Multimessenger constraints on the annihilating dark matter interpretation of the positron excess

The rise in the energy spectrum of the positron ratio, observed by the PAMELA satellite above 10 GeV, and other cosmic-ray measurements, have been interpreted as a possible signature of dark matter annihilation in the Galaxy. However, the large number of free parameters, and the large astrophysical uncertainties, make it difficult to draw conclusive statements about the viability of this scenario. Here, we perform a multiwavelength, multimessenger analysis, that combines in a consistent way the constraints arising from different astrophysical observations. We show that if standard assumptions are made for the distribution of dark matter (we build models on the recent Via Lactea II and Aquarius simulations) and the propagation of cosmic rays, current dark matter models cannot explain the observed positron flux without exceeding the observed fluxes of antiprotons or gamma-ray and radio photons. To visualize the multimessenger constraints, we introduce “star plots,” a graphical method that shows in the same plot theoretical predictions and observational constraints for different messengers and wavelengths.

Figure 1

The quantity $N_{\mathrm{cl}}⟨\xi {⟩}_M$ as a function of $M_{\min }$ for Via Lactea II (solid red line) and Aquarius (dashed blue line). The vertical line indicates the value used throughout the rest of the present work, $M_{\min }={10}^{-6}{M}_{\odot }$.

Figure 2

The Sommerfeld-enhanced fluxes $(1-f_{\odot }{)}^{2}S(v_{\odot }){\varphi }_{\mathrm{sm}}^0$ and $S_{\max }⟨{\varphi }_{\mathrm{cl}}^0⟩$ of positrons and antiprotons for the MDM3 candidate. Solid red (dashed blue) lines refer to Via Lactea II (Aquarius) density profiles. The thick (thin) curves represent the smooth (clumpy) contribution. The MED propagation model is adopted and $M_{\min }={10}^{-6}{M}_{\odot }$.

Figure 3

The smooth quantity $(1-f_{\odot }{)}^{2}S(v_{\odot }){\varphi }_{\mathrm{sm}}^0$ for the MDM3 candidate using the M2 (dot-dashed), MIN (dotted), MED (solid), and MAX (dashed) propagation models. For clarity, the clumpy component is omitted and just the results for Via Lactea II are plotted.

Figure 4

Total positron and antiproton fluxes at 50 GeV for the models in Table  and for both Via Lactea II and Aquarius parameters. The MED propagation is used and $M_{\min }={10}^{-6}{M}_{\odot }$. The solid lines indicate the fluxes deduced from PAMELA data assuming electron and proton fluxes at 50 GeV—see Eqs. (11, 12)—and the corresponding excluded regions are shown as shaded. Candidates lying above the diagonal line cannot be rescaled to explain PAMELA positron excess without overproducing antiprotons.

Figure 5

The $\gamma$-ray flux above 160 GeV as a function of the angle $\psi$ with respect to the GC. The legend in the figures is ordered according to the values of the curves at $\psi =0.1°$. The HESS measurement towards the GC is shown by the horizontal thick line and the table shows the fluxes for $\psi =0°$.

Figure 6

Number of photons above 3 GeV from unresolved subhalos at a Galactic longitude $l=0°$ for Via Lactea II and Aquarius parameters. Again, we fix $M_{\min }={10}^{-6}{M}_{\odot }$. Shown in the thick solid lines are the EGRET map for diffuse background as well as the smooth approximation of Ref. 53, both scaled to Fermi results.

Figure 7

The radio flux for case 1 (2) and Via Lactea II (Aquarius) parameters against the positron flux at 50 GeV already presented in Fig. 4. The MED propagation is used and $M_{\min }={10}^{-6}{M}_{\odot }$. The horizontal line indicates the measured flux (see 52 for details). Similarly to Fig. 4, candidates lying above the diagonal line cannot be rescaled to explain PAMELA positron excess without violating radio bounds. Shaded regions are excluded by PAMELA (assuming the electron fluxes discussed in the text) and radio observations.

Figure 8

Multimessenger bounds for several DM candidates. The MED propagation is used and $M_{\min }={10}^{-6}{M}_{\odot }$. The $e^{+}$, $\overline{p}$, $\gamma$ ray, radio (cases 1 and 2) axes are normalized to ${\varphi }_{e^{+}}(50\mathrm{GeV})=7.35\times {10}^{-9}{\mathrm{GeV}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$, ${\varphi }_{\overline{p}}(50\mathrm{GeV})=5.2\times {10}^{-9}{\mathrm{GeV}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$, ${\varphi }_{\mathrm{MW}}(\psi =0°)=1.89\times {10}^{-11}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, 0.05 Jy, and 121 Jy, respectively. The boxes encompass the values in Eqs. (11, 12) for positrons and antiprotons, and a 20% uncertainty on top of the HESS measurement for $\gamma$ rays. Notice that changing the value of $({\sigma }_{\mathrm{ann}}v{)}_0$ leads to an overall scaling of the polygon.