Role of nuclear physics in oscillations of magnetars

Strong magnetic fields have important effects on the crustal properties of magnetars. Here we study the magnetoelastic oscillations of magnetars, taking into consideration the effect of strong magnetic fields on the crustal composition (magnetized crust). We calculate global magnetoelastic (GME) modes as well as modes confined to the crust (CME) only. The ideal magnetohydrodynamics is adopted for the calculation of magnetoelastic oscillations of magnetars with dipole magnetic fields. The perturbation equations obtained in general relativity using Cowling approximation are exploited here for the study of magnetoelastic oscillations. Furthermore, deformations due to magnetic fields and rotations are neglected in the construction of equilibrium models for magnetars. The composition of the crust directly affects its shear modulus, which we calculate using three different nucleon-nucleon interactions: SLy4, SkM, and Sk272. The shear modulus of the crust is found to be enhanced in strong magnetic fields $\ge {10}^{17}$ G for all those Skyrme interactions. It is noted that the shear modulus of the crust for the SLy4 interaction is much higher than those of the SkM and Sk272 interactions in presence of magnetic fields or not. Though we do not find any appreciable change in frequencies of fundamental GME and CME modes with and without magnetized crusts, frequencies of first overtones of CME modes are significantly affected in strong magnetic fields $\ge {10}^{17}$ G. However, this feature is not observed in frequencies of first overtones of GME modes. As in earlier studies, it is also noted that the effects of crusts on frequencies of both types of magnetoelastic modes disappear when the magnetic field reaches the critical field ($B>4\times {10}^{15}$ G). Frequencies of GME and CME modes calculated with magnetized crusts based on all three nucleon-nucleon interactions, stellar models and magnetic fields, are compared with frequencies of observed quasiperiodic oscillations (QPOs) in SGR 1806-20 and SGR1900+14. As in earlier studies, this comparison indicates that GME modes are essential to explain all the frequencies, as CME modes can explain only the higher frequencies.

Figure 1

Shear modulus as a function of mass density for a neutron star of $1.4M_{\odot }$ with magnetic fields $B_{*}=0$ and $B_{*}={10}^4$ and Skyrme nucleon-nucleon interactions of Table 1.

Figure 2

Frequency of fundamental ($n=0, \ell =2$) CME mode for a neutron star of $1.4M_{\odot }$ is shown as a function of magnetic field $B_{*}=B/B_c$ where $B_c=4.414\times {10}^{13}$ G. Results of our calculations using the SLy4, SkM, and Sk272 nucleon-nucleon interactions are shown here.

Figure 3

Fundamental frequencies ($n=0$) of CME modes are plotted as a function of $\ell$ values with and without magnetic crusts of a $1.4M_{\odot }$ neutron star based on the SLy4, SkM, and Sk272 nucleon-nucleon interactions for $B_{*}={10}^4$.

Figure 4

Frequencies of first overtones ($n=1$) of CME modes are shown as a function of $\ell$ values with and without magnetic crusts of a $1.4M_{\odot }$ neutron star based on the SLy4, SkM, and Sk272 nucleon-nucleon interactions for $B_{*}={10}^4$.

Figure 5

Frequencies of CME modes corresponding to $n=0$ and $\ell =2,3,4$ are plotted as a function of neutron star mass for a magnetic field $B=8\times {10}^{14}$ G using magnetized crusts based on the SLy4, SkM, and Sk272 nucleon-nucleon interactions.

Figure 6

Comparison of the GME frequencies with pure Alfvén frequencies as well as CME frequencies is shown as a function of magnetic field using the magnetized crusts based on the SLy4, SkM, and Sk272 nucleon-nucleon interactions.

Figure 7

GME mode frequencies for $n=0$ are shown as a function of $\ell$ values with and without magnetic crusts of a neutron star of mass $1.4M_{\odot }$ based on the SLy4, SkM, and Sk272 nucleon-nucleon interactions for $B_{*}={10}^4$.

Figure 8

GME mode frequencies for $n=1$ are plotted as a function of $\ell$ values with and without magnetic crusts of a neutron star of mass $1.4M_{\odot }$ based on the SLy4, SkM, and Sk272 nucleon-nucleon interactions for $B_{*}={10}^4$.