Magnetic fields in late-stage proto-neutron stars

ABSTRACT We explore the thermal and magnetic field structure of a late-stage proto-neutron star (proto-NS). find dominant contribution to entropy in different regions star, from which we build simplified equation state (EOS) for hot neutron (NS). With this, numerically solve stellar equilibrium equations range models, including fields rotation up Keplerian velocity. approximate EOS as barotrope, discuss validity this assumption. For fixed strength, induced ellipticity increases with temperature; give quantitative formulae this. The velocity is considerably lower hotter stars, may set de facto maximum rate non-recycled NSs well below 1 kHz. Magnetic stronger than around 1014 G have qualitatively similar states both cold NSs, large-scale simple poloidal component dominating over toroidal one; argue result be universal. show that truncating solutions at low multipoles leads serious inaccuracies, especially models rapid or strong toroidal-field component.