Amplification of neutron star magnetic fields by thermoelectric effects. IV. Averaged small-scale modes and selection rules for large-scale modes.

Details Amplification of neutron star magnetic fields by thermoelectric effects. IV. Averaged small-scale modes and selection rules for large-scale modes. Amplification of neutron star magnetic fields by thermoelectric effects. IV. Averaged small-scale modes and selection rules for large-scale modes.

Feb 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...294..303w&link_type=abstract

Astronomy and Astrophysics 294, 303-312 (1995)

Astronomy and Astrophysics

Astrophysics

6

Stars: Neutron, Stars: Evolution, Stars: Magnetic Fields

Scientific paper

The investigation of neutron star magnetic field evolution driven by thermoelectric effects is continued. As in previous papers the magnetic field is assumed to be located in the liquid layer of the neutron star's envelope. The main result obtained until now was a rapid growth of small-scale toroidal fields with multipolarities in the order of n=~1000. Large-scale fields (like dipole or quadrupole modes) which decay in linear approximation, can, in general, be amplified by nonlinear interaction with small-scale modes. Two difficulties arise in this problem: (i) the handling of a large number of small-scale modes to be taken into account, and (ii) the as a matter of principle unknown structure of the seed field. The problem is solved by introducing averaged small-scale modes, which get the structure of an individual axisymmetric mode. As initial conditions we assume chaotically distributed relative weights for the individual small-scale modes. The nonlinear interaction between different modes is analysed analytically. When restricting the problem to the diagonal (and strongest) part of the interaction coefficients, it is found that poloidal magnetic fields cannot be amplified, not even in the most general, non-axisymmetric formalism. Toroidal fields can be induced by the nonlinear interaction, if any axis is physically distinguished by the initial conditions. The axisymmetric coupling rules hold approximately in the non-axisymmetric theory. The result is a preferred induction of axisymmetric, toroidal large-scale modes with even multipolarity (for instance, the quadrupole mode), while the induction of all other large-scale modes (odd-n modes, like dipole mode; even-n, non-axisymmetric modes; poloidal components) is strongly suppressed within the present model.

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