Bao and colleagues carried out the study on the influence of strong magnetic fields on the properties of nuclear pasta phases and crust-core transition in the inner crust of neutron star by using the RMF model and the self-consistent TF approximation. They found that as the magnetic field strength “B” is less than 10^17 G, the effects of magnetic field are not evident comparing with the results without magnetic field. But, as magnetic field strength is stronger than 10^18 G, the onset densities of pasta phases and crust-core transition density decrease significantly, and the density distributions of nucleons and electrons are also changed obviously. Their study is published in Physical Review C on Jan, 14, 2021.
Neutron stars offer special natural laboratories for the study of nuclear physics and astrophysics due to their extreme properties. They consist of extreme neutron-rich matter and their densities can cover more than 10 orders of magnitude from surface to center. It is generally believed that a neutron star mainly consists of four parts, an outer crust of nuclei in a gas of electrons, an inner crust of neutron-rich nuclei with electron and neutron gas, a liquid outer core of homogeneous nuclear matter, and an inner core of exotic matter with non-nucleonic degrees of freedom. From the neutron drip to the crust-core transition, i.e., the density range of inner crust, the stable nuclear shape may change from droplet to rod, slab, tube, or bubble with increasing density. As a result, the so-called nuclear pasta phases are expected to appear in the inner crust of neutron stars, which play a significant role in interpreting a lot of astrophysical observations, such as the giant flares and quasiperiodic oscillations from soft γ-ray repeaters, and glitches in the spin rate of pulsars.
The soft γ-ray repeaters and anomalous x-ray pulsars have already been confirmed as magnetars with very strong surface magnetic fields, which can be as high as 10¹⁴-10^15 G. The magnetic field strength in the core of a neutron star may even reach 10^18 G. So far, the mechanism and origin of strong magnetic fields in magnetars remain unclear, and several hypotheses have been proposed. Duncan and Thompson in their paper suggested that such strong fields could be generated by the dynamo mechanism in a rapidly rotating protoneutron star. It has also been suggested that strong magnetic fields in neutron stars may result from magnetic flux conservation during the collapse of a massive progenitor. It is still under discussion how strong the magnetic fields can be in the crust and interior of neutron stars.
Now, Bao and colleagues in their work, employed the Wigner-Seitz (WS) approximation to describe the inner crust and use the self-consistent Thomas-Fermi (TF) approximation to calculate the nonuniform matter with considering various pasta configurations. In the TF approximation, they treated the surface energy and the distributions of nucleons and electrons self-consistently. While, they adopted the RMF model to describe nucleon-nucleon interaction. In the RMF model, nucleons interact with each other via the exchange of scalar and vector mesons.
They found that the pasta phase structures and the crust-core transition density were changed obviously when, the magnetic field strength is as large as B = 10^18 G, where the binding energy per nucleon E/N is lower than the results with B = 0, and the onset densities of various pasta phases and crust-core transition density become smaller. However, the proton fraction Yp with binding energy, B = 10^18 G is larger than that with B = 0, since the protons occupy the lowest Landau level. The impacts of anomalous magnetic moments of nucleons are almost invisible in the case of B = 10^17 G, but they have to be taken into account for a stronger magnetic field as B = 10^18 G.
In general, the radius of WS cell decreases with increasing B, while the size of nucleus increases with B, which results in the charge number and nucleon number of the nucleus varying with B. The density distributions of nucleons and electrons with B = 10^18 G are clearly different from the results with B = 0.
In order to check the model dependence of the results obtained, they adopted two successful RMF parametrizations, TM1 and IUFSU, with different symmetry energies and their slopes, which play an important role in determining the properties of inner crust of neutron star with strong magnetic fields. The TM1 model has been successfully used to construct the equation of state for neutrons stars and supernova simulations. Compared with TM1 model, an additional ω-ρ coupling term is added in IUFSU model, which plays an important role in modifying the density dependence of symmetry energy and affects the neutron star properties. The symmetry energy slope L in TM1 model is as large as 110.8 MeV, while L in IUFSU model is 40.7 MeV.
“By comparing the results from these two models, we found that the features with strong magnetic fields due to the symmetry energy and its density slope are similar to the results with B = 0, which are consistent with our earlier study.”, said Bao. “A smaller slope L leads to more complex pasta structures. For the TM1 model with a larger slope L, only droplet appears in the inner crust of neutron star for B = 0. However, some non-spherical pasta phases arise before crust-core transition for B = 10^18 G, even though the crust-core transition density becomes smaller.”
“It would be interesting to further study the nuclear pasta phase with strong magnetic fields and their impacts on the observations of neutron star.”, concluded of the study.
Reference: S. S. Bao, J. N. Hu, H. Shen, “Impact of strong magnetic fields on the inner crust of neutron stars”, Phys. Rev. C 103, 015804 – Published 11 January 2021. https://doi.org/10.1103/PhysRevC.103.015804 https://journals.aps.org/prc/abstract/10.1103/PhysRevC.103.015804
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