Multimessenger constraints on the dark matter interpretation of the $Fermi$-LAT Galactic Center excess

An excess of $\gamma$ rays in the data measured by the Fermi Large Area Telescope in the direction of the Galactic Center has been reported in several publications. This excess, labeled as the Galactic Center excess (GCE), is detected analyzing the data with different interstellar emission models, point source catalogs and analysis techniques. The characteristics of the GCE, recently measured with unprecedented precision, are all compatible with dark matter particles (DM) annihilating in the main halo of our Galaxy, even if other interpretations are still not excluded. We investigate the DM candidates that fit the observed GCE spectrum and spatial morphology. We assume a simple scenario with DM annihilating into a single channel but we inspect also more complicated models with two and three channels. We perform a search for a $\gamma$-ray flux from a list of 48 Milky Way dwarf spheroidal galaxies (dSphs) using state-of-the-art estimation of the DM density in these objects. Since we do not find any significant signal from the dSphs, we put upper limits on the annihilation cross section that result to be compatible with the DM candidate that fits the GCE. However, we find that the GCE DM signal is excluded at the 95% confidence level by the AMS-02 $\overline{p}$ flux data for all purely hadronic (semihadronic) channels unless the diffusive halo size $L$ is smaller than 1.7 kpc (2.6 kpc). Such a small diffusion halo is at the $2\sigma$ significance lower limit for the results inferred from fluxes of radioactive cosmic rays and is in some tension with results from analyses performed with radio and $\gamma$-ray data. Furthermore, AMS-02 $e^{+}$ data rule out the GCE DM interpretation with pure or partial annihilation into $e^{+}{e}^{-}$. The only DM candidate that fits the GCE spectrum and fulfills all constraints obtained with the combined dSphs analysis and the AMS-02 $\overline{p}$ and $e^{+}$ data annihilates purely (or very dominantly) into ${\mu }^{+}{\mu }^{-}$, has a mass of $\sim 60\mathrm{GeV}$ and roughly a thermal cross section.

Figure 1

Flux of $\gamma$ rays produced for prompt (blue dashed line), Bremsstrahlung (dotted green line) and ICS emission from DM particles annihilating into ${\mu }^{+}{\mu }^{-}$, ${\tau }^{+}{\tau }^{-}$ and $b\overline{b}$, from top to bottom panels, for $M_{\mathrm{DM}}=50\mathrm{GeV}$ and $⟨\sigma v⟩=3\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$. We present two cases for the ICS emission with (orange dot-dashed line) and without (red dotted line) accounting for diffusion. We also display the total emission (prompt plus ICS and Bremsstrahlung), with (solid black line) and without (grey dot-dashed line) diffusion and the case with ICS, calculated without diffusion, plus prompt emission (dashed brown line). The case with prompt emission and ICS, calculated without diffusion, is the model we use in the analysis.

Figure 2

Result of the fit to the GCE surface brightness data (black data points) [14] with a DM signal calculated for a gNFW profile with $\gamma =1.2$ (dot-dashed black line) and $\gamma =1.3$ (dotted blue line) and an Einasto profile with $\alpha =0.13$ (red solid line). The error bars refer to the $1\sigma$ statistical uncertainties.

Figure 3

Best-fit for the DM parameters $M_{\mathrm{DM}}$ and $⟨\sigma v⟩$ obtained by fitting the GCE data in Ref. [14]. The values of these data points are reported in Table 2. The green data point labeled with $q\overline{q}$ denotes a DM annihilation channel into the light quarks $u$, $d$, $s$. The error bars represent the variation in the value of the DM mass and cross section obtained by fitting the GCE data obtained with different IEMs.

Figure 4

Best-fit $\gamma$-ray flux obtained with $e^{+}{e}^{-}$ (top panel) and $b\overline{b}$ (bottom panel) annihilation channels (blue dashed line) compared to the GCE data (black data points) reported in Ref. [14]. The error bars are the $1\sigma$ statistical uncertainties for energies between 0.3–70 GeV. Above 70 GeV the 95% confidence level (CL) upper limits are reported. The grey band takes into account the variation in the GCE data found by performing the analysis with different analysis techniques and IEMs.

Figure 5

Flux of $\gamma$ rays from DM particle annihilating into two channels. We show the contribution of both channels and the total flux compared to the GCE flux data.

Figure 6

Same as Fig. 5 leaving free to vary also a renormalization of the ICS contribution. For the case reported in this figure a renormalization of the ICS emission of 0.1 is found from the fit.

Figure 7

$TS$ as a function of mass for the dSphs detected with the highest significance. We also show the $TS$ for the joint likelihood analysis on the dSphs sample and the 68% and 95% containment bands for the random direction runs. We show the results for the ${\tau }^{+}{\tau }^{-}$ (top panel) and $b\overline{b}$ annihilation channels (bottom panel).

Figure 8

95% CL upper limits for $⟨\sigma v⟩$ for the ${\tau }^{+}{\tau }^{-}$ (top panel) and $b\overline{b}$ (bottom panel) annihilation channels found with the dSphs sample in Ref. [27] (black solid line) and Ref. [28] (Albert $+17$, green dashed line). We also show the 68% (yellow band) and 95% (cyan band) containment band for the limits obtained in random directions (read the main text for further details). We report the thermal cross section taken from Ref. [103].

Figure 9

95% CL upper limits for $⟨\sigma v⟩$ for the $b\overline{b}$ annihilation channel for our baseline analysis (Pace&Strigari $+19$ [27], black solid). We also show the limits obtained with the SOURCE IRFs (dashed blue), with a wider ROI of $15°\times 15°$ (red dot-dashed), selecting data above 0.5 GeV (green dotted), and using the dSphs sample from Ref. [28] (Albert $+17$, orange solid).

Figure 10

Comparison between the 95% (red dotted), 90% (blue dot-dashed) and 68% (black dashed) CL upper limits for $⟨\sigma v⟩$ obtained from the analysis of the dSphs in Ref. [27] and the DM candidate that fit the GCE flux data obtained in with different IEMs (green data point). We also display with a green band the variation in $⟨\sigma v⟩$ due to the modeling of the DM density in the inner part of the Galaxy (see Table 1). We display DM annihilating into $b\overline{b}$ and ${\mu }^{+}{\mu }^{-}$, ${\tau }^{+}{\tau }^{-}-b\overline{b}$ and ${\mu }^{+}{\mu }^{-}-{\tau }^{+}{\tau }^{-}-b\overline{b}$ channels.

Figure 11

Antiproton flux (left column) and B/C (right column) obtained in our fits compared to the AMS-02 data. The upper panels show the best fit fluxes for pure secondary production (i.e., no DM contribution). The lower panels show the best fit fluxes if we inject a DM signal compatible with the GCE SED for the $b\overline{b}$ annihilation channel (with the parameters reported in Tab. 2). The MED DM density model and $L=3\mathrm{kpc}$ are assumed. As can be seen, the fit significantly degrades if the DM signal is added. The error bars of the data points refer to the $1\sigma$ statistical uncertainties.

Figure 12

Top: 95% CL upper limits on the DM annihilation cross section found by fitting AMS-02 $\overline{p}$ data and assuming different sizes for $L$. In addition we show the best-fit DM parameters we obtain by fitting the GCE. We assume a $b\overline{b}$ annihilation channel and the MED DM density model. Bottom: same as top panel changing the DM density model to MIN, MED and MAX. The bands we show for the $\overline{p}$ upper limits include the variation in the results changing $L$ from 3 to 5 kpc.

Figure 13

Best-fit values for the DM parameters $M_{\mathrm{DM}}$ and $⟨\sigma v⟩$ that we find by fitting the GCE SED. We show the cases that best-fit the GCE SED from Sec. 3b for which only the errors on $⟨\sigma v⟩$ are reported. We also report the 95% CL upper limits we obtain from $\overline{p}$ flux data for the same DM candidates. We assume the MED DM density model and $L=2$ ($L=3$) kpc for the plot in the top (bottom) panel.

Figure 14

Best-fit values for the DM parameters $M_{\mathrm{DM}}$ and $⟨\sigma v⟩$ that we find by fitting the GCE SED. We show the same cases on Fig. 13 using the cross section into $b\overline{b}$ for both the single and double channels. For the latter cases we calculate the data points as $⟨\sigma v⟩·(1-B_r)$ taking into account the errors on both $⟨\sigma v⟩$ and $(1-B_r)$. We also report the 95% CL upper limits we obtain from $\overline{p}$ flux data using the $b\overline{b}$ channel. We assume the MED DM density model and $L=1.5$, 2.0, 3, 4 kpc (black dashed, solid, dot-dashed and dotted lines).

Figure 15

AMS-02 $e^{+}$ flux data (black data points) fitted in the optimistic approach with an analytic function (black solid line) given by sum of a LogParabola (LP, grey dotted line) and a power-law with an exponential cutoff (PLE, orange dotted line). We also show the secondary flux of $e^{+}$ calculated using the best-fit propagation parameters in Table 5 and $L=1.5$, 4, 6 kpc (red, blue and green line). The bands for each case represent the variation in the secondary flux by assuming a Fisk potential variation between 0.62–0.82 GV.

Figure 16

Best-fit values for the DM parameters $M_{\mathrm{DM}}$ and $⟨\sigma v⟩$ that we find by fitting the GCE SED. We show the cases that best-fit the GCE SED from Sec. 3b. We also report the 95% CL upper limits we obtain from $e^{+}$ flux data for the same DM candidates with the conservative (upper panel) and optimistic methods (central and bottom panels). We assume the MED DM density model and $L=4\mathrm{kpc}$ for the first two panels and $L=1.5\mathrm{kpc}$ for the bottom panel.