Constraining properties of high-density matter in neutron stars with magneto-elastic oscillations

We discuss torsional oscillations of highly magnetized neutron stars (magnetars) using two-dimensional, magneto-elastic-hydrodynamical simulations. Our model is able to explain both the low-and high-frequency quasi-periodic oscillations (QPOs) observed in magnetars. The analysis of these oscillations provides constraints on the breakout magnetic-field strength, on the fundamental QPO frequency, and on the frequency of a particularly excited overtone. By performing a new set of simulations, we are able to derive for the first time empirical relations for a self consistent model including a superfluid core which describe these constraints quantitatively. We use these relations to generically constrain properties of high-density matter in neutron stars, employing Bayesian analysis. In spite of current uncertainties and computational approximations, our model-dependent Bayesian posterior estimates for SGR 1806-20 yield a magnetic-field strength (B) over bar similar to 2.1(-1.0)(+1.3) x 10(15) G and a crust thickness of Delta r = 1.6(-0.6)(+0.7) km, which are both in remarkable agreement with observational and theoretical expectations, respectively (1 sigma error bars are indicated). Our posteriors also favour the presence of a superfluid phase in the core, a relatively low stellar compactness, M/R < 0.19, indicating a relatively stiff equation of state and/or low-mass neutron star, and high shear speeds at the base of the crust, c(s) > 1.4 x 10(8) cm s(-1). Although the procedure laid out here still has large uncertainties, these constraints could become tighter when additional observations become available.