Model of the "pasta phase" of neutron stars

This JAVA applet presents a simulation of the described "pasta phase" with competing interactions: short-range proton-proton repulsion of strength P-P, short-range neutron-neutron repulsion of strength N-N, short-range proton-neutron attraction of strength P-N, and long-range proton-proton Coulomb interactions V(R)=1/R of strength V. The short-range interactions have range R_o. The simulation is implemented on a partially-filled square lattice using Monte Carlo methods. Protons are displayed as red particles and neutrons as black particles. By default, when the simulation starts, the system shows a lattice at ~17% filling with a 10% proton-neutron ratio, but the filling and ratio can be modified, if desired.

Accurate rendition of the structure and phases of a neutron star (courtesy of Dany Page). The stellar crust consists of a Coulomb crystal of neutron-rich nuclei embedded in a neutron vapor and a uniform electron gas. The composition of the stellar core is presently unknown and may consist of deconfined strange-quark matter.

Neutron-rich matter may display complex structures at densities just below that of normal nuclei. This is because all conventional matter is "frustrated". While nucleons are correlated at short distances by attractive strong interactions, they are anti-correlated at large distances because of the Coulomb repulsion. Often these short- and long-distance scales are well separated, so nucleons bind into nuclei that are segregated in a crystal lattice. However, at densities of the order of 1013-1014 g/cm3 these length scales are comparable. Competition among short- and long-range interactions (i.e., frustration) leads to the development of complex and exotic nuclear shapes, such as cylinders, flat plates, as well as spherical and cylindrical voids. The term "pasta phases" has been coined to describe these complex structures. While the study of these pasta phases is interesting in its own right, it becomes even more so due to its relevance to the structure of the inner crust of neutron stars and to the dynamics of core-collapse supernovae.

Neutron stars contain a non-uniform crust above a uniform liquid mantle. The outer crust is understood as the region of the star spanning about 7 orders of magnitude in density; from about 104 g/cm3 to 4 * 1011 g/cm3. At these densities, the electrons - which are an essential component of the star in order to maintain charge neutrality - have been pressure ionized and move freely throughout the crust. Moreover, at these "low" densities, 56Fe nuclei arrange themselves in a crystalline lattice to minimize their overall Coulomb repulsion. This is the structure of the outermost layer of the crust. However, as the density increases, 56Fe ceases to be the most energetically favorable nucleus. This is because the electronic contribution to the energy increases faster with density than the nuclear contribution.

The figure displays how the system organizes itself into neutron-rich nuclei of complex topologies that are embedded in a neutron vapor. Such complex pasta structures may have a significant impact on various transport properties, such as neutrino and electron propagation.

As a result, it becomes energetically advantageous for the energetic electrons to capture on protons and for the excess energy to be carried away by neutrinos. The resulting nuclear lattice is now made of nuclei having a neutron excess larger than that of 56Fe. As the density continues to increase, the nuclear system evolves into a Coulomb lattice of progressively more neutron-rich nuclei until a "critical" density of about 4 * 1011 g/cm3 is reached: at this point nuclei are unable to hold any more neutrons; the "neutron drip line" has been reached.

The inner crust of the neutron star comprises the region from the neutron-drip density up to the density at which uniformity in the system is restored (approximately 1/3 to 1/2 of normal nuclear density). At these densities the system exhibits rich and complex structures that emerge from a dynamical competition between short-range nuclear attraction and long-range Coulomb repulsion. As mentioned earlier, at the lower densities present in the outer core the system organizes itself into a crystalline lattice of neutron-rich nuclei. In contrast, at densities of the order of half of nuclear-matter saturation density (or approximately 1014 g/cm3) uniformity in the system is restored and the system behaves as a uniform Fermi liquid. Yet the transition region from the highly-ordered crystal to the uniform liquid mantle is complex and not well understood. Length scales that were well separated in both the crystalline and uniform phases are now comparable, giving rise to a universal phenomenon known as "Coulomb frustration". It has been speculated that the transition to the uniform phase must go through a series of changes in the dimensionality and topology of these complex structures, colloquially known as "nuclear pasta" that may have a significant impact on various transport properties, such as neutrino and electron propagation.

Created by Eric Pelz with the help of Graduate Student Yohanes Pramudya and Professors Vladimir Dobrosavljevic, Stratos Manousakis and Jorge Piekarewicz at the National Magnetic Field Laboratory at the Florida State University.