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 ^ { 56 } Co decay lines , ^ { 44 } \mbox { Ti } 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 M _ { \odot } progenitors exploding with \sim 1.5 \times 10 ^ { 51 } erg , ejecta structures suitable to reproduce the observations involve a bulk asymmetry of the ^ { 56 } Ni of at least \sim 400 km s ^ { -1 } and a bulk velocity of at least 1500 km s ^ { -1 } .
By adding constraints to reproduce the UVOIR bolometric light curve of SN 1987A up to 600d , an ejecta mass around 14 M _ { \odot } 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 ^ { -1 } .
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 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 .