  Motivated by tension between the predictions of ordinary cold dark matter
(CDM) and observations at galactic scales, ultralight axionlike particles
(ULALPs) with mass of the order $10^{-22}~{\rm eV}$ have been proposed as an
alternative CDM candidate. We consider cold and collisionless ULALPs produced
in the early Universe by the vacuum realignment mechanism and constituting most
of CDM. The ULALP fluid is commonly described by classical field equations.
However, we show that, like QCD axions, the ULALPs thermalize by gravitational
self-interactions and form a Bose-Einstein condensate, a quantum phenomenon.
ULALPs, like QCD axions, explain the observational evidence for caustic rings
of dark matter because they thermalize and go to the lowest energy state
available to them. This is one of rigid rotation on the turnaround sphere. By
studying the heating effect of infalling ULALPs on galactic disk stars and the
thickness of the nearby caustic ring as observed from a triangular feature in
the IRAS map of our galactic disk, we obtain lower-mass bounds on the ULALP
mass of order $10^{-23}$ and $10^{-20}~{\rm eV}$, respectively.
