Spectral analysis of the Galactic e+e- annihilation emission

Abstract

We present a spectral analysis of the e+e- annihilation emission from the Galactic Centre region based on the first year of measurements made with the spectrometer SPI of the INTEGRAL mission. We have found that the annihilation spectrum can be modelled by the sum of a narrow and a broad 511 keV line plus an ortho-Ps continuum. The broad line is detected with a flux of (0.35+/-0.11)e-3 s-1 cm-2. The measured width of 5.4+/-1.2 keV FWHM is in agreement with the expected broadening of 511 keV photons emitted in the annihilation of Ps that are formed by the charge exchange process of slowing down positrons with H atoms. The flux of the narrow line is (0.72+/-0.12)e-3 s-1 cm-2 and its width is 1.3+/-0.4 keV FWHM. The measured ortho-Ps continuum flux yields a fraction of Ps of (96.7+/-2.2)%. To derive in what phase of the interstellar medium positrons annihilate, we have fitted annihilation models calculated for each phase to the data. We have found that 49(+2,-23)% of the annihilation emission comes from the warm neutral phase and 51(+3,-2)% from the warm ionized phase. While we may not exclude that less than 23% of the emission might come from cold gas, we have constrained the fraction of annihilation emission from molecular clouds and hot gas to be less than 8% and 0.5%, respectively. We have compared our knowledge of the interstellar medium in the bulge and the propagation of positrons with our results and found that they are in good agreement if the sources are diffusively distributed and if the initial kinetic energy of positrons is lower than a few MeV. Despite its large filling factor, the lack of annihilation emission from the hot gas is due to its low density, which allows positrons to escape this phase. Comment: 12 pages, 6 figures, accepted in A&A

Full text

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arXiv:astro-ph/0509298v1 12 Sep 2005
Astronomy & Astrophysics manuscript no. 3765
(DOI: will be inserted by hand later)
February 5, 2008
Spectral analysis of the Galactic e+e−annihilation emission
P. Jean1, J. Kn¨ odlseder1, W. Gillard1, N. Guessoum2, K, Ferri` ere3, A. Marcowith1, V. Lonjou1, and
J.P. Roques1
1CESR, CNRS/UPS, B.P. 4346, 31028 Toulouse Cedex 4, France
2American University of Sharjah, College of Arts & Sciences, Physics Department, PO Box 26666, Sharjah,
UAE
3LATT, CNRS/OMP, 31000 Toulouse, France
Received ; accepted
Abstract.
based on the first year of measurements made with the spectrometer SPI of the INTEGRAL mission. We have
found that the annihilation spectrum can be modelled by the sum of a narrow and a broad 511 keV line plus an
ortho-positronium continuum. The broad line is detected (significance 3.2σ) with a flux of (0.35 ± 0.11) × 10−3
photons s−1cm−2. The measured width of 5.4±1.2 keV FWHM is in agreement with the expected broadening of
511 keV photons emitted in the annihilation of positroniums that are formed by the charge exchange process of
slowing down positrons with hydrogen atoms. The flux of the narrow line is (0.72 ± 0.12) × 10−3photons s−1
cm−2and its width is 1.3±0.4 keV FWHM. The measured ortho-positronium continuum flux yields a fraction of
positronium of (96.7±2.2)%.
To derive in what phase of the interstellar medium positrons annihilate, we have fitted annihilation models
calculated for each phase to the data. We have found that 49+2
warm neutral phase and 51+3
−2% from the warm ionized phase. While we may not exclude that less than 23% of
the emission might come from cold gas, we have constrained the fraction of annihilation emission from molecular
clouds and hot gas to be less than 8% and 0.5%, respectively.
We have compared our knowledge of the interstellar medium in the bulge (size, density, and filling factor of each
phase) and the propagation of positrons with our results and found that they are in good agreement if the sources
are diffusively distributed and if the initial kinetic energy of positrons is lower than a few MeV. Despite its large
filling factor, the lack of annihilation emission from the hot gas is due to its low density, which allows positrons
to escape this phase.
We present a spectral analysis of the e+e−annihilation emission from the Galactic Centre region
−23% of the annihilation emission comes from the
Key words. Gamma rays: observation – Line: formation, profile – ISM: general
1. Introduction
In the quest for the origin of positrons, images of the anni-
hilation line emission tell us that positrons annihilate pri-
marily in the bulge of our Galaxy (Kn¨ odlseder et al. 2005
and references therein). Assuming that positrons do not
propagate far from their sources, the spatial distribution
of the annihilation emission should trace the spatial dis-
tribution of the sources. Under this hypothesis, the obser-
vations of the spectrometer SPI onboard the INTEGRAL
observatory show that the sources of the bulk Galactic
positrons seem to be associated with the old stellar pop-
ulation (Kn¨ odlseder et al. 2005).
In this paper we try to infer, from the spectral charac-
teristics of the annihilation emission measured by SPI, in-
formation on the particular processes involved in the inter-
action of Galactic positrons with the interstellar medium
(ISM). This information should provide some clues regard-
ing the origin of Galactic positrons. The identification by
spectral analysis of the ISM phase in which positrons an-
nihilate could enable one to retrieve the type of positron
sources under particular assumptions of the distance trav-
elled by positrons as a function of their initial kinetic
energy. For instance, if positrons propagate a short dis-
tance from their sources, it is then likely that the positron
sources belong to or are specifically tied to the medium in
which positrons annihilate.
The spectral characteristics of the annihilation emis-
sion (shape and intensity of the line, relative intensity
of the ortho-positronium continuum) offer valuable in-
formation on the physical conditions of the ISM where
positrons annihilate (Guessoum, Ramaty & Lingenfelter
1991; Guessoum, Jean & Gillard 2005). Several reports on
observations with Ge spectrometers suggest a width of the

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2Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission
line in the 2–3 keV range (Smith et al. 1993; Leventhal et
al. 1993; Harris et al. 1998). Using only OSSE data, Kinzer
et al. (1996) derived a positronium fraction of 0.97±0.03.
Measurements with the Ge detector TGRS onboard the
WIND mission (1995-1997) gives a compatible value of
0.94±0.04 (Harris 1998). From the line width and the
positronium fraction measurements, Harris et al. (1998)
concluded that a scenario in which annihilation does not
occur either in cold molecular clouds or in the hot phase
of the ISM is favored. Using preliminary SPI data of Jean
et al. (2003) and TGRS data of Harris et al. (1998),
Guessoum et al. (2004) showed that the bulk of the anni-
hilation occurs in warm gas. However, they do not exclude
that a significant fraction of the annihilation may occur in
hot gas and in interstellar dust. Recently, Churazov et al.
(2005) inferred from SPI measurements that the spectral
parameters of the emission can be explained by positrons
annihilating in a warm gas or in a combination of warm
and cold gases.
In the present work, we include in the spectral analy-
sis the classical model of the ISM described by McKee &
Ostriker (1977). In this model, the ISM consists of molec-
ular clouds, atomic gas in either a cold or a warm phase,
and ionized gas in either a warm or a hot phase. Each
phase is characterized by particular physical conditions
in abundance, temperature, ionization fraction and den-
sity. Since the annihilation process and the Doppler broad-
ening depend on the target properties (H atoms, elec-
trons, velocity...) positrons annihilating in a given phase
emit a particular spectrum. For instance, positrons in a
cold medium annihilate mostly by forming positronium
in flight, whereas the dominant process in a warm ion-
ized medium is radiative recombination with free elec-
trons. The spectral characteristics of the annihilation in
the various ISM phases were first studied by Guessoum
et al. (1991). They were recently revisited by Guessoum,
Jean & Gillard (2005) – herafter GJG05 – in view of the
most recent results on positron interaction cross sections
with H, H2 and He as well as a detailed study on the
annihilation in dust grains.
In the next section, we present the SPI observations
and the method used to analyse the spectral distribution
of the annihilation emission. We take into account the
SPI spectral response (continuum Compton, energy res-
olution and line deformation due to radiation damage).
In section 3, we present the results of the spectral anal-
ysis. We adopt two different approaches consisting of (a)
an adjustment of simple Gaussian and ortho-positronium
laws and (b) a fit of the ISM phase fractions using the
spectral characteristics of the annihilation in each phase
calculated by GJG05. This approach differs from that of
Churazov et al. (2005) who fit the temperature and ion-
ized fraction of the gas where annihilation occurs with a
measured spectrum based on ∼4.5 × 106s duration SPI
observations of the Galactic Centre region. In section 4,
we discuss the implications of these results for the ori-
gin and physics of Galactic positrons and in section 5, we
summarize the most important new information.
2. Observations and analysis methods
2.1. Observations and data preparation
The data analysed in this work are those of the December
10, 2004 public INTEGRAL data release. The data span
the IJD epoch 1073.394–1383.573, where IJD is the Julian
Date minus 2 451 544.5 days. In order to reduce systematic
uncertainties in the analysis, we exclude observation pe-
riods with strong instrumental background fluctuations.
These background variations are generally due to solar
flares or the exit and entry of the observatory into the
Earth’s radiation belts. After this cleaning, we obtain a
total effective exposure time of 15.2 Ms. The exposure
is rather uniform in the central regions of our Galaxy
from where most of the annihilation signal is observed
(see Kn¨ odlseder et al. 2005).
The spectrum is extracted by model fitting, assuming
that the sky intensity distribution is a ∆l ≈ 8oand ∆b ≈
7oFWHM 2D-Gaussian. This distribution is one of the
best fitting models derived by Kn¨ odlseder et al. (2005)
who studied in detail the morphology of the annihilation
emission. This spatial distribution does not correspond to
the spatial distribution of the Galactic diffuse continuum
emission, which is expected to be more extended in longi-
tude and less extended in latitude. Therefore the intensity
of the Galactic diffuse continuum emission, calculated in
the spectral analysis, is overestimated (see section 3.1).
However, this systematic error does not affect the shape
of the annihilation spectrum since the Galactic continuum
emission is fitted by a power-law and, consequently, this
overestimation factor is the same over the whole energy
band.
We perform the analysis in 1 keV wide energy bins for
a 200 keV wide spectral window covering 400–600 keV.
Each energy bin is adjusted to the data for each germa-
nium detector separately, assuming that the count rate
is due to the sum of the sky contribution and the in-
strumental background. The latter is assumed to be the
sum of 3 terms: a constant, a component proportional to
the rate of saturating GeD events (GEDSAT rate) and a
component proportional to the convolution product of the
GEDSAT rate with a 352 day exponential decay law (see
Eq. 1 in Kn¨ odlseder et al. 2005). The last two components
are tracers of the short time scale and radioactive build
up variation of the instrumental background at 511 keV,
respectively.
Figure 1 shows the resulting spectrum. For compari-
son, and to illustrate the quality of the background sub-
traction, we also show the detector averaged count rate
spectrum. While overall the background subtraction is sat-
isfactory, significant residuals remain at the location of
some of the strong background lines. For instance, the
439 keV line, emitted in the decay of the metastable
state of the69Zn isotope is not properly removed. This
metastable state has a half-life of ≈14h and consequently
the temporal variation of this background line differs from
the background model used in the model fitting. This gives

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Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission3
Fig.1. Spectrum obtained by model fitting (see text). The
instrumental background spectrum is shown for compari-
son.
rise to residuals that may induce systematic errors in the
spectral analysis.
Figure 2 presents the residuals of the detector averaged
count rate after subtraction of the background and sky
models in the 435–443 keV and 526–534 keV bands. The
residuals of the first band, which contains the 439 keV
line, show large fluctuations leading to a reduced χ2of
5.4, while the reduced χ2is 1.9 for the 526–534 keV band
which is free of strong background lines.
2.2. Spectral analysis methods
In order to avoid influences of instrumental background
lines on the spectral analysis, we select the following en-
ergy bands, which are relatively free of systematic residu-
als (see previous subsection): 406–435, 443–467, 480–570,
578–580 and 589–593 keV. They cover ≈75% of the ex-
tracted energy range. This is sufficient (1) to quantify ac-
curately the flux of the ortho-positronium continuum and
(2) to characterize the shape of the annihilation line.
The spectral response of the instrument to a narrow
(Dirac like) gamma-ray line is an instrumentally broad-
ened Gaussian plus a Compton continuum. Due to radia-
tion damage, the shape of the Gaussian is deformed with
a low energy tail1. This warping may affect the determi-
nation of the physical line width and has to be taken into
account in the analysis. A simple way to model radia-
tion damage is to convolve a Gaussian with a decreasing
exponential function of energy (see Eq. 1). The energy
scale ǫd of the exponential function quantifies the level
of degradation and is called the “degradation parameter”
hereafter. The degradation increases with time but is reg-
ularly removed by the annealing process (Roques et al.
1High energy protons and neutrons impinging on the detec-
tors displace Ge atoms in the crystal and then increase the
number of hole traps. These traps reduce the number of col-
lected holes, leading to an underestimation of the energy re-
leased by the photon in the detector.
Fig.2. Time series of residuals in number of sigma unit
obtained by subtracting the background plus sky models
to the data. Two energy bands are shown for comparison:
(a) 435–443 keV and (b) 526–534 keV. The date are in
IJD (see text).
2003). Analysis of the shapes of adjacent background lines
yields an energy resolution at 511 keV of 2.0 keV FWHM
and a mean degradation parameter ǫd= 0.3 keV, in agree-
ment with previous analyses (Roques et al. 2003; Lonjou
et al. 2005).
The Compton continuum shape and level at 511 keV
is extracted from the IRF (Imaging Response Function)
and RMF (Redistribution Matrix File) available in the
SPI data processing database. These reponse matrices
were generated by Monte-Carlo simulations (Sturner et
al. 2003). Since the annihilation emission has an extent
of ≈8oFWHM and INTEGRAL scans this emission, we
average the IRFs in the field-of-view of SPI.
The spectral response function R(E) is:
R(E) = G(E,Γinst) ⊗ e−E/ǫd+ C(E)
where G(E,Γinst) is a Gaussian with a FWHM of Γinst=
2.0 keV, ⊗ denotes a convolution product and C(E) is the
Compton continuum function. We then convolve models
of the astrophysical signal, S(E,p), with this spectral re-
sponse and fit the set of parameters p using the measured
spectrum.
(1)

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4Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission
We adopt two different approaches to characterize the
spectral distribution of the annihilation emission:
In the first approach, the “independent model”, we
model the spectrum by four independent components:
two Gaussians G(E,Γi) (to model narrow and broad 511
keV lines of FWHM Γi), the ortho-positronium contin-
uum O(E) and a power law to account for Galactic dif-
fuse continuum emission. The independent model Sl(E) is
described by:
Sl(E) = In× G(E,Γn) + Ib× G(E,Γb)
+ I3γ× O(E) + Ac
?
E
511keV
?s
(2)
where In, Γn, Ib and Γb are the flux and width
(FWHM) of the narrow and broad lines, respectively. I3γ
is the flux of the ortho-positronium continuum, which is
represented by the Ore & Powell (1949) function O(E).
Acis the amplitude of the Galactic continuum at 511 keV
and s is the slope of the power law spectrum.
In the second approach, hereafter called the “ISM
model”, we adopt the spectral characteristics (line shape
and ortho-positronium continuum relative flux) for the
different ISM phases given in the model calculated by
GJG05, and with these spectral characteristics, we adjust
the phase fractions fi so as to obtain the best fit to the
measured spectrum. The “ISM model” is described by:
SISM(E) = Ie+e−×
5
?
i=1
fi×Si(E,xgr)+Ac
?
E
511keV
?s
(3)
where Si(E,xgr) is the normalized spectral distribution
(in keV−1) of the annihilation photons in phase i with
i={molecular, cold, warm neutral, warm ionized, hot},
Ie+e− is the annihilation flux (photons s−1cm−2) and
xgrrepresents the fraction of dust grains (xgr= 1 in the
standard grain model of GJG05); xgrallows for uncertain-
ties in dust abundance and positron-grain reaction rates.
Annihilation in dust grains is significant only in the hot
phase where the standard grain model (xgr= 1) yields a
FWHM of ≈ 2 keV, as opposed to a line width of ≈ 11 keV
in the absence of grains (xgr= 0). The grain fraction has a
negligible effect in the molecular, cold and warm neutral
phases, and affects the 511 keV line width in the warm
ionized gas by less than 2%. The grain fraction is a free
parameter of the fit, and so too are the phase fractions fi,
subject to the requirement that?5
continuum emission is assumed to be a power law with am-
plitude Acat 511 keV and a fixed slope of s = -1.75 as de-
rived by OSSE measurements in this energy range (Kinzer
et al. 1999; Kinzer et al. 2000). The energy band analysed
is not large enough and the SPI exposure not sufficient to
constrain the slope accurately from the data themselves.
We also fix the line position at 511 keV since we observe a
relatively symmetric distribution of the emission around
the Galactic Centre and do not expect a Doppler shift due
i=1fi= 1.
In both cases, the spectral distribution of the Galactic
Fig.3. Fit of the spectrum measured by SPI with contri-
butions from a Gaussian line, an ortho-positronium con-
tinuum and a power-law Galactic continuum. A single
Gaussian does not give a good fit to the flux measured
in the wings of the line.
to Galactic rotation in this region. Moreover, Churazov et
al. (2005) did not measure a significant shift of the line
centroid.
The models (Eqs. 2 & 3) are convolved with the SPI
spectral response, R(E) (Eq. 1). The parameters p of each
model are fitted by minimizing the χ2. The individual er-
rors on the best fit parameters are obtained by calculating
their confidence intervals for which ∆χ2< 1 (1σ uncer-
tainty) with ∆χ2= χ2(p) − χ2
value of χ2(p).
optand χ2
optthe minimum
3. Results
3.1. Independent model
When fitting the line with a single Gaussian, we obtain
a χ2of 193.7 for 150 degrees of freedom, a line width
of (2.2±0.1) keV, a 511 keV line flux of (1.01±0.02) ×
10−3photons s−1cm−2and an ortho-positronium flux
of (4.3±0.3) × 10−3photons s−1cm−2. We clearly see a
significant excess of counts in the wings of the narrow line,
suggesting the presence of a broad line (see Fig. 3). This
broad line is presumably due to the annihilation of the
para-positronium state formed in flight. We then include
the broad line in the analysis and use the model presented
in Equation 2.
In this model, the parameters to be adjusted are the
widths of the narrow and broad lines, their intensities,
the ortho-positronium continuum flux and the level of the
Galactic diffuse continuum. Figure 4 shows the result of
the fit. We obtain a χ2value of 171.3 for 148 degrees of
freedom. The χ2value is improved by 22.4 with respect
to the χ2value obtained when we fit the line with a single
Gaussian.
The measured parameters are listed in Table 1. The
detection significance of the broad line is 3.2σ. Its FWHM
(5.36 ± 1.22 keV) is in agreement with the width of the

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Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission5
annihilation line of positronium formed in flight in H (5.8
keV; see GJG05). The total line (narrow+broad) flux is
I2γ=(1.07±0.03)×10−3photons s−1cm−2, in agreement
with the flux derived by Kn¨ odlseder et al. (2005) for the
2D Gaussian shaped emission profile. The measured ortho-
positronium flux yields a ratio I3γ/I2γ of 3.95 ± 0.32
and consequently a positronium fraction of fPs = 0.967
± 0.022, also in agreement with previous measurements
(Kinzer et al. 1999; Harris et al. 1998; Churazov et al.
2005). The statistical uncertainties of I2γand I3γ/I2γare
not obtained by combining quadratically the uncertainties
of I3γ, Inand Ibas listed in Table 1, since these parame-
ters are not independent. Instead we fit the parameters of
the function:
Sl(E) = I2γ× [fnG(E,Γn) + (1 − fn)G(E,Γb)
+ R3γ/2γO(E)] + Ac
?
E
511keV
?s
(4)
where R3γ/2γ= I3γ/I2γand fnis the fraction of 511 keV
flux in the narrow line. The width of the narrow
line (1.32±0.35 keV) can be explained by thermalized
positrons annihilating either in the warm neutral medium
(1.16 keV) or in the warm ionized medium (0.98 keV). We
also searched for a component with a 11 keV FWHM as
expected from positrons annihilating in a hot (106K) in-
terstellar grain-free gas. We obtain only an upper limit of
0.36 × 10−3photons s−1cm−2(2σ) for such a component,
whereupon we conclude that annihilation in a hot plasma
contributes less than ≈7% to the total annihilation flux.
The Galactic continuum intensity at 511 keV (Ac) is
slightly larger than the ≈ 4–6 × 10−6photons s−1cm−2
keV−1obtained by Kinzer et al. (1999) with OSSE mea-
surements. However, these authors extracted this spec-
tral component assuming a uniform distribution along the
Galactic plane with a latitude width of 5oFWHM, while
we assume a latitude width of 7oFWHM. This can explain
the factor ≈7/5 discrepancy between the two estimations.
In order to estimate systematic errors, we first per-
formed the analysis with the uncertainty of the spectrum
bins increased by a factor such that the reduced χ2is
equal to 1. This factor is found to be ≈1.075, yielding
7.5% systematic errors. Secondly, we quantified the ef-
fect on the results of possible uncertainties in the fixed
parameters (degradation parameter, slope of the contin-
uum). The uncertainty in the degradation parameter af-
fects neither the continuum intensities nor the total 511
keV flux. Performing the analysis with ǫd= 0.2 keV and
0.4 keV yields differences of less than 1.5% of the statis-
tical errors in these parameter values. Nevertheless, the
narrow and broad line widths (and fluxes) change by 14%
(and 13%) and 4.5% (and 13%) of their statistical uncer-
tainties, respectively. We adopt these values as systematic
errors for the parameters of the lines. Kinzer et al. (1999)
did not provide uncertainties in the slope of the Galactic
Centre continuum spectrum measured by OSSE. Kinzer et
al. (2001) used a slope of -1.65 to adjust the Galactic con-
Fig.4. Fit of the spectrum measured by SPI with narrow
and broad Gaussian lines, an ortho-positronium contin-
uum and a power-law Galactic continuum (constant slope
of -1.75). Note that the asymmetric shape of the lines is
due to the convolution of the Gaussian with the spectral
response of SPI (Compton continuum and degradation).
tinuum model to the OSSE data. Considering the results
presented in Table 3 of Kinzer et al. (1999), we can rea-
sonably assume an uncertainty of ±0.1 in the slope. This
yields a systematic error of ≈10% in the intensity of the
ortho-positronium continuum in our analysis, the other
parameters being not significantly affected by this change
(less than ≈1% of the statistical errors). The correspond-
ing systematic uncertainty in the fraction of positronium
is then ±0.3%.
We also constructed another spectrum by model fitting
(see section 2.1) but excluding regions of observations for
which the Crab nebula and Cyg X-1 are in the field-of-view
of SPI, in order to check whether these sources produce a
bias in the analysis results. The statistical error bars of the
spectrum are larger due to the smaller amount of data in
this dataset. The analysis of this spectrum provides results
that are statistically consistent with those presented in
Table 1.
3.2. ISM model
The parameters of this model are the phase fractions
(fi), the grain fraction (xgr), the annihilation flux (Ie+e−)
and the amplitude of the Galactic diffuse continuum at
511 keV (Ac; see Eq. 3). Figure 5 shows the best-fit model
and Table 2 the corresponding parameters. The 1σ statis-
tical uncertainties in the phase fractions were calculated
separately by searching for the 68.3% confidence interval
of a phase fraction allowing the other parameters to vary
but keeping the constraints Σifi = 1. The total annihi-
lation flux and the continuum amplitude at 511 keV ob-
tained by this analysis are consistent with the independent
model analysis. The spectral characteristics of the mea-
sured annihilation emission can be explained by positrons
annihilating only in the warm ISM. Our best fit for the

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6Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission
Table 1. Best-fit values of the free parameters (χ2=171.3
for 148 degrees of freedom). In, Γn, Ib and Γb are the
flux and width (FWHM) of the narrow and broad lines,
respectively. I3γ is the flux of the ortho-positronium con-
tinuum and Acis the amplitude of the Galactic continuum
at 511 keV. The first set of error bars refers to the 1σ sta-
tistical errors and the second set to the systematic errors.
Parameters
In (10−3s−1cm−2)
Measured values
0.72 ± 0.12 ± 0.02
Γn (keV)
Ib(10−3s−1cm−2)
1.32 ± 0.35 ± 0.05
0.35 ± 0.11 ± 0.02
Γb(keV)
I3γ (10−3s−1cm−2)
Ac (10−6s−1cm−2keV−1) 7.17 ± 0.80 ± 0.06
5.36 ± 1.22 ± 0.06
4.23 ± 0.32 ± 0.03
Fig.5. Best fit of the spectrum measured by SPI with
the warm components of the ISM and the Galactic con-
tinuum. Contributions from the molecular, cold and hot
components are not needed to explain the data.
cold phase fraction is 0, however the upper-limit for this
value is 23%, so we cannot yet reject a significant contri-
bution from this phase. The contribution of positrons in
molecular clouds and hot gas is negligible since we obtain
upper-limits of 8% and 0.5%, respectively.
The total positronium fraction (fPs= 93.5+0.3
calculated according to the intrinsic positronium fraction
of each phase predicted by the GJG05 model, weighted
by the phase fraction fi. The positronium fraction in each
phase is the sum of the contributions of positroniums
formed in flight and in thermal conditions (via charge ex-
change and radiative recombination). These contributions
were calculated using the probabilities of charge exchange
in flight and the annihilation rates tabulated in GJG05. It
should be noted that in this analysis, the fraction of ortho-
positronium continuum is tied to the phase fractions.
Applying the method described in section 3.1, we find
9% of systematic errors with this analysis, leading to
the systematic uncertainties presented in Table 2 for the
−1.6%) is
Table 2. Measured ISM phase fractions obtained with ǫd
= 0.3 keV (χ2=176.4 for 148 degrees of freedom). The
resulting positronium fraction is 0.935+0.003
of error bars refers to the 1σ statistical errors and the
second set to the systematic errors.
−0.016. The first set
ParametersMeasured values
0.00+0.08
−0.00
0.00+0.23
−0.00
fm (Molecular)
+0.02
−0.00
+0.04
−0.00
+0.02
−0.04
+0.02
−0.02
+0.00
−0.00
+0.20
−0.00
fc (Cold)
fwn (Warm Neutral) 0.49+0.02
−0.23
fwi (Warm Ionized)0.51+0.03
0.00+0.005
−0.00
−0.02
fh (Hot)
xgr (Grain fraction) 0.00+1.20
−0.00
molecular and cold phase fractions, while we obtained
+0.00
−0.04of systematic uncertainty for the warm neutral phase
fraction. However, when the fit of the phase fraction is
performed with a degradation parameter (ǫd) of 0.2 keV
(0.4 keV), the optimal fractions are 51% (47%) and 49%
(53%) for the warm neutral and warm ionized phases, re-
spectively, the other fractions do not change and the frac-
tion of positronium is 0.938 (0.933). The uncertainty in
the slope of the continuum power-law model does not af-
fect the results of the fit. Then to be conservative, the
systematic errors for the warm neutral and ionized phase
fractions are taken to be+0.02
−0.04and ±0.02 respectively, and
±0.3% for the positronium fraction.
We now present the salient characteristics of the dif-
ferent spectral forms of the annihilation radiation that
emerges from the different phases of the ISM; this will
serve as a guide in the determination of the relative con-
tributions of the different phases. The annihilation spec-
tra for the different ISM phases can be characterized by
the sum of three components: a narrow line due to the
annihilation of thermalized positrons (except in the hot
phase where the line is broad: a width of 11 keV), a broad
line emitted by the annihilation of positronium formed in
flight, and an ortho-positronium continuum.
Table 3 summarizes the spectral characteristics of the
annihilation emission in the different phases. The widths
of the 511 keV line listed in this table were extracted from
Table 3 of GJG05. The relative intensities of the different
components (Ri) and the fraction of positronium (fPs) for
each phase were calculated using the fractions of positron-
ium formed in flight in each case and the annihilation rates
tabulated in GJG05 (see Tables 2 & 4 therein), assuming
xgr = 0. Since annihilation in dust grains is significant
only in the hot phase (see section 2.2), we also calculated
the spectral characteristics (Γi, Ri& fPs) of the annihila-
tion emission from this phase with xgr= 1. The spectral
characteristics obtained by the best-fit models are also
shown for comparison. They were calculated using the re-
sults presented in Tables 1 and 2 of the present paper.
By comparing the relative intensities Ri of the annihila-
tion features in each phase with the measured ones, we

Page 7

Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission7
can conclude that the annihilation emission from a single
phase cannot explain the measured spectral characteris-
tics. A combination of annihilation emission from several
phases is needed.
In the warm ionized phase, ≈87.4% of positrons annihi-
late after thermalization, forming positroniums by radia-
tive recombinaison with free electrons, while the remaining
positrons annihilate directly with free electrons. In both
annihilation processes, the width of the 511 keV line (0.98
keV) can explain the narrow line component of the mea-
sured spectrum (Fig. 4 and 5). There is no formation of
positronium in flight in this phase since the totality of H
is ionized, thus no broad line is emitted. In the warm neu-
tral phase, 94% of positrons form positroniums in flight;
one-fourth of them annihilate producing a 511 keV line
emission with the 5.8 keV width required to explain the
broad line component observed in the SPI data. The re-
maining ≈6% of positrons thermalize and have sufficient
kinetic energy to form positroniums by charge exchange
with H atoms – one-fourth of these positroniums annihi-
late producing a narrow (Γn= 1.16 keV) but weak (Rn∼
1.2 %) 511 keV line. Consequently, the total positronium
fraction in the warm neutral phase is ≈99.9%.
Combining 49% of annihilation in the warm neutral
phase with 51% of annihilation in the warm ionized phase
as derived by the best-fit of the phase fractions yields
≈94% total positronium fraction and the measured rela-
tive fluxes Ri. The broad line component with the required
width can also be due to the annihilation of positroniums
formed in flight in cold gas. However, most of the thermal-
ized positrons annihilate directly with H in this phase (the
temperature is too low in the cold gas to allow the forma-
tion of positronium by charge exchange), and therefore the
total fraction of positronium is only due to the positroni-
ums formed in flight (≈94%). Consequently, annihilation
emission from the cold gas alone, or even combined with
the annihilation emission from the warm ionized phase
cannot (1) reproduce the measured positronium fraction
and (2) explain the shape of the annihilation spectrum.
However, a mix of annihilation emission from the cold gas
and the warm neutral phase both combined with ≈51% of
annihilation emission from the warm ionized phase can re-
produce the measured spectrum. This explains the uncer-
tainty values on the cold and warm neutral phase fractions
obtained by the best fit (see Table 2). Similar conclusions
hold for the contribution of the annihilation emission from
the molecular medium, which in addition is characterized
by (1) narrow and broad 511 keV line widths that are both
slightly larger than the cold phase’s, and (2) a positron-
ium fraction lower than those of the cold gas and the warm
phase (see Table 3). These differences significantly reduce
the possible contribution of the molecular medium to the
best-fit model. For the hot phase, the widths of the cal-
culated annihilation line, with or without grains, are too
broad and the positronium fraction too low for this phase
to contribute substantially in the model.
Table 3. Spectral characteristics of the annihilation ra-
diation in the different phases. Γn and Γb are the width
(FHWM) of the narrow and broad annihilation line, re-
spectively. Rn, Rb and R3γ are the relative flux of the
narrow line, broad line and ortho-positronium, respec-
tively. fPs is the fraction of positronium. Values of Ri
and fPsin the different phases were calculated using the
fraction of positronium formed in flight and the annihi-
lation rates tabulated in GJG05. The measured spectral
characteristics are shown for comparison. They were cal-
culated using the best-fit values of the free parameters of
the “Independent model” (Table 1) and the “ISM model”
(Table 2).
PhaseΓn
Γb
Rn
Rb
R3γ fPs
(keV) (keV) (%) (%) (%) (%)
Molecular1.716.48.4 16.7 74.9 88.8
Cold1.565.84.3 17.4 78.3 94.1
Warm Neutral1.165.81.2 17.1 81.7 99.9
Warm Ionized0.98−25.9 0.0 74.1 87.4
Hot (xgr=0)−11.00.0 59.2 40.8 41.9
Hot (xgr=1)2.011.0 48.9 5.3 45.8 17.7
Independent model1.35.4 13.8 8.0 77.8 96.7
ISM model0.985.8 13.8 8.4 77.8 93.5
4. Discussion
Our analysis suggests that Galactic positrons annihilate
primarily in the warm phases of the ISM. A similar conclu-
sion was reported in previous analyses (Harris et al. 1998;
Churazov et al. 2005). Since positron annihilation takes
primarily place in the Galactic bulge region (Kn¨ odlseder
et al. 2005), we now compare the current knowledge about
the ISM in this area (i.e., within ∼ 600 pc radius of the
Galactic Centre, corresponding to an approximative bulge
size of 8oFWHM) with our results.
4.1. Gas content in the Galactic bulge
The gas content in the Galactic center region is not well
known. The gas content of the Galactic bulge as well as
its influence on the morphological and spectral character-
istics of annihilation emission are under study and will
be presented in a future paper (Gillard et al. in prepara-
tion). Launhardt et al. (2002) analysed IRAS and COBE
data and showed that the nuclear bulge (region inside a
Galactocentric radius of ≈ 230 pc with a scale height of
≈ 45 pc) contains 7 × 107M⊙of hydrogen gas (the mass
of 2 × 107M⊙quoted in their paper has to be corrected
by a factor 3.5; Launhardt, private communication).
Launhardt et al. (2002) also argued that roughly 90%
of the interstellar mass in this region is trapped in small
high-density (∼104cm−3) molecular clouds with a volume
filling factor of a few %, while the remaining ∼10% is
homogeneously distributed and constitutes the intercloud

Page 8

8Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission
medium with an averagedensity ∼10 cm−3and probably a
high ionization fraction. From radio observations, Mezger
& Paul (1979) deduced a mass of HII gas in this region
of 1.4 × 106M⊙with an electron density ne∼ 10 cm−3
and an electron temperature Te∼ 5000 K. Observations
of the 21 cm line yield a HI mass of 3.1 × 106M⊙ in
this region (Rohlfs & Braunsfurth 1982). The mass of H2
in the nuclear bulge is estimated by subtracting this HI
mass and the HII mass derived from the model of Lazio
& Cordes (2003)2from the total mass of hydrogen gas
measured by Launhardt et al. (2002).
The rest of the gas in the Galactic bulge is contained
in the asymmetric Galactic bar. Its shape can be approx-
imated by an ellipsoid with semi-major axis ∼ 1.75 kpc
and semi-minor axes ∼ 0.6 kpc (Bissantz, Englmaier &
Gerhard 2003). The interstellar gas is not uniformly dis-
tributed across the bar, which makes its mass difficult to
estimate. Mezger et al. (1996) derived a mass of HI gas
∼ 4 × 107M⊙in the bar from far infra-red and C18O line
observations. We can resonably assume that the HI gas
mass is equally distributed between cold and warm neu-
tral gases, as in the Galactic disk (Ferri` ere 1998). Based
on13CO observations (Combes 1991) and a recent value
of the abundance ratio13CO/H2(Martin et al. 2004) we
estimate a mass of H2gas ∼ 2 × 107M⊙in the bar.
For the warm and hot ionized phases we consider the
volume inside 600 pc for which the Galactic free-electron
density model of Lazio & Cordes (2003) yields an HII gas
mass of ∼ 2 × 106M⊙. We assume that 90% of this mass is
in the warm ionized phase and 10% in the hot phase, sim-
ilar to the proportion found in the Galactic disk (Ferri` ere
1998).
From this mass model and the rough geometrical dis-
tribution of the gas in the Galactic bulge region, we de-
rive the space-average densities ?ni? of the five interstellar
phases. Since gravity is stronger in the Galactic bulge than
near the Sun, we expect the gas to be more compressed
there than locally. We then estimate the true density ni
of each phase in the bulge by multiplying its true density
ni,⊙ measured near the Sun3, by a common “compres-
sion factor” fc, whose value is set by the requirement that
?
and hence to the densities and filling factors listed in
Table 4. The true density obtained for the molecular gas
with this method is in agreement with the observations of
Launhardt et al. (2002), Martin et al. (2004) and Stark et
al. (2004).
If positrons are generated uniformly in the Galactic
bulge and annihilate in situ (i.e. without propagation)
then, in stationary conditions, the phase fraction fiof each
iΦi= 1, where Φi=?ni?/niis the volume filling factor of
phase i. This requirement leads to fc=?
i?ni?/ni,⊙≈ 3.6,
2The mass of HII derived from the model of Lazio & Cordes
(2003) is in agreement with the measurements performed by
Mezger & Paul (1979)
3with ni,⊙=1000, 40, 0.4, 0.21 and 3.4×10−3cm−3in the
molecular, cold, warm neutral, warm ionized and hot phase
respectively (Ferri` ere 1998).
Table 4. Estimates for the Galactic bulge parameters
and resulting consequence on the lifetime and diffusion
of 1 MeV positrons (see text). ?n? and n are the space-
averaged and true densities, respectively. Φ is the vol-
ume filling factor. l/2 is the typical half-size of the phase.
Kql is the energy threshold above which the quasilinear
diffusion is valid. ∆tql and dql are the time taken and
the distance travelled by positrons in quasilinear diffusion
regime. ∆tcolland dcollare the time taken and the maxi-
mum distance travelled by positrons in the collisional dif-
fusion regime. dannis the maximum distance travelled by
thermalized positrons. τannis the lifetime of thermalized
positrons. dmaxis the total distance travelled by positrons
(dmax= dql+ dcoll+ dann). The lifetime for thermalized
positrons in the hot phase was calculated assuming a nor-
mal abundance of interstellar grains (xgr=1).
molecular coldwarm
neutral ionized
warm hot
?n?(cm−3)
n(cm−3)
1.580.26 0.26 0.088.9 ×10−3
3600 1461.46 0.770.012
Φ 0.0004 0.0020.180.100.72
l/2(pc)3-30∼5 0.1-50 10-100 50-100
Kql(keV) 10−3
0.03
103
2.9
105
5.5
105
270
∆tql(yr)392.7 × 106
dql(pc) 1.0 4.847.8 43.9264
∆tcoll(yr)∼ 0∼ 031566.6 ×105
dcoll(pc)∼ 0∼ 00.100.095210
τann(yr)223500 1.3 1043.4 104
9.4 106
dann(pc)∼ 0∼ 00.040.004 172
dmax(pc)1.04.847.944.05.6 × 103
phase must be equal to its filling factor Φi. In this case, one
would expect the hot medium to be the dominant com-
ponent. However, in a 0.01 cm−3density hot medium,
1 MeV positrons thermalize in ∼4 ×106years and then
annihilate on a timescale ∼108years if there are no inter-
stellar grains in this phase; in the standard grain model
the annihilation timescale is ∼107years (GJG05). With
such long timescales it is likely that positrons escape the
hot medium (before they can annihilate), either by prop-
agation or following an encounter with a supernova shock
wave (timescales ∼ 0.5–1 Myr; Cox 1990). Positrons es-
caping the hot medium then have a high probability of
entering a warm phase due to the large filling factor of
this phase (c.f. Table 4). If such positrons annihilate in
the warm phases, then the phase fractions between the
warm neutral and warm ionized phase should be close to
the relative values of their filling factors. In order to ver-
ify whether positrons escape a given ISM phase or not,
it is necessary to estimate the distance they travel within
this phase and compare it with the typical half-size of the
phase.

Page 9

Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission9
4.2. Propagation of positrons
The distance travelled by positrons depends on their ini-
tial velocity and their energy loss rate, which is a function
of the density and the ionization fraction of the ambient
medium. The timescale for 1 MeV positrons to thermalize
in a warm medium is τw≈ 105years. Positrons then an-
nihilate with a timescale ≈3.4×104years in the 0.8 cm−3
density warm ionized phase. In the 1.5 cm−3density warm
neutral gas, positrons that do not form a positronium in
flight by charge exchange with H, take ≈1.3×104years
to annihilate. Typical sizes of warm and hot regions are
lw∼ lh∼100 pc. Roughly speaking, positrons will escape
the hot phase if the distance travelled by diffusion in a
time τh∼107years (slowing down time plus annihilation
time in the standard grain model) is greater than the typ-
ical half-size of hot region, lh/2 ∼ 50 pc, i.e., if the diffu-
sion coefficient D is greater than Dmin=
cm2s−1. On the other hand, positrons that enter the warm
phases will annihilate if the distance travelled by diffusion
in a time τw∼ 105years is less than lw/2 ∼ 50 pc, i.e., if
D is smaller than Dmax=
limits have to be compared with the quasilinear diffusion
coefficient (Melrose 1980) which can be expressed as:
l2
h
24τh∼1.3×1025
l2
w
24τw∼1.3×1027cm2s−1. These
Dql(E) = DB
?
rL
λmax
?1−δ
η−1
(5)
with DB =
the positron gyroradius, v the positron velocity, λmax
the maximum scale of the turbulence, δ = 5/3 for a
Kolmogorov turbulent spectrum, and η = δB2/?B?2the
relative perturbation in magnetic field pressure which is
often approximated to 1, since the turbulent component
of the ISM magnetic field has been estimated to be of the
same order of magnitude as the regular magnetic field.
The magnetic field strength in the Galactic Centre re-
gion was estimated to be ∼10 µG (Sofue et al. 1987; La
Rosa et al. 2005). The maximum scale λmaxwas estimated
to be ∼ 100 pc from measurements of ISM turbulence
(Armstrong et al. 1995). Then for 1 MeV positrons in the
Galactic bulge, Dql∼ 3×1026cm2s−1. This coefficient is
well above Dmin and below Dmax and leads support to
our hypothesis that positrons indeed escape the hot phase
and subsequently annihilate in the warm phases.
However, quasilinear diffusion is valid only when
positrons are in resonance with Alfv´ en waves. This condi-
tion is satisfied when:
1
3rLv the Bohm diffusion coefficient, rL
γβ >mpvA
mec
= 12.85× 10−3
BµG
√ncm−3
(6)
with γ the Lorentz factor, β =v
the positron mass and vAthe Alfv´ en speed.
When the kinetic energy of positrons drops below a
given threshold Kql, quasilinear diffusion theory breaks
down and the diffusion regime changes. Kqlis calculated
for each phase using Eq. (6) together with B = 10µG and
c, mpthe proton mass, me
the densities given in Table 4. The slowing down times
∆tqlfor 1 MeV positrons to reach Kqlare listed in Table
4 as well as the associated distances dqlwhich are obtained
by:
dql=
??1MeV
Kql
6Dql(E)
?dE
dt
?−1
dE (7)
The distances dql are lower than or of the same order
as the typical half-sizes of the corresponding phases (see
Table 4) except for the hot gas.
The diffusion regime of positrons with kinetic ener-
gies below Kqlis uncertain (interstellar winds, resonance
with other plasma waves...) and is currently under study
(Marcowith et al., in preparation). However we can esti-
mate an upper-limit to the distance dcolltravelled by these
positrons assuming that they propagate in a collisional
regime. In this case, the distance is given by:
dcoll=
??Kql
Elim
6Dcoll(E)
?dE
dt
?−1
dE (8)
where Elimis the lowest kinetic energy for which positrons
are able to form a positronium in flight by charge ex-
change in the molecular, cold and warm neutral phases or
are thermalized (Elim =
hot phases (charge exchange does not happen in these
phases since all the hydrogen is ionized).dE
loss rate. Accounting for the streaming of positrons in the
ISM, at a characteristic velocity ∼ vA, we write the dif-
fusion coefficient Dcoll(E) = vA×λcoll(E) where λcoll(E)
is the distance over which interactions gradually deflect
positrons with kinetic energy E by 90o. λcoll was calcu-
lated according to Lang (1974) for a fully ionized plasma
and using the approach of Emslie (1978) for neutral hy-
drogen. When positrons are thermalized, the distance dann
they travel before annihilation is given by:
3
2kT) in the warm ionized and
dtis the energy-
dann=
?
6Dcollτann
(9)
where τann is the annihilation lifetime of thermalized
positrons. The resulting values of dmax= dql+dcoll+dann
(see Table 4) confirm that 1 MeV positrons injected in the
hot phase should escape it, while those injected in other
phases should annihilate in them. Since positrons leaving
the hot phase most likely enter the warm phases (due to
their large filling factors) we expect that positron annihi-
lation occurs mostly in the warm phases.
It has to be noted that several authors (see Morris &
Serabyn 1996 and references therein) estimate magnetic
field values of ∼1mG in the Galactic centre region. This is
2 orders of magnitude larger than the value (10µG) used
in our study. If we assume that this value is effective ev-
erywhere in the Galactic bulge, then this increases vAby
2 orders of magnitude and rules out quasilinear diffusion
in the warm and hot phases for 1 MeV positrons (see Eq.
6). Consequently, we can only derive upper limits to the
distances travelled by positrons in these phases, by as-
suming that they propagate in a collisional regime. Here

Page 10

10Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission
Fig.6. Maximum distance travelled by positrons as a
function of their kinetic energy. Typical half-sizes of warm
and hot regions (∼50 pc) and typical sizes of cold and
molecular regions (∼5 pc) are shown for comparison.
again, a detailed investigation of the diffusion of positrons
in a non-quasilinear regime is required to derive relevant
distances of propagation.
4.3. Initial kinetic energy of positrons
The above estimates on the transport of positrons are
based on the assumption that their initial kinetic energy
is 1 MeV, which is a typical value for positrons emitted
by radioactive nuclei. The actual mean energy of positrons
from56Co, one of the proposed candidates for the source
of Galactic positrons, is 0.6 MeV. Figure 6 shows the
maximum distance dmax = dql+dcoll+dann travelled by
positrons before annihilating as a function of their ini-
tial kinetic energy in a 10 µG magnetic field. The conclu-
sions derived above, assuming 1 MeV positrons, obviously
hold for positrons with E<1 MeV even for the hot phase.
Positrons with initial kinetic energy above ∼1 MeV would
escape the warm and hot phases and would then have a
chance to annihilate in molecular clouds provided they
do not escape the Galactic bulge. However, the 1 MeV
limit should not be considered as very constraining, since
it was derived using rough estimates for the size of each
phase (see Table 4). Moreover, we have to keep in mind
that the calculated distances dmaxquantify the spatial ex-
tent of the distribution of annihilating positrons around
the source. Then the fraction of positrons produced in a
warm phase with initial energy of e.g. 2 MeV that es-
cape this warm phase to annihilate in cold or molecular
clouds, would probably be sufficiently low to be in agree-
ment with the phase fractions derived by the spectral anal-
ysis, since most of these positrons would annihilate in the
warm phase.
In our discussion, we have assumed that positrons
are generated uniformly in the Galactic bulge. This
assumption is valid in the case of numerous positron
sources, including light dark matter annihilating into
electron-positron pairs (Boehm et al. 2003). However, such
positrons should have an initial kinetic energy lower than
a few MeV to explain the measured spectrum. Other pos-
sible uniformly distributed sources in the Galactic bulge
are type Ia supernovae, novae and low mass X-ray binaries,
all of which belong to the old stellar population. However,
these sources produce their own warm and hot phases by
heating the surrounding ISM, so that they do not inject
positrons in cold atomic and molecular regions.
Low energy (<1MeV) positrons produced in the warm
phase probably stay in this phase and annihilate at a dis-
tance<∼50pc from the sources. When such positrons are
produced in the hot medium, they are likely to leave this
medium and enter the warm phase within which they will
annihilate. Then, assuming that the typical size of the
hot phase does not exceed ∼200 pc and that positrons are
produced at the edge of this phase, then the maximum
distance covered by such positrons is<∼250 pc from the
source. Therefore a single source releasing positrons in a
warm or hot region (e.g. a gamma-ray burst as suggested
by Parizot et al. 2005) might have difficulty accounting for
the observed spatial extent of the annihilation emission,
which covers a radius ∼600 pc around the Galactic centre.
5. Conclusions
The positron-electron annihilation emission spectrum can
be explained by narrow and broad 511 keV lines plus
an ortho-positronium continuum. The detection signifi-
cance of the broad line is ≈3.2σ. The broad line width
of (5.4±1.2) keV FWHM is in agreement with the value
calculated by GJG05 for positronium formed in flight by
charge exchange with H (≈5.8 keV). This value is also
in agreement with the width (≈5.3 keV) calculated by
Churazov et al. (2005). The narrow line width is (1.3±0.4)
keV FWHM. This width is consistent with the ≈1 keV
width of positrons annihilating by radiative recombina-
tion in the warm ionized medium.
Galactic positrons seem to annihilate mostly in the
warm phases of the ISM. These results are in agreement
with conclusions of Harris et al. (1998) and Churazov et
al. (2005). We estimate that ≈50 % of the annihilation
emission comes from the warm neutral phase and ≈50 %
from the warm ionized phase. The contribution of molec-
ular clouds and the hot phase are less than 8% and 0.5%,
respectively. We cannot exclude from our spectral analysis
that a significant fraction (<23%) of the emission comes
from cold gas. However in view of the gas content of the
Galactic bulge, this fraction is expected to be negligible.
A preliminary study of the interstellar gas content and
positron propagation in the Galactic bulge shows that the
phase fractions derived from the spectral analysis are in
agreement with the relative filling factors of the warm
and low temperature gases. The lack of detection of an-
nihilation in molecular and cold atomic gases could be
explained by their low filling factors. The spectral anal-
ysis suggests comparable amounts of annihilation in the
warm neutral and warm ionized phases of the ISM. This

Page 11

Jean et al.: Spectral analysis of the Galactic e+e−annihilation emission11
is in good agreement with our expectation if the positron
sources are uniformly distributed and if the initial kinetic
energy of positrons is lower than a few MeV, otherwise
they may escape the warm phase of the ISM and annihi-
late in molecular or cold atomic regions.
Despite its large filling factor, positrons do not anni-
hilate in the hot gas because its density is low enough to
allow them to escape. Using quasilinear diffusion theory
and assuming a magnetic field ∼10 µG in the Galactic
bulge, we estimate that, down to low kinetic energies,
positrons are generally confined in warm and cold regions.
In the hot phase, they should be less confined and assum-
ing that they are released in a collisional regime when
their kinetic energy drops below ∼270 keV, they have suf-
ficient kinetic energy to escape it. However, the diffusion
regime of positrons with keV energies in a hot low-density
plasma is not yet known. More detailed studies on the
Galactic bulge gas content and on the diffusive regime of
positrons as a function of their energy and the magnetic
field strength are under way and will be presented in forth-
coming papers.
According to the rough gas model described in section
4, we expect the warm ionized component to dominate the
annihilation emission in the nuclear bulge, while the warm
neutral component should dominate in the Galactic bar.
Additional exposure will make it possible to perform spec-
tra in different regions of the Galactic Centre and confirm
this prediction.
Our understanding of Galactic positron physics can
be improved by imaging and spectroscopic explorations of
Galactic regions other than the central regions, particu-
larly by measurements of the annihilation emission from
the Galactic disk, which appears to be explainable by26Al
decay (Kn¨ odlseder et al. 2005). While our understanding
of positron annihilation in the Galactic Centre region is
limited by the poor knowledge of both the sources and
initial kinetic energy of positrons and the gas content in
the Galactic bulge, the task would be easier for the disk
emission, since: (1) we know that positrons from26Al are
released in the molecular ring region since COMPTEL on-
board CGRO measured the spatial distribution of the 1.8
MeV gamma-ray line emitted during the radioactive decay
of this isotope; (2) the average energy of such positrons
has been measured to be 450 keV; (3) the distribution
and characteristics of the gas in the molecular ring re-
gion are known with better accuracy than in the Galactic
bulge. Consequently, the measured spatial distribution of
the annihilation emission from the disk would teach us
how far from the sources positrons annihilate and this will
lead to estimates of their diffusion coefficient. The spec-
tral characteristics of the disk emission would tell us in
what phases of the ISM positrons annihilate. Since much
26Al is located in the molecular ring region, we expect to
measure a strong 6.4 keV FWHM line component due to
the annihilation of positronium formed in flight in H2(see
Fig. 5 of GJG05). On the other hand, the significance of
the annihilation emission from the disk is still weak (3–4σ)
after one year of the INTEGRAL mission. Additional ex-
posure is needed to allow the spectral analysis to provide
constraining results.
Additional note: After acceptation of this manuscript,
a related paper (Weidenspointner et al. 2005) recently sub-
mitted, confirms that the spatial distribution of the positro-
nium continuum emission measured using SPI data, is
consistent with the 511 keV line emission distribution.
Acknowledgements. We are grateful to R.J. Murphy for useful
discussions on the energy loss rate of positrons in the ISM.
We thank the anonymous referee for suggestions that have im-
proved the quality of this paper.
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