Requirements to detect the monoenergetic photon signature of thermal cold dark matter in PeV-scale split supersymmetry

Split supersymmetry scenarios with PeV-scale scalar masses circumvent many of the restrictions on supersymmetry coming from experimental limits on $CP$ violation, flavor-changing neutral currents, and the Higgs boson mass. We consider the situation where the lightest supersymmetric particle is either a $W$-ino or Higgsino and the majority of its cold dark-matter relic density is of thermal origin, in which case its mass is specified to be 2.3 TeV for a $W$-ino or 1.1 TeV for a Higgsino. We examine the potential for indirect detection, at present and future $\gamma$-ray telescopes, of the monoenergetic photon lines that would result from the annihilation of these particles near the galactic center. We show how the possibility for detection depends on the precise form of the galactic dark-matter halo profile and examine what performance attributes a $\gamma$-ray detector would need in order to register a $5\sigma$ discovery.