Exciting dark matter and the INTEGRAL/SPI 511 keV signal

We propose a dark matter candidate with an “excited state” 1–2 MeV above the ground state, which may be collisionally excited and deexcites by $e^{+}{e}^{-}$ pair emission. By converting its kinetic energy into pairs, such a particle could produce a substantial fraction of the 511 keV line observed by the International Gamma-Ray Astrophysics Laboratory/SPI in the inner Milky Way. Only a small fraction of the dark matter candidates have sufficient energy to excite, and that fraction drops sharply with galactocentric radius, naturally yielding a radial cutoff, as observed. Even if the scattering probability in the inner kpc is $\ll 1\%$ per Hubble time, enough power is available to produce the $\sim 3\times {10}^{42}$ pairs per second observed in the galactic bulge. We specify the parameters of a pseudo-Dirac fermion designed to explain the positron signal, and find that it annihilates chiefly to $e^{+}{e}^{-}$ and freezes out with the correct relic density. We discuss possible observational consequences of this model.

Figure 1

The fraction of pairs with velocity above $v_{\mathrm{thresh}}$ of 600, 800, or $1000\mathrm{km}/\mathrm{s}$, for $v_{\mathrm{rms}}=200\mathrm{km}/\mathrm{s}$ (solid line) and $v_{\mathrm{rms}}=180\mathrm{km}/\mathrm{s}$ (dashed line). The approximate half-max radius of the observed 511 keV emission (vertical dotted line) is shown for reference.

Figure 2

Model curves for the constant sigma model in Eq. (2), taking ${\sigma }_{\mathrm{mr}}=1.3\times {10}^{-26}{\mathrm{cm}}^2(\frac{0.3\mathrm{GeV}/{\mathrm{cm}}^3}{{\rho }_0}{)}^2=2.4\times {10}^{-27}-1.2\times {10}^{-25}{\mathrm{cm}}^2$, both unsmoothed (thin line) and smoothed by a 3° FWHM beam (thick line) to approximate the spatial response of SPI. In all cases the solid red lines represent our fiducial model ($M=500\mathrm{GeV}$, $v_{\mathrm{thresh}}=850\mathrm{km}/\mathrm{s}$, and halo parameters $v_{\mathrm{rms}}=200\mathrm{km}/\mathrm{s}$, and Merritt index $\alpha =0.2$), and dashed blue lines represent variations of one parameter. (a) $M=400$, 500, 600 GeV with $\delta$ held fixed at 1 MeV so that $v_{\mathrm{thresh}}=950$, 850, $776\mathrm{km}/\mathrm{s}$, respectively. (b) $v_{\mathrm{thresh}}=800$, 850, $900\mathrm{km}/\mathrm{s}$ keeping $M=500\mathrm{GeV}$ while $\delta$ now varies above and below 1 MeV. (c) The Merritt profile index $\alpha$ is varied (see Eq. (6)). (d) The rms velocity in the inner Milky Way is varied. This is assumed to be constant with radius. The observed 6° FWHM signal (lower dotted line) and that signal plus an arbitrary baseline of 0.002 (upper dotted line) are shown in (a). The SPI zero is set by measurements 10° off the galactic plane to correct for instrumental background.

Figure 3

Same as Fig. 2, but using the full expression for the inelastic scattering cross section (Eq. (a2)) derived in the Appendix, setting the coupling ${\lambda }_{+}={\lambda }_{-}=0.18$ and $\rho =0.4\mathrm{GeV}/{\mathrm{cm}}^3$.

Figure 4

Excitation diagrams for $\chi \chi \to {\chi }^{*}\chi$.

Figure 5

Decay of the excited state into the ground state.

Figure 6

Diagrams contributing to thermal equilibrium in the dark sector and between the dark sector and the visible sector.