  We derive, from the work of M. Ratner on joinings of time-changes of
horocycle flows and from the result of the authors on its cohomology, the
property of orthogonality of powers for non-trivial smooth time-changes of
horocycle flows on compact quotients. Such a property is known to imply P.
Sarnak's M\"obius orthogonality conjecture, already known for horocycle flows
by the work of J. Bourgain, P. Sarnak and T. Ziegler.
