Positron annihilation spectrum from the Galactic Center region observed by SPIINTEGRAL

a r X i v :a s t r o -p h /0411351v 2 26 D e c 2004Mon.Not.R.Astron.Soc.000,1–12(2003)Printed 2February 2008(MN L A T E X style ?le v2.2)

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

E.Churazov,1,2R.Sunyaev,1,2S.Sazonov,1,2M.Revnivtsev,1,2D.Varshalovich,31Max-Planck-Institut f¨u r Astrophysik,Karl-Schwarzschild-Strasse 1,85741Garching,Germany 2Space Research Institute (IKI),Profsoyuznaya 84/32,Moscow 117997,Russia 3Io?e Institute,Polytekhnicheskaya 26,St Petersburg 194021,Russia 2February 2008ABSTRACT The electron-positron annihilation spectrum observed by SPI/INTEGRAL during deep Galactic Center region exposure is reported.The line energy (510.954±0.075keV)is consistent with the unshifted annihilation line.The width of the annihilation line is 2.37±0.25keV (FWHM),while the strength of the ortho-positronium continuum suggests that the dominant fraction of positrons (94±6%)form positronium before 0e07ffa9d1f34693daef3ee9pared to the previous missions these deep INTEGRAL observations provide the most stringent constraints on the line energy and width.Under the assumption of an annihilation in a single-phase medium these spectral parameters can be explained by a warm T e ～7000?4104K gas with the degree of ionization larger than a few 10?2.One of the wide-spread ISM phases -warm (T e ～8000K)and weakly ionized (degree of ionization ～0.1)medium satis?es these criteria.Other single-phase solutions are also formally allowed by the data (e.g.cold,but substantially ionized ISM),but such solutions are believed to be astrophysically unimportant.The observed spectrum can also be explained by the annihilation in a multi-phase ISM.The fraction of positrons annihilating in a very hot (T e ≥106K)phase is constrained to be less than ～8%.Neither a moderately hot (T e ≥105K)ionized medium nor a very cold (T e ≤103K)neutral medium can make a dominant contribu-tion to the observed annihilation spectrum.However,a combination of cold/neutral,warm/neutral and warm/ionized phases in comparable proportions could also be con-sistent with the data.

Key words:Galaxy:center –gamma rays:observations –ISM:general

1INTRODUCTION

The annihilation line of positrons at 511keV is the bright-

est gamma-ray line in the Galaxy.First observed with a NaI

scintillator as a ～476keV line coming from the Galactic

Center (GC)region (Johnson,Harnden &Haymes,1972;

Johnston &Haymes,1973),it was subsequently unambigu-

ously identi?ed with a narrow (F W HM <3.2keV)e +e ?

annihilation line using germanium detectors (Leventhal,

MacCallum,Stang,1978).Since then many balloon ?ights

and several space missions have measured the spatial distri-

bution and spectral properties of the line.A summary of the

high energy resolution observations of the 511keV line prior

to INTEGRAL and the ?rst SPI/INTEGRAL results can be

found in Jean et al.(2003)and Teegarden et al.(2004).

Positrons in the Galaxy can be generated by a number

of processes,including e.g.radioactive β+decay of unstable

isotopes produced by stars and supernovae,jets and out-

?ows from the compact objects,cosmic rays interaction with the interstellar medium (ISM),and annihilation or decay of dark matter particles.An important problem is to deter-mine the total e +e ?annihilation rate in the Galaxy and to accurately measure the spatial distribution of the annihila-tion radiation.This is a key step in determining the nature of the positron sources in the Galaxy.Another problem is to measure the annihilation spectrum including the 511keV line itself and the 3γcontinuum arising from the decay of ortho-positronium.This information reveals the properties of the ISM where positrons are annihilating.Here we concentrate on the latter problem and report below the measurements of the e +e ?annihilation spectrum (including 3γcontinuum)based on SPI/INTEGRAL obser-vations of the GC region over the period from Feb.,2003through Nov.,2003.The core of the data set is a deep 2Msec GC observation,carried out as part of the Russian Academy of Sciences share in the INTEGRAL data.Previously re-ported results on the 511keV line shape (Jean et al.2003)

2Churazov et

al.

Figure 1.Spectrum of the e +e ?annihilation radiation (?xed background model)detected by SPI from the GC region and the best ?t model (thick solid line,see Table 1for parameters).The dotted line shows the ortho-positronium radiation and the dashed line shows the underlying power law continuum.

are based on a signi?cantly shorter data set.We use here a completely independent package of SPI data analysis and for the ?rst time report the results on the ortho-positronium continuum measurements based on the SPI data (Fig.1).The imaging results will be reported elsewhere.

The structure of the paper is as follows.In Section 2we describe the data set and basic calibration procedures.Section 3deals with the spectra extraction.In Section 4we present the basic results of spectral ?tting.In Section 5we discuss constraints on the annihilation medium.The last section summarizes our ?ndings.

2OBSER V ATIONS AND DATA ANALYSIS SPI is a coded mask germanium spectrometer on board IN-TEGRAL (Winkler et al.,2003),launched in October 2002aboard a PROTON rocket.The instrument consists of 19individual Ge detectors,has a ?eld of view of ～16?(fully-coded),an e?ective area of ～70cm 2and the energy reso-lution of ～2keV at 511keV (Vedrenne et al.,2003,Attie et al.,2003).Good energy resolution makes SPI an appropriate instrument for studying the e +e ?annihilation line.

2.1Data set and data selection

A typical INTEGRAL observation consists of a series of pointings,during which the main axis of the telescope steps through a 5x5grid on the sky around the position of the source.Each individual pointing usually lasts s few ksec.A detailed description of the dithering patterns is given by Winkler et al.(2003).For our analysis we use all data avail-able to us,including public data,some proprietary data (in particular,proposals 0120213,0120134)and the data avail-able to us through the INTEGRAL Science Working Team.All data were taken by SPI during the period from Feb.,2003through Nov.,2003.The choice of this time window was motivated by the desire to have as uniform a data set as possible.The ?rst data used are taken immediately after the ?rst SPI annealing,while the last data used were taken prior to the failure of one of the 19detectors of SPI.While analysis of the GC data taken after Nov.2003is possible,the amount of data (in public access)which can be used for background modeling is at present limited.Prior to actual data analysis all individual observations were screened for periods of very high particle background.We use the SPI anticoincidence (ACS)shield rate as a main indicator of high background and dropped all observations with an ACS rate in excess of 3800cnts/s.Several additional observations were also omitted from the analysis,e.g.those taken during cooling of SPI after the annealing procedure.For our analysis we used only single and PSD events and when available we used consolidated data provided by the INTEGRAL Science Data Center (ISDC,Courvoisier et al,2003).2.2Energy calibration As a ?rst step all observations have been reduced to the same gain.Trying to keep the procedure as robust as pos-sible we assume a linear relation between detector channels and energies and use four prominent background lines (Ge 71at 198.4keV;Zn 69at 438.6;Ge 69at 584.5keV and Ge 69at 882.5keV,see Weidenspointner et al.,2003for the compre-hensive list of SPI background lines)to determine the gain and shift for each revolution.While the linear relation may not be su?cient to provide the absolute energy calibration to an accuracy much higher than 0.1keV over the SPI broad energy band,the relative accuracy is high (see Fig.2).Shown in the top panel is the energy of the background 511keV line as a function of the revolution number.While the deviation from the true energy of the e +e ?line is ～0.07keV,the RMS deviation from the mean energy is only 0.0078keV.The best ?t energy of the background line for the combined spectrum of all SPI observations within 30?of GC is 510.938keV,compared to the electron rest energy of 510.999keV.The energies quoted below were corrected for this systematic shift.In the bottom panel of Fig.2we show the instrument resolution at 511keV as a function of the revolution number.Since the background (internal)511keV line is kinematically broadened we used two bracketing lines (at 438and 584keV)to calculate the resolution at 511keV.The sawtooth pattern clearly seen in the plot is caused by the gradual degradation of the SPI resolution due to the detector exposure to cosmic rays and due to the annealing procedure (around revolution 90)which restores the resolution.The net result is that the mean resolution near 511keV is ～2.1keV (FWHM)and over the whole data set the resolution changes from ～2.05keV to ～2.15keV.All the data,reduced to the same energy gain,were then stored as individual spectra (one per pointing and per

Positron annihilation spectrum from the Galactic Center region

3

Figure 2.The upper panel shows the energy of the background

511keV line vs the revolution number.With the assumed linear

channel/energy relation the line is shifted from the true energy of

the e +e ?annihilation line by ～0.07keV,the RMS deviation from

the mean energy is only 0.0078keV.The bottom panel shows the

intrinsic energy resolution of SPI at the 511keV line evaluated

from ?tting two narrow background lines at 438and 584keV.

Statistical errors are omitted for clarity.

detector)with 0.5keV wide energy bins.These spectra are

used for subsequent analysis.

2.3Background modeling

Once obvious spikes and ?ares are removed from the SPI

data,the background in the remaining ”clean”data is rather

stable and it typically does not vary by more than ～10%.

However the 511keV line observed from the GC region pro-

duces an excess signal at the level of 1-2per cent of the

background line and therefore variations of the background

have to be taken into account.Ideally one would prefer to

have a background model which is based on some accurately

measurable quantities (like charged particles count rate)so

that the background subtraction does not introduce extra

noise to the data.Since no such model has been provided

so far,we use the same data set to build a provisional back-

ground model.When doing so one has to bear in mind that

the statistical signi?cance of the accumulated data is limited

(when narrow energy bins are considered)and the model has

to be kept as simple as possible to provide a robust result.

The simplest background model,which we found acceptable

at the present stage of SPI analysis,assumes that the back-

ground is linearly proportional to the Ge detectors saturated

event rate and time.An example of observed and predicted

background for the 900-1200keV range is shown in Fig.3.

Such a broad band was selected to show variations of the

background more clearly.The points in Fig.3show actual

Time, days 0501001502001.71.8

1.9Figure 3.Count rate in the 900-1200keV range (averaged over all 19SPI detectors)as a function of time.Zero time corresponds to the beginning of the data set.The curve shows the predicted count rate in the same band based on a simple background model.measurements (averaged over all 19SPI detectors),while the line connects predicted background values.One can see that most of the prominent background variations are well reproduced by the adopted model.However,for some rev-olutions further improvement of the model is possible once more data,especially blank-?eld observations,become pub-licly available.For the purpose of the GC data reduction we then re-generated a background model using all data excluding the central 30?(radius)region centered at GC.The total (dead time corrected)exposure of the background ?elds used is 3.7Msec.To verify the quality of the background model in the en-ergy range of interest (i.e.around 511keV)we used 0.5Msec SPI observations of the Coma region.While these particu-lar observations were also part of the data set used for the generation of the background model,they contribute only ～10%to the total background exposure.Applying exactly the same procedure (described below)used for the Galac-tic Center observations we extracted the spectrum assuming that the spatial distribution of the line ?ux has a shape of a Gaussian with FWHM=6?centered at the Coma cluster (Fig.4left panel).As for the Galactic Center observations we used an additional model consisting of a Gaussian plus constant (Fig.4right panel).By construction the left plot is basically the di?erence between the spectrum coming from the Coma region and the mean spectrum over the entire background data set which contains many Galactic Plane pointings with bright sources.Therefore,a small negative bias,seen in the left panel of Fig.4,is a natural result.For the right panel (allowing for an additional free background component constant over all detectors)this negative bias is not present.For both panels no signi?cant spectral features are present near the 511keV line.For comparison we show in Fig.4a line at 511keV with parameters similar to those observed in the GC region.No evidence for spectral features near 511keV is seen in the Coma ?eld,suggesting that the background is removed with a su?cient accuracy.

2.4Spectra extraction For the GC spectra we use the data obtained when the main axis of the instrument was within 30?of the GC direction with an overall exposure time of ～

3.9Msec (dead time cor-

4Churazov et

al.

Figure 4.Data points show the background subtracted spectra obtained from the 0.5Msec SPI observations of the Coma region using the same procedure as is used for the Galactic Center region.For the left panel the spatial model is 6?Gaussian,centered at Coma cluster,while the background is ?xed.For the left panel the model consists of a Gaussian plus a constant with the free normalization.For comparison superimposed on each plot is a Gaussian line at 511keV (dotted lines;rebinned to the data resolution)with the total ?ux as seen from the GC region.An even ～5times weaker line would be seen in this 0.5Msec observation.

rected).The spatial model used is a simple Gaussian with

FWHM ranging from 2to 26?.Using available response ?les

(results of Monte-Carlo modeling,described by Sturner et

al.,2003)the count rate was predicted for every pointing

and every SPI detector.Two models are used to extract the

spectra.In the ?rst model the normalization of the model

(in a given energy band)was then obtained from a simple

linear χ2?t to the data:

i A ×P i ?(D i ?B i )

Positron annihilation spectrum from the Galactic Center region

5

Figure 5.Dependence of the ?ux in the 508-514keV band on the

width of the spatial Gaussian for model I with a ?xed background

(solid circles)and model II with a free constant background (solid

squares).The dotted connecting solid triangles shows the behav-

ior of the χ2in model II.

χ2is reached for the FWHM ～6?.The absolute value of the

χ2for 6?Gaussian is 0.9992per degree of freedom (for 38969

d.o.f.).Given that the S/N for individual observation is very

small,the absolute value of χ2is not a very useful indicator

of the acceptability of the model.However its closeness to

unity shows that observed variations of count rates are very

close to those expected from a pure statistical noise.

The width of the distribution suggested by the above

analysis (～6?)is rather close to the value derived for the

central bulge from OSSE observations (Kinzer et al.,2001),

while the earlier analysis of a shorter SPI data set sug-

gested a somewhat broader distribution ～9?(Kn¨o dlseder et

al.,2003)although consistent with 6?within the quoted un-

certainties.The behavior of the curves in Fig.5indicates

that the 6?Gaussian does not account for the total ?ux of

511keV photons coming from the GC region and an ex-

tra component (broader than 6?Gaussian)is needed.This

result is robust against various assumptions on the SPI in-

ternal background.Since the topic of this paper is the shape

of the annihilation spectrum we will not elaborate on par-

ticular spatial models.Subsequently we use only the spectra

extracted using a 6?Gaussian.However,we veri?ed that all

the major spectral parameters (except for the overall nor-

malization)are insensitive to the width of the spatial model.

3NET SPECTRA AND SPECTRAL

MODELING

The spectra extracted with a 6?Gaussian,using two back-

ground models (?xed and free background),are shown in Fig.1and Fig.6.The signi?cance of the narrow line detec-tion is 54.1and 23.8σrespectively (based on the 508-514energy band).When ?tting the spectra over the energy range near 511keV it was assumed that the SPI energy resolution is equivalent to the convolution of photon spectra with a Gaussian having FWHM ～2.1keV.For ?tting spectral lines and the weak continuum on the red side of a line one has to verify the normalization and shape of the low energy tail in the SPI spectral response.At present a Monte-Carlo simu-lated SPI energy response matrix (spi_rmf_grp_0003.fits ,Sturner et al.,2003)is available,which is constructed for broad continuum channels.According to this matrix the to-tal o?-diagonal tail of the SPI response for ～511keV pho-tons amounts to ～30%of the ?ux.The tail however is very extended (few hundred keV)and between 450keV (lower energy boundary used for spectral ?tting below)and 511keV only about 3-4%of the line ?ux are due to o?-diagonal response.Shown in Fig.7is a typical situation one can ex-pect for the GC spectra.The thin solid line shows a Gaus-sian line with a total intensity of unity.The dashed line is an ortho-positronium continuum with the total ?ux 4.5times larger than the line ?ux (i.e.the case of annihila-tion through positronium formation).For comparison the dotted line shows the low energy tail of the narrow line estimated from the available response matrices.One can see that indeed the contribution of the tail is very minor (few per cent relative to the positronium continuum above 400keV).We however routinely included this component in the subsequent spectral ?tting,linking its ?ux to the normalization of the narrow 511keV line.The impact of the o?-diagonal tail on the continuum is even smaller and we neglected the tail in the continuum modeling.E.g.for the positroniuum continuum (the hardest continuum com-ponent used in the model)an account for the tail contri-bution above 450keV can change the normalization by less than 2%.The ?ux ratio of the positronium continuum and the narrow 511keV line determines the positronium fraction F P S =2/(1.5+2.25?F 2γ/F 3γ),where F 2γand F 3γare the line and continuum ?ux,respectively.For large ?ux ratios (see Table 1)the positronium fraction is a weak function of the ratio and unless the Monte-Carlo simulated o?-diagonal response is underestimated by a large factor (larger than ～5)we do not expect any drastic changes in spectral parameters.For the ortho-positronium continuum we use the spec-trum of Ore &Powell (1949).To allow for broadening of the ortho-positronium continuum edge at 511keV (SPI en-ergy resolution and intrinsic broadening of the edge)we con-volved the continuum with a Gaussian having a width from 2.1to 7.keV.The ?ts were found to be fairly insensitive to the exact value of the edge broadening (unless it is very large)and instead of introducing an extra free parameter we ?xed the width of the ortho-positronium edge at 4keV.The best ?t parameters to the spectra are shown in Table 1.For comparison we show in Table 2the spectral parameters derived by various missions in the past.It is clear that the results are in broad agreement.Deep INTEGRAL observations provide the most stringent constraints on the line centroid and on the width of the 511keV line.

6Churazov et al.

Figure6.Spectrum of the annihilation radiation from the GC region(6?Gaussian)in the400-600keV range derived from the model with the constant background as a free parameter(model II).For comparison a background spectrum,scaled by a factor of0.01,is shown with a solid line.The annihilation line coming from the GC region thus corresponds to the level of～2-2.5%of the SPI background511 keV.The observed continuum radiation below511keV is at the level of0.4%from the instrument background continuum,except for the energies close to the positions of the strong background lines where the useful signal is at the level of0.1%of the background. Table1.Best?t parameters for the GC spectra calculated for a6?(FWHM)Gaussian spatial model.Quoted errors are1σfor a single parameter of interest.

Single Gaussian+Ortho-positronium+power law

Positron annihilation spectrum from the Galactic Center region7 Table2.Parameters of GC e+e?annihilation spectrum obtained by various missions.

8Churazov et

al.

Figure8.The e?ective FWHM of the511keV line versus the

fraction of annihilation through the positronium formation.The

gray area is the width and the positronium fraction observed by

SPI.There are two groups of theoretical curves:cold-T e≤5000

K(dotted lines)and warm/hot-T e≥7000K(solid lines).The

temperature is?xed for each curve(the labels next to the curves),

but the ionization fraction varies so that plasma changes from

neutral to completely ionized along the curve.For cool temper-

ature curves and for the8000K curve the points correspond-

ing to the ionization degree of0.01and0.1are marked with the

open and solid squares respectively.Each high temperature curve

has two regimes,shown by thin and thick solid lines respectively.

Thin(thick)lines correspond to the ionization fractions smaller

(larger)than expected for collision dominated plasma at this tem-

perature.For ISM the overionized state(regime shown by thick

lines)is more natural than the underionized(thin lines).Finally

the dashed line shows the relation between the line width and

positronium fraction for a completely ionized plasma as a func-

tion of temperature.

that the ISM changes from neutral to completely ionized.

One can identify two groups of curves in Fig.8demonstrat-

ing di?erent behavior.

The?rst group of curves corresponds to cool gas with

a temperature below～6000K.In the cold and neutral ISM

about94%of the positrons form positronium in?ight,while

the rest fall below the positronium formation threshold of

6.8eV and eventually annihilate with bound electrons.The

eFWHM of the line produced by positronium formation is

～5.3keV,while the annihilation with bound electrons pro-

duces FWHM of～1.7keV(e.g.Iwata,Greaves&Surko,

1997)due to the momentum distribution of bound elec-

trons.The eFWHM in the total annihilation spectrum is

～4.6keV.If the ionization fraction in the cold gas increases

above～10?3,then Coulomb losses start to be important

and the fraction of positrons forming positronium in?ight

decreases.For the positrons falling below6.8keV three pro-

cesses are important-radiative recombination,annihilation

with free electrons and annihilation with bound electrons.

For ionization fractions of the order of a few10?2and tem-

peratures～103K the annihilation with bound electrons

causes the decrease of the net positronium fraction to～90-

80%.If the ionization degree is more than a few per cent then

only radiative recombination and annihilation with free elec-

trons are important and the positronium fraction and the

line width converge to the values expected for completely

ionized plasma.

The second group of curves corresponds to tempera-

tures higher than～7000K.At these temperatures thermal-

ized positrons can form positronium via charge exchange

with hydrogen atoms and this process dominates over radia-

tive combination and direct annihilation unless the plasma

is strongly ionized.As a result for moderate degree of ion-

ization the positronium fraction is very close to unity.Only

when the plasma is signi?cantly ionized(of the order of6-

10%for～8000K gas and more for higher temperatures)the

annihilation with free electrons starts to be important and

the positronium fraction declines with increasing ionization

degree(almost vertical tracks in Fig.8).

The above calculations probe the various combinations

of the temperature and ionization,ignoring the physical pos-

sibility of such combinations.We now compare the results of

INTEGRAL observations with the simulations and discuss

plausible conditions.

The observed positronium fraction and the line width

are shown in Fig.8as a shaded 0e07ffa9d1f34693daef3ee9paring the

simulated curves with the results of observations one can

conclude that low and high temperature solutions are possi-

ble.The low temperature solution corresponds to tempera-

tures below1000K,while for the high temperature solution

falls into the range from7000to4104K.

4.1Positrons annihilating in various ISM phases

The standard model of ISM in the Milky Way(e.g.McKee

&Ostriker1977,Heiles2000,Wol?re et al.,2003)assumes

that there are several distinct phases:Hot(T e≥few105K),

Warm(T e～8000K)and Cold(T e≤100K).

From Fig.8it is clear that hot(T e≥105K)ionized

medium does not give a dominant contribution to the ob-

served annihilation spectrum.Indeed positrons annihilating

in such a medium would produce too small positronium

fraction and a much too broad annihilation line.One can

increase the positronium fraction in such gas by requiring

the low ionization fraction(i.e.increase the role of charge

exchange)below the values expected in the collisionally ion-

ized plasma.Such situation seems to be very unplausible

and the width of the line remains too large anyway.One

can easily limit the contribution of a very hot(T e≥106

K),completely ionized plasma to the observed spectra,by

adding a broad line to the?t.E.g.for T e=106K the ex-

pected FWHM is～11keV(Crannell et al.,1976)and the

90%con?dence limit on the contribution of such a line to the

observed?ux is≤17%.Given that at106K the direct anni-

hilation and radiative recombination rates are nearly equal

and assuming that the bulk of the remaining line photons

are due to annihilation through the positronium formation,

one can conclude that not more than～8%of positrons an-

nihilate in a hot(>106K)medium.

A qualitatively similar conclusion is valid for a cold

Positron annihilation spectrum from the Galactic Center region9 (T e≤103K)neutral gas.While the positronium fraction is

consistent with the observed one,the width of the line(～4.5

keV)is much too broad.One can decrease the line width by

forcing a large ionization fraction(more than10?2).For cold

and dense gas(e.g.in molecular clouds or cold HI clouds)

such an ionization fraction is much larger than expected.

On the other hand in the warm phase of the ISM

(T e～8000?104K)the ionization fraction varies sub-

stantially from less than～0.1to more than0.8.This phase

alone can explain the observed annihilation line width and

the positronium fraction.E.g.for8000-104K plasma one

needs an ionization degree of several per cent to get both

the line width and positronium fraction consistent with ob-

servations.For2104K plasma the ionization fraction has to

be of the order of0.4.At temperatures higher than3104K

even plasma in collisional ionization equilibrium is strongly

ionized(>99%).In real ISM one can usually expect stronger

ionization than for collisionally ionized plasma.The corre-

sponding parts of the curves in Fig.8(i.e.ionization fraction

larger than for collisionally ionized plasma)are shown by

the thick solid lines.

Given the characteristic shapes of the curves in Fig.8 a combination of annihilation spectra coming from warm ISM and having various degrees of ionization could produce the annihilation spectrum consistent with observations.This conclusion is broadly consistent with earlier analysis of e.g. Bussard et al.,1979or Guessoum et al.1991.

4.2The fraction of positronium formed in?ight As was mentioned above,the shape of the annihilation line produced in the neutral or partly ionized medium can di?er from a Gaussian.In fact for the majority of the theoreti-cal curves in Fig.8the annihilation line is composed of a rather broad FWHM≥5keV component(in?ight positro-nium formation)and much narrower FWHM～1.0-1.7keV component(due to radiative recombination with free elec-trons,charge exchange of thermalized positrons and annihi-lation with bound electrons).An example of the annihilation spectrum structure is shown in Fig.9.The broad compo-nent(dashed line)is due to in-?ight positronium formation, while narrower components are associated with thermal-ized positrons.The same model spectrum(further smoothed with the SPI intrinsic resolution)is again shown in Fig.10 in comparison with the SPI spectrum.In terms of theχ2 such model yields comparable values,e.g.χ2=192.2for 195d.o.f.for the model with free background(cf.Table1).

The change of the line width along the curves is primar-ily caused by the variation of the relative weights of these two components.Measurements of these weights would pro-vide a more powerful test for the ISM composition than the e?ective width of the composite line.We therefore?t the ob-served spectra with the model consisting of two Gaussians instead of one as a simpli?ed way to evaluate the contri-butions of in-?ight and thermalized annihilations.Since for the in-?ight positronium formation the width of the anni-hilation line depends only weakly on other parameters,we ?xed the width of the second Gaussian at5.5keV,while the width of the?rst Gaussian remained free.The energy of the two Gaussians were set to be 0e07ffa9d1f34693daef3ee9pared to the sin-gle Gaussian model(see Tables1,3)this model reduces the χ2by8.9and by3.9for the“?xed background”and

“free Figure9.The structure of the annihilation spectrum for8000K plasma with the degree of ionization～0.1.Dotted line shows the ortho-positronium continuum,short-dashed line is the2-γdecay of positronium formed in?ight,thin solid line-2-γdecay of positronium formed by thermalized positrons,thin long-dashed line-direct annihilation of thermalized positrons.The thick solid line shows the total annihilation spectrum.

background”spectra respectively.Given that only one free parameter(normalization of the second Gaussian)is added to the model,the F-test suggests that the probability of getting such a reduction inχ2is2.6%and5%for the two spectra,respectively.

Using2-Gaussian models one can conclude that the best ?t fraction of the broad Gaussian in the total line?ux is ～30%.One can compare this value with the expected con-tributions of the broad(in?ight)and narrow(thermalized) components in the warm medium as a function of the ioniza-tion degree as shown in Fig.11.One can see that for8000K plasma one needs ionization degrees in the range of0.07-0.17 to have an appropriate relation between the broad and nar-row components.As is mentioned above the curves shown in Fig.11essentially re?ect the changes of the positrons ther-malized fraction as a function of the ionization state.

The same2-Gaussian models can be used to get more quantitative constraints on the contribution of the cold neu-tral phase to the annihilation budget.The90%con?dence limit on the contribution of the broad(5.5keV wide)Gaus-sian is～39%.Let us assume that this component is due to in-?ight positronium formation in a cold neutral gas.About 6%of positrons in the cold gas fall below the positronium formation threshold and annihilate with bound electrons, thus contributing to the narrower component of the line.The conservative assumption that the rest of the positrons are thermalized in a warm(～104K)strongly ionized(≥50%) medium and annihilate through the positronium formation implies an upper limit on the fraction of annihilations in

10Churazov et al.

Table3.Best?t parameters for the same spectra as in Table1,when a second Gaussian with the width?xed at5.5keV is added.This second Gaussian mimics the broad line produced by the in?ight positronium formation.Only essential parameters are quoted.

Double Gaussian+Ortho-positronium+power law

Positron annihilation spectrum from the Galactic Center region11

First of all-a small statistical error on the line cen-troid achieved by SPI(～0.075keV)corresponds to the un-certainty in velocity of～44km/s.The measured line energy coincides(within the uncertainties)with the unshifted line and therefore there is no evidence of bulk motion of the anni-hilating medium with velocities larger than～40km/s.Note that further improvement in the line statistics will require an accurate account for the Earth and Solar system motion relative to the GC since the magnitude of the velocities is of the same order.

The limits on the gas di?erential motions are not as strict.Consider e.g.the envelope of a star or supernova isotropically expanding with the velocity v.The intrinsically monochromatic line will then be observed as a boxy spectral feature with the full width of1022×v

103km/s keV.Given that the observed width is～2.4keV and for some ISM phases the intrinsic line can be relatively narrow～1-1.5 keV,velocities larger than～800km s?1can be excluded.

5CONCLUSIONS

Deep observations of the Galactic Center region by SPI/INTEGRAL have yielded the most precise parameters of the annihilation line to date.The energy of the line is consistent with the laboratory energy with an uncertainty of 0.075keV.The width of the annihilation line is constrained to～2.37±0.25keV(FWHM)and the positronium fraction to94±6%.Under a single phase annihilation medium as-sumption the most appropriate conditions are:the tempera-ture in the range7000-40000K and the degree of ionization ranging from a few10?2for low temperatures to almost complete ionization for high temperatures.E.g.annihilation of positrons in one of the canonical ISM phases-8000K gas with an ionization fraction of～10%-would produce an annihilation spectrum very similar to the one observed by INTEGRAL.Under the assumption of annihilation in a multi-phase medium,the contribution of a very hot phase (T e≥106K)is constrained to be less than～8%.Neither moderately hot(T e≥105K)ionized medium nor very cold (T e≤103K)neutral medium can make a dominant contri-bution to the observed annihilation spectrum.

Further accumulation of the Galactic Center exposure with INTEGRAL and improvements in the background knowledge and calibration should make possible detailed?ts of the data with the composite annihilation spectrum.Accu-rate separation of various components will place tight con-straints on the width and the relative amplitude of annihi-lation features formed in?ight and after thermalization.It will therefore be possible to make an accurate census of the distribution of annihilating positrons over ISM phases.

Simultaneously accurate information on the spatial dis-tribution of the annihilation?ux(especially in the latitudal direction)can be e?ciently combined with the data on the spatial distribution of various ISM phases thus constrain-ing the distribution of positron sources and the transport of positrons in the Galaxy.6ACKNOWLEDGEMENTS

We would like to thank SPI PIs V.Schoenfelder, G.Vedrenne,J.-P.Roques and V.L.Ginzburg,V.V. Zheleznyakov,A.M.Cherepashchuk,S.A.Grebenev and C. Winkler for their support.We are grateful to J.Berakdar, A.Lutovinov and L.Vainshtein for useful discussions and the referee,B.J.Teegarden,for a very helpful report.

This work is based on observations with INTEGRAL, an ESA project with instruments and science data cen-ter funded by ESA member states(especially the PI coun-tries:Denmark,France,Germany,Italy,Switzerland,Spain), Czech Republic and Poland,and with the participation of Russia and the USA.

The dominant part of the GC exposure used in the pa-per comes from deep(2Ms)GC observations carried out as part of the Russian Academy of Sciences share of the INTEGRAL data.

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