Continuum $\gamma$-ray emission from light dark matter positrons and electrons

The annihilation of light dark matter was recently advocated as a possible explanation of the large positron injection rate at the Galactic center deduced from observations by the SPI spectrometer aboard INTEGRAL. The modelling of internal Bremsstrahlung and in-flight annihilation radiations associated to this process drastically reduced the mass range of this light dark matter particle. We estimate critically the various energy losses and radiations involved in the propagation of the positron before its annihilation—in-flight or at rest. Using a simple model with monoenergetic positrons injected and confined to the Galactic bulge, we compute energy losses and gamma-ray radiations caused by ionization, Bremsstrahlung interactions as well as in-flight and at rest annihilation and compare these predictions to the available observations, for various injection energies. Confronting the predictions with observations by the CGRO/EGRET, CGRO/COMPTEL, INTEGRAL/SPI, and INTEGRAL/IBIS/ISGRI instruments, we deduce a mass upper bound of 3 to $7.5\mathrm{MeV}/c^2$ for the hypothetical light dark matter particle. The most restrictive limit is in agreement with the value previously found by Beacom and Yüksel and was obtained under similar assumptions, while the $7.5\mathrm{MeV}/c^2$ value corresponds to more conservative choices and to a partially ionized propagation medium. We stress how the limit depends on the degree of ionization of the propagation medium and how its precision could be improved by a better appraisal of data uncertainties.

Figure 1

Energy losses of positrons in a 51% ionized medium ($n_H=0.1{\mathrm{cm}}^{-3}$): energy loss rate per unit path length $\frac{dE}{dx}$ as a function of the positron’s Lorentz factor $\gamma$. Losses through Coulomb collisions within an ionized medium (dotted) prevail on ionization of the neutral phase (dashed), but both greatly exceed Bremsstrahlung losses (plain).

Figure 2

Differential in-flight annihilation cross section—given for instance by Aharonian and Atoyan ([54] Eq. (5), misprint corrected)—as a function of the reduced photon energy, for various positron energies. Still energetic positrons annihilate with thermal electrons into two photons that share the total available energy, with a minimum energy of $m_e{c}^2/2$ by photon.

Figure 3

Light dark matter ($E_{\mathrm{inj}}=10\mathrm{MeV}$) radiation spectra: positron annihilation spectra (in-flight: IA; $2\gamma$ at rest; $3\gamma$ at rest), positron energy loss spectra (internal Bremsstrahlung: IB; Bremsstrahlung: B $e^{+}$), electron Bremsstrahlung spectrum (B $e^{-}$) and total spectrum (plain).

Figure 4

Total dark matter radiation spectrum for increasing injection energies $E_{\mathrm{inj}}$ (1, 3, 5, 10, 50, and 100 MeV). In a partially ionized medium (dotted curves), higher energy losses through ionization lead to lower external Bremsstrahlung fluxes than in a completely neutral medium (solid curves).

Figure 5

Comparison between the total diffuse spectrum expected from a 20° wide region at the Galactic center and the diffuse fluxes measured by IBIS (Krivonos et al. 2006 [43]; full squares), SPI (Strong et al. 2005 [44]; circles), COMPTEL (Strong et al. 1999 [46]; open squares) and EGRET (Hunter et al. 1997 [48]; triangles). The model curves are the sum of the CR interactions component computed by Strong et al. [44] (lower line), and the dark matter related component, computed in Sec. 3 for injection energies $E_{\mathrm{inj}}=1$, 3, 5, 10, 50, and 100 MeV, in a neutral (solid curves) or 51% ionized medium (dashed curves).

Figure 6

Longitude profile of the 3–10 MeV diffuse flux measured by COMPTEL in a latitude band of $\pm 5°$ (histogram). Left: the data is compared to a global model (thick line) including the GALPROP model of diffuse emission from cosmic-ray interactions, composed of a dominating inverse Compton component (dotted line) and a smaller Bremsstrahlung component (dashed line), to which we added the model of LDM emission (thin solid line), computed here for an injection energy $E_{\mathrm{inj}}$ of 10 MeV and assumed to have a Gaussian morphology with 8° FWHM. As the discrepancy between the COMPTEL data and the GALPROP model concerns high longitudes as well as the Galactic center, trying to explain all of the Galactic bulge gap through the LDM emission is not reasonable because the outer-bulge disparity would remain unexplained. Right: thus, in Sec. 4d we dismiss the idea of modeling the observations completely; we acknowledge the relatively flat profile of the COMPTEL data in the inner disk region and use the mean intensity as a baseline, requiring that an eventual excess caused in the Galactic bulge by LDM radiation remains within data uncertainties.

Figure 7

Comparison between the total diffuse spectrum expected from a 20° wide region at the Galactic center and the diffuse fluxes measured by IBIS (full squares), SPI (circles), COMPTEL (open squares), and EGRET (triangles). Instead of taking the predictions from cosmic-ray interaction codes as a base level for our LDM model like in Fig. 5, we now use a powerlaw (straight line) $\gamma$-ray background—already displayed in Fig. 5—compatible with both SPI and COMPTEL data.

Figure 8

Total integrated flux in the 1–3, 3–10 and 10–30 MeV COMPTEL energy bands for an 8° diameter region around the Galactic center. Horizontal lines show the flux (solid lines) derived from the mean COMPTEL intensity in a wider fraction of the disk $(|l|<30°,|b|<5°)$ and its $1\sigma$ (dashed) and $2\sigma$ (dotted) upper values. The sum of the COMPTEL flux and of the LDM flux is shown as a function of the positron injection energy $E_{\mathrm{inj}}$, for a completely neutral propagation medium (circled solid lines) and for 51% ionized medium (crossed dashed-dotted lines). It should be noticed that combining the three COMPTEL energy bands instead of considering them independently would bring a sensitivity improvement and lead to more severe exclusions; for instance, injection at $E_{\mathrm{inj}}=10\mathrm{MeV}$ is excluded by the 1–3 and 3–10 MeV energy bands at $3.6\sigma$ and $5.6\sigma$ respectively ($x_i=0$), while the combination of both bands leads to a $6.9\sigma$ exclusion.