Neutron stars are the remnants of the supernova explosion of massive stars (Fig. 1), and they are the most compact stars in the universe. Their mass of one to two solar masses is confined under the influence of their own gravity to an almost perfect sphere of about 10 km radius, i.e. the density inside a neutron star exceeds even that of an atomic nucleus. These conditions cannot be produced on Earth. If we want to improve our knowledge of the matter and the interactions between the smallest constituents of matter such as neutrons, protons, electrons, muons, but also, hyperons and quarks, we need to understand the structure of neutron stars (Fig. 2). In this respect a particular class of neutron stars called magnetars plays a special role.

Magnetars are the strongest magnets in the Universe. Estimates indicate that they could reach magnetic fields with a strength at the surface of up to some 10¹⁵ Gauss, which would make them about 100 billion times stronger than the strongest magnetic fields on the solar surface (to say nothing of Earth). Sometimes magnetars produce giant gamma-ray bursts, which are thought to arise from a catastrophic reorganization of their magnetic field. During these outbreaks astronomers observe a number of discrete frequencies in the associated X-ray spectrum, which should come from pulsations of the star itself according to established models. Therefore, these observations would be the first evidence of oscillations in neutron stars and one could use them to study their structure. This asteroseismology would be analogous to seismology on Earth or helioseismology on the Sun.

The magnitudes of the observed frequencies fit well with torsional, elastic shear oscillations in the crust of neutron stars. As the exact pulsation frequencies depend on the properties of the matter in the crust, these frequencies can tell us about the state of this matter. But not all pulsations can be explained as shear pulsations. The frequencies of the so-called Alfvén oscillations caused by the magnetic field are in the observed frequency range as well (for magnetic fields from 10¹⁴ to 10¹⁵ Gauss). These Alfvén oscillations are not confined to the solid crust, but also provide information on the composition of the liquid core of the neutron star.

In his PhD thesis at the Max Planck Institute for Astrophysics, Michael Gabler together with colleagues at other institutions developed a model that combines these two types of pulsations. The properties of the coupled system can be investigated by relativistic magneto-hydrodynamic simulations. It turns out that the coupling strength and the resulting magneto-elastic oscillations depend on the magnetic field strength: For weak magnetic fields shear oscillations dominate are present in the crust, while for strong fields Alfvén oscillations dominate. In the interesting range of about 10¹⁵ Gauss, the purely elastic pulsations in the crust are absorbed very efficiently by the Alfvén oscillations of the core. Therefore, only coupled (i.e. magneto-elastic) pulsations, whose frequencies are in good agreement with the observed values, can explain the observations.

In order to observe the oscillations, they have to modulate the intensity of the electromagnetic radiation emitted by the neutron star. A model (Fig. 3) describes the coupling of the magnetic field inside the star to the field of the magnetosphere around the star. Because of the coupling, the external magnetic field oscillates as well, inducing very strong electric currents in the magnetosphere. Photons emitted by the star or in the gamma-ray burst are scattered by the electrical charge carriers (electrons and positrons) of these currents. This resonant cyclotron scattering is very effective and can explain the observed modulation of hard X-rays, as has been shown in Monte Carlo simulations. The X-ray or gamma-ray spectra, which were calculated using the core-crust-magnetosphere model, will be very useful for the design of new X-ray observatories .

Note

For his dissertation "Coupled core-crust-magnetosphere oscillations of magnetars" Michael Gabler received the PhD Award 2012 of the Excellence Cluster Universe in the category "Theory".

Michael Gabler and Ewald Müller

References

PhD thesis, Michael Gabler, TU München, Nov. 2011

Gabler, M., Cerdá-Durán, P., Font, J.A., Müller, E., Stergioulas, N; accepted by MNRAS , arXiv:1208.6443

Gabler, M., Cerdá-Durán, P., ,Stergioulas, N, Font, J.A., Müller, E.; MNRAS 2012, 411, arXiv:1109.6233

Gabler, M., Cerdá-Durán, P., Font, J.A., Müller, E., Stergioulas, N.; MNRAS 2011, 410L, arXiv:1007.0856