Diffuse Gamma Rays in 3D Galactic Cosmic-ray Propagation Models

0.7 MB·

by  R. Kissmann

ff
Di use Gamma Rays in 3D Galactic Cosmic-ray
Propagation Models
R. Kissmann1,a), F. Niederwanger1, O. Reimer1and A. W. Strong2
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0 1Institutfu¨rAstro-undTeilchenphysik,LeopoldFranzensUniversita¨tInnsbruckTechnikerstraße25/8,
2 6020Innsbruck,Austria
n 2Max-Planck-Institutfu¨rextraterrestrischePhysik,Garching,Germany
a
J a)Correspondingauthor:[email protected]

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Abstract.ThePicardcodeforthenumericalsolutionoftheGalacticcosmicraypropagationproblemallowsforhigh-resolution
] modelsthatacknowledgethe3DstructureofourGalaxy.Picardwasusedtodeterminediffusegamma-rayemissionoftheGalaxy
E over the energy range from 100MeV to 100TeV. We discuss the impact of a cosmic-ray source distribution aligned with the
H Galacticspiralarmsforarangeofsuchspiral-armmodels.Asexpected,theimpactonthegamma-rayemissionismostdistinct
intheinverse-Comptonchannel,whereimprintsofthespiralarmsarevisibleandyieldpredictionsthatarenolongersymmetric
.
h totherotationalaxisoftheMilkyway.Wewillillustratethesedifferencesbyadirectcomparisontoresultsfrompreviousaxially
p symmetric Galactic propagation models: we find differences in the gamma-ray flux both on global scales and on local scales
- relatedtothespiralarmtangents.Wecomparegamma-rayfluxandspectraaton-armvs.off-armprojectionsandcharacterizethe
o
differencestoaxiallysymmetricmodels.
r
t
s
a
[ INTRODUCTION

1
v ThefactthatourGalaxydoesnothaveanazimuthallysymmetricshapeislatelybeingacknowledgedinrecentGalactic
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cosmic-raypropagationmodels[see,e.g.,1,2,3,4,5,6].ThesemodelsfocusontheobservationthatourGalaxyhas
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a spiral structure [see 7] and implications for the transport of cosmic rays within the Galaxy. This respective spiral
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structurewillmanifestitselfinthedistributionofISMgas[see8]andtheinterstellarmagneticfield[see,e.g.9,10]
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0 butalsointhedistributionofcosmic-raysources[see,e.g.1,2,11].
. Theimpactofthesourcedistributiononthecosmic-rayfluxanddistributionwithintheGalaxyhasbeenstudied
1
0 byseveralgroups[see1,2,4,12,5,13,6].Itwasshownthatagoodagreementwiththeobservedcosmic-raydataat
7 Earth[see1,13]canbefoundbothinmodelswithanaxisymmetricsourcedistributionandinmodelsusingasource
1 distribution motivated by the observed three-dimensional structure of our Galaxy. Different spatial distributions of
: the sources lead to different spatial distributions of the cosmic-ray flux, which should lead to distinct effects on the
v
i emissionofradiationbytheinteractionofcosmicrayswiththeinterstellarmediumresultinginthedifferentmodels.
X
Here, we focus on the imprint of non-axisymmetric source distribution on the gamma-ray emission from our
r Galaxy.ForthisweusesimulationsperformedwiththePicardcode.Thiscodewasintroducedin[14]andisoptimised
a
forsuchspatiallythree-dimensionalnumericalmodelling.InthefollowingweintroducethePicardcodewithafocus
on recent enhancements. Subsequently we discuss the ensuing gamma-ray emission for our models and show the
relatedenergyspectra.
THEPICARDCODE
The Picard code was introduced in [14] with a focus on spatially three-dimensional numerical modelling of Galac-
tic cosmic-ray transport problems. The code is optimised to find steady-state solutions to the cosmic-ray transport
equation:
∂ψ ∂ ∂ 1 ∂ (cid:26) p (cid:27) 1 1
i =q((cid:126)r,p)+∇·D∇ψ + p2D ψ −∇·(cid:126)vψ − p˙ψ − (∇·(cid:126)v)ψ − ψ − ψ, (1)
∂t i ∂p pp∂p p2 i i ∂p i 3 i τ i τ i
f r
butitcanalsobeappliedtosolvetime-dependentproblems.Anumericalsolutiontothesteady-stateproblemisfound
be discretising the differential operators in equation (1) in space and momentum and then finding an approximate
solution to the resulting linear system of equations. In Picard the linear system of equations can be solved using
differentstandardtechniques,includingarangeofmultigridmethods[see15]ortheBiCGStabmethodasdescribed
in[16],withthepossibilitytoaddothersolversintothemodularframeworkofthecode.
Picard features all relevant transport processes inherent in equation (1): spatial diffusion, spatial convection,
momentumdiffusionandrelevantenergy-lossprocesses.Fluxesoflightspeciesdependonthoseofheavierspeciesdue
tothepossiblefragmentationorradiative-decayprocesses.Thisisrealisedthroughthefragmentationandradiative-
decay timescales τ and τ , respectively, together with a consideration of a related source term for other species.
f r
TheresultingnuclearnetworkisefficientlyimplementedinPicard,leadingtoanumericallyoptimisedandaccurate
treatmentofcouplednuclearspecies[see13].
ProminentfeaturesofthePicardcodeincludethepossibilitytoconsideranisotropicspatialdiffusion[foradis-
cussionsee,e.g.17,18]andarbitraryconvectionvelocities(cid:126)v.ThenumericalsolverisMPI-parallel,thusfacilitating
the possibility to achieve up to deca-parsec scale resolution by making use of large-scale distributed-memory com-
puters.ThenumericalsolutioncomputedusingPicardisacquiredwithauser-definedaccuracywithouttheneedto
check the quality of the numerical solution a-posteriory. Picard is continuously expanded where, e.g., the currently
ongoingimplementationofanimprovedinterstellarradiationfieldisdiscussedby[19].
Withthiscodewestudiedtheimplicationsofspiral-armcosmic-raysourcedistributionsonthespatialvariability
of the cosmic-ray flux in [5]. Additionally, we showed in [13] that the transport parameters in equation (1) can be
adaptedtosuchlocalisedsourcedistributions,thusleadingtoagoodagreementbetweenpredictedcosmic-rayfluxes
at Earth and corresponding observations. For the secondary to primary ratios there appears a dependence on the
distancetothenearestsourcesinmodulesusingsuchlocalisedsources.Inthefollowingwewilladdresstheimpact
ofthesemodelsontheGalacticdiffusegamma-rayemission.
GAMMA-RAYEMISSION
In[13]wefoundthataGalacticcosmic-raypropagationmodelfeaturinglocalisedsourcescanreproducecosmic-ray
measurementsatEarthaswellasamodelwithunderlyingaxisymmetry.Incontrasttosuchanaxisymmetricmodel,a
spiral-armsourcedistributionleadstoalocalisationofthecosmic-rayflux,atleastfortheprimarycosmic-rayspecies.
Thedistinctdifferenceinspatialdistributionbetweenthedifferentmodelscanbeexpectedtoleadtodifferencesinthe
resultinggamma-rayfluxinthedifferentmodels.Inthefollowingwefocusonthecomparisonbetweenamodelusing
anaxisymmetricsourcedistributionandoneusingaspiral-armsourcedistributionwithfourspiralarms.Detailscan
befoundin[5]and[13],wherethisspecificmodelisreferredtoastheSteiman-model.
Therelevantchannelsfordiffusegamma-rayemissionareπ0-decay,bremsstrahlung,andinverseCompton(IC)
radiation.Theemissivityoftheformertwooftheseprocessesresultsfromtheproductofthegas-densitywiththere-
spectivecosmic-raydensity–inthiscasenucleonsandelectrons,respectively.Therefore,itisnoteasytodistinguish
whetheraspatialfeatureinthegamma-rayemissionresultsfromlocalstructuresinthegasdistributionorthecosmic
raydistribution.SincecurrentmodelsoftheGalacticradiationfieldarespatiallymuchsmootherthanthegasdistribu-
tion[see20,21,22],theICchannelisamuchclearertracerofthelocalisationofthesourceswithinourmodels.This
is obvious when investigating the gamma-ray emission in Fig. 1. A comparison shows that the Galactic plane near
theGalacticcentrebecomesslightlybrighterforthemodelwithaspiral-armsourcedistribution.Otherwiselocalised
featuresaffectedbythedifferentsourcemodelsarenotreadilyapparent.
InthefollowingwewillfocusontheregionneartheGalacticcentre,wherethelocalisedfeaturesofthecosmic-
raydistributionintheSteiman-modelhavethemostobviousimpactonthegamma-rayemission.Thisiscausedbythe
spiralarmsthataretightlywoundaroundtheGalacticcentreleadingtoseveralspiralarmtangentsneartheGalactic
centre along which the projected source intensity is enhanced. This is shown in Fig. 2 where the projected source
intensityneartheGalacticcentreregionisshown.Thespecificspiral-armtangentsareconsistentwithobservations
[7]sincetheSteimanmodelisdrivenbyobservationsoftheGalacticspiralarms[23].Thespecificspiral-armtangents
visible in Fig. 2 are tangents to the Sagittarius / Carina arm at l ∼50◦, l ∼-16◦, and l ∼-75◦, to the Scutum / Crux
Centaurusarmatl∼30◦andl∼-50◦,theNormaarmatl∼19◦andatl∼-30◦,andthePerseusarmatl∼-22◦.
5e-21 1e-17
FIGURE1:All-skygamma-rayemissionat E = 10TeVforanaxisymmetric(top)andafour-arm(bottom)source
γ
distribution.Thegamma-rayemissionisshowninunitsofcm−2s−1sr−1MeV−1.
InFig.2wealsoshowtheICemissionatanenergyof∼100GeV.Theincreaseingamma-rayfluxatthepositions
ofthespiral-armtangentsisobviousatthisenergy.High-energyelectronsaretightlycoupledtotheirsourcesdueto
theirveryhighenergylosses[5].Therefore,therelatedgamma-rayemissiontracesthesesourceregionsleadingtoan
imprintofthespiral-armtangentsalsoonthegamma-rayemission.Inthetotalgamma-rayemissiontheseeffectsare
not so obvious, because of the impact of the gas-distribution discussed above and also because the Galactic diffuse
gamma-ray emission is in many directions dominated by π0-decay emission. In the following we investigate the
quantitativeimpactofthespiral-armsourcedistributiononthegamma-rayemission.
GAMMA-RAYSPECTRA
Foraquantitativeanalysiswecomparegamma-rayspectraaton-armandoff-armpositions.InFig.3corresponding
results are shown for spiral-arm tangents of the Norma and the Sagittarius arm. Obviously, the on-arm flux is sig-
nificantlyhigher inbothcases andforall gamma-rayemissionchannels. Especially,forBremsstrahlung andICthe
on-armspectraarealsoharder.Forthesechannelswefoundthatthepower-lawindexcanincreaseby0.1orevenmore
ataspiral-armtangentascomparedtoanoff-armposition.ThisissomewhatmorepronouncedfortheSagittariusarm,
becauseinthecaseoftheNormaarmtheoff-armregionisinaregionfeaturingseveralotherspiral-arms.Thus,the
Normaoff-armregioniscontaminatedbythepresenceofotherclose-bycosmic-raysources.
ThespectralhardeningoftheICfluxcanbeexplainedbytheenergydependenceoftheelectron’senergylosses.
Duetotheirrapidincreasewithenergy,high-energyelectronssufferfromthemostsevereenergylosses.Therefore,
high-energy electrons can only be found in the close vicinity of their sources. In [5] a significant hardening of the
electronspectrumwasobservedforon-armpositions.Thisnaturallytranslatesintoahardeningoftheresultingphoton
spectrumforasightlineinthedirectionofaspiral-armtangent.
The π0 channel shows only mild change in spectral slope. This is also consistent with the observations in [5]
wheretheprotonfluxwasfoundtomainlychangeinamplitudefromanon-armtoanoff-armposition.Thisreflects
thefactthatthespatialdistributionofnuclearcosmicraysismainlydrivenbyspatialdiffusionduetotheirratherlow
energy losses. Also in gamma rays this channel mainly features a change in amplitude when comparing an on-arm
40 −1]
30 10-13 sr
20 −2
s
10 −2
b b 0 m
10 10-14 −1c
20 V
e
30 M
40 [
50 0 50
l l
FIGURE2:Left:Projectedsourceintensityforthefour-armsource-distributionmodel.Spiral-armtangentsarevisible
as enhanced intensity in the Galactic plane. Right: Inverse Compton gamma-ray emission at 100 GeV for the same
model.
100 100
total flux total flux
] 10-1 IC ] 10-1 IC
−1 Bremsstrahlung −1 Bremsstrahlung
sr pion decay sr pion decay
−2 10-2 −2 10-2
s s
−2 −2
m 10-3 m 10-3
c c
V V
Me 10-4 Me 10-4
[ [
γ γ
J J
10-5 10-5
10-6 10-6
102 103 104 105 106 107 108 102 103 104 105 106 107 108
E[MeV] E[MeV]
FIGURE 3: Spectra for the the different gamma-ray emission channels for two of the spiral-arm tangents. In each
ploton-armandoff-armdataarecompared,wheretheon-armspectraaretheoneswiththehigherfluxes.Ontheleft
resultsareshownforatangentoftheNormaarmwiththeon-armdatatakenat-30◦ longitudeandtheoff-armdata
takenat-35◦longitude.OntherightcorrespondingdataforaSagittarius-armtangentareshownwiththeon-armdata
takenat50◦longitudeandtheoff-armdatatakenat62◦longitude.Resultsareintegratedoveracirclewitharadiusof
2◦.
andanoff-armregion.
Since the total flux in both cases is dominated by π0 decay, the change in slope for the total flux is also rather
small.OnlyintheenergyregimefromafewuptoafewhundredGeV,wherethecontributionofICemissiontothe
totalgamma-rayfluxislargest,thespectrumatanon-armpositionbecomesharderwithachangeinpowerlawindex
of up to 0.05. In the present case we used the same source-distribution for electrons and nuclei. In a model using
differentsourcedistributionsthecorrespondingchangeswouldbecomelarger,forsuchlocalisedsourcedistributions
aswerediscussedinthiscase.Infact,forhigh-energyelectronsitwillbeimportanttoconsidertheactualsources[see
24,25,26]whenaimingforanaccuratemodelforthediffusegamma-rayemissionintheGalacticplane.Ourmodel
showsthatlocalisedsourceswillnotonlyhaveanimpactonthegamma-rayemissionintheGalacticplane,butcanalso
affectthelocalspectralslope.Thiswillmakeatemplate-fittingapproachatleastmoreproblematicthanaphysically
motivatedmodellingapproachbasedonthepropagationphysicsofGalacticcosmicrays.Oneshouldbeawarethat
inthecurrentapproachonlythedistributionofthecosmic-raysourceswasadaptedtotheGalacticstructure.Withan
adoptionofthegas-,magneticfield-,andpossibilitytheinterstellarradiationdistributionthedifferencesbetweenan
axisymmetricapproachandoneacknowledgingtheactualstructurecanbecomeevenlarger,holdingthepossibilityto
alsoexplainthesmall-scalestructureinthegamma-rayemissionintheGalacticplane.
CONCLUSIONS
InthisstudyweshowedthatPicardisreadytopredictgamma-rayfluxesforacomparisonwithdatainthecontextof
Galacticcosmic-raytransportmodelstakingintoaccountthethree-dimensionalstructureofourGalaxy.Weshoweda
firstquantitativediscussionoftheimpactoflocalisedsourcesontheGalacticdiffusegamma-rayemission.Wefound
ahardeningofthegamma-rayemissionspectruminthedirectionofthecosmic-raysourcesfortheleptonicemission
channels.Sinceinourmodeltheemissionisdominatedbyπ0 decaythechangeinslopeforthetotalgamma-rayflux
is rather small and also limited to energies between 1 and a few hundred GeV, where the leptonic channels provide
a comparatively large fraction of the total emission. The current analysis was focussed on the impact of the source
distribution.Whilethiscanonlybeviewedasafirststep,withthefutureneedtoincludethefullGalacticstructurefor
gas-, magnetic field-, and interstellar radiation-distribution, only a dissemination of the individual effects can show
therespectiveimpactonchangesinthegamma-rayemission.
ACKNOWLEDGMENTS
The computational results presented have been achieved (in part) using the HPC infrastructure LEO and MACH of
theUniversityofInnsbruck.
FN acknowledges financial support from the Austrian Science Fund (FWF) project number I1345, in collaboration
withtheFrenchScienceFund(ANR),projectIDANR-13-IS05-0001.
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