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Interpreting the X-ray Flash XRF 060218 and its associated supernova A. De Ru´jula Theory Unit, CERN, 1211 Geneva 23, Switzerland; Physics Department, Boston University, USA Forty years after their discovery, and in spite This is where located GRBs must be concentrated. of a very large body of observations, the opera- The probability to detect events does not vanish tion of the ‘engine’ responsible for long-duration abruptly at α>θ , since a point’s radiation is forward j Gamma-Ray Bursts (GRBs) and X-ray flashes collimated, but not infinitely so. The degree of colli- 8 0 –as well as the mechanisms generating their mation and the energy boost of the radiation from a 0 radiation– are still the subject of debate and given point are dictated by the Doppler factor δ(θ )= p 2 study. In this respect a recent event1, XRF 1/[γ(1 βcosθ )], with θ the angle betweenthe point’s p p n 060218, associated2 with SN 2006aj, is particu- directio−n of motion and the observer’s direction. For a larly significant. It has been argued that, for the γ 1 and θ 1, to an excellent approximation, p J first time, the break-out of the shock involved δ(θ≫) = 2γ/[1 +≪(γθ )2]. To be fully precise, I ought p p 2 in the supernova explosion has been observed, to average over the distribution of emitting points8, but thanks to the detection of a thermal component some trivial limiting cases will suffice here. ] 3 h in the event’s radiation ; that this XRF was not For observer’s directions, θob, beyond the cone’s rim p a GRB seen ‘off-axis’, but a member of a new (θob > θj) the point-averaged δ(θp) rapidly tends to 4 h i - class of energetically feeble GRBs ; and that its δ(θ ), the limit for a point-like source. The properties o ob ‘continued engine activity’ may have been driven of GRBs seen at such angles, for which δ is a rapidly di- r t by a remnant highly-magnetized neutron star, a minishing function of θ , are easy to predict. Relative s 5 ob a magnetar . I argue, on grounds based on obser- to the average GRB, their ‘isotropic equivalent’ energy, [ vations and on limpid verified hypothesis, that E δ3, as well as the ‘peak energy’ of the photons iso ∝ there is a common, simpler alternative to these in their pulses, E δ/(1+z), must be small, declining 1 p∝ views, with no thermal component, no new fee- in a correlated way (to be precise, I introduced the ef- v 7 ble GRBs, and no steady engine activity. fect of the cosmological redshift, z). The time-widths of 9 XRF peaks, ∆ (1+z)/δ must be relatively large. The Many astrophysical systems, such as quasars and ∝ 3 peak-to-peakintervals,stillrelativeto GRBs, arenotaf- micro-quasars,emitrelativisticjets. The‘engines’gener- 0 fected;theenginedeterminesthem,anditisnotmoving. ating ‘long’ GRBs are the supernovae (SNe) ‘associated’ . 1 Since what I have described are the observed properties with them. The radiation we perceive as a GRB cannot 0 of XRFs, it is natural to propose that they are GRBs be isotropic,if only because the availableenergyin a SN 8 seen off-axis9,10, even if the argument is less compelling event is insufficient. Thus, GRBs must be beamed, and 0 intheθ 1/γlimit. Thetraditionaldistinctionbetween : it is natural to assume that the source of their radiation j≫ v is a jet, emitted by their engine SN. A highly relativistic XRFs and GRBs is that the former have Ep<50 keV. i IshallassumethatXRF060218,whichhasalltheXRF X beam suggests itself for, as a simple consequence of spe- propertiesIhavedescribed,isalsoanordinaryGRBseen cial relativity, its radiation is highly forward-collimated r a and boosted in energy. The beam consists of a succes- off-axis. As weproceed,this viewwillgainsupport. The opposite view4 will be discussed anon. sionof ejecta, for a GRB’s radiationtypically consists of To proceed, we need some observational input. The an aperiodic succession of ‘pulses’. Before the interac- spectrum of the ‘prompt’ radiation of GRBs and XRFs tions with the ambient matter significantly affect it, the is well described by the ‘Band’ function11. For the rela- ejected matter responsible for a pulse must trace a cone tivelylowX-rayenergiesofinteresthere,thefirstaddend initsvoyage,asitfreelyexpands(initsrestsystem)and of this function, a ‘cutoff power-law’(CPL), suffices: moves inertially in space. Up to this point, practically all interpretations of GRBs are concordant6,7. EdN /dE =aEǫExp( E/E ), (1) γ CPL p Letθ bethe(half)openingangleoftheconewecited, | − j and let α be the angle, relative to the cone’s axis, of whereE andN arephotonenergiesandnumbers,aisa γ a given radiation-emitting point, which moves with the normalizationand ǫ 0 is a good approximationcase by common bulk Lorentz factor, γ, of the emitting region case,averygoodap∼proximationonaverage11. Thepeak (γ=1/p1 β2;β v/c). Theprobabilityofanobserver energy of individual photons decreases during a pulse, to be locat−ed in th≡e direction α, with a precision dα, is rapidlytending to E (t) b/t2, with b acase-by-casepa- p ≈ dP αdα. On axis, dP =0. Since α θ , dP (whose rameter. This correlation between times and energies is j ∝ ≤ integralisquadratic)ismaximalatthecone’srim,α=θ . better known and studied in its complementary forms: j 2 XRF 060218 1!!!!!!!!!!0""""""""""!!!!!!!!!!-8&&&&&&&&&& XRF 060218 V -9 1!!!!!!!!!!0""""""""""-1!!!!!!!!!!0%%%%%%%%%% Synchrotron B 1!!!!!!!!!!0""""""""""!!!!!!!!!!-1!!!!!!!!!!""""""""""1 ICS X-ray AG U 11!!!!!!!!!!!!!!!!!!!!00""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!-1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$2 X-ray flare o (s) 104 UUVVWM11 !!!!!!!!!!!!!!!!!!!!33333333332222222222++++++++++1111111111!!!!!!!!!!$$$$$$$$$$ 11!!!!!!!!!!00""""""""""!!!!!!!!!!--11!!!!!!!!!!##########43 tp - t XUVW2 0000000000++++++++++//////////..........----------,,,,,,,,,,++++++++++**********)))))))))) !!!!!!!!!!""""""""""!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$ SN2006aj (((((((((('''''''''' 103 !!!!!!!!!!""""""""""!!!!!!!!!!!!!!!!!!!!########## ICS Optical humps 1 10 102 103 !!!!!!!!!!""""""""""!!!!!!!!!!!!!!!!!!!!4444444444 EEnneerrggyy ((eeVV)) !!!!!!!!!!"""""""""""""""""""" !!!!!!!!!!"""""""""""""""""""""""""""""" !!!!!!!!!!""""""""""4444444444 !!!!!!!!!!""""""""""5555555555 !!!!!!!!!!""""""""""6666666666 777777777788888888881111111111----------++++++++++,,,,,,,,,,22222222223333333333 !1.4 UVM1 XFIRGF.10:60(2a1)8U. p(pbe)rLpoawneerl:ptahnee(l:0.t3h–e10UVkeOVT)Xflu-rxay(frfloumx3R,14e,f1.53o)f, −1])m !1.6 UVW1 !" !" 1fo0r5dsi)ff:eVre,nBt,UUV,OUTVfiWlte1r,sU(VfroMm1,baonttdomUVtoWt2o.pbetween104− −−12ns !1.8 U !" UVW2 m tdheecrienacsrienagsiennger‘lgayg-itnimteervs’alosf12t,heanpdeatkhseorfelGatRioBnpbueltsweseeinn cgre(W !2.0 B !" cpThuaolksoiensigwngiidnǫttho=saa0cn,cdowueenntmeratghyyeeinxtitpmeercevtadltseh1p3ee,nsrpdoeeucngtchreulymo∆foE∝fpat,−pa1a/n2rd-. B/FEP[g01 !!22..42 !V" !" o ticular GRB pulse to be roughly described by: L !2.6 0.3 0.4 0.5 0.6 0.7 0.8 0.9 EdNγ/(dEdt)=aExp( Et2/b). (2) Log10[E(eff)(eV)] − HavingpositedthatXRF060218isbutaGRBseenoff FIG. 2: (a) Comparisons of Eq. (2), with data corrected for axis, it behooves me to test whether it satisfies Eq. (2). extinction16. Upperpanel: The‘Et2law’,withtp t0thepeak − The X-ray3,14,15 and optical3 observations of this single- position at various energies and t0 the common peak start- peak event are shown in Fig. 1. The top part is the X- time at all E. The line is the expected tp−t0∝1/√E. (b) Lower panel: Thespectraldependence. Dataandpredictions ray flux in the cumulative (0.3–10) keV interval, fit in a are slightly shifted, to avoid superposition. At UVOT ener- particular model16, in which Eq. (2) is the approximate gies,theexponentialinEq.(2)is 1anddPEF/dλ E2,the expectation9. In Fig. 2a, I test the ‘Et2 law’ implied dashed line, whose normalization≈is fixed bythe X-r∝aydata. by Eq. (2), by plotting (versus energy) the peak times of the optical and UV ‘humps’ of Fig. 1b, and of their presume, concluded that a thermal component is unnec- sisterX-raypeak,measuredinthreeenergysub-intervals. essary. These authorscite Amatiet al.4 for the assertion In Fig. 2b, I show the test of the spectral behaviour of thatXRF060218isnotaGRBseenoffaxis,butarepre- Eq. (2). For lack of space, the three X-ray intervals, sentative of a new class of sub-energeticGRBs. Presum- whose relative spectrum satisfies Eq. (2), are not shown. ably that is why what is known about Ep(t) in ‘normal’ Using them as normalization, one can predict the ‘peak GRBs was not judged to be relevant. energy fluxes’ (per unit wave-lengh) in the optical and Amati et al.4 base their cited conclusion on the fol- UV channels, and compare them, as in Fig. 2b, with the lowing fact. If one makes a scatter log-log plot of the observations. The results are fairly satisfactory. Ep values versus total fluence17 of a collection of GRBs, Inthestandardinterpretation3 ofthisXRF,athermal onefindsthattheyfall,withnotmuchscatter,closeto a spectrum EdN /dE R2(t)E3Exp[ E/T(t)] is added straight line. A similar result is obtained18 for a log-log γ ∝ − to the CPL spectrum of Eq. (1), with a varying radius [(1+z)Ep,Eiso] plot of GRBs of known z, the ‘Amati and temperature, R(t) and T(t), fit, bin by bin, to the correlation’. These results are ‘phenomenological’, the observations. The CPL spectrum masks the tell-tale E3 lines’ slopes and normalizations are fit to the results. thermal dependence. The time dependence of the ex- To understand the origin of the correlations between tracted T(t) is roughly 1 t/√t2+∆2, which is the ‘prompt’ observables, such as E and E , one must p iso ∝ − expecteddependenceofE (t),toabetterapproximation specify the radiation mechanism. Let us posit that it p than E (t) t−2, in the model I have quoted9. is inverse Compton scattering (ICS) of ‘ambient’ pho- p Had Cam∝pana et al.3 used a time-dependent E (t), tonsby the electronsina GRB’s jet19,asverifiedinRef. p they would have obtained the results in Fig. 2, and, I 9. In that case, the δ-, and γ-dependences of E and p 3 since it has very low E and E , it belongs to a new p iso class. My critique of this logic is that, as I argued at 4 the beginning, GRBs are not seen on axis, but on-edge. Since the opposite premise is tacit in Amati et al.4, one 3.5 cannotbesurethisinterpretationoftheirlogiciscorrect. In the X-ray flux shownin Fig. 1a, there is a ‘plateau’ 3 ] V tail labeled ‘Synchrotron Afterglow’, fit, as the rest of ke the curve, to a given model16. The whole curve has a k/ 2.5 a ‘canonical’shape,sketchilyseenlongagoinGRB980425, e p and nine others GRBs21. The X-ray and radio after- E 2 GRB ) glows (AGs) of GRB 980425 were attributed to a non- z 1+ 1.5 XRF relativistic shock22,23. Alternatively, since they coincide ( [ with the expectation for an off-axis relativistic jet of g lo 1 an otherwise normal GRB, they were attributed to the jet21,24. A large fraction of the X-ray AGs recently ob- 0.5 servedbySwiftandothersatellitesare‘canonical’. Their plateau phases are, as in the case5 of XRF 060218, at- 0 tributedtoacontinuedengineactivity25,perhapsdriven 49 50 51 52 53 54 55 byamagnetarremnant5,26. Inthealternativeview,once log[ Eiso/erg ] again, the plateau is due to the moving jet27. The difference between these views may be important, not only FIG.3: The[(1+z)Ep,Eiso]correlation8. XRF060218isthe becauseofthedifferentunderlyingGRBtheories,butbe- star. The cross marks theaverage expectation for GRBs9. cause of its implications on the associated SNe. Suffice E can be specified. For a point-like source, they are9 it to imagine21,24 that the X-ray and radio emissions at- iso (1+z)E γδ and E δ3. Since δ decreases, at fixed tributed to a SN were actually emitted by a relativistic p iso γ, by order∝s of magnitud∝e as θ increases, and γ cannot jet having long departed from the SN location. ob be much smaller than ‘typical’ (for otherwise we would The algebra required to discuss GRB afterglows is a not be observing a GRB or an XRF), we conclude that bit longer than the one I have been using. For this rea- the case-by-case variability is dominated by δ. Thus, we son,I shallnextstatesomeresultswithcitations,butno expect(1+z)E (E )1/3. Sinceweusedthepoint-like proof. The‘alternativeview’Irepeatedlyquoted9,21does p iso ∝ limit, valid for large θ , this result is for XRFs. not require, so far, any conceptual changes or additions, ob In the opposite extreme at which a GRB is seen at an as it confronts the data. The steady ‘continued engine angleθ θ , the integrationoverthe source’sradiating activity’, for instance, is instead the inevitable inertia ob j ≪ points masks the dependence on θ , so that the ‘effec- of the relativistic jet, its ending ‘break’ occurring when ob tive’ averaged Doppler factor8 becomes δ γ. Thus, for the interstellarmedium begins tosignificantlydecelerate hard GRBs, (1+z)E γ2 and E γ3,∝implying that the jetted material21. The rapidly-varying spectra of X- p iso ∝ ∝ (1+z)E (E )2/3. Since the observer’s angle varies raylightcurves,aswell asthe plethoraof differentSwift p iso continuous∝ly, we expect8 the XRFs and GRBs to lie, in light-curve shapes, with and without ‘breaks’, were not the [(1+z)E ,E ] log-log plane, close to a line whose unexpected28,29. In the realm of ‘fireball models’, very p iso slope varies smoothly from 1/3 to 2/3. This is tested manynovelphenomena–otherthantheshockbreak-out, in Fig. 3. The crossing lines are t∼he predicted average the steady engine activity, and the subenergetic GRBs values for GRBs, for the advocated origin of the target that I have discussed here– have been invoked to under- light that is Compton up-scattered9. XRF 060218is the standGRBsandXRFs. Toeachofthesephenomena,the star in Fig. 3. Incidentally, the above reasoning also ex- ‘other view’ I have often cited –the Cannonball Model– plains the observed correlations with (or between) other offers a simpler alternative. And it is always the same. prompt observables: peak luminosity, lag-time, rise-time Abinitio,the‘firecone’andcannonballmodelsdiffered and variability8. GRB 980425 is an out-lier from cor- inalmostallrespects: supernovaeasengines(debatedvs relations involving E , its ‘second E ’, due to ICS by assumed), the substance of the ejecta (e+e− pairs vs or- p p electrons scattered by the jet20, is what was observed. dinarymatter),theroleofshocks(decisivevsabsent),the We have been led to conclude that XRF 060218 is a mechanismofγ-raygeneration(synchrotronradiationvs normal GRB seen off-axis, among other reasons,because ICS), to name a few6,7. One difference still remaining it satisfies the correlation we discussed. Amati et al.4 underlies the conflicting views I have discussed. It is the conclude that XRF 060218 is not a normal GRB and is jet’s initial opening angle, θ : a few degrees (as in ra- j not seen off-axis, because it lies in a similar correlation. dio images of quasars), vs 1 milli-radian. Moreover, a This logical inconsistency, I believe, has a purely logical θ (t) thatincreaseswithtim∼e, vs one thateventuallyde- j origin. Their argument4 is the following: GRBs are seen creases. Thelastandapparently9,21 surprisingfeature–a close-to-axis, GRBs satisfy the Amati correlation, XRF jet that does not expand– is observedin sharper (X-ray) 060218does it as well, so this object is seenon axis and, images of quasars, e.g. Pictor A (Ref. 30). 4 The fraction of SNe that are associated to GRBs and atthe speedoflight, orofrelativistic sound(c/√3), and XRFsis θ−2,differingby 300foraonedegreevsaone is moving with the typical initial γ 103 required by milli-rad∝ianjangle. Forθ ∼1mradthefractionofSNeas- the data9,21. For the same reason, the∼quest for simplic- j sociatedwithGRBsis,wi∼thinratherlarge‘cosmological’ ity,theoriginalfireballmodelshadsphericalsymmetry6. uncertainties, close to all Type Ic SNe9,21, very far from The correct answer must lie in between these two ex- the standard view14. This is one more reason why the tremes, surely closer to the former than to the latter. opening angle is so decisive. The value of θ adopted in j the cannonballmodel correspondsto θ 1/γ,i.e. to the Aknowledgements. I am indebted to my colleagues j ∼ conesweptbyaobjectwhich,initsrestsystem,expands Shlomo Dado and Arnon Dar for a long collaboration. 1 Cusumano,G.etal.GRB0606218: Swift:BATdetectionof versus Intrinsic: The Correlation between Intensity and a possible burst. GCN Circ. 4775 (2006). the Peak of the νFν Spectrum of Gamma Ray Bursts. 2 Masetti, N. et al. GRB0606218: VLT spectroscopy. GCN Astrophys. J., 534, L227 (2000). Circ. 4803 (2006). 18 Amati, L. et al. 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