Dark matter interpretation of the Fermi-LAT observations toward the outer halo of M31

An excess $\gamma$-ray signal toward the outer halo of M31 has recently been reported. Although other explanations are plausible, the possibility that it arises from dark matter (DM) is valid. In this work we interpret the excess in the framework of DM annihilation, using as our representative case WIMP DM annihilating to bottom quarks, and we perform a detailed study of the systematic uncertainty in the $J$-factor for the M31 field. We find that the signal favors a DM particle with a mass of $\sim 45–72\mathrm{GeV}$. While the mass is well constrained, the systematic uncertainty in the cross section spans 3 orders of magnitude, ranging from $\sim 5\times {10}^{-27}–5\times {10}^{-24}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. This high uncertainty is due to two main factors, namely, an uncertainty in the substructure nature and geometry of the DM halos for both M31 and the Milky Way (MW), and correspondingly, an uncertainty in the contribution to the signal from the MW’s DM halo along the line of sight. However, under the conditions that the minimum subhalo mass is $\lesssim {10}^{-6}{M}_{\odot }$ and the actual contribution from the MW’s DM halo along the line of sight is at least $\sim 30\%$ of its total value, we show that there is a large overlap with the DM interpretations of both the Galactic center (GC) excess and the antiproton excess, while also being compatible with the limits for the MW dwarf spheroidals. More generally, we summarize the results from numerous complementary DM searches in the energy range 10 GeV–300 GeV corresponding to the GC excess and identify a region in parameter space that still remains viable for discovery of the DM particle.

Figure 1

The line of sight looking toward M31’s outer halo. The size of M31’s DM halo is indicated with a dashed cyan circle, which corresponds to a projected radius of 300 kpc, for an M31-MW distance of 785 kpc. The dash-dot lime-green circle shows the outer boundary of the SH region ($r_{\tan }=117\mathrm{kpc}$), which we use for the DM fit. M31’s population of satellite galaxies is shown with red open circles. M33 can be seen in the lower left corner. Also plotted are some notable gas clouds in the region, namely, the M31 cloud (orange region surrounding the M31 disk), Wright’s cloud (WC), and Complex H. See text for more details.

Figure 2

Left panel: $\mathrm{\Delta }{\chi }^2$ profile for the three different fit variations: spherical halo (SH): solid black curve; spherical halo north (SHN): dash-dot turquoise curve; spherical halo south (SHS): dashed grey curve. The light grey dotted lines show the 1, 2, and 3 sigma contour levels, for 1 degree of freedom. Right panel: best-fit spectra overlaid to the corresponding data. Arrows give the $1\sigma$ upper limits.

Figure 3

Top panel: concentration-mass relations from Refs. [30], [79], [80], [9], and [81]. Middle panel: different DM density profiles for M31. The region bounded by the red dashed lines corresponds to the SH. Bottom panel: mass dependence of the boost factor for different parameters. The name in the legend specifies the model of the concentration-mass relation, and in parentheses the numbers give (in order) the power of the minimum subhalo mass, the PL index of the subhalo mass function, and the fraction of the halo resolved in substructure. The red dashed lines correspond to the mass range for M31 and the MW.

Figure 4

MW $J$-factors for three different geometries, as indicated above each map. Maps are shown in Galactic coordinates with a Mollweide projection. The corresponding axis ratios are given in Table 1. For the prolate halo $\mathrm{q}=1.67$, and for the oblate halo $\mathrm{q}=0.6$. The color scale ranges from the minimum halo value to $1/10$ the maximum halo value. The DM model is “Einasto high” from Table 2. Note that these particular maps do not show individually resolved substructures, although they are included in the analytical model.

Figure 5

Top: ratio of the $J$-factor ($J$) for different MW halo geometries compared to a spherical halo ($J^{\mathrm{Sph}}$), for an Einasto density profile. Middle: gradient ratio for the $J$-factor calculated with the line of sight centered at three different Galactic latitudes (with $l=121°$). The ratio is calculated with respect to a latitude of $b=-50°$ ($J_{\mathrm{TR}}$), which is comparable to the region used for tuning the isotropic spectrum in Ref. [32]. The middle data points at $l=-21.5°$ correspond to the M31 field. In all cases the $J$-factors are integrated over the region 0.4° to 8.5°, using the Einasto high model from Table 2. Bottom: ratio of the $J$-factor ($J$) for different M31 halo geometries compared to a spherical halo ($J^{\mathrm{Sph}}$), for an Einasto density profile.

Figure 6

$J$-factors for M31 and the MW. The grey band is the $J$-factor uncertainty for M31 from this work. The blue band is the $J$-factor uncertainty for the MW from this work. The markers are the M31 calculations for the NFW (squares) and Einasto (circles) profiles, with the boost factor. Parameters for the different variations are given in Table 2. The solid curves are independent calculations for M31 from Ref. [32] (extending to 14 degrees) and Ref. [47] (extending to 10 deg). Likewise the dashed lines are independent calculations for the MW. The dash-dot lines toward the bottom show the smooth M31 profiles corresponding to the markers. The vertical dotted red lines show the boundaries of M31’s IG, SH, and FOH (the fit is performed over the SH).

Figure 7

DM parameter space. The red and coral data points are for M31’s outer halo. The red data point corresponds to case I, for which $J=J_{\mathrm{MW}}+J_{\mathrm{M}31}$. The coral data point is for case 2, for which $J=J_{\mathrm{M}31}$. The best-fit values for the three fit variations used in this analysis are all very similar, so here we plot the mean, and the error bars show the full systematic uncertainty range. Note that the error bars in the cross section assume that the minimum subhalo mass is ${10}^{-6}{M}_{\odot }$, and they include the uncertainty due to the halo geometry. Contours for the GC excess are shown in black, and contours for the antiproton excess are shown in teal. Numerous limits from other targets are also overlaid, including the MW satellites shown with purple curves, and M31’s inner galaxy shown with a red curve. See Sec. 4 for more details, as well as Appendix.