Positron annihilation spectrum from the Galactic Centre region observed by SPI/INTEGRAL ...

20 Pages·2010·0.7 MB·English

Mon.Not.R.Astron.Soc.000,1–20(2001) Printed6October 2010 (MNLATEXstylefilev2.2)
Positron annihilation spectrum from the Galactic Centre
region observed by SPI/INTEGRAL, revisited:
annihilation in a cooling ISM?
0
1
0 E. Churazov,1,2 S. Sazonov,2 S. Tsygankov,1,2 R. Sunyaev,2,1 D. Varshalovich3
2

t
c 1 Max-Planck-Institut fu¨rAstrophysik, Karl-Schwarzschild-Strasse 1, 85741 Garching, Germany
O
2 Space Research Institute (IKI), Profsoyuznaya 84/32, Moscow 117997, Russia
3 Ioffe Physical Techincal Institute, Polytekhnicheskaya 26, St Petersburg 194021, Russia
5

]
E 6October2010
H
.
h ABSTRACT
p We analyse SPI/INTEGRAL data on the 511 keV line from the Galactic Centre,
- accumulatedover∼6yearsofobservations.WedecomposetheX-rayandsoftgamma-
o
ray emission of the central part of the Milky Way into a relatively compact “Bulge”
r
t and a more extended “Disk” components and report their spectral properties. The
s
a Bulge component showsa prominent 511keV line andessentially no flux at 1.8 MeV,
[ while the Disk component on the contrary contains a prominent 1.8 MeV line and a

very weak annihilation line.
1
Weshowthatthespectralshapeoftheannihilationradiation(thenarrow511keV
v
4 lineandtheassociatedothro-positroniumcontinuum)issurprisinglywelldescribedby
6 a model of annihilation of hot positrons in a radiatively cooling interstellar medium
8 (ISM). The model assumes that positrons are initially injected into a hot (∼106 K),
0 volumefillingISM,whichisallowedtofreelycoolviaradiativelosses.Theannihilation
. time in suchamedium is longerthanthe coolingtime fortemperatures higherthan a
0
few 104 K. Thus, most of the positrons annihilate only after the gas has cooled down
1
0 to∼105 K,givingrisetoannihilationemissioncharacteristicofawarm,ionizedISM.
1
Key words: Galaxy: centre – gamma rays: observations – ISM: general
:
v
i
X
r
a 1 INTRODUCTION at thecentreoftheMilky Waywith aFWHMof 6–8◦ (e.g.
Jean et al. 2003; Kn¨odlseder et al. 2005; Churazov et al.
Although the annihilation line of positrons at 511 keV
2005), while the 511 keV flux coming from the Galactic
is the brightest gamma-ray line in the Galaxy, the ori- planeismuchlessconstrainedbytheINTEGRALdata(e.g.
gin of the annihilating positrons in not yet firmly es-
Teegarden et al. 2005; Bouchet et al. 2008). No significant
tablished. First observed with a NaI scintillator as a
variabilityinthenarrow511keVlinehasbeenfoundinthe
∼476keVlinecomingfromtheGalacticCentre(GC)region
SPI data (Tsygankov & Churazov 2010). The spectrum of
(Johnson, Harnden,& Haymes 1972; Johnson & Haymes
the annihilation radiation from the Galactic Centre region
1973), it was subsequently unambiguously identified with
observedbySPIcanbereasonablywelldescribedasacom-
a narrow (full width at half maximum, FWHM< 3.2
bination of a narrow line (∼2–3 keV Gaussian at 511 keV)
keV) e+e− annihilation line using germanium detectors
and a three-photon continuum. The flux ratio between the
(Leventhal,MacCallum, & Stang 1978). Since then many
three-photon continuum and the narrow line suggests that
balloonflightsandseveralspacemissions(e.g.Gehrels et al.
themajority of positrons form positronium prior to annihi-
1991; Mahoney,Ling, & Wheaton 1994; Teegarden et al.
lation (e.g. Churazov et al. 2005; Jean et al. 2006).
1996; Purcell et al. 1997) have measured the spatial distri-
Inspiteofnumerousobservations,theorigin ofthe511
bution and spectral properties of theline.
keV emission from the GC is not established. The problem
Since2003,INTEGRALdataonthe511keVlineemis- can besummarised as follows:
sion became available. These data show that there is a
strong, ∼ 10−3phot s−1 cm−2, source of 511 keV photons • The morphology of the observed 511 keV line emission
(cid:13)c 2001RAS
2 Churazov et al.
doesnotfitthedisk-likespatialdistributionofsuchobvious indicator of high background. Several additional observa-
sources of positrons as i) massive stars, which produce β+ tions were also omitted from the analysis, e.g. those taken
unstable nuclei like 26Al or ii) π+’s generated by the inter- shortlyafterSPIannealingprocedures(Roqueset al.2003).
action of cosmic rays with the interstellar medium (ISM). Forouranalysis weused acombination of single and pulse-
Thisfavoursscenarioswithamoreprominentcentralexcess shape-discriminator (PSD) events (see Roqueset al. 2003,
(“bulge dominated”), including the old stellar population for details) and treated them in thesame way.
(e.g.supernovaeIa),activityofSgrA∗ andtheannihilation
of dark matter particles.
• Thespectrumoftheannihilationemission (narrowline 2.1 Energy gain and resolution
width and the flux ratio of the line and three-photon con-
For each detector, a linear relation between theenergy and
tinuum)suggeststhatpositronsareannihilatinginawarm,
thechannelnumberwasassumedandcalibrated(separately
∼ 104 K, and slightly ionized, ∼ a few %, medium (e.g.
for each orbit), using the observed energies of lines at ∼
Churazov et al. 2005; Jean et al. 2006).Such an ISMphase
198, 438, 584, 882, 1764, 1779, 2223 and 2754 keV (see
does exist in the Galaxy, but its spatial distribution is
Weidenspointneret al.2003,foracomprehensivelistofSPI
stronglyconcentratedtowardstheplane,posingtheproblem
backgroundlines).WiththiscalibrationtheRMSdeviation
of “finding” theright ISM phaseby a positron.
ofthebackground511keVlineenergy(revolutionbased)is
Recently an attempt to build a self-consistent pic- 0.0066keVwhilethemeanenergyofthelineis510.926keV.
ture was presented by Higdon, Lingenfelter, & Rothschild Thereisthusasmalldeviationofthelinemeanenergyfrom
(2009); Lingenfelter, Higdon, & Rothschild (2009), who as- the electron rest energy (510.999 keV): ∆E = 0.07 keV;
sumed that the spatial propagation of positrons, pro- it can be attributed to the simplified linear energy/channel
duced via β+ decay of 56Ni, 44Ti and 26Al, is governed relation. This deviation is comparable to the statistical un-
by a diffusion process with the effective diffusion coeffi- certainty on the line energy (see §5) and no attempt was
cient different in the bulge and the disk of the Galaxy. made tocorrect for this effect.
During diffusion the positrons enter the HII and HI en- Since the background 511 keV line (produced by the
velopes of molecular clouds, in particular those forming a positrons annihilating in the body of the detector) is kine-
“TiltedDisk”(Ferri`ere, Gillard, & Jean2007)within1.5kpc matically broadened, we used the two bracketing lines (at
oftheGC.ThemodelofHigdon, Lingenfelter, & Rothschild 438 and 584 keV) to calculate the resolution at 511 keV as
(2009),withareasonablesetofassumptions,canexplainthe FWHM511 = 0.5×(FWHM438 +FWHM584). The result-
basic properties of theannihilation radiation. ing value is FWHM511 =2.175 keV when averaged over all
Here we take an alternative route and consider a pos- observations in thevicinity of theGalactic Centre.
sibility that a significant fraction of positrons are born in
the hot ISM, which is eventually able to cool via radiative
2.2 Background modeling
losses and perhapsviaadiabaticexpansion. Weshowbelow
that with these assumptions the spectral properties of the Inthebackgroundmodelingwefollowed theschemeusedin
511 keVlinecan beeasily explained.However,to makeour Churazov et al. (2005). Namely, the background count rate
pictureself-consistent oneneedstomodelthethermalstate B(i,E) in detector i at energy E is assumed to be propor-
oftheISM,whichisbeyondthescopeofthepresentpaper. tional to the detector saturated (i.e. above 8 MeV) event
This paper is based on the INTEGRAL data accumu- rate Rsat and time t:
lated over ∼ 6 years of observations and aims at placing
tighter constraints on the spectral and spatial properties of B(i,E)=C(i,E)+α(i,E)×Rsat+β(i,E)×t, (1)
theannihilation emission.
where i = 1,19 is the detector number. The coefficients
α(i,E) and β(i,E) of this linear relation were determined
separately for each detector/energy channel using all the
2 DATA AND BACKGROUND HANDLING availableSPIdata,whiletheconstantC(i,E)wasestimated
usingonlythedataawayfrom theGalactic planeandaway
SPIisacodedmaskgermaniumspectrometeronboardIN- from bright sources. The whole data set was divided into
TEGRAL (Winkler et al. 2003), launched in October 2002 14 time intervals (defined by theannealing periods and the
aboard a PROTON rocket. The instrument consists of 19 dates of individual detector failures1) and the coefficients
individualGedetectors,hasafieldofviewof∼30◦ (atzero α(i,E), β(i,E) and C(i,E) were determined separately for
response), aneffectivearea at 511keVof ∼70cm2 anden- eachinterval.Thisprocedure,althoughnotprovidingaper-
ergyresolution of∼2keV(Vedrenneet al.2003).Thegood fectdescriptionofthebackground,worksreasonablywellat
energy resolution makes SPI an appropriate instrument for allenergiesand,giventhesmallnumberoffreeparameters,
studyingthespectrum of e+e− annihilation emission. is very robust. For instance, the relative RMS deviation of
Forouranalysisweusealldataavailabletousbymid- the 600–1000 keV flux (averaged over one revolution) from
2009, including public data, some proprietary data (in par- thecount rate predicted bythis model is ∼1.3 10−3.
ticular, proposals 0420073, 0520071 and parts of 0620059). Along with our reference background model, we made
Prior to actual data analysis, all individual observations
were screened for periods of very high particle background.
WeusetheSPIanticoincidence(ACS)shieldrateasamain 1 Threeoutofthe19SPIdetectorshadfailedbytheendof2009.
(cid:13)c 2001RAS,MNRAS000,1–20
Positron annihilation spectrum from the Galactic Centre 3
Figure 1.Exposure map(inGalactic coordinates) showingallthe observations used inthepresent analysis. Off-Galactic-plane obser-
vationswereusedfordeterminingtheinstrumentbackground.Foreachobservation,theeffectiveobservingtimeisaddedtothepixelin
themapcontainingthepointingdirectionofthetelescope’s axis.Thetotal exposureisabout70Ms.Pixelsare2degrees onaside.
severalexperimentsbydividingthefulldataset intodiffer- counts and the exposure map gives the count rate image,
ent time intervals and modifying the selection criteria used which is crudely converted into units of phot/s/cm2 using
forcleaningthedatafrombackgroundflares.Intheseexper- theeffectiveareaforanon-axispointsource.Suchmapswill
imentswegeneratedseveral“alternative”backgroundmod- provideacorrectpointsourcefluxifthetelescopeispointed
els. Below we usethesemodels totest thesensitivity ofour directly towards the source. But given the large size of the
results to thedetails of the background modeling. SPIFoV(∼30◦ diameteratzeroresponse)andsparsecover-
ageofthesky,’lightbucketmapping’producesrathercrude
maps, while the procedure itself is very simple and robust.
Weuselight bucketmappingtoget aglobal surface bright-
3 IMAGING
nessmaportofollowthevariationsofthesurfacebrightness
Imaging with coded mask telescopes often requires addi- along and across the Galactic plane with poor angular res-
tionalassumptionstobemadeontheskysurfacebrightness olution. Note that in this mode SPI is used as a collimated
distribution, e.g. sparsity of compact sources or regular be- instrument and its mask imaging capabilities are not ex-
haviour of diffuse emission. This is especially important for ploited.Thenetflux(differencebetweentheobservedcount
the SPI telescope, which has only n = 19 independent de- rateandpredictedbackgroundmodel)crucially dependson
tectors/pixels. This makes image reconstruction in a single thequality of thebackground model.
observation problematic, given that a typical image recon-
structionprocedurereliesonthesmallnessoftheparameter
3.1.1 Scans along the Galactic plane
1/n with respect to unity. We have chosen not to make a
priori assumptions about thespatial distribution of sources
In Fig. 2 we show slices of the Galaxy along the Galac-
and restricted ourselves to three different types of “imag-
tic plane in three energy bands. Each slice has a width of
ing”:(i)lightbucketimaging,(ii)simpleparametricmodels 16◦ perpendicular to the Galactic plane and is centred at
and (iii) linear decomposition of the sky surface brightness b=0◦ . Thestep along the Galactic planeis 2◦ for thetwo
into few simple templates. upperpanels and 4◦ for thebottom panel.
Intheupperpanel(50–100keV),threeprominentpeaks
correspond (from left to right) toCyg X-1,Galactic Centre
3.1 Light bucket mapping
and the Crab Nebula. The width ∼30◦ and the complex
In this simple “imaging” procedure, for each observation, structureofthepeaksnearthemaximum(clearlyvisiblefor
the background subtracted counts in a given energy band Cyg X-1) are due to the presence of the mask and partly
are summed over all detectors and the resulting signal is due to the intrinsic variability of the sources. The few re-
addedtothepixelofthemapcorrespondingtothetelescope gionswithnegativefluxescorrespondtoobservationswhere
pointingdirection.Similarlytheexposuremapisformedby theactual background countrate ishigher thanthemodel-
adding the exposure times (see Fig. 1). The ratio of the predictedbackgrounddescribedin§2.2.Notethatthemodel
(cid:13)c 2001RAS,MNRAS000,1–20
4 Churazov et al.
0
0
0
100 0 -100
l, deg
Figure2.Scans(lightbucketimaging)alongtheGalacticplanein3energybands.Fluxesareaveragedover2◦binsoverland±8◦ over
b. For the 1804–1813 keV band, the width of the bins along l is 4◦ . By construction all points are statistically independent (except
through the background subtraction). Vertical grey bars show the positions of the series of scans perpendicular to the Galactic plane
discussedin§3.1.2.ThepositionsoftheCrabNebula,CygX-1andCentaurus Aaremarkedwiththeverticaldottedlines.
background was calculated using a set of “blank fields”, the “blank fields” is higher than that from some patches of
whose definition is problematic given the large size of the theGalactic place free of strong sources.
SPI FoV. The sets of blank fields are different in each of Themorphology ofthesliceinthe508–514 keVband2,
the14timeintervalsusedinthebackgroundmodelling(see
§2.2).Forthisreason,itispossiblethattheactualfluxfrom
2 See Teegardenetal. (2005) for an earlier version of a similar
plot.
(cid:13)c 2001RAS,MNRAS000,1–20
Positron annihilation spectrum from the Galactic Centre 5
containing the 511 keV line (Fig. 2, middle panel), is with the black curves the expected light bucket profiles for
markedly different. With the 2◦ bins along the Galactic thecasewherethespatialdistributionofthefluxinthe508–
plane,theonlyprominentfeatureisthepeakattheGalactic 514 keV band follows the “Bulge” model described later in
Centre,withtheextentalonglroughlysimilartotheextent §3.5.Theexpectedprofileswerecrudelyestimatedassuming
of the peak near Cyg X-1 at low energies. The peak flux is that theaxis of theinstrument was movingalong b at fixed
∼ 10−3 phot s−1 cm−2. As already emphasized, this value l,whilekeepingtheposition angle fixed.Thiscauses visible
is not a precise measure of the true 511 keV flux from the asymmetry in the peak of the l ∼ 0◦ profile, reflecting the
GalacticCentreregion,butitshouldbeaccuratetoafactor particularorientationoftheSPIcodingmaskrelativetothe
of better than 2 if the source size does not exceed several source. In reality, the observed profiles are combinations of
degrees. observations with varying position angle and varying l and
No strong asymmetry of the positive and negative hence they may differ from the simulated profiles in subtle
longitude wings of the central peak is apparent in the details. Broadly, the light bucket imaging shows theoverall
light bucket profiles (see, however, Weidenspointneret al. consistencywithabulge-dominateddistributionofthe508–
2008, who report an excess flux for negative longitudes 514keVfluxandindicatesthatthediskemissionisweakat
and Bouchet et al. 2008, who do not find strong evidence l∼ -45◦ .
for asymmetry). An excess at negative longitudes l ∼ -
25◦ is visible in the light bucket profile in Teegarden et al.
3.2 Simple parametric models
(2005) (their Fig. 2). Renormalization of their fluxes to
the units used in Fig. 2 suggests an excess at the level We now use a simple function – two-dimensional Gaussian
∼ 1.5 10−4 phot s−1 cm−2. In our analysis the flux at l ∼ – to model the spatial distribution of the annihilation line
-25◦ isessentially consistentwithzero.Ifanything,thepro- emission neartheGalacticCentre.Thedatacollectedwhen
files shown in Fig. 2 suggest an excess in the 508–514 keV the INTEGRAL pointing direction was within 30◦ of the
flux at positive longitudes l ∼ 25◦ . However, our experi- GC were used. Two models were considered:
ments with “alternative” background models mentioned in
§t2o25.◦a2)flshucoxawneexdacpetphssea/atdraeafiwtceieatikothfsep∼rur1ni0oe−gua4staipvshyeomotmrs−pet1orsycimt(icv−oe2rrlaoetnsp|gloi|tn∼udd2ien0sg–. GGD(l,(lb,)b) ==FF11××ee−−(cid:26)(cid:26)ll2WW2llllnn2222++bbWW22llbbnn2222(cid:27)(cid:27),+F2×e−(cid:26)bW2Dln22(cid:27), (2)
We therefore conclude that, with the present knowledge of
whereG(l,b)isthesurfacebrightnessdistributionasafunc-
the SPI background, light bucket profiles do not provide
tionofGalacticlongitudeandlatitude,F isthefluxandWl,
compellingevidenceforasymmetryinthe508–514 keVflux
Wb are the full widths at half maximum along l and b, re-
along theGalactic plane.
spectively. The second model has an additional component
Finally in the bottom panel of Fig. 2, the slice of the
that is aimed to account for emission elongated over the
Galactic plane in the 1804–1813 keV band, containing the Galactic plane. Since only the data within 30◦ of the GC
1.8MeVlineof26Al,isshown.Unlikethe511keVemission, wereused(30◦ correspondstothedeviation oftheSPI axis
thereisabroad peak (muchbroaderthan theSPI response
from the GC), the “infinite” extent of this component over
to a point source), centred at the GC. This distribution is
l means that the surface brightness of this component does
qualitatively consistent with the Comptel (Plu¨schke et al. not decrease much at a distance of ∼45◦ from theGC.
2001) and earlier INTEGRAL results (Wanget al. 2009).
To verify the sensitivity of the results to a particular
functional form, we also used an exponential law instead of
theGaussian:
3.1.2 Scans perpendicular to the Galactic plane
A similar approach of light bucket mapping can be applied E(l,b) =F1×e−rWl2l2+Wbb22, (3)
itno2th0e07s,p2ec0i0a8l sacnadns20o0f9t.heThGealpaocstiitciopnlasnoefatlhoengscbanpserifnorlmaerde ED(l,b) =F1×e−rWl2l2+Wbb22 +F2×e−W|bD| .
denoted with the gray vertical lines in Fig. 2. Three out of For a given pair of Wl and Wb, the model is convolved
fourscansweremadeasasequenceofpointingsstartingand with the simulated SPI response (Sturneret al. 2003) and
ending ∼30◦ away from the plane on either side of it. The comparedwiththecountrateinthe508–514keVbandinin-
pointing direction was changing in ∼2◦ steps. The remain- dividualdetectorsduringindividualobservations.Thebest-
ing “scan” at l=0 had been done earlier as a set of point- fittingvalueof F1 for theone-component model or thepair
ings directly at the plane and ∼25◦ above and below the of values F1 and F2 for the two-component model is calcu-
plane.Theadvantageofmaking“fast”(taking10–15hours) lated.Hereandinallthesubsequentanalysis,weusesimple
scans overaselected region of thesky is thatthequality of χ2 statistics. Theproblemsofusingtheχ2 criterion forlow
thebackgroundmodelingcanbeverified/improvediftypical photon counting statistics are circumvented following the
variations of the detector background occur on longer time recipe of Churazov et al. (1996). Namely, the standard de-
scales. viation associated with the count rate in a given spectral,
The scans in the 508–514 keV band in the direction spatial or time bin is evaluated using the mean count rate
perpendiculartotheGalacticplaneatl∼0◦ ,22◦ ,-45◦ are averaged overa large numberof “nearby” similar bins.
showninFig.3.Thesignalisclearlyvisibleatl∼22◦ andis Typicalvaluesofχ2 perdegreeoffreedomforourmod-
closetozeroforl∼-45◦ .Toguidetheeye,wehaveplotted els are ≈ 1.01. Given the large number of degrees of free-
(cid:13)c 2001RAS,MNRAS000,1–20
6 Churazov et al.
0
-40 -20 0 20 40
b, deg
Figure 3. Scans (light bucket imaging) perpendicular the Galactic plane at l∼ 0◦ , 22◦ ,-45◦ inthe 508–514 keV energy band. The
solidanddashedcurvesapproximatelyshowtheexpectedprofilesatl∼0◦ and20◦ ifthespatialdistributionofthefluxinthe508–514
keVbandisadequately describedbythe“bulge”componentdescribedin§3.5.
dom (∼250000= numberof detectors times thenumberof of the minimum for the two-component model does not de-
observations) and the very low signal-to-noise ratio of the pendmuchonthewidthoftheextendedcomponentoverb.
annihilation signal in individual observations, this value is WetriedforthesecondcomponentWD =2◦ ,WD =6◦ and
nInosttaeauds,etfuhleinchdaicnagteorofofχt2heca“nabbseoluusteed”qtouacloitmypoafrtehedimffeordeenlt. WD =10◦ aswell asan exponentialshape e−nW|bD| o instead
of the Gaussian, and got essentially the same best-fitting
models or place constraints on themodel parameters. parameters (8◦ × 6◦ ) for the central Gaussian.
Theresultingcontoursofχ2forbothmodels(asafunc-
tion of the parameters Wl and Wb) are plotted in Fig. 4. Weemphasizeherethatthepresenceofthesecondcom-
The dashed lines correspond to the one-component model ponent does not necessarily imply that the Galactic disk
(pure2D Gaussian), while the solid lines correspond to the is ”detected”, but rather that a single symmetric Gaus-
two-component model GD(l,b) (see eq. 2). The black dots sian/exponential component is not a perfect description of
mark the positions of χ2 minima. Contours are spaced by thedata.
∆6th◦χe(2itfw=toh-3ec.oomTneph-oecnobemensptto-mnfioettnditnelgm)3vo.adleuleissoufsetdh)eawniddt∼h8s◦a×re61◦0◦(fo×r Wb∼A2n◦ecxapnoanlesnotbiaelushseadpetoe−dnesW|cl|lroib−entW|hbb|eocewnittrhalWcolm∼p3o◦naenndt
(see Table 1) instead of a Gaussian. In fact, the largest im-
Clearly, for the pure 2D Gaussian model the data sug- provement in the χ2 is achieved when both the central and
gest a significant flattening of the distribution towards the
diskcomponentsaredescribedasexponentialfunctions(Ta-
plane.Ifanadditionalcomponent,extendedalongtheplane, ble1).Whilethedifferencein theχ2 betweenvariousmod-
is included (the two-component model in eq. 2), then the
els (e.g. one-component exponential versus one-component
best-fitting central Gaussian is much more symmetric in l
Gaussian)isformallystatisticallysignificant,itcorresponds
andb.Theimprovementinχ2forthetwo-componentmodel tolessthan1%changeinthe∆χ2valuerelativetothe“null
comparedtotheone-componentmodelis∼40.Theposition
hypothesis”ofazerofluxinthe508–514 keVbandoverthe
entiredataset.Atthislevel,aparticularvalueof∆χ2 fora
given model might besensitive tothesubtlefeatures of the
3 NotethatweusedagridoverFWHMvalueswitha1◦stepand dataset.Ourexperimentswithdifferentbackgroundmodels
a7◦ ×6◦ Gaussian gives almostthesameχ2 as the best-fitting have indeed shown that the ranking of models in terms of
8◦ ×6◦ Gaussian. χ2 can slightly vary.Forexample, the rankingof theGaus-
(cid:13)c 2001RAS,MNRAS000,1–20
Positron annihilation spectrum from the Galactic Centre 7
40
30
20
10
0
4
3
2
1
-50 -40 -30 -20 -10 0 10 20 30 40 50
Figure5. χ2asfunctionofthetiltθofatwo-dimensionalGaus-
sian(solidblackline).ThetiltismeasuredrelativetotheGalac-
Figure 4. Contours of χ2 as a function of the FWHM along ticplane.Positivevaluesofthetiltcorrespondtothemajoraxis
pointingtowardspositivebatnegativel.Foreachvalueofthetilt
l and b when the spatial distribution of the 508–514 keV flux
thebestfittingvaluesoftheFWHMintwodimensionswereiden-
is described by a 2D Gaussian. The dashed lines correspond to
tifiedonacrudeFWHMgridwithstepsof∼1◦ .Theratioofthe
the pure 2D Gaussian model (G(l,b) in eq. 2), while the solid
linescorrespondtothemodelGD(l,b)ineq.2,whichincludesan FWHMs (Wl/Wb) is shown in the bottom panel. The minimum
additionalextendedcomponent.Blackdotsmarkthepositionsof of the χ2 is achieved at θ =12◦ and Wl =14◦ , Wb =4◦ . The
theχ2minima.Contoursarespacedby∆χ2=3.Thebest-fitting largevariationsoftheWl/Wbratioareowingtothecrudenessof
valuesofthewidthare10◦ ×6◦ and7–8◦ ×6◦ forthefirstand thegridandaveryshallowminimuminthefunctionχ2(Wl/Wb)
for a given θ. As |θ| increases the Gaussian converges to a sym-
secondmodel,respectively.
metric structure (Wl/Wb ≈ 1). For comparison, the red dotted
lineshowstheχ2 asafunctionofthetiltifWl andWb arefixed
attheirbest-fittingvaluesof10◦ and6◦ ,respectively,forθ=0.
sian+Gaussian and Gaussian+exponential models in Table
1canchangedependingontheparticularbackgroundmodel.
Despite the difference in the functional forms, the
3.4 Tilted Gaussian
flux in the central component does not depend strongly
on the model used; it varies between 8.4 10−4 and Higdon, Lingenfelter, & Rothschild (2009) have suggested
9.3 10−4phot s−1 cm−2 for all two-components models. that a significant fraction of positrons is annihilating in a
“Tilted Disk” of neutral gas inside the central 3 kpc re-
gion oftheGalaxy.This“Tilted Disk”isoneofthecompo-
nents of the Ferri`ere, Gillard, & Jean (2007) model of the
interstellar gas distribution in the innermost part of the
3.3 Position of the centroid
MilkyWay,basedonearlierresultsofLiszt & Burton(1980)
Usingtheone-componentexponentialmodel(thefirstmodel (see also Liszt & Burton 1996). The Tilted Disk (see Fig. 4
in eq. 3) with Wl = 3◦ and Wb = 2◦ , we tried to vary the in Ferri`ere, Gillard, & Jean 2007) in projection to the sky
centroid of the distribution over a few degrees around the plane has an apparent size of ∼18◦ by ∼5◦ and is tilted by
GC and calculated the changes in the χ2. The best-fitting ∼ 30◦ with respect to the Galactic plane. Since the extent
positionisat(l,b)=(−0.1◦,−0.2◦)andtheminimalχ2 dif- of the Disk in l and b resembles the dimensions of the 511
fersfromthevalueat(l,b)=(0,0)by2.3.Whilethismeans keV source, Higdon, Lingenfelter, & Rothschild (2009) sug-
that formally the statistics of accumulated data is already gest that the positrons reach the disk and annihilate there.
sufficient to measure sub-degree shifts of the centroid, we To test further the Tilted Disk model we fit the data
believethatsystematicuncertaintiesandtheobviouscrude- with a two-dimensional Gaussian allowing for rotation of
ness of the spatial model preclude any firm conclusion. We the major axis. The results are shown in Fig. 5. The best-
can conservatively conclude from this exercise that the po- fittingrotationangleandthewidthsoftheGaussianintwo
sition of the centroid is consistent within ∼0.2◦ with the directionsareθ∼12◦ andWl =14◦ ,Wb=4◦ ,respectively.
position of thedynamic centreof theMilky Way. Theimprovementinχ2comparedtoθ=0◦ (andWl =10◦ ,
(cid:13)c 2001RAS,MNRAS000,1–20
8 Churazov et al.
from L´opez-Corredoira, Cabrera-Lavers, & Gerhard (2005)
and shown in Fig. 6:
• Disk (eq.2–5 in L´opez-Corredoira et al.)
• Disk with a Hole (eq.6–7 in L´opez-Corredoira et al.)
• Bulge (see §3 in L´opez-Corredoira et al.).
This is by no means a comprehensive list of possible tem-
plates (see e.g. Kn¨odlsederet al. (2005) for a systematic
analysis of various templates). However, the hope is that
these spatial templates will capture the most basic proper-
tiesofthe508–514keVfluxdistribution,evenifthephysical
motivation is questionable or the details of shape are not
correct.
We also used slightly modified (truncated) versions of
thesetemplates:foreachtemplatewesettozerothesurface
brightness in all regions where it is smaller than 10% of
Figure 6. The model templates used for fitting the data inthe the peak value. The motivation behind this modification is
508–514keVband(fromtoptobottom):Disk,DiskwithaHole, an attempt to have a template that has a bulge or disk-
Bulge. The projected surface brightness distributions shown are type morphology at high surface brightness but lacks the
based on the 3D models of stellar density distribution adopted extended low surface brightness regions, which might make
fromL´opez-Corredoira,Cabrera-Lavers,&Gerhard(2005). a significant contribution to the total flux.
For a given set of templates, the surface brightness for
eachtemplateisconvolvedwiththesimulatedSPIresponse
Wb = 6◦ ) is ∆χ2 ≈ 7. As discussed already, the values of (Sturneret al. 2003) yielding an expected count rate in the
∆χ2oftheorderofafewareformallystatisticallysignificant
508–514 keV band in individual detectors during individ-
iftheerrorsareduetocountingPoissonnoiseonly.Thetotal
ualobservations.Thebest-fittingnormalizationsofthetem-
changeoftheχ2 whenatwo-dimensionalGaussianisadded platesarethencalculated inordertominimizetheχ2 devi-
tothemodelis∼8000.Comparingthesenumbers,itisclear
ation between theraw data and the model.
thatevenmodestsystematicsinthedatacouldaffectprecise
The χ2 values for the various spatial models are given
derivation of the source spatial characteristics. Taking the
in Table 1. The fluxes quoted in Table 1 are the integrated
resultsshowninFig.5atfacevalue,amarginallysignificant
modelfluxes(withbest-fittingnormalization) overasquare
improvement in the fit is possible if the annihilation region 80◦ × 80◦ region around the GC. The choice of the region
is tilted by ∼12◦ with respect to theGalactic plane.
forthecalculation oftheintegrated modelfluxisratherar-
As |θ| increases beyond 25◦ , the Gaussian con- bitrary. The 80◦ × 80◦ region is not uniformly covered by
verges to an almost symmetric structure. The tilt of θ ∼
observations,andareaswiththesmallest errors(largest ex-
30◦correspondsto∆χ2 ≈23foranalmostsymmetricGaus-
posures) dominate in the determination of the best-fitting
sianwithWl =9◦andWb=7◦.Wethereforeconcludethat
normalization. On the other hand, underexposed (or even
a version of a the Tilted Disk of Ferri`ere, Gillard, & Jean
notobservedatall)areascanstillprovideasignificantcon-
(2007) is not particularly favored by SPI data compared to
tributiontothetotalintegratedflux.Anexampleofaclear
a structure with zero tilt. However, moderate values of the
overestimation of the flux due to this effect is seen for the
title .20◦ are allowed bythe SPI data.
pure “Disk” models in Table 1. These models have poor
χ2, but predict a large integrated flux, since their normal-
ization is largely set by the innermost bright region of the
3.5 Decomposition using plausible templates
Galaxy. This becomes an especially severe problem when
The simple light bucket imaging and parametric fitting of dealingwithfluxesintegratedoververylargeareas(e.g.the
the508–514keVfluxdonein§3.1and3.2suggestthatarea- fluxfromtheentireGalacticdisk).Forthisreason,wequote
sonable description of the data in the central radian could fluxesintegratedoverthe80◦ ×80◦ regionratherthanfrom
beachievedwithanalmost symmetricGaussian atthecen- thewhole Milky Way.
tre and a more extended component along the plane. The Table 1 strongly suggests that the spatial distribution
stellarbulgeandstellardiskarethemostobviousstructural of the 508–514 keV flux in the inner region of the Galaxy
componentsoftheGalaxythatqualitativelyfitthisdescrip- is more extended along the Galactic plane than perpendic-
tion. In fact, there are plenty of disk-like structures (cold ular to it. This is clear from the parameters of the single-
gas,massivestars,cosmicrayinducedgamma-rayflux,etc) component parametric models (see also Fig. 4) and from
and very few components that show a prominent peak at thecomparison oftheχ2 valuesfor theone-component and
the GC. One of the known centrally-peaked distributions two-component (e.g. two Gaussians) models.
is that of the NIR light, which is a tracer of the old stel- Among the one-component models, the exponential
lar population of the Galaxy. For this reason, we decided model has a slightly better χ2 than the Gaussian model or
to restrict our analysis to three simple templates, corre- theBulgemodel. Forthetwo-component models, theexpo-
sponding to stellar components of the Milky Way, adopted nential Bulge + Gaussian Disk has the smallest χ2 among
(cid:13)c 2001RAS,MNRAS000,1–20
Positron annihilation spectrum from the Galactic Centre 9
Table1.Fittingthe508–514keVsurfacebrightnesswithtemplatesandparametricmodels.Quoted∆χ2valueswerecalculatedrelative
to the “null hypothesis” of zero flux in the 508–514 keV band over the entire data set. The data within 30◦ from the GC were used.
Quoted fluxes correspond to the integrated model fluxes (with best-fitting normalization) over a 80◦ × 80◦ square region around the
GC.
Spatial template −∆χ2 F1 F2
Component1 Component2 phots−1 cm−2 phots−1 cm−2
Templates describedin§3.5withthesurfacebrightnesstruncated at10−5 ofmaximum
Disk - 6837.7 (2.20±0.03)10−3 -
Disk/Hole - 6660.3 (2.22±0.03)10−3 -
Bulge - 8252.4 (1.12±0.01)10−3 -
Bulge Disk 8252.5 (1.11±0.03)10−3 (2.4±6.4)10−5
Bulge Disk/Hole 8252.5 (1.11±0.03)10−3 (2.0±6.2)10−5
Templates withthesurfacebrightness truncatedat10−1 ofmaximum
Disk - 6964.0 (1.83±0.02)10−3 -
Disk/Hole - 6758.9 (1.85±0.02)10−3 -
Bulge - 8229.1 (0.97±0.01)10−3 -
Bulge∗ Disk 8252.9 (0.87±0.02)10−3 (2.4±0.5)10−4
Bulge Disk/Hole 8253.0 (0.87±0.02)10−3 (2.3±0.5)10−4
G(l,b)andGD(l,b)modelsfromeq.2and3
GaussianWl=10◦ ,Wb=6◦ - 8223.4 (0.96±0.01)10−3 -
GaussianWl=8◦ ,Wb=6◦ Gaussian,WD=2◦ 8260.3 (0.84±0.02)10−3 (2.9±0.5)10−4
GaussianWl=8◦ ,Wb=6◦ Gaussian,WD=6◦ 8262.8 (0.84±0.02)10−3 (3.1±0.5)10−4
GaussianWl=8◦ ,Wb=6◦ Gaussian,WD=10◦ 8263.7 (0.84±0.02)10−3 (3.3±0.5)10−4
GaussianWl=8◦ ,Wb=6◦ Exponential,WD=2◦ 8262.6 (0.84±0.02)10−3 (3.1±0.5)10−4
GaussianWl=8◦ ,Wb=6◦ Exponential,WD=6◦ 8262.6 (0.84±0.02)10−3 (3.7±0.6)10−4
Exponential Wl=3◦ ,Wb=2◦ - 8265.4 (1.01±0.01)10−3 -
Exponential Wl=3◦ ,Wb=2◦ Gaussian,WD=2◦ 8284.1 (0.93±0.02)10−3 (2.1±0.5)10−4
∗ -TheBulgecomponent oftheDisk+Bulgemodelisusedinthespectralanalysisin§5.
thesetofmodelsconsideredhere.Itisclearthati)thetrue Table2.EffectivedistanceDneededtorecalculatetheobserved
distribution of the 508–514 keV flux is likely more compli- flux from the 80◦ × 80◦ region around the GC into the lumi-
cated than any of the models used and ii) the relatively nosityfordifferentspatialcomponents.Twocolumnscorrespond
modest(althoughstatistically significant)changesintheχ2 to different cutoffs in the surface brightness distribution of each
among different models (containing the Bulge component) component (relative to the maximal surface brightness of this
suggestthatthebasicpropertiesofthedistributionarecap- component).
tured by ourmodels.
The uncertainty in the choice of the spatial model Spatialtemplate Effectivedistance, kpc
directly translates into the uncertainty of the 508–514 cutoff=10−5 cutoff=0.1
keV flux. In particular, the total flux of the Bulge com- Disk 7.74 8.98
ponent varies among all two-component models (both Disk/Hole 7.79 8.99
parametric and based on templates) from 0.84 10−3 to Bulge 5.89 6.93
1.1110−3 phot s−1 cm−2.Atthesametime,thetotalBulge
+ Disk flux (integrated over the 80◦ × 80◦ region) varies
from 1.10 10−3 to1.14 10−3 phot s−1 cm−2. notedabove,theresultingluminositiesrelyonthemodel3D
Since some of the spatial templates used in Table 1 distribution and for this reason theyare model dependent.
are projections of the 3D models (based on stellar distri-
bution), it is easy to recalculate the observed flux F into
the total luminosity L of the corresponding component as
4 26Al DECAY
L = 4πD2×F. Here D depends on the 3D distribution of
the volume emissivity and on the region used to calculate 26Al is one of the obvious and accountable sources of the
the flux F. The values of D are given in Table 2. Using positrons in the Galaxy (see e.g. Diehl et al. 2008). This
the effective distances from Table 2 for the templates trun- radioactive isotope with the half-life time of 7.17 105 years
cated at 10% of the maximal surface brightness, the total is produced by massive stars, which primarily occupy the
luminosity of the Bulge component is ∼ 5.0 1042 phot s−1, disk of the Galaxy. The positrons are produced in 81.7%
while the total Disk luminosity is ∼ 2.3 1042 phot s−1. As of decays, with the mean energy of 543 keV; in 99.8% a
(cid:13)c 2001RAS,MNRAS000,1–20
10 Churazov et al.
1.809 MeV photon is emitted4. Assuming that the fraction
of positrons forming positronium is fps (see §5), the fluxes
in the 511 keV and 1.8 MeV lines per 1 positron produced
via 26Aldecay are:
F511 =0.817(cid:2)(1−fps)+ 14fps(cid:3)×2=1.63(cid:2)1− 34fps(cid:3), (4)
F1.8 =0.998.
Here we assume that i) the fraction of para-positronium is
1/4 and ii) all positrons annihilating without formation of
positronium (fraction 1−fps) produce a narrow 511 keV
line. The factor 2 in the above expression accounts for the
2 photons produced in two-photon annihilation. Therefore,
F511 =0.409,0.471 and1.637×F1.8,forfps =1,0.95 and0,
respectively (see §5 for details).
Itisinterestingtocomparethisrelationwiththefluxes
obtained from the light-bucket images in the 508–514 keV
and 1805–1813 keV energy bands, which should contain
mostofthe511keVand1809keVlinefluxes,unlessthelines
arestronglybroadened.ShowninFig.7isalight-bucketlon-
gitudescan oftheGalactic planeovertheregion l=±60◦ .
The blue thick crosses show the flux in the 508–514 keV
band, while the thin red crosses show the observed flux in
the 1805–1813 keV band scaled by a factor of 0.409. These
red crosses correspond to the expected 511 keV line flux
arising from 26Al decay under the assumption that 100%
Figure 8. Spectra of the Bulge (top row) and Disk (bottom
of positrons annihilate through the formation of positron-
row) near 511 keV and 1809 keV, obtained using the decompo-
ium. It will be observed later (§5) that this assumption is
sition of the data with the two-component Disk+Bulge model.
supported by spectral data. Clearly, the high 511 keV line
The red line in the top-left panel shows the best-fitting model
flux from the GC region cannot be explained by 26Al de- (Gaussian at 511 keV and ortho-positronium continuum; see §5
cay(unlessthepositronsproducedinthediskaresomehow below for details). The flux in the 511 keV line in this model
transported to thecentral region; see e.g. Prantzos 2006). is F511 = 0.84 10−3phots−1 cm−2. The blue curve in the top-
One can use the same set of templates as in §3.5 and rightpanel showsaGaussianlineat1.809MeV.Thefluxinthe
repeat the analysis for a set of energies to obtain the spec- Gaussian was calculated as F1.8 =F511/0.409, corresponding to
trum associated with each spatial component. We did this the assumption that all positrons are produced by 26Al decay
using the Disk+Bulge model, which was applied to all ob- and the fraction of annihilations via positronium is fps = 1.0
(see eq. 4 and §5). The bottom row shows the spectrum of the
servations with the INTEGRAL pointing direction within
Diskcomponent.IncontrasttotheBulgespectrum,the1.8MeV
30◦ from GC. Since we do not explicitly account for com-
lineisveryprominentinthespectrum(bottom-rightpanel).The
pact sources in this procedure, the low energy parts of the
redlineshows thebest-fitting Gaussianat1.809MeV,withflux
spectraobtainedmaynotbereliable.However,nearthe511 F1.8=4.110−4phots−1 cm−2.Thebluelineinthebottom-left
keVand1.8MeVlinesthecontributionofindividualsources panelnowshowsa511keVlinewithfluxF511=0.409×F1.8.
shouldnotbecrucial.Nevertheless,thissimplifyingassump-
tionshouldbekeptinmindwheninterpretingtheresulting
spectra, shown in Fig. 8.
The upper row in Fig. 8 shows the spectrum of the line with the resulting flux F1.8 is plotted in the top-right
panel as a Gaussian line centered at 1.809 MeV. Clearly
Bulgecomponentinthevicinityofthe511keVand1.8MeV
such a strong line at 1.8 MeV is in stark contrast to the
lines.Theredlineinthetop-leftpanelshowsthebest-fitting
data, which show no evidence for 1.8 MeV emission in the
model (Gaussian at 511 keV and ortho-positronium contin-
Bulge spectrum.
uum;see §5 below for details). Theflux in the511 keVline
in this model is F511 = (0.84±0.03) 10−3phot s−1 cm−2. The bottom row in Fig. 8 shows the Disk component
spectrum in the vicinity of the 511 keV and 1.8 MeV lines.
Note that this flux was obtained from the spectral analysis
In contrast to theBulge spectrum, the1.8 MeV line is now
and it differs slightly from the “Bulge” flux obtained from
very prominent in the data (bottom-right panel). The red
the analysis of the count rate in the 508–514 keV band,
lineshowsthebest-fittingGaussian at 1.809 MeVwithflux
iqnutoottehdeienxpTeacbtleed1fl.uxThinetvhaelu1e.8FM51e1Vwliansetuhseinngrtehcealrceulalattioend F1.8 =(4.1±0.5) 10−4phot s−1 cm−2. The blueline in the
F1.8 =F511/0.409,correspondingtotheassumptionthatall bottom-leftfigurenowshowsa511keVlinewithfluxF511 =
positrons are produced by 26Al decay and the fraction of 0.409×F1.8.Thedatadoshowthepresenceofa511keVline
in the Disk component, although our experiments with the
annihilations via positronium is 100% (see eq. 4 and §5). A
alternative backgroundmodels and various spatial patterns
demonstrate that the parameters of the line near 511 keV
4 http://www.nndc.bnl.gov/mird/. are not determined reliably.
(cid:13)c 2001RAS,MNRAS000,1–20