Magnetic collapse of a neutron gas: Can magnetars indeed be formed?

Abstract

A relativistic degenerate neutron gas in equilibrium with a background of electrons and protons in a magnetic field exerts its pressure anisotropically, having a smaller value perpendicular than along the magnetic field. For critical fields the magnetic pressure may produce the vanishing of the equatorial pressure of the neutron gas. Taking it as a model for neutron stars, the outcome could be a transverse collapse of the star. This fixes a limit to the fields to be observable in stable neutron star pulsars as a function of their density. The final structure left over after the implosion might be a mixed phase of nucleons and meson condensate, a strange star, or a highly distorted black hole or black "cigar", but no any magnetar, if viewed as a super strongly magnetized neutron star. However, we do not exclude the possibility of a superstrong magnetic fields arising in supernova explosions which lead directly to strange stars. In other words, if any magnetars exist, they cannot be neutron stars.

A non-perturbative study of the evolution of cosmic magnetised sources

“…The classical Maxwellian contribution B 2 produces a decelerated fluid expansion in the direction of the magnetic field (z), as the latter produces a negative pressure or tension in its direction, and an accelerated expansion in the directions perpendicular to it due to a positive pressure. However, we obtain the opposite effect from the statistical contribution of B in the equation of state for the magnetised electron-positron gas mixture: the pressure in the direction parallel to the field increases and that in the perpendicular direction decreases [39,40,46,51]. Although the dominant effect in the dynamics comes from the contribution B 2 , we can observe that including the magnetised electron-positron gas leads to a slight acceleration of the cosmic rate of expansion.…”

“…Instead of considering idealised fluids whose interaction with the magnetic field is unspecified (as in [32,33,34,35,36]), or a collision-less kinetic theory approach (suited to free streaming collision-less conditions as in [37]), we consider fluid sources that satisfy physically motivated equations of state that are well suited for an early Universe cosmic fluid interacting with a magnetic field within a hydrodynamical regime, namely: a mixture of ideal gasses of magnetised fermions [39,40,41] whose equation of state reflects the full anisotropic effects of the magnetic field. Evidently, this field introduces anisotropic momentum fluxes that modify the energy-momentum tensor and thus affect the evolution of the state variables.…”

Dynamics of a self-gravitating neutron source

“…where the first term in the right hand side is the statistical contribution and the second is the vacuum contribution [9]. Explicitly, we have…”

“…which is divergent, but can be renormalized, and for fields of intensity B < 10 18 G its contribution is not important [9], hence we will neglect this term in the remaining of the present article. Equation (2.8) can be easily integrated in the case that concerns us (T = 0), leading to…”

“…the well known Pauli Paramagnetism). The choice η = ±1, [9] is equivalent to consider different phases of the system. The appearance of the threshold of the value of the magnetic field for each one of these cases can be seen if we analyze the expressions of the functions f η and s η in (2.11).…”