A consistent interpretation of recent CR nuclei and electron spectra GiuseppeDiBernardo DepartmentofPhysics,UniversityofGothenburg,SE-41296,Gothenburg,Sweden 1 CarmeloEvoli 1 0 SISSA,viaBonomea265,34136Trieste,Italy 2 DanieleGaggero,DarioGrasso1 n a INFN,SezionediPisa,LargoBrunoPontecorvo3,56127Pisa,Italy J 0 LucaMaccione 1 DeutschesElektronen-Synchrotron,Notkestraße85,22607Hamburg,Germany ] E MarioNicolaMazziotta H IstitutoNazionalediFisicaNucleare,SezionediBari,70126Bari,Italy . h p - o r t s Abstract a [ Wetrytointerprettherecentlyupdatedmeasurementofthecosmicrayelectron(CRE)spectrum 1 observedbyFermi-LAT,togetherwithPAMELAdataonpositronfraction,inasingle-component v scenarioadoptingdifferentpropagationsetups;wefindthatthemodelisnotadequatetorepro- 0 ducethetwodatasets,sotheevidenceofanextraprimarycomponentofelectronsandpositrons 3 is strengthened. Instead, a doublecomponentscenariocomputedin a Kraichnan-likediffusion 8 setup(whichissuggestedbyB/Candp¯data)givesasatisfactoryfitofallexisitingmeasurements. 1 . Weconfirmthatnearbypulsarsaregoodsourcecandidatesfortherequirede± extra-component 1 andwe showthatthepredictedCRE anisotropyin ourscenariois compatiblewithFermi-LAT 0 recentlypublishedconstraints. 1 1 : v i 1. Introduction X r LastyeartheFermi-LATCollaborationpublishedthee+ +e− spectrumintheenergyrange a between20GeVand1TeV,measuredduringthefirstsixmonthsoftheFermimission[1]. That result came in the middle of an interesting debate which arose after that ATIC and PAMELA collaborationsreportedsomeanomalousresults:ATICobservedabumpinthee++e−spectrum at around 600 GeV, while PAMELA found the positron fraction e+/(e+ +e−) to increase with energyabove10GeV:thesefeaturesarehardlycompatiblewiththestandardscenarioinwhich [email protected] PreprintsubmittedtoElsevier January11,2011 CR electrons are accelerated in supernova remnants (SNRs) and positrons are predominantly of secondaryorigin, and were interpretedby many authorsas a possible signature of decay or annihilationofDarkMatter(DM)particles,evenifamoreconventionalinterpretationinterms of astrophysicalsources (namely pulsars) was also considered. Fermi-LAT spectrum does not displaythefeatureseenbyATIC,beingcompatiblewithasinglepowerlaw;theabsenceofthat featurewaslaterconfirmedbytheH.E.S.S.Cherenkovtelescopewhosespectrumbelow1TeV isinagreementwithFermi-LAT’s.Soonafterthatmeasurementwaspublished,someofus,with othermembersofFermicollaboration,showedthataninterpretationofthee+ +e− spectrumis possiblewithinaconventionalmodelinwhichSNRsaretheonlyprimarysourcesofCREs[2]. Below20GeV,however,wefoundthepredictionsofthatmodeltobeintensionwithpre-Fermi data; furthermore,thepositronfractionmeasuredbyPAMELAwasnotreproducedwithinthat framework. We thereforeproposed, in the same paper, a scenario which invokedthe presence of an extra component of e− + e+: it was argued that such extra-componentcan naturally be producedby near middle-agedpulsars. An alternative interpretation based on the annihilation of DM particles was also discussed but considered disfavoured. Other possible origins of the required e+ +e− extra-componentwere proposed by other Authors: e.g. enhanced secondary productioninstandardSNRs[3]oraninhomogeneousdistributionofsourcesintheGalaxy[4]. Recently,theFermi-LATCollaborationreleasedanewmeasurementoftheCREspectrumbased on one year data. The observed spectrum extends down to 7 GeV[5] and is confirmed to be compatiblewith asinglepower-lawwith spectralindex3.08±0.05. Hintsofa deviationfrom apurepower-lawbehavior,alreadyfoundinthesixmonthdata,arestillpresentintheupdated spectrum,whoselowenergypartiscompatiblewithpre-Fermimeasurementandnotreproduced bythemodelsweproposedinRef. 2:thisconsiderationcallsforsomerevisionsofourscenario. Moreover,afterthereleaseofPAMELAantiprotondatasomeofusused(seeRef.6)therecently developed DRAGON 2 package[7] to perform a combined maximum likelihood analysis on B/C and antiproton data and found that the “conventionalmodel”, based on the assumption of the existence a Kolmogorov-like turbulence in the ISM, is not the most adequate to describe the measurements: wethereforeproposedanewmodelbasedonaKraichnan-liketurbulence. This resultgivesanotherreasontorevisethemodelsdescribedinRef. 2. 2. Thepropagationsetups The CR propagation in the Galaxy is described by a well known diffusion-loss equation whichcanbesolvedanalitically,undersimplifyingassumptions,ornumerically,makinguseof GALPROP or DRAGON packages. This equation includes several free parameters which need to be tunedby comparisonwith data: D andδ, i.e. thenormalizationandenergydependenceof 0 the diffusioncoefficient, the Alfve´nvelocityv which parametrizesthe levelof reacceleration, A the height of the Galactic diffusion region z , and the injection index of the CR species γ . h p Moreover,whenconsideringdata belowa fewGeV/nalso the modulationdueto solaractivity playsasignificantroleandmustbetakenintoaccount.Thefirststepofourwork,beforestarting to investigatethe e+ +e− spectrum, consists in fixing the propagationparameters, i.e. D and 0 δ, and the level of reacceleration. The datasets which constrain these data are secondary-to- primaryratios, in particularB/Cand p¯/p. In thefollowingwe willconsiderthreepropagation models, which are defined as follows. 1) The PD modelis a plain diffusion one, in which we 2Codeavailableathttp://www.desy.de/∼maccione/DRAGON/ 2 (a) (b) Figure1: Panela)PredictedB/Ccomparedwithdata. Redlines: Kolmogorovmodel(KOL);blue: Kraichnanmodel (KRA);green:plaindiffusion(PD).Solidlines:Φ=450MV;triple-dottedlines:Φ=300MV.Panelb)Theoretical p¯ spectraarecomparedwithdata;solidlines:Φ=550MV;dashedlines:LIS. triedtoreproduceCRdatawithnoreacceleration,hencesettingv = 0. Inthismodelδ = 0.6. A 2) The KOL model is the so called “conventional model”, built assuming a Kolmogorov-like turbulence,whichfixesδ=1/3;inthismodelthereaccelerationisquitehigh:v =30km/s. 3) A TheKRAmodelassumesaKraichnanspectrumforthegalacticturbulentmagneticfield,hence setting δ = 1/2. Reacceleration is lower: v = 15km/s. At low energya modifiedbehaviour A ofthediffusioncoefficientisadoptedto reproducethepeakat1GeV inB/Cdata. Thismodel waspresentedinRef. 6andobtainedastheresultofacombinedmaximumlikelihoodanalysis basedonB/Cand p¯/pmeasurements. Thecomparisonbetweendataandmodelpredictionsfor B/Cand p¯/pcanbeseeninFig. 1(a)andFig. 1(b). WerefertoRef. 6forthecompletelistof parameterswechoseforthe3models. 3. ModelingtheCREspectrumwithasingleGalacticcomponent (a) (b) Figure2:Panela): thee−+e+spectrumfortheKOL(red),KRA(blue)andPD(green)diffusionsetups. Theelectron sourcespectralindexesare1.60/2.50below/above4GeVfortheKOLmodeland2.00/2.43and2.0/2.40below/above2 GeVfortheKRAandPDmodelsrespectively. Panelb):e+/(e−+e+).Φ=550MV. 3 Figure3: Thee− +e+ total spectrumandpositronfraction (inthebox)forourtwo-component model. Dottedline: propagatedstandardcomponentwithinjectionslopeγe− =2.00/2.65above/below4GeVandEceu−t=3TeV;dot-dashed line:e±componentwithγe± =1.5andEceu±t =1.4TeV.Bluesolidline:modulatedtotalspectrum(Φ=550MV).Blue dashed:LIStotal. We start our analysis by trying to interpret CRE spectrum with single-componentmodels. We evaluated these modelwith DRAGON numericalpackage[6] and verified that our results are reproducedby GALPROP[9, 10] underthesame physicalconditions. We considerthe threedif- fusion setups (KOL, KRA and PD) discussed in the previoussection and for each of them we tunethefreeparametersinvolvedinthecalculationagainstFermi-LATdata. Wefindthatarea- sonablefitofFermi-LATspectrumcanbeobtainednormalizingthemodelstodataat≃10GeV and adoptingthe followinginjectionindexes: 2.50 in the KRA model, 2.43forthe KOL, 2.40 forthePD (seeFig. 2(a)). ItisworthnoticingthatKOLmodelrequiresasharpspectralbreak (i.e. aninjectionindexof1.60below4GeV)toavoidananomalousbehaviorwhichwouldoth- erwiseariseinthepropagatedspectrum:thecombinedeffectofreaccelerationandenergylosses createsapronouncedbumpintheunmodulatedspectrumatlowenergy,whichisonlypartially smearedoutbysolarmodulation. ThiseffectissmallerinKRAmodelandabsentinPDsetup, sointhesecasesamuchsofterbreakisrequired: 2.0insteadof1.60istheindexbelow2GeV. However, the main drawbackof a single componentapproach, concerningFermi-LAT data, is that–nomatterwhatpropagationmodelisadopted–itisimpossibletoreproduceallthefeatures revealedintheCREspectrum,inparticulartheflatteningobservedataround20GeV(whichwas alsorecentlyfoundbyPAMELA[11])andthesofteningat∼500GeV.Concerningthepositron fraction,theresultscanbeseeninFig.2(b). Clearly,below10GeVthee+/(e−+e+)measured by PAMELA can be reproducedin the KRA and PD modelswhile the fit is unsatisfactory for the KOL:again, low reaccelerationmodelsseem to providea better descriptionof low energy data. None of the single componentrealizations, however, can reproducethe rising behaviour observedbyPAMELAabove10GeV. 4. Twocomponentsmodels In the followingwe try to reproduceall data in a two-componentscenario. The first com- ponent(standard)consistsofelectronsacceleratedinSNRs andasecondarycontributionofe− 4 ande+originatedbytheinteractionofthehadronicpartofCRswithinterstellargas.Thesecond one(extra-component)ismadeofe−ande+injectedintheISMwithacommonspectrumofthis kind:Qe±(E)= Q0(cid:16)EE0(cid:17)−γe± e−E/Eceu±t,wheretheinjectionindexisharder:γe± <2.Wealsoassume thatbothsourceclasseshavethesamecontinuousspatialdistribution. Thenormalizationofthe twocomponentsisperformedintwosteps.1)Wetunethestandardcomponenttoreproduceboth thee−+e+spectrummeasuredbyFermi-LATandthee+/(e−+e+)measuredbyPAMELAbelow 20GeV,wheretheeffectoftheextracomponentissupposedtobenegligible. Remarkably,this is possible only if we use propagationsetups with low reacceleration, namely either the KRA orthePD,becausethelow-energypartofPAMELApositronratiocan’tbereproducedinKOL setup. Since the KRA[6] also provides the best combined fit of B/C and antiproton data (see Sec. 2), we will stick to this model from now on. The required source spectral slopes for the electronstandardcomponentisγe− =2.00/2.65below/above4GeVforthispropagationmodel. FromFig. 3the readercansee assuch aset-upallowsa remarkablygoodfitofFermi-LATas wellasotherexperimentaldata. Suchindexisquitesteepifcomparedtotheoreticalpredictions regardingFermiaccelerationmechanism,butweremindthereaderthatwemodeledthestandard componentintheapproximationofacylindricallysymmetricsourcedistribution,whichmaybe less realistic for high energyelectronswhere the local distribution is relevant. Accountingfor thespiralarmdistributionofSNRsmayresultinadifferentrequirementfortheinjectionindex. Indeed,beingtheSunintheso-called“localspur”situatedinainterarmregion,theaveragedis- tancefromSNRsislargerthaninthesmoothcase:asaconsequence,aharderinjectionspectrum mayberequiredtocompensateforthelargerenergylossesandreproducetheobservedspectrum. Clearly, in the absence of the extra e±component, high energyCRE and positronfraction data wouldcompletelybemissed (seedottedline inFig. 3). 2)We tunethe extra-componenttore- produceFermi-LATand H.E.S.S. high energyCRE data. We find here thatthis is possible by takingγe± = 1.5and Ecut = 1.0÷1.5TeV (see Fig.3). Thisissimilar to whatdonein Ref. 2 but in that paper a KOL diffusion was used (so low energypositron data were not reproduced in thatcase). Itis interestingthatpreliminarye− spectrummeasuredbyPAMELA [11] is also nicelyreproducedbyourextra-componentmodels: above100GeVthisspectrumissofterthan thee−+e+measuredbyFermi-LATbytheexactamountwhichisrequiredtoleaveroomthee+ extra-component. 5. Theroleofastrophysicalnearbysources Thenatureoftheextra-componentofprimaryelectronsandpositronsthatweinvokedinthe previoussectionisanintriguingmatterofdebate,andthepossiblescenariosincludebothanex- oticexplanation(involvingannihilationordecayofParticleDarkMatter)orapurelyastrophys- icalinterpretation. Hereweconcentrateonthesecondpossibility. Differentlyfromtheprevious section,wetreattheextracomponentasoriginatingfromadiscretecollectionofsources;wethen treatelectronandpositronpropagationfromthosesourcestotheSolarSystembysolvingana- lyticallythediffusion-lossequationsimilarlytowhatdoneinRef. 2. Thelargescale(standard) componentisinsteadmodeledwithDRAGONasdoneintheprevioussection;forconsistency,we treatanalyticalandnumericalpropagationunderthesamephysicalconditions. Thepropagation setupadoptedistheKRAone. Therearebasicallytwoclassesofobjectsweconsider:SNRs(as sourcesofelectronsonly)andpulsars(assourcesofelectron+positronpairs). SNRsarethewell knownnaturalcandidatesasCRaccelerators,andalsotheconventionalcomponentisexpectedto originatefromobjectsofthiskind;consideringindividualSNRsinthenearbyISMisimportant 5 (a) (b) Figure4: Standardcomponent+nearbypulsarsandSNRs. Panela): e++e−spectrum. EnergyreleasebyeachSNR: 2×1047erg. Pulsarefficiency: ≃ 30%. Φ = 500MV. Panelb): theintegratedexpectedanisotropy,asafunctionof minimumenergy,iscomparedtoFermi-LATtheupperlimits[12]. duetothefactthatathighenergy(abovesomehundredGeV)diffusemodelsdon’tgiveaproper descriptionofrealitysincethelosslengthduetosynchrotronandICbecomescomparabletothe averageSNRmutualdistancesothatonlyfewsourceswithinfewhundredparsecsareexpected todominate.Pulsars,instead,areveryinterestingcandidatesasprimarysourcesofbothelectrons andpositrons. Theyareextremeastrophysicalenvironmentsthatreleaseverylargeamountsof energy(∼1052÷1054erg)duringtheirlifetime.Thee−+e+pairsareexpectedtobeproducedin themagnetospherebytheinteractionofcurvaturephotonswiththepulsarmagneticfield;those particlesarethenexpectedtobeacceleratedattheterminationshockofthepulsarwindnebula (PWN).Thepossibilitythatelectronsandpositronsfromnearbypulsarscandominatethehigh energy tail of the CRE spectrum and explain the rising behavior of the positron fraction was alreadyproposedinRef. 13andstudiedinmorerecentpapers(e.g. Refs14and15). Similarly tothe approachtakeninRef. 2, wemodeltheemissionfromSNRs andpulsarsasapoint-like burst; for pulsarswe also introducea time delaywith respecttothe birth ofthe object: sucha delayismotivatedbythefactthatelectronsandpositronsareexpectedtobetrappedinthePWN until it mergeswith the ISM. We assume that for bothSNRs and pulsars particlesare injected with a powerlaw spectrum upto an exponentialcutoff; the injectionindexis howeverset in a differentwayforthetwoclassesofobjects. We consideredallobservedSNRs within2kpcas taken from the Green catalogue [16] and the pulsars within 2 kpc from Earth taken from the ATNF catalogue [17]. We verified that more distant objects give a negligible contribution. In Fig. 4(a)werepresenttheCREspectrumobtainedforareasonablecombinationofparameters, namely: for SNRs: spectral index γe−SNR = 2.2, cutoff energy EcSuNtR = 2 TeV, electron energy releaseperSNESNR =2×1047erg;forpulsars:γe± =1.5,cutoffenergyEcut =1TeV,efficiency ηe± ≃ 30%. We see from Fig. 4(a) that the main contribution comes from Monogem pulsar; thisisduetotheproximityofthissourceandtotheintroductionofthedelaybetweenthepulsar birthandtheactualinjectionofthepairsintheISM;withoutconsideringsuchdelay,Monogem contributionwoulddecreasesignificantlyandothernearbyyoungpulsar,suchasVela,wouldbe the mostimportantsourcesin the highenergyregion; instead, in ourframeworkelectronsand positronsfromVelaareexpectedtobestilltrappedinthesurroundingnebulaandthereforenot yetobservedintheCREspectrum. Itisimportanttocheckiftheseresultsarecompatiblewith 6 recentlypublishedupperlimitsontheanisotropyine−+e+ flux[12]. Ourpredictionisplotted in Fig. 4(b). The importantresult is that our scenario is not excludedby anisotropymeasure- ments;thereadermaynoticethatMonogempulsar(redsolidline)andVelaSNR(blackdashed line) contributemostto the totalanisotropy(the blacksolid line). However,the total expected anisotropyisveryclosetothemeasuredupperlimit, soafuturedetectionatlevel∼ 1%at∼ 1 TeVtowardstheportionoftheskywhereVelaandMonogemarelocatedistobeexpected. 6. Conclusions The spectacular data on CR electrons and positrons, together with measurements on light nuclei and antiprotons, suggest that a double-componentapproach to the leptonic part of CRs computedintheframeworkofaKraichnan-liketurbulenceprovidesagoodself-consistentsce- nariowhichsatisfactorilyreproducesallexistingobservations. Inthispicture,inadditiontothe conventionalcomponentacceleratedinSNRs,acontributionfrompulsars,asemittersofe−+e+, permits to correctly fit both the features revealedby Fermi-LAT in the CRE spectrum and the e−/(e++e−)measuredbyPAMELA.Theexpectedanisotropyinthedirectionofthemostpromi- nent CRE candidate source, Monogem pulsar, is compatible with the present upper limit just releasedbyFermi-LATcollaborationandmaybedetectableinafewyears. 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