Evidence for an anticorrelation between the duration of the shallow decay phase of GRB X-ray afterglows and redshift

0.2 MB·English

by  G. Stratta

Astronomy&Astrophysicsmanuscriptno.ms˙rev˙english (cid:13)c ESO2009
January21,2009
LettertotheEditor
Evidence for an anticorrelation between the duration of the shallow
decay phase of GRB X-ray afterglows and redshift
G.Stratta1,D.Guetta2,V.D’Elia2,M.Perri1,S.Covino3,andL.Stella2
9
0 1 ASIScienceDataCenter,viaG.Galilei,00044Frascati,Italy⋆
0
2 2 INAF-OsservatorioAstronomicodiRoma,viaFrascati33,00040MontePorzioCatone,Italy

n
3 INAF-OsservatorioAstronomicodiBrera,viaBianchi46,23807,Merate(LC),Italy
a
J

2 Received....;accepted....

] ABSTRACT
E
H Context.One of the most intriguing features discovered by Swift is a plateau phase in the X-ray flux decay of about 70% of the
. afterglowsofgamma-raybursts(GRBs).Thephysicaloriginofthisfeatureisstillbeingdebated.
h Aims.Weconstraintheproposedinterpretations,basedontheintrinsictemporalpropertiesoftheplateauphase.
p Methods.Weselectedandanalyzed alltheSwift/XRTGRBafterglowsatknownredshift observedbetweenMarch2005andJune
- 2008featuringashallowdecayphaseintheirX-raylightcurves.
o
Results.Foroursampleof21GRBswefindananticorrelationofthelogarithmofthedurationoftheshallowphasewithredshift,
r
t withaSpearmanrank-ordercorrelationcoefficientofr=−0.4andanullhypothesisprobabilityof5%.Whenwecorrectthedurations
s forcosmologicaldilation,theanticorrelationstrenghtens,withr=−0.6andanullhypothesisprobabilityof0.4%.Consideringonly
a
thoseGRBsinoursamplethathaveawell-measuredburstpeakenergy(8outof21),wefindananticorrelationbetweentheenergy
[
oftheburstandtheshallowphaseduration,withr=-0.80andanullhypothesisprobabilityof1.8%.

1 Conclusions.Iftheburstenergyanticorrelationwiththeshallowphasedurationisreal,thenthedependence oftheshallowphase
v on redshift could be the result of a selection effect, since on average high-redshift bursts withlower energies and longer plateaus
7 wouldbemissed.Aburstenergyanticorrelationwiththeshallowphasedurationwouldbeexpectediftheendoftheplateauarises
5 fromacollimatedoutflow.Alternativescenariosarebrieflydiscussedinvolvingapossiblecosmologicalevolutionofthemechanism
2 responsiblefortheX-rayshallowdecay.
0
Keywords.gamma-raybursts–??–??
.
1
0
9
1. Introduction in the X-rays (Liang et al. 2007). This idicates either that the
0
X-rayandopticalafterglowhavedifferentoriginsorthatthemi-
:
v In the pre-Swift era the X-ray afterglows of gamma-ray bursts crophysicalparametersdeterminingtheinstantaneousenergyin
i couldbeobservedonlyaftermanyhoursaftertheburst,whenthe
X fluxtypicallyshowedasmoothpowerlaw-likedecay,t−α,with the electrons and magnetic field evolve in time (Panaitescu et
al.2006).Someofthemodelsproposedtointerpretthephysical
r anindexofaboutα ∼ 1.Hereafter,werefertothisasthestan-
a origin of the shallow decay phase are summarized in Zhang et
dard X-ray afterglow decay phase. The Swift mission (Gehrels
al.(2007).
etal.2004)hasrevolutionizedGRBstudiesinmanyrespectsby
Severalstudieshaveaddressedtheintrinsicpropertiesofthe
observingtheX-rayafterglowphasefromafewdozenseconds
X-ray shallow phase, in particular by testing whether a depen-
aftertheburst(e.g.Zhangetal.2007).
denceexistsbetweentheintrinsicdurationoftheshallowphase
TheshallowdecayphaseobservedintheX-rayfluxofabout
andtheburstenergetics.Resultsobtainedso fararediscordant.
∼ 70% of the afterglows (e.g. Panaitescu 2007) is one of the
Ananticorrelationbetweentheintrinsicdurationoftheshallow
mostintriguingfeaturesdiscoveredbySwift.Thisphaseusually
phase and the burst energetics has been found in some works
becomesvisibleafewhundredsecondsaftertheburst,afterthe
(e.g. Sato et al. 2007; Dado et al. 2008), while in some others
steep decay in the prompt emission, and it lasts for ∼ 1 − 10
it wasnot(e.g.Lianget al. 2007;Nava etal. 2007).Sato et al.
ks (Nousek et al. 2006; Zhang et al. 2006). No spectral evolu-
(2007)arguethatthesediscrepanciesmaybeassociatedwiththe
tionisobservedin eitherthe0.3-10keVrangeduringtheshal-
largeuncertaintiesaffectingtheburstenergeticsestimatesand/or
low phase or in the subsequent decay phase (e.g. Liang et al.
inmodelingtheX-rayshallowphaseandestimatingthetempo-
2007; Butler and Kochevski 2007). This lack of X-ray spec-
ralbreakbetweentheshallowandthestandardphases.Someof
tral variations has suggested that the observed X-ray temporal
thediscrepanciesmightalsobeascribedtothedifferentsizeand
steepeningisnotassociatedwiththecrossingofacharacteristic
qualityoftheGRBsamplesusedbydifferentauthors.
synchrotronfrequency(e.g. the cooling frequency).Opticalaf-
terglow lightcurvesoften show a different behavior from those A linear dependencebetween the logarithmof the duration
of the shallow phase, and the logarithm of the burst istropic
⋆ INAFpersonnelresidentatASDC equivalentenergy would be expected if the temporalbreak be-
2 Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
dominated by features such as spikes or flares that may affect
GRB 060714 @ z=2.71 themeasurementofthedecayindex;iii)sinceouranalysiscon-
centrateson the study of the intrinsic propertiesof the shallow
1 phase,weconsideredonlyGRBsatknowndistances.Inthisway
0.1
weselected21GRBs(outofatotalofabout60burstsatknown
redshiftforwhichthestatisticsweregoodenoughtocarryouta
detailedtemporalanalysis).Thesample, aswellthe redshiftof
GRB 070306 @ z=1.4959
eachburst,isgiveninTable1.InFigure1thelightcurvesofthree
1 GRBsfromour‘goldensample’(seebelow),takenfromEvans
0.1 et al. (2007),are plotted after rescaling of the temporalaxis to
theirrestframe.Theshapeofthe lightcurvesclearlyshowsthe
wellknown‘canonical’behavior(e.g.Nouseketal.2005).Since
GRB 060729 @ z=0.54
ourgoalistomeasurethedurationoftheshallowphase,wefit-
tedtheobservedlightcurveswithpowerlawsas:
1
0.1
10 100 1000 Fν(t)∝ttt−−−ααα021 t1tt<<>ttt<12 t2 (1)
restframe time since GRB trigger (s)
Fig.1. X-ray afterglow lightcurves from Evans et al. (2007) In Eq. (1), t < t1 indicates the interval where the typical
wherethetemporalaxishasbeenrescaledtotheburstrestframe initial steep decay from the prompt is observed, t1 < t < t2
for3GRBsofour‘goldensample’adifferentredshift(see§2). correspondstotheshallowdecayphase,andt >t2 tothesubse-
quentstandarddecay.Inthiswork,weconsidert asameasure
2
ofthedurationoftheshallowdecay.ForGRB060614andGRB
tweentheshallowphaseandthestandardphasewereinterpreted 060814,weexcludedtheinitialsteepdecayfromthefitbecause
as‘jetbreak’time(tj)andtheGRBenergycorrectedforbeam- it could not be well-fitted by a power-law decay. We also ex-
ing factor were constant(e.g. Frail et al. 2001).Indeed, the jet cluded fromthe fit those intervalsin which flares were present
openinganglecanbeestimatedfromthetimetjatwhichtherel- for t < t1 in the lightcurvesof other GRBs (see last columnof
ativisticbeaming(1/Γ(tj)whereΓ(tj)isthefireballLorentzfac- Tab.1).
tor) becomes equal to the geometric beaming of the fireball of Table 1 shows the selected dataset where t represents the
2
half-openingangleθj,thatis,θj ∝(t3j/Eiso)1/8(Sarietal.1999), observedepochatwhichtheshallowphasesteepenstothestan-
whereE istheequivalentisotropicenergy.Atthattime(t ),the dard decay (calculated from the burst onset as determined by
iso j
afterglowlightcurvedecaysteepens.Thebeamedcorrecteden- Swift/BAT), and α represents the temporal index of the shal-
1
ergyisE =E (1−cosθ )∼ E θ2.IfE isconstant,itfollows low decay region. Errors are given at the 1σ confidence level.
γ iso j iso j γ
thatE ∝t−1.ThecorrelationfoundbyGhirlandaetal.(2004) In some cases Eq. (1) provided a poor approximation of the
iso j
steepeningfromtheshallowphasetothestandardone.Wethus
between the intrinsic peak energies and the beaming-corrected
burst energies tells that the relation E ∝ t−1 is still (nearly) checkedwhetherotherestimatesofthetemporalbreakbetween
iso j the shallow phase and the standard phase obtained assuming
validforGRBswithsimilarintrinsicpeakenergy.Inthejetsce-
morecomplexmodels(e.g.Willingaleetal.2007;Ghiselliniet
nario, the lightcurve steepening is expected to be achromatic.
al. 2008) provided different results and we find no significant
Thisconditionis barelysatisfied if we considerboththe X-ray
differenceswithintheuncertainties,exceptfortwocases1.
andtheopticalenergydomains,since,asmentionedabove,sev-
We first checked whether any commonintrinsic value t′ of
eralX-rayshallowphasesarenottrackedintheopticalregime. 2
theepochatwhichtheX-rayshallowdecayends(t′ =t /(1+z))
However,byrestrictingtheenergyrangetotheX-rays,thecon- 2 2
exists for all GRBs. The observed epoch t covers 3 orders of
dition is satisfied since the lack of any spectral variation is a 2
magnitudes(0.5-80ks).Theintrinsicepocht′ stillcoversawide
characteristicfeatureoftheX-rayshallowphaseandthesubse- 2
rangeofvalues(0.2-50ks,Tab.1).Wefindnoevidenceofclus-
quentstandarddecayphase.
tering around any particular value. We then checked whether
In the present paper we consider a sample of GRBs with a
there is any redshift dependence on t . We found that an anti-
well-monitoredX-raylightcurveandknownredshift,whichun- 2
correlationexistsbetweenthelogarithmoft andz,witharank
ambigously showed a shallow decay phase. We find clear evi- 2
correlationfactorof -0.4.With 19degreesoffreedom,the null
dence of a redshift dependence of the duration of the shallow
hypothesisisrejectedata95%confidencelevel.Aftercorrecting
decayphase.
t forcosmologicaldilation,wefoundthattheanticorrelationis
2
strengthened,witharankcorrelationfactorof-0.6:thenullhy-
2. Thesampleanddataanalysis pothesis is now rejected at 99.6% (non-directionalprobability)
confidencelevel(Fig.2).Thattheanticorrelationalreadypresent
The X-ray afterglow lightcurves supplied by the UK Swift
fort becomesmoresignificantaftercorrectionforcosmological
Science Data Centre at the University of Leicester were used 2
dilationprovidesevidencethatthecorrelationisgenuineandnot
(Evans et al. 2007). The sample was built by selecting in the
biasedby the redshiftcorrection.To confirmthisresult,we se-
SwiftarchiveallGRBsobservedintheperiodfromMarch2005
lecteda”goldensample”of10GRBsfromouroriginal21GRB
toJune2008withthefollowingcharacteristics:i)a0.3-10keV
samplebyconsideringonlythoseGRBswiththebestXRTcov-
XRTlightcurvefeaturingshallowbehaviorwithtemporalindex
erageinallthethreetypicalSwift/XRTX-raylightcurvecompo-
α < 0.8 (i.e. shallower than the ‘standard’fireball modelpre-
1
dictions, e.g. Sari et al. 1998), over a temporalinterval greater 1 Willingaleetal.(2007)estimatedforGRB060607Aadurationof
than 0.5 ks (so that the power-law decay index can be mea- T = 56+4 ks and Ghisellini et al. (2008) for GRB 050319 estimated
a −3
sured accurately); ii) the shallow decay interval should not be T =7ks(thelatterisintherestframe).
A
Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle 3
GRB t [ks] α z E [1052]erg E [keV] Comments
2 1 iso peak,i
050315 9.0±0.2 −0.2±0.1 1.949 − − steepphaseexcluded
050319 2.7±0.1 0.1±0.2 3.240 − − −
050401 5.0±0.3 0.63±0.02 2.90 35±7A 467±110(1) −
050505 6.4±0.4 0.1±0.1 4.27 19.5±3.1N 622±211(2) −
051109A 2.0±0.1 0.54±0.03 2.346 6.5±0.7A 539±200(1) −
060502A 30±2 0.43±0.09 1.51 − − −
060526 20±2 0.11±0.07 3.21 2.6±0.3A 105±21(1) flareexcluded
060607A 12.9±0.2 0.44±0.02 3.082 12.2±1.8N 535±164(2) flareexcluded
060614 47±2 0.05±0.03 0.125 0.21±0.09A 55±45(1) steepphaseexcluded
060714 3.6+1.2 0.24±0.05 2.71 − − flareexcluded
−0.7
060729 77±1 0.12±0.02 0.54 − − flareexcluded
060814 9.9±0.2 0.25±0.06 0.84 7.0±0.7A 473±155(1) flareexcluded
061121 3.6±0.5 0.25±0.04 1.314 22.5±2.6A 1289±153(1) −
070306 27.2±0.8 0.11±0.02 1.4959 − −
070529 2+2 0.7±0.1 2.4996 − − −
−1
070611 50+10 0.1±0.1 2.04 − − −
−13
070802 5+2 0.1±0.2 2.45 − − −
−1
080310 4.5±0.9 0.7±0.1 2.42 − − flareexcluded
080430 15+8 0.4±0.1 0.767 − − −
−3
080605 0.55±0.03 0.68±0.04 1.6398 − − −
080607 1.5±0.2 0.1+0.9 3.036 − − flareexcluded
−0.3
Table1. SelectedsampleofGRBswithknownredshiftthatpresentsashallowdecayphase.
(1)FromAmatietal.2008;(2)FromNavaetal.2007.
nents(e.g.Nouseketal.2005),whichareaninitialsteepdecay 1 and Figure 2), we find that t′ anticorrelateswith E , with a
2 iso
followed by the shallow and then standard decay. Despite the rank correlation factor of –0.80 and null hypothesisrejected at
decreaseinthesampleofGRBs,theanticorrelationbetweenthe 98.2%confidencelevel(Fig.2).Ifwerestrictourselvestocon-
logarithmoft andzpersists,witharankcorrelationfactorof- sideringonlythoseGRBswithsimilarintrinsicpeakenergy,we
2
0.85.(Thenullhypothesisisrejectedat99.2%confidencelevel.) still find marginalevidence of the anticorrelation,although the
Thegoldensampleis markedwithredopencirclesin Figure2 statisticsarepoor(Fig.2).Eventhoughafirmconclusioncould
andinboldfaceinTable1. notbereached,thisresultisconsistentwiththeresultsobtained
Thesefindingscannotbeinterpretedasduetoanenergyde- byDadoetal.(2008)andSatoetal.(2007),whileatoddswith
pendenceofthedurationoftheshallowphaseasonemaycon- findingsbyLiangetal.(2007)andNavaetal.(2007).
clude for example from Figure 1 where the shallow phase at Asmentionedin§1,theanticorrelationbetweent′ and E
2 iso
energiesof 1-37 keV (for GRB 060714at z=2.711)in the rest suggeststhatt couldbeconsideredasthejetbreaktimeof(the
2
frame is shorter than the one at 0.5-15 keV (for GRB 060729 partof)thefireballthatgivesrisetotheX-rayafterglow(see§1).
atz=0.54).Infact, itis wellknownthatthehardnessratio,de- Severalsuggestionshavebeenmadetoreconcilethejetinterpre-
finedasthefluxratiointhe0.3–1.5keVand1.5–10keVenergy tationwithfeaturesobservedinsomeGRB,suchasachromatic
bands,doesnotshowanyevidenceofvariationsalongtheshal- evolutionofthebreakorthetemporalbreakatlaterepochs.For
lowphase(e.g.ButlerandKocevski2007;Liangetal.2007). example, the two-component jet model (e.g. Peng et al. 2005;
The anticorrelation of the intrinsic duration of the X-ray Racusinetal.2007)explainsthelackofasimultaneousoptical
shallow phase with redshift that we discussed above may be break as a deficit in the optical emission from the narrower of
a consequence of an anticorrelation of t′ with burst energy. the two jets, responsible for the two X-ray temporalbreaks. In
2
Indeed, the GRBs that we observe at high-redshift are on av- another model, Ghisellini et al. (2007) propose to interpret the
eragemoreenergeticthanthelow-redshiftonesduetoasimple observedX-rayplateauasthesumoftwocomponents:thelate
selection effect. We cannot see faint GRBs at large distances. promptemission(internalshockbetweenlateemittedshells)and
Therefore,shorter plateaus might be observedmore frequently theafterglow.ThetemporalbreakattheendoftheX-rayshallow
at high redshiftbecause associated with more energetic GRBs. decayphaseistheproofthattheLorentzfactorofthelateshells
Alternatively,theanticorrelationoft′ withzcanbeexplainedas (typically smaller than that of the external shell giving rise to
2
acosmologicalevolutionofthemechanismthatgivesrisetothe theafterglow)hasreachedthe1/θj value(see§1).Whetherthe
shallowdecay.Webrieflydiscussbothpossibilitieshere. break is tracked in the optical band dependson the relative in-
tensity of each component. The second break at later times is
producedwhentheLorentzfactoroftheshellproducingtheaf-
2.1.Theburstenergydependenceoft′ terglowhasreachedthe1/θ value.
2 j
To verify the dependence of the energy of the burst from t′ is
2
notaneasygoalsincetheGRBenergetics,usuallyestimatedby 2.2.Evidenceofcosmicevolution?
E , is often affected by large uncertainties in the burst spec-
iso
tral parameters, the peak energy E of the EF spectrum in Giventheuncertaintiesaffectingtheburstenergeticevaluations
peak E
particular. For this reason, we considered only those GRBs of andthepoorstatisticsavailabletodefinitivelyconfirmtheanti-
our sample for which precise measurementsof Epeak are avail- correlationbetweenEisoandt2′,wespeculateonanotherpossible
able (e.g. Amati et al. 2008;Nava et al. 2007).For 8 GRBs of interpretation of the redshift anticorrelation with t′ where the
2
oursample(3ofwhicharepartofthe‘goldensample’,seeTab. shallow phase depends on an external component that evolves
4 Pleasegiveashorterversionwith:\authorrunning and/or \titilerunning priorto \maketitle
3. Conclusions
In this work we analyzed 21 GRBs with known redshift that
feature a shallow phase in the X-ray lightcurve. Our main re-
sult is a clear anticorrelationof the intrinsic durationof the X-
ray shallow phase with redshift. Considering only those GRBs
in our sample that have well-measured burst peak energy, we
findmarginalevidenceforburstenergyanticorrelationwiththe
shallow phase duration.The latter anticorrelationwouldbe ex-
pected if the observed temporal break (t ) arises from a col-
2
limated outflow. In this case, the t′ anticorrelation with z can
2
be interpreted as the evidence of a selection effect since high-
redshift bursts with lower energies and shorter plateaus would
be missed. However, a larger sample of bursts at known red-
shiftwithwell-measuredburstspectralparametersisrequiredto
definitivelyassesstheE anticorrelationwitht′.Inanalterna-
iso 2
tive scenario, the shallow phase may arise from a mechanism
that operates differently at high redshift, such as for example
fromX-raydustscatteringoranevolutionoftheintrinsicGRB
propertiesasforexampletheinnerengine(Guettaetal.inprepa-
ration).Finallywenotethatbyvirtueofitsredshiftdependence
(though with large scatter), the observed X-ray shallow phase
duration (t ) may be regarded as an additional figure of merit
2
tosingleouthigh-redshiftGRBs directlyfromX-raysobserva-
tions.Thismightprovideusefulinformationforburstfollow-up
campaignsatopticalandNIRwavelengths.
Acknowledgements. Wethank theanonymous referee forhis/her useful com-
ments.Thisworkissupported inItalyfromASIScience DataCenterandby
ASIgrantI/024/05/0andMIURgrant2005025417.
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