The 511 keV emission from positron annihilation in the Galaxy

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 1990s with OSSE/CGRO (Oriented Scintillation Spectrometer Experiment on GRO satellite/Compton Gamma Ray Observatory) showed that the emission is strongly concentrated toward the Galactic bulge. In the 2000s, the spectrometer SPI aboard the European Space Agency’s (ESA) International Gamma Ray Astrophysics Laboratory (INTEGRAL) allowed scientists to measure that emission across the entire Galaxy, revealing that the bulge-to-disk luminosity ratio is larger than observed at any other wavelength. This mapping prompted a number of novel explanations, including rather “exotic” ones (e.g., dark matter annihilation). However, conventional astrophysical sources, such as 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, in contrast to the rather well-understood propagation of high-energy ($>\mathrm{GeV}$) particles of Galactic cosmic rays, understanding the propagation of low-energy ($\sim \mathrm{MeV}$) positrons in the turbulent, magnetized interstellar medium still remains a formidable challenge. The spectral and imaging properties of the observed 511 keV emission are reviewed and candidate positron sources and models of positron propagation in the Galaxy are critically discussed.

Figure 1

Spectrum of ortho-positronium annihilation with the three-photon continuum. From 345.

Figure 2

OSSE 511 keV line map of the Galactic center region (top panel) and corresponding exposure map (bottom panel). From 374.

Figure 3

511 keV line map (top panel) and positronium continuum map (bottom panel) derived from 1 year of INTEGRAL/SPI data. From 254 and 458, respectively.

Figure 4

511 keV line map derived from 5 years of INTEGRAL/SPI data. From 459.

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 accounts for the Galactic diffuse continuum emission. From 227.

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 lines) or 50% ionized (dotted lines) media. This constrains the injected positron energy (or, equivalently, the mass of decaying and/or annihilating dark matter particles) to a few MeV. From 414.

Figure 7

Map of Galactic ${}^{26}\mathrm{Al}$ $\gamma$-ray emission after 9-year observations with COMPTEL/CGRO. From 357.

Figure 8

Azimuthally averaged surface densities of interstellar atomic, molecular, and ionized hydrogen as functions of the Galactic radius. The total gas (bottom panel) includes a 40% contribution by helium. Notice the change of scale at $R=2\mathrm{kpc}$. For $R<2\mathrm{kpc}$ (bulge) data are derived by 145, based on a compilation of earlier works: 399 for the molecular gas in the central molecular zone, 282 for the neutral gas in the tilted disk, and 105 for the ionized gas. In all panels, disk data ($R>2\mathrm{kpc}$) are from 114 (solid lines); 344 (dotted lines); 334 for H I, and 333 for ${\mathrm{H}}_2$, respectively (dashed lines); and 236 for H I and 358 for ${\mathrm{H}}_2$, respectively (dot-dashed lines). The curve in the H II panel is from the NE2001 free-electron density model of 105 (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).

Figure 9

Space-averaged volume densities of interstellar ${\mathrm{H}}_2$, H i, and H II, averaged along the solar circle ($R=R_{\odot }$), as functions of distance from the Galactic plane $Z$. Data: ${\mathrm{H}}_2$ from 73, rescaled to $X_{\mathrm{CO}}=2.3\times {10}^{20}{\mathrm{cm}}^{-2}{\mathrm{K}}^{-1}{\mathrm{km}}^{-1}\mathrm{s}$, as in 344; H i from 124, scaled up by a factor of 1.58 such as to match the H i surface density of 344. All other curves are from the same sources as in Fig. 8.

Figure 10

Surface densities of $\mathrm{\text{stars}}+\mathrm{\text{gas}}$, SFR, SN rates, and scale heights of gas and stars as a function of galactocentric distance. The star profiles are from the data of Table  and the gas profile is the one of 114 (bottom panel of Fig. 6). Data for SFR are from 287 (open cicles); 83 (filled circles); 302 (open squares); 187 (filled squares). The solid curve is an approximate fit, normalized to $2M_{\odot }{\mathrm{yr}}^{-1}$ 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 ).

Figure 11

Composite magnetic energy spectrum in our Galaxy. The thick solid line is the large-scale spectrum. The thin solid and dashed or dotted lines give the Kolmogorov and two-dimensional turbulence spectra, respectively, inferred from the 315 study. The two-dimensional turbulence spectrum is uncertain; it probably lies between the dashed [$E_B(k)\propto k^{-2/3}$] and dotted [$E_B(k)\propto k^{-5/3}$] lines. From 191.

Figure 12

Dark matter density profile (top panel) and rotational velocity (bottom panel) 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 419.

Figure 13

Mass fraction of ${}^{56}\mathrm{Ni}$ as a function of ejecta velocity after a SNIa explosion. The space-averaged profile of the 3D mode [solid curve from 392] is compared to observational data (dotted curve). Both theory and observations find non-negligible amounts of ${}^{56}\mathrm{Ni}$ in the outer (high-velocity) ejecta. From 392.

Figure 14

Distribution of emitted positron kinetic energies as estimated by 403 (dashed curve) compared to the spectrum of escaping positrons from W7, as estimated by 85 (solid curve) and 308 (solid histogram). The slowing of the positrons leads to the mean energy shifting from 632 to 494 keV. From 314.

Figure 15

The energy spectra of positrons from the decay of ${\pi }^{+}$ 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, and 100.0 GeV. From 328, updated by R. Murphy.

Figure 16

The total cross section of $\gamma +\gamma \to e^{+}+e^{-}$ reaction as a function of the Lorentz factor of created positron in the center-of-mass frame (solid curve). The total cross section ${\sigma }_a$ for two-photon pair annihilation reaction $e^{+}+e^{-}\to \gamma +\gamma$ (unpolarized) is indicated as a dotted curve.

Figure 17

Illustration of the two schemes conceived for the positron production activity of Sgr $A^{*}$. In (1), protons are injected and/or accelerated every $\sim {10}^5\mathrm{yr}$ following the tidal disruption of a star, and their collisions with the ISM produce positrons (after ${\pi }^{+}$ decay). In (2), Sgr $A^{*}$ produces quasicontinuously positrons at a high rate, except when its accretion flow is interrupted by the passage of the shock front of a nearby SN explosion (expected to occur on a time scale of $\sim {10}^5\mathrm{yr}$); the last SN explosion created the SN remnant Sgr East ${10}^4\mathrm{yr}$ ago and its expansion interrupted the accretion flow 300 yr ago [according to 446]. Despite the discontinuous $e^{+}$ injection in both cases (1) and (2), the annihilation of positrons and the resulting 511 keV emission are in a quasisteady steady state (3) if positrons diffuse in the bulge, because of the long time scale of the latter process ($\sim {10}^7\mathrm{yr}$).

Figure 18

Schematic representation of the inner Galaxy at different linear (bottom and left axis) and angular (top and right axis) scales. The main features discussed in Sec. 4b4 (SMBH scenario) appear on the figures, as, e.g., CND (circumnuclear disk, left panel), CMZ (central molecular zone, middle panel), and the tilted HGD (holed gaseous disk, containing atomic and molecular gas, right panel). If indeed Sgr $A^{*}$ is the main positron source, (most of) its positrons have to diffuse through the CMZ into the bulge. Notice that the size of the CMZ corresponds to the size (FWHM) of the inner bulge in the first model of SPI data fitting (Table ). The size of the outer SPI bulge in that same model is indicated by a dotted circle in the rightmost panel.

Figure 19

Possible Feynman diagrams for light annihilating dark matter particles.

Figure 20

Maps of the Galactic 511 keV emission (flux in ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$), as observed from SPI (in all panels, thin isocontours from 459) and from observationally based or theoretical estimates. (A) Observed ${}^{26}\mathrm{Al}$ (and, presumaby, ${}^{44}\mathrm{Ti}$) map (from 357); (B) accreting binary systems (SNIa and, presumably, LMXRBs, see text); (C) observed hard LMXRBs (from 46). The robustly expected $e^{+}$ annihilation from radioactivity in the disk (upper panel) is not yet fully seen by SPI.

Figure 21

Intensity of 511 keV emission as a function of Galactic longitude. All fluxes are integrated for latitudes $|b|<15°$. In all panels, the thick solid curve corresponds to SPI observations, i.e., the map of Fig. 20. (We note that SPI maps and fluxes are provided here for illustration purposes only; quantitative comparison of model predictions to data should only be made through convolution with the SPI response matrix.). The thick dotted histogram (top and middle panels) is the observed longitude distribution of LMXRBs (from 179); the latter closely resembles the theoretically estimated longitude distribution of SNIa (thin solid curve in the upper panel), which has been normalized to a total emissivity of $1.6\times {10}^{43}{e}^{+}{\mathrm{s}}^{-1}$, with $\mathrm{bulge}/\mathrm{disk}=0.45$ (maximum bulge-to-disk ratio for SNIa from Table ). Also, in the upper panel, the lower dashed curve corresponds to the expected contribution of the ${}^{26}\mathrm{Al}$ and ${}^{44}\mathrm{Ti}$ ${\beta }^{+}$ decay from massive stars. The thin solid histogram in the middle panel is the observed longitude distribution of hard LMXRBs (from 46) and it has the same normalization as the thick histogram. In the bottom panel, the SPI 511 keV profile is compared to profiles expected from dark matter annihilation (Table ).

Figure 22

The processes leading to $\gamma$-ray production from positron annihilation. Adapted from 185.

Figure 23

Energy loss rate for positrons in ISM conditions. For synchrotron losses, the pitch angle is taken as $\pi /2$.

Figure 24

$\gamma$-ray spectra from the annihilation in flight in the ISM for various initial kinetic energies of positrons.

Figure 25

Probability for a positron to annihilate in flight as a function of its initial kinetic energy, in a neutral medium (solid line) and an ionized medium (dashed line). $Y_e$ represents the ionization fraction.

Figure 26

Fraction of positrons forming positronium in flight by charge exchange with atomic hydrogen as a function of the ionization fraction ($Y_e$) in a warm component of the interstellar medium (electron density $n_e=0.1{\mathrm{cm}}^{-3}$, electron temperature $T_e=8000\mathrm{K}$) and in a solar flare ($n_e=5\times {10}^{13}{\mathrm{cm}}^{-3}$, $T_e=1.16\times {10}^4\mathrm{K}$).

Figure 27

Cross sections for ionization, excitation, charge exchange, radiative recombination, and direct annihilation interactions of positrons with atomic hydrogen and free electrons. Also shown is the Maxwellian distribution for a temperature of 8000 K (in arbitrary units).

Figure 28

Annihilation spectra for the five ISM phases. Adopted temperatures (see Table ) are 10 K (molecular), 80 K (cold), 8000 K (WNM and WIM), and ${10}^6\mathrm{K}$ (hot) and ionization fractions are 0 for the neutral phases (molecular, cold, and WNM) and 1 for the ionized phases (WIM and hot).

Figure 29

Confidence regions of the fit of the temperature and ionization fraction to the SPI data obtained after 1 yr of mission. The best fit values are $T=7800\mathrm{K}$ and $y_e=0.1$.

Figure 30

Best fit of the spectrum measured by SPI using the warm components of the ISM and the Galactic continuum. Contributions from the molecular, cold, and hot components are not needed to explain the data. From 227.

Figure 31

Positron stopping distance $D$ in various phases of the ISM (characterized by typical densities $n_H$ and ionization fractions $x$) as a function of positron energy $E$. Horizontal dashed lines display typical sizes of the corresponding ISM phases. In the left panel, the lower dashed curve displays positron gyroradius $r_g$ in a magnetic field of $B=5\mu \mathrm{G}$, and the shaded area displays the minimum scale length ${\lambda }_{\mathrm{MIN}}$ of MHD Alfvén waves [the latter being calculated by 226]; both $r_g$ and ${\lambda }_{\mathrm{MIN}}$ are enhanced by a factor of ${10}^9$.

Figure 32

Minimum and maximum extents of the spatial distributions of 1 MeV positrons slowing down to 100 eV, along (top panel) and perpendicular (bottom panel) to the regular Galactic magnetic field, taking into account the turbulent behavior of the field lines as well as realistic values for the density in each ISM phase. From 226.

Figure 33

Mean free path of energetic particles parallel to the magnetic field direction, as a function of particle rigidity in the interplanetary medium; circles and upward pointing triangles denote the measured values and upper limits, respectively. From 42.

Figure 34

Regions of the ISM in the $B$ vs $n$ (magnetic field vs number density) plane. Physical conditions for HIM, WIM, WNM, and the inner bulge are discussed in Sec. 3, while IPM stands for the interplanetary medium. The two lines correspond to Eq. (23) for MeV positrons, with the particle mean free path $\lambda =0.3\mathrm{AU}$ (solid line, appropriate for the interplanetary medium from Fig. 33), and $\lambda =1000\mathrm{AU}$ (dotted line, provided for illustration purposes only, since its value is unknown in the ISM). In regions of the ISM found to the left of those lines, reacceleration effects may be important for positrons (provided there is a sufficient level of small-scale turbulence), as suggested from observations of the IPM.

Figure 35

Possible configurations of the large-scale magnetic field of the Milky Way. Top panel: As derived from Faraday polarization measurements of the MW, according to 190. Bottom panel: Sketch of the observable components of the large-scale magnetic field of the disk galaxy NGC253 (which shows, however, signs of starburst activity, unlike the Milky Way); the halo magnetic field is even and pointing outward, whereas the dotted parts are not observed. From 203.