Morphology of $\gamma$-ray emission induced by $e^{\pm }$ from annihilating self-interacting dark matter

With the Fermi-LAT data, quite a few research groups have reported a spatially extended GeV $\gamma$-ray excess surrounding the Galactic center (GC). The physical origin of such a GeV excess is still unclear, and one interesting possibility is the inverse Compton scattering of the electrons and positrons from annihilation of self-interacting dark matter (SIDM) particles with the interstellar optical photons. In this work, we calculate the morphology of such a $\gamma$-ray emission. For the annihilation channel of $\overline{\chi }\chi \to \varphi \varphi \to e^{+}{e}^{-}{e}^{+}{e}^{-}$, the inverse Compton scattering (ICS) dominates over the bremsstrahlung on producing the GeV $\gamma$-ray emission. For the SIDM particles with a rest mass $m_{\chi }\sim$ tens GeV that may be favored by the modeling of the Galactic GeV excess, the ICS radiation at GeV energies concentrates along the Galactic plane. The degrees of asymmetry high up to $\ge 0.3$ are found in some regions of interest, which in turn proposes a plausible test on the SIDM interpretation of the GeV excess.

Figure 1

The left panel: the energy spectrum of $e^{\pm }$ resulting in $\chi \chi \to \varphi \varphi \to e^{+}{e}^{-}{e}^{+}{e}^{-}$ for $m_{\chi }=50\mathrm{GeV}$. The right panel: the prompt (i.e., the final state radiation of DM annihilations) and the ICS spectra; both are averaged in the regions of $|l|<5°$ and $2°<|b|<5°$.

Figure 2

The count maps of ICS $\gamma$ rays (in the energy range of 1–3.16 GeV) are shown in the regions of $|b|<30°$ and $|l|<30°$ and in unit of photons ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$. In the left panel, the regions of $|b|<2°$ are kept while in the right panel such a region is masked.

Figure 3

The coordinate transformation. In the left panel, the $z$ axis is perpendicular to the Galactic plane in the Galactic coordinate system. In order to better reveal the rotational asymmetry we choose a new coordinate system (i.e., the right panel) in which the new $z$ axis is the original $x$ axis pointing from sun to the GC.

Figure 4

The spatial distribution of the ICS emission viewed in the coordinate system of $(\theta ,\phi )$. The figures above are offered as an illustration of rotational asymmetry of two count maps in Fig. 2.

Figure 5

The regions of interest adopted in estimating the DOA of the spatial distribution of diffuse $\gamma$-ray emission. The left panel is for ROI I (i.e., $b>0°$, $l>0°$, and $0°<\phi <90°$). The right panel is for ROI II, which is different from ROI I by masking $b<2°$.

Figure 6

The left column presents the count maps of $\gamma$ rays in logarithmic scale in the Galactic coordinate system. And the two kinds of APS illustrated in the right column are in the new coordinate system: the solid line represents $C_l$ while the dotted line stands for $D_l$. We make the maps of count to HEALPIX grids with $\mathrm{NSIDE}=512$ and expand it to $l_{\max }=1024$. Top panel shows results in ROI III for prompt emission of SIDM annihilation while middle panel is for ICS. The bottom panel is same as middle panel except in ROI IV.