The gamma-ray light curves and spectra are presented for a set of theo
retical Type Ta supernova (SN Ia) models including deflagration, deton
ation, delayed detonation, and pulsating delayed detonations of Chandr
asekhar-mass white dwarfs, as well as merger scenarios that may involv
e more than the Chandrasekhar mass and helium detonations Of sub-Chand
rasekhar-mass white dwarfs. The results have been obtained with a Mont
e Carlo radiation transport scheme that takes into account all relevan
t gamma-transitions and interaction processes, The result is a set of
accurate line profiles that are characteristic of the initial Ni-56 ma
ss distribution of the supernova models. The gamma-rays probe the isot
opic rather than merely the elemental distribution of the radioactive
elements in the ejecta. Details of the line profiles (including the li
ne width, shift with respect to the rest frame, and line ratios) are d
iscussed. With sufficient energy and temporal resolution, different mo
del scenarios can clearly be distinguished. Observational strategies a
re discussed for current and immediately upcoming generations of satel
lites (Compton Gamma Ray Observatory [CGRO] and International Gamma-Ra
y Astrophysical Laboratory [INTEGRAL]), as well as projected future mi
ssions including presently unavailable equipment such as Laue telescop
es, With CGRO, it is currently possible with sufficiently early observ
ations (near optical maximum) to distinguish helium detonations from e
xplosions of Chandrasekhar-mass progenitors and of those involving mer
gers up to a distance of about 15 Mpc. This translates into one target
of opportunity every 8 years. SNe Ia up to about 10 Mpc would allow d
etailed CGRO studies of line ratios of Co-56 lines. INTEGRAL will be a
ble to perform detailed studies of the Co-56 line profiles with a rang
e comparable to CGRO, The superior sensitivity of INTEGRAL for low ene
rgies makes detection and detailed study of the positron annihilation
line and appropriate low-energy Ni-56 lines possible up to about 10-15
Mpc for all models. This capability means that this lower energy rang
e may be the most useful for INTEGRAL detection and study of SNe Ia. S
uch studies will allow the determination of the precise time of the ex
plosion. Whereas the current generation of gamma-ray detectors will al
low the study of supernovae that are discovered by other means, a new
generation of proposed gamma-ray detectors with sensitivity of about 1
0(-6) photons s(-1) cm(-2) would generate the opportunity to discover
supernovae by their ii-ray emission up to a distance of approximate to
100 Mpc. This would allow a systematic study of the variety of SNe Ia
in terms of their gamma-ray properties, independent of their optical
properties. In addition, since gamma-rays are not obscured by the host
galaxy, such experiments would, for the first time, provide absolute
supernova rates. Relative rates as a function of the morphology of and
position in the host galaxy could be studied directly.