  Ultralight bosonic fields in the mass range $\sim (10^{-20}-10^{-11})\,{\rm
eV}$ can trigger a superradiant instability that extracts energy and angular
momentum from an astrophysical black hole with mass $M\sim(5,10^{10})M_\odot$,
forming a nonspherical, rotating condensate around it. So far, most studies of
the evolution and end-state of the instability have been limited to initial
data containing only the fastest growing superradiant mode. By studying the
evolution of multimode data in a quasi-adiabatic approximation, we show that
the dynamics is much richer and depend strongly on the energy of the seed, on
the relative amplitude between modes, and on the gravitational coupling. If the
seed energy is a few percent of the black-hole mass, a black hole surrounded by
a mixture of superradiant and nonsuperradiant modes with comparable amplitudes
might not undergo a superradiant unstable phase, depending on the value of the
boson mass. If the seed energy is smaller, as in the case of an instability
triggered by quantum fluctuations, the effect of nonsuperradiant modes is
negligible. We discuss the implications of these findings for current
constraints on ultralight fields with electromagnetic and gravitational-wave
observations.
