Hypernuclear matter in strong magnetic field

Anomalous X-ray pulsars and soft γ-ray repeaters are observationally identified with highly magnetized neutron stars with surface magnetic field ∼ 10 14 -10 15 G [1][2][3]. This class of compact stars has been conjectured theoretically as "magnetars" [4][5][6][7], i.e., neutron stars which posses magnetic fields that are by several orders of magnitude larger than the canonical surface dipole magnetic fields B ∼ 10 12 -10 13 G of the bulk of pulsar population, which are commonly deduced from the magnetic-dipole radiation model of pulsar spindown in combination with measured spin and spin-down rates. The integral properties of magnetars, i.e., mass, radius, moment of inertia, etc will depend sensitively on the equation of state of matter in strong magnetic fields, if the central fields are sufficiently strong. Furthermore, other processes, such as the cooling and the magnetic field evolution will sensitively depend on the composition of matter in strong magnetic fields. Fermionic matter in strong magnetic field experiences two well-known quantum mechanical phenomena: the Pauli paramagnetism and the Landau diamagnetism. The first is due to the interaction of the spin of the fermion with the magnetic field and, therefore, is relevant for both charged and uncharged fermions. The second phenomenon is relevant only for charged particles, and is particularly strong for light particles, which in the case of compact stars are the leptons.

Neutron star sequences may feature massive objects with masses M ∼ 2M ⊙ . These massive compact stars are likely to develop cores which are composed of matter that differs from the ordinary nuclear matter composed of only neutrons and protons. One possibility is that heavy baryons (hyperons) will appear once the Fermi energy of neutrons becomes of the order of their rest mass. Although the hyperons were considered even before the discovery of pulsars and their identification with the neutron stars [8], their presence in the cores of neutron stars is still quite uncertain, for different theoretical models predict quite different outcomes for the maximum mass of hypernuclear compact stars, often in contradiction with the known empirical data on pulsar masses. The models that are based on relativistic density functional methods [9][10][11][12] predict masses that are not much larger than the canonical mass of a neutron star which clearly contradicts modern observations. Masses of the order of ≤ 1.8M ⊙ were obtained in non-relativistic phenomenological models [13,14], while microscopic models based on hyperon-nucleon potentials, which include the repulsive three-body forces, predict low maximal masses for hypernuclear stars [15,16]. The avenues for reconciliation of the large pulsar mass and the hyperonization (and more generally strangeness) of dense matter have been explored recently in Refs [17][18][19][20][21][22][23][24][25][26][27][28].

The influence of strong magnetic fields on the highly dense electron gas in the context of neutron star matter was studied in Refs. [29][30][31][32][33]. The strong magnetic field effects on dense nuclear matter (n, p, e system) have been studied previously in Refs. [34][35][36][37][38][39][40]. The structure of strongly magnetized neutron star branch of compact objects was studied for different field configurations (toroidal, poloidal, etc) in Refs. [41][42][43]. In the case of the adjacent branch of white dwarfs, strong magnetic fields were found to lead to highly super-Chandrasekhar mass (M ∼ 2.3 -2.6M ⊙ ) white dwarfs [44][45][46], which can be related to the observed features of a number of peculiar Type Ia supernovae [47].

It has been known for some time that the magnetic field can affect the hydrostatic equilibrium of compact stars and may render large fields configurations unstable. In the simplest form it can be formulated for uniform self-gravitating fluids [48]. In the case of neutron stars the Chandrasekhar-Fermi limiting field strength is ∼ 10 18 G [49]. Fully relativistic calculations confirm the simple Newtonian estimates [41][42][43]. Instabilities related to the anisotropy of the pressure were also discussed in the literature. These types of instabilities may arise due to the change of the sign of the derivative of either the transverse pressure or the parallel pressure with respect to the density, which leads eventually to vanishing of the respective pressure. These instabilities have been discussed for electron gas [50] and strange quark matter [51][52][53] due to the vanishing of transverse pressure and for magnetized fermionic systems [54] and quark matter [55,56] due to parallel pressure (but see [57,58]).

The studies of magnetized dense matter were mainly carried out in the limit of uniform field distribution, some notable exceptions are Refs. [35,54,59]. The processes of supernova collapse will leave behind a strongly non-uniform field distribution of frozen-in fields. Any dynamo mechanism generating fields will carry th

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