XRF 050406 late-time flattening: an inverse Compton component?

0.7 MB·

by  A. Corsi

Astronomy&Astrophysicsmanuscriptno.Corsi c ESO2008
(cid:13)
February5,2008
XRF 050406 late-time flattening: an inverse Compton component?
A.Corsi1,2,3 andL.Piro1
7
0
0 1 IASF-Roma/INAF,ViaFossodelCavaliere100,00133Roma,Italy.
2 2 Universita`deglistudidiRoma“LaSapienza”,PiazzaleAldoMoro5,00185Roma,Italy.
3 INFN-SezionediRomac/oDip.diFisica-Universita`deglistudidiRoma“LaSapienza”,PiazzaleAldoMoro5,00185Roma,Italy.
n
a
J
8 ABSTRACT

3 Aims.WeinvestigateforpossibleevidenceofinverseCompton(IC)emissionintheX-rayafterglowofXRF050406.
v Methods.Intheframeworkofthestandardfireballmodel,weshow how thelate-timeflatteningobserved intheX-raylightcurvebetween
8 104sand 106scanbeexplainedinasynchrotron-plus-ICscenariowhentheICpeakfrequencycrossestheX-rayband.
∼ ∼
5 Results.Wethusconclude thattheappearance ofanICcomponent abovethesynchrotrononeatlatetimessuccessfullyaccountsforthese
1 X-rayobservations.
4
0
6
Keywords.Gammarays:bursts–X-rays:Individuals(XRF050406)–X-rays:bursts–radiationmechanisms:non-thermal
0
/
h
p
1. Introduction TheX-raylightcurveofXRF050406showssomeveryin-
-
o terestingfeatures.InadditiontoanX-rayflare(Burrowsetal.
r The “Burst Alert Telescope” (BAT; Barthelmyetal. 2005) 2005b), it is characterized by a flattening at late times (t &
t
s on board Swift (Gehrelsetal. 2004) was triggered by 4200sfromthetrigger).Inthisworkwetestwhethertheflat-
a GRB 050406 on April 6, 2005, at 15:58:48.40 UT
: tening can be related to the appearance of an IC component
v (Parsonsetal. 2005). The BAT located the burst at
(e.g., Wei&Lu 1998; Panaitescu&Kumar 2000; Wei&Lu
i RA=02h17m53s and Dec= 50 1052 (J2000), with an
X ◦ ′ ′′ 2000; Sari&Esin 2001), in the context of the standard fire-
−
uncertainty of 3 arcmin (Krimmetal. 2005). The photon
r ballmodel(e.g. Sarietal.1998).InSect.2wesummarizethe
a index of the 15 350 keV time-averaged spectrum was
observed properties of the broad-band afterglow. We refer to
−
Γ = 2.38 0.34 (Krimmetal. 2005). Because of the spec-
the 0.2 10 keV light curve and spectral analysis presented
±
tral softness, this burst was classified as an X-ray flash −
byRomanoetal.(2006)andtoTable1inSchadyetal.(2006)
(XRF; Heiseetal. 2001). The 15 350 keV fluence was
for the opticaldata. In Sect. 3 we constrainthe parametersof
−
(1.0+1.13) 10 7 ergscm 2 (Romanoetal.2006).Assuminga
0.36 × − − thefireballinasynchrotron-plus-ICscenarioandinSect.4we
reds−hiftofz = 2.44(Schadyetal. 2006), theisotropicenergy
presentourconclusions.
releasewas 1.4 1051ergs. Hereafter, F(ν,t) t αν β is the flux density at the ob-
∼ × − −
The “X-Ray Telescope” (XRT; Burrowsetal. 2005a) im- server’stimetandobse∝rvedfrequencyν;αandβarethetempo-
agedtheBATfieldstartingfrom84safterthetrigger,andthe ralandspectralindicesrespectively;E = E/(1052ergs)isthe
52
X-ray counterpart of XRF 050406 was found during the on- isotropicequivalentenergyoftheshockinunitsof1052ergs;n
ground analysis (Cusomanoetal. 2005; Capalbietal. 2005). istheparticlenumberdensityoftheambientmediuminunitsof
The “Ultra-Violet/Optical Telescope” (UVOT; Romingetal. 1particle/cm3;ǫ = ǫ /10 2isthefractionoftheshocken-
B, 2 B −
2005) also started imaging about 88 s after the trigger. The ergy,whichgoesi−nmagneticenergydensitybehindtheshock,
optical afterglow was not detected on-board (Landsmanetal. in units of 10 2; ǫ = ǫ /0.5 is the fraction of shock en-
− e,0.5 e
2005), but subsequent on-ground analysis revealed a source ergy that goes into accelerating the electrons, in units of 0.5;
within the XRT error circle (Roletal. 2005). Late-time ob- p is the power-law index of the electron energy distribution
servations ( 7.8 hr after the burst) performed by the (Sarietal. 1998). We adopt z = 2.44 for the redshift of the
∼
Magellan/Clay Telescope revealed a single faint source (R = source(Schadyetal.2006).
22.0 0.09)locatedatRA=02h17m52s.3andDec= 50 1115
◦ ′ ′′
± −
(J2000;Bergeretal.2005a,b).
2. Theoptical-to-X-rayafterglow
Send offprint requests to: A. Corsi – Alessandra.Corsi@iasf- The0.2 10keVlightcurveofXRF 050406showscomplex
−
roma.inaf.it behavior (Burrowsetal. 2005b), with a power-law decay un-
2 A.CorsiandL.Piro:XRF050406:anICcomponent?
Table1.ClosurerelationshipsbetweentheX-rayafterglowspectralandtemporalindices(β = 1.1 0.3,α = 1.58 0.17)of
1
± ±
XRF050406inthestandardsynchrotronfireballmodelforawindorISMenvironment.Inparenthesis:relationshipsinanISM
modifiedfortheeffectofICcooling.The(u)marksthoserelationshipsthatarenotaffectedbyICemission.
ISMenvironment Windenvironment
Expectedrelation Observedvalue Expectedrelation Observedvalue
a) ν <ν <ν 2α β=0(u) 2.1 0.4 2α+β 1=0 3.3 0.5
c X m − ± − ±
b) ν <ν <ν 2α 3β+1=0(u) 0.86 0.96 2α 3β+1=0 0.86 0.96
c m X − ± − ±
c) ν <ν <ν 2α 3β=0(u) 0.14 0.96 2α 3β 1=0 1.1 1.0
m X c − − ± − − − ±
d) νm <νc<νX 2α−3β+1=0(α+ 3β22(−26ββ+)1 =0) 0.86±0.96(0.48±0.31) 2α−3β+1=0 0.86±0.96
−
derlyinga flare peakingat about210 s after the trigger and a 2005; Romanoetal. 2006). On the other hand, if the flare
flatteningbetween 104 sand 106 s.Excludingtheflare,a markstheonsetoftheafterglow(Piroetal.2005;Galli&Piro
∼ ∼
brokenpower-lawmodelwithα =1.58+0.18,α =0.50 0.14, 2006),theanalysispresentedhereisvalidfort>210s.
1 0.16 2 ±
andt 4200syieldsagoodfittoth−edata(Romanoetal. Several authorshave considered the effect of IC emission
break
∼
2006). inGRBX-raylightcurvesatlatetimes(e.g. Wei&Lu2000;
The mean X-ray energy index was β = 1.1 0.3 during Sari&Esin2001).Inthissectionwetestamodelinwhichthe
±
the first 600 s after the trigger and β = 1.06 0.24 between steeppartoftheX-raylightcurveisproducedbysynchrotron
±
600 s and 2 104 s (Romanoetal. 2006). These results emissionwhilethelate-timeflatteningisduetotheappearance
∼ ∼ ×
were obtainedby fitting the data with an absorbedpower-law ofanICcomponentatthatpointintime.
modelwithhydrogencolumndensity(N )fixedtotheGalactic
H
value of 2.8 1020 cm 2 (Dickey&Lockman1990). The 3σ
× − 3.1.Synchrotroncomponent
upper-limitfor thetotal (Galacticplusintrinsic) N alongthe
H
lineofsightis9 1020cm−2(Romanoetal.2006). InTable1wesummarizetheclosurerelationshipsbetweenthe
×
The first UVOT observations were performed in the V- spectralindexβandtheearlytemporaldecayindexα forthe
1
band,between113sand173s.Thehighestfluxwasmeasured X-rayafterglowofXRF050406.Therelation
ina50slongexposure,starting113safterthetrigger.During
f(p)
(thSicshoabdsyerevtaatli.on2,0t0h6e)m; aefatseurrecdormreacgtnioitnudfeorwGasa1la8c.t9i2c±e0x.t3in1cmtioagn νm =2×1013 f(2.5) (1+z)1/2ǫB1/,−22ǫe2,0.5E512/2td−3/2Hz (1)
(E(B V)=0.022magandA /E(B V)=3.1, Schlegeletal.
1998)−, this corresponds to a VV-band−flux of 0.11 0.04 mJy. istheinjectionfrequency,with f(p)= p−2 2,and
± (cid:16)p−1(cid:17)
Sinceatabout100sthe0.2keVfluxwas 0.05mJy(usinga
conversionfactorof6.5×10−11 ergcm−2∼count−1 andaspec- νc =2.7×1015(1+z)−1/2ǫB−,3−/22E5−21/2n−1td−1/2(1+x)−2Hz (2)
tralindexofβ 1.1,asfoundby Romanoetal.2006),theob-
∼ isthecoolingfrequency(Sari&Esin2001);t istheobserver’s
servedoptical-to-X-rayspectralindexat100s,β 0.15, d
opt X
− ∼ timeinunitsofdays;xistheratiooftheICtosynchrotronlu-
turnedouttobeextremelyflat.Suchaflatvaluewasnotfound
minosity, i.e. x √ǫ /ǫ in the fast-cooling regime and x
in the analysis performed by Schadyetal. (2006), where the ∼ e B ∼
√ǫ /ǫ (t/t0 ) (p 2)/(2(4 p)) intheslow-coolingIC-dominated
mean optical and X-ray flux between 220 s and 950 s were e B× IC − − −
regime 1(Sari&Esin 2001); t0 is the time at which the tran-
considered. IC
sition fromslow coolingto fast coolingtakes place (when ν
m
equalsν ).ItisimportanttonotethatifICisanefficientcool-
c
3. SynchrotronplusICmodel ingmechanism,thetransitionfromfastcoolingtoslowcooling
isdelayedbyafactorofǫ /ǫ (Sari&Esin2001).
e B
As seen in the previous section, the X-ray light curve of
Inthecaseofaconstantdensityinterstellarmedium(ISM),
XRF 050406 is characterized by a steep decay followed by
we indicate in parenthesis the closure relationships modified
a flattening after t 4200 s (see e.g. Fig. 1). Recently,
for the inclusion of IC emission. In particular in scenario d),
∼
Chincarinietal.(2005)andNouseketal.(2006)foundthatthe
the same relation of case b) holds, when considering only
X-ray light curves of Swift GRBs usually present an initial
synchrotron emission. However, the addition of IC modifies
steep decay (t . 500 s), followedby a shallowerone and, fi- the expression of ν for a factor of (1 + x) 2. Since during
c −
nally, by further steepening. In the case of XRF 050406, the
the slow cooling regime, x evolves with time, the temporal
temporaldecayobservedbeforethebreak(α1 1.58)isnotas decay index at ν ν changes from 3/4(p 1) + 1/4 to
∼ c
steepasusual(3 α 5, Tagliaferrietal.2005)andthecur- 3/4(p 1)+1/4 (p≥2)/(8 2p)(Sari&Esin20−01;Corsietal.
≤ ≤
vaturerelationα=β+2isnotsatisfied.Theseargumentssug- − − − −
2005)andthecorrespondingclosurerelationshipchangesasin-
gestthattheemission precedingthe late-timeflatteningcould
dicatedinparenthesisinTable1.Inscenarioc),sincetheflux
be part of the afterglow (Romanoetal. 2006) rather than the
atν ν doesnotdependontheexpressionofν ,theclosure
c c
tailofthepromptemission.Inthisscenario,thesuperimposed ≤
relationshipisnotmodified.Finally,inthefast-coolingregime,
flarecouldbeinterpretedintheframeworkofthelateinternal-
shockmodel(Burrowsetal.2005b;Fan&Wei2005;Wuetal. 1 Theseexpressionsforxarevalidifx2 >>1(Sari&Esin2001).
A.CorsiandL.Piro:XRF050406:anICcomponent? 3
x does not depend on time, thus the temporal decay index at
frequenciesaboveν doesnotchange(casesa)andb)).
c
On the basis of the closure relationships, scenarios b), c),
and d) are compatible with the observations in both an ISM
anda windenvironment(Chevalier&Li1999).Hereafter,we
willlimitourdiscussiontotheISMcase.
We have seen in Sect. 2 that the optical-to-X-rayspectral
index before the flare is rather flat. In a standard synchrotron
scenario,suchaflatvaluecannotbeexplainedunlessthesyn-
chrotronpeak frequencyis between the opticaland the X-ray
band. In Fig. 1 we show that setting ν (100 s) 0.03 keV
c
∼
(peak frequencybetween the opticaland the X-ray band)and
ν (100s) 0.2keV(caseb)inTable1),marginalconsistency
m
∼
withthedatacanbeobtained.However,undertheseconditions,
ν crossestheV-bandaround2 103s;untilthattime,thelight
m
×
curve(Fig.1)featuresarise,whileXFR050406wasnolonger
visibleat 600sabovethebackground(Schadyetal.2006),
∼
suggestingaprogressivefadingoftheopticalafterglow(theV-
band upper-limits adopted here are standard 3σ upper-limits,
thusthe correspondinglimitingfluxesare 3timeshigherthan
the1σupper-limitsreportedby Schadyetal.2006).Notealso
thatinasynchrotronscenario,β&0.5atfrequenciesabovethe
peakone.Sinceν (100s) 0.03keVandν (100s) 0.2keV
c m
∼ ∼
imply β = 0.5 for ν ν ν = 0.2 keV, in Fig. 1 we are
c m
≤ ≤
minimizing the peak-flux value required to fit the optical and
X-raydataat100s,thusminimizingtheriseintheopticalflux
observeduntilthepeakfrequencyisabovetheopticalband.
To account for a decreasing optical emission, the syn-
chrotronpeakfrequencyshouldbe belowthe opticalband.In
Fig.1. 0.2 10 keV (upper panel, solid line), V-band (lower
thiscase,tofittheearlyX-rayafterglowwhileoverestimating
−
panel,dottedline),andR-band(lowerpanel,dashedline)light
as little as possible the optical flux around 100 s, the best
choice is to set ν (100 s) 1014 Hz and ν (1∼00 s) 0.2 keV curvesinastandardsynchrotronfireballmodelwithǫB =0.19,
c m
(caseb)inTable1).Infac≤t,thenβ =0.5,which∼istheflat- ǫe = 6.3 10−2, E52 = 0.5, n = 0.1, p = 2.5, so as to fit
opt X ×
− the observed optical and X-ray fluxes at 100 s, i.e. to satisfy
testvalueallowedinastandardsynchrotronscenariowhenthe
theconditionsν (100s) 0.2keV,ν (100s) 0.03keV(see
peak frequencyis below the opticalband(and p > 2). Under m c
∼ ∼
text).The0.2 10keVdatapoints(upperpanel,crosses),the
these assumptions, normalizing to the observed X-ray flux at
−
V-banddatapoints(lowerpanel,triangles),andthetheR-band
100 s, the predicted V-band flux is overestimatedfor a factor
data point (lower panel, box) are taken from Romanoetal.
of 5.IntheR-band,thepredictedlightcurvewilldecrease
ast∼1/4 untilthetimeatwhichν crossestheband( 2300s) (2006),Schadyetal.(2006),andBergeretal.(2005a),respec-
− m
and as t−34(p−1)−41 up to the time of the Magellan/Cl∼ay obser- tively.TheR-bandlightcurveanddatapointhavebeenshifted
vation (t 3 104 s). Since in this case the measured X- downbyafactorof10forclarity.
∼ ×
rayspectralandtemporalindicesimply p = 2.5 0.3,then
t−34(p−1)−14 =t−1.375,andweexpecttheprehdiictedR-b±andfluxto To model the flattening observed in the X-ray afterglow
bearoundafactorof 2abovetheMagellan/Claydatapoint. at late times, we add the contribution of an IC component.
∼
Requiring additional extinction in the GRB host galaxy or a Following the prescriptions given by Sari&Esin (2001), the
contributiontotheearlyX-rayfluxcomingfromtherisingpart IC spectrum is modeled as a power-law spectrum similar to
of the flare (or a combination of these two effects) helps ac- the synchrotron one, plus logarithmic corrections when rele-
countforthebroad-bandobservations,asweseeinthefollow- vant in the considered regime. In the power-law approxima-
ingsection. tion, the IC spectrum is normalized to a peak-flux value of
fIC = 2 10 7 f n (R/1018), where f is the peak flux
max × − max max
ofthesynchrotroncomponentandRisthefireballradiusincm
3.2.ICcomponent
(Sari&Esin2001).
To constrain the values of E , n, ǫ , ǫ that reliably cir-
52 e B
To model the observed early-time emission within the syn-
cumscribetheportionofparameterspacecompatiblewiththe
chrotronfireballmodelwechoosescenariob)ofTable1with
scenariowearetesting,wesetthefollowingconditions:
ν (100 s) 1014 Hz and ν (100 s) 0.2 keV. We thus set
c m
≤ ∼
p=2.5. 0.1keV.ν (100s).0.3keV, (3)
m
4 A.CorsiandL.Piro:XRF050406:anICcomponent?
Fig.2. The shadowedregionsare the partsof the ǫ -ǫ plane wherethe conditionsexpressedby Eq. (3) (dottedlines), Eq. (4)
B e
(dashed line), Eq. (5) (solid lines), Eq. (6) (dash-dottedlines), Eqs. (7) and (8) (dash-dot-dot-dottedlines) are simultaneously
satisfied, for E = 5 andn = 100(upper-leftpanel), E = 5and n = 150(upper-rightpanel), E = 5 and n = 200(lower-
52 52 52
left panel), and E = 10 and n = 100 (lower-right panel). The long-dashed line marks the portion of the ǫ -ǫ plane where
52 B e
(p 2)
x = ǫe 1/2 >10iftIC > 106sand x(106s) = ǫe 1/2 106 s −2(4−−p) >10iftIC < 106,soastoassurethat x> 1upto106s,which
(cid:16)ǫB(cid:17) 0 (cid:16)ǫB(cid:17) (cid:18) t0IC (cid:19) 0
isnecessaryfortheconsistencyofourformulation(Sari&Esin2001).
ν (100s).1014Hz, (4) Consideringthatinboththefastandslowcoolingregimes
c
the IC light curve at a given frequencyis expected to decline
50×10−3mJy. f0s.y2nkeV(100s).70×10−3mJy, (5) onlyafterνmIC becomeslowerthanthatfrequency,Eqs.(7)and
(8)aresettoreproducetheobservedshapeofthelate-timeflat-
0w.h2ekreeVf0os.y2rnkfeVsy(n100(1s0)0s=) =fmsfyasnxyn(cid:16)ν0cν.(2m10(k10e0Vs0)s(cid:17))−0−.50.5if 0ν.2mk(e1V00−ps/)2,>if taecnoinngst.aInnttohrer0is.2in−g1p0rokfieVlebuapntdo,1th0e5IsC,wchoimlepaofnteerntthsahtoiutlsdhhoauvlde
ν (100s)<00.2.2kekVeV(dependimnagxo(cid:16)nνcE(10q0.s()3(cid:17))and(cid:16)νsmu(1p0p0os)s(cid:17)ingthat startdecreasing,andaround106sitshouldnolongerbevisible
m
Eq.(4)isvalid). abovethebackground.Wenumericallytestedforwhichvalues
Equations(3)and(4)taketherequirementtooverestimate ofǫB andǫe theaboveconditionsaresimultaneouslysatisfied,
aslittleaspossibletheearly-timeopticalfluxintoaccount(see once the values of E52 and n are fixed. Figure 2 shows some
Sect.3.1)andreproducetheobservedX-rayspectralandtem- examples on how the conditions expressed in Eqs. (3) to (8)
poralindices(for p = 2.5,seeTable1);Eq.(5)isanormaliza- determinetheallowedrangeofparametervalues.
tionconditionontheX-raylightcurvebasedontheobserved Amongthepossiblecombinationsofparameterssatisfying
0.2 10keVfluxat100snormalizedtoafrequencyof1018Hz theconditionswesettodeterminethemostpromisingportion
(at −the center of the X-ray band). Moreover,to relate the ob- oftheparameterspace,oneshouldthenspecificallycheckfor
served flattening to the appearance of an IC component, the agreementwiththeactualdata.Infact,inFig.3weshowhow,
followingconditionshavetobesatisfied: for ǫB = 1.9 10−4, ǫe = 0.25, E52 = 5, n = 100, the ap-
×
pearanceofanICcomponentcanbeaviablemodeltoexplain
4.5 10 6mJy. fIC (105s) .10 5mJy, (6)
× − max − the late-time flattening observed in the X-ray light curve of
νIC(105s) &5keV, (7) XRF050406.
m
Forthesamesetofparameters,wealsocomputedthepre-
νIC(106s) .0.2keV. (8) dicted V- and R-bandlightcurves. As expected(Sect. 3.1), if
m
A.CorsiandL.Piro:XRF050406:anICcomponent? 5
Fig.3.Synchrotron-plus-ICmodelpredictionsforthe0.2 10keVlightcurvewithǫ =1.9 10 4,ǫ =0.25,E =5,n=100,
B − e 52
− ×
p = 2.5.The dash-dottedline representsthe synchrotroncomponent,while the dash-dot-dot-dottedline the IC one.The solid
lineistheresultingtotalflux.Themodelpredictionsarecomparedwiththe0.2 10keVdatapoints(crosses)byRomanoetal.
−
(2006).
nolocalextinctionisadded,thepredictedV-andR-bandfluxes ral indices after the flare for p = 2.5) and normalizing the
are overestimated of a factor of 5 and 2.4, respectively. synchrotron spectrum to fit the observed X-ray flux level at
∼ ∼
Ina“SmallMagellanicClouds”(SMC)-likeenvironment(Pei 300s,the0.2keVlightcurveatt.300swillriseslowly(as
∼
1992), an intrinsic extinction of A(V ) 0.32 mag in the t 1/4),andthe0.2keVfluxat100swillbeloweredbyafactor
int −
∼
GRB site (at z = 2.44) allows consistency to be recovered of (300s/100s)−1/4 3 with respect to the previous solu-
with theopticaldata(Fig. 4, upperpanel);thisimpliesan ab- tion(30(0Fisg/1.003)s).−3E(p−x1t)/r4a−1p/4ola∼ting to the optical band, the expected
sorption column density of NH 0.32 1.6 1022cm−2. In V-bandflux willoverestimatetheobservedonebya factorof
∼ × ×
such an environment,due to the lower metallicity, the upper- 5/3 2,insteadof 5.
limit of 9 1020 cm−2 set by the XRT analysis should be ∼ Un∼derthishypoth∼esis,wecanshiftthetimeinEqs.(3)and
×
increased by a factor of 7 (Strattaetal. 2004), and thus (4)from100sto300sandmodifythenormalizationcondition
∼
therequiredNH shouldbecomparedwiththisincreasedlimit. onthesynchrotroncomponent(Eq.(5))tofittheobservedX-
The numericaltest that guidedus in findingthis solutionwas rayfluxaftertheflare:
repeated for E = 0.5, 1, 2, 3, 5, 10, combined with
52
n = 10, 50, 100, 150, 200, 250, 300, 350, 400. Solutions 8 10 3mJy. fsyn (300s). 20 10 3mJy. (9)
× − 0.2keV × −
are found for E = 3, 5, 10 (Fig. 5, right-to-left) and for
52
n=100, 150, 200. Similar to what donebefore,we numericallysearchedfor
the valuesofǫ andǫ thatallowusto satisfy simultaneously
B e
IfbeforetheX-rayflare(sayt. 300s)thereissomecon- thoseconditions,foragivenchoiceofE andn.Solutionsare
52
tributionfromtherisingpartoftheflareitself(asonemayex- foundforE =0.5,1,2,3(seeFig.6)andvaluesofnbetween
52
pectinalateinternalshockscenario),wecanrelaxthenormal- 100and400.InFig.7wefindacombinationofparameterval-
izationconditiontosomeextent.Settingν (300 s) 0.2keV ues, ǫ = 9.0 10 4, ǫ = 0.36, E = 1, n = 350for which
m B − e 52
∼ ×
(so as to reproduce the observed X-ray spectral and tempo- the predictedlightcurveagreeswith the data.In thiscase the
6 A.CorsiandL.Piro:XRF050406:anICcomponent?
Fig.5. Numerical test results showing for which values of ǫ
B
and ǫ the conditions expressed by Eqs. (3) to (8) are simul-
e
taneously satisfied (and x > 10 up to 106 s). We repeated
this search for E = 0.5, 1, 2, 3, 5, 10 combined with
52
n = 10, 50, 100, 150, 200, 250, 300, 350, 400. Solutions
are foundfor E = 3 and n = 100, 150, 200 (shadowedre-
52
gionontheright);E = 5andn = 100, 150, 200(shadowed
52
regioninthecenter);E = 10andn = 100, 150, 200(shad-
52
owedregionontheleft).Thethreeregionsrepresent,foreach
valueofE ,thesuperpositionofregionssimilartothoserep-
52
resentedinFig.2,eachcorrespondingtoonevalueofnamong
the ones allowed for the considered value of E . For exam-
52
ple,thecentralregionisthesuperpositionofthethreeregions
shown in the upper-left, upper-right, and lower-left panels of
Fig.2.
Fig.4. Synchrotron-plus-ICmodelpredictionscomparedwith
theobserveddatainthecaseǫ =1.9 10 4,ǫ =0.25,E =
B − e 52
×
5,n=100, p=2.5(upperpanel)andǫ =9 10 4,ǫ =0.36,
B − e
×
E = 1, n = 350, p = 2.5 (lowerpanel).In the upperpanel, We can finally focus on the spectral predictions of the
52
theV-band(dottedline)andR-band(dashedline)lightcurves modelwe areproposingto explainthe XRF 050406late-time
include a SMC-like local (z = 2.44) extinction of A(V ) flattening. In a synchrotron-plus-IC scenario, since the light
int
∼
0.32mag;inthelowerpanel,theV-band(dottedlines)andR- curveflatteningisassociatedwithνIC crossingtheX-rayband,
m
band(dashedlines)lightcurvesincludeanSMC-likeextinction thespectralindexshouldvarybetweenthevaluesof 1/3(for
−
ofA(V ) 0.13mag(thicklines)oraGalactic-likeA(V ) t . 105 s the X-ray band is below νIC) and (p 1)/2 for
int ∼ int ∼ c ∼ −
0.15mag(thinlines).InbothpanelstheR-bandlightcurveand the first solution proposed here (Fig. 3) and between 0.5 (for
datapointhavebeenshifteddownbyafactorof10forclarity. 2 104 s . t . 2 105 stheX-raybandisbetweenνIC and
× × c
νIC)andp/2(pluslogarithmictermcorrections)forthesecond
m
solution(Fig.7).Thepredictedmeanspectralindicesbetween
logarithmic correctionsto the IC spectrum are significant be- 2.0 104sand106sare<β> 0.4and<β> 0.8forthe
× ∼ ∼
tween 0.2 10 keV, and they have been added to the power- first and second solutions, respectively.Comparing those val-
−
lawapproximation.TheICspectrumhasbeennormalizedtoa ues with the mean spectral index of β = 1.1 0.3, measured
±
peak-fluxvalueof fIC = 14/45 f σ nR (Sari&Esin before the flattening (Romanoetal. 2006), it is evidentthat a
max × max T
2001),whereσ istheThompsoncrosssection. hardeningshouldbeobservedatlatetimes.
T
In the opticalband(Fig. 4, lowerpanel),the additionof a For XRF 050406, about 60 source counts were collected
Galactic-likeextinctionterm (Cardellietal. 1989, with R = between 2.0 104 s and 106 s, so that a detailed spec-
V
∼ × ∼
3.1),withA(V ) 0.15magintheGRBsite(z=2.44),allows tralanalysiscannotbeperformed.Aratioof1.8 0.5between
int
∼ ±
us to explain both the R- and V-band observations. A SMC- hard (H : 0.2 1.0 keV) and soft (S : 1.0 10 keV) pho-
− −
like environment with A(V ) 0.13 mag could also be an tonsinthewholeintervaltimeistheonlyinformationthatone
int
∼
alternativesolution. The impliedvalues of the local N are can get from this faint source (private communication by P.
H
∼
0.15 1.79 1021cm 2and 0.13 1.6 1022cm 2,bothfully Romano, 2006). Comparing this with 0.5 . H/S . 1.0 ob-
− −
× × ∼ × ×
compatiblewith the upper-limitfromthe X-rayanalysis. (For tained by Romanoetal. (2006) after the flare (see the lowest
an SMC-like environment, as already noted, this upper-limit panel in Fig. 3 of Romanoetal. 2006), the spectrum during
shouldbeincreasedbyafactorof 7.) the late-time flattening seems to be harder, but no firm con-
∼
A.CorsiandL.Piro:XRF050406:anICcomponent? 7
4. Conclusions
We discussedtheXRF050406afterglowinthecontextofthe
standardfireballmodel.Withinasynchrotron-plus-ICscenario,
wetestedwhetherthelate-timeflatteningobservedintheX-ray
lightcurvecanbeexplainedbytheappearanceofanICcompo-
nent.Wefoundthatsettingǫ =1.9 10 4,ǫ =0.25,E =5,
B − e 52
×
and n = 100canexplainthe X-rayobservations.Considering
the optical data as well, we noted that the early optical-to-X-
ray spectral index appears rather flat and requires additional
extinction to recover consistency with the data. We also pro-
posedasecondsolutionwithǫ =9 10 4,ǫ =0.36,E =1,
B − e 52
×
n = 350,wheretheoptical-to-X-raynormalizationproblemis
solvedrequiringthatatt < 210ssomecontributiontotheX-
ray emission comes from the rising part of the flare. Using a
Galactic-orSMC-likeextinctioncurve,theN requiredbythe
H
opticaldata is consistentwith the upper-limitfoundin the X-
rayanalysis.
Acknowledgements. L. Piro acknowledges the support of the EU
throughtheEUFPC5RTN“Gamma-rayburst,anenigmaandatool”;
A.Corsi acknowledges thesupport of anINFNgrant. Wethank Pat
Romanoforperformingthespectralanalysisofthelate-timedataand
Fig.6. The shadowed regions are the parts of the ǫB-ǫe plane providingtheinformationnecessarytotestanimportantaspectofthe
where the required conditions (see text) are simultaneously presentwork;A.CorsiwouldalsoliketothankPatRomanoforinter-
satisfied (and x > 10 up to 106 s). Solutions are found for estinggeneraldiscussions,GiovanniMontaniforimportantcomments
E = 0.5 and n = 350, 400 (upper-leftpanel), E = 1 and andsuggestions,andPatriciaSchadyforusefuldiscussionsoftheop-
52 52
n=200, 250, 300, 350, 400(upper-rightpanel),E =2and ticaldata.
52
n = 150, 200, 250, 300, 350(lower-leftpanel),and E = 3
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