New insights on hadron acceleration at supernova remnant shocks

0.07 MB·English

by  Damiano Caprioli

New insights on hadron acceleration at
supernova remnant shocks
DamianoCaprioli
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AbstractWeoutlinethemainfeaturesofnucleiaccelerationatsupernovaremnant

forwardshocks,stressing the crucialrole playedby self-amplifiedmagneticfields
]
E indeterminingtheenergyspectrumobservedinthisclassof sources.Inparticular,
H we show how the standard predictionsof the non-lineartheory of diffusive shock
. accelerationhas to be completedwith an additionalingredient,which we propose
h
to be the enhancedvelocityof the magnetic irregularitiesparticlesscatter against,
p
- toreconcilethetheoryofefficientparticleaccelerationwithrecentobservationsof
o gamma-raybrightsupernovaremnants.
r
t
s
a
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1 Introduction

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v
6 Supernova remnants (SNRs) have been regarded for many decades now as the
1 sourcesofGalacticcosmicrays(CRs), bothbecauseoftheir energeticsandofthe
0 factthatstrongshocksareexpectedtonaturallyaccelerateparticleswithpower-law
0
energydistributions,accordingtotheso-calledFermimechanism.
.
2 Clear-cutevidencesofparticleaccelerationinSNRshavebeenfoundmanyyears
0
agoinradiotoX-raysynchrotronemission,thereforeattestingthepresenceofelec-
3
trons with energiesas high as 10-100TeV. On the otherhand,direct evidencesof
1
: protonaccelerationare muchless clear:the most prominentsignatureofhadronic
v accelerationhasbeenindividuatedinthe g -rayemissionfromthedecayofneutral
i
X pionsproducedinnuclearinteractionbetweenrelativisticnucleiandtheinterstellar
r medium[13].ThefirstSNRsdetectedintheTeVg -rays,however,didnotunravel
a
the question, since in this energy range it is hard to disentangle whether the ob-
servedspectrum(typicallyexhibitingacut-offaround 10TeV)istheresulteither
∼
DamianoCaprioli
Princeton University, 4 Ivy Ln, 08544 Princeton (NJ), US. e-mail:
[email protected]
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2 DamianoCaprioli
ofthehadronicmechanismdescribedaboveorofinverse-Comptonscattering(ICS)
ofrelativisticelectronsonsomephotonbackground.
Coupling the TeV observations of Cherenkov telescopes as HESS, VERITAS
andMAGICwiththeGeVobservationsoftheFermisatellite,however,ithasbeen
possible to assess the nature of the emission, at least in some paradigmaticcases:
SNRRXJ1713.7-3946 turnedouttobemostlyconsistentwithaleptonicscenario
[1]while,onthecontrary,Tycho’sSNRhasbeenconvincinglymodeledaccording
tothehadronichypothesis[12].Themainelementallowingsuchadistinctionisthe
slope ofthe observed g -ray spectrum:fora (cid:181) E q CR energydistribution,ICS is
−
expectedtoproduceaflatterpower-lawphotonspectrum, (cid:181) Eg−(q+1)/2,whilepion
decayandbremsstrahlungproduceaspectrumparalleltotheparents’one,(cid:181) Eg−q.
Both GeV and TeV observations are —in basically all the cases— consistent
with spectra steeper than E 2, as showed in Fig. 1 (see ref. [4] for more details).
−
TheonlySNRsshowingaGeVslopesmallerthan2areinfacttheaforementioned
RXJ1713.7-3946 andVelaJr.,whoseemissionmaybeaccountedforbyinvoking
astrongphotonbackgroundmakingICSdominateoverpiondecay.Whenthespec-
trumissteeperthanE 2 acrossmanyenergydecades,however,ahadronicmecha-
−
nismisfavored,instead,sincebremsstrahlungistypicallynegligibleinSNRs.
Fig. 1 Slopes qg of theg-ray spectra as inferred inthe GeV/TeV band forboth confirmed and
candidateSNRs,asinthelegend.Datafromtable1inref.[4].
Newinsightsonhadronaccelerationatsupernovaremnantshocks 3
But this behavior has another important consequence in terms of the process
responsible for particle acceleration (of both electrons and protons, which share
thesamespectruminrigidity):ithastobeabletoproduceparticlespectrasteeper
thanE 2.Thisapparentlyharmlessrequirementisatoddswithanytheoryofeffi-
−
cient particleaccelerationatSNRs developedin thelast 30years since,according
to Fermi’s mechanism, the expected slope is a function of the shock compression
ratio only,andnamely q= r+2. Forstrongshocks r= g+1 =4, with g =5/3the
r 1 g 1
gasadiabaticindexand,intu−rn,q=2.Whenacceleratio−nisefficient,though,one
couldexpecttheshocktobemodifiedbytheback-reactionoftheacceleratedparti-
cles,whosepressuremaybecomecomparablewiththeramone. Thesimplestway
toaccountforthiseffectisconsideringthatCRsarerelativisticparticlesforminga
gaswithadiabaticindexg =4/3,whichwouldprovideacompressionratior=7
cr
andinturnq=1.5.Theescapeofhigh-energyparticlesmayinadditionmakethe
shock behave as partially radiative, increasing r even furtherand pushing q down
to1 1.2.Inanycase,averysolidpredictionofthenon-lineartheoryofdiffusive
−
shock acceleration (NLDSA) is that the CR spectrum has to be invariably flatter
than E 2 at the highestenergies, and being flatter and flatter for largerand larger
−
accelerationefficiencies(formoredetailsonCRmodifiedshockssee,e.g.,ref.[11]).
Therefore,independentlyofthepossibleorigin(leptonicorhadronic)oftheob-
served GeV emission, Fermi-LAT’sobservationsforce us to rethinkourtheory of
CR acceleration,challengingthe paradigmwhichrequiresSNR shocksto channel
fractionaslargeas10-30%oftheirkineticenergyintoacceleratedparticlesinorder
tobethepotentialsourcesofGalacticCRs.
2 Magnetic fieldamplificationand particleacceleration
A fundamentaltile in the mosaic of the comprehensionof particle accelerationin
(young)SNRshasalsocomefromthedetectionofnarrowX-raybrightrimsimme-
diatelydownstreamoftheirforwardshocks.Thenon-thermalnatureoftheirspectra
hasbeenaccountedforasduetosynchrotronemissionofrelativisticelectrons,while
theirnarrowness(typicallylessthan0.01pc)pointstomagneticfieldsaslargeasa
fewhundredsm G,almosttwoordersofmagnitudelargerthanthetypicalinterstellar
one.Suchanevidencehasbeenwelcomedbytheoristsforseveralreasons.
Thesuper-Alfve`nicstreamingofCRsupstreamoftheshockhasbeenpredicted
•
toleadtotheexcitationofseveralmagneticmodesviaplasmainstabilities[14,2].
A higher level of magnetization enhances particle diffusion and allows the
•
achievement of larger energies, arguably up to a few PeV, namely enough to
accountforthekneeobservedintheGalacticCRsdetectedatEarth[3].
The pressure in magnetic turbulencemay be so large to overcomethe gasone,
•
thereforepreventingtheCRpressuretomodifytheshocktooseverely[8].
Finally,magneticfield self-generationmay have a key role also in determining
• the CR spectral slope, and therefore in reconciling NLDSA theory with g -ray
observations,whichiswhatwewanttooutlinehere(alsoseeref.[5]).
4 DamianoCaprioli
Without delving into the details of a kinetic theory of plasmas, we can state that,
being the accelerated particles and the magnetic fields coupled through resonant
scattering, the whole system has to gradually reduce the relative velocity of CRs,
whose diffusion velocity is basically the shock velocity in the upstream reference
frame,u,andofmagneticirregularities,whosephasevelocityisoftheorderofthe
Alfve`n speed, v =B/√4pr . In other words, magnetic field amplification might
A
be considered as an inevitable consequenceof an efficientCR acceleration while,
ontheotherhand,anenhancedlevelofmagnetizationisanecessaryconditionfor
anefficientparticlediffusionandacceleration:iftheinitialAlfve`nicMachnumber
M =u/v islarge(asittypicallyisisintheinterstellarmagneticfield),ittendsto
A A
bereducedbyanon-linearinterplaybetweenparticlesandfields.
Wemodelsuchaninterplaybyadoptingthesemi-analyticformalismforNDLSA
outlined in ref. [5] and references therein, which proved to be quick but very ac-
curate for non-relativistic shocks [9]. We solve the equations of hydrodynamics
coupled with a kinetic description of the non-thermalparticles (via the diffusion-
convection equation, eq. 2.5 in ref. [5]) and a fluid description for the generation
ofmagneticturbulenceviaresonantstreaminginstability (eq.2.18inref.[5]).The
dynamicalfeedbackofbothacceleratedparticlesandamplifiedmagneticfieldsare
Fig.2 Toppanel:pressure inCRsattheshock, P ,expressed asafractionoftherampressure
cr
r u2,andpredicteddownstreammagneticfield,B ,asafunctionoftheinjectionefficiencyh .The
d
environmentalparametersarethoserelevantforatypicalSNRintheearlySedovstage(seeref.[5]
formoredetails).Bottompanel:CRspectralslopeobtainedwhentheAlfve`nvelocityiscalculated
intheself-amplifiedmagneticfieldd B(solidlinewithtriangles)oraccordingtoastandardNLDSA
theoryassumingMA(B0) 1(dot-dashedline).
≫
Newinsightsonhadronaccelerationatsupernovaremnantshocks 5
self-consistentlyretainedin thisapproach,aswellasthe escapeofthehighesten-
ergyparticlesfromtheupstreamboundary[7].
ThekeyroleofmagneticfieldamplificationindeterminingtheCRspectral
slopeistoenhancethevelocityofthescatteringcenters,i.e.,thephaseveloc-
ity of the magnetic waves, v (cid:181) d B. Since the compression ratio shaping
A
∼
the CR spectra is not the one of the fluid, but rather the one of the veloc-
ityoftheirscatteringcentersaheadandbehindtheshock,whenv becomes
A
a non-negligible fraction of u, it is in principle possible for diffusive shock
accelerationtoproducespectrasteeperthanE 2.
−
More precisely, the compression ratio felt by the fluid between upstream and
downstreamis theusual r=u /u 4forstrong,CR modifiedshocks,whilethe
u d
≥
compressionratiofeltbyCRs isinstead r˜=(u +v )/(u +v ). Accordingto
u A,u d A,d
theargumentabove,however,thecouplingbetweenCRsandmagneticfieldisex-
pectedtoproducewavesstreamingagainstthefluidintheupstream(inthedirection
oppositetotheCRgradient),whiledownstreamtheturbulenceshouldbeefficiently
isotropised(v 0).
A,d
∼
The net effect is that r˜=(1 M 1)r and, in turn, if M (d B) becomes small
− A−,u A
enough,the predictedslope of the CR spectrum q= r˜+2 may becomelargerthan
r˜ 1
2, even for strong shocks and large CR pressures. On−the other hand, a steeper
CR spectrum allocates less pressure(which in turn generatesless magnetic field),
thereforeweneedanon-linearcalculationtounderstandwhicheffectdominatesthe
determination of the spectral slope when acceleration is efficient: the pressure in
CRs,whichmakestheshockmorecompressible,orratherthereducedjumpinr˜.
Since CR injection has not been understoodfrom first principles, yet, we can-
notbutparametrizeit: we allow h , i.e., the fractionof particle crossing the shock
withamomentumlargeenoughtobeinjectedintotheaccelerationmechanism,to
varybetween 10 7 and 0.1.Suchalargerangeofinjectionefficiencyreflects
−
∼ ∼
differentregimesofCRacceleration,spanningfromunmodifiedshocks(wherethe
pressureinCRs, P isexpectedtobenegligiblewithrespecttotherampressure),
cr
to stronglymodifiedones, in which the shockstructure is deeply affectedby CRs
andinwhichmagneticfieldamplificationisveryeffective.Atsaturation,infact,we
havethatP =d B2/8p P /M (see 2.1inref.[5]fortheexactdependence).
B cr A
∼ §
Ourresultsare showedin Fig. 2 fora SNR about3000yrold,i.e., in the early
Sedovstage.ForamuchwiderdiscussionoftheSNRevolutionintermsofitsnon-
thermal content the reader may refer to refs. [6, 5]. In the top panel, P and the
cr
downstreamfield B are showed asfunctionof h : theyreproducethe test-particle
d
caseforh <10 5,showalinearincreaseforaboutadecadeandfinallysaturateto
−
about10-20∼%and100-200m G,respectively,aboveh 10 4.
−
∼
Theveryreasonof this saturation,which amongotherthings assesses the mild
dependenceofourfindingsonh ,isthatthewholesystemreactstohighinjectionef-
ficienciesbysteepeningtheCRspectruminordertoaccommodatealmostthesame
6 DamianoCaprioli
energyinnon-thermalparticles,asdemonstratedinthebottompanelofFig.2(solid
line).SpectraassteepasE 2.2 E 2.5 correspondtothehighestaccelerationeffi-
− −
−
cienciesandtothefieldsinferredinthedownstreamofyoungshellSNRs(seefigure
3 in ref.[5]).The spectralslope obtainedisalso comparedwith the onepredicted
byatwo-fluidtheoryofNLDSA,q=(3g 1)/2,wheretheCR contributionis
eff
−
accountedforviaacompressionratiomodulatedbyaneffectiveadiabaticindexof
the gas+CR fluid [10], namely g = 5+3Pcr (dot-dashedline in the bottom panel
eff 3 3Pcr
ofFig.2).Itisworthrecallingthatthela−tterslope,alreadyclearlyinconsistentwith
theobservationsreportedinFig.1,representsanupperlimittotheonewhichwould
bepredictedbytakingintoaccountalsotheescapeofCRs,whichwouldmakethe
shockpartiallyradiative,inprincipleincreasingrwellabove7[11].
Theonlywaytoaccommodatethetypicalefficiencies(10-20%)requiredfor
SNRstobethesourcesofGalacticCRs,andthehighlevelsofmagnetization
observed(afew100m G),withCR spectrasteeperthanE 2 istomodifythe
−
standardtheoryofNLDSA.
Weproposeherethataccountingforthefeaturesofthemagneticfieldpro-
ducedbytheCR streamingisapossiblewaytobuildaconsistentpictureof
efficient NLDSA in SNRs, actually reversing the usual trend which relates
largerandlargerCRaccelerationefficiencieswithflatterandflatterspectra.
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