The 511 keV emission from positron annihilation in the Galaxy

The 511 keV emission from positron annihilation in the Galaxy

N. Prantzos CNRS, UMR7095, UMPC and Institut d’Astrophysique de Paris, F-75014, Paris, France    C. Boehm LAPP - 9 Chemin de Bellevue - BP 110 F-74941 Annecy-le-Vieux , France    A. M. Bykov A.F. Ioffe Institute of Physics and Technology, Russian Academy of Sciences, 194021, St. Petersburg, Russia    R. Diehl Max Planck Institut für Extraterrestrische Physik, D-85741 Garching, Germany    K. Ferrière Laboratoire d’Astrophysique de Toulouse-Tarbes, Université de Toulouse, CNRS, 14 avenue Edouard Belin, F-31400 Toulouse, France    N. Guessoum American University of Sharjah, College of Arts & Sciences / Physics Dpt., P.O Box 26666, Sharjah, UAE    P. Jean CESR, 9, Av. du Colonel Roche, B.P. 4346, 31028 Toulouse Cedex 4, France    J. Knoedlseder CESR, 9, Av. du Colonel Roche, B.P. 4346, 31028 Toulouse Cedex 4, France    A. Marcowith L.P.T.A., Université Montpellier II, CNRS, Place Eugène Bataillon, 34095 Montpellier, France    I. V. Moskalenko Hansen Experimental Physics Laboratory and Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305, U.S.A.
   A. Strong Max Planck Institut für Extraterrestrische Physik, D-85741, Garching, Germany    G. Weidenspointner Max Planck Institut fur Extraterrestrische Physik, Garching, Germany, and
MPI Halbleiterlabor, Otto-Hahn-Ring 6, 81739 Muenchen, Germany
July 18, 2019

The first gamma-ray line originating from outside the solar system that was ever detected is the 511 keV emission from positron annihilation in the Galaxy. Despite 30 years of intense theoretical and observational investigation, the main sources of positrons have not been identified up to now. Observations in the 1990’s with OSSE/CGRO showed that the emission is strongly concentrated towards the Galactic bulge. In the 2000’s, the SPI instrument aboard ESA’s INTEGRAL -ray observatory allowed scientists to measure that emission across the entire Galaxy, revealing that the bulge/disk luminosity ratio is larger than observed in any other wavelength. This mapping prompted a number of novel explanations, including rather “exotic” ones (e.g. dark matter annihilation). However, conventional astrophysical sources, like type Ia supernovae, microquasars or X-ray binaries, are still plausible candidates for a large fraction of the observed total 511 keV emission of the bulge. A closer study of the subject reveals new layers of complexity, since positrons may propagate far away from their production sites, making it difficult to infer the underlying source distribution from the observed map of 511 keV emission. However, contrary to the rather well understood propagation of high energy (GeV) particles of Galactic cosmic rays, understanding the propagation of low energy (MeV) positrons in the turbulent, magnetized interstellar medium, still remains a formidable challenge. We review the spectral and imaging properties of the observed 511 keV emission and we critically discuss candidate positron sources and models of positron propagation in the Galaxy.

Valid PACS appear here, +

I Introduction

The existence of a particle with equal mass but opposite charge to that of the electron was predicted by Dirac (1931), who named it ”anti-electron”. Unaware of Dirac’s prediction, Anderson (1932) found the first experimental hints for such a particle in cloud-chamber photographs of cosmic rays, and he named it positron. His finding was confirmed the following year by Blackett and Occhialini (1933), who identified it with Dirac’s anti-electron. One year later, Klemperer and Chadwick (1934) detected the characteristic -ray line at 511 keV resulting from e-e annihilation, a convincing proof that positrons are indeed electron’s antiparticles. That same year, Croatian physicist Mohorovicic (1934) predicted the existence of a bound system composed of an electron and a positron (analogous to the hydrogen atom, but with the proton replaced by a positron), which he called ”electrum”. This state was experimentally found by Deutsch (1951) at MIT and became known as positronium.

For about 30 years after their discovery, all detected positrons were of terrestrial origin. Those detected by Anderson (1932) and Blackett and Occhialini (1933) were created by cosmic ray interactions with molecules in Earth’s atmosphere. Joliot and Curie (1934) identified another positron producing process: radioactivity of artificially created unstable nuclei. The first positrons of extraterrestrial origin were reported by de Shong et al. (1964), who loaded a spark chamber on a stratospheric balloon to detect positrons within the cosmic rays. Ginzburg (1956) had already suggested that high energy p-p interactions in cosmic rays would produce pions , which would decay to positrons (via decays) . The production rate of those pions was evaluated by Pollack and Fazio (1963) who predicted a -ray flux from the Galaxy at 511 keV of 10 cm s.

The properties of e-e annihilation were explored in the 1940’s. Direct e-e annihilation produces a single -ray line at 511 keV, while the annihilation of positronium produces a composite spectrum with a lower energy continuum and a 511 keV line (Ore and Powell, 1949 and Sec. II.1). Stecker (1969) was the first to point out that in the conditions of the interstellar medium, most positrons would annihilate after positronium formation; this would reduce the 511 keV flux from cosmic rays to values lower than evaluated by Pollack and Fazio (1963).

The 511 keV emission of e annihilation was first detected from the general direction of the Galactic center in the early 1970’s, by balloon-borne instruments of low energy resolution (Johnson et al., 1972). It was unambiguously identified a few years later with high resolution Ge detectors (Leventhal et al., 1978). It is the first and most intense -ray line originating from outside the solar system that was ever detected. Its flux on Earth (10 cm s), combined with the distance to the Galactic center (8 kpc1111 pc(parsec)=3.26 light years = 3.09 10 cm.), implies the annihilation of 2 10 e s (Sec. II.2.3), releasing a power of 10 erg s or 10 L  in -rays. Assuming a steady state, i.e. equality between production and annihilation rates of positrons, one should then look for a source (or sources) able to provide 2 10 e s. If the activity of that site were maintained to the same level during the 10 yr of Galaxy’s lifetime, a total amount of positrons equivalent to 3 M  would have been annihilated.

Several years earlier, the Sun had already become the first astrophysical laboratory for the study of positron annihilation Crannell et al. (1976). The solar annihilation -ray line had been detected with a simple NaI instrument aboard the OSO-7 satellite Chupp et al. (1975). The Solar Maximum Mission (SMM), designed for solar flare observations and launched in 1980, featured a -ray spectrometer with exceptional stability. Based on detailed measurements with SMM, positrons in solar flares were found to originate from flare-accelerated particles when hitting the upper photosphere. Nuclear interactions of flare-accelerated protons and ions with atomic nuclei of the photosphere produce radioactive nuclei and pions that decay by emission of positrons, which annihilate locally Ramaty et al. (1983); Murphy et al. (2005b).

Imaging the Galaxy in annihilation -rays was considered to be the exclusive way to identify the cosmic e sources (assuming that the spatial morphology of the -ray emission reflects the spatial distribution of the sources, i.e. that positrons annihilate close to their production sites). Because of the difficulties of imaging in the MeV region, progress was extremely slow in that field: only in the 1990s were the first constraints on the spatial distribution of the 511 keV emission in the inner Galaxy obtained by the OSSE instrument aboard the Compton Gamma Ray Observatory (CGRO, Cheng et al., 1997; Purcell et al., 1997). The most reliable imaging of the 511 keV emission was obtained by the SPI instrument aboard ESA’s INTEGRAL Gamma Ray Observatory: the emission is strongly concentrated in the inner Galaxy (the bulge, Knödlseder et al., 2005) and a weaker emission is detected from the Galactic disk (Weidenspointner et al., 2008a), unlike the situation in any other wavelength.

Several candidate sources of positrons were proposed over the years: radioactivity from decay of unstable nuclei produced in stellar explosions, high energy interactions occurring in cosmic rays or near compact objects (like pulsars and X-ray binaries) or the supermassive black hole in the Galactic center, etc. For a long time, radioactivity from Co produced in thermonuclear supernovae (SNIa) appeared as the most promising candidate, provided that just a few per cent of the released positrons could escape the supernova remnant and annihilate in the interstellar medium. However, none of the candidate sources has a spatial pattern resembling the one of the detected -ray emission. In particular, the release of the first year of SPI data, revealing the bulge but not yet the disk, prompted a series of ”exotic” explanations involving dark matter particles, superconducting cosmic strings, etc. The confirmation of disk emission a few years later, made such explanations lose much of their interest, without completely eliminating them up to now.

The spectral analysis of the 511 keV emission established already at the late 1970’s that most of the positrons annihilate after positronium formation (Bussard et al., 1979). This result constitutes an important diagnostic tool for the physical properties of the annihilation medium, as analyzed in Guessoum et al. (1991). Only recently, i.e. in the 2000’s, was it realized that the spectral analysis may also provide important hints on the e source(s). In particular, positrons appear to annihilate at low energies, while in most candidate sources they are produced at relativistic energies; during the long period of their slowing down, positrons may travel far away from their sources, making the detected -ray emission useless as a tracer of their production sites. Unfortunately, propagation of low energy positrons in the turbulent, magnetized interstellar plasma of the Galaxy, is poorly understood at present.

In this paper we present a synthetic view of the various facets of this complex issue, concerning the production, propagation and annihilation of positrons in the Galaxy, in relation with the characteristic signature of that annihilation, namely the 511 keV emission. The paper is structured as follows:

In Sec. II we first present a historical account of observations of the 511 keV emission, which illustrates the difficulties of -ray line astronomy in the MeV range. We also provide a summary of the latest SPI/INTEGRAL data analysis, of relevant observations in other wavelengths and of the constraints imposed on the e sources.

Sec. III provides astrophysical background material concerning the stellar and supernova populations of the Milky Way, as well as the properties of the various phases of the interstellar medium (ISM) and of the Galactic magnetic fields in which positrons propagate. This material can be skipped at a first reading by astronomers, but it contains important and updated information, which is used in all other sections.

In Sec. IV we discuss the physical processes and candidate sources of positron production (radioactivity from stars and supernovae, high energy processes in cosmic rays, compact objects and the central supermassive black hole, dark matter, other ”exotica”, etc.) and, in some cases, we present new estimates of their e yields. We discuss critically the properties of those sources, in the light of the observational constraints presented in Sec. II.

Sec. V summarizes the various physical processes of e slowing down and annihilation, taking into account the properties of the ISM, as well as the corresponding -ray spectral signature. The spectral analysis of the SPI data is then used to constrain the energy of the emitted positrons (thus eliminating some of the candidate sources) and to constrain the properties of the annihilation medium. The results of this analysis offer some hints for e propagation away from the sources.

The intricacies of low energy positron propagation are discussed in some depth in Sec. VI, in the light of recent work. The implications of e propagation for the 511 keV emission are also discussed. This is not a mature topic yet, and our poor knowledge of the plasma properties in the inner Galaxy prevents any definitive conclusions. A synthetic summary of the subject and directions for future research are presented in the last section.

Ii Observations

Gamma-ray observations in the MeV domain (from 100 keV up to a few MeV) provide access to Galactic positrons through three main windows:

i) Emission from e annihilation at sub-relativistic energies, with its prominent 511 keV line and the associated three-photon continuum from positronium annihilation;

ii) Continuum emission at energies E0.5 MeV from energetic positrons propagating through interstellar space and annihilating ”in-flight”;

iii) Emission of characteristic gamma-ray lines from radioactive nuclei, such as Al and Ti, which also produce positrons by -decay.

In this section, we describe the relevant observations and the constraints that they impose on our understanding of Galactic positrons (see also Diehl and Leising, 2009). We start with a brief description of the radiative signatures of positron annihilation.

ii.1 Radiative signatures of positron annihilation

The annihilation of a positron with an electron releases a total (rest-mass) energy of 1022 keV in the form of two or more photons. Direct annihilation of a e-e pair at rest produces two photons of 511 keV each. The situation is more complex in the case of positronium (Ps). The ground state of positronium has two total spin states, depending on the relative orientations of the spins of the electron and the positron. The singlet state has antiparallel spins, total spin S=0, is denoted as and is known as para-positronium (p-Ps). The triplet state has parallel spins, total spin S=1, is denoted as and is known as ortho-positronium (o-Ps). From the (2S+1) spin degeneracy, it follows that Ps will be formed 1/4 of the time in the p-Ps state and 3/4 of the time in the o-Ps state. 222The energy difference between the two spin states (”hyperfine splitting”) is 8.4 10 eV. Transitions between these states similar to the spin-flip transition in hydrogen, which produces the astrophysically-important 21 cm line, are unimportant due to the short Ps lifetimes (see text).

Spin and momentum conservation constrain the release of annihilation energy in the form of photons. Para-positronium annihilation releases two photons of 511 keV each in opposite directions (as in the case of direct e-e annihilation). Ortho-positronium annihilation requires a final state with more than two photons from spin conservation; momentum conservation distributes the total energy of 1022 keV among three photons333 Annihilation into a larger number of photons (an even number for para-positronium, an odd number for ortho-positronium) is possible, but the corresponding branching ratios are negligible (10 for four photons in the case of para-Positronium or five photons in the case of ortho-positronium). Even lower are the branching ratios for annihilation into neutrino-antineutrino pairs. Finally, a single-photon annihilation is also possible, provided momentum conservation is obtained through positronium being bound to another particle, such as a dust grain. None of those cases is important in astrophysical settings. producing a continuum of energies up to 511 keV (Fig. 1). The corresponding lifetimes before annihilation (in vacuum) are 1.2 10 s for p-Ps and 1.4 10 s for o-Ps.

If a fraction of the positrons annihilate via positronium formation, then the 3-photon -ray continuum of ortho-positronium will have an integrated intensity of


The remaining fraction will annihilate directly to 2 photons of 511 keV each, to which should be added the 2-photon contribution of the para-Positronium state; thus, the 2-photon (511 eV line) intensity will be:


By measuring the intensities of the 511 keV line and of the Ps continuum one can then derive the positronium fraction


which offers a valuable diagnostic of the physical conditions of the ISM where positrons annihilate, (see discussion in Sec. V.E).

The state of Ps can be formally treated as the one of hydrogen atom. The corresponding Schroedinger equations are identical, with the reduced mass being half of the electron mass in the case of Ps. Because of that, the frequencies of the de-excitation spectral lines of are roughly half of those of the H atom (Canter et al., 1975). Radiative recombination of ortho-Ps could, under certain circumstances, be observed in the near infra-red by next generation instruments (see Ellis and Bland-Hawthorn, 2009).

Figure 1: Spectrum of ortho-positronium annihilation with the three-photon continuum (from Ore and Powell, 1949).

ii.2 Observations of MeV emission from e annihilation

ii.2.1 Early balloon and satellite observations

The first evidence for Galactic 511 keV emission was obtained in the early 1970’s, through a series of balloon flights by teams from Rice University. Johnson et al. (1972) announced the first detection of a celestial gamma-ray line originating from outside the solar system. Using a sodium iodine (NaI) scintillation detector they observed a spectral excess with a flux of ph cms at an energy of keV during a balloon flight in 1970. A second balloon flight of the same team in 1971 confirmed this signal (Johnson and Haymes, 1973). Although the authors mentioned e annihilation as a possible origin of the observed feature, the significant offset between observed (473 keV) and expected (511 keV) line centroid led them to conclude that the feature was, perhaps, due to radioactive decay of unknown origin.

Leventhal (1973) proposed an interesting alternative explanation that could reconcile observations with a positron origin of the feature. As e annihilation in the interstellar medium occurs mainly via positronium, a superposition of a narrow line at 511 keV and a continuum emission below 511 keV is expected (Fig. 1). Because of the poor spectral resolution of the NaI detector and the low signal/noise ratio of these balloon flights these two contributions could not be disentangled, and were reported as a single emission peak at an energy of  keV, in reasonable agreement with the observations.

It took five years before a group from Bell-Sandia (Leventhal et al., 1978) could confirm this conjecture. With their high-resolution balloon-borne germanium (Ge) detector they could separate the line and continuum components of the emission. Leventhal et al. (1978) located the narrow component (FWHM=3.2 keV) at an energy of keV, consistent with the expectations for e annihilation at rest. The observed line flux of 10 ph cms was below the value reported by Johnson et al. (1972), as expected if the earlier measurements were a superposition of two components. Leventhal et al. (1978) also detected the positronium continuum component, and the comparison of line and continuum intensities implied that 92% of the annihilations occurred after the formation of a positronium atom.

Subsequent observations of the Galactic center by different balloon-borne instruments in the 1970’s found a surprising variability of the 511 keV line flux (Haymes et al., 1975; Leventhal et al., 1980; Albernhe et al., 1981; Gardner et al., 1982). But Albernhe et al. (1981) recognized that the flux measured by the various balloon experiments increased with increasing size of the detector’s field of view, which could mean that the annihilation emission was extended along the Galactic plane. Riegler et al. (1981) proposed a different scenario, based on analysis of their HEAO-3 satellite data. These data showed a decline by almost a factor three of the 511 keV flux between fall 1979 and spring 1980, suggesting that positron annihilation was variable in time. From the 6 months interval between the observations they inferred a maximum size of 0.3 pc of the annihilation site, which implies gas densities for the annihilation medium of - cm. These extreme conditions suggest that the positrons were produced by a compact source such as a massive black hole within 4 of the Galactic center (Lingenfelter et al., 1981).

While balloon-borne experiments seemed to establish the variability of the 511 keV emission (Leventhal et al., 1982; Paciesas et al., 1982; Leventhal et al., 1986), contemporaneous observations by the Solar Maximum Mission (SMM) satellite did not confirm such a trend. SMM carried a NaI-detector with a large field of view (130) and provided the first long-term monitoring of the inner Galaxy (1980-1987). The variability of the 511 keV emission was constrained to be less than 30% (Share et al., 1988, 1990). The apparent disagreement between the balloon and SMM observations could still be understood by assuming an extended distribution of 511 keV emission along the Galactic plane; however, in order to reconcile the observations with a time variable source one had to adopt rather complex scenarios. For example, Lingenfelter and Ramaty (1989) suggested the combination of a steady, extended 511 keV emission along the Galactic plane and a compact variable source at the Galactic center (assumed to be active from 1974 through 1979) in order to explain all data available at that time. Such a scenario could not be ruled out, since no imaging of the 511 keV emission had been achieved and the morphology and spatial extent of the positron annihilation emission were essentially unconstrained.

The hypothesis of a time variable central Galactic positron source was revitalized in the early 1990s by the observation of transient -ray line features with the SIGMA telescope. The french coded mask imager SIGMA was launched in 1989 on board the soviet GRANAT satellite. It was the first imaging -ray instrument, with an angular resolution of 15 arcmin and it used NaI detectors covering the energy range 35-1300 keV. In October 1991, an unusual spectrum was observed from 1E 1740.7-2942, during an outbreak of this hard X-ray source which lasted 17 hours (Bouchet et al., 1991; Sunyaev et al., 1991). Superimposed on a candidate typical black hole continuum spectrum, there appeared a strong (flux  ph cm s) and broad (FWHM  keV) emission line centered at about 440 keV. If interpreted as broadened and redshifted annihilation line, this observation seemed to make 1E 1740.7-2942 be the long sought compact and variable source of positrons. Follow-up observations led to the classification of 1E 1740.7-2942 as the first micro-quasar (Mirabel et al., 1992): a binary system involving a compact object (neutron star or black hole, see sec. IV.B.3) accreting material from its companion and emitting part of the accreted energy in the form of jets. It was therefore proposed that 1E 1740.7-2942 would occasionally emit jets of positrons (produced in e-e pairs), some of which would annihilate in the inner edge of the accretion disk as presumably observed by SIGMA; the remaining positrons would eventually lose their energy and give rise to time-variable narrow 511 keV line emission. Different SIGMA teams also reported narrow and/or broad -ray lines near 511 keV, lasting for a day or so, from the transient X-ray source “Nova Muscae” (Sunyaev et al., 1992; Goldwurm et al., 1992) and the Crab nebula (Gilfanov et al., 1994). Another transient -ray line source was discovered from archival HEAO 1 data by Briggs et al. (1995).

However, the line feature seen by SIGMA was not seen in simultaneous observations of 1E 1740.7-2942 performed with the OSSE (Jung et al., 1995) and BATSE (Smith et al., 1996a) instruments aboard the NASA Compton Gamma Ray Observatory (CGRO, launched in 1991). Besides, BATSE data did not confirm the transient event seen by SIGMA from the Crab nebula (Smith et al., 1996a). Moreover, the search on 6 years of BATSE data did not reveal any transient line feature from any direction of the sky (Smith et al., 1996b; Cheng et al., 1998). Similarly, 9 years of SMM data did not show any transient event from the Galactic center direction (Harris et al., 1994a) or the Crab nebula (Harris et al., 1994b). A reanalysis of HEAO 3 data then revealed that the drop in 511 keV flux reported earlier by Riegler et al. (1981) was not significant (Mahoney et al., 1994). Thus, the idea of a steady 511 keV Galactic emission was gradually established.

The contradictory results obtained during the 1980s and early 1990s provide a dramatic illustration of the difficulties affecting the analysis of -ray line data. In this domain, astrophysical signals rarely exceed the instrumental background by more than a few percent and any systematic uncertainty in the treatment of the background immediately disturbs the analysis. In particular, the time variability of the instrumental background (due to changing radiation environments along the orbital trajectory, or due to solar activity) can easily fake time variable signals. In addition, hard X-ray sources often exhibit highly variable continuum emission components that may further affect the data analysis and require their proper modeling; this concerns, in particular, the densely populated regions towards the Galactic center, which were not spatially resolved by older instruments.

ii.2.2 Early mapping of the spatial distribution of e annihilation

Before the launch of CGRO in 1991 with its OSSE collimated (11.4 x 3.8) spectrometer, the spatial distribution of 511 keV line emission was only poorly constrained. Hypotheses on a possible extent of the emission were mainly based on theoretical expectations (Kozlovsky et al., 1987), on the different fluxes received by detectors with different fields of view (Albernhe et al., 1981; Dunphy et al., 1983), and on a marginal detection of the 511 keV line near Galactic longitude with the balloon-borne GRIS telescope (Leventhal et al., 1989; Gehrels et al., 1991). Nine years of OSSE observations drastically improved this situation.

OSSE data could clearly exclude a single point source as the origin of observed 511 keV line emission (Purcell et al., 1994). The data were best understood in terms of an extended source consisting of a symmetrical bulge (centered on the Galactic center) and emission from the Galactic plane. Cheng et al. (1997) and Purcell et al. (1997) established the first 511 keV line emission map of the central Galactic ridge (Fig. 2). Beyond the aforementioned components, there was hint of a third component located at Galactic coordinates of longitude and latitude , dubbed the Positive Latitude Enhancement (PLE). However, the intensity and morphology of this feature were only weakly constrained by the data (Milne et al., 2001b), and the non-uniform exposure of the sky may have biased the sky maps (Von Ballmoos et al., 2003). Kinzer et al. (1996), Kinzer et al. (2001) and Milne (1998) studied the spatial distribution of the continuum emission from positronium annihilation and concluded that it follows closely the distribution of the 511 keV line. However, no PLE was visible in the continuum emission image (Milne et al., 2001a).

Figure 2: OSSE 511 keV line map of the galactic center region (top) and corresponding exposure map (bottom) (from Purcell et al., 1997).

At this point one should mention that images in the hard X-ray and soft -ray domains are obtained through complex non-linear iterative deconvolution techniques, and they generally represent only a family of solutions, which explains the observed data within the given statistical and convergence constraints. The reader should be aware of this particularly important point when inspecting all images in this paper. For instance, other OSSE images of the Galactic 511 keV line emission are presented in (Milne et al., 2001a) or (Milne et al., 2002).

Several models have been proposed to describe the spatial distribution of the annihilation emission observed by OSSE (Prantzos, 1993; Purcell et al., 1994; Kinzer et al., 1996; Purcell et al., 1997; Milne:2000; Kinzer et al., 2001; Milne et al., 2001b). They all had in common a two-component emission from a spheroid located in the inner Galaxy and from the extended Galactic disk (see Sec. III.A for a detailed discussion of the Galaxy’s morphology). However, both morphology and relative intensity of these two components were only poorly constrained by the data; depending on the adopted model, the spheroidal component was claimed to be dominant or sub-dominant, i.e the Galactic spheroidal-to-disk flux ratio was only constrained in the broad interval . The uncertainty on the total Galactic 511 keV line flux was also rather large, spanning the range 1-3 10 ph cms.

Despite the considerable progress achieved by OSSE observations, the origin of Galactic positrons remained unclear. The data did not constrain the morphology of the 511 keV emission enough to clarify the underlying source population(s). Yet, the strong concentration of the 511 keV emission towards the Galactic bulge led several authors to suggest that the decay of radioactive Co, produced by Galactic Type Ia supernovae (SNIa), should be the dominant Galactic positron source (Kinzer et al., 1996, 2001; Milne et al., 2002). The emission from the Galactic disk was generally attributed to radioactive decays of Al, Co and Ti produced by a variety of stellar sources (Purcell et al., 1994; Kinzer et al., 1996; Purcell et al., 1997). In fact, Al had already been detected from the inner region of the Galaxy through its characteristic -ray line at 1809 keV in the 1979/1980 HEAO-C data Mahoney et al. (1982), and its contribution to Galactic-disk e production was established (Sec. II.B.2 and IV.A.2).

ii.2.3 Imaging with INTEGRAL/SPI

With the launch of ESA’s INTEGRAL observatory (Winkler et al., 2003) in 2002 for a multi-year mission, a new opportunity became available for the study of Galactic e annihilation. The SPI imaging spectrometer (Vedrenne et al., 2003) combines for the first time imaging with high-resolution spectroscopy. The spatial resolution of (FWHM) of SPI, though inferior to telescopes optimized for slightly lower energies (SIGMA, IBIS), is superior to that of OSSE; its energy coverage and sensitivity around the annihilation line and its large field of view allow an improved study of the 511 keV emission morphology. The spectral resolution of  keV (FWHM, at 0.5 MeV) is comparable to that of other Ge detectors employed on balloons or the HEAO 3 satellite, allowing for a spatially resolved fine spectroscopy of the signal (including the underlying continuum emission).

Figure 3: 511 keV line map (top) and positronium continuum map (bottom) derived from one year of INTEGRAL/SPI data (from Knödlseder et al., 2005 and Weidenspointner et al., 2006, respectively).

The first 511 keV line and positronium continuum all-sky maps have been presented by Knödlseder et al. (2005) and Weidenspointner et al. (2006), respectively, based on approximately one year of SPI data (Fig. 3). The two maps are compatible with each other (within their uncertainties), suggesting that the positronium fraction does not vary over the sky. The images illustrate the remarkable predominance of the spheroidal component. In contrast to OSSE data, which suggested a relatively strong disk component, the Galactic disk seemed to be completely absent in the first year SPI images. Model fitting indicated only a marginal signal from the Galactic disk, corresponding to a bulge-to-disk flux ratio (Knödlseder et al., 2005). This strong predominance of the Galactic bulge, unseen in any other wavelength, stimulated ”unconventional” models involving dark matter (Sec. IV.C). However, Prantzos (2006) pointed out that the data could not exclude the presence of disk emission of a larger latitudinal extent (resulting from positrons propagating far away from their sources), which could be rather luminous and still undetectable by SPI, because of its low surface brightness.

Figure 4: 511 keV line map derived from 5 years of INTEGRAL/SPI data (from Weidenspointner et al., 2008a).

After accumulating 5 years of INTEGRAL/SPI data the 511 keV line emission all-sky image revealed also fainter emission extending along the Galactic plane (Fig. 4). With a much improved exposure with respect to the first year (in particular along the Galactic plane), 511 keV emission from the Galactic disk is now clearly detected (Weidenspointner et al., 2008a). However, the detailed quantitative characterization of components of 511 keV emission requires parameterizing these in the form of (necessarily idealized) spatial emission models fitted to the data. No unique description emerges at present, since both the spheroid and the disk may have faint extensions contributing substantially to their total -ray emissivities. It turns out that the bulge emission is best described by combining a narrow and a broad Gaussian, with widths (FWHM, projected onto the sky) of 3 and 11, respectively. Another, more extended component is needed to fit the data, a rather thick disk of vertical extent 7 (FWHM projected on the sky). The model implies a total e annihilation rate of 2 10 e s and a spheroid/disk ratio of 1.4 (Table 1). It should be noted, however, that alternative models, involving extended components of low surface brightness (thus far undetected by SPI) are also possible. One such alternative (Weidenspointner et al., 2008b) involves a centrally condensed but very extended halo and a thinner disk (projected vertical extent of 4), with a spheroid/disk ratio of 6 (Table 1).

With more SPI data, it was possible to proceed to more detailed constraints on the morphology of the disk emission. The flux in the disk component remains concentrated to longitudes ; no significant 511 keV line emission has been detected from beyond this interval so far. The accumulated SPI data yield a flux from negative longitudes of the Galactic disk that is twice as large as the flux from an equivalent region at positive longitudes. The significance of this asymmetry is still rather low, about . Indications for such an asymmetry were already noticed in the OSSE data (M. Leising, private communication). It should be noted, however, that a different analysis of the same SPI data finds no evidence for a disk asymmetry (Bouchet et al., 2008, 2010), although it cannot exclude it, either. Clearly, clarifying the asymmetric or symmetric nature of the disk profile should be a major aim of the 511 keV studies in the years to come444INTEGRAL will continue operations until 2012, at least..

( cm s) (10 s) (10 s )
Bulge + thick disk
Narrow bulge 2.7 2.3 4.1
Broad bulge 4.8 4.1 7.4
Thick disk 9.4 4.5 8.1
Total 17.1 10.9 19.6
Bulge/Disk 0.8 1.4 1.4
Halo + thin disk

Halo 21.4 17.4 31.3
Disk 7.3 2.9 5.2
Total 28.7 20.3 36.5
Halo/Disk 2.9 6 6
Table 1: Two model fits of the Galactic 511 keV emission (from Weidenspointner et al., 2008b): fluxes, photon emissivities and e annihilation rates (computed for a positronium fraction of =0.967, see Sec. II.B.4). Notice that ”thin” and ”thick” disks have not the same meaning as in Sec. III.

ii.2.4 Spectroscopy with INTEGRAL/SPI

Before INTEGRAL, the spectral shape of the positron annihilation emission was only poorly constrained by observations. All high-resolution observations suggested a modest line broadening of FWHM 2 keV (Leventhal et al., 1993; Smith et al., 1993; Mahoney et al., 1994; Harris et al., 1998). The excellent spectral resolution of SPI allows now for the first time to study the spectrum of this emission in great detail and for different regions.

Spectral results for the Galactic spheroidal emission were presented by Churazov et al. (2005) and Jean et al. (2006), based on the first year of SPI data. The line displays no spectral shift, i.e. it has an energy =5110.08 keV (Churazov et al., 2005) and it is composed of two spectral components (assumed to be represented by Gaussians): a narrow line with a width of FWHM= keV and a broad component with a width of FWHM= keV (Fig. 5). The width of the broad line is in agreement with the broadening expected from positronium annihilation via charge exchange with hydrogen atoms (see section V.B.2). The narrow line component contains of the total annihilation line flux while the broad one makes up the remaining of the flux. Table 2 summarizes the results of the spectral analysis of the Galactic 511 keV emission after the first year of SPI data.

SPI also clearly detected the ortho-positronium continuum with an intensity that corresponds to a positronium fraction of =972 % (Jean et al., 2006; see Eq. 3). This value is in good agreement with earlier measurements obtained by OSSE (973 %, Kinzer et al., 1996) and TGRS (944 %, Harris et al., 1998).

The shape of the annihilation line and the relative intensity of the ortho-positronium continuum are closely related to the physical conditions such as temperature, ionisation stage and chemical abundances of the interstellar medium in which positrons annihilate. These conditions, obtained from the analysis of the measured spectrum, are presented and discussed in Sec. V.E. Important complementary information on the energies of the annihilating positrons is obtained from the analysis of the observed continuum emission at somewhat higher energies (above 511 keV and into the MeV region), as discussed in the next section and Sec. V.B.

Figure 5: Fit of the spectrum of the annihilation emission measured by SPI with narrow and broad Gaussian lines and an ortho-positronium continuum. The power-law account for the Galactic diffuse continuum emission (Jean et al., 2006).
Parameters Measured values
I   (10 s cm) 0.72 0.12 0.02
  (keV) 1.32 0.35 0.05
I   (10 s cm) 0.35 0.11 0.02
  (keV) 5.36 1.22 0.06
I   (10 s cm) 4.23 0.32 0.03
A   (10 s cm keV) 7.17 0.80 0.06
Table 2: Results of spectral analysis of Galactic 511 keV emission from the region within 8from the Galactic center. , , and are the flux and width (FWHM) of the narrow and broad lines, respectively, is the flux of the ortho-positronium continuum and is the amplitude of the Galactic continuum at 511 keV. The first set of error bars refers to 1 statistical errors and the second set to systematic errors (from Jean et al., 2006).

ii.3 Relevant observations at MeV energies

ii.3.1 The MeV continuum

Positrons are typically emitted at relativistic energies, in some cases even far above 1 MeV (Sec. IV). They behave essentially like relativistic electrons of cosmic rays, by producing bremsstrahlung and inverse-Compton emission while slowing down to the thermal energies (eV) of the interstellar medium, where they eventually annihilate. But positrons may also annihilate ”in flight” while still having relativistic energies, giving rise to a unique -ray continuum signature at energies above 511 keV (as the center-of-mass energy is transferred to annihilation photons; Sec. V). The shape and amplitude of this -ray emission depend on the injection spectrum of positrons and the corresponding total annihilation rate. For positrons injected at low energies (of the order of MeV, such as those released by radioactivity), the amplitude of the in-flight annihilation continuum above 1 MeV is quite small, while for sources injecting positrons at much higher energy (such as cosmic-ray positrons from pion decay), the annihilation -ray spectrum would extend up to GeV energies and include a considerable -ray flux. The high energy -ray continuum above 1 MeV therefore constrains the energy and the annihilation rate of relativistic positrons, when all other sources of such high energy emission are properly accounted for.

Diffuse Galactic continuum emission has been well-measured at least in the inner part of the Galactic disk (longitudes ) in the hard-X-ray through -ray regime by INTEGRAL, OSSE, COMPTEL, and EGRET Bouchet et al. (2008); Kinzer et al. (1999); Strong et al. (1994). The spectrum of the underlying continuum emission in the 511 keV region is best represented as a power-law with index 1.55 Bouchet et al. (2008) and is mostly due to emission from cosmic-ray electrons and positrons (Sec. IV.2.2). The corresponding emission processes are modelled in detail in e.g. the GALPROP code (Strong et al., 2007), which includes 3D distributions of interstellar gas and photon fields, as well as all relevant interaction cross sections and constraints from near-Earth observations of cosmic-ray fluxes and spectra. This model reproduces well the entire range of -ray observations, from keV to GeV energies; however, there exist tantalizing hints of residual emission in the MeV region, when comparison is made to COMPTEL measurements 555 The CGRO/COMPTEL data points have an uncertainty of up to a factor 2 due to the difficulty of producing skymaps with a Compton telescope with high background. The most reliable COMPTEL values come from a maximum-entropy imaging analysis and are model-independent, but the zero level is uncertain and contributes to the systematic error. The enormous gap in sensitivity between the current Fermi mission (30 MeV) and the 1-30 MeV range (sensitivity factor 100 !) highlights the urgent need for new experiments in the MeV range.: the data points appear to lie on the high side of model predictions. In view of the possible systematic uncertainties of such measurements, but also of the parameters of GALPROP code and the possible contributions of unresolved X-ray binaries, some (though little) room is still left for a contribution of in-flight e annihilation to the MeV continuum.

Figure 6: Spectrum of the inner Galaxy as measured by various instruments, compared to various theoretical estimates made under the assumption that positrons are injected at high energy: the four pairs of curves result from positrons injected at 100, 30, 10 and 3 MeV (from top to bottom) and correspond to positrons propagating in neutral (solid) or 50% ionized (dotted) media (from Sizun et al., 2006). This constrains the injected positron energy (or, equivalently, the mass of decaying/annihilating dark matter particles) to a few MeV.

The physics of the in-flight annihilation of positrons will be analyzed in Sec. V. Here we simply note that the corresponding constraints on the injection energy of positrons wee pointed out many years ago by Agaronyan and Atoyan (1981). They showed that the positrons which are responsible for the Galactic 511 keV line cannot be produced in a steady state by the decay of the created in proton-proton collisions or else the in-flight annihilation emission should have been detected. A similar argument was used by Beacom and Yüksel (2006) and Sizun et al. (2006) to constrain the mass of the dark matter particle which could be the source of positrons in the Galactic spheroid (see section IV.C). If such particles produce positrons (in their decay or annihilation) at a rate which corresponds to the observed 511 keV emission, then their mass should be less than a few MeV, otherwise the kinetic energy of the created positrons would have been sufficiently high to produce a measurable -ray continuum emission in the 1-30 MeV range (Fig. 6). The same argument allows one to constrain the initial kinetic energy of positrons and thus to eliminate several classes of candidate sources, like e.g. pulsars, millisecond pulsars, magnetars, cosmic rays etc., as major positron producers (Sec. IV. D).

ii.3.2 Gamma-rays and positrons from radioactive Al

Al is a long-lived (half-life =7.4 10 yr) radioactive isotope. It decays by emitting a positron, while the de-excitation of daughter nucleus Mg emits a characteristic -ray line at 1808.63 keV. Based on predictions of nucleosynthesis calculations in the 1970’s, Arnett (1977) and Ramaty and Lingenfelter (1977) suggested that its -ray emission should be detectable by forthcoming space instruments. The detection of the 1809 keV line from the inner Galaxy with the HEAO-C germanium spectrometer Mahoney et al. (1982) came as a small surprise (Clayton, 1984) because of its unexpectedly high flux (4 10 cm s). Being the first radioactivity ever detected through its -ray line signature, it provided direct proof of ongoing nucleosynthesis in our Galaxy (see review by Prantzos and Diehl, 1996).

Several balloon experiments, and in particular the Gamma-Ray Spectrometer (GRS) aboard the Solar Maximum Mission (SMM) rapidly confirmed the HEAO-C finding (Share et al., 1985). Early experiments had large fields of view (130 for SMM, 42 for HEAO-C) with no or modest imaging capabilities. The first map of Galactic 1.8 MeV emission was obtained with the COMPTEL instrument aboard CGRO (Diehl et al., 1995), which had a spatial resolution of 3.8 (FWHM) within a field of view of 30. The sky map derived from the 9-year survey of COMPTEL is shown in Fig. 7. Unlike the 511 keV maps of Fig. 3 and 4 the Al emission is concentrated along the Galactic plane (brightest within the inner Galactic radian) and is irregular, with emission maxima aligned with spiral-arm tangents. The Cygnus region stands out as a significant and bright emission region. The ”patchy” nature of the Al-ray emission suggests that massive stars are the most important contributors to Galactic Al, as suggested at a time when the morphology of Al emission was unknown (Prantzos, 1991 and Sec. IV.A.2). It is consistent with the (statistically significant) similarity to the Galactic free-free emission map, which reflects electron radiation from HII regions ionized from the same massive stars that eventually release Al(Knödlseder, 1999).

The total flux of Al -rays depends slightly on the measuring instrument. In terms of statistical precision, the SMM result of 4.00.4 10 ph cmsrad has been considered the canonical value. Imaging instruments, however, have consistently reported lower flux values of 2.60.8 10 ph cmsrad (COMPTEL) and 3.10.4 10 ph cmsrad (SPI), respectively. The latest SPI value is compatible with the full range of measured values by other instruments (within statistical uncertainties), and we adopt it here. The detected flux translates into a decay rate of Al which depends slightly on the adopted 3D distribution of Al in the Galaxy (Diehl et al., 2006). The most recent analysis of SPI data results in a rate of = 4.3 10 s or 2.7 M/Myr (Wang et al., 2009). Assuming a steady state, i.e. equality between production and decay rates, this is also the present production rate of Al in the Galaxy; recent models of massive star nucleosynthesis can readily explain such a production rate (Diehl et al., 2006 and Sec. IV.A.2).

Figure 7: Map of Galactic Al -ray emission after 9-year observations with COMPTEL/CGRO (from Plüschke et al., 2001).

Being predominantly a -emitter (with a branching ratio of =82%, see Table 7) Al is itself a source of positrons. The corresponding Galactic e production rate is = 3.5 10 s . This constitutes a significant contribution to the total Galactic e production rate (Sec. II.A.3 and Table 1): 17% of the total e annihilation rate and almost half of the (thick) disk in the double bulge+thick disk model, or 10% of the total and 70% of the thin disk in the Halo+thin disk model. We shall see in Sec. IV that positrons from other -decaying nuclei can readily explain the remaining disk emissivity, while the bulge emissivity remains hard to explain.

ii.4 Summary of observational constraints

The results of the analysis of Galactic -ray emissions in the MeV range can be summarized as follows:

1) Intensity: The total rate of positron annihilation observed in -rays is at least =2 10 s, depending on the adopted source configuration. Most of it comes from the bulge (unless there is important emission from an extended, low surface brightness, disk).

2) Morphology: The bulge/disk ratio of e annihilation rates is 1.4; however, substantially different ratios cannot be excluded if there is important emission of low surface brightness (currently undetectable by SPI) either from the disk or the spheroid. About half of the disk emission can be explained by the observed radioactivity of Al (provided its positrons annihilate in the disk). There are hints for an asymmetric disk emission with flux ratio 0)/0)1.8, which has yet to be confirmed.

3) Spectroscopy: The ratio of the 511 keV line to the E511 keV continuum suggests a positronium fraction of 972 % and constrain the physical conditions in the annihilation region. The observed continuum at MeV energies can be mostly explained with standard inverse Compton emission from cosmic ray electrons. A contribution from unresolved compact sources is possible, while a (small) contribution from high-energy (MeV) positrons annihilating in flight cannot be excluded.

These are the key observational constraints that should be satisfied by the source(s) and annihilation site(s) of Galactic positrons. We shall reassess them in the light of theoretical analysis in the end of Sec. IV and V.

Iii The Galaxy

The expected spatial distribution and intensity of the positron annihilation emission obviously depends on the corresponding distribution of the potential e sources, as well as on the properties of the ISM in which positrons first slow down and then annihilate. One may distinguish two types of e sources, depending on whether their lifetimes () are shorter or longer than the lifetime of positrons in the ISM (). Calculation of the total e production rate requires in the former case () an estimate of (i) the Galactic birthrate of the sources and (ii) the individual e yields (i.e. the average amount of positrons released by each source). In the latter case (), the total number of such sources in the Galaxy is required, as well as the individual e production rate of each source. In the former class belong supernovae or novae and the corresponding positron production rate is ; in the latter class belong e.g. low mass XRBs or millisecond pulsars, and the corresponding positron production rate is .

The galactic distribution of any kind of stellar source of positrons is somewhat related to the distribution of stars in the Milky Way. Similarly, the birthrate of any kind of positron source is somewhat related to the Galactic star formation rate. In this section we present a summary of current knowledge about the stellar populations of the Milky Way and their spatial distribution and we discuss the birthrates of stars and supernovae. Since the slowing down and annihilation of positrons depend on the properties of the ISM, we present a brief overview of the ISM in the bulge and the disk of the Milky Way. Positron propagation depends also on the properties of the Galactic magnetic field, which are reviewed in Sec. III.D. Finally, the main properties of the Milky Way’s dark matter halo are presented in Sec. III.E.

iii.1 Stellar populations

The Milky Way is a typical spiral galaxy, with a total baryonic mass of 5 10 M, of which more than 80% is in the form of stars. Stars are found in three main components: the central bulge, the disk and the halo, while the gas is found essentially in the plane of the disk. Because of its low mass, estimated to 4 10 M i.e. less than 1% of the total, (Bell et al., 2007), the Galactic halo plays no significant role in the positron production. The bulge contains 1/3 of the total mass and an old stellar population (age10 Gyr). The dominant component of the Milky Way is the so-called thin disk, a rotationally supported structure composed of stars of all ages (0-10 Gyr). A non negligible, contribution is brought by the thick disk, an old (10 Gyr) and kinematically distinct entity identified by Gilmore and Reid (1983).

To a first approximation, and by analogy with external galaxies, the bulge of the Milky Way can be considered as spherical, with a density profile either exponentially decreasing with radius or of Einasto-type (exp(-A ). Measurements in the near infrared (NIR), concerning either integrated starlight observations or star counts revealed that the bulge is not spherical, but elongated. Recent models suggest a tri-axial ellipsoid, but its exact shape is difficult to determine ( López-Corredoira et al., 2005; Rattenbury et al., 2007) because of the presence of a Galactic bar. The mass of the bulge lies in the range 1-2 10 M. (Dwek et al., 1995; Robin et al., 2003). By comparing colour-magnitude diagrams of stars in the bulge and in metal-rich globular clusters, Zoccali et al. (2003) find that the populations of the two systems are co-eval, with an age of 10 Gyr.

The innermost regions of the bulge, within a few hundred pc, are dominated by a distinct, disk-like component, called the Nuclear Bulge which contains about 10% of the bulge stellar population (1.5 10 M) within a flattened region of radius 23020 pc and scaleheight 455 pc Launhardt et al. (2002). It is dominated by three massive stellar clusters (Nuclear Stellar Cluster or NSC in the innermost 5 pc, Arches and Quintuplex), which have a mass distribution substantially flatter than the classical Salpeter IMF 666Stars are born with a mass distribution called Initial mass function (IMF). Observed IMFs of young stellar clusters in the Milky Way and other galaxies have similar IMFs, with the upper part (M1 M) described by a power-law (, where is the slope of the IMF; in most cases, =1.35 (as determined by Salpeter, 1955, for the local IMF.Figer (2008). Finally, in the center of the Milky Way, at the position of SgrA source, lies the supermassive Galactic black hole (SMBH) with a total mass of 4 10 M (Gillessen et al., 2008).

The Sun is located in the thin disk of the Milky way, at a distance of 8 kpc from the Galactic center; a recent evaluation, based on Cepheids, gives =7.940.37(statistical)0.26(systematic) kpc (Groenewegen et al., 2008 and references therein). Furthermore, the Sun is not located exactly on the plane, but at a distance from it 25 pc, as evaluated from the recent analysis of the Sloan Digital Sky Survey (SDSS) data (Jurić et al., 2008).

In studies of the Milky Way the solar neighborhood plays a pivotal role, since local properties can, in general, be measured with greater accuracy than global ones. The total baryonic surface density of the solar cylinder777The solar cylinder is defined as a cylinder of radius 500 pc centered on Sun’s position and extending perpendicularly to the Galactic plane up to several kpc. is estimated to =48.8 M(Flynn et al., 2006), with 13 M belonging to the gas (see Sec. III.B). This falls on the lower end of the dynamical mass surface density estimates( from kinematics of stars perpendicularly to the plane) which amount to =50-62 M (Holmberg and Flynn, 2004) or 57-66 M(Bienaymé et al., 2006). Thus, the values for the baryon content of the solar cylinder, summarized in Table 3, should be considered rather as lower limits (Flynn et al., 2006): the total stellar surface density could be as high as 40 M.

The density profiles of the stellar thin and thick disks can be satisfactorily fit with exponential functions, both in the radial direction and perpendicularly to the Galactic plane. The recent SDSS data analysis of star counts, with no a priori assumptions as to the functional form of the density profiles finds exponential disks with scalelengths as displayed in Table 3 (from Jurić et al., 2008). The thin and thick disks cannot extend all the way to the Galactic center, since dynamical arguments constrain the spatial co-existence of such rotationally supported structures with the pressure-supported bulge. The exact shape of the “central hole” of the disks is poorly known (see, e.g. Freudenreich, 1998; Robin et al., 2003, for parametrizations), but for most practical purposes (i.e. estimate of the total disk mass) the hole can be considered as trully void of stars for disk radius 2 kpc.

The data presented in this section (as summarized in Table  3), allow one to estimate the total mass of the thin and thick disks as =2.3 10 M and =0.5 10 M, respectively, in the galactocentric distance range 2-15 kpc. Overall, the disk of the MW is twice as massive as the bulge.

Thin Thick
Mass density (M pc) 4.5 10 5.3 10
Surface density (M pc) 28.5 7
Scaleheight (pc) 300 900
Scalelength (pc) 2600 3600
Star mass (10 M) 2.3 0.53
(Gyr) 5 10
(dex) -0.1 -0.7

: The indice here denotes quantities measured at Galactocentric distance =8 kpc. Average quantities are given within .

Table 3: Properties of the stellar populations of the thin and thick disk.

iii.2 Interstellar matter

Interstellar matter is primarily composed of hydrogen, but it also contains helium ( by number or by mass) and heavier elements, called “metals” ( 0.12 % by number or by mass in the solar neighborhood). All the hydrogen, all the helium, and approximately half the metals exist in the form of gas; the other half of the metals is locked up in small solid grains of dust. Interstellar dust manifests itself through its selective absorption of starlight (leading to extinction, reddening, and polarization of starlight) and through its thermal infrared emission. Dust grains cover a whole range of radii, from  Å to m, as implied from the overall shape of extinction curves which can be reproduced with a power-law distribution in radius, (Mathis et al., 1977; Kim et al., 1994; Boulanger et al., 2000). Overall, gas and dust appear to be spatially well correlated (Boulanger and Perault, 1988; Boulanger et al., 1996).

Interstellar gas can be found in molecular, atomic (cold or warm) and ionized (warm or hot) forms. The physical properties of the different gas components in the Galactic disk were reviewed by Ferrière (2001) and are summarized in Table  4. The gas properties in the Galactic bulge are less well established, but on the whole, all gas components appear to be hotter and denser in the bulge than in the disk (Ferrière et al., 2007).

Spatially, the molecular gas is confined to discrete clouds, which are roundish, gravitationally bound, and organized hierarchically from large complexes (size  pc, mass ) down to small clumps (size  pc, mass ) (Goldsmith, 1987). The cold atomic gas is confined to more diffuse clouds, which often appear sheet-like or filamentary, cover a wide range of sizes (from a few pc up to  kpc), and have random motions with typical velocities of a few km s (Kulkarni and Heiles, 1987). The warm and hot components are more widespread and they form the intercloud medium.

The different gas components also differ by their spatial distributions at large scales. The observational situation was reviewed by Ferrière (2001) for the Galactic disk and by Ferrière et al. (2007) for the Galactic bulge. Fig. 8 gives the radial variation of the azimuthally-averaged surface densities of H, Hi, Hii and the total gas (accounting for a 28% contribution from He), while Fig. 9 gives the vertical variation of their respective space-averaged volume densities averaged along the solar circle (at ). The total interstellar masses of the three gas components in the Galactic disk are uncertain and their sum in the Galactic disk, i.e. between 2 and 20 kpc, is probably comprised between and .

Phase (K) (cm)
Molecular (MM)
Cold neutral (CNM)
Warm neutral (WNM)
Warm ionized (WIM)
Hot ionized (HIM)
Table 4: Physical properties (typical temperatures, hydrogen densities and ionization fractions) of the different ISM phases in the Galactic disk.
Figure 8: Azimuthally-averaged surface densities of interstellar atomic, molecular and ionized hydrogen as functions of Galactic radius. The total gas (bottom) includes a 40% contribution by helium. Notice the change of scale at =2 kpc. For 2 kpc (bulge) data are derived by Ferrière et al. (2007), based on a compilation of earlier works: Sawada et al. (2004) for the molecular gas in the Central Molecular Zone, Liszt and Burton (1980) for the neutral gas in the tilted disk, and Cordes and Lazio (2002) for the ionized gas. In all panels, disk data (2 kpc) are from: Dame (1993) (solid); Olling and Merrifield (2001) (dotted) ; Nakanishi and Sofue (2006) for HI and Nakanishi and Sofue (2003) for H, respectively (dashed); and Kalberla and Dedes (2008) for HI and and Pohl et al. (2008) for , respectively (dot-dashed). The curve in the HII panel is from the NE2001 free-electron density model of Cordes and Lazio (2002) (for simplicity, we identified the H density with the free-electron density, i.e., we neglected the contribution of free electrons originating from He in the HIM).

Since most of the transport and annihilation of positrons takes place in the Galactic bulge, its gas distribution deserves a more detailed description. In the bulge, the interstellar gas is roughly equally divided between the neutral (molecular + atomic) and ionized components, and the neutral component is molecular. The molecular gas tends to concentrate in the so-called central molecular zone (CMZ; Morris and Serabyn, 1996), a thin sheet parallel to the Galactic plane, which, in the plane of the sky, extends out to  pc at longitudes and  pc at and has a FWHM thickness  pc. Projected onto the Galactic plane, the CMZ would appear as a ellipse inclined (clockwise) by to the line of sight (Sawada et al., 2004). Outside the CMZ, the molecular gas is contained in a significantly tilted disk (Liszt and Burton, 1978; Burton and Liszt, 1992), extending in the plane of the sky out to  kpc on each side of the GC and having a FWHM thickness  pc. According to Liszt and Burton (1980), the tilted disk has the shape of a ellipse, which is tilted (counterclockwise) by out of the Galactic plane and inclined (near-side down) by to the plane of the sky. The tilted disk is also believed to feature an elliptical hole in the middle, just large enough to enclose the CMZ. The spatial distribution of the atomic gas is arguably similar to that of the molecular gas (Burton and Liszt (1992), but see also Combes (1991) for another point of view), with this difference that the atomic layer is about three times thicker than the molecular layer, both in the CMZ and in the tilted disk. The ionized gas, for its part, is not confined to either the CMZ or the tilted disk; it appears to fill the entire bulge and to connect with the ionized gas present in the disk.

The dramatic density and temperature contrasts between the different ISM phases as well as the supersonic random motions observed in all of them bear witness to a highly turbulent state. Mainly responsible for this turbulence are the powerful winds and terminal supernova explosions of the most massive stars. Interstellar turbulence manifests itself over a huge range of spatial scales, from  cm up to  cm; throughout this range, the power spectrum of the free-electron density in the local ISM is consistent with a Kolmogorov-like power law (Armstrong et al., 1995).

Figure 9: Space-averaged volume densities of interstellar H, Hi and HII, averaged along the solar circle (), as functions of distance from the Galactic plane . Data: H from Bronfman et al. (1988), rescaled to , as in Olling and Merrifield (2001); Hi from Dickey and Lockman (1990), scaled up by a factor 1.58 such as to match the Hi surface density of Olling and Merrifield (2001). All the other curves are from the same sources as in Fig. 8.

iii.3 Star formation and supernova rates

Determination of absolute values of star formation rates (SFR, in M) constitutes one of the most challenging tasks in modern astrophysics (Kennicutt, 1998). In the case of the Milky Way, methods based on counts of various short-lived objects (with lifetimes less than a few Myr, like e.g. pulsars, SN remnants or OB associations) are used. Those methods establish in fact the relative star formation rate across the Galactic disk. Surface density profiles of various stellar tracers appear in Fig. 10. For the calibration of the SFR profile one needs to know either the total SFR of the MW disk or the local one in the solar neighborhood. A “ball-park” estimate of the former value is obtained by noting that the late spectral type (Sbc) of the MW suggests a slow formation at a relatively steady rate over the past 10 Gyr, leading to =M/2.3 M. Most empirical estimates of the present-day total Galactic SFR, based on the aforementioned tracers (and assumptions on the IMF) produce values within a factor of two of the (e.g. McKee and Williams, 1997; Robitaille and Whitney, 2010, and references therein).

In the context of Galactic positrons, special attention should be paid to the star formation activity in the central regions of the bulge. The massive star population of the three major star clusters inside the Nuclear Bulge clearly indicate important recent star formation, obviously fed from the gas of the Central Molecular Zone (CMZ). Deep field observations of late-type stars with the NICMOS/HUBBLE Figer et al. (2004) and with SINFONI/VLT Maness et al. (2007) suggest that the star forming activity in that region has proceeded at a relatively steady rate, of the order of a few 10 M/yr, over the past 10 Gyr.

Figure 10: Surface densities of stars+gas, SFR, SN rates and scaleheights of gas and stars as a function of Galactocentric distance. Star profiles are from data of Table II and gas profile is the one of Dame (1993) (bottom pane of Fig. 6). Data for SFR are from : Lyne et al. (1985) (open cicles); Case and Bhattacharya (1998) (filled circles); McKee and Williams (1997) (open squares); Guibert et al. (1978) (filled squares). The solid curve is an approximate fit, normalized to 2 Myr for the whole Galaxy. The same curve is used for the CCSN rate profile (third panel), normalized to 2 CCSN/century; the SNIa rate profile is calculated by Eq.  4  and normalized to 0.5 SNIa/century (Table 5).
SNIa Core collapse SN

Stellar mass Spectral type Specific rate Rate Specific rate Rate

10 M SNuM century SNuM century

1.4 E0 0.044 0.062 - -

Nuclear Bulge
0.15 Sbc/d-Irr 0.17-0.77 0.025-0.115 0.86-2.24 0.13-0.33

Thin disk
2.3 Sbc 0.17 0.4 0.86 2

Thick disk
0.5 E0 0.044 0.022 -

Total bulge
1.5 0.087-0.18 0.13-0.33

Total disk
2.8 0.42 2

Total Milky Way
4.3 0.5-0.6 2.13-2.33

Bulge/Disk ratio
0.5 0.21-0.43 0.06-0.15

SNuM: = 1 SN per 10 M per century; : See Sec. III.A for references; Mannucci et al. (2005); Very uncertain, in view of uncertainties in star formation efficiency and slope of IMF (see text).

Table 5: Supernova rates in the Milky Way

From the theoretical point of view, SN are now classified mainly in thermonuclear supernovae (the explosion energy being due to the thermonuclear disruption of a white dwarf accreting matter in a binary system) and core collapse supernovae (CCSN, where the energy originates from the gravitational collapse of the iron core of a massive star having exhausted all its nuclear fuel). Thermonuclear supernovae are identified with SNIa (lacking hydrogen in their spectra) and are observed in all types of galaxies: old ellipticals with no current star formation, but also young, star forming, spiral and irregular galaxies. All other supernova types (SNII, SNIb, SNIc) are exclusively observed in the star forming regions of spirals (i.e. inside spiral arms) and irregulars888The degree of mass loss suffered by the massive star prior to the explosion determines the appearance of the core collapse supernova as SNII (little H lost), SNIb (all H and little He lost) or SNIc (all H and most He lost)..

No supernovae have been observed in the Galaxy in the past four centuries, and the handful of so called “historical supernovae” offers a very biased estimate of the Galactic SN frequency Tammann et al. (1994). All methods used to determine the Galactic SN rate which are based exclusively on Galactic data suffer from various systematic uncertainties and converge to a value of = a few per century (Diehl et al., 2006 and references therein). The most accurate way to evaluate the Galactic SN rate is, probably, through statistics of SN rates in external galaxies. The work of Mannucci et al. (2005), corrected for various observational biases, offers a valuable database for such an estimate and can be used, along with the stellar masses of the various Galactic components (Sec. III.A) , to derive the Galactic rate of the main SN types (Table 5).

The spatial distribution of core collapse SN in the MW should obviously follow the one of the SFR (Fig.  10). Such an azimuthally averaged surface density masks the fact that CCSN are exclusively concentrated inside spiral arms. The scaleheight of core collapse SN should be comparable to the scaleheight of the molecular gas, i.e. less than 100 pc, and little varying with Galactocentric distance. More difficult is the evaluation of the radial profile of SNIa, since the progenitor white dwarfs may originate from stars of a wide variety of stellar masses (1-8 M) and corresponding lifetimes (10-0.05 Gyr). Various models have been developed in order to calculate the SNIa rate (e.g. Greggio, 2005). A useful empirical approach is the one adopted in Scannapieco and Bildsten (2005), where the SNIa rate is calculated as the sum of two terms: one depending on the stellar mass and one on the SFR of the system, i.e.


with parameters and empirically determined (Scannapieco and Bildsten, 2005; Sullivan et al., 2006). The parametrized SNIa profile in the Milky Way disk appears in the third panel of Fig. 10. Taking into account the nature of the SNIa progenitors, it is expected that the distribution of SNIa vertically to the disk plane will follow the corresponding distribution of the thin disk, i.e. with a scaleheight of 300 pc (an insignificant contribution from the thick disk is also expected).

iii.4 Interstellar magnetic fields

The magnetic field strength, , in cold, dense regions of interstellar space can be inferred from the Zeeman splitting of the 21-cm line of Hi (in atomic clouds) and centimeter lines of OH and other molecules (in molecular clouds). In practice, it is the line-of-sight component of the magnetic field, , that is measured. With appropriate statistical corrections for projection effects, it is found that in atomic clouds, is typically a few G, with a slight tendency to increase with increasing density (Troland and Heiles, 1986; Heiles and Troland, 2005), while in molecular clouds, increases approximately as the square root of density, from G to G (Crutcher, 1999, 2007).

The interstellar magnetic field, , in the ionized medium is generally probed with Faraday rotation measures of Galactic pulsars and extragalactic radio sources. Here, too, the quantity that is actually measured is . Faraday rotation studies have provided the following interesting pieces of information.

1) has a uniform (or regular) component, , and a random (or turbulent) component, . Near the Sun, G and G (Rand and Kulkarni, 1989). Away from the Sun, increases toward the GC, to G at  kpc (Han et al., 2006), i.e., with an exponential scale length  kpc. In addition, decreases away from the midplane, albeit at a very uncertain rate; for reference, the exponential scale height inferred from the rotation measures of extragalactic sources is  kpc (Inoue and Tabara, 1981).

2) In the Galactic disk, is nearly horizontal and generally dominated by its azimuthal component. It is now widely accepted that reverses several times with decreasing radius, but the number and radial locations of the reversals are still highly controversial (Rand and Lyne, 1994; Han et al., 1999; Vallée, 2005; Han et al., 2006; Brown et al., 2007). These reversals have often been interpreted as evidence that is bisymmetric (azimuthal wavenumber ), while an axisymmetric () field would be expected from dynamo theory. In reality, Men et al. (2008) showed that neither the axisymmetric nor the bisymmetric picture is consistent with the existing pulsar rotation measures, and they concluded that must have a more complex pattern.

3) In the Galactic halo, could have a significant vertical component. For the local halo, Taylor et al. (2009) obtained G above the midplane () and G below the midplane (), whereas Mao et al. (2010) obtained G toward the north Galactic pole and G toward the south Galactic pole. In contrast to the situation in the Galactic disk, the azimuthal component of shows no sign of reversal with decreasing radius.

4) At low latitudes (basically, in the disk), appears to be roughly symmetric in (Rand and Lyne, 1994; Frick et al., 2001), while at high latitudes (in the halo), appears to be roughly antisymmetric/symmetric in inside/outside the solar circle (Han et al., 1997, 1999). Finding to be symmetric in the disk and antisymmetric in the inner halo is consistent with the predictions of dynamo theory and with the results of galactic dynamo calculations (e.g., Ruzmaikin et al., 1988; Moss and Sokoloff, 2008). However, there is no reason to believe that is simply a pure quadrupole (in the disk) and a pure dipole (in the inner halo), sheared out in the azimuthal direction by the Galactic differential rotation. In this respect, one should emphasize that the picture of an azimuthally-sheared pure dipole, originally proposed by Han (2002) and often used in the cosmic-ray propagation community (e.g., Alvarez-Muñiz et al., 2002; Prouza and Šmída, 2003), is supported neither by numerical simulations of galactic dynamos nor by observations of external edge-on galaxies, which generally reveal X-shaped field patterns (Beck, 2008).

A more global method to map out the spatial distribution of rests on the observed Galactic synchrotron emission. Relying on the synchrotron map of Beuermann et al. (1985) and assuming equipartition between magnetic fields and cosmic rays, Ferriere (1998) found that the total magnetic field has a local value G, a radial scale length  kpc, and a local vertical scale height  kpc. Besides, synchrotron polarimetry indicates that the local ratio of ordered (regular + anisotropic random) to total fields is (Beck, 2001), implying an ordered field G near the Sun.

In the vicinity of the GC, the interstellar magnetic field has completely different properties from those prevailing in the Galactic disk. In that region, systems of nonthermal radio filaments were discovered, which run nearly perpendicular to the Galactic plane and pass through it with little or no distortion (Yusef-Zadeh et al., 1984; Liszt, 1985). The morphology of the filaments strongly suggests that they follow magnetic field lines, and radio polarization measurements (assuming synchrotron emission) confirm that the magnetic field in the filaments is oriented along their long axis (Tsuboi et al., 1985; Reich, 1994). From this, it has naturally been concluded that the interstellar magnetic field near the GC is approximately vertical, at least close to the midplane. Farther from the midplane, the filaments tend to lean somewhat outwards, consistent with the interstellar magnetic field having an overall poloidal geometry (Morris, 1990).

The radio filaments have equipartition or minimum-energy field strengths G (Anantharamaiah et al., 1991; LaRosa et al., 2004, and references therein). On the other hand, the fact that the filaments remain nearly straight all along their length suggests that their magnetic pressure is stronger than the ram pressure of the ambient interstellar clouds, or, equivalently, that their field strength is  mG (Yusef-Zadeh and Morris, 1987).

Low-frequency radio observations of diffuse nonthermal (supposedly synchrotron) emission from a region centered on the GC imply that the diffuse ISM near the GC has a minimum-energy field strength G – possibly up to G if the cosmic-ray proton-to-electron energy ratio is as high as 100 and the filling factor of the synchrotron-emitting gas is as low as 0.01 (LaRosa et al., 2005). A more reliable estimation of the general field strength in the GC region emerges from the recent analysis of Crocker et al. (2010), which combines radio and -ray data and comes to the conclusion that G.

Far-infrared/submillimeter polarization studies of dust thermal emission from the GC region indicate that the magnetic field inside GC molecular clouds is roughly parallel to the Galactic plane (Novak et al., 2003). More precisely, the field direction appears to depend on the molecular gas density, being nearly parallel to the plane in high-density regions and nearly perpendicular to it in low-density regions (Chuss et al., 2003). Near-infrared polarization studies of starlight absorption by dust also find the magnetic field inside GC molecular clouds to be roughly horizontal, although without any obvious correlation between field direction and gas density (Nishiyama et al., 2009).

Zeeman splitting measurements have yielded mixed results. In the circumnuclear disk, the innermost molecular region with radius  pc, Killeen et al. (1992) and Plante et al. (1995) derived line-of-sight magnetic fields  mG and  mG, respectively. Farther from the GC, Crutcher et al. (1996) measured values of ranging between and  mG toward the Main and North cores of Sgr B2. In contrast, Uchida and Guesten (1995) reported only non-detections, with upper limits to  mG, toward 13 selected positions within a few degrees of the GC (including Sgr B2).

Faraday rotation measures have also yielded somewhat disparate results. The disparity lies not so much in the absolute value of , which is generally estimated at a few G (e.g., Tsuboi et al., 1985; Yusef-Zadeh and Morris, 1987; Gray et al., 1991), but more in the -dependence of its sign. Novak et al. (2003), who collected all the available rotation measures toward synchrotron sources within of the GC, found that reverses sign both across the rotation axis and across the midplane. A different pattern was uncovered by Roy et al. (2005), who derived the rotation measures of 60 background extragalactic sources through the region and obtained mostly positive values, with no evidence for a sign reversal either with or with .

The properties of the turbulent magnetic field are not well established. Rand and Kulkarni (1989) provided a first rough estimate for the typical spatial scale of magnetic fluctuations,  pc, although they recognized that the turbulent field cannot be characterized by a single scale. Later, Minter and Spangler (1996) presented a careful derivation of the power spectrum of magnetic fluctuations over the spatial range  pc; they obtained a Kolmogorov spectrum below  pc and a flatter spectrum consistent with 2D turbulence above this scale. In a complementary study, Han et al. (2004) examined magnetic fluctuations at larger scales, ranging from to 15 kpc; at these scales, they found a nearly flat magnetic spectrum, with a 1D power-law index .

Figure 11: Composite magnetic energy spectrum in our Galaxy. The thick solid line is the large-scale spectrum. The thin solid and dashed/dotted lines give the Kolmogorov and two-dimensional turbulence spectra, respectively, inferred from the Minter and Spangler (1996) study. The two-dimensional turbulence spectrum is uncertain; it probably lies between the dashed [ ] and dotted [] lines (from Han et al., 2004).

The, poorly understood at present, properties of the turbulent Galactic magnetic field as well as its overall configuration, are extremely important for understanding positron propagation in the Milky Way (Sec. VI).

iii.5 The dark matter halo

A large body of observational data on the extragalactic Universe suggests that its mass is dominated by non-baryonic dark matter. In the presently widely accepted ”standard” cosmological model (CDM, for Cold Dark Matter with cosmological constant ) dark matter accounts for a fraction 24% of the overall matter/energy budget of the Universe, baryons for 4 % and dark energy - or cosmological constant - for the remaining 72% (Bartelmann, 2009).

The presence of dark matter in spiral galaxies is deduced from the fact that their rotation curves beyond a radius of 3 scalelengths do not fall off as rapidly as expected from their baryonic content. In the case of the Milky Way, the rotation curve is poorly determined beyond the Sun’s location (R=8 kpc). It is then assumed, rather than directly inferred from observations, that the MW is found inside a dark matter halo with a density profile similar to those found in numerical simulations of structure formation in a CDM universe (e.g. Navarro et al., 1997). In the absence of baryons such simulations predict approximately universal density profiles , with being itself a positive function of radius : (”Einasto profile”). Because of finite numerical resolution, values of cannot yet be reliably determined in the inner halo. Some simulations find =1.5 in the inner galaxy (Moore et al., 1999), but the analysis of one of the largest simulations so far (Navarro et al., 2008) suggests that =0.90.1, i.e. a value compatible with the value of =1 in the classical NFW profile (Navarro et al., 1997). For values of 1 mass diverges as 0 (cuspy profiles). Including interactions of dark matter with baryons (Blumenthal et al., 1986) or with a central black hole (Gondolo and Silk, 1999) generically tend to enhance the cusp (e.g. Sellwood and McGaugh, 2005).

Figure 12: Dark matter density profile (top) and rotational velocity (bottom) of the Milky Way; the various components (bulge, stellar disk, gas and dark halo) contributing to the latter are also indicated. In both panels thick and thin solid curves correspond to NFW and isothermal (”ISO”) dark halo profiles, respectively. Data points are from Sofue et al. (2008).

The shape of the dark matter density profile in the inner Galaxy is obviously crucial for the corresponding profile of the putative positrons released from dark matter decay, annihilation or de-excitation (see Sec. IV.3). Since dark matter is sub-dominant in the inner Galaxy (see Fig. 12) , observations of the rotation curve cannot help to determine its density profile. Analyzing observations of the optical depth of the inner Galaxy to microlensing events (which are affected only by the baryonic mater) Binney and Evans (2001) find 0.3. On the other hand, rotation curves of dwarf galaxies (which are dominated by dark matter) systematically suggest flat profiles (Gentile et al., 2007; Spano et al., 2008) with 0, such as those obtained in the case of cored isothermal dark halo (see also Merritt, 2010). A useful parametrization of the density profiles is


where and are, respectively, the characteristic mass/energy density and radius of the halo and are parameters with values (found, either from simulations or from observations), reported in Table 6.

DM profile: ISO BE NFW M99

2 1 1 1.5

2 3 3 3

0 0.3 1 1.5

5 10 20 30

(M pc)
5. 10 7. 10 1.0 10 1.7 10

(GeV cm)
1.89 2.65 0.38 0.065

ISO: Isothermal; BE: Binney and Evans (2001); NFW (Navarro et al. 1997); M99 (Moore et al. 1999)

Table 6: Models for the Milky Way dark halo profile.

The shape of the dark halo profile may deviate from spherical symmetry. A triaxial shape arises naturally from the fact that gravitational collapse of the halo starts first (and proceeds more rapidly) in one direction. However, other processes may subsequently erase it (e.g. gas cooling, Kazantzidis et al., 2004). Various observations in the Milky Way have been interpreted as suggesting a spherical (Martinez-Delgado et al., 2004), oblate (Martinez-Delgado et al., 2004) or prolate (Helmi, 2004) dark halo, but in any case, deviations from spherical symmetry appear to be small.

Structure formation in the CDM model leads to a hierarchy of dark haloes embedded within the main halo of a galaxy. Since smaller galaxies are more dark matter dominated than larger ones, the strongest signal from dark matter annihilation may not arise from the main halo, but from satellite galaxies. This important issue has been extensively studied recently. Analyzing one of the largest ”Milky Way size” simulations so far, Springel et al. (2008) find that the most intense emission is expected to arise from the main halo. We shall further discuss this point in Sec. IV.D.3.

Iv Positron production: processes and sources

iv.1 Radioactivity from stellar nucleosynthesis

iv.1.1 Radioactivity

Positrons are emitted by the -decay of unstable nuclei which turns a proton into a neutron, provided the mass difference between parent and daughter nucleus is (where is electron’s mass and the light velocity). -decay of unstable nuclei produced in stellar explosions was one of the earliest candidates proposed to explain the Galactic 511 keV emission (Clayton, 1973).

Astrophysically important e emitters are produced in proton-rich environments, either hydrostatically (e.g. in massive star cores) or explosively (in novae or SN explosions); in both cases, proton captures occur on shorter timescales than the corresponding lifetimes of -decaying nuclei along the nucleosynthesis path. Important e emitters are also found in the Fe-peak region and are produced in the so-called Nuclear Statistical Equilibrium (NSE) regime, at temperatures K. In the short timescale of the explosion (1 s in SNIa and in the inner layers of CCSN) weak interactions can hardly operate and material is nuclearly processed under the effect of strong interactions alone, moving in the neutron vs. proton () plane along a trajectory. The original stellar material is essentially composed either of Si () in the case of CCSN or of C () and O () in the case of the white dwarf progenitors of SNIa; this ratio is mostly preserved during the explosion. Since the last stable nucleus with is Ca (), NSE reactions produce mostly unstable Fe-peak nuclei, which decay later back to the nuclear stability valley by electron captures (EC) or e emission. This is typically the case of the most abundant Fe-peak nucleus Fe (), which is produced as Ni () through the decay chain Ni Co Fe; the first decay proceeds by EC and the second one by both EC and e emission, with branching ratios of 81% and 19%, respectively (Nadyozhin, 1994).

Nuclide Decay chain Decay mode Lifetime Associated -ray lines Endpoint e Mean e Sources
and e BR Energy in keV (BR) energy (keV) energy (keV)
Ni Ni Co EC 6.073 d 158(0.99), 812(0.86) SNIa
Co Fe e (0.19) 77.2 d 2598(0.17), 1771(0.15) 1458.9 610
Na Na Ne e (0.90) 2.61 y 1275(1) 1820.2 215.9 Novae
Ti Ti Sc EC 59.0 y 68(0.94), 78(0.96) Supernovae
Sc Ca e (0.94) 3.97 h 1157(1) 1474.2 632.
Al Al Mg e (0.82) 7.4 10 y 1809(1) 1117.35 543.3 Massive stars

() BR:Branching Ratio (in parenthesis); () EC: Electron capture

Table 7: Astrophysically important positron-emitting radioactivities

Other important astrophysical e emitters are displayed in Table 7, along with various relevant data. An important feature of -decay is that positrons are released with energies in the MeV range, i.e. they naturally satisfy the constraint imposed by the continuum observations of the inner Galaxy in that energy range (see Sec. II.B.1).

Contrary to all other e sources presented in this section, it is well established that stellar radioactivities contribute at a non-negligible level to the e production rate, because of the observed presence of Al in the disk (see Sec. II.B.2). The uncertainties related to their overall contribution stem from two factors:

i) In the case of short-lived radioactivities (i.e. with lifetimes short compared to the characteristic timescales of SN expansion) positrons are released in high density environments and in magnetic fields of unknown configuration. Those conditions render difficult the evaluation of the fraction of e escaping to environments of sufficiently low density for their annihilation photons to be detectable. This is the case of Co in SNIa.

ii) In some cases of long-live radioactivities, the corresponding stellar yields and/or the frequencies of the nucleosynthesis sites are quite uncertain. Indirect methods should then be used to evaluate their contribution to the Galactic e production. This is the case of Ti.

iv.1.2 Massive stars: Al and Ti

The observed irregularities in the Al -ray emission along the plane of the Galaxy as shown in the COMPTEL map Diehl et al. (1995) suggest that massive stars are the dominant source, as these are the only candidate Al sources clustered along spiral arms (see Prantzos and Diehl, 1996, and Sec. II.B). Al is produced in such stars both hydrostatically (during H-burning) and explosively (in the C-Ne-O) layers; it is ejected by the Wolf-Rayet stellar winds in the former case and by the supernova explosion in the latter. Limongi and Chieffi (2006) find that in their Z models explosive nucleosynthesis is always dominant; however, models with rotation and at Z (appropriate for the inner Galaxy) may modify this conclusion somewhat. Stellar nucleosynthesis models find typical yields of 10 M of Al per star, which combined with the derived CCSN frequency in the Galaxy (Table 5) results in a production rate comparable to the observed one of 2.7M/Myr; thus, the nucleosynthesis of Al is considered to be rather well understood quantitatively (within a factor of 2). Independently of theoretical considerations, however, the observed Galactic decay rate of Al corresponds to a production rate of s in the Galactic disk.

Ti is produced in the innermost layers of the supernova, in the ”-rich freeze-out” regime of NSE (Meyer, 1993, Thielemann et al., 1996). Its yields are much more uncertain than the ones of Al because of uncertainties either in the nuclear reaction rates (which affect its yields by a factor of 2, The et al., 2006; Magkotsios et al., 2008) or, most importantly, in the explosion mechanism itself (Woosley and Weaver, 1995; Timmes et al., 1996). Moreover, asphericity effects (due e.g. to rotation) appear to be critical, leading to the production of substantially higher Ti yields (and Ti/Ni ratios) than in the case of spherically symmetric models (Nagataki et al., 1998).

Observations offer little help in this case. Ti has been directly detected in the Cassiopeia A (CasA) SN remnant, through its -ray lines, both with COMPTEL/CGRO (Iyudin et al., 1994) and with SPI/INTEGRAL (Renaud et al., 2006). Its presence is also indirectly derived in SN1987A, the closest observed supernova in the past four centuries, since it is required to explain the late lightcurve (Motizuki and Kumagai, 2004). In both cases the derived Ti yield is M, substantially larger than predictions of spherically symmetric models, but comparable to predictions of aspherical models. Asphericity is also favoured for CasA and SN1987A on the basis of other observables (Prantzos, 2004, and references therein). Does this mean that typical sources of Ti are aspherical and have the aforementioned yield?

CasA is found at a distance of 3 kpc from the Earth in the outer Galaxy (outside the active star forming regions of the inner Galaxy) and its age is estimated to 300 yrs (much larger than the Ti lifetime). That a supernova with such properties is the only one detected so far through its Ti lines, despite the sensitivity of COMPTEL/CGRO and SPI/INTEGRAL Galactic surveys, appears to be statistically improbable (The et al., 2006; Renaud et al., 2006). It may imply that typical Ti sources are rare, i.e. with frequencies much lower than the CCSN frequencies of Table 5, and, consequently, much larger yields. Sub-Chandrasekhar mass SNIa (i.e. thermonuclear SN induced by surface He-detonation, see Sec. IV.4) are potential candidates, since they produce 10–20 times more Ti than a typical massive star explosion (Woosley and Weaver, 1994); but, provided that such objects exist and have the required yields, their frequencies are totally unknown.

In those conditions, the only way to evaluate the Galactic Ti production rate is through a nucleosynthesis argument, based on i) the solar (Ca/Fe) ratio (Lodders, 2003) , i.e the ratio of the stable products of Ti and Ni decays and ii) the knowledge of the current production rate of Fe, based on disk SN frequencies of Table 5 and on presumably well-known typical yields of Fe: 0.7 M (see Sec. IV.A.4) and 0.07 M (from the observed lightcurve of SN1987A, Arnett et al., 1989). The production rate of Ti is then:


and the corresponding e production rate is e s, i.e. comparable to the one of Al. Thus, the two long-lived radioactivities together may account for most, if not all, of the disk production rate of positrons, as revealed by the SPI/INTEGRAL analysis. The same analysis, applied to the bulge (and assuming the bulge Ca/Fe ratio to be solar) leads to a e production rate three times smaller, i.e. an insignificant fraction of the obervationally required rate for that region.

iv.1.3 Hypernovae and -ray bursts

Hypernovae are very energetic supernova explosions, with typical observed kinetic energies 10 ergs (i.e. about ten times larger than normal supernovae) and ejected Ni masses of 0.5 M (e.g. Nomoto et al., 2007). Their properties are usually interpreted in terms of aspherical explosions of rotating massive stars (with mass 30 M). The rotating Fe core implodes to a black hole, around which the surrounding material forms a short-lived (0.1 s) accretion disk. The gravitational energy of accretion is partially transferred (by some still unclear mechanism) to two jets along the rotation axis, which launch the supernova explosion. Heavy nuclei (among which Ni) are formed in the hot basis of the jet and ejected in the ISM. This model was originally proposed to account for the phenomenon of Gamma-Ray Bursts (GRB), the most powerful electromagnetic beacons in the Universe, releasing 10 erg in short flashes of -rays beamed along the jet direction (the ”collapsar” model of Woosley, 1993). Observed metallicities of GRB host galaxies are typically few times lower than solar (Savaglio et al., 2008); such low metallicities prevent substantial losses of mass and angular momentum and allow for a rapid rotation of the core at the moment of the explosion, a crucial ingredient of the collapsar model.

Hypernovae/GRBs have been suggested as potential sources of the Galactic positrons, produced either from the Ni decay (Nomoto et al., 2001; Cassé et al., 2004) or from pair creation, as photons backscattered from the ionized medium ahead of the jet interact with the GRB -ray photons (Parizot et al., 2005; Bertone et al., 2006). Because of the complex (and still very uncertain) nature of those objects, the corresponding positron yield is virtually unknown. In the light of the observational (and theoretically motivated) constraint of low metallicity for the progenitor stars, the existence of such objects in the metal-rich bulge (see Sec. III.A.1) should be excluded. Besides, a small bulge/disk ratio would be logically expected in that case, contrary to observations.

iv.1.4 Thermonuclear supernovae (SNIa)

SNIa display a remarkable uniformity in their properties, like e.g. the peak luminosity, which is attributed to the power input of 0.7 M of radioactive Ni (Arnett, 1982)999In fact, the Ni mass may vary by a factor of 10, as shown by Stritzinger et al. (2006), who find values in the range of 0.1-0.9 M for a sample of seventeen well observed SNIa. However, obervations indicate that the shape of the SNIa light curves is associated to the Ni mass (with brighter SNIa fading more slowly) and after correction is made for that effect (Phillips, 1993) SNIa can indeed be used as “standard candles” for the determination of cosmological distances (see Leibundgut, 2001 for a review).. There is general agreement that SNIa result from the thermonuclear disruption of a white dwarf, igniting explosively its carbon. The thermonuclear flame may propagate either subsonically (deflagration) or supersonically (detonation) inside the white dwarf; Mazzali et al. (2007) show that the SNIa variety can be understood within a single, combined, model, involving both deflagration and detonation. There are two main scenarios for the precursors of SNIa: the single degenerate (SD) model, in which accretion is made from a main sequence or red giant companion (Whelan and Iben, 1973); and the double degenerate (DD) model, which involves the merging of two white dwarfs in a close binary system (Webbink, 1984; Iben and Tutukov, 1984). Parthasarathy et al. (2007) discuss all available observational evidence and find that the SD channel is by far the dominant one (but see Gilfanov and Bogdán, 2010 for a different view).

Most studies of SNIa were made in the framework of the SD scenario and, up to the late 1990s with one-dimensional (1D) models. Detailed 1D models exploring the various possibilities (and the corresponding parameter space) have been developed over the years. Perhaps the most successful 1D model developed so far is the so-called W7 model (Nomoto et al., 1984), the physics of which has been updated in Iwamoto et al. (1999); it is a deflagration model producing in its inner layers 0.7 M of Ni and negligible amounts of other positron emitters. A more accurate description of reality is pursued by the upcoming generation of multi-dimensional models (Travaglio et al., 2004, Bravo and García-Senz, 2006, Schmidt and Niemeyer, 2006, Röpke et al., 2007, Röpke and Niemeyer, 2007). Preliminary results show interesting features for the stratification of radioactivities, in particular the presence of substantial Ni amounts within outer, high velocity, layers (Fig.  13).

Figure 13: Mass fraction of Ni as a function of ejecta velocity after a SNIa explosion. The space-averaged profile of 3-D mode (solid curve from Röpke et al. (2007)) is compared to observational data (dotted curve). Both theory and observations find non-negligible amounts of Ni in the outer (high velocity) ejecta. Figure from Röpke et al. (2007).

The fate of the -decay products (-rays and positrons) in the expanding SNIa ejecta has been extensively studied in 1D (Gómez-Gomar et al., 1998, Milne et al., 2004), and more recently, in 3D models (Isern et al., 2007, Sim and Mazzali, 2008). Generically, before peak luminosity, the SNIa envelope is opaque, and both the energy of the explosion and of -decay are deposited in and diffuse outwards through the ejecta. After the peak of the bolometric lightcurve (20 days after the explosion) the luminosity evolves from radioactive energy deposits and increasing energy leakage in a way following (surprisingly closely, given the interplay of these processes) the decay rate of Co. About 6 months later, the ejecta are completely transparent to -rays and the SNIa luminosity results almost exclusively from energy deposited by positrons from ongoing radioactive decays. If positrons are trapped (escape) a flattening (steepening) of the light curve results. How many positrons ultimately escape to the ISM depends on the distribution of the parent radioactivities within the supernova, the evolution of its density, temperature and ionization profiles and, most importantly for the late phases, on the unknown configuration of its magnetic field. Progenitor white dwarfs have field strengths of 10-10 G. Chan and Lingenfelter (1993) found that, in the case of radially combed magnetic fields and fully mixed ejecta a substantial fraction of Co positrons (10%) may escape. Building on the same ideas, Milne et al. (1999) compared SNIa models to observations of late lightcurves of a dozen SNIa (mostly in B and V bands) and concluded that, typically, a few % of positrons finally escape the ejecta; the average positronic yield of a SNIa is (SNIa)8 10 (corresponding to an escape fraction of 0.03). They also found that the mean energy of escaping positrons is 0.5 MeV (Fig.  14).

Figure 14: Distribution of emitted positron kinetic energies as estimated by Segre (1977, dashed curve) compared to the spectrum of escaping positrons from W7, as estimated by Chan and Lingenfelter (1993, solid curve) and Milne et al. (1999, solid histogram). The slowing of the positrons leads to the mean energy shifting from 632 to 494 keV . Figure from Milne et al. (1999).

The corresponding Galactic positron yield is then estimated as


where is the SNIa frequency in Table 5. The total e yield is comparable to the observed Galactic one, but the bulge/disk positron emissivity ratio is B/D0.4, considerably less than derived from observations.

This simplified picture may not apply to SNIa in general, though. Bolometric observations (including the near IR) of the late lightcurves of SN 2000cx (a rather peculiar at early times SNIa) and of SN 2001el and SN2003hv (two typical SNIa), interpreted in the framework of 1D models, suggest that no positrons escape (Sollerman et al., 2004, Stritzinger and Sollerman, 2007, Leloudas et al., 2009); in that case, despite their large -decay yields, the SNIa would be insignificant e producers.

However, 3D effects may considerably alter the stratification of radioactivities inside the SNIa (Blinnikov et al., 2006), allowing for substantial amounts of Ni to be mixed out to the surface (Fig. 13) and for the released positrons to escape at early times (i.e. when the lightcurve is dominated by -rays, and not yet e deposition) without being noticed. Studying the very early optical spectra of six SNIa, Tanaka et al. (2008) find indeed indications for asphericity and substantial amounts of Ni present in the high velocity ejecta (10 000 - 15 000 km/s). Positrons produced by the subsequent decay of Co may escape the ejecta if the magnetic field of the supernova is radially combed. Observations indicate that this may be the dominant configuration of magnetic fields in young SN remnants (e.g. Milne et al., 1993; Kothes and Reich, 2001) although the origin of such a configuration is not yet clearly understood (Jun and Norman, 1996, Schure et al., 2008). On the other hand, the late lightcurve of SNIa may also be (at least partially) powered by internal conversion and Auger electrons released from the decay of Co (Seitenzahl et al., 2009), thus allowing for some Co positrons to escape. Thus, the issue of the positron yield of SNIa is not settled yet: may well be as high as envisioned by Milne et al. (1999) (albeit for different reasons), but also much lower.

When the SN becomes sufficiently diluted, the annihilation -ray photons may be directly observed. Kalemci et al. (2006) find no such signal in observations with SPI/INTEGRAL of the SN remnant SN1006. They exclude then SNIa as major e producers in the Galaxy under the assumption that the e lifetime is 10 yr. However, even the low energy positrons of -decay may live much longer before annihilation and then escape the SN remnant, especially in the case of a radially combed magnetic field.

iv.1.5 Novae

Novae result from explosive H-burning on the surfaces of white dwarfs in binary systems. Accretion of material from the companion star increases the density, pressure and temperature at the base of the white dwarf envelope, up to the point where hydrogen ignites in degenerate conditions and burns explosively at peak temperatures of several 10 K. The ejected mass is 10 M and is substantially enriched with the material of the white dwarf, leading to CO or to ONe novae (see, e.g. Hernanz, 2005 for a review).

Major positron producers are N and F (produced in the hot-CNO cycle) and, in the case of ONe novae, Na (produced in the hot-NeNa cycle). The short lifetimes of N and F (=862 s and 158 min, respectively) make unlikely a substantial escape of their positrons from the nova ejecta. Positrons from Na decay certainly escape and recent calculations suggest that up to 10 M of this nucleus may be produced in ONe novae (Hernanz and José, 2006), releasing up to =10 e.

The novae frequency in the Galaxy is estimated to 35 yr ( (Shafter, 1997; Darnley et al., 2006). About 1/3 of those may originate from ONe white dwarfs (Gil-Pons et al., 2003), leading to a Galactic e production rate of 1.5 10 s, ie. smaller by two orders of magnitude than the observed rate in the bulge or in the disk. It should be noticed that ONe novae appear mostly close to the Galactic plane (della Valle and Livio, 1998).

iv.2 High energy processes in cosmic rays and compact objects

iv.2.1 High energy processes

1a. Inelastic p-p collisions

Relativistic protons and heavier nuclei are present in many astrophysical environments in the Galaxy. Their inelastic interactions with interstellar gas produce secondary particles including numerous neutral and charged pions and kaons , . In turn, decay of positively charged mesons produces secondary positrons. The dominant channel is pion decay , , though a non-negligible contribution comes from the charged kaon decays. The two main kaon decay modes contributing to the secondary spectrum are (63.5%) and (21.2%). The processes as the source of secondary cosmic ray positrons and diffuse ray emission have been thoroughly studied (e.g., Strong et al., 2007 and references therein). A review of the experimental data for pion production in proton-proton collisions and relevant cross section parameterizations 50 GeV were presented by Blattnig et al. (2000). New parameterizations of neutral and charged pion cross sections which provide an accurate description of the experimental data in a wide energy range from the pion production threshold up to TeV are discussed in Kelner et al. (2006), Kamae et al. (2006, 2007).

The energy spectra of positrons from the decay of mesons produced in collisions of isotropic monoenergetic protons with protons at rest are shown in Fig. 15; they typically present a maximum at MeV.

Figure 15: The energy spectra of positrons from the decay of produced in collisions of isotropic monoenergetic protons with protons at rest for various proton kinetic energies (from bottom to top): 0.316, 0.383, 0.464, 0.562, 0.681, 1.0, 1.78, 3.16, 10.0, 100.0 GeV (Murphy et al., 1987).

1b. pair production

Positrons can also be produced in photon-photon interactions when the product of their energies is where is the angle between the photon directions. The total unpolarized cross section for the creation of by two photons can be expressed as a function of a dimensionless velocity of the produced particles in the center of mass frame:


where cm is the Thomson scattering cross section (Breit and Wheeler, 1934; Greiner, 2003).

In Fig. 16 the cross section is presented as a function of the Lorentz factor of created positron in the center of mass frame. The positron production due to photon-photon collisions is suppressed at the threshold and reaches a maximum at .

The production of a -pair by a single photon is possible in magnetic fields 10 G observed in highly magnetized objects such as pulsars and magnetars (Klepikov, 1954; Daugherty and Harding, 1983). This occurs with significant probability when the photon energy is MeV, where is the external magnetic field strength in units Gauss and is the angle between the photon direction and the magnetic field.

Figure 16: The total cross section of reaction as a function of the Lorentz factor of created positron in the center of mass frame (solid). The total cross section for two-photon pair annihilation reaction (unpolarized) is indicated as a dotted curve.

iv.2.2 Galactic cosmic rays

The majority of positrons in cosmic rays (CR) are believed to be secondaries produced by interactions of relativistic particles with interstellar gas; however recent measurements of positron fraction in cosmic rays by PAMELA (Adriani et al., 2009) indicate that there may be another component at high energies. If produced by CR interactions, the positron fraction is expected to decrease with energy (Moskalenko and Strong, 1998) while the PAMELA data show it rises above 10 GeV. The origin of this additional component is intensively debated. The ideas proposed can be roughly divided into two broad classes: conventional sources, such as SNR or nearby pulsars (e.g. Blasi, 2009 and references therein) and exotic sources such as WIMP annihilation or decay (e.g. Arvanitaki et al., 2009 and references therein). The predicted behaviour of the positron fraction at energies higher than currently measured (100 GeV) depends on the model and can be used to distinguish between different possibilities.

In this section we will discuss positrons produced by conventional CR interactions with interstellar gas. The most important factors are the energetics of cosmic rays and their diffusion in the interstellar medium (for more details see, e.g., Strong et al., 2007).

The major CR sources are believed to be supernovae (SN) and their remnants (SNR) with some fraction coming from pulsars, compact objects in close binary systems, and stellar winds. Recent observations of X-ray and -ray emission from SNRs Pannuti et al. (2003); Aharonian et al. (2006) reveal the presence of energetic electrons, thus testifying to efficient acceleration processes near these objects. The total power of Galactic CR sources needed to sustain the observed CR density is estimated at 10 erg s which corresponds to approximately erg per SN, if the SN rate in the Galaxy is 1 every 30 years (Table 5). This value is 10% of the corresponding total kinetic power of the SN ejecta, an efficiency which is in agreement with the predictions of diffusive shock acceleration theory (Blandford and Eichler, 1987; Jones and Ellison, 1991). After injection into the interstellar medium (ISM), cosmic rays remain contained in the gaseous disk for 15 myr and in the Galaxy for 100 Myr before escaping into intergalactic space (Berezinskii et al., 1990). Note that the latter value is much larger than estimates based on the so-called leaky-box model (Yanasak et al., 2001); see Strong et al. (2007)for a full discussion of this point.

Propagation of cosmic rays in the ISM is usually modelled as diffusion, where the energetic particles scatter on iregularities (fluctuations) of the turbulent Galactic magnetic field (see Sec. III.D). The diffusion equation may include stochastic reacceleration in the ISM, convection by the Galactic wind, continuous and catastrophic energy losses, nuclei fragmentation, radioactive decay, and production of secondary particles and isotopes (for a recent review of cosmic ray transport, see Strong et al., 2007). Isotopes of light elements (Li, Be, B) in cosmic rays are almost all secondaries produced in spallations of heavier (CNO) nuclei during CR propagation. If the diffusion is fast (slow), the secondary nuclei are present, after propagation, in small (large) amounts; therefore, the relative abundances of secondary and primary nuclei can be used to determine the propagation parameters101010 The stable secondary/primary ratio does not allow one to derive a unique set of propagation parameters. The radioactive isotope abundances are then used to break the degeneracy. Four radioactive isotopes, Be, Al, Cl, and Mn, are commonly used to probe the effective Galactic volume filled with cosmic rays and derive the CR confinement time in the Galaxy. Their half-lives range from 3.07 10 yr (Cl) to 1.60 10 yr (Be) with the shortest half-life being most sensitive to the local structure.. The derived propagation parameters (timescale of CR confinement, diffusion coefficient, etc.) are model dependent and can vary significantly (e.g., Ptuskin et al., 2006).

The production spectra of secondary particles are determined by the kinematics of the collision and depend on the ambient spectrum of cosmic rays while their propagation is governed by the same propagation equation as for other cosmic ray species. The production rate of secondary positrons slightly depends on the assumed propagation model and is about s (Porter et al., 2008), i.e.