We perform multi-dimensional, time-dependent radiation transfer simulations for hard X-ray and gamma-ray emissions, following radioactive decays of 56Ni and 56Co, for two-dimensional delayed detonation models of Type Ia supernovae (SNe Ia). The synthetic spectra and light curves are compared with the sensitivities of current and future observatories for an exposure time of 10^6 seconds. The non-detection of the gamma-ray signal from SN 2011fe at 6.4 Mpc by SPI on board INTEGRAL places an upper limit for the mass of 56Ni of lesssim 1.0 Msun, independently from observations in any other wavelengths. Signals from the newly formed radioactive species have not been convincingly measured yet from any SN Ia, but the future X-ray and gamma-ray missions are expected to deepen the observable horizon to provide the high energy emission data for a significant SN Ia sample. We predict that the hard X-ray detectors on board NuStar (launched in 2012) or ASTRO-H (scheduled for launch in 2014) will reach to SNe Ia at sim15 Mpc, i.e., one SN every few years. Furthermore, according to the present results, the soft gamma-ray detector on board ASTRO-H will be able to detect the 158 keV line emission up to sim25 Mpc, i.e., a few SNe Ia per year. Proposed next generation gamma-ray missions, e.g., GRIPS, could reach to SNe Ia at sim20 - 35 Mpc by MeV observations. Those would provide new diagnostics and strong constraints on explosion models, detecting rather directly the main energy source of supernova light.
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