  We present an analysis of highly magnetized neutron stars "magnetars", in
search for high frequency oscillations in the recurrent emission from the soft
gamma repeater SGR 1806-20, and we discuss the physical interpretation of these
oscillations and its implications on the neutron star properties and structure.
We present evidence for Quasi-Periodic Oscillations (QPOs) in the recurrent
outburst activity from SGR 1806-20 using RXTE observations. By searching for
timing signals at the frequencies of the QPOs discovered in the 2004 December
27 giant flare from the source, we find three QPOs at 84, 103, and 648 Hz in
three different bursts. The first two QPOs lie within 8.85% and 11.83%,
respectively, from the 92 Hz QPO detected in the giant flare. The third QPO lie
within 3.75% from the 625 Hz QPO also detected in the same flare. The detected
QPOs are found in bursts with different durations, morphologies, and
brightness, and are vindicated by Monte Carlo simulations. We also find
evidence for candidate QPOs at higher frequencies in other bursts with lower
statistical significance. The fact that we can find evidence for QPOs in the
recurrent bursts at frequencies relatively close to those found in the giant
flare is intriguing and can offer insight about the origin of the oscillations.
We confront our findings against the available theoretical models and discuss
the physical interpretation of these QPOs. The leading interpretation for the
origin of magnetar QPOs suggests that these toroidal seismic oscillatory modes
are most likely to be excited by a crustquake of the neutron star crust. Other
models have been proposed to explain the magnetar QPO phenomena including
magnetospheric oscillations, magnetic flux tubes and modes of a passive debris
disk. Theoretical modeling and observation of QPOs will be very useful in
putting stringent constraints on neutron star equation of state.
