Galactic annihilation emission from nucleosynthesis positrons

15 Pages·2012·0.87 MB·English

A&A543,A3(2012) Astronomy
DOI:10.1051/0004-6361/201118721 &
(cid:2)c ESO2012 Astrophysics
Galactic annihilation emission from nucleosynthesis positrons
P.Martin1,2,A.W.Strong1,P.Jean3,A.Alexis3,andR.Diehl1
1 MaxPlanckInstitutfürextraterrestrischePhysik(MPE),Postfach1312,85741Garching,Germany
2 UJF/CNRS,InstitutdePlanétologieetd’AstrophysiquedeGrenoble(IPAG),UMR5274,BP53,38041GrenobleCedex9,France
e-mail:[email protected]
3 UPS/CNRS, Institut de Recherche en Astrophysique et Planétologie (IRAP), UMR5277, BP44346, 31028 Toulouse Cedex 4,
France
Received22December2011/Accepted25April2012
ABSTRACT
Context.TheGalaxyhostsawidespreadpopulationoflow-energypositronsrevealedbysuccessivegenerationsofgamma-raytele-
scopesthroughabrightannihilationemissionfromthebulgeregion,withafaintercontributionfromtheinnerdisk.Theexactorigin
oftheseparticlesremainscurrentlyunknown.
Aims.Weestimatethecontributiontotheannihilationsignalofpositronsgeneratedinthedecayofradioactive26Al,56Niand44Ti.
Methods.WeadaptedtheGALPROPpropagationcodetosimulatethetransportandannihilationofradioactivitypositronsinamodel
ofourGalaxy.Usingplausiblesourcespatialdistributions,weexploredseveralpossiblepropagationscenariostoaccountforthelarge
uncertaintiesonthetransportof∼MeVpositronsintheinterstellarmedium.Wethencomparedthepredictedintensitydistributions
totheINTEGRAL/SPIobservations.
Results.Weobtainsimilarintensitydistributionswithsmallbulge-to-diskratios,evenforextremelarge-scaletransportprescriptions.
Atleasthalfofthepositronsannihilateclosetotheirsources,evenwhentheyareallowedtotravelfaraway.Inthehigh-diffusion,
ballisticcase,upto40%ofthemescapetheGalaxy.Inproportion,thisaffectsbulgepositronsmorethandiskpositronsbecausethey
are injected further off the plane in a tenuous medium, while disk positrons are mostly injected in the dense molecular ring. The
predictedintensitydistributionsarefullyconsistentwiththeobservedlongitudinally-extended disk-likeemission,butthetransport
scenariocannotbestronglyconstrainedbythecurrentdata.
Conclusions.Nucleosynthesispositronsalonecannotaccountfortheobservedannihilationemissionintheframeofourmodel.An
additionalcomponentisneededtoexplainthestrongbulgecontribution,andthelatterisverylikelyconcentratedinthecentralregions
ifpositronshaveinitialenergiesinthe100keV−1MeVrange.
Keywords.astroparticlephysics–gammarays:ISM–nuclearreactions,nucleosynthesis,abundances
1. Introduction clearthattherealchallengeofpositronastrophysicsisnottofind
anoriginfortheseparticles,buttoidentifythesourceorcombi-
Overthe pastdecades,ithasbecomeclear thatourGalaxycan nationorsourcesthatdominatestheproduction.
producesubstantialamountsof antimatterand give rise to sev-
Inthispaper,wefocusonthelow-energypositronpopulation
erallarge-scalepopulationsofantiparticlesthatcoexistwithour
andononelikelysourcefortheseparticles:thedecayofradioac-
matter environmentat the current cosmic time. In particular, a
tivespeciesproducedbytheongoingnucleosynthesisactivityof
sizeable number of positrons apparently fill the entire Galaxy
ourGalaxy,inparticular26Al,56Niand44Ti.Recentworkshave
fromtheverycentretotheperipheralregions.
shownthattheseelementscouldaccountfortheannihilationsig-
The Galactic population of positrons is usually divided
nalobservedbysuccessivegenerationsofgamma-raytelescopes
into low-energy (typically ≤10MeV) and high-energy (typi-
(Prantzos2006;Higdonetal.2009).Inthiswork,weaimatpro-
cally ≥100MeV) particles, and it seems that there is more
viding an additional, alternative assessment of that possibility.
than historical or experimental reasons to do that (Prantzos
We adapted the GALPROP public code for cosmic-ray propa-
et al. 2011). While high-energy positrons can be observed di-
gationtosimulatethetransportandannihilationofradioactivity
rectlyasacosmic-raycomponentintheinterplanetarymedium,
positrons in a model of our Galaxy. Using source spatial pro-
low-energy positrons are revealed indirectly through gamma-
files based on typical distributions of massive stars and super-
rayobservationsoftheskyinthe∼100keV−1MeVrange.The
novae,we exploredhow the annihilationintensity distributions
latterhaveindeedshownanunambiguoussignatureofelectron- varyupondifferentprescriptionsforthetransport.Thepredicted
positronannihilationfromtheinnerGalacticregions,intheform
emissionswerethencomparedtothepresentlyavailableobser-
ofalineat511keVandacontinuumbelow. vations,comingmostlyfromtheINTEGRAL/SPIinstrument.
That our Galaxy can produce and host a substantial popu-
We start by recalling the main points of the physics of
lation of positrons is actually not a surprise. There are many
positron annihilation and transport in Sect. 2, and by summa-
physical processes able to provide non-thermal positrons over
rizing the main observational facts about Galactic low-energy
a broad range of energies (photon-photon pair production, ra-
positrons in Sect. 3. In Sect. 4, we present the characteristics
dioactive decay, hadronic interactions, ...), and as many astro-
of 26Al, 56Ni and 44Ti in terms of contribution to the Galactic
physicalphenomenalikelytobethesitesofoneormoreofthese
populationof positrons. We introducein Sect. 5 the code used
processes(pulsars,X-raybinaries,supernovae,cosmicrays,...).
to model the propagation and annihilation of positrons in the
If we add more speculative channels like dark matter particles
Galaxy.Then,wepresentthesimulatedcasesinSect.6anddis-
creatingpositronsthroughtheirannihilationordecay,itbecomes
cusstheirresultsinSect.7.
ArticlepublishedbyEDPSciences A3,page1of15
A&A543,A3(2012)
2. Positronphysics along and across the field lines, likely with differentproperties
in the paralleland perpendiculardirections;the processcan be
2.1.Positronannihilation
quite efficient, provided there are adequate MHD waves with
Galactic low-energy positrons are associated with the strong whichpositronscaninteract.
511keV celestial signal. For several reasons that will be re- From recent theoretical developments, it seems that inter-
viewedinSect.3,theyarebelievedtobeinjectedintheGalaxy stellarMHDturbulencecanbedecomposedintoAlfvenic,slow
withinitialenergiesbelowafewMeV.Ontheotherhand,low- and fast magnetosonic modes. These modes are thought to be
energy positrons are created non-thermal in all the potential injectedatspatialscalesoftheorderof∼1020−1021cm,asare-
sourceprocesses,withmeaninitialenergiesofafew100keVat sult of differential rotation of the Galactic disk, superbubbles,
least.Toannihilate,however,mostwillhavetobesloweddown
and stellar winds and explosions. The turbulent energy is re-
to near-thermal energies, at least below ∼100eV. This energy
distributed to smaller spatial scales through the interaction of
lossproceedsmostlythroughionisation/excitationandCoulomb
wave packets in a so-called turbulencecascade. In the process,
interactionsin the interstellargas,and itcan take ∼105yrfora MHD modes can suffer various damping processes that could
typicalinterstellardensityof1cm−3(Jeanetal.2006).Overthat haltthecascade,thuspreventingthepropagationofMHDmodes
timepositronstravelatrelativisticspeeds,whichopensthepos- tosmallerwavelengths.
sibilityforlarge-scaletransport(seebelow).
The properties of the turbulence cascade depend on the
There is a variety of processes by which positrons can an-
mode, and this has implications for the collisionless transport
nihilate with electrons: direct annihilation with free or orbital of energetic particles. The so-called Kolmogorov scaling ap-
electrons,formationof positroniumby radiativerecombination plies to the Alfvenic and slow magnetosonic modes (Lithwick
with freeelectronsorbycharge-exchangewith atoms,etc. (for
& Goldreich2001;Cho et al. 2002).In that case, however,the
acompletereview,seeGuessoumetal.2005).Thephysicaland turbulent energy is preferentially redistributed perpendicularly
chemicalpropertiesofthemediumwheretheannihilationtakes tothemagneticfield,whichleadstoaninefficientscatteringof
placesetthedominantannihilationchannelsandasaresult,each
relativistic particles. Conversely, the fast magnetosonic modes
interstellarmedium(ISM)phasehasatypicalannihilationspec-
follow the so-called Kraichnan scaling in an isotropic cascade
trum. As we will see later, most low-energypositrons seem to (Cho etal. 2002;Cho & Lazarian2003),andthey were shown
annihilate through the formation of a positronium atom (Ps),
to have the dominant contribution to the scattering of cosmic
which is a short-lived bound state between a positron and an
raysintheISM(Yan&Lazarian2004).
electron.Thiscanoccurintwodifferentways:eitherbycharge-
Jeanetal.(2009,hereafterJGMF09)havemadeanextensive
exchange, when non-thermalised positrons with typical kinetic
studyofboththeballistic andcollisionlesstransportmodesfor
energy of ∼10−100eV rip off electrons from H or He atoms; positron kinetic energies ≤10MeV, and we briefly summarise
orbyradiativerecombination,whenthermalisedpositronscom-
below their findings about collisionless transport. The authors
bine with thermalised electrons. The Ps atoms occur in 75%
focused on wave-particle resonant interactions occurring when
of the cases as ortho-Ps (parallel particle spins), which decays
the gyroradiusof the positron is of order of the parallel wave-
overμstimescalesinto3photonsproducingacontinuumbelow
length of the MHD modes. In μG fields, this corresponds to
511keV,andin25%ofthecasesaspara-Ps(anti-parallelparti- scales of of ∼109−1010cm for 1−10MeV particles, more than
clespins),whichdecaysovernstimescalesinto2photonswith
10 ordersof magnitudesmaller than the scales at which turbu-
511keVenergies(inthecentre-of-massframe).
lenceisinjected.
Apart from the processes mentioned above, positrons can
A minimum wavelength for the MHD modes of the tur-
also annihilate directly with electrons at energies higher than
bulence cascade is set by Landau damping occurring as the
∼100eV and give rise to a Doppler-broadened line extending
mode frequency approaches the cyclotron frequency of ther-
frommec2/2toEk+mec2/2,whereEkisthepositronkineticen- mal protons. This corresponds to ∼108−109cm scales in most
ergyandm theelectron/positronmass.Thischannelcalledin-
e ISM phases and defines a minimum energy for particle-wave
flightannihilationisnegligibleforpositronenergiesof≤1MeV,
resonant interactions. In the case of positrons, this minimum
but it becomesincreasingly importantat higher and higher en- energy is of order of ∼10−100keV, except in hot media with
ergies. In typical ISM conditions, in-flight annihilation occurs
highmagneticfieldintensities,whereitcanexceed1MeV.Yet,
for a maximum of ∼20−30% of positrons with initial energies damping processes can cut off the turbulent cascade at higher
≥10GeV(thisproportiondecreasesforstrongermagneticorra-
wavelengthsifthedampingrateexceedstheenergytransferrate,
diationfields,seeSizunetal.2006;Chernyshovetal.2010).
andthisiswhatisthoughttohappenforsomeISMconditions.
JGMF09 determined that in the mostly neutral phases of the
ISM, ion-neutralcollisions halt the cascade at spatial scales of
2.2.Positrontransport
order∼1016−1018cm forAlfvenwavesand ∼1017−1019cm for
Once injected in the ISM, relativistic positrons can propagate fast magnetosonicwavesin warm and cold atomic phases, and
awayfromtheirsourcesintwoways,whichwewilltermballis- at scales of order ∼1017−1020cm for both waves in molecular
ticandcollisionlesstransport.Intheformercase,positronssim- phases(wherelargerscalescorrespondtosmaller gasdensities
plyfollowhelicoidaltrajectoriesalongmagneticfieldlinesand fortheatomicphases,andtolargercloudsizesforthemolecu-
they experience repeated interactions with gas particles; in the lar phases). In the ionised phases of the ISM, the Alfven wave
process,positronsprogressivelylosetheirenergybutexperience cascade can proceed undamped down to the minimum spatial
little deviations1. In the latter case, positrons are additionally scalesinboththehotandwarmmedia,whilethefastmodesex-
scattered by magneto-hydrodynamic (MHD) perturbations as- perience significant viscous damping at scales ∼1013−1014cm
sociated with the interstellar turbulence and they random walk in the warm medium, and strong Landau damping at scales
∼1017−1018cminthehotmedium2.
1 SeeSect.3ofJeanetal.(2009),thepitchangleoftheparticlesre-
mainsnearlyconstantdownto∼10keV,andthepropagationperpendic- 2 Exceptmaybeforquasi-parallel waves,ifwavepropagationangles
ulartothefieldlinesisnegligible. arenotefficientlyrandomisedinwave-waveinteractions.
A3,page2of15
P.Martinetal.:Galacticannihilationemissionfromnucleosynthesispositrons
The above results indicate that the turbulence cascade is
quenchedatspatialscalesordersofmagnitudegreaterthanthose
required for resonant interactions of 1−10MeV positrons, ex-
cept for Alfven waves in ionised media3. Yet, JGMF09 argue
thatthescatteringbyAlfvenwavesisverylikelyinefficientdue
tothestronganisotropyoftheassociatedturbulence.Thealter-
nativeofCerenkovresonancewithfastmodes,inwhichnopre-
cisegyroradiusisrequiredfortheinteraction,couldpotentially
takeplacebutunderveryrestrictiveconditionsinvolvingquasi-
parallelfastwavesandnearlyperpendicularpositronmotion.On
the otherhand,non-resonantinteractionswith fast modeswere
proved to be quite efficient at scattering sub-MeV electrons in
thesolarwind(Ragot2006),andasimilarprocessmaywellop-
erateforlow-energypositronsintheISM.Anotheroptionforan
efficientcollisionlesstransportoflow-energypositronsisthein-
Fig.1.IntensitydistributionoftheGalactic511keVemissionobtained
jectionofturbulencedirectlyattherelevantsmallspatialscales,
bymodel-fittingtoabout7yearsofINTEGRAL/SPIobservations,us-
for instance through the streaming instability but more gener-
ing the parameterized components adopted in Weidenspointner et al.
ally by any kind of fluid or kinetic instability. JGMF09 con- (2008a).
cluded that positron scattering off cosmic-ray-driven waves is
inefficient,butthatscatteringoffself-generatedwaveswouldde-
byWeidenspointneretal.(2008b)fortwosetsofequally-likely
serveadetailedinvestigation.Overall,JGMF09havepresented models4. With valuesoforder2−6,theB/D luminosityratio is
several arguments against the scenario of collisionless trans-
higher than those obtained for the distributions of classical as-
port of low-energy positrons, but the issue cannot yet be con-
trophysicalobjectsorinterstellargas(withthecaveat,however,
sideredasdefinitelysettled.IndependentlyofJGMF09,Higdon
thattheouterdiskemissionispoorlyconstrained;seeSect.7.2).
etal.(2009,hereafterHLR09)alsocametotheconclusionthat
Valuableinformationaboutwhereexactlypositronsendtheir
the predominantly neutral phases of the ISM do not host the
lives could be obtained from the spectral analysis the 511keV
small-scale turbulence required for the resonant scattering of
line, permittedby the high energyresolution of the SPI instru-
∼MeV positrons. Yet, these authors argued from observations
ment. The annihilation emission observed with SPI in the in-
ofparticlepropagationintheinterplanetarymediumthat∼MeV
nerGalacticregions,the511keVlineandthecontinuumbelow
positrons should diffuse on MHD fluctuations in the ionised down to ∼400keV, indicates that most positrons annihilate in
phasesoftheISM,eveniftheexactnatureoftheprocessremains
thewarmmediumoftheISM(Churazovetal.2005;Jeanetal.
unknown.
2006). Approximately one half annihilate in the warm ionised
phase, throughthe formationof Ps by radiativerecombination.
Theotherhalfofthepositronsannihilatein thecoldandwarm
3. Positronobservations
neutralphasesshortlybeforethermalisation,throughtheforma-
3.1.Constraintsontheannihilationsites tion of Ps by charge-exchange.Most of the positrons that feed
the 511keV line emission therefore annihilate throughthe for-
In trying to identify the origin of low-energy positrons, the
mation of a Ps state. The so-called positroniumfraction f in-
mapping of the annihilation emission by successive genera- Ps
ferred from SPI is quite high, of the order of ≥95%, and the
tions of balloon- and space-bornegamma-rayinstruments pro-
remaining few % correspond to direct annihilation with free
vided a valuable piece of information. The most accurate pic-
electronsinthewarmionisedmedium.
ture available today is provided by the SPI telescope onboard
the INTEGRAL satellite, which has been in orbit for about
9 years and is planned to operate at least until 2014. More 3.2.Constraintsontheinjectionenergy
than 100Ms of allsky observationsconcentratedmostly on the
We now turn to constraints on the origin of positrons, and in
Galacticdiskandbulgearenowavailable.Fromthis,itisclear
particular on their initial energy and on the reasons why the
that the morphologyof the annihilation line emission is domi-
positrons involved in the 511keV line emission are generally
nated by a strong central emission consisting of a very peaked
part (FWHM of 2−3◦) at the Galactic centre surrounded by consideredtobelow-energyparticles.Foragivenpositronpop-
a wider contribution (FWHM of 8−10◦) from an outer bulge ulation, the level of in-flight radiation at any gamma-ray en-
ergy ≥m c2/2 increases with the initial energy of the parti-
or halo (see Fig. 1). This inner emission comes on top of a e
fainter disk-like component extending up to at least |l| < 50◦. cles, which allows to get constraints on this parameter from
observations in the 1−100MeV range. Under the assumption
The most interesting feature of this distribution is the rela-
tively high bulge-to-disk (B/D) ratio that is obtained for the that positrons remain confined to the Galactic bulge regions
from their injection to their annihilation, Sizun et al. (2006)
511keVluminosity.Fittingprojected3Dspatialdistributionsto
theINTEGRAL/SPIdata,luminositiesof1.2/3.1×1043e+/sfor and Beacom & Yüksel (2006) concluded that the positrons re-
the bulge,and of 0.8/0.5×1043 e+/s for the disk were inferred sponsible for the 511keV emission must be injected with ini-
tial energies below a few MeV otherwise their in-flight anni-
3 Note that Ptuskin et al. (2006) investigated turbulence dissipation hilation would give rise to an emission excess from the bulge,
through resonant interactions of cosmic rays, and concluded that this incontradictionwiththeCGRO/COMPTELobservationsinthe
process may quench the Kraichnan turbulence cascade of fast modes 1−30MeV range.A less stringentconstraintofa few GeV can
at scales ∼1013cm. While this was invoked as an explanation for the
∼1GeV/nucleonpeakintheratiosofsecondary-to-primarynucleiob- 4 Thevaluesarealsobasedontheassumptionofapositroniumfraction
servedinthelocalcosmicrays,itmayalsoberelevantforthetransport of0.967,asdeterminedbyJeanetal.(2006)fromthespectralanalysis
oflower-energyparticles. oftheannihilationemission.
A3,page3of15
A&A543,A3(2012)
be obtained assuming an injection of positrons ∼105yr ago by radionuclides: the plausible large-scale spatial distribution of
anon-stationarysourceprocess,followedbyaslowing-downin their injection sites, the spectrum they have when they are re-
a magnetic field of a few 100μG in the inner Galactic regions leasedintotheISM,andtheirproductionrateinferredfromthe
(Chernyshovetal.2010).Wewillhoweverfocusonastationary estimated nucleosynthesis yields for the parent isotopes. For a
sourceinthiswork. more detailed discussion aboutthe subject, we refer the reader
Constraints on the initial energy of positrons annihilating toPrantzosetal.(2011).
in the bulge could also be obtained from other radiations than
in-flightannihilation.Positronswithenergies≥100MeVwould
26
4.1.The Alradio-isotope
emit throughinverse-Comptonscattering, Bremsstrahlung,and
synchrotron,andaddtheircontributiontothegamma-rayandra-
The 26Al isotope is believed to be produced predominantlyby
dioemissionfromcosmicraysinteractingwiththeISM(Strong
massive stars at various stages of their evolution, with typi-
etal. 2007,2011).Yet,the productionrate ofpositronsannihi- cal total yields of a few 10−4−10−5M(cid:7) per star (Prantzos &
lating at low energyverylikely outnumbersthat of cosmic-ray
Diehl 1996). It is released in the ISM by stellar winds and by
electrons/positrons. In the model of Galactic cosmic rays used
core-collapsesupernovaexplosions.The mean 26Al lifetime of
in Strong et al. (2010), the injection rate of primary electrons about 1Myr allows it to escape its production site and diffuse
with energies 100MeV−100GeV is ∼1042 e−/s; adding sec- ∼10−100pc away before decayinginto 26Mg. The transportof
ondaryelectrons/positronscreatedbyinelasticcollisionsofcos-
26Al away from its stellar sources imply that the majority of
mic ray nuclei with interstellar gas approximately doubles the
26AlpositronsarereleaseddirectlyintotheISManddonotsuf-
rate (Porter et al. 2008). As seen previously, however, the
ferenergylossespriortotheirinjection.
positronannihilationrateinferredfromINTEGRAL/SPIobser-
vations is a few times 1043 e+/s; so if these positrons were to The distribution of 26Al in the Galaxy is truly diffuse and
have initialenergies≥100MeV, theywould certainlydominate follows that of massive stars, as confirmed by the mapping of
the1809keVdecayemission(Plüschkeetal.2001)anditscor-
theGalactichigh-energyorradioemission,atleastovercertain
relation with the microwave free-free emission from HII re-
energy ranges. Although current models of the Galactic high-
gions or the infrared emission from heated dust (Knödlseder
energyand radio emission can probablyaccommodatea popu-
etal.1999).TheGalacticmassdistributionof26Alinferredfrom
lationofhigh-energypositronsinadditiontoconventionalcos-
the1809keVemissionisstronglyconcentratedatgalactocentric
micraysfromsupernovaremnants,itseemsimprobablethatthis
radii 3 to 6kpc, at the position of the so-called molecular ring
additionalcomponenthavesimilarinjectionenergiesandaflux
anorderofmagnitudehigher.Moreover,theverydifferentmor- (Martin et al. 2009). The injection sites of 26Al positrons are
thusexpectedtobedistributedinanannulardiskandalongspi-
phologiesof the 511keV and ∼10MeV−100GeV skies do not
ralarms(suchasthethindiskandspiralarmscomponentsthat
seem to support a high initial energy for positrons, since they
representthe contributionof localised HII regionssurrounding
wouldfirsthaveto lose theirhighinitialenergiesmostlyin the
massivestarsintheNE2001modelfortheGalacticdistribution
disk and ultimately annihilate in a very narrow region in the
offreeelectronsbyCordes&Lazio2002).
Galacticbulge.
Because of the long lifetime of 26Al, positrons are very
likely injected into the ISM with their original, unaltered
4. Positronsources β-spectrum. The latter is described by the formula given in
Positronsarenaturallycreatedintheβ+-decayofsomeunstable Cofha∼n0.&4MLeinVgeannfdelaterm(a1x9i9m3u,mheorefa1ft.e2rMCeLV9.3W) eanndohteashearemtehaant
proton-richnuclei.Themainspeciesanticipatedtosignificantly
contributetothepositronproductionthroughβ+-decayare26Al, most26Alpositronsareverylikelyreleasedinthehot,tenuous,
andhighlyturbulentinteriorsofthesuperbubblesblownbymas-
56Ni and 44Ti (22Na may also bring some contribution, but we
sivestarclusters.Intheseconditions,relativisticpositronsmay
willnotconsiderithere;seePrantzos2004).Nucleosynthesisis
well experience stochastic, second-order Fermi acceleration in
oftentakenasthemostplausibleoriginfortheGalacticpositrons
thestrongMHDturbulence,orevenregular,first-orderFermiac-
becausetheexistenceanddecayoftheabove-mentionedspecies celerationinthemanyprimary/secondaryshocksthattravelthe
canbeestablishedfromvariousexperimentalresults.Themost
bubbles. This could significantly modify the initial β-spectrum
direct evidence comes from observations of the characteristic
and bring positrons to higher energies, which could increase
gamma-raylinesorfluorescenceX-raylinesthataccompanythe theirrangeandmovetheirannihilationsitesfurther.Thiseffect
decayoftheabove-mentionedisotopes(seeforinstanceRenaud
is, however,beyondthe scopethe presentpaperand wouldde-
et al. 2006; Leising & Share 1990). Then, indirect proof can
serveadedicatedstudy.
be obtained from the interpretation of supernovae lightcurves,
The total injection rate of 26Al positrons can be computed
which are powered by the energetic decay products of 56Ni
and44Ti,orfromthemeasurementofpresent-daycosmicabun- from the estimated total stationary 26Al mass of 1.7−2.7M(cid:7)
in the Galaxy (Martin et al. 2009; Wang et al. 2009), where
dancesofthedaughternuclei,whichresultfromthecumulated
the uncertaintyon the total Galactic 26Al mass arises from un-
nucleosynthesis history of the Galaxy (Motizuki & Kumagai
certainties on the exact spatial distribution of the isotope in
2004; The et al. 2006). The isotope production yields inferred
from these various observations would actually be sufficient the Galaxy. Taking into account a β+-decay branching ratio
to provide after β+-decay the estimated ∼1043 e+/s that power of 0.82, this translates into a 26Al positron injection rate of
thediffuseannihilationemissionobservedbyINTEGRAL.Yet, (0.20−0.31)×1043e+/s.
as we will see below, these yields cannot be straightforwardly
translated into a Galactic positron injection rate because all 44
4.2.The Tiradio-isotope
positronsdonotnecessarilyescapetheproductionsitesoftheir
parentradio-isotopes. The44TiisotopeissynthesisedbyexplosiveSi-burningdeepin
In the following, we present the properties of the thestellarejectaduringcore-collapseandthermonuclearsuper-
positrons produced by the decay of the three above-mentioned nova explosions (ccSNe and SNe Ia respectively),with typical
A3,page4of15
P.Martinetal.:Galacticannihilationemissionfromnucleosynthesispositrons
yields of a few 10−4−10−5M(cid:7) per event. The mean 44Ti life- that Zirakashvili & Aharonian (2011) considered the possibil-
timeisabout85yr,whichimpliesthattheradio-isotoperemains ity that positrons from the 44Ti decay chain constitute a pool
trappedintheyoungsupernovaremnantuntilitdecaysinto44Sc of mildly relativistic particles that can be accelerated to ultra-
andthen44Ca.Most44Tipositronsarethereforereleasedinthe relativisticenergiesin theremnantsof supernovaexplosionsof
envelope of the exploded star and their further transfer to the all types. In their model, the ∼1MeV positrons from 44Sc de-
ISMdependsontheunknowntransportconditionsintheejecta cayundergostochasticpre-accelerationupto ∼100MeVin the
and on the explosion properties. This must be taken into ac- turbulentupstreamregionofthereverseshock,andarethenfur-
count when translating 44Ti yields into positron injection rates theraccelerateduptomulti-TeVenergiesbythediffusiveshock
(seebelow). acceleration mechanism at the shock. This effect is, however,
The injection sites of 44Ti positrons sample the time- beyondthescopethepresentpaper.
averaged distribution of supernova explosions in our Galaxy. The total injection rate of 44Ti positrons can be computed
Core-collapse supernovae proceed from massive stars and are from the frequenciesof ccSNe and SNe Ia, and the 44Ti yields
thusdistributedlikethem,inathinannulardiskandalongspiral and positron escape fractions for each type of event. From
arms(seeSect.4.1).Thermonuclearsupernovaehaveaslightly Tammann et al. (1994),ccSNe are estimated to occur at a rate
moresubtle evolutionarypathwayandactually dependon both ∼2.1 ccSNe/century while SNe Ia occur at a rate ∼0.4 SNe
the old and young stellar populations. Sullivan et al. (2006) Ia/century. Using the empirical relation from Sullivan et al.
showed from observations of external galaxies that the rate of (2006), on which we based the spatial distribution of SNe Ia,
SNe Ia depends on both the star formation rate and the total theoccurrencerateofSNeIais
stellar mass5. The spatial distribution of SNe Ia is therefore a
R = M ×(5.3±1.1)×10−14yr−1 M−1
combination of that of massive stars and that of stellar mass. SNIa (cid:3) (cid:7)
In our Galaxy, most of the stellar mass is distributed in an ex- +SFR×(3.9±0.7)×10−4yr−1(M(cid:7)yr−1)−1 (1)
ponential disk with a central hole and in a ellipsoidal bulge,
with approximately the same mass in each component: 2.15 we also find a rate of ∼0.4 SNe Ia/century if we take a total
and 2.03 × 1010M(cid:7), respectively (see the determinationof the starformationrateSFR = 4M(cid:7)yr−1 (Diehletal.2006)andthe
three-dimensionalshapesandparametersinRobinetal.2003). above-mentionedtotalstellarmassM(cid:3) =(2.15+2.03)×1010M(cid:7)
Overall,thesourcedistributionfor44Tipositronshasthreecom- (Robinetal.2003).Then,astarformationrateof4M(cid:7)yr−1cor-
ponents:athinannulardisk(forccSNeandpromptSNeIa),and respondsto∼2.1ccSNe/centuryfora typicalinitialmassfunc-
an exponential disk with central hole and a bulge (for delayed tion(seeTable1inDiehletal.2006).Regardingthe44Tiyields
SNe Ia).Furtherdown,we quantifythe relativecontributionof of supernovae,observationalestimates are veryscarce (two di-
eachcomponenttothetotalsourceterm. rect detections, Cassiopeia A and G1.9+0.3, and one indirect,
Because oftheintermediatelifetimeof44Ti, thepopulation SN1987A; see Renaud et al. 2006; Borkowski et al. 2010;
ofdecaypositronsenteringtheISMmaybeaffectedbythees- Motizuki & Kumagai 2004), so it is risky to compute some
averageGalactic 44Ti productionrate by integratingtheoretical
cape from the stellar ejecta. Martin et al. (2010) computed the
escape or survival fractions of 44Ti positrons for two extreme yieldsoverarangeofsupernovaprogenitors.Instead,wesimply
transportmodesintheejecta:eitherpositronscanfreelystream assumedthatccSNeandSNeIaejectonaverage2.0×10−4M(cid:7)
through the stellar envelope, or they are trapped at their birth and 2.0× 10−5M(cid:7) per event, respectively. These values agree
withthecompilationofobservationalconstraintsdoneinMartin
place by some strong magnetic turbulence. In the free stream-
etal.(2010)andwiththerecently-estimatedrangeforG1.9+0.3
ingcase,theescapefractionsarequitehigh,rangingfrom97%
(Borkowski et al. 2010). Overall, this corresponds to a mean
finorthlieghttra2ppMe(cid:7)d ecjaescet,atthoe8s3u%rvivfoarl mfraocrteiomnsasasriveelo1w4eMr,(cid:7)raenjegcitnag; Galactic44Tiproductionrateof4.2×10−6M(cid:7)yr−1,roughlycon-
from 91% to 36% for the same mass range (assuming in both sistent with the estimate of 5.5 × 10−6M(cid:7)yr−1 by The et al.
cases a typical 1051erg explosion kinetic energy)6. Although (2006) based on the present-day solar 44Ca abundance and a
44Tipositronsdosufferenergylossesontheirwayoutofthestel- Galacticchemicalevolutionmodel.This44Tiproductionratecan
larejecta,themeanenergyoftheescaping/survivingpopulation betranslatedintoapositronproductionratebyapplyingafactor
0.94fortheβ+-decaybranchingratioofthedecaychainandus-
remainsclosetotheinitialone,whateverthetransportmode.So
most 44Ti positrons are injected into the ISM with a spectrum inganescapefractionof100%.Intheabsenceofstrongobserva-
tionalconstraints,thelattervaluewaschosenbecausetheescape
close to the original, unaltered β-spectrum, which has a mean
of ∼0.6MeV and a maximum of 1.5MeV. We note, however, fractioninmodelsis≥50%formostejectamasses,explosionen-
ergies,andtransportconditions,sousing100%givesthecorrect
order of magnitude and allows an easy scaling of the results.
5 Ascenariobasedonlyonstellarmass,thatisontheolderandlower- Eventually, the 44Ti positron injection rate is 0.34× 1043 e+/s
massstarpopulation,isruledoutat>99%confidencelevel.
(with only ∼2% being contributed by SNe Ia), and we con-
6 Theseestimatesfor theescape fractionsareconsistent withthere-
sider an uncertainty range of ±50% due to the uncertainty on
sults obtained by CL93, except for the 14M(cid:7) ejecta mass, for which theGalactic44Tiproductionrate7.
theyfoundasurvivalfractionof8%onlyinthetrappedcase.Theori-
ginofthediscrepancymaylieintheapproximationtheyusedintheir
calculation, while Martin et al. (2010) performed the complete inte- 4.3.The56Niradio-isotope
gration over time and energy. Another difference between both stud-
ies is that CL93 added a so-called slow positron survival fraction for The 56Ni isotope is synthesised by explosive Si-burning deep
positronsthatarethermalisedbutdonotannihilateinthecontinuously- in the stellar ejecta during core-collapse and thermonuclear
thinningejecta.Yet,intheejectaassumedtobeneutral,thedominant
annihilationprocessispositroniumformation,whichoccursovercom- 7 InTheetal.(2006),theauthorsfounda∼2timeslargeruncertainty
parativelyveryshorttimescalesoncepositronshavebeensloweddown rangefortheGalactic44Tiproductionrateduetounknownparameters
below ∼100eV. So if neutral atoms are indeed the dominant species in the Galactic chemical evolution model; they also note that the en-
intherapidly-coolingejecta,nomorethanafew%ofthethermalised tirerangemaybeshiftedtolower valuesifthereisanucleosynthesis
positronsareexpectedtosurvive. channeltoproduce44Cadirectly.
A3,page5of15
A&A543,A3(2012)
supernovaexplosions,withtypicalyieldsoftheorderof10−1M(cid:7) availableonGalacticcosmicrays(directparticlemeasurements,
perevent.Thecharacteristictimeofthedecaychainto56Coand diffuseemissionsinradioandathighenergies).Nevertheless,it
thento56Feis<1yr,whichimpliesthatallpositronsarereleased isgeneralenoughtobeadaptedtootherstudiesofparticletrans-
inthestellar ejectaatthelatesupernova/earlyremnantphase. portintheGalaxy.
This makes escape a critical point, which actually counterbal- In the following, we briefly review the constituents of the
ancesthelarge56Niyields. GALPROPmodelthatarerelevanttothestudyofnucleosynthe-
Although 56Ni is produced by both ccSNe and SNe Ia, sispositrons.Wealsointroducethemodificationsimplemented
we will see below that SNe Ia are expected to dominate over tosimulate thepropagationandannihilationofpositronsin the
ccSNe in terms of contribution to the Galactic positron popu- Galaxy.
lation throughthat isotope.Consequently,the injection sites of
56Ni positrons follow the time-averaged distribution of SNe Ia
5.1.Transportprocesses
inourGalaxy.Thesourcedistributionhasthreecomponentslike
thatof44Tipositrons–athinannulardisk,anexponentialdisk, GALPROP numerically solves a general diffusion-convection
and a bulge – but the relative contribution of each component equation for a given source distribution. The transport mech-
to the total positron productionrate is different, as we will see anisms included in the code are diffusion in position and
below. momentum, convection away from the plane and the associ-
Becauseoftheshorttimescaleofthe56Nidecaychain,the atedadiabaticcooling,momentumlossesfrommanyprocesses,
population of decay positrons eventually entering the ISM is radioactive decay, and nuclear fragmentation. The equation is
strongly affected by the travel through the stellar ejecta. The solved using a Crank-Nicholsonimplicit second-orderscheme,
escape of 56Ni positrons is favoured by ejecta mixing, which with free particle escape assumed at the spatial boundaries.
liftsironuptothelower-densityejectasurface,andbylowcon- A typical simulation is run for decreasing time steps until a
finement, which decreases the column density experienced by steadystate isachievedforallspeciesovertheentirecomputa-
positronsin the ejecta. Modelsexploringthese effects result in tionalgrid.Thepresentmodellingofpositronpropagationinthe
escapefractionsupto∼10%forSNeIa,whileescapefractions Galaxyincludesdiffusionin positionand energylosses, butno
for ccSNe reach a few % only for the light and rare type Ib/Ic convectionordiffusivereacceleration(andofcoursenonuclear
explosionsand in the limiting case of a fully mixedejecta (see process).
for instance CL93). The comparison of such predictions with Byconstruction,thetransportinpositionspaceistreatedas
thelatelightcurvesofSNeIaindicatesanescapefractioninthe adiffusiveprocessandwewillexplaininSect.6.2howthiscan
range ∼2−6% (Milne et al. 1999, but see also the warning of be justified for the cases we considered.We modified the code
Lair et al. 2006). Alternatively, Martin et al. (2010) translated to allow the simulation of inhomogeneous diffusion (with dif-
the non-detection of 511keV emission from the youngest and ferent properties in the bulge and in the disk for instance). To
mostnearbysupernovaremnantsinto an upperlimit on the es- avoidpotentialproblemsarisingfromdiscontinuitiesinthegrid
cape fraction of 12% for SNe Ia. Overall, SNe Ia are thought ofdiffusioncoefficients,weimplementedsmoothtransitionsbe-
to be the dominantsource of 56Ni positronswhen comparedto tweenregionswith differentdiffusionproperties.Inthecase of
ccSNe:theirloweroccurrencerate(0.4versus2.1SNe/century) a more efficient positron diffusion in the disk compared to the
is compensatedby their higheriron yield per event(0.6versus bulge(see Sect. 6.2),the diffusioncoefficientis describedbya
0.1M(cid:7),typically),andtheiraveragepositronescapefractionis Gaussian-type function having its lowest value at the Galactic
verylikelyoneorderofmagnitudehigher.Duetothestrongen- centreand reachingits highestvaluebeyonda certain scale ra-
ergylossesexperiencedinthefreshanddenseejectaofSNeIa, diusandheightabovetheplane.
escaping/surviving56Nipositronsverylikelyhaveaspectraldis- Regardingthetransportinmomentumspace,GALPROPin-
tribution that differs from the original β-spectrum. Depending cludes the main energyloss processes for high-energycharged
ontheactualmixinganddensityprofileoftheejecta,themean particles, such as Bremsstrahlung, inverse-Compton, and syn-
kinetic energy of the positron population may be shifted from chrotron, but the dominant one in the keV−MeV range
∼0.6MeV at decay to ∼0.3MeV or even below when entering are Coulomb interactions and ionisation/excitation of atoms.
the ISM (see Fig. 4 of CL93).We will discusslater on the im- Ionisation/excitationareimplementedfollowingtheprescription
pactofthiseffectonthepredictedannihilationemission. ofPagesetal.(1972),basedonBethe’stheoreticalformula,with
Withthepreviously-adoptedSNIaoccurrencerateof0.4per experimental values for the ionisation potentials of neutral H
century and a typical 56Ni yields of 0.6M(cid:7), the total positron andHe,andwithoutcorrectionforthedensityeffect.Coulomb
injection rate can be computed by taking into account a fac- losses are implemented following the prescription of Ginzburg
tor of 0.19for the β+-decaybranchingratio of the decaychain (1979)forthecoldplasmalimit.Asnotedbelow,wealsoimple-
and assuming an escape fraction of 5%. This corresponds to a menteddirectin-flightannihilationinthecode.Thisconstitutes
56Nipositroninjectionrateis1.53×1043e+/s.Yet,thepositron an additional catastrophic loss process, but its contribution for
escape fraction is a crucial parameter that is not strongly con- MeVpositronsisinsignificant.
strainedbyobservations.Wethereforeconsideredanuncertainty
Overall, the transport equation solved for positron propa-
range of one order of magnitude for this factor, for a range
gation in the Galaxy (until a steady state is achieved) is the
of 1 to 10%. This translates into an uncertainty range on the
following
56Nipositroninjectionrateof(0.31−3.10)×1043e+/s.
(cid:2) (cid:3)
∂ϕ ∂
=∇(D∇ϕ)− ϕE˙ +Q (2)
5. Thetransportcode ∂t ∂Ep p
ThepropagationofpositronsintheGalaxywasmodelledwitha whereϕisthepositrondistributionfunction,Disthespatialdif-
modifiedversionofthepublicly-availableGALPROPcode(see fusion coefficient, E˙ is the positron energy loss rate, and Q is
p
http://galprop.stanford.edu). The code was originally the source term. All these quantities depend on position r and
createdtoanalyseinaconsistentwaythegrowingbodyofdata positron energy E . The equation does not contain an explicit
p
A3,page6of15
P.Martinetal.:Galacticannihilationemissionfromnucleosynthesispositrons
Table1.Bulge,disk,andtotalannihilationradiationluminositiesfor56Ni,44Ti,and26Alpositronsinthethreetransportconfigurationstested.
Source Transport Bulge(R≤3kpc) Disk(R>3kpc) TotalGalaxy Bulge/Diskratio Annihilationfraction
A 0.32 0.58 0.91 0.56 1.00
56Nionly
B 0.16 0.47 0.63 0.35 0.68
C 0.09 0.39 0.48 0.22 0.57
A 0.01 0.18 0.20 0.08 1.00
44Tionly
B 0.01 0.11 0.12 0.10 0.63
C 0.01 0.10 0.11 0.06 0.59
A 0.01 0.13 0.14 0.08 1.00
26Alonly
B 0.01 0.10 0.11 0.09 0.77
C 0.01 0.09 0.10 0.07 0.73
A 0.35 0.90 1.25 0.39 1.00
56Ni+44Ti+26Al
B 0.18 0.68 0.86 0.27 0.69
C 0.10 0.59 0.69 0.17 0.56
Notes. Alsoindicated arethecorresponding bulge-to-disk ratios, and the fractionsof positrons that annihilate inthe Galaxy. Theluminosities
inCols.3to5aregiven in1043phs−1 for themeanpositron injectionratesdeterminedinSect.4.Theycorrespond to511keV emissionfrom
parapositroniumanddirectannihilation,forapositroniumfraction f =0.95.
Ps
term for annihilation. As we will see below in Sect. 5.3, the volume and has a very extended distribution across the plane.
annihilation rate is computed at each position from the rate of The GALPROP code uses a two-componentmodelfor the HII
positronsbeingsloweddownbelow∼100eV. distribution:athindisktracinglocalisedHIIregionsintheplane,
mostly in the molecular ring and spiral arms, and a thick disk
representingthe morediffuse warm ionised gasthatexists out-
5.2.Interstellarmedium
side the well-defined HII regions. The former is modelled by
GALPROP includes average analytical spatial distributions for the 2D/axisymetric thin disk componentof the NE2001 model
the main gas states: molecular (H ), atomic (HI), and ionised (Cordes&Lazio2002),whilethe latterismodelledbya verti-
2
(HII). These distributions are used in the computation of the calexponentialdistributionwiththescaleheightdeterminedby
propagationofcosmic-raysthroughouttheGalaxy,forthedeter- Gaensleretal.(2008).
minationofenergylossesforinstance.Then,fortheprediction
ofdiffuseemissionsfromcosmicraysinteractingwithinterstel-
5.3.Annihilation
lar gas (such as Bremsstrahlung or π0 production and decay),
GALPROPallowstorecoverthefinespatialstructureofthegas Initspublicly-availableversion,GALPROPdoesnotincludean-
through the use of the observed gas column densities (in the nihilationprocesses.AsexplainedinSect.2.1,positronscanan-
HI 21cm and CO 2.6mm emission lines). In our simulations nihilate with electrons through a variety of processes, the rel-
oftheannihilationemission,however,weusedonlytheanalyti- ative importance of which depend on the characteristics of the
calgasdistributionsbecausetheobservationalconstraintsatour medium where the annihilation takes place. Yet, GALPROP
disposal,comingmostlyfromINTEGRAL/SPI,haveanangular does not include a fine description of the ISM at the typical
resolutionseveraltimesabovethatofHIorCOsurveys. scales of the variousgasphases, butonly the averagedandax-
Atomic hydrogenis the dominantgasphase in termsof to- isymetricgasdistributionsdescribedabove.Atagivenposition
talmassandhasarelativelylargefillingfactor.TheGALPROP in the space grid, the annihilation of positrons could not occur
code uses a 2D analyticaldistributionfor HI. The radialdistri- inadefinite,well-identifiedphasebutinanaveragemediumre-
butionistakenfromGordon&Burton(1976),whilethevertical sultingfromthesuperpositionofthelarge-scaledistributionsof
distribution is from Dickey & Lockman (1990) for 0 ≤ R ≤ molecular,atomicandionisedgas.
8kpcandCoxetal.(1986)forR ≥ 10kpc,withlinearinterpo- Weimplementedpositronannihilationinthefollowingway:
lationbetweenthetworanges. therateofpositronannihilationatagivenpositionintheGalaxy
Moleculargasaccountsforaboutathirdofthetotalgasmass is based on the rate of positrons being slowed down below
oftheMilkyWay,butitisconcentratedincomplexesofdense, ∼100eV, that is the energy below which positrons may expe-
massive clouds with low filling factors. The GALPROP code riencechargeexchangein-flight.Theoretically,thisappliesonly
employs a 2D analytical distribution for H , using the model totheneutralphasesbecauseinionisedphasespositronsformPs
2
from Ferrière et al. (2007) for R ≤ 1.5kpc, the model from byradiativerecombinationorannihilatedirectlyaftercomplete
Bronfmanetal.(1988)for1.5kpc<R<10kpc,andthemodel thermalisation. In the warm ionised phase, the thermalisation
fromWouterlootetal.(1990)forR≥10kpc. from100eV energiesandthesubsequentannihilationoccuron
The ionised hydrogen makes up about 10% of the total shorttimescalescomparedtotheslowing-down,solimitingthe
gas mass of the Milky Way and is therefore the least mas- modellingto ≥100eV energieshasnoconsequencesonourre-
sive component. Yet, It actually occupies most of the Galactic sults. In the hot phase, however, the thermal or near-thermal
A3,page7of15
A&A543,A3(2012)
positrons have long lifetimes owing to the very low density. 6.1.Sourcesparameters
In the disk, these positronsare thus expected to be transported
Inthissection,wepresentthe2Dsourcespatialdistributionsthat
outof the hot cavities, verylikely by strong turbulence,and to
wereadoptedforthedifferentpositronsource.WesawinSect.4
annihilate in the denser surrounding phases (Jean et al. 2006,
2009). This happens on time scales ≤1Myr, of the order of that the injection sites of radioactivity positrons follow a spa-
tialdistributionintheGalaxythathasthreecomponents:astar-
theslowingdowntime,andsoonceagainlimitingourselvesto
≥100eV energies will not strongly alter the results (especially formingdiskconsistingofanannulusandspiralarms(forparent
isotopescomingfrommassivestars,theirccSNe,andalsofrom
since the cell size in our spatial grid is larger than the typical
sizeofhotcavities,∼100pc). promptSNe Ia), togetherwith an exponentialdisk with central
holeandanellipsoidalbulgecontainingmostofthestellarmass
Thecorrespondingpositronannihilationemissivityqforpo-
(forparentisotopescomingfromdelayedSNeIa).
sitionrandphotonenergyE reads
γ Forthestar-formingdisk,weusedtheazimuthally-averaged
(cid:4) (cid:5) radial profile of the Galactic star formation rate determinedby
s(E , f )
q(r,E )= γ Ps ϕ(r,E )E˙ (r,E ) (3) Boissier&Prantzos(1999);sincemassivestarshaveshortlife-
γ 4π p p p 100eV
timesofafewMyr,theirdistributionandthatofccSNeclosely
where f isthePsfraction,andthe s(E , f )functiongivesthe followsthatofthestarformingactivity.Theverticalprofilewas
Ps γ Ps
spectraldistributionoftheradiation.Yet,sincewedonottrack assumedtobeexponentialwithascaleheightof200pc.
the annihilation in individual ISM phases, we cannot directly Thestellarmassdiskandbulgecomponentsweremodelled
modelthe annihilationspectrumoverthe Galaxy.We therefore bythefunctions:
fixedthespectralcharacteristicsoftheannihilationradiation:the (cid:6) (cid:7)
Ps fraction was taken to be fPs = 0.95, the 511keV line was fD(r,z)=nD,0× e−RDr,h −e−RDr,c ×e−ZD|z|,h (4)
assumed to have a Gaussian shape and a width of 6keV, and (cid:8) (cid:9)
the Ps continuum was described by the Ore & Powell (1949) −1 r2 + z2
formula.We thenfocusedon the intensity distributionoverthe fB(r<RB,c,z)=nB,0×e 2 R2B,h ZB2,h (5)
(cid:8) (cid:9)
sky,whichisobtainedbyintegratingtheaboveemissivityalong
−1 r2 + z2
theline-of-sightforeachdirectiontothesky8. fB(r≥RB,c,z)=nB,0×e 2 R2B,h ZB2,h ×e−12(r−RB,c)2 (6)
WealsoimplementedinourversionoftheGALPROPcode
the process of direct in-flight annihilation. In that case, it was where(r,z)aretheGalactocentricdistanceandtheheightabove
implementedwithitscompletedifferentialcross-sectionbecause theGalacticplaneandtheindicesD/Bstandfordiskandbulge,
itdependsonlyontheboundandfreeelectrondensity.However, respectively.Theseformulaapproximatetheusualprescriptions
we do notinsist on that aspectbecause in-flightannihilationis for the stellar disk and bulge shapes (see for instance Robin
negligibleforMeVpositrons. etal.2003).EachcomponentD/Bisdescribedby1densitynor-
malisationfactorn and3geometricalparameters(R ,Z ,R ):a
0 h h c
scaleradiusandheight,acutoffradius.Weadoptedthefollow-
6. Simulationsetups ingtriplets:(2.5,0.3,1.3)forthedisk,and(1.6,0.4,2.5)forthe
bulge, in units of kpc. The normalisation factors are computed
Thenumericalmodeldescribedaboveallowedustosimulatethe
fromthedatagiveninSect.4foreachparentradio-isotope.
propagationofnucleosynthesispositronsandcomputetheiran-
nihilationemissionfortheentireGalacticsysteminaclearand
consistent way. The predicted annihilation emissions basically 6.2.Diffusionparameters
relyontwoinputs:thesourcespatialdistributionandtheprop-
The recent theoretical studies reviewed in Sect. 2.2 could not
agationparameters.Thesourcedistributionswereconsideredto
conclusivelydetermineif the transportof low-energypositrons
bemorefirmlyestablishedthanthe transportconditions,sowe
isballisticorcollisionless.Strongargumentswerepresentedin
fixedthesourcespatialparameterstothevaluesgiveninSects.4
favourofaballistictransport,inparticularintheneutralphases,
and 6.1 and exploredhow the annihilation emission vary upon
differentprescriptionsforthetransport. but these conclusionsare not yet backedby solid experimental
evidence.We thereforetested two extremetransportconfigura-
All simulations presented in this paper were made in
tionsinthediffusionapproximation,withsmallandlargecoef-
2D cylindrical geometry. The spatial grid extends from 0
ficientscorrespondingtocollisionlessandballistictransport,re-
to20kpcinGalactocentricradiusr,witha stepsize of250pc,
and from −4 to 4kpc in Galactic height z, with a step size of spectively.Thisallowedustoassesstheimpactontheresulting
annihilationemission.Inaddition,wesimulatedanintermediate
100pc. This implies that the Galactic halo extends up to 4kpc
case of inhomogeneous diffusion, where the transport was as-
oneithersideonthe Galacticplane.Thespatialboundarycon-
sumed to be collisionless in the Galactic bulge and ballistic in
ditions at the edges of the spatial domain assume free particle
theGalacticdisk.Below,wepresentthesetransportscenariosin
escape,whichmeansthattheultimatefateofpositronsiseither
moredetail,includingthediffusioncoefficientsusedinthecode.
to annihilatein thedisk or haloif theyare slowed downbelow
100eV, or to escape if they diffuse far enough. The resolution We recallhere thatGALPROP doesnotincludea fine descrip-
of our space grid corresponds to ∼1−2◦ at the distance of the tionoftheISMwithdistinctphases,andsodiffusionshouldbe
implementedwith average propertiesover a few 100pc scales.
Galacticcentre,whichisaboutthesizeofthestrongestpeakin
In addition,we assumed in all cases an isotropic diffusion, but
the511keVsignal.Theenergygridrunsfrom100eVto2MeV
anisotropiesmaywellexistfordiffusionalongtheGalacticplane
onalogarithmicscale,with156energybins.
and off that plane towards the halo, or along spiral arms and
acrossthem.
8 Note that our results can be rescaled to any other Ps fraction than
the f = 0.95adopted:forinstance,the511keVintensitiespresented Case A: We tested the scenario of a collisionless transport
Ps
herecanbeconverted tothecaseofadifferent Psfractiong aftera with homogeneous properties over the whole Galaxy. For the
Ps
multiplicationby(1−0.75g )/(1−0.75f ). ionised phases of the ISM, this option actually remains partly
Ps Ps
A3,page8of15
P.Martinetal.:Galacticannihilationemissionfromnucleosynthesispositrons
open in the work of JGMF09 and is invoked in HLR09 (see the ISM phase. In this situation, ∼MeV positrons have large
Sect. 2.2). As a limiting case, we assumed that it holds for meanfreepathsofseveralkpcintermsofpitchanglescattering.
all ISM phases over the entire Galaxy. In this scenario, we Onsmallscales,thetransportisanisotropicandpositronsfollow
implicitly assumed the existence everywhere in the Galaxy of magneticfieldlinesinaballisticmotion.Onlargerscales,how-
MHDturbulencewithasufficientenergydensityintherequired ever,weexpectanisotropizationofthetransportbystrongran-
wavelengthrange,sothatlow-energypositronscanbeefficiently domfluctuationsoftheGalacticmagneticfieldontypicalscales
scattered. The corresponding random walk process was then ∼100pc (an argumentthatis commonlyinvokedin cosmic-ray
treated in the diffusion approximation with a coefficient of the studies;seeforinstancePtuskinetal.2006).Intheballisticsce-
form: nario,wethereforeapproximatethetransportbyadiffusionwith
(cid:8) (cid:9) acharacteristicmeanfreepathL ,thelargestscaleofmagnetic
D (R)=βD R δ (7) fluctuations.ThecoefficientthenBtakestheform
w 0 R
0 1
(cid:6) R (cid:7)0.33 Dc(R)= βcLB (9)
D (R)= 3.7×1027cm2s−1×β (8) 3 (cid:8) (cid:9)
w
1MV L
D (R)= 3.1×1030cm2s−1×β B · (10)
where R = p/e is the rigidity of the particle and β = v/c. The c 100pc
adoptednormalisationfactor D aswellas the spectralindexδ
0 In this case, the diffusion coefficient has a very modest rigid-
are taken from cosmic-ray propagation studies interpreting lo-
cal cosmic-ray measurements at ∼1−100GeV in the frame of ity/energydependencedown to a few 10keV, and the range of
particlesis thereforeimposed by the energydependenceof the
a Galactic cosmic-ray propagation model. The spectral depen-
dence of the diffusion coefficient is assumed to hold down to slowing-downprocesses.Weassumedthatdiffusionishomoge-
∼MeVenergies,whichsofarremainsunproven(seeSect.2.2). neousovertheGalacticvolume,whichisequivalenttoassuming
On the other hand, the resulting diffusion coefficient is small that large-scale magnetic turbulence is homogeneous over the
enough that the typical range of a MeV positron in a 1cm−3 Galaxy.
densitymediumisoforder∼10pc,meaningthatnucleosynthe-
sis positrons annihilate close to their sources (technically, they 7. Theresults
hardly escape the cell where they were injected). We assumed
thatdiffusionishomogeneousovertheGalacticvolume,which In this section, we present the predicted Galactic annihilation
isequivalenttoassumingthatthecharacteristicsofmagnetictur- emissionof26Al,44Ti,and56Nipositrons,forthevarioustrans-
bulencearehomogeneousovertheGalaxy. port configurations considered. We compare these to one of
Case B: We then tested an intermediate, inhomogeneous thelatestmodelsoftheallsky511keVemissionobtainedfrom
transport scenario, where the transport is collisionless in the INTEGRAL/SPI observations. Last, we discuss our results in
Galactic bulge and ballistic elsewhere, notably in the Galactic lightofotherrecenttheoreticalstudies.
disk.ThelimitbetweenthetworegionsissetataGalactocentric
radiusofabout3kpc.Theformofthediffusioncoefficientinthe
7.1.Predictedintensitydistributions
ballisticcaseisgivenbelow.Thisscenarioactuallyismotivated
bytheobservationthatthebulgeandthediskhavedifferentISM We present in Figs. 2–4 the 511keV intensity distributions
compositions:thebulgeislargelydominatedbythehotionised obtained in each transport configuration for 26Al, 44Ti, and
phase,whilethediskismostlyfilledwithneutralgas.Estimates 56Ni positrons, respectively. To facilitate the comparison, each
forthefillingfactorsofthewarmneutralmedium,warmionised skymap shows the parapositronium annihilation only, for a
medium, and hot medium are respectively (0.2,0.1,0.7) for positroniumfractionof0.95andatotalGalacticpositroninjec-
the bulge and (0.5,0.3,0.2) for the disk, while the molecular tion rate of 1043 e+/s, of the same order as that inferred from
medium and cold neutral medium occupy comparatively neg- observations.Toemphasisethetrendsanddifferences,weshow
ligible volumes (Jean et al. 2006; Higdon et al. 2009). From in Fig. 6 the longitudeprofilesfor each skymap.To help inter-
Sect.2.2,thisdifferencemayimplythatpositronswouldbemore pretingtheseresults,welistinTable1theannihilationfraction
efficiently confinedin the bulge by small-scale MHD waves in andthe annihilationluminositiesforthe bulge,disk, andentire
thepredominantionisedphases,whiletheywouldstreammore Galaxy.
easily in the disk where damping mechanisms prevent small- Forasametransportscenario,theskymapslookprettysimi-
scale MHDperturbationsinthe predominantneutralphases.In lar:theintensityishighestintheinnerGalaxyandprogressively
reality,large-scalediffusionpropertiesoverafew100pcscales fades away with increasing longitude until it has dropped by
reflecttheactualISMcompositionineachGalacticregion(like about an order of magnitude in the outer Galaxy. The impact
thefactthattheionisedphasesofthediskoccupy50%ofthevol- of the transportscenario onthe resultingintensity distributions
umeandthuswouldmoderatetheeasierstreamingexperienced remainslimiteddespitevaryingthediffusioncoefficientbythree
in the neutral phases). In our simulations, however,we pushed ordersofmagnitude.
the contrast between bulge and disk to the maximum and set Inthefullycollisionlessscenario,positronshaveveryshort
theformertobefullycollisionlessandthelattertobefullybal- rangesandthey all annihilateclose to their injection sites. The
listic.Thischoiceclearlyisbiasedtowardsreproducingthehigh intensity distributions in that case reflect the source distribu-
observedbulge-to-disk511keVluminosityratio,butwewillsee tions (and are therefore strongly driven by our assumptions
thatevenwiththatassumption,ourpredictionsdonotagreewith aboutthe latter). The normalisedintensity profilesfor 44Ti and
theINTEGRAL/SPIresults. 26Al positrons are almost identical, because they have a simi-
Case C: Last, we tested the scenarioof a ballistic transport larsourcedistributiondominatedbythestar-formingdisk.They
withhomogenouspropertiesoverthewholeGalaxy.Thiscaseis exhibita plateau overthe inner ±30◦ in longitudethat actually
suggestedbythe workofJGMF09,whoconcludedthat∼MeV correspondsto the molecular ring at a Galactocentric radiusof
positronsarelikely notscatteredbyMHD turbulencewhatever ∼4.5kpc. In contrast, the emission from 56Ni positrons peaks
A3,page9of15
A&A543,A3(2012)
Fig.2.Predicted511keVintensitydistributionsfortheannihilationof Fig.3.Predicted511keVintensitydistributionsfortheannihilationof
26Alpositronsineachtransportconfiguration.Fromtoptobottom,the 44Tipositronsineachtransportconfiguration.Fromtoptobottom,the
transport was assumed to be collisionless everywhere (case A, small transport was assumed to be collisionless everywhere (case A, small
diffusion coefficient), collisionless in the bulge and ballistic out of it diffusion coefficient), collisionless in the bulge and ballistic out of it
(caseB,inhomogeneouscase),andballisticeverywhere(caseC,large (caseB,inhomogeneouscase),andballisticeverywhere(caseC,large
diffusioncoefficient).Thegivenintensitiescorrespondtoparapositron- diffusioncoefficient).Thegivenintensitiescorrespondtoparapositron-
iumannihilationonlyandwerenormalisedtoapositroninjectionrate iumannihilationonlyandwerenormalisedtoapositroninjectionrate
of1043e+/s,withapositroniumfractionof0.95. of1043e+/s,withapositroniumfractionof0.95.
attheGalactic centresince56Nipositronsarepreferentiallyre- collisionless scenario can be expected to be representative of
leased in the inner regions. It is interesting to note that when whatisobtainedwhenpositronsareinjectedintotheISMwitha
56Nipositronsareconfinedtothevicinityoftheirsources(sce- muchsmalleraverageenergythanthatoftheiroriginalβ-decay
narioA),theydonotgiverisetoahighly-peaked511keVsignal spectrum, whatever the transport conditions (this is especially
from the inner bulge, resulting for instance from massive an- relevantto56Nipositronsthatmaybeconsiderablyslowed-down
nihilation in the strong concentration of molecular gas in the ontheirwayoutofthestellarejecta).Inthatcase,positronslose
central∼200pc;instead,theyseem toannihilatein amoredis- theirinitially-smallkineticenergyovershortdistancesandthus
tributed fashion over the entire bulge. The results of the fully annihilateclosetotheirsources.
A3,page10of15