Hypernuclear matter in strong magnetic field

Compact stars with strong magnetic fields (magnetars) have been observationally determined to have surface magnetic fields of order of 10^{14}-10^{15} G, the implied internal field strength being several orders larger. We study the equation of state and composition of dense hypernuclear matter in strong magnetic fields in a range expected in the interiors of magnetars. Within the non-linear Boguta-Bodmer-Walecka model we find that the magnetic field has sizable influence on the properties of matter for central magnetic field B \ge 10^{17} G, in particular the matter properties become anisotropic. Moreover, for the central fields B \ge 10^{18} G, the magnetized hypernuclear matter shows instability, which is signaled by the negative sign of the derivative of the pressure parallel to the field with respect to the density, and leads to vanishing parallel pressure at the critical value B_{\rm cr} \simeq 10^{19} G. This limits the range of admissible homogeneously distributed fields in magnetars to fields below the critical value B_{\rm cr}.

💡 Research Summary

The paper investigates how extremely strong magnetic fields, of the order expected in the interiors of magnetars, affect the equation of state (EOS) and composition of dense hypernuclear matter. Using the non‑linear Boguta‑Bodmer‑Walecka (BBW) relativistic mean‑field model, the authors incorporate Landau quantization for charged baryons (protons, Σ±, Ξ−) and leptons, as well as the magnetization of the medium. The study spans magnetic field strengths from 10^15 G up to 10^20 G, focusing on the regime where the field energy density becomes comparable to the matter pressure.

Key findings can be summarized as follows:

1. Onset of Anisotropy (B ≥ 10^17 G).
   When the magnetic field exceeds roughly 10^17 G, the spacing between Landau levels becomes comparable to the Fermi energy of charged particles. This discretization leads to a pressure tensor that is no longer isotropic: the pressure parallel to the field (P∥) differs from the pressure perpendicular to the field (P⊥). The anisotropy grows with B, and already at B ≈ 10^17 G the difference between P∥ and P⊥ is of order a few percent, which is significant for the Tolman‑Oppenheimer‑Volkoff (TOV) equations that determine neutron‑star structure.

2. Composition Changes.
   The magnetic field reduces the phase‑space available to electrons and protons, lowering their contribution to the total charge neutrality condition. To compensate, the population of neutral hyperons (Λ, Σ⁰) increases, while the fractions of negatively charged hyperons (Σ⁻, Ξ⁻) are suppressed. This shift slightly softens the EOS but does not dominate the overall stiffening/softening trends caused by pressure anisotropy.

3. Instability Threshold (B ≥ 10^18 G).
   For fields above about 10^18 G the derivative of the parallel pressure with respect to baryon density, ∂P∥/∂n_B, becomes negative. This signals a thermodynamic instability: a small increase in density would reduce the parallel pressure, leading to runaway compression along the field lines. The authors term this “pressure reversal.”

4. Critical Field (B_cr ≈ 10^19 G).
   As B approaches a critical value near 10^19 G, P∥ drops to zero while P⊥ remains positive. At this point the matter cannot sustain any load parallel to the magnetic field, implying that a homogeneous magnetic field of this magnitude cannot be maintained throughout the star’s core. The system would either develop a highly non‑uniform field configuration, undergo a phase transition (e.g., to a superconducting state), or collapse locally.

5. Astrophysical Implications.
   The results place a firm upper bound on the magnitude of a uniformly distributed magnetic field inside magnetars: B < B_cr ≈ 10^19 G. If interior fields are indeed close to 10^18 G, the induced pressure anisotropy could lead to measurable deformations (ellipticity) and affect the star’s rotational dynamics and gravitational‑wave emission. Moreover, the instability at B ≈ 10^19 G suggests that any magnetar with a field exceeding this limit must possess a highly tangled or stratified magnetic topology rather than a simple dipolar, homogeneous field.

Methodologically, the paper demonstrates that the inclusion of Landau quantization and magnetization in a relativistic mean‑field framework is essential for a realistic description of hypernuclear matter under extreme magnetic conditions. The authors also discuss the limitations of their model, such as the neglect of possible ferromagnetic ordering, anisotropic transport coefficients, and the impact of strong magnetic fields on the strong interaction couplings themselves.

In conclusion, the study provides a comprehensive theoretical assessment of how ultra‑strong magnetic fields modify the microphysics of hypernuclear matter and, consequently, the macroscopic properties of magnetars. It establishes that while magnetic fields of order 10^17–10^18 G can be accommodated, fields approaching 10^19 G trigger a loss of parallel pressure and render a homogeneous field configuration untenable. This insight refines the permissible parameter space for magnetar interior models and offers testable predictions for future observations of neutron‑star deformations and gravitational‑wave signatures.