Equation of state of a dense and magnetized fermion system

Abstract

The equation of state of a system of fermions in a uniform magnetic field is obtained in terms of the thermodynamic quantities of the theory by using functional methods. It is shown that the breaking of the O(3) rotational symmetry by the magnetic field results in a pressure anisotropy, which leads to the distinction between longitudinal-and transverse-to-the-field pressures. A criterion to find the threshold field at which the asymmetric regime becomes significant is discussed. This threshold magnetic field is shown to be the same as the one required for the pure field contribution to the energy and pressures to be of the same order as the matter contribution. A graphical representation of the field-dependent anisotropic equation of state of the fermion system is given. Estimates of the upper limit for the inner magnetic field in self-bound stars, as well as in gravitationally bound stars with inhomogeneous distributions of mass and magnetic fields, are also found.

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

“…However, leptons and baryons could interact with the field through their charges (if they are charged) and via their anomalous magnetic moment (if they are neutral). In any case the interactions with the field (via charges or anomalous magnetic moment) lead to a momentum-energy tensor with anisotropic stresses [39,41]. We assume hereafter that the only particle species interacting with the magnetic field are electrons and positrons (charged leptons), protons (charged baryons) and neutrons (neutral baryons).…”

“…In general the equation of state for these species in presence of a timedependent magnetic field can be written as follows [39,41,51]:…”

“…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.…”

Magnetized strange quark matter in a quasiparticle description

“…Other thermodynamic quantities, such as the energy density and pressure, can then be calculated from the formulae derived in the previous section II. A little difference is that the Maxwell contribution have been included in our numerical calculations, i.e., the quasiparticle contribution Ω f is replaced by [42][43][44]]…”

Effects of strong magnetic fields on hybrid stars

“…According to virial theorem arguments, which give an upper estimate for the magnetic inside neutron stars, they can possess central magnetic fields as large as 10 18−20 G, see e.g. [7,8,9,10].…”