Gamma-ray spectroscopy of positron annihilation in the Milky Way

16 Pages·2016·3.44 MB·English

A&A586,A84(2016) Astronomy
DOI:10.1051/0004-6361/201527510 &
(cid:13)c ESO2016 Astrophysics
Gamma-ray spectroscopy of positron annihilation in the Milky Way
ThomasSiegert1,RolandDiehl1,2,GerasimKhachatryan1,MartinG.H.Krause3,2,1,FabriziaGuglielmetti1,
JochenGreiner1,2,AndrewW.Strong1,andXiaolingZhang1
1 Max-Planck-InstitutfürextraterrestrischePhysik,Gießenbachstr.1,85741Garching,Germany
e-mail:[email protected]
2 ExcellenceClusterUniverse,Boltzmannstr.2,85748Garching,Germany
3 Universitäts-SternwarteLudwig-Maximilians-Universität,81679München,Germany
Received6October2015/Accepted30November2015
ABSTRACT
Context.TheannihilationofpositronsintheGalaxy’sinterstellarmediumproducescharacteristicgamma-rayswithalineat511keV.
Thisgamma-rayemissionhasbeenobservedwiththespectrometerSPIonESA’sINTEGRALobservatory,confirmingapuzzling
morphologywithbrightemissionfromanextendedbulge-likeregion,whileemissionfromthediskisfaint.Mostknownorplausible
sourcesofpositronsare,however,believedtobedistributedthroughoutthediskoftheMilkyWay.
Aims.Weaimtoconstraincharacteristicspectralshapesfordifferentspatialcomponentsinthediskandbulgeusingdatawithan
exposurethathasdoubledsinceearlierreports.
Methods.Weexploithigh-resolutiongamma-rayspectroscopywithSPIonINTEGRALbasedonanewinstrumentalbackground
methodanddetailedmulti-componentskymodelfitting.
Results.Weconfirmthedetectionofthemainextendedcomponentsofcharacteristicannihilationgamma-raysignatures,altogether
at58σsignificanceinthe511keVline.ThetotalGalactic511keVlineintensityamountsto(2.74±0.25)×10−3 phcm−2s−1 for
our assumed model of the spatial distribution. We derive spectra for the bulge and disk, and a central source modelled as point-
like and at the position of Sgr A*, and discuss spectral differences. The bulge (56σ) shows a 511 keV line intensity of (0.96±
0.07)×10−3phcm−2s−1togetherwithortho-positroniumcontinuumequivalenttoapositroniumfractionof(1.080±0.029).Thetwo-
dimensionalGaussianthatrepresentsthediskemission(12σ)hasanextentof60+10degreesinlongitudeandaratherlargelatitudinal
−5
extentof10.5+2.5degrees;thelineintensityis(1.66±0.35)×10−3phcm−2s−1withamarginaldetectionoftheannihilationcontinuum
−1.5
andanoveralldiffuseGalacticcontinuumof(5.85±1.05)×10−5phcm−2s−1keV−1at511keV.Thediskshowsnofluxasymmetry
betweenpositiveandnegativelongitudes,althoughspectraldetailsdiffer.Thefluxratiobetweenbulgeanddiskis(0.58±0.13).The
centralsource(5σ)hasanintensityof(0.80±0.19)×10−4phcm−2s−1.
Keywords.gammarays:ISM–gammarays:diffusebackground–ISM:general–line:profiles–techniques:spectroscopic
1. Introduction mapsappearedtoshowanextensionoftheemissioninthegalac-
tic centre region towards positive latitudes (Dermer & Skibo
Positronsinourgalaxyhavebeenstudiedwithmanydifferentas-
1997).
tronomicalinstrumentsthroughthegamma-raysatthecharacter-
Prior to the launch in 2002 of the INTEGRAL space-
isticenergyof511keVproducedduringtheirannihilationinthe
craft(Winkleretal.2003),informationhadbeenobtainedwith
interstellarmedium(ISM).Followingearlyreportsofalinenear
little imaging capability and often with limited spectral resolu-
this energy, the first high resolution measurements (Leventhal
tion.Forexample,thefieldofview(FoV)oftheOSSEcollima-
etal.1978)establisheditsidentificationaspositronannihilation.
torswas3.8by11degreesanditsspectralresolutionat511keV
Early indications of variability were later shown to have been
about 10%. Observations with the good energy resolution of
due to comparing measurements of extended emission made
withinstrumentshavingdifferentfieldsofview(Albernheetal. Germanium detectors had been obtained only with wide field
instruments on balloons and on HEAO-3. The SPI gamma-ray
1981;Leventhaletal.1986;Shareetal.1988).
spectrometer instrument on INTEGRAL provided a significant
Two remarkable transient annihilation events found with
advance,withacodedmaskallowingimagingat∼2degreepre-
SIGMA(e.g.Bouchetetal.1991;Goldwurmetal.1992)were
cision, and Ge detectors with ∼2 keV intrinsic spectral resolu-
apparentlyassociatedwithahardX-raysource,1E1740.7-2942,
tion(Vedrenneetal.2003;Roquesetal.2003).
near the centre of the galaxy, that was consequently termed
the “Great Annihilator”. Neither contemporaneous (Jung et al. The INTEGRAL sky survey has excellent exposure of
1995;Smithetal.1996b)norlong-termmonitoringofthesource the entire inner Galaxy. This led to a first all-sky image
(Sunyaev et al. 1991; Harris et al. 1994; Smith et al. 1996a; of positron annihilation gamma-rays (Knödlseder et al. 2003,
Chengetal.1998)providedconfirmationofsuchactivity. 2005).INTEGRALdataconfirmedthatannihilationgamma-ray
OSSE on the Compton Gamma-Ray Observatory (CGRO) emission is dominated by a bright and extended region centred
made extensive observations of the 511 keV emission, con- intheGalaxy;onlyrelativelyweakemissionwasseenfromthe
firming the nature of the emission as constant, extended along extended plane of the Milky Way outside the central region.
the galactic plane with a strong concentration towards the The morphology was found to be much more symmetric about
Galactic centre (Purcell et al. 1993, 1997). Deconvolved sky theGalaxy’scentreandtohaveanextentof10−12◦ (FWHM);
ArticlepublishedbyEDPSciences A84,page1of16
A&A586,A84(2016)
no extension towards northern latitudes was seen. Attempts to Table1.Exposuretimesintheregionsoftheskyusedinthiswork.
separate bright bulge from faint disk emission led to some dis-
cussionandconfusionaboutan“asymmetry”(Weidenspointner
|l| <15◦ 15◦−60◦ 60◦−105◦ 105◦−180◦
et al. 2008; Higdon et al. 2009; Skinner et al. 2010). But later, T+ 21.8 17.6
as the disk emission was found, the apparent asymmetry was T− 30.8 20.4 15.6 30.7
morereadilyexplainedbyaslightoffset(∼1◦)ofthecentroidof
thebrightbulge-likemodel(Bouchetetal.2010;Skinneretal. Notes.Thetimeshavebeenextractedfromtheexposuremap(Fig.1)
2012). inthelistedlongituderangesandforlatitudes|b| < 45◦ ineachcase.
The spectrum of positron annihilation measured with SPI T+andT−aretheexposuretimesforpositiveandnegativelongitudes,
demonstrated that the dominating line at 511 keV was centred respectively,giveninMs.
attheexpectedenergy,andslightlybroadened(Jeanetal.2006).
Thepresenceofthecharacteristiccontinuumfromthree-photon
warmcloudphases,i.e.theregionwheretheannihilationtakes
annihilation,alreadypointedoutfromearliermeasurements(e.g.
place (Jean et al. 2006; Churazov et al. 2005, 2011), the prop-
Leventhal et al. 1978; Kinzer et al. 2001), was also confirmed.
agation distances are smaller. Thus, irrespective of whether the
The interpretation of positron annihilation occurring in a par-
positrons are produced in young massive stars near the clouds,
tially ionised medium with typical temperatures near 8000 K or,morediffusely,onkpcscalesinSNeIaofmucholder,accret-
wassupported(Churazovetal.2005,2011).
ing white dwarves, they will annihilate predominantly in these
CandidatepositronsourceshavebeenreviewedbyPrantzos
warm phases. The distribution of such gas, weighted by source
etal.(2011),andinclude: and propagation effects, is what is essentially observed in the
1. radioactivedecayofβ+unstableisotopes,suchas56Ni,44Ti, 511keVlineemission,andnotdirectlytheirsourcedistribution.
26Al, or 13N, produced in nucleosynthesis sources through- In this paper, we report a new study of measurements with
outtheGalaxy; INTEGRAL/SPI data accumulated over eleven years. We em-
2. accreting binary systems, producing jets loaded with pair ploy coded mask imaging together with high-resolution spec-
plasma,microquasarsbeingtheprominentexamples; troscopy, enhanced by a new approach to instrumental back-
3. pulsars,becausecurvatureradiationproducesandejectspair groundspectra.Weaimatdeterminingdetailsoftheannihilation
plasma; spectra,inparticularthe511keVlinecentroidenergyandbroad-
4. thesupermassiveblackholeinourGalaxy’scentre(SgrA*) ening,whichcharacterisesthekinematicsandtemperatureofthe
throughvariousmechanisms; annihilationregion,andalsotheannihilationline-to-continuum
5. dark matter decay or annihilation, as dark matter would be ratio,whichcharacterisesthefractionofannihilationsthattake
gravitationallyconcentratedintheinnerGalaxy. placeviatheformationofapositroniumatom.Ouranalysisdis-
criminatesbetweenthespectraofthebulgeanddiskregions,and
Although each of these sources have been studied in some de- ofcandidatepointsources.
tail(e.g.Martinetal.2012;Guessoumetal.2006;Boehmetal.
2004, for nucleosynthesis, microquasars, and dark matter, re-
spectively), quantitative estimates of their contributions leave 2. Dataandtheiranalysis
considerable uncertainties (see discussions in Prantzos et al.
2.1. Instrumentanddata
2011,andtheirTableIX,seealsoSect.4ofthispaper).Thelo-
cations and distributions of the various possible sources within The SPI camera utilises the coded mask technique for imag-
theGalaxyofferawaytoconstraintheirrelativeimportance,if ing gamma-ray sources. In this technique, a mask with occult-
annihilationisassumedtooccurclosetotherespectivesources ingtungstenblocksandholesintheapertureofthegamma-ray
(<∼100 pc) (Prantzos et al. 2011). Most of the above candi- cameraimprintsashadowgramofacelestialsourceontoamulti-
date sources would be distributed along the disk of the Milky elementdetectorarray.Thisarrayconsistsof19high-resolution
Way; Sgr A* and dark matter contributions would be concen- Gedetectorsthatmeasurephotonsbetween20keVand8MeV
tratedinthecentralregionoftheGalaxy,andsomesourcessuch withaspectralresolutionof∼2.2keVat662keV.Dataconsist
as supernovae of type Ia (SNe Ia) or low-mass X-ray binaries ofenergy-binnedspectraforeachpointingontheskyandeach
(LMXRBs) might plausibly be related to an extended bulge or ofthe19Gedetectors.DuringtheongoingINTEGRALmission,
a thick disk. But combined with expected source numbers and fouroftheSPIdetectorsfailed,reducingtheeffectivearea.
positronyields,thepuzzlestillremains,andnoconclusivecan- Exposuresaretakeninsuccessivepointingsofthetelescope
didatehasemerged. of typically 1800 s duration, moving the telescope pointing by
More complexities arise because once ejected from their ∼2 degrees along a rectangular 5 × 5 pattern between point-
sources, the positron annihilation may occur at a distance far ingstoshifttheshadowgramofthesourceinthedetectorplane.
from their origins. Because the positrons are produced at high Surveys concatenate adjacent sky region pointing patterns; the
energy (MeV to GeV), many positrons will leave the source, FoV of SPI is 16◦ × 16◦ (partially coded FoV: 34◦ × 34◦).
andpropagateinthesurroundinginterstellargas.Positronsslow Instrumental background practically remains constant between
down to energies of a few eV and annihilation may occur. The adjacent pointings, thus allowing it to be discriminated against
propagationofpositronsintheGalaxyhasbeenextensivelyin- themask-encodedsignalfromthesky.
vestigated(Guessoumetal.1991,2005;Jeanetal.2009;Alexis For our analysis, we used exposures of various parts of the
etal.2014).Bythedetectionofcosmicrayelectronsatloweren- Galaxy,accumulatedoverelevenyearsoftheINTEGRALmis-
ergies(<∼MeV),ithasbeenshownthattheycanpropagateonkpc sion, during orbit numbers 21 to 1279, with gaps due to en-
scalesintheISM(e.g.Lingenfelteretal.2009).Detailedpropa- hancedsolaractivity,calibration,orannealingperiods.Theex-
gationcalculations(Higdonetal.2009;Alexisetal.2014)have posuresforparticularregionsintheskyaregiveninTable1.
shownthatpositronsmaypropagateuptokpcdistancesormore The difference in exposure between positive and negative
when they face a very low density, and hot ISM phase before longitudes, integrated over all latitudes, is less than 7% (see
annihilation.Incontrast,whenpositronsenterthemuchdenser, Fig. 1). Data selections are applied to suppress contamination,
A84,page2of16
T.Siegertetal.:Gamma-rayspectroscopyofpositronannihilationintheMilkyWay

45
0
−135 −90 −45 45 90 135
−45
Fig.2. Image showing the model components as assessed in the sky
modelfitstudy.ThecomponentsarerelatedtotheonesfromSkinner
Fig.1. Sky exposure with SPI for the data set analysed. The units of etal.(2014),seeTable2fordetails.Theweightedsumoffluxesforeach
themaparegivenincm2s.Theequivalentexposuretimeiscalculated celestialcomponentinthe80binsintheanalysedenergybandfrom490
for19detectorswithaneffectiveareaof∼75cm2 forphotonenergies to530keVisshown.Twoadditionalpointsourcestoimprovethefit,
around511keV.Thecontours,startingfromtheinnermost,correspond theCrabandCygX-1,arenotshown.Theimagehasbeenscaledby
toexposuresof22Ms,16Ms,9Ms,4Ms,2Ms,1Ms,0.5Ms,and takingthecuberoottoemphasisethelowsurface-brightnessandextent
0.1Ms,respectively.Thetotalexposuretimeis160Ms. ofthedisk.
e.g.fromsolarflareevents.Ourdatasetthusconsistsof160Ms 2.3. Celestialemissionmodelling
of exposure, with 73590 telescope pointings. Taking into ac-
count the detectors failures, 1214799 individual spectra are to Inourspectralfits,weuseamulti-componentdescriptionofthe
beanalysed. distribution of the emission over the sky. In a recent analysis
of a similar data set in a single 6 keV energy bin, centred on
the 511 keV line, Skinner et al. (2014) propose a representa-
2.2. Analysismethod tionofthepositronannihilationskyinwhichtheemissionfrom
thediskisrepresentedbyatwo-dimensionalGaussianfunction
Ouranalysismethodisbasedonacomparisonofmeasureddata
withdifferentwidthsinlongitudeandlatitude,andthatfromthe
withpredicteddatafrommodels.Thecomparisonisperformed
bulge as the sum of three components: two symmetrical three-
inadataspaceconsistingofthecountsperenergybinmeasured
dimensional Gaussians and a third component which is consis-
ineachofSPI’sdetectorsforeachindividualexposure(pointing)
tentwithapointsource.OneoftheGaussiansrepresentingthe
aspartofthecompleteobservation.
bulgeisoffsettonegativelongitudeswhiletheothercomponents
Wedescribedatad perenergybinkasalinearcombination
k are centred at the Galactic centre (in the case of the point-like
oftheskycontribution,i.e.modelcomponentsM ,towhichthe
ij component,thepositionisactuallytakenasthatofSgrA*,see
instrument response matrix R is applied for each image ele-
jk Fig.2).PointsourcesareaddedatthepositionsoftheCrab,and
ment j, and the background, i.e. components B for line and
ik CygX-1.Althoughsuchmodellingincludescorrelationsamong
continuum instrumental background. Scaling parameters θ for
i components, it can be seen as an alternative to having a large
N areprovidedforskyandN backgroundcomponents:
I B number of pixels on the sky or orthogonalised functions that
(cid:88) (cid:88)NI (cid:88)N(cid:88)I+NB havenoastrophysicalbasis,asitassociatesskycomponentswith
d = R θM + θ B . (1) plausibleandexplicitsourceregions.Thesixcomponentsused
k jk i ij i,t ik
formodellingthecelestialemissionintheenergyrangefrom490
j i=1 t i=NI+1 to530keVarelistedinTable2.Asthelatitudeandlongitudeex-
We fit these scaling parameters, using the maximum likeli- tentofthediskareconsideredthemostuncertainparameters,for
hood technique, applied to energy bins covering the spectral ourspectroscopicanalysisinfineenergybins,wescantheplau-
range of interest. The energy band used, from 490 to 530 keV sibleparameterregionwith100differentdiskshapes/extentsin
with 0.5 keV energy bins, is chosen to allow the study of the both,longitudeandlatitudewidth(seeSect.3.1.1).
shapeofthe511keVannihilationline,togetherwiththeortho- In total, we use N = 6 components to model the celestial
I
positronium continuum, and a Galactic gamma-ray continuum. emission in this energy range, in addition to a two-component
The scaling parameters θ for the N sky components are set background model (N = 2), described below. The celestial
i I B
constantintime,whilethescalingparametersforthe N back- emissioninthisenergyrangeisdominatedbythebright511keV
B
ground components, θ , are allowed to vary with time t (see line emission from the Galaxy’s centre, modelled by a nar-
i,t
Sect.2.4). row bulge (NB) and a broad bulge (BB), and the low surface-
For each camera configuration, corresponding to a given brightness disk. In the centre of the Milky Way, a point-like
numberofworkingdetectors,aspecificimagingresponsefunc- source, called Galactic Centre Source (GCS) was used to de-
tionisappliedtoeachoftheskymodelcomponentstoaccount scribe the morphology. The two strongest continuum sources
for the shadowgram of the mask. These response functions are in the sky, the Crab and Cygnus X-1, have been added to the
differentfortheoff-diagonalterms,whichaccountforscattering skymodelsinordertoimprovethemaximumlikelihoodfit(see
indeaddetectorsfollowedbydetectioninanotherdetector.This Sect.3.1.4forthesignificancesofthesepointsourcesintheanal-
effectcreatesatailintheexpectedspectrumtowardsloweren- ysedenergyrange).
ergies.Forphotonsbetween490and511keV,thistailcontains In our model fitting we obtain model amplitudes in each
about3%ofthelineflux(seealsoChurazovetal.2011). of the 80 energy bins, for each of the sky model components,
A84,page3of16
A&A586,A84(2016)
Table2.Characteristicsoftheskymodelcomponentsassumedinour shapedcontinuumC(E)(seeEqs.(2)–(5)).
analysis.
(cid:18) E (cid:19)αj
C(E) = C (2)
0,j
511keV
Comp. G.Lon. G.Lat. Lon.extent Lat.extent
(cid:32) (cid:33)
position position (FWHM) (FWHM) G(E) = A exp −(E−E0,ij)2 (3)
[deg] [deg] [deg] [deg] 0,ij 2σ
ij
NB −1.25 −0.25 5.75 5.75 1 (cid:18) τ (cid:19)
BB 0.00 0.00 20.55 20.55 T(E) = exp − ij ∀E >0 (4)
τ E
Disk 0.00 0.00 141.29 24.73 ij
GCSa,b −0.06 −0.05 0.00 0.00 L(E) = (G⊗T)(E)
CCyragbXa -1a −17715..3444 −53..0778 00..0000 00..0000 = (cid:114)π2A0τ,ijσij exp2τij(E−2Eτ20,ij)+σ2ij
ij ij
Notes.TheparametersaresimilartothoseofSkinneretal.(2014),ex-
cinegpttofoart2hDeegxrtiednstcoafnthfoerdaiskto.tTalhmedaxisikmeuxmtenlitkhealishboeoednocvheorsaelnla8c0cboirnds- ×erfcτij(E√−E0,ij)+σ2ij· (5)
(seeSect.3.1).(a)Anextentof0◦isequivalenttoapointsource.(b)The 2σijτij
GalacticCentreSourcehasbeenchosentocoincidewiththepositionof
In Eqs. (2)−(5), C is the amplitude of the continuum at
SgrA*(seetextfordetails). 0,j
511 keV for detector j, and α the respective power-law index.
j
A istheamplitudeoflineiindetector j,E isrelatedtothe
0,ij 0,ij
peakvalue1ofthelineshape,σ istheintrinsicwidthofalinein
ij
thuscomprisinganindividualspectrumofcelestialemissionper a particular detector, and τ the degradation parameter in units
ij
component.Hencewearenotbiasedtowardsanyexpectedspec- ofkeV.
tralshapefromcelestialemission.Withtheexceptionofexplor- The time period used for accumulation, three days, is suit-
ingtheeffectsofchangingthediskparameters(whicharemost able (i.e. short enough) to investigate the gradual change in
uncertain;seeSect.3.1.1),wedonotaltertheshapeparameters detector responses due to cosmic-ray bombardment. By fitting
oftheimagemodelcomponents.Wethusdonotfollowtheop- the integrated spectra per detector in the chosen time-intervals,
timisation of all sky components (i.e. NB, BB, CGS, and disk) weobtainaconsistentdatabaseofbackgroundanddetectorre-
asstudiedinasingle6keVwideenergybin,butuseadditional sponseparameters(C ,α , A , E ,σ ,τ )whichprovides
0,j j 0,ij 0,ij ij ij
spectralinformation,andanalysecrosscorrelationamongcom- the ingredients to re-build the instrumental background at each
ponents(seeAppendixA.4). energy,time,andpereachdetector.Thereafter,wecanmodelthe
changesbetweendetectorannealings2intheparametersdescrib-
ingtheresponseofeachdetectorasalinearfunctionoftimeand
2.4. Backgroundmodelling
energy.
Our approach to instrumental background is not restricted to The last step of background modelling is then the predic-
datainaspecificenergybin,andexploitsthephysicalnatureof tion of background for our dataset of interest, which we use to
background.Westudybackgroundlineswiththeircharacteristic study celestial signals on top of the background, in each spe-
shape,temporalchanges,andrelativeintensitiesbetweendetec- cificenergyrangeofinterest.Thedatabaseparametersrepresent
tors, and validate their behaviour on the basis of the associated essentially the behaviour of the background dominated count
physicalprocesses.Bycombiningdataacrossabroaderrangeof rates in the instrument because the varying sky contribution is
energyandtimeperiods,webuildaself-consistentdescriptionof smeared out. The database parameters allow us to reconstruct
spectral detector response and background characteristics, sep- a background pattern, i.e. the expected count rate of each de-
arately for continuum background and each line. At the same tectorrelativetoeachothers,forinstrumentalbackgroundlines
time,weensureconsistencyofinstrumentalaspects(e.g.theres- and instrumental background continuum. Due to the nature of
olution as it behaves with energy and time) as well as physical theseprocesses,thepatternisdifferentforthesetwobackground
constraints(linesfromthesameisotopesbehaveidentically).We components,linesandcontinuum,foreachanalysedenergybin.
thusseparatelong-termstablepropertiesoverthemissionyears The short-term pointing-to-pointing variations as traced by an
fromvariationsonshortertimescalescausedbycosmic-rayin- instrumental rate (here: side shield assembly total rate of the
tensityvariationsanddetectordegradation.Gamma-raycontin- SPIinstrument,SSATOTRATE),areimprintedontopofthepre-
uum and line backgrounds are treated separately, according to definedpatternsforacoherentdescriptionofthebackgrounddue
theirdifferentphysicalnature. tocosmicrays.
Special care is, however, needed to obtain the proper abso-
Wefirstdeterminewhatbackgroundlinesarerequiredtobe
lutenormalisationofthisbackgroundmodel.Therelativedetec-
taken into account by examining spectra accumulated over all
tor contributions to total continuum and line backgrounds may
detectors and the whole length of the data set. Then we apply
not be properly normalised, as each of these are derived from
spectralfittingtodataaccumulatedoverperiodslongenoughfor
adatasetstretchingfurtherintime.Therefore,were-normalise
adequatedetailincharacteristicspectralsignatures.Lineshapes
are thus determined for each detector over sufficiently long in- thebackgroundmodelasre-builtfromthedatabaseagaintothe
tegrationtimestoensurethatlinecentroidsandwidthsarewell
1 ThepeakvalueofthisconvolvedlineshapeisapproximatelyE =
defined beyond statistical uncertainties but only as long as the peak
E −τforτ<1keV.
degradation becomes significant to change the line shape. The 0
2 Duetocosmicraybombardment,thelatticestructureoftheGede-
lineshapeL(E)weuseforthespectralfitsistheconvolutionof
tectorsisdamagedgradually,whichcausesdeteriorationoftheirspec-
a Gaussian function G(E) with an exponential tail function to- tralresolvingproperties.Therefore,twiceayear,thedetectorarrayis
wards lower energies T(E), describing the degradation of each heatedupto100◦CtorepairthelatticestructureoftheGedetectors.
detector j, changing with time, superimposed on a power-law Thisiscalledannealing.
A84,page4of16
T.Siegertetal.:Gamma-rayspectroscopyofpositronannihilationintheMilkyWay
actualdata,byfittingatime-dependentscalingparameter,θ in
i,t 2255
Eq.(1),perbackgroundcomponentinadditiontotheproposed
skymodelscalingparameters.
In general, the detection of diffuse emission with a coded- bin 2200
masktelescopelikeSPI,i.e.emissiononangularscalescompa- gy
rabletotheFoV,reliesonthecorrectcomparisonoffluxinone ner
pointingwiththatinanother.Suchemissionwilladdonlysmall er e 1155 OPortshiotr−onium +
vtlaaalrrgisaeigt-isnocanalsl.eFferuomrmtihsesiritosmnpodaretut,reitrnhngeoathfveereroalbagsteievrcevoandtteirotienbcsuttoairroonruafntridoomsatpeoaxrtttheicneudtleoad-r ficance p 1100 γ2−9raσy Continuum 5kl5ine18eV1σ γC−ornatyinuum
targetontheskywillnotvarymuchasthe5×5ditheringisper- gni 17σ
formed.Itwillhoweverlikelychangewhenthetargetdirection Si 55
of pointings is redirected by a significant fraction of the tele-
scopeFoVormore.Thefixedrelativedetectorpatterns,derived
forinstrumentalbackgroundlinesandinstrumentalbackground 00
449900 550000 551100 552200 553300
continuum, are our key tools allowing the shadowgrams from
Energy [keV]
themasktobedistinguished,astheychangebetweenpointings.
Systematic mismatches of the celestial and background detec- Fig.3.Detectionofgamma-raysfromtheGalaxyinthespectralrange
tor patterns may make it more difficult to find mask-encoded ofpositronannihilationsignatures.Thesignificanceofdetectingasig-
sky signals, and can thus reduce the sensitivity. We perform a nalfromthesky,summedoverallspatialcomponentsasdescribedin
thetext,isgivenforeach0.5keVwidebininunitsofσ.Wecanidentify
re-normalisation of background detector patterns whenever the
theintenselineat511keV,togetherwithanortho-positroniumcontin-
telescopeisre-orientedtotargetalocationintheskythatismore
uumfrompositronannihilation,andanunderlyinggamma-raycontin-
distantfromthecurrentthan∼oneFoV;re-scalingbyfittingat
uumemissioncomponent.
three-dayintervalsforeachofthetwobackgroundcomponents
isadequatetorecoverpropernormalisation.
Theadequacyofourbackgroundmodelhasbeenassessedin
Fig.5,showingχ2−d.o.f.foreachenergybin.FortheentireSPI-
Table 3. Correlation coefficients for the six simultaneously fitted sky
camera (black), the values scatter around a value of 1713 (cor-
components.
respondingtoareducedχ2 of1.0014with1211021degreesof
freedom(d.o.f.))andfallwellintoa3σgoodness-of-fitinterval
NB BB Disk GCS Crab CX-1
(orangearea).Noparticularenergyregionisoveremphasisedin
themaximumlikelihoodfits,noraresingledetectorsdeviant.In NB 1.000
BB −.836 1.000
total,ourbackgroundmodelfittingdetermines3772parameters
Disk .118 −.365 1.000
perenergybin.
GCS −.535 .224 −.028 1.000
Crab −.018 .050 −.102 .004 1.000
CX-1 −.005 .003 .051 .001 −.004 1.000
3. ResultsandInterpretation Notes.Meancoefficientsaregivenacrossallenergybins.
Wedeterminespectraofskyemissionfromfitsofintensityco-
efficients for each energy bin in a 40 keV wide range around
the 511 keV line. Figure 3 shows for each energy bin the de-
tection significance of the celestial signal, based on our as-
sumed description of the sky in terms of the six components
in Table 2 (see Sect. 2.3). The significance is calculated using
continuum emission from the Galaxy (Bouchet et al. 2011) is
the likelihood-ratio between a background-only fit to the data
the strongest signal in the disk, clearly detected even in this
andafitincludingthebackgroundplussixcelestialsources.The
40 keV band. The two strongest continuum sources in this en-
difference of d.o.f. in each energy bin is consequently 6. The
ergy band, the Crab and Cyg X-1 (point sources), are also de-
dominantannihilationlineat511keVisveryclearwithatotal
tected, at 31σ and 11σ, respectively; their spectral parameters
significance of 58σ, but characteristic ortho-positronium con-
areconsistentwithliteraturevalues(seeSect.3.1.4).Inthecen-
tinuum on the low-energy side of the line is also detected with
tre of the Galaxy, an additional point-like source (or cusp, i.e.
high significance, as is the underlying diffuse Galactic contin- a point-like source that was recognised above the diffuse bulge
uumemission(Bouchetetal.2011).Thecontinuumemissionis
emissiontoimprovetheoverallfittoINTEGRALobservations
predominantlyfromthediskandfromtheCrabandCygX-1.
in the 511 keV annihilation line) is needed to improve the fit.
Fixing the positions and extents of the other components, we
3.1. Differentemissioncomponents findasignificanceof5σforthiscomponent.
Thesignalsfromthedifferentskycomponentscannotbede-
TheinnerGalaxyisfoundtobethebrightestregionoftheanni-
terminedindependently,andwehavecalculatedcorrelationco-
hilation gamma-ray sky, confirming previous findings. It is de-
efficients for the values found for their intensities from the co-
tectedwithasignificanceofmorethan56σ(e.g.Jeanetal.2006;
variancematrixinthemaximumlikelihoodfits.Thesearegiven
Churazov et al. 2011). We also detect a signal away from the
inTable3.Averagevaluesaregivensincetheenergydependence
inner Galaxy. Our disk-like emission component has a signifi-
isnegligible,beinglessthan0.01%.
cance of 12σ. The surface brightness of annihilation radiation
for this disk component is rather low. The diffuse gamma-ray Wenowdiscusstheresultsforeachoftheskycomponents.
A84,page5of16
A&A586,A84(2016)
−1V)] 00..44 TγNO−oarCttrharoool nwB−tPiu nlil’ungsu:ee m : sII:p ==Ae c60Ct ..r=19u 46m0±±. 200(7.b.70±e670s,,t. 2fFfiP0Wst =pHa 1Mr.a0Sm8KY0e ±=te0 r2.s0.)52:99±0.17 keV, ∆E0 = 0.09±0.08 keV −1V)] 11..00 TγNO−oarCttrharoool nwD−tPi insli’unksu :es m :p IIe: ==cA t51Cru ..=26m 165 ±±(.b530e8..23s±55t1 ,,fi. 0fFtP 3Wps a=Hr a0Mm.9Se0KYt2e ±=r0s 2).1:.4972±0.51 keV, ∆E0 = 0.16±0.18 keV
e 00..33 e 00..88
k k
5 5
0. 0.
−1s ( 00..22 −1s ( 00..66
−2m −2m
c c 00..44
h h
p 00..11 p
−30 −30 00..22
1 1
x [ x [
u 00..00 u
Fl Fl 00..00
449900 550000 551100 552200 553300 449900 550000 551100 552200 553300
Energy [keV] Energy [keV]
(a) Bulge. (b) Disk.
Fig.4.Spectrumofannihilationgamma-raysfromthebulgea)andthediskb).Thebestfitspectrumisshown(continuousblackline),asdecom-
posedinasingle511keVpositronannihilationline(dashedred),thecontinuumfromannihilationthroughortho-positronium(dashedolive),and
thediffusegamma-raycontinuumemission(dashedblue).Fittedandderivedparametersaregiveninthelegends.Seetextfordetails.
2000 sametime,fortheenergyregion490to530keV.Wefindthatthe
diskextentisalsosensitivetohowthecentralpartsoftheGalaxy
are modelled, due to their overlap (see Appendix A.4 for fur-
5000 1000 or therdiscussionofthebulgemorphologydependence).Scanning
ect solutionswithdifferentdiskextents,givenafixed/optimalcon-
et
d.o.f. 0 0 per d filigkeulriahtoioondosfoltuhteiobnuligne,eaanchd peonienrtgysobuirnc.esI,nwteotfialn,dfoarmaagxrimiduomf
2χ − o.f.) 10 × 10 different longitude and latitude widths, ranging from
d. σ = 15◦,...,150◦, and σ = 1.5◦,...,15◦, respectively, models
− l b
−5000 −10002χ( havebeencalculatedforeachofthe80bins,andthenfittedto-
gether with the other five sky model components and the two
background model components. All model scaling parameters,
−2000 fluxperenergybinandcomponent,havebeenre-optimisedfor
490 500 510 520 530 eachpointofthismodelgrid.
Energy [keV] Figure 6 shows the dependence of the disk and the bulge
Fig.5.Backgroundmodelperformancemeasuredbyχ2-d.o.f.foreach 511 keV line intensity on the assumed disk-extent parameters.
energy bin (i) for the entire SPI camera (left axis, black data points); Contoursindicatetheuncertaintyonthediskextent,asderived
and(ii)fortwoexampledetectors(rightaxis,detector00blue,detector from the component-wise fit. As the disk becomes larger, its
13green).Theidealvalueof0.0(correspondingtoareducedχ2of1.0) 511keVlinefluxestimateincreasesbecausealsoverylowsur-
is shown as a dotted line, together with the 1, 3, and 5σ uncertainty face brightness regions in the outer disk, and at high latitudes,
intervals for a χ2-statistic with 1211021 d.o.f. The majority of points contribute to the total flux (top). The individual relative uncer-
fallintothe3σband.Noexcessisevidenteitherintheenergydomain
taintiesofeachtilearealmostconstantat∼20%forthedisk,and
orforparticulardetectors.
∼5%forthebulge.Thebulge511keVlineintensityishardlyde-
pendent on the disk size (bottom). Over the disk longitude and
latitude grid, the line flux changes by ∼15%, whereas the 1σ-
3.1.1. ThediskoftheGalaxy uncertaintyontheline-fluxfromthisscanisessentiallyconstant
at 0.96 × 10−3 phcm−2s−1 (see Sect. 3.1.2 for further discus-
The disk of the Galaxy is represented in our model by a two- sion).IntheinnerpartsoftheGalaxy(|l| <∼ 45◦),confusionbe-
dimensional Gaussian. We find a longitude extent of 60+10 de- tween the bulge and the disk components causes the bulge to
−5
grees,andalatitudeextentof10.5+2.5degrees(1σvalues).Inan appearweakercomparedtothedisk.Theuncertaintyofthein-
−1.5
independentanalysisforthe511keVlineinasingle6keVwide tensityofthe511keVlinecanbeestimatedfromthetangentsof
energy bin (Skinner et al. 2014), the disk extension parameters equalfluxastheyintersectthe(2∆log(L) = 1)-contours(where
are found in the range of 30-90◦ in longitude and around 3◦ in L is the likelihood, see Appendix A.1 for details). A disk ex-
latitude. Their study included the impact of different bulge pa- tentaround60◦inlongitude,and10.5◦inlatitude,assuggested,
rametersanddifferentbackgroundmethods.Assumingtheback- doesnotagreewithdiskparametersobtainedbyothermethods,
ground model described in Sect. 2.4 and the above mentioned focussingonthelineonly(e.g.Bouchetetal.2010).Thespectra
bulgemodel,inourspectrallyresolvedanalysis,wecanreduce per component retain their line shape and properties in a rea-
theuncertaintyonthe(model-dependent)diskextent. sonably wide region around these best values, and systematic
Our best disk extent is obtained by optimising for both the changesintotalannihilationintensityremainsmallcomparedto
annihilation line and Galactic continuum components at the statisticaluncertainties.
A84,page6of16
T.Siegertetal.:Gamma-rayspectroscopyofpositronannihilationintheMilkyWay
Disk 511 keV line flux 00..55 Total Disk l>0 spectrum (best fit parameters):
111524...772555 6σ5σ4σ3σ 3.0 −1keV)] 00..44 NγO−arCtrhrooonw−tPi nli’unsu:e m : II: ==A 20C ..=68 872±±.6106..31±740,,. 4fFP9Ws =H 0M.8S9KY7 ±=0 3.1.0577±0.34 keV, ∆E0 = 0.30±0.14 keV
Disk latitude extent [deg] 115896.....2227755555 4σ1σ2σ 3σ 5σ 122...505−3−2−1Line flux [10 ph cm s] −3−2−1ux [10 ph cm s (0.5 000000......223311
3.75 1.0 Fl
00..00
2.25 6σ 5σ 6σ 0.5
0.75
449900 550000 551100 552200 553300
7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5127.5142.5157.5 Energy [keV]
Disk longitude extent [deg]
Total Disk l<0 spectrum (best fit parameters):
111524...772555 6σ5σ4σ3σBulge 511 keV line flux 1.0 −15 keV)] 0000....4455 γNO−arCtrhrooonw−tPi nli’unsu:e m : II: ==A 20C ..=18 003±±.0108..11±820,,. 4fFP4Ws =H 0M.8S4KY8 ±=0 1.1.5890±0.19 keV, ∆E0 = 0.07±0.17 keV
Disk latitude extent [deg] 115896.....2227755555 4σ1σ2σ 3σ 5σ 0000....6789−3−2−1Line flux [10 ph cm s] −3−2−1Flux [10 ph cm s (0. 000000......121233
3.75
00..00
2.25 6σ 5σ 6σ 0.5 449900 550000 551100 552200 553300
0.75
Energy [keV]
7.5 22.5 37.5 52.5 67.5 82.5 97.5 112.5127.5142.5157.5
Disk longitude extent [deg] Fig.7.Spectrumofannihilationgammaraysfromtheeastern(top),and
Fig.6.Dependenceofthe511keVlineintensityinthedisk(top)and western(bottom)hemisphereoftheGalaxy’sdisk.Thefittedparameters
the bulge (bottom) as a function of the choice of the disk extent (1σ are given in the legends, colours are the same as in Fig. 4. No flux
Gaussianwidthvalue).Lineintensitiesareshownasshading,seescale asymmetryisfound.
on right-hand axis. Overlaid are the uncertainty contours for the disk
size,asderivedfromthemaximumlikelihoodfitsinthegrid-scan.See
the Crab and Cyg X-1 continua was set to −2.23 (Jourdain &
AppendixA.3formoredetailsandotherparameterimpacts.
Roques2009).
We find a 511 keV line intensity for the disk
of (1.66 ± 0.35) × 10−3 phcm−2s−1. Our Galactic
Figure 4b shows the disk spectrum for these optimum disk gamma-ray continuum flux density of (5.85 ± 1.05) ×
sizeparameters. 10−5 phcm−2s−1keV−1 at 511 keV corresponds to3
We characterise these spectra in more detail, deriving the (5.99 ± 1.07) × 10−6 phcm−2s−1sr−1keV−1 integrated
511 keV line intensity (I ), the width, characterised as kine- acrossthefullsky,consistentwithresultsbyStrongetal.(2005)
L
maticbroadening(FWHMSKY),thecentroidshift,interpretedas andBouchetetal.(2011)4.Themeasured511keVlinewidthin
Doppler-shiftfrombulkmotion(∆E = E −E ),theortho- the disk is (2.47±0.51) keV (FWHM). This is in concordance
0 peak lab
positronium intensity (I ), and the positronium fraction (f ). with the bulge value (see, however, the discussion in Sect. 4.1;
O Ps
We represent the expected spectral components by a Gaussian seealsoSect.3.1.2).The511keVlineshift,(0.16±0.18)keV,
511 keV line, an ortho-positronium continuum (Ore & Powell is consistent with zero. The ortho-positronium continuum has
1949), and a power-law representing the diffuse Galactic anintensityof(5.21±3.25)×10−3phcm−2s−1.
gamma-ray continuum – each convolved with the SPI spectral Our statistics from eleven years of data allow us to de-
response function and the parametrised kinematic broadening rive spectral parameters separately for the eastern (l > 0◦)
(see Sect. 2.4). We use Monte Carlo sampling to determine the and the western (l < 0◦) hemisphere (see Fig. 7). Here, the
uncertainties of the fitted spectral characteristics, parametrised Gaussian-shaped disk component is masked on alternate sides
through the 511 keV line centroid, width, and amplitude, the (l > 0◦, and l < 0◦), which results in fitting now seven
ortho-positroniumamplitudeatthemeasuredlinecentroid,and
3 Herewetruncatetheemissionat1%ofthemaximalsurfacebrigh-
thecontinuumflux-densityat511keV.Asthepower-lawindex
ness;alongtheGalacticplanetheintensityalwaysisabovethatthresh-
for the diffuse Galactic continuum is poorly determined in our
oldandisthereforetakenintoaccountas2π;towardshigherlatitudes,
spectralband,andinanycasehasrathersmallimpactonthean- 99%oftheemissionareenclosedwithin∼70◦.Hence,thediskemis-
nihilationcomponentvalues(<∼3%),wedecidedtofixitsvaluea sionenclosesasolidangleof3.11πsr.Note,thatthisvalueistherefore
priorito−1.7(Kinzeretal.1999,2001;Strongetal.2005;Jean modelandthresholddependent.
etal. 2006;Churazovet al.2011; Bouchetet al.2011), consis- 4 Strongetal.(2005)andBouchetetal.(2011)focusedonabroader
tentwithournarrow-bandfits.Likewise,thepowerlawindexfor energyrangeandonthecentralpartoftheMilkyWay.
A84,page7of16
A&A586,A84(2016)
individual sky components. The 511 keV line intensities are Total GCS spectrum (best fit parameters):
((w00e..88fi70n±±d00n..o1124d))is××k11a0s0−y−3m3pmphhectcrmmy−−i2n2sst−−h11effoloirnreththfleeu(xl(le<s>;0i◦n0)◦cr)oenrgetigroainos.tnT,tohaunasdn, −1eV)] 00..0044 γNO−arCtrhrooonw−tPi nli’unsu:e m : II: ==A 20C ..=88 300±±.0106..71±790,,. 0fFP5Ws =H 0M.9S3KY5 ±=0 3.1.4867±0.64 keV, ∆E0 = −0.27±0.31 keV
k
earlierreport(Weidenspointneretal.2008),oureast-westratio 5 00..0033
miso1v.0ed9,±by0.s2h4i.ftTinhgetahseymnamrreotwry-bisulrgeeduccoemdp,oifnnenottcawomayplfertoemlytrhee- −1s (0.
center by about −1.25◦ in longitude and −0.25◦ in latitude, as −2m 00..0022
describedabove(seeSkinneretal.2014).Wefindaneast/west h c
rfaotriothfeodritffhuesoerGthaol-apcotiscitgroanmiumma-craoyntcinounutimnuoufm(1o.f2(80±.860.±970).2a0n)d. −310 p 00..0011
Allvaluesareconsistentwith1.0. ux [ 00..0000
Fl
−−00..0011
3.1.2. Thebulgeregion
449900 550000 551100 552200 553300
Energy [keV]
We model the central part of the Milky Way by a combination
Fig.8.Spectrumofannihilationgammaraysfromthepoint-likesource
of two 2D-Gaussians, NB and BB, from Skinner et al. (2014).
(GCS) superimposed onto our extended bulge model in the Galaxy’s
There,theNBisfoundtobecenteredat(l,b)=(−1.25◦,−0.25◦)
centre.ThefitanditscomponentsareindicatedasaboveinFig.4.
withGaussianwidthsof(σ,σ ) = (2.5◦,2.5◦),theBBisfound
l b
centeredat(l,b)=(0◦,0◦)andextendsto(σ,σ )=(8.7◦,8.7◦)
l b
(see Table 2). The correlation between the NB and BB com-
ponents (see Table 3) with a value of −0.836 is not surpris- ortho-positronium continuum is consistent with zero (<2σ),
ing, as two (or more) model components coincide/overlap spa- and assuming there is none leads to a slightly smaller value,
tially,whenmappedontothesky(seediscussioninSect.4and (510.59±0.35)keV.
AppendixA.3).Wedefinethebulgecomponentfromthesuper-
positionofthesetwoGaussians,NBandBB.Thisdefinitionrep-
3.1.4. Othersources
resentsananalyticaldescriptionofanobject’sshapeonthesky,
independentandnot basedonastronomical,model-biaseddefi- The Crab pulsar (Jourdain & Roques 2009) and Cygnus
nitionsoftheGalacticbulge,e.g.asdefinedbyastellarpopula- X-1(Jourdainetal.2012)aretheonlyknownGalacticsources
tionorbyinfraredemission.Wepreferherethisdefinition,asan strongenoughtoinfluenceouranalysisandareincludedascon-
alternativeandcomplementtoastrophysicalmodelfitting,con- stantpointsources.
sideringthatsuchstudies(Weidenspointneretal.2008;Higdon TheCrabisdetectedinourenergybandat31σsignificance.
etal.2009)remainedquestionable. Usingapower-lawwithafixedphotonindex5of−2.23(Jourdain
In Fig. 4a, the spectrum of the bright bulge shown. It has & Roques 2009), we find a flux density of (2.20 ± 0.07) ×
511keVlineintensityof(0.96±0.07)×10−3 phcm−2s−1 and 10−5 phcm−2s−1keV−1 at511keV.Ouroverallfluxinthisen-
is detected with an overall significance of 56σ. The bulge an- ergybandisconsistent,thoughonthehighsideof,theanalysis
nihilation emission can be characterised by a 511 keV line of acrossthefullenergyrangeofSPI(Jourdain&Roques2009).It
astrophysical width (2.59 ± 0.17) keV, and a positronium isequivalenttoabout40%ofthetotaldiffuseGalacticgamma-
fraction of (1.080 ± 0.029), consistent with other recent stud- raycontinuumemission.
ies (Jean et al. 2006; Churazov et al. 2011). The line peak ap- CygnusX-1isdetectedat11σsignificance.Itsspectrumis
pearsat(511.09 ± 0.08)keV.ThediffuseGalacticgamma-ray described well by a single power-law spectrum with a (fixed)
continuum is a minor contribution in the bulge; its intensity is power-lawindexof−2.23,andaresultingfluxdensityof(0.65±
(0.27 ± 0.20)×10−5phcm−2s−1keV−1. 0.06)×10−5 phcm−2s−1keV−1.CygX-1istimevariable,with
a hard, a soft, and possibly an intermediate state (McConnell
et al. 2002; Rodriguez et al. 2015). At 511 keV, the measured
flux difference between the hard and the soft state is about
3.1.3. TheGalacticcentreregion
1.5×10−4phcm−2s−1keV−1(McConnelletal.2002).Ourmea-
suredaverageofthedifferentpossiblespectralstatesofCygX-1
TheimmediatevicinityinthedirectionofthecentreoftheMilky
are in good agreement with recent measurements of Rodriguez
Way could be discriminated in Skinner et al. (2014) as a sepa-
etal.(2015).AsCygX-1isonlyaweaksourceinthevicinityof
rate source or cusp. Given the spatial model that we adopt, the
511keV,andonlyusedforimprovingthemaximumlikelihood
GCSisdetectedwithasignificanceof5σandwecanprovidea
fit,notimevariabilityhasbeentested.
firstspectrumfromtheannihilationemissionofthissource.The
The correlations between the continuum sources and the
511keVlineintensityis(0.80±0.19)×10−4 phcm−2s−1 (see
otherskymodelcomponentsarenegligible,exceptforthecorre-
Fig.8).Itsannihilationemissionischaracterisedbyabroadened
lationwiththedisk.Ineithercase,andespeciallyforCygX-1,
linewithawidthof(3.46±0.64)keV(FWHMaboveinstrumen-
the flux depends on the size of the disk emission model. If the
talresolution),andapositroniumfractionof(0.94±0.19).There
disk is chosen to be (unrealistically) short, the flux density of
isaslighthintofanunderlyingbroadcontinuumwithafluxden-
CygX-1captures(erroneously)apartofthisdiskemission.
sityestimate of(0.06±0.05)×10−5 phcm−2s−1keV−1.There
isnoevidenttimevariabilitydowntoscalesofmonths.
5 Theenergyrangechosenisnotenoughtoconstrainthepower-law
The annihilation line is centred at (510.73 ± 0.31) keV index. The fitted value for the power-law index, given our data, is
if the spectrum is described by the above mentioned spec- (−1.41±1.52)fortheCrab,and(−2.9±4.5)forCygX-1.Theresulting
tral model. Formally, there are indications of a red-shift: The fluxvalueschangebylessthan0.3%.
A84,page8of16
T.Siegertetal.:Gamma-rayspectroscopyofpositronannihilationintheMilkyWay
Table 4. Upper limits (2σ, in units 10−5 phcm−2s−1) for 511 keV 4.2. Annihilationconditions
gamma-raylineemissionoriginatingfromtheCraborCygX-1.
The positronium fraction, f = 2/(3 + 9IL), expresses how
Ps 2 4IO
manypositronsannihilatethroughanintermediatestateofform-
Narrowline Broadline
ing a positronium atom. It can be derived from the intensities
Crab 6.62 7.44
of511keVline I andortho-positroniumcontinuum I ,andis
CygX-1 1.27 1.89 L O
a prime diagnostic of annihilation conditions. Formation of the
Notes.Limitsforanarrow(1.6keVFWHM),andabroadline(3.5keV positronium atom is only efficient below energies of ∼100 eV
FWHM)aregiven. and is facilitated in a partially neutral medium through charge
exchange reactions with atoms and molecules. In principle, the
ionisationstate,temperature,andcomposition(H,He,gas/dust)
canbederivedfromthepositroniumfraction,comparingmodels
We detect no (<2σ) annihilation signals in these additional andtheirpredictedpositroniumfractionswithvaluesdetermined
sources.Upperlimitsare givenforbothsourcesinTable4, as- fromspectralfits(Churazovetal.2005,2011;Jeanetal.2006;
suming either a disk-like, i.e. narrow 511 keV line (1.6 keV Guessoumetal.2010).
FWHM), or a GCS-like, i.e. broad 511 keV line (3.5 keV Themeasuredpositronium fractionsinthebulgeandin the
FWHM),respectively. diskasawholeare(1.08±0.03)and(0.90±0.19),respectively.
Inadditiontooursixcomponentmodel,wesearchedforpos- Comparingtheeasternandwesternhemisphereofthedisksep-
siblepoint-likeannihilationemissioninthesatellitegalaxiesof arately, we find values of (0.90 ± 0.16) and (0.85 ± 0.18), re-
theMilkyWay,becauselightdarkmatterparticlesmayalsobea spectively. All values are consistent within uncertainties, and,
candidatesourceofpositrons(Boehmetal.2004;Gunionetal. moreover,withthetheoreticalphysicallimitof1.0.Ourchoice
2006;Hooperetal.2004;Picciotto&Pospelov2005;Pospelov ofenergyregion(490to530keV)mayresultinabiastowards
et al. 2008), and dwarf galaxies are believed to be dark matter highortho-positroniumflux.Thetotalannihilationspectrumof
dominated (e.g. Simon & Geha 2007; Strigari et al. 2008). We the Galaxy shows a positronium fraction of (0.99 ± 0.07). We
find≥2σexcessemissioninonlysixof39candidatesources(17 conclude that the annihilation conditions based on only fPs are
of39showa1σexcess),whichisinsignificantconsideringthe thesamethroughouttheentirediskandinthebulgewithinmea-
numberoftrials(Siegertetal.,inprep.). surementuncertainties.
We also searched for a 511 keV line from the Andromeda Asecondorderdiagnosticsofannihilationconditionsisthe
Galaxy (M31, modelled as a point-source), (l/b) = (121.17/− shape, and particularly the width, of the 511 keV annihilation
21.57)◦ (Evans et al. 2010), finding an upper limit of 1 × line. Here, kinematics of the positron population, and the gas
10−4phcm−2s−1(2σ). todustratiooftheambientmedium,aredrivingprocesses.The
parameterswhichdescribetheannihilationconditionsarelisted
inTable6forallcomponents.
In the two disk hemispheres, we find a velocity spread of
4. Discussion (950±100)kms−1and(1800±200)kms−1,respectively,above
theinstrumentallinewidth.Thisapparentdifferenceintheline
4.1. Mutualspectralparametercompatibilities
widthinthetwodiskhalvescanbeinterpretedinseveralways,
In Table 5, we provide a summary of the fitted spectral param- depending on the relative contributions of kinematic and ther-
etersforallcomponentsincludedinouranalysis,andthefitted mal broadening. The contribution from Galactic kinematics is
parameters for a total, i.e. Galaxy-wide spectrum which serves probably small as the estimated velocity dispersion from in-
as a conservative average of positron annihilation throughout terstellar gas is ∼100 kms−1 (Dame et al. 2001), or up to
the Milky Way. The line and continuum intensities of the sin- 300kms−1 ifthepositronsoriginateintheβ+-decayof26Alin
gle components add up to the total Galaxy-wide intensities, as thedisk(Kretschmeretal.2013).Asweareperformingline-of-
expected. The widths of the single components formally range sight integration over a whole hemisphere, we might be influ-
from1.59keVto3.46keVandareconsistentwithameanvalue encedbypeculiarsamplingofdifferentannihilationregions,but
fromtheentireGalaxyexceptfortheeasternandwesternhemi- thenitwouldbesurprisingtoobservethesameflux.
sphere of the disk. The western hemisphere of the disk shows
a smaller line width (FWHM of (1.59 ± 0.19) keV) than the
4.3. SourcesthroughouttheGalaxy
easternhemisphere((3.07±0.34)keV).Wefinda2.8σsignif-
icanceforthetwohalvestodifferfromeachother.Eachofthe Inthebrightbulge,theannihilationlineiswellrepresentedbya
twohalvesdifferby1.4σfromthecombineddiskspectrum(see singleGaussian-shaped511keVline,andthepositroniumcon-
AppendixA.5forfurthercomparisons;seealsoSect.4.2).Line tinuumisclearlyidentified.InthediskoftheGalaxy,theanni-
widths above the instrumental resolution are in bulge and disk hilation continuum from ortho-positronium is only marginally
(total) (2.59±0.17) keV and (2.47±0.51) keV (FWHM), re- seen, the underlying Galactic-diffuse continuum is however
spectively,i.e.theyareidenticalwithinuncertainties.Likewise, clearly detected, while only marginal in the bulge region. We
the line width of the bulge differs by 2.7σ, compared to the interpretthisasadiskannihilationsignaturewithitscharacter-
line width of the western disk, and by 0.9σ to the eastern one. isticshapeandratherhomogeneoussurfacebrightness,whichis
The GCS line width appears broader (3.46 ± 0.64 keV) but subdominantwhenviewingtowardsbulgeduetotheothercom-
is still consistent within 2σ uncertainties, compared to bulge ponentswhichhavelargersurfacebrightnesses.
and disk (total). The GCS is discussed in Sect. 4.4, separately. Thebulge-to-disk(B/D)fluxratiois0.58±0.13;the(model-
The Doppler-shifts, ∆E0, are essentially consistent with zero dependent6) luminosity B/D ratio is 0.42±0.09. As increasing
shift within 2σ. The positron fractions are consistent with 1.0
throughout the galaxy (see below). The spectral fit quality is 6 Basedoneffectivedistancestothebulgeof8.5kpc,andtothedisk
foundadequateforallourmodelcomponents. of10.0kpc.
A84,page9of16
A&A586,A84(2016)
Table5.Spectralparametersforeachskycomponentandrespectiveχ2fitvalueswithd.o.f.
Cont.flux LineFlux FWHM ∆E o-PsFlux Pos.frac. χ2/d.o.f.
0
dens.
TheBulge 0.27(20) 9.6(7) 2.59(17) 0.09(8) 61.4(7.6) 1.08(3) 66.47/74
Disk(−180◦<l<180◦) 5.58(1.03) 16.6(3.5) 2.47(51) 0.16(18) 52.1(32.5) 0.90(19) 71.98/74
Disk(l>0◦) 2.66(49) 8.7(1.4) 3.07(34) 0.30(14) 26.8(13.7) 0.90(16) 83.79/74
Disk(l<0◦) 3.08(44) 8.0(1.2) 1.59(19) 0.07(17) 21.0(11.8) 0.85(18) 68.42/74
GCS 0.06(5) 0.8(2) 3.46(64) −0.27(31) 2.8(1.8) 0.94(19) 64.94/74
Crab 2.20(7) <0.7 −(−) −(−) −(−) −(−) 66.97/78
CygnusX-1 0.65(6) <0.2 −(−) −(−) −(−) −(−) 73.38/78
Galaxy(total) 8.79(85) 27.4(3) 2.61(23) 0.15(9) 116.3(29.3) 0.99(7) 75.00/74
Notes.Continuumfluxdensitiesaregivenasthevalueat511keVinunitsof10−5phcm−2s−1keV−1,lineandortho-positroniumfluxesaregiven
in10−4phcm−2s−1,FWHMofthecelestialemissionlineinkeV,thecentroidshift∆E =E −E inkeV.Theupperlimitsgivenfortheline
0 peak lab
fluxfromtheCrabandCygX-1are2σvaluesandthecorrespondingχ2quotedarewithnoline.Onesigmauncertaintiesaregiveninbrackets.
Table6.Spectralparametersandconvertedphysicalpropertiesforthe Massivestars(26Al: N˙e+ = 0.4×1043 e+s−1),core-collapse
maincomponents. supernovae (44Ti: N˙e+ = 0.3 × 1043 e+s−1), LMXRBs (N˙e+ ≈
1−2×1043 e+s−1),andSNeIa(N˙e+ ≈ 1−2×1043 e+s−1)can
Velocity Bulkmotion add up to the total positron production rate in the Milky Way.
spread But escape from sources and transport in the ISM surrounding
TheBulge 1500(100) 53(47) thesources(escapefraction)isakeyaspectforbothSNeIaand
Disk(total) 1450(300) 94(106) LMXRBs(inparticularmicroquasars),whichcanresultinmajor
Diskl>0◦ 1800(200) 176(82) uncertaintiesintheseabsolutenumbers(Alexisetal.2014).
Diskl<0◦ 950(100) 41(100) Detailed calculations of the positron escape fraction in the
GCS 2050(400) −159(182) 56Ni→56Co→56Fe-decaychain,dominatingthepositronproduc-
Galaxy(total) 1550(150) 88(53) tioninSNeIa,predict5±2%escape,basedontheassumptionof
unmixed ejecta in W7 model (deflagration) calculations (Chan
Notes.Thevaluesarequotedinunitsofkms−1.Onesigmauncertain-
& Lingenfelter 1993). Observational support for this theoreti-
tiesaregiveninbrackets.
calestimatehasbeenfoundbysubsequentstudies(Milneetal.
1999), investigating the bolometric late-time light curves of a
exposure now reveals disk emission at low surface-brightness setofSNeIa,withanaverageescapefractionvalueof3.5±2%
fromanextendedandthickdisk,thismayexplainwhyourB/D (seealsoMilneetal.2001andthediscussionbyKalemcietal.
ratioislowerthaninpreviousanalyseswithlessdata,whereB/D 2006).Fromtheir56NiyieldandGalactictypeIasupernovaoc-
wasreported>1(Knödlsederetal.2003,2005;Weidenspointner currence rate estimates, SNe Ia are expected to produce about
et al. 2008). The bright bulge would preferably suggest origins N˙e+ ≈(1.6 ± 0.6)×1043e+s−1.Similarvalueshavebeenfound
of the positrons among old stellar populations, such as from by others (Martin et al. 2012), and thus would make SNe Ia
SNe Ia, novae, LMXRBs, and microquasars (see discussion by throughtheir56Ni-decaysoneofthedominantpositronproduc-
Prantzos et al. 2011). Our best-fit latitude extent of the empir- ersintheGalaxy.Notethatthepositronescapefractionhasnot
ical disk model favours a rather large scale height (∼1 kpc). beenmeasureddirectly,yet.
ThissuggeststhatpositronsmaybeejectedfromX-raybinaries Formicroquasars,positronproductionhasbeenproposedto
and may annihilate further away from the sources, resulting in arise from photon-photon interactions in their jets or closer to
a low surface-brightness (Prantzos 2008; Prantzos et al. 2011). thecompactgamma-raysource(Beloborodov1999b;Guessoum
Accretingblack-holebinariesmaybemorefrequentinthebulge et al. 2006), with a rough estimate of the average positron pro-
(3000sources,Bandyopadhyayetal.2009)thaninthedisk,and ductionrateof≈1041e+s−1permicroquasar.Assumingthetotal
could also reproduce the observed brightness distribution and measuredannihilationrateof(3.5−6)×1043 e+s−1 torepresent
diskextent.Wehaverecentlymeasuredpositronannihilationin a steady state, it is necessary that several hundreds of micro-
the black hole binary V404 Cyg, which is in the Galactic disk quasarsareactiveateachtimetomeettheconstraint.Thisiscon-
, at (l/b) = (73.12◦/−2.09◦), and ∼125 pc above the Galactic sistent with the expected/estimated number of black hole bina-
plane,supportingtheconjectureofmicroquasarsasasourceof riesintheMilkyWay,between103andafew104(Romani1992;
Galacticpositrons(Siegertetal.2015,inreview). Portegies Zwart et al. 1997; Sadowski et al. 2008), weighted
Positron production rates can be estimated from our mea- withanaveragedutycycle(i.e.flaring(microquasar)vs.quies-
surements, assuming a steady state and effective source dis- cent(XRB)state)between10−3−10−2.However,itisnotknown
tances (see above). We obtain values of 2 × 1043 e+s−1 and how many positrons annihilate directly in pair plasma ejecta
3×1043e+s−1,forbulgeanddisk,respectively.Theseestimates or escape the source. A similar estimate was carried out by
aremodel-dependent,buthelptodiscusstheorderofmagnitude Weidenspointner et al. (2008), who suggested LMXRBs to be
forthepositronproductioninthedifferentcomponents. responsible for the asymmetric spatial distribution reported at
Radioactivityfromtheβ+-decayof26Aland44Tioriginating thattime.Nosuchasymmetryisnowobserved.
inmassivestarscontributestopositronproductionand511keV TheFermibubbles(Su&Finkbeiner2012)mightraise an-
diskemission,assuggestedfromthe26Almorphologythrough- other type of candidate positron source: It has been suggested
outtheGalaxyderivedwithCOMPTEL(Diehl1995;Oberlack thattheFermibubblesaremanifestationsofrecentjetactivityof
etal.1996;Plüschkeetal.2001),andrecentlywithSPI(Bouchet SgrA*(Su&Finkbeiner2012;Yangetal.2012),andthusmay
etal.2015);seediscussionbyMartinetal.(2012). bereminiscent of ordinaryradio lobesin externalgalaxies (see
A84,page10of16