Detail of spectral power density derived from auto-correlation function of d/dt(SST) for Indian Ocean. (ICOADS STT).
The magnitude of this peak in a broader context can be seen here:
The circa 9y peak is close to half the period of precession of the lunar orbital plane. (Nodal precession).
Contrary to extra tropical oceans this does not seem to be combined with the 8.85 year cycle.
Examination of cross-correlation of tropical and extra-tropical Indian Ocean shows this results form warmer water being drawn out of the tropics:
The above link gived details about the data source and processing.