Magnetic fields and the favorability of chiral density waves in neutron stars

The possible existence of inhomogeneous chiral condensates, such as chiral density waves (CDWs), in the cores of neutron stars has garnered considerable theoretical interest. However, recent studies using nucleon-meson models incorporating electric charge neutrality, β equilibrium, and fermionic vacuum fluctuations suggest that CDW phases are energetically unfavorable under realistic neutron star conditions due to the softness of the resulting equation of state (EoS). In this work, we reexamine the viability of CDW phases in dense nuclear matter by introducing a strong magnetic field as an external symmetry-breaking background. Motivated by observations of magnetars and theoretical predictions of ultrastrong internal magnetic fields ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>≳</a:mo> <a:msup> <a:mn>10</a:mn> <a:mn>18</a:mn> </a:msup> <a:mspace width="0.16em"/> <a:mi mathvariant="normal">G</a:mi> </a:mrow> </a:math> ), we extend the nucleon-meson model to include magnetic catalysis and Landau quantization effects. We analyze the phase structure, focusing on the onset and stability of the CDW in magnetized matter, and compute corresponding neutron star mass-radius relations by solving the Tolman-Oppenheimer-Volkoff equations. Our results indicate that strong magnetic fields lower the critical baryon chemical potential for the onset of the CDW phase by up to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mo>≈</d:mo> <d:mn>200</d:mn> <d:mspace width="0.16em"/> <d:mi>MeV</d:mi> </d:mrow> </d:math> compared to the zero-field case and stiffen the EoS in the relevant density regime, potentially allowing for stable neutron stars with anisotropic cores. These findings suggest that strong magnetic fields in neutron stars could make spatially modulated chiral phases possible in astrophysical environments.