormaliza-
tween injectionand the losses operatingin the system along
tionandslopeofapower-lawfittothe0.2–5TeVdatain0.1
the orbital evolution. In this sense, SUPC and INFC of LS
phase-binningalong the orbit (Aharonian et al. 2006). The
5039 may indeed represent qualitatively different physical
use of a power-law fit was limited by low statistics in such
scenarios,asnotedalreadybyAharonianetal. (2006). Let’s
shorter sub-orbital intervals, i.e., higher-orderfunctional fit-
consider first the maximum energy to which leptons are ac-
tings such as a power-law with exponential cutoff were re-
celeratedinthecasethelatterproceedsinashock. Thehigh
ported to provide a no better fit and were not justified. To
temperatureofthestarandthehardspectrumoftheVHEradi-
directlycomparewiththeseresults,wehaveappliedthesame
ationmeasuredimply(unlessaveryhardinjectionproceeds)
approachto treat the modelpredictions, i.e., we fit a power-
that IC musthappenin the Klein-Nishinaregime. For dom-
law in the same energyrangeand phasebinning. Thiscom-
inant IC cooling, shock acceleration and cooling timescales
equalityimpliesthatEmax ∝(B/w)3.3,whereBisthemag- parisonisshowninFig. 2. Wefindarathergoodagreement
betweenmodelpredictionsanddata.
netic field and w is the target photon energy density. Since
w ∝d−2,withdthebinaryseparation,andBisadecreasing Fig. 1 also shows the spectral energy distribution predic-
functionofd,e.g.,B ∝d−1,Emaxincreasesbyafactor∼10 tionsextendedforenergiesabove1GeV.Thesteeperthepri-
maryspectrumis,thehigherthefluxproducedatlowerener-
from periastron (in the SUPC broad-orbital range) to apas-
gies, whatisparticularlynotablefortheSUPC broadphase-
tron (in the INFC broad-orbitalrange), leading to a spectral
interval(seeboldandthinlinesofFig.1). Theminimumflux
hardeningaroundINFC.Atthehighestenergies,synchrotron
losses(whichtimescaleis∝ E−1)areexpectedtodominate neededforasourcetobedetectedbyGLASTaftera1-month
and1-yearofoperationinall-skysurvey,foraE−2 source.4
andsteepenthespectrum. ThechangeoverenergyfromICto
Atthesefluxlevels,a20%-uncertaintyinthedeterminationof
synchrotrondomination of the radiative losses depend on B
andd;ifBisnotexactly∝1/d,itmayalsointroduceaspec- theflux,aresultingsignificanceabout8σ,andaspectralindex
determinedtoabout6%wouldbeachieved.Evenwhenthese
tralhardeningatapastron.Finally,adiabaticlosseshappening
sensitivities maybe slightly worse for a low-latitude source,
withthetypicalscalesofthesystemassociatedwiththeflow
if this model is correct, GLAST should be able to quantify
patterns–i.e.,thestand-offdistanceofthepulsarwindshock
the orbitalvariabilityafter a few monthsof integration. The
(whichscaleswith, andislessthanthedistancebetweenthe
stars), divided by the post-shock speed (∼ c/3)– generates factthatthesystemperiodicityis∼3.9daysallowsforafast
build-up of integration time around each of the portions of
a timescale that is independentof energy and, for LS 5039,
theorbit.Amonth-integrationaroundSUPCwillbeobtained
closetoorevensmallerthantheKlein-Nishinacoolingtimes.
after ∼2 months of all-sky survey, putting this model to the
In general, if leptonsenter the productionregion with a rate
test soon after GLAST launch.5 Our model also predicts a
describedbyapower-lawwithindexα0,inthecaseofdom-
clearanti-correlationbetweentheexpectedoutputatTeVand
inantradiativelosseseitherbysynchrotronorThompsonIC,
GeV energies, which can be seen comparingthe lightcurves
theslopeoftheinteractingpopulationissteppenedtoα0+1.
shown in Figs. 1 and 3. The lower the energy range, the
InthecaseofdominancebyKlein-NishinaIC,thedecreasein
thecrosssectionissuchthatthedistributionindexisslightly
4www-glast.slac.stanford.edu/software/IS/glast latperformance.htm
modified or even hardened at most by < 0.5 in index, with
5 LS5039ispositionally coincident with3EGJ1824-1514(Hartmanet
hardeningdecreasing with the ratio U⋆/UB (Moderskiet al. al. 1999,Paredesetal. 2000),whoseaverageγ-rayfluxabove100MeVis
2005).Inthecaseofadiabaticdominance,theslopeofthein- ∼ 3.5×10−7 photonscm−2 s−1. Ourmodelpredictions areconsistent
withthisobservationtoo.
GLAST TESTINGOF A PULSARMODELOF LS5039 3
more anti-correlated the signal is, what is a consequence of fluenceoftheorbitalinclinationangleisminoralongallen-
the phase-dependence of the cascading and absorption pro- ergyintervalswithinourtheoreticalmodel.Predictionsofthe
cesses. A hardness ratio defined within the GLAST energy model at lower γ-ray energy domains are ready for testing
domain does not vary as much as it does when constructed with GLAST. We find that GLAST is able to judge on this
combiningthefluxesatlowandhighγ-rayenergies(afactor model within one year. Features both at the lightcurve and
of 3versusanorderofmagnitude),butitmaybeusefulasa spectrallevel can be recognized. Additionaltests will come
firstcheckbeforeintegrationtimeisachievedfordetermining at higher energy yet beyond the current reach, e.g., behav-
thespectrum.ThisisshowninFig. 4. ior of the spectra at shorter phase intervals to be compared
with data from the next generation of ground-based instru-
4. CONCLUDINGREMARKS ments: H.E.S.S.II,andtheplannedCerenkovTelescopeAr-
AdetailedmodelingofLS5039,undertheassumptionthat ray(CTA).
it contains a pulsar, is able to fully describe the challenging
H.E.S.S.-observedphenomenologyfoundinthesystem. Ob-
servedlightcurve,spectra(Fig. 1),andshort-timescalespec-
tral variability (Fig. 2) are matched with a variable spec- We acknowledgethe use of IEEC-CSIC computercluster,
trum of primary particles along the orbit, where two phase J. M. Paredes and O. Reimer for comments, and support by
intervals are considered. It is interesting to see that the in- grantsMEC-AYA2006-00530andCSIC-PIE200750I029.
REFERENCES
AharonianF.,etal.2006,A&A460,743 KirkJ.G.,BallL.&SkjaeraasenO.,Astropart.Phys1999,10,31
DuboisR.2006,ProceedingsofScience(MQW06)068,intheProceedings Paredes,J.M.,Mart´ı,J.,Ribo´,M.,&Massi,M.2000,Science,288,2340
oftheVIMicroquasarWorkshop,Sept.18-22,2006,Como,Italy. Sierpowska-BartosikA.&TorresD.F.2007,ApJLetters671,145
Casares,J.,Ribo´,M.,Ribas,I.,etal.2005,MNRAS,364,899
Hartman,R.C.,etal.,1999,ApJS,123,79
ModerskiR.,SikoraM.,CoppiP.S.,&AharonianF.2005,MNRAS,845
4 A. SIERPOWSKA-BARTOSIK & D.F. TORRES
TABLE1
MODELPARAMETERS
Parameter Adoptedvalue
Constantleptonspectrumalongtheorbit
FractionofLSDinleptons:β 10−2
Slopeofthepower-law:Γe −2.0
Variableleptonspectrumalongtheorbit
FractionofLSDinleptonsatINFCinterval:β 8.0×10−3
Slopeofthepower-lawatINFCinterval:Γe −1.9
FractionofLSDinleptonsatSUPCinterval:β 2.4×10−2
Slopeofthepower-lawatSUPCinterval:Γe −2.4
GLAST TESTINGOF A PULSARMODELOF LS5039 5

5 SUPC apastron INFC periastron SUPC apastron INFC 5 SUPC apastron INFC periastron SUPC apastron INFC
-1 s ] 4 -1 s ] 4
-2 m -2 m
c c
ph 3 ph 3
-12 10 -12 10
V [ 2 V [ 2
e e
T T
1 1
> 1 > 1
F F
0 0
i = 30o i = 60o
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
orbital phase orbital phase
FIG.1.—Top:Lightcurvesforphotonswithenergyabove1TeVfordifferentbinaryinclinations(dot-dashed:i=300,solidlines:i=600),comparedwith
H.E.S.S.data. Blacklinesstandforresultsobtainedwithavariableinteractingspectrumalongtheorbit;green(light)linescorrespondtotheconstantspectrum
case.Bottom:SpectraaroundINFC(inred)andSUPC(inblue).H.E.S.S.dataisshowninthesamecolors.Resultsforbothcasesofinteractingelectronspectra
aregiven.Shadedregionsareenergyrangesforwhichwestudythelightcurvesbelow.Thetwohorizontallinesbetween1and100GeVrepresentsensitivitiesof
GLASTintheall-skysurveymode.
6 A. SIERPOWSKA-BARTOSIK & D.F. TORRES
FIG. 2.—Shadedareasintheleft(right)panelshowthechangeinthenormalization(photonindex)ofapower-lawphotonspectrafittedtothetheoretical
predictionforeachofthe0.1binsofphase.Thepresentedresultsareforthemodelofthevariableinteractingspectrum.Thetwodifferentcolorsoftheshading
standforthetwoinclinationanglesconsidered. Thesizeoftheshadinggivesaccountoftheerrorinthefittingparameters. DatapointsrepresenttheH.E.S.S.
resultsfortheequalprocedure:apower-lawfittotheobservationalspectraobtainedinthesamephasebinning.
GLAST TESTINGOF A PULSARMODELOF LS5039 7

3-11-2-1F ( 100-10 GeV) [ 10 ph cm s ] 01234567 SUPC apastron INFC periastron SUPC apastron INFC -9-2-1F (10-100 GeV) [ 10 ph cm s ] 0123 SUPC apastron INFC periastron SUPC apastron INFC - 8-2-1F (1-10 GeV) [ 10 ph cm s ] 01234 SUPC apastron INFC periastron SUPC apastron INFC
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
orbital phase orbital phase orbital phase
FIG. 3.—Predictedtheoreticallightcurvesfortheenergyintervals100GeV–1TeV,10–100GeV,and1–10GeV.Bothinclinationanglesandinteracting
leptonspectraconsideredareshown(dot-dashed: i=300,solidlines:i=600,blacklines:variablespectrumofprimaryleptons,green(light)lines:constant
spectrumalongtheorbit).
8 A. SIERPOWSKA-BARTOSIK & D.F. TORRES

V)) 0,25 SUPC apastron INFC periastron SUPC apastron INFC V)) 0,03 SUPC apastron INFC periastron SUPC apastron INFC
Ge 0,20 Ge
0 0
1 1
F(1- 0,15 F(1- 0,02
V)/ V)/
e e
HR (F(10-100 G 000,,,001050 23 HR (F(10-10 G 00,,0001
o o
i = 30 i = 30
o o
-0,05 i = 60 i = 60
-0,01
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0
orbital phase orbital phase
FIG. 4.—Hardnessratiosasafunctionoforbitalphase,fortwoinclinationangles(dot-dashed: i=300,solidlines:i=600).Colorstylefollowsthatused
inpreviousfigures.TheenergyregimesconsideredareF(1−10GeV),F(10−100GeV),andF(102−103GeV).