Generation of strong magnetic fields in hybrid and quark stars driven by the electroweak interaction of quarks

Abstract

Abstract. We study the generation of strong large scale magnetic fields in compact stars containing degenerate quark matter with unbroken chiral symmetry. The magnetic field growth is owing to the magnetic field instability driven by the electroweak interaction of quarks. In this system we predict the enhancement of the seed magnetic field 10 12 G to the strengths (10 14 − 10 15 ) G. In our analysis we use the typical parameters of the quark matter in the core of a hybrid star or in a quark star. We also apply of the obtained results to model the generation of magnetic fields in magnetars.The origin of strong magnetic fields B ∼ 10 15 G in magnetars [1] is a puzzle for modern astrophysics. Despite the existence of multiple models describing the generation of such magnetic fields, which are based on magnetohydrodynamics of stellar plasmas, none of them can satisfactory describe the observational data. Recently, in [2], we proposed the new approach to generate strong magnetic fields in quark matter owing to the instability of the magnetic field driven by the electroweak interaction of quarks. In the present work we summarize the results of [2] and discuss the applicability of this model for the generation of magnetic fields in magnetars.Let us consider a dense quark matter consisting of u and d quarks. The density of this matter is supposed to be high enough for the chiral symmetry to be restored. In this case we can take that quarks are effectively massless. Therefore we can decompose the quark wave functions into left and right chiral components, which evolve independently, and attribute different chemical potentials µ qL,R , where q = u, d, for each chiral component.Generalizing the results of [3,4], we get that, in the external magnetic field B, there is the induced electric current J = ΠB, Π = 1 2π 2