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 52 andn=150, 200(lower-rightpanel). References Barthelmy,S.D.,Barbier,L.M.,Cummings,J.R.,etal.2005, SpaceSci.Rev.,120,143 Berger,E.,Kulkarni,S.R.,Fox,D.B.,etal.2005a,ApJ,634, clusion can be reached due to the large errors. Since hard- 501 ening is a natural expectation in a synchrotron-plus-IC sce- Berger, E., Oemler, G., & Gladders, M. 2005b, GRB nario, we then investigated on the compatibility of our pre- CoordinatesNetwork,3185 dictionswiththeobservedH/S.UsingtheXRTPCresponse2 Burrows,D. N., Hill, J. E., Nousek,J. A., etal. 2005a,Space (Grade0-12,on-axiscounts,infiniteextractionregion),assum- Sci.Rev.,120,165 ingN =2.8 1020cm 2,andnormalizingthespectrumsoas H − Burrows,D.N.,Romano,P.,Falcone,A.,etal.2005b,Science, × tohaveabout60countsintotal,wecomputedaroughestimate 309,1833 oftheexpectedH/Sratioforaspectrumwith<β> 0.4and Capalbi, M., Perri, M., Romano, P., et al. 2005, GRB ∼ <β> 0.8,obtainingH/S =2.4 0.7andH/S =1.5 0.4 CoordinatesNetwork,3184 ∼ ± ± forthetwospectra3;thosevaluesof H/S arebothcompatible Cardelli,J.A.,Clayton,G.C.,&Mathis,J.S.1989,ApJ,345, withtheobservedvalueof1.8 0.5withintheerrors.Although 245 ± aconclusivestatementisnotallowed,encouragingindications Chevalier,R.A.&Li,Z.-Y.1999,ApJ,520,L29 infavorofthepresentmodelasamechanismforthelate-time Chincarini,G.,Moretti,A.,Romano,P.,etal.2005,ApJ,sub- flatteningariseglobally. mittedto,astro-ph/0506453 We thus conclude that future observations of brighter Corsi,A.,Piro,L.,Kuulkers,E.,etal.2005,A&A,438,829 sources,possiblyallowingperformanceoftime-resolvedspec- Cusomano, G., Kennea, J., Burrows, D. N., et al. 2005, GRB troscopy during the late-time flattening, will be a key to con- CoordinatesNetwork,3181 firmingorrejectingthescenariowearesuggestinganditspo- Dickey,J.M.&Lockman,F.J.1990,ARA&A,28,215 tentialextensionasageneralexplanationforthiskindoflate- Fan,Y.Z.&Wei,D.M.2005,MNRAS,364,L42 timebehaviorinGRBX-raylightcurves. Galli,A.&Piro,L.2006,toappearinA&A,astro-ph/0510852 Gehrels,N.,Chincarini,G.,Giommi,P.,etal.2004,ApJ,611, 1005 2 http://heasarc.nasa.gov/Tools/w3pimms.html 3 Tocheckforconsistency,wealsocomputedtheexpectedhardness Heise, J., in’tZand,J., Kippen,R. M., & Woods, P. M. 2001, ratioforβ = 1.1and100sourcecounts.Weobtained H/S = 0.98 Gamma-RayBurstsintheAfterglowEra,16 0.19,consistentwiththevaluesofH/S foundbyRomanoetal.(2006±) Krimm, H., Barbier, L., Barthelmy, S., et al. 2005, GRB aftertheflare. CoordinatesNetwork,3183 8 A.CorsiandL.Piro:XRF050406:anICcomponent? 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XRF 050406 late-time flattening: an inverse Compton component?

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