Spectral evolution and the onset of the X-ray GRB afterglow

0.14 MB·English

by  P. A. Evans

Spectral evolution and the onset of the X-ray GRB afterglow
P.A. Evans, J.P. Osborne, R. Willingale and P.T. O’Brien
X-rayandObservationalAstronomyGroup,Dept.ofPhysics&Astronomy,UniversityofLeicester,Leicester,
1 UK,LE17RH
1
0
Abstract. BasedonlightcurvesfromtheSwiftBurstAnalyser,weinvestigatewhethera‘dip’featurecommonlyseeninthe
2
early-timehardnessratiosofSwift-XRTdatacouldarisefromthejuxtapositionofthedecayingpromptemissionandrising

n afterglow.Weareabletomodel thedipassuch afeature,assuming theafterglow risesaspredicted bySariandPiran[1].
a UsingthismodelwemeasuretheinitialbulkLorentzfactorofthefireball.Forasampleof23GRBswefindamedianvalue
J ofG =225,assumingaconstant-densitycircumburstmedium;orG =93ifweassumeawind-likemedium.
0 0
1
Keywords: GammaRayBursts
3
PACS: 98.70.Rz,95.75.Wx

]
E
H INTRODUCTION
.
h The early Swift-XRT observations of GRBs have long been seen to exhibit spectral evolution ([2]; [3]). A feature
p
seen in a number of GRBs is a ‘dip’ in the hardness ratio (i.e. a softening followed by a hardening;see Fig. 1a) at
-
o theendofthesteepdecayphase.TheSwiftBurstAnalyserlightcurves([4]),whichareinunitsoftheintrinsic(i.e.
r unabsorbed)flux and accountfor spectral evolution,suggestthat this may correspondto the ‘turn-on’on the X-ray
t
s afterglow(Fig.1b).
a Theriseoftheafterglowwasconsideredby[1],whopredictedthatitriseast2 untilsometimet atwhichpointit
[ p
peaksandbeginstodecay.Thistimetpcorrespondstothedecelerationradius:theradiusatwhichtherestmassenergy
1 ofthematerialsweptupbythefireballequalstheenergyofthefireball.FromthisonecandeterminethebulkLorentz
v factoratthedecelerationradiusofthefireball(e.g.[1];[5]).
3
2 1
9 G 3E [1+z]3 8
0 iso
= (1)
5 2 32p nm c5h t3
. p p!
1
0 WhereEisoistheisotropicequivalentenergyoutputoftheGRB,nisthenumberdensityofthecircumburstmedium,
1 andh istheradiativeefficiencyofthefireball.
1 Thisassumesthatthedensityisconstant,i.e.theGRBisinanISM-likeenvironment.Ifweinsteadassumethatthe
: environmentiswind-like(i.e.r (cid:181) r−2)wefind:
v
i
X G 0 Eiso[1+z] 14
ar 2 =(cid:18)8p Ampc3h tp(cid:19) (2)
whereAisthedensitynormalisation.FollowingMolinarietal.weassumeh =0.2,n=1cm−3 andA=3×1035
cm−1;notingthatdependenceontheseunknownsisweak.
In this paper we will thereforeconsiderwhether the X-ray hardnessratio dip can be used to constrainthe rise of
theX-rayafterglowandhencetheinitialbulkLorentzfactor,giventheSari&Piranmodel.Itshouldbenotedthatthe
presenceofaplateauphaseinX-raydataisofteninterpretedasasignofcontinuedenergyinjectionintothefireball
insomeformorother(e.g.[6]).Itislikelythatthiswillmodifythefireballdynamicssomewhat,howeversince the
rate of energyinjection is muchlower than the rate of energyoutputin the promptGRB, we believewe can safely
disregardthiseffect.
Hardness ratio of GRB 060729 BAT−XRT data of GRB 060729
1000 0.01
s 100
eV c/ 110 10−3
k 0.1
−10 01.00−13 V) 10−4
1.5 11000−04 0 ke 10−5
1.5 keV c/s 010.010.11100 sity (Jy @ 1 1100−−76
0.3− 1100−−243 x den 10−8
1.5 Flu 10−9
o 10−10
ati 1
R
0.5 10−11
0 1 10 100 1000 104 105 106 107
100 1000 104 105 106 107
Time since BAT trigger (s)
Time since BAT trigger (s)
FIGURE1. The(1.5–10)/(0.3–1.5)keVhardnessratioofGRB060729(leftpanel),showingthe‘dip’featurearound100–200
s after the trigger. The reconstructed 10 keV flux density light curve from theBurst Analyser light curve (right panel) –which
accountsforthisspectralevolution–showsafeatureatthissametime,suggestiveoftheoverlapofthedecayingpromptemission
andrisingafterglow.
MODELFITTING
Toinvestigatewhetherthehardnessratiodipcanindeedbecausedbytheriseoftheafterglow,wefitthehard(1.5–10
keV)andsoft(0.3–10keV)XRTbanddatafromtheXRTlightcurverepository([7],[8])simultaneously.Wefittwo
components:the first modelsthe decayingpromptemission which we parameterise with the pulse modeldescribed
byWillingaleetal. (2005);thehardnessratioofthiscomponentdecreases(i.e.softens)asa power-law.Thesecond
componentmodelistheafterglow,whichwetreatasspectrallyinvariant.Thiscomponentiszerountilsometimet at
a
whichtheafterglow‘starts’,thereafteritrisesast2untilt whereafteritbreakstoagenerict−a decay.
p
We do not fit the entire light curve, since we are only interested in the transition from the prompt to afterglow
emission.Iftheafterglowlightcurveshowsevidenceforafurtherbreakafterthatreferredtoabove,thedataafterthis
breakareexcludedfromthefit.Similarlyanybreaksorflareswhichoccurbeforethepromptemissionfollowsasingle
power-lawareexcluded;iftheburstshowsnoneofthesefeaturestheentiredatasetisfitted.Examplefitsareshownin
Fig.2.
RESULTS
We identified GRBs with knownredshift, a clear dip feature in the hardnessratio, no flares close to or overlapping
thedip,andwhereSwiftobservedthroughoutthedipfeature.Thisgaveanlistof23GRBs.Histogramsoftheinitial
LorentzfactorsdeterminedfromthesefitsaregiveninFig.3.ForanISM-likeenvironmentthemedianvalueis225,
withmostvaluesbeingabove100,inagreementwithmeasurementsintheliterature(e.g.[5],[9],[10],[11]).Onthe
otherhand,ifweassumeawind-likeenvironmentthemedianvalueoftheinitialLorentzfactorisonly93,andisbelow
50forseveralbursts;thisisclosetothelimitimposedbythecompactnessproblemandmaysuggestthattheseGRBs
cannothaveoccurredinawind-likeenvironment.WenotethatallofourvaluesarewellbelowG =1000,whichhas
0
beenproposedasalowerlimitonthebulkLorentzfactorgiventheGeVemissiondetectedbyFermi-LAT(e.g.[12]).
Howevernone of the GRBs in our sample are those which were also observedby the LAT. Also note that [13] and
Haoscoëtetal.(theseproceedings)havearguedthatGeVphotonscanescapefromaFireballwithbulkLorentzfactors
substantiallybelow1000.
GRB 061110A GRB 060729
Dark Grey: Hard −− Light Grey: Soft 0 Dark Grey: Hard −− Light Grey: Soft
0
100 0
1
0
0
10 1
0
s)−1 1 s)−1 1
e ( e ( 1
Count rat 00.0.11 Count rat 0.010.1
10−3 10−3
0−4
10−44 14
3 3
R 2 R 2
H H
1 1
0 0
100 1000 104 105 1000 104
Time since trigger (s) Time since trigger (s)
FIGURE2. Examplesfits.Thedot-dashedlinesshowtheindividualcomponents.Thetoppanelshowsthefitteddata,thebottom
panel the hardness ratio. The latter is not fitted, but is calculated from the top panel, and is shown to illustrate how the model
reproducesthedipfeature.Leftpanel:GRB061110A.Rightpanel:GRB060729
CONCLUSIONS
WehaveshownthatadipfeatureseenintheX-rayhardnessratiosofGRBsattheendofthesteepdecayphasecanbe
interpretedastheturn-onoftheX-rayafterglow,whichrisesinaccordancewiththepredictionsof[1].Bymodelling
thisrisewehavedeterminedtheinitialbulkLorentzfactorfor23GRBs,findingamedianvalueof225assumingan
ISM-likecircumburstmedium,or93forawind-likemedium.
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