Proceedingsofthe363.WE-HeraeusSeminaron:“NeutronStars and Pulsars”(Postersand contributedtalks) Physikzentrum BadHonnef, Germany,May.14−19,2006, eds.W.Becker,H.H.Huang, MPEReport291,pp.116-119 A multicomponent model for the optical to γ-ray emission from the Crab Pulsar R. Campana1, E. Massaro1, G. Cusumano2, and T. Mineo2 1 Department of Physics, Universityof Rome“La Sapienza”, Rome, Italy 2 INAF– IASF-Pa,Palermo, Italy 7 0 0 2 n Abstract. We present a multicomponent model to ex- theemissionofthesecondpeak(P2)becomeshigherthan a plain the features of the pulsed emission and spectrum the first one (P1), and where it is present a significant J of the Crab Pulsar, on the basis of X and γ-ray ob- emission from the region between the two peaks (bridge 9 servations performed with BeppoSAX, INTEGRAL and orinterpeak,IP).Thisbehaviourcontinuesuptoabout10 CGRO. This model explains the evolution of the pulse MeV, where the pulse almost sharply returns to a shape 1 shapeandofthe phase-resolvedspectra,rangingfromthe similar to the optical light curve. A satisfactory explana- v 3 optical/UV to the GeV energy band, on the assumption tion for these changes has not been found so far. 5 that the observed emission is due to several components. Onthe basisofhighqualityBeppoSAXdata,covering 2 The first component, CO, is assumed to have the pulsed a wide energy range (from 0.1 to 300 keV), we already 1 double-peaked profile observed at the optical frequencies, proposed a two component model (Massaro et al., 2000) 0 7 while the second component, CX, is dominant in the in- toexplainthebehaviourofthelightcurve.Hereweextend 0 terpeak and second peak phase regions. The spectra of this model, reanalysing the whole set of BeppoSAX Crab / these components are modelled with log-parabolic laws. observations with new ISGRI-INTEGRAL data at higher h p Moreover,toexplainthepropertiesofthepulsedemission energies (Mineo et al., 2006). We found that the energy - in the MeV-GeV band, we introduce two more compo- spectraofthesecomponentsarenotdescribedbyasimple o nents, COγ and CXγ, with phase distributions similar to power law, but show a spectral steepening towards high r t those of CO and CX and log-parabolic spectra with the energies. We model these components with log-parabolic s a same curvature but different peak energies. This multi- spectraldistributions.Moreover,toexplainthebehaviour : componentmodelisabletoreproduceboththebroadband in the MeV/GeV band as observed by COMPTEL and v i phase-resolved spectral behaviour and the changes of the EGRETonboardCompton-CGRO,twomorecomponents X pulse shape with energy. We also propose some possible are introduced, both with a similar shape and spectrum r physical interpretations in which CO and CX are emitted of the X-ray counterparts. A complete description of the a by secondary pairs via a synchrotron mechanism while data analysis and of the model can be found in Massaro COγ and CXγ can originate either from Compton scat- et al. (2006). tered or primary curvature photons. 2. The two-component model: optical to hard X-rays 1. Introduction The study of the phase distributions of pulsars’ signals As presented in Massaro et al. (2000), Crab X-ray light in the various bands of the electromagnetic spectrum is curve is well reproduced by two phase-components. The important to obtain information on the geometry and lo- first component, called CO, is assumed to have the same cation of the emission regions in the magnetosphere. At pulsed profile observed at optical frequencies, while the γ-ray energies, in particular, the three brightest sources second component, CX, is described by an analytical (Vela, Crab and Geminga) show remarkably similar pat- model whoseshape is determinedby comparingCO+CX terns with two main peaks at a phase separation ranging with the observed pulse profiles, and that dominates at from 0.40 to 0.48. the interpeak (IP) and second peak (P2) phase regions The CrabPulsar(PSRB0531+21)is characterizedby (Fig. 1). a rather stable phase distribution throughout the whole Usingthehigh-statisticsobservationsofBeppoSAXwe electromagnetic spectrum with a double peak structure. performed a phase-resolved spectral analysis and found It is wellknownthat the pulse shape of the Crabchanges that the photon indices of P1, P2 and IP are changing with energy in the X and soft gamma-ray ranges where with energy, and linearly increasing with Log E (Fig. 2). R.Campana et al.: A multicomponent model for theoptical to γ-ray emission from theCrab Pulsar 117 100 -1s] 2 m c V e k F [ 2 E 10-1 Fig.1. The two components CO and CX of the model at 100 101 102 103 104 105 106 107 theenergiesof8.85keV(left)and75.2keV(right).Inthe Energy [keV] upper panels: the model comparedwith BeppoSAX data. Fig.3. Broadband spectra of the total averaged pulse In the lower panels: C and C (adapted from Massaro O X with the four components of the model. Upward point- et al. 2000). ing triangles: LECS; brown circles: MECS; diamonds: HPGSPC; downward pointing triangles: PDS; leftward 2.6 pointing triangles: FIGARO II; squares: COMPTEL; P1 (First peak) crosses: EGRET. Dashed line: C ; dash-dotted line: C ; O X Ip (Interpeak) 2.4 dot-dot-dashed line: C ; dash-dash-dotted line: C . P2 (Second peak) Oγ Xγ Offpulse (Nebula) 2.2 x e 2 d n 3. Extension of the model to the MeV/GeV I n band: the need for two more components o1.8 ot h P CGRO COMPTEL and EGRET observations (Kuiper et 1.6 al.,2001;Thompson,2004)providedabove∼10MeVlight curves of a good statistical quality which show that the 1.4 pulse shapeissimilartothatofC ,althoughsomeminor O 1.2 differencesarepresent.Atenergieshigherthan∼500MeV the emission from IP and P2 increases, and this seems to 0.1 1 10 100 Energy [keV] reproduce the behaviour of the X-ray emission. In order to explain such a finding, we assume that there are two Fig.2. Photon indices of P1, IP and P2 as measured by more, high-energy spectral components, C and C , Oγ Xγ the four NFI of BeppoSAX and by INTEGRAL-ISGRI. both with a log-parabolic spectral distribution and with the same pulse shape of the lower-energycomponents C O andC .TobeconsistentwiththeupperlimitstotheTeV X WefoundthatthespectraofCO andCX arewellfitted pulsed emission (e.g. Lessard et al., 2000) we added also by a log-parabolic spectral law, anexponentialcutofftobothC andC ,attheenergy Oγ Xγ E = 15 GeV. This model therefore has 6 adjustable pa- c F(E)=KE−(a+bLogE) (1) rameters,i.e.thepeakenergies,curvaturesandnormaliza- tionsoftheC andC components.Assumingthatthe Oγ Xγ where K is the flux at 1 keV and E is the energy in curvatures are equal to the C and C ones (b = 0.16), O X keV.Theparameterbdescribesthe“curvature”ofthelog- wearethenabletoreproducethebroadbandenergyspec- parabola.Theenergy-dependentspectralindexcanbeob- trum of the total (averaged) pulse and of the P1, IP and tained from the previous equation: α(E)=a+2b Log E. P2 phase regions (see Figs. 3, 4 and 5) and the ratios of According to this spectral law, the spectral energy dis- P2/P1 and IP/P1 fluxes (in the same phase intervals of tribution (SED) has a maximum at the energy E = Kuiper et al., 2001;Figs.6 and7). We stress thatthere is p 10(2−a)/2b. The curvature parameter b is equal to 0.16 for no constraintonE :infig.6we plotalsothe P2/P1ratio c bothC andC ,whilethe peakenergiesarerespectively for various values of C cutoff energy ranging from 9 to O X Oγ 12 keV and 178 keV. 15 GeV. 118 R.Campana et al.: A multicomponent model for theoptical to γ-ray emission from the Crab Pulsar 2.5 2 -1s] 2 cm atio1.5 V 10-1 1 r F [ke P2/P 2 E 1 0.5 100 102 104 106 100 101 102 103 104 105 106 107 108 Energy [keV] Energy [keV] Fig.4. Broadband spectra of P1 with the four compo- Fig.6. P2/P1 ratio as derived from the model. Data nents of the model. Upward pointing triangles: LECS; pointscomefromvariousexperiments(Kuiperetal2001). brown circles: MECS; diamonds: HPGSPC; downward Thevariousextrapolationsabove1GeVcorrespondtodif- pointing triangles: PDS; leftward pointing triangles: IS- ferent values of the cut-off energy of the C spectrum; Oγ GRI;squares:COMPTEL;crosses:EGRET.Dashedline: from top to bottom: 9, 11, 13 and 15 GeV. C ;dash-dottedline:C ;dot-dot-dashedline:C ;dash- O X Oγ dash-dotted line: C . Xγ 0.8 100 0.6 o ati 2 -1ms] P/P1 r0.4 c I v 10-1 ke 0.2 F [ 2 E 0 100 101 102 103 104 105 106 107 10-2 Energy [keV] 100 101 102 103 104 105 106 Fig.7.IP/P1ratioasderivedfromthemodel.Datapoints Energy [keV] come from various experiments (Kuiper et al 2001). Fig.5. Broadband spectra of P2 with the four compo- nents of the model. Upward pointing triangles: LECS; brown circles: MECS; diamonds: HPGSPC; downward high-energy pulsar emission models, either in the polar pointing triangles: PDS; leftward pointing triangles: IS- cap or outer gap models (e.g. Cheng et al., 2000; Zhang GRI;squares:COMPTEL;crosses:EGRET.Dashedline: & Cheng, 2002). C ;dash-dottedline:C ;dot-dot-dashedline:C ;dash- O X Oγ Assuming that the lower-energy components C and dash-dotted line: C . O Xγ C are produced by synchrotron emission of secondary X electron-positron pairs created in the pulsar magneto- sphere,thehigher-energycomponentsC andC could 4. Physical interpretation Oγ Xγ be due to: An open question is the physical origin of these compo- nents, that phenomenologically explain the observations 1. Emissionofcurvatureradiationfromprimaryparticles with a very good approximation,in the framework of the accelerated in the magnetospheric gaps. R.Campana et al.: A multicomponent model for theoptical to γ-ray emission from theCrab Pulsar 119 2. Emission from inverse Compton scattering of the syn- Lessard R. W., Bond I. H., Bradbury S. M., et al., ApJ, 531, chrotron photons by the secondary pairs themselves 942-948, (2000). (Synchrotron-Self-Compton mechanism). Massaro E., Cusumano G., Litterio M., and Mineo T., A&A, 375, 397-404, (2000). The different shape of the “O” and the “X” components MassaroE.,CampanaR.,CusumanoG.,andMineoT.,A&A, is presumably due to the different location in the magne- 459, 859-870, (2006). [astro-ph/0607410] tosphere of the emission regions. Mineo T., Ferrigno C., Foschini L. et al., A&A, 450, 617-623, (2006). Thompson D. J., in Cosmic Gamma Ray Sources, Kluwer 5. Conclusions ASSL series, 304, edited by K. Cheng and G. Romero, (2004). [astro-ph/0312272] Several models have appeared in the literature based on Zhang L. and Cheng K. S., ApJ,569, 872-877, (2002). either polar cap or outer gap geometries. Usually, these models are focused on reproducing either the total spec- trumorthe phaseprofile,andgenerallythey arenotfully satisfactory in explaining the complex observational pic- ture. Moreover, the possibility that the observed features ofthepulsedsignalcanarisefromthesuperpositionoftwo or more distinct components is not taken into account. We followedanother approachand searchedfor a pos- sible interpretation of the Crab signal based on the su- perposition of two or more components that provides a consistent description of the spectral and phase distri- butions. Clearly, it is only a phenomenological model, but it could furnish some constraints to more detailed, physically-based emission models. In particular it is im- portanttoverifywhetheratenergieshigherthan∼1GeV the pulse shape tends to be dominated by C . The Xγ GLAST/LAT experiment (Gehrels et al., 1999), with its large collecting area, will give us very useful data in this range that will permit to better estimate the model pa- rameters. Another interesting perspective is whether this model can be adapted to the other γ-ray pulsars. For Vela and Geminga the main problem is that their pulse profiles changeverymuchindifferentspectralbandsandno clear trend, like the P2/P1 ratio in Crab, has been found to now.Inthe γ-rayband, however,Kanbach(1999)showed thatthepeakratiosofallthesethreepulsarshavearather similarbehaviour.Thiscanbe anindicationthatgeomet- rical effects may be more relevant at energies lower than γ-rays and that components like C or C , if existing O X in Vela and Geminga, are not detected because they are more beamed than the high energy photons. Acknowledgements. This work was financially supported by Universit`a di Roma La Sapienza. R.C. also acknowledges the support by theWE-Heraeus foundation duringthe seminar. References ChengK.S.,RudermanM.,andZhangL.,ApJ,537,964-976, (2000). Gehrels N., Michelson P., et al., Aph,11, 277-282, (1999). Kanbach G., Proc. 3rd INTEGRAL Workshop, Astrophys. Lett. Comm., 38, 17, (1999). KuiperL.,HermsenW.,CusumanoG.,etal.,A&A,378,918- 935, (2001).