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We present an analysis of highly magnetized neutron stars "magnetars", insearch for high frequency oscillations in the recurrent emission from the softgamma repeater SGR 1806-20, and we discuss the physical interpretation of theseoscillations and its implications on the neutron star properties and structure.We present evidence for Quasi-Periodic Oscillations (QPOs) in the recurrentoutburst activity from SGR 1806-20 using RXTE observations. By searching fortiming signals at the frequencies of the QPOs discovered in the 2004 December27 giant flare from the source, we find three QPOs at 84, 103, and 648 Hz inthree 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 liewithin 3.75% from the 625 Hz QPO also detected in the same flare. The detectedQPOs are found in bursts with different durations, morphologies, andbrightness, and are vindicated by Monte Carlo simulations. We also findevidence for candidate QPOs at higher frequencies in other bursts with lowerstatistical significance. The fact that we can find evidence for QPOs in therecurrent bursts at frequencies relatively close to those found in the giantflare is intriguing and can offer insight about the origin of the oscillations.We confront our findings against the available theoretical models and discussthe physical interpretation of these QPOs. The leading interpretation for theorigin of magnetar QPOs suggests that these toroidal seismic oscillatory modesare most likely to be excited by a crustquake of the neutron star crust. Othermodels have been proposed to explain the magnetar QPO phenomena includingmagnetospheric oscillations, magnetic flux tubes and modes of a passive debrisdisk. Theoretical modeling and observation of QPOs will be very useful inputting stringent constraints on neutron star equation of state.

Evidence for Quasi-Periodic Oscillations in the Recurrent Emission from  Magnetars and their Implications on the Neutron Star Properties and Equation  of State