Coulomb Crystal Model Helps Scientists Understand Neutron Star Formation

The inside of stars are very hot and highly dense. The matter found in the cores of old white dwarfs and the crusts of neutron stars are usually highly compressed. The heat and the intense gravitational force in the center of the star crush matter. The scientific community has long believed a star’s core will contain Coulomb crystals that form at temperatures potentially as high as 100 million Kelvin.

A Coulomb crystal is created when a system of minute point charges are arranged in a perfect lattice. When this object is placed in a field of uniform but opposite charges it creates a Coulomb crystal. The difference between Coulomb crystals and normal crystals is that every charge at the nodes in the lattice interact with each other through coulomb forces. An exposed nuclei is aligned into the lattice at densities and temperatures where the kinetic energy of ions used is about 175 times lower than the typical potential energy of Coulomb forces repulsions between them. This makes the coulomb attraction between the ions much stronger than the interactions between the forces around them.

Denis A. Baiko and Andrew A. Kozhberov, research scientists at Ioffe Institute in Saint Petersburg, Russia, look to clarify the physics of these crystals in their paper published in the journal Physics of Plasmas, AIP Publishing.

This study is the first simultaneous analysis of the effects of strong magnetic fields and electron screening on an ion’s motion in a Coulomb crystal.

"This project is the most detailed description of these crystals to date," Baiko said in the AIP press release. "This is especially important in astrophysics for our understanding of evolution of neutron stars and white dwarfs."

When a star runs out of Hydrogen gas, it dies and succumbs to its own gravity. Stars, like our sun, die and form white dwarfs. Very large stars follow the same life cycle but become neutron stars. Baiko used a realistic model of a neutron star crust and the matter found within, which led to his examination of Coulomb crystals.

The team of researchers used a series of mathematical calculations to study the properties of phonons, which is the name given to the vibrations within the lattice of Coulomb crystals. According to the release, during the experiment, crystals of different densities were also exposed to a range of temperatures.

The team experimented with different combinations. The experiment started with an ideal Coulomb crystal and then the complexity was increased to match real life processes inside the stars. They added “a polarizable electron background, magnetization of ion motion and several lattice structures,” said the study. The scientists found all these effects changed the phonons in different ways. According to the release, Baiko said these calculations can be used to understand thermodynamic, kinetic and elastic properties of Coulomb crystals in neutron star crusts and white dwarf cores.

The team hopes they will be able to calculate electrical and thermal conductivities of electrons due to inelastic electron-phonon scattering in strongly magnetized Coulomb crystals. This affects the rate of heat transfer in the lattice. In the hot cores of stars, the temperature, magnetic field and thermal conductivity need to be calculated to reconstruct thermal and magnetic histories of these fascinating stellar objects.

"What is exciting about this work is that one can take into account several diverse physical effects simultaneously and obtain new, enlightening and relevant results using rather modest means," Baiko said. "It's nice."