Observational constraints on the external shock prior emission hypothesis of GRBs

0.84 MB·English

by  Tesla Birnbaum

Mon.Not.R.Astron.Soc.000,1–??(2011) Printed25January2013 (MNLATEXstylefilev2.2)
Observational constraints on the external shock prior
emission hypothesis of GRBs
Tesla Birnbaum⋆1, Bing Zhang1, Bin-Bin Zhang2 and En-Wei Liang3
2
1Department of Physics and Astronomy, University of Nevada Las Vegas, Las Vegas, NV 89154, USA
1
2Department of Astronomy and Astrophysics, Pennsylvania State University,UniversityPark, PA 16802, USA
0
3Department of Physics, Guangxi University, Nanning 530004, China
2

n
a
Accepted 2012January22.Received2012January22;inoriginalform2011May24
J

4
2
ABSTRACT

An intriguing hypothesis, that there exists a decaying X-ray emission component be-
]
E fore the GRB trigger,has been suggested in order to explain the shallow decay phase
H oftheX-rayafterglowdetectedinmanySwiftGRBs.Ifthis“prioremission”isfroman
external shock, one would expect a corresponding optical emission component during
.
h the GRB prompt emissionphase.In this paper we apply the availableprompt optical
p emission data (both detections and upper limits) to constrain such a scenario. We fit
- the shallow and normal decay segments of the XRT light curves in our sample with
o
r a T∆-shifted single power law, and extrapolate the X-ray flux back to the time of the
t early optical observations. We then use the synchrotron spectrum predicted by the
s
a standardexternalshockmodeltoextrapolatefromtheX-rayfluxtotheopticalband,
[ and obtain the possible range of the predicted optical flux. Finally, we compare the

predictions with the observations. In the cases where later optical data are available,
2
we also compare the shapes of the optical light curves to the predicted optical light
v
6 curvesfromthe externalshock prioremissionmodel. We find that for a goodfraction
2 of GRBs (4 out of 8; up to December 2006),the available data already impose severe
1 constraints on the hypothesis. In particular, the expected optical flux from the prior
5 external shock model is higher than what the data allow. We conclude that if the
. shallow-decayX-raycomponentwere froma prioremissioncomponent,it would have
5
0 to be of an internal origin with optical flux suppressed.
1
Key words: gamma-rays:bursts, shock waves, radiation mechanisms: non-thermal
1
:
v
i
X
r 1 INTRODUCTION three phases. Of these phases, the shallow decay phase has
a definitely posed the biggest challenge. Generally, no spec-
Thanks to the vast collection of data on GRBs and their
tral evolution is observed across the temporal break from
afterglows in the Swift era (Nousek et al. 2006; O’Brien
the shallow to the normal decay phase (Liang et al. 2007).
et al. 2006; Willingale et al. 2007; Evans et al. 2009), we
This suggests that the shallow-to-normal transition should
nowhaveadetailed pictureofthetemporalbehaviorofthe
be either hydrodynamical or geometrical in origin. Many
X-ray emission from these violent cosmic explosions. Using
such physical models of the shallow decay phase have been
light curves obtained by the X-Ray Telescope (XRT) on-
discussed in the literature, but none has been successful in
board the Swift satellite, five phases that are common to
interpretingalltheobservations(Zhang2007andreferences
many X-ray afterglow light curves were identified: a steep
therein).
decay phase, a shallow decay phase, a normal decay phase,
apostjetbreakphase,andX-rayflares(Zhangetal.2006). An intriguing hypothesis was proposed by Yamazaki
Notallburstsexhibitallfivephases.Thenormaldecayand (2009). According to this hypothesis, there was already ac-
postjetbreakphaseswerepredictedpre-Swift andarewell- tivity from the central engine before the GRB itself. The
explained by the standard external shock afterglow model X-rayfluxis already decayingbefore theGRB trigger. Due
(M´esz´aros&Rees1997;Sarietal.1998;Rhoads1999;Sariet to a bad choice of reference time (the GRB trigger time),
al.1999).Swift observationshavechallengedtheGRBcom- this power-law-decaying prior emission component (ejected
munitytocreatephysicalmodelsthataccountfortheother atatime−T∆ withrespecttotheGRBtriggertime,which
we define as T = 0) appears as an artificial broken power
law with a plateau stretching out to T ≈ T in the log-log
∆
⋆ E-mail:[email protected] diagram. In order to observe the single power law behavior
(cid:13)c 2011RAS
2 T. Birnbaum, B. Zhang, B.-B. Zhang and E.-W. Liang
oftheprioremissioncomponent,oneneedstomovethetime emissionmodel)andearlyopticalobservations(eitherdetec-
zero point to −T , which we define as t = 0. According to tions or upper limits). We searched through the literature
∆
Kobayashi & Zhang (2007), the time zero point of external to find theGRBs which either clearly exhibit a shallow de-
shock emission should coincide with the beginning of the cay segment in their XRT light curve or have been fit with
corresponding central engine activity. So for prior emission a shallow decay segment. Specifically, the candidate bursts
it should be at t = 0, while for the main GRB it should were taken from Table 1 of Liang et al. (2007) and Table 2
be at T = 01. The observed X-ray afterglow is dominated ofLiangetal.(2009).Wefurthernarroweddownthesample
by the prior emission component, which outshines the X- tothoseGRBswithearlyopticalobservations,usingTable5
ray emission associated with themain GRB outflow during fromYostetal.(2007a)andTable2fromYostetal.(2007b)
the shallow and normal decay phases. A systematic study for detections, and Table 3 from Yost et al. (2007b) for up-
of Swift/XRTlight curvesfrom GRBs detected before mid- per limits. Thus, the effective cutoff date for our sample is
2009 (Liang et al. 2009) suggests that the prior emission December2006, abouttwoyearsintotheSwift mission. Al-
model provides a unified interpretation of both the canon- together, our sample consists of eight bursts(Table 1) with
ical X-ray light curves and the light curves that seem to a total of 11 early optical detections and 17 early optical
follow a single power law decay (which are the ones with upper limits. In the interest of comparing the optical light
negligibly short T ). In addition, Liang et al. (2009) also curves of these GRBs to those predicted by the external
∆
foundthatbothtypesoflightcurvesintheirsamplecanbe shock prior emission model, we have included as much of
roughly explained by theexternal shock model. the available optical data for these bursts as possible. The
Ifapriorexplosionindeedhappened,thisprioroutflow references for the optical light curve data are given in Ta-
must sweep up the ambient medium and form an external ble 1. Since most of the prompt optical observations from
shock.Thelong-lastingpriorX-rayemissionthatisinvoked Yost et al. (2007a,b) are in the R-band, we include only
to interpret the X-ray plateaus is most likely from this ex- theR-bandopticallightcurves.TheonlyexceptionisGRB
ternalshock.Ifthisisthecase,thenthesameexternalshock 060927, for which theincluded prompt optical observations
would give rise to an optical emission component that fol- and optical light curve data are at a wavelength (8190 A˚)
lowsthesameplateaubehavior.Thiscanbetestedwiththe near thei-band(Ruiz-Velasco et al. 2007).
available optical data, especially during the earliest obser- Beforewecancomparethepromptopticalobservations
vationalepoch.Ingeneral,opticalemission observedduring andopticallightcurvesfromtheliteraturetothepredictions
theprompt phasemaybeamix of thisprioremission com- oftheexternalshockprioremission model,theopticaldata
ponentandseveralotheremissioncomponents,includingthe must be corrected for Galactic and host galaxy extinction.
optical counterpart of the prompt GRB emission, and the We corrected the optical data for Galactic extinction using
reverse shock and forward shock emission associated with the empirical Milky Way (MW) extinction law, extinction
the prompt outflow. As discussed in Ioka et al. (2006), the coefficients, and R =3.08 from Pei(1992), along with the
V
ejecta associated with the prompt emission would stream values of A from Schlegel et al. (1998). In order to cor-
B
into the trail of the prior component blastwave with modi- recttheopticaldataforhostgalaxyextinction,wesearched
fied medium density profile, leading to another pair of for- theliteratureoneachburstinoursamplefortheextinction
ward and reverse shocks (for the dynamics setting of the law and AV or EB−V value which provided the best fit to
threeshock system,see Zhang& M´esz´aros 2002). Therela- its afterglow spectral energy distribution (SED). We then
tiveimportanceofemissioncontributiontotheopticalband usedtheappropriateresultsfrom theliteraturetocalculate
dependsonmanyparameters.Thereverseshockcomponent thehostgalaxyextinction,onceagainrelyingontheempir-
can dominate or be outshone by the forward shock compo- ical MW, Large Magellanic Cloud (LMC), and Small Mag-
nentintheopticalband.Thedetectedpromptopticalemis- ellanic Cloud (SMC) extinction laws and parameters from
sionfluxisthereforeallowedtobehigherthanthepredicted Pei (1992).
flux.Ontheotherhand,ifthepromptopticalfluxorupper The host galaxy extinction information and references
limitisalreadybelowtherangeofthepredictedopticalflux, for each GRB are given in Table 1. For GRB 060927 and
thentheexternalshockprioremissionmodelwouldberuled GRB061222A, thecitedauthorswereunabletodistinguish
out. This is the motivation and strategy of thispaper. between the three extinction laws. We chose the SMC ex-
tinctionlawbasedontheconclusionsofSchadyetal.(2007,
2010),that,inmostcases,itprovidesanacceptablefittothe
host galaxy extinction profile. It should also be noted that
2 SAMPLE SELECTION AND DATA
the host galaxy extinction of GRB 050401 is the subject of
REDUCTION
debate.WehavedecidedtousetheanalysisofWatsonetal.
(2006), although higher values of A have been advocated
In order to create a sample for this study, we need bursts V
byDe Pasquale et al. (2006) and Kamble et al. (2009).
with bothX-rayplateaus(which can befit within theprior
The calculated values (in magnitudes) of the host
galaxy extinction A and Galactic extinction A are
λemit λobs
given in Table 1. The error on A is due to propagat-
1 Quimby et al. (2006) have explored the effects that changing λemit
the afterglow reference time has on the X-ray and optical light ingtheerroronthehostgalaxyvalueofAV orEB−V taken
fromtheliterature,andtheerroronR givenbyPei(1992).
curves for the ambiguous case of GRB 050319, a burst in our V
SincethehostgalaxyA valuesforGRB051109AandGRB
sample.InouranalysisofGRB050319,weadoptedtheirdefined V
ttr0asT =0,whichmarksthestartofthepromptemissioneven 061222Aarelimits,theerrorsontheirAλemit onlytakeinto
thoughtheactualtriggerhappened laterduetoaninstrumental account the error on RV. We were unable to calculate the
slewingeffect. host galaxy extinction for GRB 050822 since there is no
(cid:13)c 2011RAS,MNRAS000,1–??
Constraints on GRB external shock prior emission 3
Table 1. Optical light curve references, redshifts,host galaxy extinction information, values of host galaxy and Galactic extinction, and
spectralfitresultsforoursampleGRBs.
GRB z Hostgalaxy Host Galactic Fitting Galactic Host β χ˜2 (ν)
extinction Aλemit Aλobs interval NH∗ NH∗
information (mag) (mag) (ks) (1022 cm) (1022 cm)
050319a 3.24b AV =0.21±0.08,MWc 0.53±0.20 0.028 6.24-82.77 0.0126 0.34 1.19±0.07 0.83(374)
050401d 2.90b AV =0.62±0.06,SMCe 2.4±0.2 0.167 0.46-20.09 0.044 1.57 1.00±0.07 0.78(365)
050822 1.2f unknown ? - 6.41-516.15 0.014 0.118 0.90±0.04 1.03(421)
051109Ag 2.35b AV <0.10,SMCc <0.3189±0.0008 0.487 3.73-636.40 0.16 0.93 1.29±0.03 1.03(560)
060729 0.54b AV =0.04±0.02,LMCc 0.05±0.03 - 0.70-2,221.24 0.045 0.099 1.14±0.01 1.16(749)
060927h 5.47h EB−V =0.07±0.03h,SMC 1.1±0.5 - 0.11-10.86 0.046 0.860 1.0±0.1 0.50(208)
061121i 1.31b AV =0.40±0.04,LMCc 0.80±0.08 0.116 0.59-348.63 0.04 0.607 1.09±0.03 0.88(587)
061222A 2.088j AV >5.0j,SMC >14.74±0.04 - 0.23-723.42 0.09 3.82 1.13±0.03 1.15(692)
*Taken from Evans et al. (2009) and held constant in spectral fit; aOptical light curve data from Greco et al. (2005a), Kiziloglu et al.
(2005), Misraet al.(2005a), Sharapov et al.(2005), Wo´zniak et al. (2005), Quimbyet al.(2006), Huanget al. (2007), and Kambleetal.
(2007); bLiangetal.(2007); cSchadyetal.(2010); dOpticallightcurvedatafromD’Avanzoetal.(2005), Grecoetal.(2005b), Kahharov
et al. (2005), Misra et al. (2005b), Rykoff et al. (2005), De Pasquale et al. (2006), Watson et al. (2006), and Ghirlanda et al. (2007);
eWatson et al. (2006); fButler (2007); gOptical light curve data from Yost et al. (2007a); hOptical light curve data, redshift, and host
galaxy extinction informationfromRuiz-Velascoet al.(2007); iOptical lightcurve data fromEfimov et al.(2006), Halpernet al.(2006),
Halpern&Armstrong(2006a,b), Melandrietal.(2006), Pageetal.(2007), andUeharaetal.(2011); jPerleyetal.(2009)
information about its host galaxy extinction profile in the 3 MODEL
literature.WedidnotcalculateGalacticextinctionforGRB
In this paper we focus on the XRTdata in theshallow and
050822,GRB060729,GRB060927,andGRB061222Asince
normaldecayphases(darkblackpointsinFig.3).Wedonot
alloftheincludedopticalfluxdensitiesfortheseburstshave
consider the post jet break phase as the jet break happens
alreadybeencorrectedforGalacticextinctionbyeitherYost
muchlater.UsingtheprioremissionmodelandEq.[2]from
et al. (2007a,b) or Ruiz-Velascoet al. (2007). The errorson
Liang et al. (2009) as our prescription, we fit5 the shallow
A were negligible.
λobs and normal decay segments of each XRTlight curve to the
The Swift/XRT data for the GRBs in our sample are
function
taken from the Swift data archive2. We developed an IDL
packagewhichinvokesthestandardHEASofttools(e.g.,Xs- F =F T +T∆ −α (1)
elect, Ximage, Xspec, Swift tools) to automatically process 0 T
(cid:18) ∆ (cid:19)
theXRTdataforanygivenburst.Thedetailsoftheproce-
allowing thenormalization constant F , time shift constant
dure of our package are described in Zhang et al. (2007b). 0
T , and temporal decay index α to vary in the fit. Here
Our final data products3 include the XRT light curves (in ∆
T is the time measured since the GRB trigger. The fitting
physicalunits),extractedovertheenergyrange0.3−10keV.
intervals are loosely based on the time ranges given in Ta-
These data products have been applied to study statistical
ble1ofLiang etal. (2007). Oncetheparameters havebeen
properties of X-ray afterglows in a series of papers (Zhang
determined for a particular burst, Eq. [1] can be used to
et al. 2007b; Liang et al. 2007, 2008, 2009).
extrapolatetheX-rayfluxduetotheprioremissioncompo-
Fortheburstsinoursample,thespectralindexβforthe
nentfromtheshallowdecaysegmenttoearliertimes(i.e.,to
XRT band is obtained by fitting the time-integrated spec-
the time of the early optical observations of interest). The
trum (Evans et al. 2009) of the shallow and normal decay
results of the XRTlight curvefitsare given in Table 2.
phases with a simple power law model in Xspec. The spec-
The external shock model predicts a broken power law
tral fit also includes two-component neutral hydrogen col-
synchrotron spectrum (M´esz´aros & Rees 1997; Sari et al.
umn density N and N , with corresponding val-
H,host H,Gal 1998). For a constant density medium, a fast cooling spec-
uestakenfromthelate-timespectraldataintheSwift/XRT
trum(ν <ν )isexpectedatearlytimes,whichtransitions
GRBspectrumrepository4 (Evansetal.2009).Theirvalues c m
toaslow coolingspectrum(ν <ν )atlatertimes(Sariet
were held constant in our spectral fit, which are collected m c
al. 1998). In our analysis, since T ∼ 103 −104 s (typical
in Table 1 along with the GRB redshift z and the spectral ∆
observed shallow-to-normal break time), the prior emission
fittingresults.
externalshockshouldhavealreadyenteredtheslowcooling
All the errors quoted in this paper correspond to the
regimebythetimeoftheGRBtrigger.Thus,weapplyslow
1σ errorson thequantities,unlessotherwise indicated.The
cooling throughout the modeling.
convention F ∝ t−αν−β is adopted. The zero points and
ν We first determine the spectral regime in which the
effectivefrequenciesfortheopticalbandsfromBessell(1979)
XRT band is located by using the X-ray α and β data and
are adopted.
comparing the data with the closure relations of the exter-
nal shock models (Zhang & M´esz´aros 2004). Our approach
is similar to that used by Racusin et al. (2009). We use the
2 ftp://legacy.gsfc.nasa.gov/swift/data/
3 Availablefromhttp://grb.physics.unlv.edu/swift 5 Using the routine MPFITFUN.PRO (Markwardt 2009):
4 http://www.swift.ac.uk/xrt_spectra/ http://purl.com/net/mpfit
(cid:13)c 2011RAS,MNRAS000,1–??
4 T. Birnbaum, B. Zhang, B.-B. Zhang and E.-W. Liang
Table 2.Resultsoftemporalfitsandspectralregime/modeldeterminations.
GRB Fitting F0 T∆ α χ˜2 (ν) Regime Model αpred
interval (10−11 erg (ks)
(ks) s−1 cm2)
050319 6.11-84.79 2.1±0.3 17±10 1.5±0.4 0.51(27) νX >νc ISM,p>2 1.29±0.11
050401 0.14-20.09 87±4 0.53±0.05 1.13±0.03 2.21(132) νX >νc ISM,p>2* 1.00±0.11
050822 6.41-523.32 1.5±0.3 12±5 1.1±0.1 1.24(72) νm<νX <νc ISM,p>2* 1.35±0.06
051109A 3.73-639.16 15±2 3.3±0.7 1.33±0.04 1.17(94) νX >νc ISM,p>2* 1.44±0.05
060729 0.70-2,221.24 2.93±0.05 120±7 1.96±0.05 1.69(813) νm<νX <νc ISM,p>2* 1.71±0.02
060927 0.11-10.86 4.4±0.5 2.7±1.8 2.5±1.0 1.19(29) νm<νX <νc Wind,p>2 2.0±0.2
061121 0.30-353.10 35.8±0.9 2.6±0.1 1.35±0.02 1.18(412) νX >νc ISM,p>2* 1.14±0.05
061222A 0.23-724.62 10.2±0.2 8.5±0.4 1.56±0.02 1.72(317) νm<νX <νc ISM,p>2* 1.70±0.05
*αandαpred notconsistentwithinerrorforthisregimeandmodel
value of β from our spectral fit to evaluate the slow cool- If ν is below ν , then most likely ν < ν < ν . The
opt c m opt c
ing closure relations, with each model/regime combination minimumpossible optical fluxdensityin thisregimeoccurs
yieldingapredictedvalueofthetemporaldecayindexα . when ν is just aboveν , so that
pred X c
We then compare the values of α to the value of α ob-
tained from our temporal fit, lookpirnegdfor the model/regime F (T )=F (T ) νopt −(β−1/2) (4)
combination for which α−αpred = 0 (within 1σ error). Of opt,min obs X obs (cid:18) νX (cid:19)
course, the decision typically was not clear cut. For six out
This is marked as the second dashed line in Fig. 1a. In the
oftheeight GRBsinoursample, αwasnotconsistent with
most extremecases, onemay haveboth ν andν between
α from any of the model/regime combinations within m c
pred
theoptical andX-raybands.Therefore thelowest fluxden-
error. In these cases, we chose the model and regime with
sity allowed corresponds to ν =ν .ν , so that
whichthedatawasmostconsistent(minimizing|α−α |). m c X
pred
Ultimately, the XRT band is found to be either in the ν 1/3
ν <ν <ν or the ν >ν spectral regime6. The results F (T )=F (T ) opt (5)
m X c X c opt,min obs X obs ν
of our spectral regime and model determinations are given (cid:18) X (cid:19)
in Table 2. One ambiguous case was GRB 050822. ItsXRT This corresponds tothe third dashed line in Fig. 1a.
datawerenearlyequallyconsistentwiththreemodel/regime Inthecasethatν <ν <ν (Fig.1b),themaximum
m X c
combinations:νX >νcforISMandWind(p<2),andνm < possibleopticalfluxdensityoccurswhenνX isjustbelowνc
νX < νc for ISM (p > 2). We chose the last model/regime andνoptisinthesameregimeasνX (Eq.[3]).Theminimum
combinationforGRB050822becausetheresultingpredicted possible optical flux occurs when ν is just above ν and
X m
rangefortheopticalfluxactuallyencompassesthepredicted ν <ν .ν (Eq. [5]).
opt m X
rangescorrespondingtotheothertwomodel/regimechoices. In both Fig. 1a and Fig. 1b, the thicker part of the
Next, we apply the XRT light curve fit results to ex- range corresponds to the maximum prediction, for which
trapolate the prior emission X-ray flux back to the time of there are no spectral breaks between the X-ray and optical
the optical observations (Tobs), and derive the mean X-ray bands. The thinner part of the range, which includes the
spectral density as minimum prediction, represents the case in which there is
F T +T −α onespectralbreakbetweenthebands.Thedash-dottedline
FX(Tobs)= ν0 obsT ∆ (2) in Fig. 1a corresponds to the extreme case in which there
X (cid:18) ∆ (cid:19) aretwospectralbreaksbetweentheX-rayandopticalbands.
where ν ≈4.8×1017 Hz(2 keV)7 is applied. In all cases, we have introduced an error on the prediction,
X
Wethenapplytheslowcoolingmodel(Fig.1bofSariet which includes the uncertainties in β, F0, T∆, and α, with
al. 1998) to predict the range of optical flux density. In the the prior emission model and external shock synchrotron
case that ν >ν (Fig. 1a), the maximum possible optical model applied and errors properly propagated.
X c
fluxdensityoccurswhenν >ν ,sothattheopticalband Thefinalpredictedrangefortheopticalfluxdensitycan
opt c
lies in the same spectral regime and one can do a simple thenbecomparedtotheopticalobservationswithproperex-
extrapolation of X-ray flux density based on the power law tinctioncorrection.Ifalloftheextinction-correctedprompt
spectral fits(top dashed line): optical observations fall within their predicted ranges, then
thedatawouldshownoinconsistencywiththehypothesisof
F (T )=F (T ) νopt −β (3) anexternal-shock-originprioremission.Ifsomeorallofthe
opt,max obs X obs (cid:18) νX (cid:19) observationslieabovetheirpredictedranges,thiswouldnot
count as evidence against this hypothesis, because the ob-
served optical fluxcan havecontributionsfrom theinternal
dissipation region andthereverse/forward shockassociated
6 In some cases, a burst is consistent with both ISM and Wind
withthepromptemission,besidesthecontributionfromthe
models within the samespectral regime. For the analysis below,
prioremissioncomponent.However,anobservationthatlies
the medium density profile does not enter the problem. So we
careaboutthespectral regimeonly. below its predicted range would put a severe constraint on
7 ApproximatelogaverageoftheXRTenergyrange theexternal shock prior emission model.
(cid:13)c 2011RAS,MNRAS000,1–??
Constraints on GRB external shock prior emission 5
ν >ν
X c
1
ν>m LmJy
νopt β ~ -p/2 Hnsity 0.01
De
x
u
Fl 10-4
ν
F
g
lo β ~ -(p-1)/2 10-61 10 100 1000 104 105 106
m
ν TimeHsL
<
pt
o
ν
Figure 2. Example optical (solid) and X-ray (dashed) light
curves derived from the external shock prior emission model
β ~ 1/3
with typical parameter values: tm = 2500s (p = 2.3, ǫe = 0.3,
ǫB = 0.01, EK = 1052 erg, n = 0.5, z = 1.0) and T∆ = 0s
(black),500s(red),1250s(green),2500s(blue),10000s(pink).
These light curves were generated by our GRB afterglow code
whichusestheresultsofSarietal.(1998)andZhangetal.(2007a)

asaprescription.
Optical XRT
logν

ν <ν <ν
m X c The interpretation becomes more complicated in the
caseswherelateropticalobservationsareavailable.Inthese
cases,onemayexaminetheoverallshapeoftheopticallight
m
ν curve to determine whether or not it is consistent with the
>
pt external shock prior emission model. If the prior emission
o
ν time is chosen as the zero point, the X-ray lightcurve and
β ~ -(p-1)/2 optical lightcurve typically havedifferent shapes. In partic-
ular, if ν < ν early on, the optical lightcurve would
opt m
displayaninitialrisewithF ∝t1/2 (wheretistimemea-
opt
suredfromtheprioremissionzeropoint)followedbyadecay
ν
F
g (Sari et al. 1998). With T∆ shift, the shapes of both X-ray
o m
l ν and optical lightcurves are distorted. In particular, the op-
<
pt tical lightcurve as measured since the GRB trigger may be
o
ν well fit bya smooth broken power law
β ~ 1/3 F =F T +T∆ −w2 + T +T∆ wα −w1 (6)
0"(cid:18)Tm+T∆(cid:19) (cid:18)Tm+T∆(cid:19) #
whereT isthetimereferencedfromtheGRBtriggerwhen
m
ν crosses ν and w is the smoothing factor (Liang et al.
m opt
2007). Figure 2 shows the comparison between the X-ray

and optical lightcurves for various values of T . It is found
∆
Optical XRT thatthedifferencebetweentheshapesofthetwolightcurves
logν reduces as T increases, and essentially disappears as T
∆ ∆
exceeds t (the time referenced from prior emission when
m
Figure 1. Cartoon spectra based on the results of Sari et al. ν crosses ν ).
m opt
(1998). For each possible spectral regime for νX, there are min- If the optical lightcurve does not follow the predicted
imum and maximum possibilities for the corresponding optical
shapeoftheexternalshockprioremissionmodel,onewould
fluxdensity(section3).
conclude that it is dominated by another component. In
that case, the allowed optical emission level from the ex-
ternal shock prior emission component should be at most
the highest predicted prior emission lightcurve allowed by
the data. Additionally, the predicted prior emission optical
light curve should lie within the predicted range delineated
bythe bars in Figure 1.
(cid:13)c 2011RAS,MNRAS000,1–??
6 T. Birnbaum, B. Zhang, B.-B. Zhang and E.-W. Liang
102 104 102
GRB 050319 GRB 050401 GRB 050822
102
100 100
mJy) mJy) 100 mJy)
Flux density ( 10-2 Flux density ( 10-2 Flux density ( 10-2
10-4 10-4
10-4
10-6 10-6 10-6
102 103 104 105 106 101 102 103 104 105 106 107 101 102 103 104 105 106 107
Time since trigger (s) Time since trigger (s) Time since trigger (s)
104 102 102
GRB 051109A GRB 060729 GRB 060927
102 100
100
mJy) 100 mJy) mJy) 10-2
Flux density ( 10-2 Flux density ( 10-2 Flux density ( 10-4
10-4
10-4 10-6
10-6 10-6 10-8
101 102 103 104 105 106 107 101 102 103 104 105 106 107 101 102 103 104 105 106
Time since trigger (s) Time since trigger (s) Time since trigger (s)
104 106
GRB 061222A
GRB 061121
104
102
102
mJy) 100 mJy)
Flux density ( 10-2 Flux density ( 100
10-2
10-4
10-4
10-6 10-6
101 102 103 104 105 106 107 101 102 103 104 105 106 107
Time since trigger (s) Time since trigger (s)
Figure3.ThegreyandblackasterisksaretheXRTlightcurvedata.TheredlineisthefitofEq.[1]totheblackXRTlightcurvedata
points.ThegreenbarsrepresentthepredictedrangesfortheopticalfluxdensityatTobs.Thethickerpartofthegreenbarcorresponds
to the maximum prediction for which there are no spectral breaks between the XRT and optical bands. The thinner part of the green
bar,whichincludestheminimumprediction,isobtainedbyassumingthereisaspectralbreakbetweenthebands.ForGRB061121,the
dash-dotted portion of the green bar represents the extreme minimum prediction obtained by assuming there are two spectral breaks
between theXRTandoptical bands.Thedarkbluecirclesandtrianglesrepresenttheoptical detections andupperlimits,respectively.
Thedashedblacklinesarethepredicted optical lightcurvesfromtheexternal shockprioremissionmodel,as constrainedbythe green
rangesandtheoptical data. ForGRB061121, thedashedlightbluelineisthefitofEq.[1]totheopticallightcurvedatainwhichT∆
isfixedtothevaluefromtheXRTlightcurvefit.
(cid:13)c 2011RAS,MNRAS000,1–??
Constraints on GRB external shock prior emission 7
4 RESULTS AND DISCUSSION diction in which ν < ν < ν < ν . It is clear that the
m opt X c
overallshapeoftheopticallightcurveisnotconsistentwith
Theresultsofthespectralfits,burstredshifts,extinctionin-
the smooth, T -shifted single power law predicted by the
formation,andtheinclusivelistofthereferencesfortheopti- ∆
external shock prior emission model. This suggests that, if
callightcurvedataaregiveninTable1.TheXRTlightcurve
there is a prior emission external shock optical component,
fits and spectral regime determinations are given in Table
it is dominated by other optical components. The dashed
2. The XRT light curve data, associated fits, extinction-
black line shows the maximum prior emission optical light
corrected optical observations, and predicted ranges are
curveallowed bythe data.
shown in Figure 3. The green bars in the plots have the
The results for GRB 061222A are similar to those for
same meanings as the bars shown in the cartoon spectra in
GRB 050822, except in this case, the early optical upper
Figure 1 and explained in section 3. Thedashed black lines
limits are nearly four orders of magnitude above the green
are the maximum predicted optical light curves from the
range.Thisisexplainedbythelarge amountofhost galaxy
external shock prior emission model allowed by the data.
extinction (nearly 15 magnitudes) for this burst. Because
If the optical data constrain the dashed black line to be
GRB 061222A is a dark burst, we don’t know whether the
below the green range, for self-consistency we instead plot
actual level of optical flux is consistent with the prediction
a dashed line corresponding to the minimum optical light
of the external shock prior emission model. Thus, based on
curve allowed by the external shock prior emission model,
thelimiteddataavailable,weconcludethatthisburstisnot
eventhoughitclearlycontradictsthedata.Thedashedlight
inconsistent with ourhypothesis.
blue line in the plot for GRB 061121 is a fit to its optical
Overall,theopticaldataofGRB050822, GRB060729,
light curve data (discussed in section 4.2). Looking at Fig-
GRB 060927, and GRB 061222A are not inconsistent with
ure 3, one can see that the results for each GRB are a bit
the hypothesis that the prior emission, if it exists, arises
different.In general, we can assign the burststo one of two
from an external shock. However, dueto the lack of optical
groups: those that are consistent (or at least, not inconsis-
lightcurvedataforcomparison(inthecasesofGRB050822,
tent)withtheexternalshockprioremissionhypothesis,and
GRB060729, andGRB061222A), orexcessopticalflux(in
those that are inconsistent with the external shock prior
thecaseofGRB060927),theseburstsdonotmakeastrong
emission hypothesis.
caseforthehypothesis.Inotherwords,theresultsforthese
GRBs do not constrain or rule out theexternal shock prior
emission hypothesis.
4.1 “Consistent” Bursts: GRB 050822, GRB
060729, GRB 060927, and GRB 061222A
4.2 Inconsistent Bursts: GRB 050319, GRB
TheearlyopticalupperlimitsofGRB050822liewithinthe
050401, GRB 051109A, and GRB 061121
thickpartofthegreenrange,correspondingtothemaximum
prediction in which ν < ν < ν < ν . However, since The early optical detection of GRB 050319 falls within the
m opt X c
these data are just upper limits and not actual detections, thinner part of the green range. This is consistent with the
theactuallevelofopticalfluxfromthisdarkburstcouldlie prediction in which thereis one spectral break between the
anywhereinthegreen rangeorevenbelowthegreenrange. X-ray and optical bands: ν < ν < ν < ν . How-
m opt c X
In fact, since we were unable to correct these upper limits ever, the optical light curve data clearly do not exhibit the
for host galaxy extinction, the limits (and thus the actual smooth, T -shifted single power law behavior predicted by
∆
level of optical flux) could even be above the green range. theexternalshockprioremissionmodel.Thissuggeststhat,
Regardless, the facts that these are only upper limits, and even if the prior emission does originate from an external
thatevenwithoutcorrectionforhostgalaxyextinctionthey shock, the optical prior emission component is dominated
lie within the green range, lead us to the conclusion that byotheropticalcomponents.Thus,themaximumpredicted
GRB050822isnotinconsistentwiththeexternalshockprior prior emission optical light curve should lie below the ac-
emission hypothesis. tual optical light curve data. However, plotting the dashed
GRB 060729 has been studied (e.g., by Grupe et al. line below all of the optical data would place the predicted
2007, Curran et al. 2009) in many optical bands. However, prior emission light curve below the green range, which is
there is no additional R-band data in the literature. We notself-consistent.Thus,thedashedblacklineisultimately
find the early R-band optical upper limit and detections of constrained by the green range in this case. We must con-
GRB 060729, which have been corrected for both Galactic clude that GRB 050319 is not consistent with the external
and host galaxy extinction, lie within the thinner part of shock prior emission hypothesis.
the green range. This is consistent with the case in which The situation is similar for GRB 050401 and GRB
there is one spectral break between the X-ray and optical 051109A. Although the early optical detections of these
bands: ν <ν < ν < ν . Due to the lack of additional bursts fall within the thinner part of the predicted green
opt m X c
R-band data, we cannot make any further comparisons of range corresponding to ν < ν < ν < ν , the shapes
m opt c X
thisbursttopredictionsoftheexternalshockprioremission oftheoptical light curvesarenot consistent with theshape
hypothesis,andconcludethattheavailableR-banddatafor predictedbytheexternalshock prioremission model. Once
GRB 060729 are not inconsistent with this hypothesis. again, the predicted prior emission optical light curves are
For GRB 060927, the early optical data is at a wave- ultimately constrained by the bottom of the green range,
length near the i-band, and fortunately there is additional andwemustconcludethatGRB050401andGRB051109A
optical data in this band in the literature. The prompt i- are not consistent with the external shock prior emission
bandopticalfluxdensityfallswithinthethickerpartofthe hypothesis.
green predicted range, corresponding to the maximum pre- GRB 061121 is the only burst in our sample for which
(cid:13)c 2011RAS,MNRAS000,1–??
8 T. Birnbaum, B. Zhang, B.-B. Zhang and E.-W. Liang
the early optical data fall below the green range. Conse- Virgili for helpful discussion. This work is partially sup-
quently,theonlywaytoexplainthisburstwithintheexter- ported by NASA NNX10AD48G and NSF AST-0908362.
nal shock prior emission model is to introduce the ad hoc ThisresearchhasalsomadeuseofdatasuppliedbytheUK
assumption that there are two spectral breaks between the SwiftScienceDataCentreattheUniversityofLeicester,and
X-ray and optical bands (ν < ν . ν < ν ), as indi- by the NASA/IPAC Extragalactic Database (NED) which
opt m c X
catedbythedash-dottedextensionofthegreenrange.Even isoperatedbytheJetPropulsionLaboratory,CaliforniaIn-
after making this ad hoc assumption, there are still issues stituteof Technology, undercontract with NASA.
with GRB 061121. At first glance the shape of the optical
light curveappearspromisingly similar tothatoftheX-ray
lightcurve.ThiscouldbeconsistentwithEq.[6]andFigure
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