Amplification of neutron star magnetic fields by thermoelectric effects. VI. Analytical approach.

Details Amplification of neutron star magnetic fields by thermoelectric effects. VI. Analytical approach. Amplification of neutron star magnetic fields by thermoelectric effects. VI. Analytical approach.

May 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...309..203w&link_type=abstract

Astronomy and Astrophysics, v.309, p.203-212

Astronomy and Astrophysics

Astrophysics

22

Neutron Star, Stars: Magnetic Fields

Scientific paper

From numerical calculations in previous papers it is known that in young, hot neutron stars small-scale toroidal magnetic field modes can be amplified. This amplification was discussed as a first step of a scenario, where the typical 10^12^-10^13^G dipole magnetic field of pulsars is generated after the birth of neutron stars. Two physical effects - the thermo-Hall effect and the thermoelectric effect - are responsible for this phenomenon. The numerical calculations show that the growing magnetic field is concentrated in a thin layer (less than 100m thick) just below the neutron star surface (less than 100m deep). The growth rate is in the order of years and reaches its maximum for multipolarities n =~1000, what is equivalent to sinus-like field variations with meridional wavelengths of =~100m. By applying an analytical approximation (the magnetic field and temperature functions are assumed to be Gauss functions of the depth z) we derive simple formulas for the maximum position and width of the magnetic field and temperature functions, which show the dependence of these parameters on the material quantities like heat and electric conductivities and on input parameters like the neutron star's mass and radius, the surface temperature and the multipolarity. Moreover, an analytical formula for the growth rate as a function of n is found, demonstrating the competition of different physical effects and confirming qualitatively the results of previous numerical calculations. Finally, a general criterion is found: The thermoelectric field amplification acts as long as T_s6_^4^/g_s14_>100 (T_s6_ - surface temperature in 10^6^K, g_s14_ - surface gravity in 10^14^cm/s^2^)

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