The all-sky distribution of 511 keV electron-positron annihilation emission

20 Pages·2005·1.19 MB·English

A&A441,513–532(2005) Astronomy
DOI:10.1051/0004-6361:20042063 &
(cid:1)c ESO2005 Astrophysics
The all-sky distribution of 511 keV electron-positron
(cid:1)
annihilation emission
J.Knödlseder1,P.Jean1,V.Lonjou1,G.Weidenspointner1,N.Guessoum2,W.Gillard1,G.Skinner1,
P.vonBallmoos1,G.Vedrenne1,J.-P.Roques1,S.Schanne3,B.Teegarden4,V.Schönfelder5,andC.Winkler6
1 Centred’ÉtudeSpatialedesRayonnements,CNRS/UPS,BP4346,31028ToulouseCedex4,France
e-mail:[email protected]
2 AmericanUniversityofSharjah,CollegeofArts&Science,PhysicsDepartment,POBox26666,Sharjah,UAE
3 DSM/DAPNIA/SAp,CEASaclay,91191Gif-sur-Yvette,France
4 LaboratoryforHighEnergyAstrophysics,NASA/GoddardSpaceFlightCenter,Greenbelt,MD20771,USA
5 Max-Planck-InstitutfürExtraterrestrischePhysik,Postfach1603,85740Garching,Germany
6 ESA/ESTEC,ScienceOperationsandDataSystemsDivision(SCI-SD),2201AZNoordwijk,TheNetherlands
Received24September2004/Accepted20May2005
Abstract.Wepresentamapof511keVelectron-positronannihilationemission,basedondataaccumulatedwiththeSPIspec-
trometeraboardESA’sINTEGRALgamma-rayobservatory, thatcoversapproximately∼95%ofthecelestialsphere.Within
the exposed sky area, 511 keV line emission is significantly detected towards the galactic bulge region and, at a very low
level,fromthegalacticdisk.Thebulgeemissionishighlysymmetricandiscentredonthegalacticcentrewithanextension
of∼8◦ (FWHM).Theemissionisequallywelldescribedbymodelsthatrepresent thestellarbulgeorhalopopulations. The
detectionsignificance of thebulgeemissionis∼50σ, thatof thegalacticdiskis∼4σ.Thediskmorphology isonlyweakly
constrainedbythepresentdata,beingcompatiblewithboththedistributionofyoungandoldstellarpopulations.The511keV
linefluxfromthebulgeanddiskcomponentsis(1.05±0.06)×10−3phcm−2s−1and(0.7±0.4)×10−3phcm−2s−1,respectively,
correspondingtoabulge-to-diskfluxratiointherange1−3.Assumingapositroniumfractionof f =0.93thistranslatesinto
p
annihilationratesof(1.5±0.1)×1043 s−1and(0.3±0.2)×1043 s−1,respectively.Theratioofthebulgeluminositytothatof
thediskisintherange3−9.Wefindnoevidenceforapoint-likesourceinadditiontothediffuseemission,downtoatypical
fluxlimitof∼10−4 phcm−2s−1.Wealsofindno evidence forthepositivelatitudeenhancement that hasbeenreported from
OSSEmeasurements;our3σupperfluxlimitforthisfeatureis1.5×10−4phcm−2s−1.Thediskemissioncanbeattributedto
theβ+-decayoftheradioactivespecies26Aland44Ti.Thebulgeemissionarisesfromadifferentsourcewhichhasonlyaweak
ornodiskcomponent. Wesuggest thatTypeIasupernovae and/or low-massX-raybinariesaretheprimecandidatesforthe
sourceofthegalacticbulgepositrons.Lightdarkmatterannihilationcouldalsoexplaintheobserved511keVbulgeemission
characteristics.
Keywords.gammarays:observations–line:profiles–Galaxy:center
1. Introduction (Rudaz & Stecker 1988; Boehm et al. 2004), and stars ex-
pelling radioactive nuclei produced by nucleosynthesis, such
Sincethefirstdetection(Johnson&Haymes1973)andthesub-
assupernovae(Clayton1973),hypernovae(Casséetal.2004),
sequentfirmidentification(Leventhaletal.1978)ofthegalac-
novae (Clayton & Hoyle 1974), red giants (Norgaard 1980),
tic 511 keV annihilation line, the origin of galactic positrons
and Wolf-Rayetstars (Dearborn& Blake 1985). Itseems dif-
hasbeenalivelytopicofscientificdebate.Amongtheproposed
ficulttodisentangletheprimarygalacticpositronsourcebased
candidates for sources of positrons figure cosmic-ray interac-
onlyontheoreticalgrounds,mainlyduetothe(highly)uncer-
tions with the interstellar medium (Ramaty et al. 1970), pul-
tain positron yields, but also due to the uncertain distribution
sars (Sturrock 1971), compact objects housing either neutron
anddutycycleofthesourcepopulations.
stars or black holes (Ramaty & Lingenfelter 1979), gamma-
Help is expected from a detailed study of the 511 keV
ray bursts (Lingenfelter & Hueter 1984), (light) dark matter
line emission morphology. The celestial 511 keV intensity
distribution should be tied to the spatial source distribution,
(cid:3) Based on observations with INTEGRAL, an ESA project with
althoughpositrondiffusionandeffectsassociatedwiththean-
instruments and science data centre funded by ESA member states
(especially the PI countries: Denmark, France, Germany, Italy, nihilation physics may to some extent blur this link. First es-
Switzerland, Spain), Czech Republic and Poland, and with the par- timationsofthe511keVemissionmorphologywereobtained
ticipationofRussiaandtheUSA. bytheOrientedScintillationSpectrometerExperiment(OSSE)
Article published by EDP Sciences and available at http://www.edpsciences.org/aaor http://dx.doi.org/10.1051/0004-6361:20042063
514 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission
on-board the Compton Gamma-Ray Observatory (CGRO) 2. Observationsanddatapreparation
satellite (Purcell et al. 1994; Cheng et al. 1997; Purcell et al.
The data that were analysed in this work consist of those in-
1997; Milne et al. 2000; Milne et al. 2001), but observations
cluded in the December 10, 2004 public INTEGRAL data
wererestrictedtotheinnerGalaxy,givingonlyalimitedview
release (i.e. orbital revolutions 19−76, 79−80, 89−122) plus
ofthe511keVemissiondistribution.WiththelaunchofESA’s
the INTEGRAL Science Working Team data of the Vela re-
INTEGRAL satellite in October 2002, a new gamma-ray ob-
gion observed during revolutions 81−88. The data span the
servatory is available that allows a detailed study of positron
IJD epoch 1073.394−1383.573, where IJD is the Julian Date
annihilation signatures. In particular, the imaging spectrome-
minus2451544.5days.
terSPI(Vedrenneetal.2003),oneofthetwoprimeinstruments
We screenedthedata foranomalouslyhighcountingrates
on-boardINTEGRAL,hasbeenoptimisedforthestudyofline
(typicallyoccurringatthebeginningandtheendofanorbital
radiation, combining high-resolution spectroscopy (R ∼ 250
at511keV)withmodestangularresolution(3◦FWHM). revolutiondueto theexitandentryofthe radiationbelts) and
for periods of solar activity (as monitored by the SPI antico-
Wepresentinthisworkanall-skymapof511keVgamma- incidence system) and excluded these periods from the data.
ray lineemission, with thegoalsofdeterminingthemorphol- This data screening has turned out to be crucial for reduc-
ogy of the emission in the Galaxyand of searchingforprevi- ing the systematic uncertaintiesin the data analysis related to
ously unknownsourcesof511keV emission anywherein the instrumental background variations. After data screening, the
sky.Thepresentpublicdataarchivedoesnotyetcovertheen- datasetconsistsof 6821pointedobservations,with a totalex-
tire celestial sphere, but the unexposed regions are limited to posure time of 15.3 Ms. Typical exposure times per pointing
afewareasathighgalacticlatitudes,comprisinglessthan5% are 1200−3400 s, but a few long staring observations of up
ofthesky.Theresultingpoint-sourcesensitivityisbetterthan to113ksexposuretimearealsoincluded.
2×10−4phcm−2s−1formanyregionsalongthegalacticplane, Figure 1 showsa map of the resulting effective SPI expo-
allowing for the first time the extractionof informationabout sure at 511 keV. The maximum exposure of 2.1× 108 cm2s
thedistributionofpositronannihilationallovertheGalaxy.We occurs towards the galactic centre region thanks to data ob-
donotaddressthedistributionofpositroniumcontinuumemis- tained during a long dedicated observation of this region1. A
sion in this paper, since the subtraction of the diffuse galac- relativelyuniformexposureof∼3×107cm2shasbeenachieved
tic continuum emission is a distinct data analysis challenge. forgalacticlongitudes|l|≤50◦andlatitudes|b|≤15◦.Regions
A map of positronium continuum emission will be presented of peculiarly high exposure (∼5 × 107 cm2s) are found in
elsewhere(Weidenspointneretal.,inpreparation). Cygnus,VelaandtowardstheLargeMagellanicCloud.Inad-
dition,particularlywellexposedsources(>∼2×107 cm2s) are
Earlierresultsonthe511keVlineemissionmorphologyas theCrabnebula,3C273,NGC4151,M94,NGC936(during
observed by SPI have been presented by Jean et al. (2003a), theSN2003gsoutburst)andtheComacluster.Unexposedre-
Knödlseder et al. (2004), and Weidenspointner et al. (2004), gionsarefoundmostlyatintermediategalacticlatitudes(|b| ∼
and were based on observations performed during the galac- 30◦−60◦),andtowardsthesouthgalacticpole.
tic centre deep exposure (GCDE) of 2003. Using a “light A mapoftheresultingnarrow-line3σpoint-sourcesensi-
bucket” approachwhich neglects the coding propertiesof the tivity of SPI at 511 keV is shown in Fig. 2. To evaluate the
SPI mask, Teegarden et al. (2005) derived upper limits on sensitivity, an energy band of 7 keV centred at 511 keV has
electron-positronannihilation radiation from the galactic disk been used. The choice of such a relatively wide band elimi-
using core-programme data combined with open-programme natesanybiasduetothegermaniumdetectordegradationand
observationsatlowgalacticlatitudes(|b|≤20◦).Inthepresent annealingcycles,aswellasanybias/effectduetogaincalibra-
paperweprovideforthefirsttimeanall-skyanalysisusingall tionuncertainties.Italsotakesintoaccountmoderate511keV
publicdataofthefirstINTEGRALmissionyear. linebroadening,asreportedbyJeanetal.(2003a).
Over large regions of the sky, and in particular in the
Spectroscopiccharacteristicsofthe511keVlinebasedon galacticplane,asensitivitybetterthan2×10−4 phcm−2s−1 is
SPI data have been published by Jean et al. (2003a), Lonjou reached.Abestpoint-sourcesensitivityof5×10−5phcm−2s−1
et al. (2004), and Churazovet al. (2005). We will present the
isachievedtowardsthegalacticcentredirection.Thesensitiv-
511 keV line profile that we obtain from the all-sky dataset ity to extended diffuse emission becomes slightly worse with
elsewhere(Jeanetal.,inpreparation).
increasingemissionsize,anddependsontheexposurepattern
intheregionofinterest.Forexample,fora2dangularGaussian
This paper is organised as follows. Section 2 describes
surface brightness distribution centred on the galactic centre,
the observations and the data preparation. Section 3 explains
the511keVlinesensitivityworsensfrom5×10−5phcm−2s−1
the treatment of the instrumental background. In Sect. 4, we
foragalacticcentrepoint-sourceto7×10−5phcm−2s−1foran
presentthefirstall-skymapof511keVgamma-raylineradia-
extendedsourceof8◦ FWHM.
tionanddeterminethemorphologyoftheemission.Section4
Only single-detector event data have been analysed in
also describesearchesforcorrelationswith tracersofgalactic
this work (multiple-detector event data do not contribute sig-
source populationsin order to shed light on the origin of the
nificantly to the SPI sensitivity at an energy of 511 keV;
positrons.In Sect. 5 we discussthe implicationsof theobser-
vations for the galactic origin of positrons, and we conclude 1 To obtain the effective exposure time, the exposure has to be
inSect.6. dividedbytheeffectiveareaat511keVofabout75cm2.
J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 515
Fig.1. Mapof theeffectiveSPIexposure at 511keV forthedataset analysed inthiswork. Thecontours arelabelledinunitsof107 cm2s,
correspondingto13ks(0.1),133ks(1),667ks(5),and1.3Ms(10)ofeffectiveexposuretimes.
1 2 2 5 followingbythepointingnumberp,thedetectornumberdand
theenergybine,isthengivenby
5
b =bcont +bline (1)
2 p,d,e p,d,e p,d,e
25 2 5 2 5 2 (note that for the analysis presented in this work a sin-
1 0.5 1 gle energy bin has been used, covering the energy inter-
5 2 1 val 507.5−514.5 keV; however, for clarity and reference in
2
5 1 5 5 future works we give here the complete energy-dependent
5 5 2
2 formalism).
5 2 The time variation of the continuum component is ex-
trapolated from that observed in an continuum energy band
Fig.2. SPI narrow line 3σ point-source sensitivity at 511 keV for adjacenttothe511keVline.We usedtheenergyband E =
theanalysisinterval507.5−514.5keV(contoursarelabelledinunits 523−545keV,situatedabovethe511keVline,inordertoadejx-
of10−4phcm−2s−1).
cludeanybiasduetopositroniumcontinuumemissionthatap-
pearsbelow511keV.Toreducethestatisticaluncertaintythat
cf. Roques et al. 2003). Energy calibration was performed arises from the limited counting statistics, we smoothed the
orbit-wise, resulting in a relative (orbit-to-orbit) calibration timevariationbylocallyadjustingtherateofsaturatedevents
precisionof∼0.01keVandanabsoluteaccuracyof∼0.05keV inthegermaniumdetectors(GEDSAT)totheadjacentcounting
(Lonjouetal.2004). rate(GEDSATturnedouttoprovideagoodfirstordertracerof
The data have been analysed by sorting the events in a thebackgroundvariationinSPI;cf.Jeanetal.2003b).Thepre-
3-dimensional data-space, spanned by the (calibrated) event dictednumberofcontinuumbackgroundcountsindata-space
energy, the detector number, and the SPI pointing number. bin(p,d,e)isthengivenby
Anenergybinningof0.5keVhasbeenchosen,wellbelowthe
bcont = g ×T
instrumentalenergyresolutionof2.12keVat511keV. p,d,e p,d p,d
(cid:1) (cid:1)
×(cid:1) ∆e × (cid:1)pp(cid:5)+=∆pp−∆p e(cid:5)∈Eadjnp(cid:5),d,e(cid:5), (2)
3. Backgroundmodelling e(cid:5)∈Eadj∆e(cid:5) pp(cid:5)+=∆pp−∆pgp(cid:5),d×Tp(cid:5),d
ThemostcrucialstepinSPI dataanalysisconsistsofthepre-
where
cisemodellingofthetimevariabilityoftheinstrumentalback-
ground. In the region of the 511 keV line, the instrumental – g is the GEDSAT rate for detector d, averaged over
p,d
backgroundconsists of a nearly flat continuum and a (broad- the time period spanned by pointing p, given in units
ened)instrumental511keVlineoriginatingfrompositronan- ofcountss−1;
nihilation within the telescope (Teegarden et al. 2004). Since – Tp(cid:5),d isthelifetimefordetectordduringpointing p(cid:5),given
the time variation of the continuum component differs from inunitsofseconds;
thatofthelinecomponentwemodelthemindependently.The – ∆ is the energy bin size for spectral bin e, given in units
e
background model for a given data-space bin, indexed in the ofkeV(here∆ =0.5keV);and
e
516 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission
– np(cid:5),d,e(cid:5) is the number of observed counts for pointing p(cid:5),
detectord,andenergybine(cid:5),giveninunitsofcounts.
Thenumberofpointingsusedforsmoothing,givenby2∆ +1,
p
isdeterminedforeachpointing panddetectord bysatisfying
theconstraint
 
min p(cid:5)+∆p Tp(cid:5),d ≥Tmin. (3)
∆p≥0 p(cid:5)=p−∆p
AnaccumulatedlifetimeofT = 20hhasshowntoprovide
min Fig.3.ResidualcountrateasfunctionofpointingnumberfortheDETE
an optimum compromise between reducing the statistical un-
(top) and ORBIT-DETE (bottom) background models for the energy
certainty (due to the limited number of events in the adjacent
band507.5−514.5keV.Inadditiontothebackgroundmodelsthebest
energy band) and reducing the systematic uncertainty (due to
fitting2dGaussiansurfacebrightnessmodel(cf.Sect.4.2.2)hasbeen
thefactthattheGEDSATratedoesnotpredictthebackground
subtractedfromthedata.Forclarity,thedatahavebeenrebinnedinto
to infinite precision). In other words, continuum background groupsof50pointings.Theshadedareaindicatescountratevariations
variations shorter than ∼20 h are modelled by the GEDSAT of±0.5%.Forcomparison,themaximum511keVlinesignalampli-
ratewhilevariationsonlongertimescalesaremodelledbythe tudecorrespondstoapproximately∼2%oftheobservedcountrate.
observedeventrateinthe523−545keVband.
The time variation of the line component was modelled
foreachdetectord andenergybine separatelyusinga multi-
deep exposure (GCDE) of the INTEGRAL core program: a
componenttemplateoftheform
slow(5◦/day)scanofthegalacticplanefromnegativetowards
(cid:9)
t positive longitudes combined with rapid (3◦/h) excursions in
bline =β(1) +β(2) ×g +β(3) g (t(cid:5))e(t(cid:5)−t)/τdt(cid:5). (4)
p,d,e d,e d,e p,d d,e d galacticlatitude.Asresult,thelongitudeprofileofthe511keV
t0 lineemissionisencodedincountratevariationsontimescales
Thistemplateconsistsofaconstanttermβ(1) plustheGEDSAT ofdayswhilethelatitudeprofileisencodedincountratevaria-
d,e
rateg scaledbyβ(2) plustheGEDSATrateg (t(cid:5))convolved tionsontimescalesofhours.WithinafewhourstheSPIinstru-
p,d d,e d mental backgroundis sufficiently stable to be accurately pre-
withanexponentialdecaylaw,scaledbyβ(3) (theconvolution
d,e dicted by our model, hence the latitude profile is rather well
integralistakenfromthestartoftheINTEGRALmissiont up
0 determined. However, on timescales of days the background
todatet).Thecoefficientsβ(di,)eofthetemplateareadjusteddur- variations are more difficult to predict to sufficient accuracy,
ingtheanalysisforeachSPIdetectordandenergybineusing
potentiallyleadingtosystematictrendsinthedeterminationof
amaximumlikelihoodfittingprocedure(again,intheanalysis
thelongitudeprofile2.
presented in this paper only a single energybin is used). The
In order to improve the background model on long
constanttermhasbeenintroducedtoprovidefornon-linearities
timescales, we studied also a class of models where we ad-
between the background variation and the GEDSAT rate. In
justthelongtermvariationsduringmodelfitting.Forthispur-
fact, it turnsoutthat β(1) are negative.An equallygoodback-
d,e pose we adjust the model parameters β(2) not only for all
ground predictor is obtained if the GEDSAT rate raised to a d,e
SPI detectors but also for time intervals of fixed duration T.
powerof∼1.1istaken,butusingaconstantinsteadofapower-
Inthisway,systematicuncertaintiesinthebackgroundmodel
lawhastheadvantageofhavingthebackgroundvariationtem-
on timescales longer than T are removed. Fitting the back-
platedecomposedintoalinearcombinationofterms.Thethird
groundforeachorbitalrevolution(T ∼ 3days)isadequateto
component makes provision for a long term build-up that is
reduce systematic trends well below the statistical uncertain-
seenintheintensityofthe511keVbackgroundline,andthat
ties(cf.bottompanelofFig.3).Thismethodissimilar tothe
istentativelyattributedtoproductionoftheisotope65Znwhich
methodthatweappliedinourearlierworks(Jeanetal.2003a;
hasadecaytimeofτ = 352days.Theprecisevalueofτisin
Knödlsederetal.2004;Weidenspointneretal.2004),withthe
factweaklyconstrainedbythepresentdata,andalinearslope
differencethatwenowalsofitthebackgroundmodelforeach
providesan equally goodfit of the instrumental511 keV line
of the SPI detectors separately, and that we included in ad-
background.
dition a constant term and a build-up term in the model (see
Although the background model defined by Eqs. (1)–(4),
Eq. (4)). Hereafter this second background model is called
whichhereafteris calledmodelDETE, predictstheinstrumen-
ORBIT-DETE.
tal backgroundto good accuracy, significant residuals remain
aftersubtractingoffthebackgroundmodelandamodelofthe
2 In a preliminary analysis in which we treated a much smaller
sky intensitydistribution fromthe data (cf. Fig. 3). We found
dataset, systematic background uncertainties suggested a significant
thattheseresidualscanleadtosystematicbiasesinthestudyof
elongation of the galactic centre bulge emission along the galac-
themorphologyofthe511keVemission,inparticularforthe
tic plane. This elongation was artificial and had been produced by
determination of the longitude profile of the emission. These background variations that were not fully explained by our model.
biasescanbeexplainedbythetelescopepointingstrategythat Removingtheshortperiodofdatawiththestrongestbackgroundvari-
has been adopted for a large fraction of the galactic centre ationsremovedalsotheapparentelongationofthebulgeemission.
J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 517
(cid:1)
The introductionof additionalparametersin ORBIT-DETE ek = M R fk+b isthe predictednumberofcountsin data
i j=1 ij j i
with respect to DETE leads to a substantial loss in sensitiv- space bin i after iteration k (b being the predictednumberof
i
ity. Thedetectionsignificanceof galacticcentre 511keV line instrumental background counts for bin i), N and M are the
emissiondropsfrom∼50σforDETEto∼22σforORBIT-DETE. dimensions of the data and image space, respectively, and λk
However,itwasfoundthatthestatisticalaccuracyofthemor- is an acceleration factor that is obtained by constrained max-
phologydetermination,whichisdrivenbythecountratecon- imum likelihood fitting (with the constraint that the resulting
trast in the data-space rather than the count rate level, is not skyintensitiesremainpositive).
degradedbytheintroductionofadditionalparameters,aslong To avoid noise artefacts in the weakly exposed regionsof
asT >∼2days.Consequently,usingtheORBIT-DETEmodelfor thesky,weweightedtheimageincrementwithaquantitythat
the morphologicalcharacterisation of the 511 keV line emis- is(cid:1)related to the sensitivity of the instrument, given by wj =
sionistheoptimumchoicethatkeepsahighstatisticalaccuracy ( N R )1/2.Weverifiedthatintroducingthisweightinghadno
i=1 ij
whilereducingthesystematicuncertaintiesintheanalysis. impactontheimagereconstructioninthewellexposedregions
On the other hand, despite the systematic uncertainties, of the sky. In addition, we smoothed the iterative corrections
DETE is accurate enough to allow for a precise determina- onthe righthandside of Eq.(5) usinga 5◦ ×5◦ boxcaraver-
tion of 511 keV line flux levels. This is related to the fact age.Inthiswaytheeffectivenumberoffreeparametersinthe
thatfluxmeasurementsrequireanaveragedeterminationofthe reconstructionisreducedandimagenoiseisdampedtoanac-
countratelevelandarenotsensitivetothecountratecontrast. ceptablelevel.Theapplicationofmoresophisticatedimagere-
Apparently,the countrate residuals approximatelyaverage to constructionmethodsinvolvingwaveletbasedmulti-resolution
zero(cf.Fig.3). algorithms aiming at a complete suppression of image noise
Wethereforeoptedforatwostepapproachwherewefirst (Knödlsederetal.1999a)willbepresentedelsewhere.
determinethemorphologyusingORBIT-DETE,andthen,using
The resulting all-sky image of the 511 keV line emission
the optimum morphologyparameters, determine the 511 keV
isshowninFig.4,longitudeandlatitudeprofilesoftheemis-
flux using DETE. In this way we recover the good sensitivity
sionareshownin Fig.5.We havechosento stopthe iterative
of SPI for 511 keV flux measurementsthat was reducedby a
procedure after iteration 17 since at this point the recovered
factorof∼2bytheusageofORBIT-DETE.Thecomparisonof
flux and the fit quality correspond approximately to the val-
the flux levels determined using DETE and ORBIT-DETE pro-
uesthatweachievebyfittingastrophysicalmodelstothedata
vides us with a measure of the systematic uncertainty in the
(cf. Sect. 4.2). In this way we make sure that we are not in
fluxdetermination,whichingeneralissmallerthanthestatis-
theregimeofoverfitting,whichischaracterisedbysubstantial
ticaluncertaintyobtainedwithDETE.Weaddthesystematicto
imagenoiseandartificialimagestructures.Ontheotherhand,
thestatisticaluncertaintyinquadratureandquotetheresultas
simulationsshowedthatfaintdiffuseemission,asexpectedfor
totalerroronthefluxmeasurement.Incaseswhereuncertain-
exampleforagalacticdiskcomponent,wouldnotberecovered
tiesinthemorphology(suchasthesizeoftheemissionregion)
atthispoint.
introducesomeuncertaintyontheflux,wehavealsoaddedthis
Figure 4 reveals that the 511 keV sky is dominated by
uncertaintytothetotalerrorinquadrature.
prominent emission from the bulge region of the Galaxy.
Beyondthe galactic bulge,no additional511keV emission is
4. Results seen all over the sky, despite the good exposure in some re-
gions(e.g.Cygnus,Vela,LMC,anticentre,northgalacticpole
4.1.Imaging
region). The 511 keV emission appears symmetric and cen-
Todetermineamodelindependentmapofthe511keVgamma- tred on the galactic centre, with indications for a slight lati-
ray line intensity distribution over the sky, we employed the tudeflattening.Thelatitudeflatteningcouldbeeitherduetoan
Richardson-Lucy algorithm (Richardson 1972; Lucy 1974). inherentasymmetryofthebulgecomponentorduetothepres-
This type of algorithm is widely used for image deconvolu- enceofanunderlyingfaintgalacticdiskcomponent.Indeed,if
tion, andhasin particularbeensuccessfully employedforthe theRichardson-Lucyiterationsarecontinued,afaintdisk-like
analysisofgamma-raydataofCGRO(Knödlsederetal.1999a; structure emerges(cf. Fig. 6). Yet the image starts to become
Milneetal.2000). polluted by noise and we cannot exclude the possibility that
We implemented the accelerated version ML-LINB-1 of the apparentdisk emission is artificially created by the expo-
Kaufman (1987) of the Richardson-Lucy algorithm for our surepatternthatfollowsthe galacticplane.Thereforewe em-
analysis, which iteratively updates the sky intensity distribu- ploymorequantitativemethodsinthenextsectiontoassessthe
tion fk → fk+1usingtherelation significanceofthepossiblediskemission.
j j
 (cid:10) (cid:11)  By fitting Gaussian functions to the longitude and lat-
(cid:1)
fjk+1 = fjk+λkwjfjk iN=1(cid:1)iNen=kii1−Ri1j Rij (5) dietxiuctdeaentetsp,orhfoofithwleeesveemor,fisthstihaotenthitmeoea∼mg1ei3s◦s(ico×fn.1pF0r◦iogfi(.Fle5Ws)HarwMeen).oeFtsiwtgimeulraletree5ptirhnee--
sentedbyGaussianfunctions.Theemissionisbetterdescribed
where R is the instrumental response matrix (linking the by a compact (FWHM∼5◦) core and a more extended halo
ij
data space, indexed by i, to the image space, indexed by j), (FWHM 10◦−20◦). We want to emphasise, however, that this
n is the number of counts measured in data space bin i, qualitativeanalysisshould notbe pushedtoo far, since image
i
518 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission
Fig.4. Richardson-Lucy image of 511 keV gamma-ray line emission (iteration 17). Contour levels indicate intensity levels of 10−2, 10−3,
and10−4phcm−2s−1sr−1(fromthecentreoutwards).
Fig.5.LongitudeandlatitudeprofilesoftheimageshowninFig.4(integrationrange|l|≤30◦,|b|≤30◦).
Fig.6.Richardson-Lucyimageafteriteration25.ContourlevelsaresimilartoFig.4.
J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 519
deconvolutionis a non-linearprocess which is easily affected Table1.Morphologyoftheemissionassuminga2dangularGaussian
byimagenoiseandexposurebiases. surfacebrightnessdistribution.
Quantity Measuredvalue
4.2.Morphologicalcharacterisation
RMLR(DOF) 462.2(5)
4.2.1. Method l −0.6◦±0.3◦
0
To make a quantitative assessment of the morphology of the b0 +0.1◦±0.3◦
511 keV line emission we use a maximum likelihood multi- ∆l(FWHM) 8.1◦±0.9◦
component model fitting algorithm. Assuming Poisson noise ∆b(FWHM) 7.2◦±0.9◦
for the measured number ni of events in each of the N data- 511keVflux(10−3phcm−2s−1) 1.09±0.04
spacebins,thealgorithmmaximisestheloglikelihood
(cid:5)N
lnL= n lne −e −lnn!, (6)
i i i i
i=1 emission appears slightly offset from the galactic centre
(cid:1)
wheree = α sk +b(β)isthepredictednumberof(source direction, at the statistical 2σ level, but we do not claim that
plusbacikgroukndk)ciountisindataspacebini, sk =(cid:1)M fkR is thisoffsetis significant.Fromourearlieranalyseswe learned
i j=1 j ij
that the centroid can be shifted by this amount simply from
the sky intensity model fk folded into the data space (R be-
ingtheinstrumentalrespojnsematrix),b(β)isthebackgriojund the combined effect of statistical and systematic biases in the
i
model(cf.Fig.1),andα andβarescalingfactorsforthesky modellingoftheinstrumentalbackground.
k
intensity and the background model, respectively, that are Within the statistical uncertainties, the emission appears
adjustedbythefit. fullysymmetric,withanextensionof∼8◦(FWHM).Formally,
Detection significances (and parameter errors) are esti- wedetermineamarginalemissionflatteningof∆b/∆l=0.89±
mated using the maximum likelihood ratio test (Cash 1979). 0.14.Thetotal511keVfluxis(1.09±0.04)×10−3phcm−2s−1,
We calculate the maximum log likelihood-ratio MLR = wherethequotederrorincludestheuncertaintyintheextentof
−2(lnL −lnL )betweentwomodels(hypotheses),wherefor theemissionandthestatisticalandsystematicmeasurementer-
0 1
thefirstoneweconstrainanumber poftheparameterstospe- rors(cf.Sect.2).
cific values (resulting in L ) while for the second one all pa- The RMLR of 462.2 that has been obtained using the
0
rametersareleftfree(resultingin L ).InthecasethatL pro- ORBIT-DETEbackgroundmodelconvertsintoa formaldetec-
1 1
videsasatisfactoryfitofthedata,MLRisthendistributedlike tion significance of 22σ. Using the DETE background model
aχ2 distributionwithpdegreesoffreedom.Statisticalparame- andincludingthesystematicuncertaintiesresultsinasubstan-
p
tererrorswereestimatedusingtheformalismofStrong(1985). tiallyhigherdetectionsignificanceof34σ.Neglectingsystem-
Throughoutthispapertheerrorbarsquotedare1σ. atic uncertainties would even boost the detection significance
We call the maximum log likelihood-ratio (MLR) of a towards49σ.
model the difference between the log likelihood obtained by
fittingallmodelparametersandtheloglikelihoodobtainedby
fittingonlythebackgroundmodeltothedata(i.e.forL allpa- 4.2.3. Galacticmodels
1
rametersα andβvaryfreelywhileforL allα areconstrained
k 0 k To determine the galactic positron-electron annihilation rate
tozeroandonlytheβareallowedtovary).Tocomparemod-
requires modelling the spatial distribution of the positron-
elswithdifferentnumbersoffreeparameters,wequotethere-
electron annihilation. The 511 keV photon luminosity L
ducedmaximumloglikelihood-ratio,RMLR = MLR−DOF, 511
is related to the positron luminosity L through L =
with DOF being the number of free parametersα of the sky p 511
k (2−1.5f )× L where f is the positronium (Ps) fraction, de-
intensitymodel. p p p
fined as the fraction of positrons that decay via positronium
formation(Brown,&Leventhal1987).Using f =0.93±0.04
p
4.2.2. 2dsurfacebrightnessdistribution that has been determined from OSSE observations (Kinzer
etal.2001)resultsinaconversionfrom511keVphotonlumi-
Asafirststepwecharacterisetheapparentmorphologyofthe
nosityto a positron-electronannihilationrate of L = (1.64±
511keVlineemissionontheskyusinga2dangularGaussian p
0.06)×L .
surface brightness distribution for which we determined the 511
centroid,l ,b ,thelongitudeandlatitudeextent,∆l,∆b,andthe We herecomparemodelsof bulge,disk,andhalo compo-
0 0
nentswiththe data.Based ongalacticmodeldensitydistribu-
511keVlineflux.Theresultsofthisanalysisaresummarised
tions ρ(x,y,z) we calculate the expected all-sky 511 keV in-
inTable1,thebestfittingmodelintensitydistributionisshown
tensity f(l,b)towardsdirection(l,b)byintegratingthevolume
inFig.8.
emissivityρ(x,y,z)alongthelineofsights:
The analysis confirms our earlier findings (Jean
et al. 2003a; Knödlseder et al. 2004; Weidenspointner
(cid:9)
etal.2004)ofacompactandsymmetric511keVlineemission 1
f(l,b)= ρ(x,y,z)ds (7)
distribution towards the galactic centre. The centroid of the
4π
520 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission
Table2.Galaxymodelfittingresults(seetext).Thecolumnsgive(1)themodel,(2)theRMLR(obtainedusingtheORBIT-DETEbackground
model) andthenumber offreemodel parameters(DOF),(3)thebulgescalelength,(4)thebulgescaleheight,(5)−(8)the511keV photon
luminosityofthemodelcomponents,and(9)−(12)thetotal4πintegrated511keVlineall-skyfluxineachofthemodelcomponents.Theprime
indicates model components for which the scaling parameters were adjusted by the fit.Thefigures in parenthesis quoted inCols. (5)−(12)
indicate1σuncertaintiesinthelastdigit.
Model RMLR R z L (1043phs−1) 511keVlineflux(10−3phcm−2s−1)
0 0 511
(DOF) (kpc) (kpc) bulge disk halo total bulge disk halo total
G0 447.5(1) 0.91 0.51 1.04(3) 1.04(3) 1.22(4) 1.22(4)
G1 445.7(1) 0.97(3) 0.97(3) 1.19(4) 1.19(4)
G2 450.8(1) 0.98(3) 0.98(3) 1.18(3) 1.18(3)
G3 462.2(1) 0.98(3) 0.98(3) 1.18(3) 1.18(3)
E1 441.8(1) 0.99(4) 0.99(4) 1.19(4) 1.19(4)
E2 453.1(1) 1.01(3) 1.01(3) 1.19(3) 1.19(3)
E3 464.9(1) 1.00(3) 1.00(3) 1.17(3) 1.17(3)
S 459.0(1) 0.96(3) 0.96(3) 1.19(3) 1.19(3)
F
E 459.0(1) 0.93(2) 0.93(2) 1.19(3) 1.19(3)
F
P 456.5(1) 0.94(3) 0.94(3) 1.16(3) 1.16(3)
F
S 456.3(1) 0.94(2) 0.94(2) 1.22(3) 1.22(3)
PR
G0’ 462.5(3) 0.52(6) 0.45(5) 0.94(4) 0.94(4) 1.09(4) 1.09(4)
E0’ 464.2(3) 0.37(5) 0.42(7) 0.98(5) 0.98(5) 1.15(5) 1.15(5)
H’ 468.4(4) 1.6(3) 1.6(3) 2.2(4) 2.2(4)
Shells 469.0(2) 0.97(3) 0.97(3) 1.13(3) 1.13(3)
E3+D0 466.3(2) 0.95(3) 0.11(5) 1.05(4) 1.11(4) 0.4(2) 1.53(5)
G0’+D0 465.2(4) 0.48(6) 0.46(6) 0.87(4) 0.15(5) 1.03(5) 1.01(5) 0.6(2) 1.61(7)
E0’+D0 466.2(4) 0.34(4) 0.44(8) 0.92(5) 0.14(5) 1.06(5) 1.07(6) 0.5(2) 1.61(8)
H’+D0 468.2(5) 0.09(8) 1.2(3) 1.3(3) 0.4(3) 1.6(5) 2.1(5)
Shells+D0 472.2(3) 0.91(4) 0.15(5) 1.05(4) 1.05(4) 0.6(2) 1.62(6)
E3+D1 468.8(2) 0.93(4) 0.23(8) 1.15(6) 1.09(5) 0.8(3) 1.90(9)
G0’+D1 468.6(4) 0.47(6) 0.45(6) 0.84(5) 0.31(9) 1.15(6) 0.98(5) 1.1(3) 2.1(1)
E0’+D1 469.5(4) 0.33(4) 0.42(8) 0.89(5) 0.29(9) 1.17(7) 1.03(6) 1.0(3) 2.1(1)
H’+D1 470.4(5) 0.3(1) 1.2(3) 1.4(3) 0.9(4) 1.5(4) 2.4(5)
Shells+D1 474.9(3) 0.88(4) 0.29(8) 1.17(6) 1.03(5) 1.0(3) 2.0(1)
(the galactic centre has been assumed to be at a distance of modelshavetriaxialmorphologiesthatdifferintheorientation
R(cid:9) = 8.5kpc).Galactic511keVphotonluminositiesare cal- angles,thescalelengths,andtheradialdensityprofiles.Details
culatedbyintegratingρ(x,y,z)overthegalacticvolume, ofthemodelsaregiveninAppendixA,theresultsoftheanaly-
(cid:9)
sisaresummarisedinTable2,andbestfitting511keVintensity
Lp = ρ(x,y,z)s2dsdΩ (8) distributionsareshowninFig.8.
assuminganouterGalaxyradiusofR =15kpc. The best fitting bulge models are E3, G3, SF, and EF.
max
Reasonably good fits are also obtained for P and S , while
Since the 511 keV line emission is primarilyarising from F PR
only moderate fits are achieved for the remaining models.
the galactic centre region we fitted in a first step models of
Ourrankingis similarto thatestablishedfromthe analysisof
thegalacticstellarbulgetothedata.Toaccountforuncertain-
the DIRBE and DENISnear-infrareddata (Dwek et al. 1995;
tiesinourknowledgeaboutthemorphologyofthiscomponent
Freudenreich 1998; Picaud & Robin 2004). The best fitting
(whicharerelatedtoourlocationinthegalacticplaneamidthe
bulge models fit the data as well as the adjusted 2d angular
obscurationbyinterstellardust)wecomparedavarietyofpro-
Gaussiansurfacebrightnessdistribution.Thismeansthatmod-
posedbulgemodelstothedata.Themodelsweregatheredfrom
elsofthegalacticstellarbulgeareabletoexplainsatisfactorily
Dweketal.(1995)andFreudenreich(1998),whomodelledthe
themorphologyofthe511keVbulgeemission.
distributionofKandMgiantstarsusingDIRBEnear-infrared
skymaps,andfromPicaud&Robin(2004)whoanalyseddata Inasecondstepwefittedthe511keVemissionusingpara-
fromtheDENISnear-infraredsurvey.Thereisanaccumulating metric models of the galactic bulge and halo morphology in
bodyofevidencethatthestellardistributioninthebulgeisbar- order to determine the scale of the emission. For the bulge
shaped,andexceptformodelsG0andE0,allemployedbulge modelsG0’andE0’weadjusttheradialscalelength(R )and
0
J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission 521
Table3.Summaryof model fittingresults.Fluxesaregivenastotal
4πintegratedall-skyvalues.Annihilationrateshavebeencalculated
assuming f =0.93.
p
Quantity Bulge Halo Disk
Flux(10−3phcm−2s−1) 1.05±0.06 1.6±0.5 0.7±0.4
L (1043phs−1) 0.90±0.06 1.2±0.3 0.2±0.1
511
L (1043s−1) 1.50±0.10 2.0±0.5 0.3±0.2
p
Totalflux(10−3phcm−2s−1) 1.5−2.9
TotalL (1043phs−1) 1.0−1.7
511
TotalL (1043s−1) 1.6−2.8
p
B/Dfluxratio 1−3
B/Dluminosityratio 3−9
outer 0.5−1.5 kpc shell, confirmingthe existence of a narrow
core plus an extended halo of 511 keV emission that has al-
readybeensuggestedbytheimaginganalysis(cf.Sect.4.1).
Fig.7. Radial dependence of the 511 keV volume emissivity as de-
In a third step we added galactic disk components to the
rivedfromthebulgemodel“Shells”.
bulgeandhalomodels.Forthegalacticdiskwetestedmodels
of young (model D0) and old (model D1) stellar populations
(Robin et al. 2003). With both modelswe find clear evidence
verticalscaleheight(z ),whileforthegalactichalomodelH’
0 for511keVlineemissionfromthegalacticdisk.Addingdisk
we determine the density slope powerlaw index (n), the in-
models D0 and D1 to bulge or halo models consistently im-
ner cutoff radius (a ), and the axis ratio ((cid:10)). In addition, we
c provesthefitleadingtoadetectionofthediskemissionatthe
employeda modelcomposedofa setof galactocentricnested
3−4σlevel3.Formally,D1providesabetterfitthanD0,butthe
shellsofconstantdensity(model“Shells”)todeterminethera-
differenceismarginal.Thesignalfromthediskisstilltoofaint
dialdensityprofileofthe511keVemission.Wevariedtheradii
inourpresentdatasettodeduceanythingaboutitsmorphology.
oftheshellsandthenumberofshellsinordertomaximisethe
Theflux,luminosityandannihilationrateinthebulge,halo
MLR,whilstlimitingthenumberofshellstotheminimumre-
and disk components are summarised in Table 3. Recall that
quiredtosatisfactorilydescribethedata.
the bulgeandhalo componentsare alternativesandtheir con-
Thedatasuggestasymmetricbulgeemissionprofile,with
tributionshouldnotbeaddedtoderivethetotalgalacticvalues.
scalelengthsbetween300and600pc.TheRMLRsarecompa-
Either component provides an almost equally good fit to the
rabletothebestfittingbulgemodelsthatwetestedbefore.The
data.Duetotheirdegeneracyfittingbothsimultaneouslyisnot
dataareequallywellfittedbyamodelofthegalactichalo,with
meaningful.
adensitypowerlawindexofn=3.0±0.3,aninnercutoffradius
of a = 0.39±0.08kpc, and a flattening of (cid:10) = 0.81±0.12. The halo model leads to a considerably larger flux, lu-
c
minosity and annihilation rate than the bulge model due to
Most studies of the stellar halo population suggest power in-
the presence of a flat and extended tail in this distribution
dicesbetween2.4and3.5andflatteningsintherange0.6to1.0,
whiletheinnercutoffradiusisbasicallyundetermined(Robin (cf.Fig.8).Currently,ourdatadonotallowtodetectthistail,
andthus,theydonotallowtodiscriminatebetweenbulgeand
etal.2000,andreferencestherein).Ourvaluesarecompatible
halomodels.Futuredeepobservationsatintermediategalactic
with those of the stellar halo population, but the large uncer-
latitudesthatarescheduledfortheINTEGRALAO-3observ-
tainties in the stellar halo morphologydo notallow firm con-
ing period aim in measuring this emission tail, promising to
clusionstobedrawn.
provideconstraintsthatwillallowinthe futuretodisentangle
The nested shell model provides the best fit to the data
betweenthedifferentemissionmorphologies.
thankstoitsflexibilityinadjustingtheradialdensityprofileof
The data suggest bulge-to-disk 511 keV flux ratios in the
theemission.Asatisfactoryfitisachievedbyusingtwoshells
withradii0−0.5and0.5−1.5kpc;splittinguptheseshellsina range1−3,wherethelowerboundaryisobtainedfortheshort
scale-length old stellar disk model D1 which suggests larger
finerbinning,movingtheshellinterfaceradiusoraddingmore
disk flux values than the young stellar disk model D0. Halo-
shells does not significantly improve the fit. In particular, we
to-disk 511 keV flux ratios are even larger, in the range 2−4,
detectnosignificant511keVbulgeemissionfromgalactocen-
tricdistances>∼1.5kpc.Theradialdependenceofthe511keV
3 Using the quoted RMLRs, the formal significance of the disk
volumeemissivityisplottedinFig.7.Forillustrationweadded emissionamountsonlyto2−3σ.However,thetabulatedRMLRshave
the result of a third shell to the figure that covers radial dis- beenobtainedusingtheORBIT-DETEbackgroundmodelwhichisless
tancesof1.5−3.0kpcandforwhichthefluxisconsistentwith sensitive to 511 keV line emission than the DETE model. Using the
zero. Our fit reveals a drop in the annihilation emissivity by procedureoutlinedinSect.3wereducethefluxuncertaintiesandin-
one order of magnitude between the inner 0−0.5 kpc and the creasethedetectionsignificanceto3−4σ.
522 J.Knödlsederetal.:Theall-skydistributionof511keVelectron-positronannihilationemission
Fig.8.All-skymapsofthebestfittingmodelsof511keVgamma-raylineemission(seetextforadescriptionofthemodels).Contourlevels
indicateintensitylevels(fromthecentreoutwards)of10−2,10−3,and10−4phcm−2s−1sr−1.TheresultingRMLRsofthemodelfitsarequoted
intheupper-rightcornerofthepanels.
owingtothelargerfluxinthehalocomponent.Thelargeuncer- Inotherwords,toproducethesame511keVfluxatEarth,the
taintyintheseratiosarisesfromthelowintensityofthegalac- intrinsicluminosityofthebulgehastobelargerthanthatofthe
ticdiskcomponent,whichfortheanalyseddatasetisjustabove disk4. Itisthereforeimportantto quoteexplicitlythequantity
theSPIdetectionlimit. forwhichwediscussthebulge-to-diskratio.Thesamerational
also holds for the halo-to-disk 511 keV photon luminosity
We also note that the bulge-to-disk 511 keV photon lu-
minosity ratio is much higher than the bulge-to-disk flux
ratio and lies in the range 3−9. This difference is ex- 4 Thedifferencebetweenbulge-to-diskfluxandluminosityratiois
p(cid:12)lained by the(cid:12)fact that the average squared distance s¯2 = onlyimportantforourhomeGalaxyandisrelatedtothefactthatthe
ρ(s)s2dsdΩ/ ρ(s)dsdΩ,whichdefinesthedistanceatwhich Sun is located within the galactic radius. For external galaxies this
asourceofluminosityLp producestheobserved511keVline difference disappears since their bulge and disk appear at the same
flux,issmallerforthegalacticdiskthanforthegalacticbulge. distancetous.