On the quasi-periodic oscillations in magnetars

Abstract

We study torsional Alfvén oscillations of magnetars, that is neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system (X, Y), where and and a1 is the radial component of the magnetic field. In this coordinate system, the one+two‐dimensional evolution equation describing the quasi‐periodic oscillations (QPOs), see Sotani et al., is reduced to a one+one‐dimensional equation where the perturbations propagate only along the y‐axis. We solve the one+one‐dimensional equation for different boundary conditions and the open magnetic field lines, that is magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field as well as closed magnetic lines, i.e. magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPO frequencies: a family of ‘lower’ QPO frequencies which is located near the x‐axis and a family of ‘upper’ frequencies located near the y‐axis. According to Levin, the fundamental frequencies of these two families can be interpreted as the turning point of the continuous spectrum. We find that the upper frequencies are multiples of the lower ones by a constant equalling 2n+ 1. For the closed lines, the corresponding factor is n+ 1. By using these relations, we can explain both the lower and the higher observed frequencies in SGR 1806−20 and SGR 1900+14.

Bayesian timing analysis of giant flare of SGR 180620 by RXTE PCA

“…Those QPO frequencies are also detected by us. In addition, we have detected several more QPO frequencies (21, 59, and 116 Hz) with the Bayesian method, which were also predicted by Colaiuda et al (2009). signal has a higher significance in a subinterval of the considered time interval and the fast convergence of the MCMC procedure already provided.…”

“…In particular, by studying Alfvén oscillations, in the stellar interior and in the absence of crust, Colaiuda et al (2009) could reveal the existence of Alfvén continua (as suggested by Levin 2007). The edges of this continuum have been used to explain the observed QPOs.…”

“…This has been demonstrated from the recent theoretical results for the QPOs, which have been interpreted as magneto-elastic oscillations. These calculations have shown how the observations constrain the mass, the radius, the thickness of the crust, and the strength of magnetic field of these stars (Sotani et al 2007;Samuelsson & Andersson 2007;Colaiuda et al 2009;Cerdá-Durán et al 2009), while one could even set severe constrains in the geometry of the interior magnetic field (see Sotani et al 2008a). …”

“…These oscillations have been interpreted initially as torsional oscillations of the crust (Samuelsson & Andersson 2007;Sotani et al 2007), while later the Alfvén oscillations of the fluid core have been taken into account (Levin 2007;Sotani et al 2008b;Colaiuda et al 2009;Cerdá-Durán et al 2009;Hoven & Levin 2011;Gabler et al 2011;Colaiuda & Kokkotas 2010). These studies suggest how the observations can constrain the mass, the radius, the thickness of the crust, and the strength of magnetic field of NSs.…”

Shear oscillations in the hadron–quark mixed phase

“…Since the central objects in SGRs are considered to be magnetars which are strongly magnetized neutron stars, the discovered QPOs in giant flares could be due to neutron star oscillations. In order to explain these QPO frequencies theoretically, a lot of numerical attempts have been done not only by the shear oscillations in the crust of neutron stars but also by the magnetic oscillations [17,18,19,20,21,22,23,24,25,26,27]. In addition, ascribing the observed QPOs to shear oscillations in the crust of neutron stars, the possibilities are also pointed out to reveal the properties of inhomogeneous nuclear matter in the crust [28,29,30,31,32].…”