  Solitonic boson stars are stable objects made of a complex scalar field with
a compactness that can reach values comparable to that of neutron stars. A
recent study of the collision of identical boson stars produced only
non-rotating boson stars or black holes, suggesting that rotating boson stars
may not form from binary mergers. Here we extend this study to include an
analysis of the gravitational waves radiated during the coalescence of such a
binary, which is crucial to distinguish these events from other binaries with
LIGO and Virgo observations. Our studies reveal that the remnant's
gravitational wave signature is mainly governed by its fundamental frequency as
it settles down to a non-rotating boson star, emitting significant
gravitational radiation during this post-merger state. We calculate how the
waveforms and their post-merger frequencies depend on the compactness of the
initial boson stars and estimate analytically the amount of energy radiated
after the merger.
