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We consider multi-messenger constraints on very heavy dark matter (VHDM) fromrecent Fermi gamma-ray and IceCube neutrino observations of isotropicbackground radiation. Fermi data on the diffuse gamma-ray background (DGB)shows a possible unexplained feature at very high energies (VHE), which we havecalled the "VHE Excess" relative to expectations for an attenuated power lawextrapolated from lower energies. We show that VHDM could explain this excess,and that neutrino observations will be an important tool for testing thisscenario. More conservatively, we derive new constraints on the properties ofVHDM for masses of 10^3-10^10 GeV. These generic bounds follow from cosmicenergy budget constraints for gamma rays and neutrinos that we developedelsewhere, based on detailed calculations of cosmic electromagnetic cascadesand also neutrino detection rates. We show that combining both gamma-ray andneutrino data is essential for making the constraints on VHDM properties bothstrong and robust. In the lower mass range, our constraints on VHDMannihilation and decay are comparable to other results; however, ourconstraints continue to much higher masses, where they become relativelystronger.

Constraining Very Heavy Dark Matter Using Diffuse Backgrounds of Neutrinos and Cascaded Gamma Rays