  Comparison of theoretical line profiles to observations provides important
tests for supernova explosion models. We study the shapes of radioactive decay
lines predicted by current 3D core-collapse explosion simulations, and compare
these to observations of SN 1987A and Cas A. Both the widths and shifts of
decay lines vary by several thousand kilometers per second depending on viewing
angle. The line profiles can be complex with multiple peaks. By combining
observational constraints from 56Co decay lines, 44Ti decay lines, and Fe IR
lines, we delineate a picture of the morphology of the explosive burning ashes
in SN 1987A. For M_ZAMS=15-20 Msun progenitors exploding with ~1.5 *10^51 erg,
ejecta structures suitable to reproduce the observations involve a bulk
asymmetry of the 56Ni of at least ~400 km/s and a bulk velocity of at least
~1500 km/s. By adding constraints to reproduce the UVOIR bolometric light curve
of SN 1987A up to 600d, an ejecta mass around 14 Msun is favoured. We also
investigate whether observed decay lines can constrain the neutron star (NS)
kick velocity. The model grid provides a constraint V_NS > V_redshift, and
applying this to SN 1987A gives a NS kick of at least 500 km/s. For Cas A, our
single model provides a satisfactory fit to the NuSTAR observations and
reinforces the result that current neutrino-driven core-collapse SN models can
achieve enough bulk asymmetry in the explosive burning material. Finally, we
investigate the internal gamma-ray field and energy deposition, and compare the
3D models to 1D approximations.
