# Whats at the center of a neutron star?

What is nuclear pasta? Somebody told me that the inside of a neutron star was made of nuclear pasta. Also is the inside of a neutron star some sort of liquid?

When you have a massive glacier the ice at the bottom is under so much pressure it stays in it's liquid form. So is the inside of a neutron star also a liquid? What is the star even made of any more?

• What about the Wikipedia entry on the structure of neutron stars or that of nuclear pasta itself is unclear to you? Please show research effort and ask a more specific question. "Someone told me" is clearly inferior to "According to this referenced Wikipedia article"... – ACuriousMind Aug 21 '16 at 14:27
• This question shows, that you did not put much efford into some research yourself. So called pasta phases of nuclear matter are located inside the outer layers (crust) of a neutron star. Inside the star is matter at extreme densitys (much higher than nuclear density $\sim 0.17\mathrm{fm}^3$). This matter consists of unbound neurons, proton, electrons and more exotic species. The internal structure, composition and equation of state is still in active research. From an equation of state point of view this interior is often described as an ideal fluid. – N0va Aug 21 '16 at 16:07
• This question should not be closed as unclear. It asks a perfectly well-defined question ("what is nuclear pasta") and gives some of the OP's ideas towards what it is. I would be very interested in seeing an intuitive answer. – knzhou Aug 22 '16 at 4:03
• @ACuriousMind To be fair, the wikipedia page on pasta is woeful (and incorrect). – Rob Jeffries Aug 22 '16 at 7:57
• @ACuriousMind I didn't even see the Wikipedia page, I'm in a hotel and the wifi is messed up so sometimes only Yahoo answers works. Also I was talking about neutron stars in skype and my friend actually said "I think the centers are nuclear pasta or something" – EasyPeasy Aug 22 '16 at 12:06

The structure of a neutron star can be summarised as follows.

An outer crust, consisting of a solid lattice of nuclei in a degenerate gas of ultrarelativistic electrons. At densities $>4\times10^{14}$ kg/m$^3$, there is an inner crust where it becomes energetically feasible for neutrons to drip out of the nuclei, but the (increasingly n-rich) nuclei maintain their identity in a solid lattice. As densities $>10^{17}$ kg/m$^{3}$ the nuclei lose their identity and "dissolve" into a (super)fluid of degenerate neutrons with a small fraction (1%) of protons and electrons. Then at densities approaching $10^{18}$ kg/m$^3$ there may be some other phase change - either into a solid neutron core, quark matter or through the creation of additional hadronic degrees of freedom.

Nuclear pasta fits into the region between the inner crust and the n,p,e fluid, at densities between about $3\times 10^{16}$ kg/m$^3$ and $10^{17}$ kg/m$^3$. The basic idea is that the equilibrium state of the gas is found by minimising the overall energy density. $$u = n_N (M(A,Z)c^2 + L) + u_n + u_e + ,$$ where $n_N$ is the number density of nuclei, $M(A,Z)$ is the rest mass of the equilibrium nucleus of atomic mass $A$ and atomic number $Z$ (inverse beta decay drives the equilibrium towards n-rich nuclei with large $A$ and high $A/Z$), $u_n$ and $u_e$ are the energy densities of the degenerate neutron and electron gases, which depend only on their number density. $L$ is a (negative) energy density associated with the lattice of nuclei - i.e. some sort of crystal lattice has a lower energy.

The key thing here is the $(M(A,Z) + L)$ term. At lower densities it can be assumed that the nuclei are relatively isolated and pseudo-spherical, so that a semi-empirical mass formula will yield an estimate of $M$. But at densities above $3\times 10^{16}$ kg/m$^3$, the nuclei fill more than 10% of the volume, they are surrounded by neutrons that reduce the surface energy term, and they are becoming so large ($A>300$) that they become susceptible to fission (c.f. the Bohr-Wheeler condition for spontaneous fission).

What this means is that the equilibrium structure of the nuclear matter is no longer in the form of pseudo-spherical, individual nuclei. The nuclei distort and join together in various density-dependent forms; first spaghetti - long strings of nuclear matter with a neutron sauce; then lasagna - planes of nuclear matter with a neutron sauce. At even higher densities the roles reverse - the neutrons are in strings and planes surrounded by nuclear matter.

At densities above $\sim 10^{17}$ kg/m$^3$ the binding energy of the nuclear matter becomes so low that it is more favourable for the nuclei to dissolve into free neutrons (plus a few protons and electrons).

I am not an expert on this subject, and to be honest I have no idea how these models can ever be tested. Getting a small wormhole connection to a neutron star interior to probe it is a tough call --- probably impossible.

Neutron stars may be onion layered. The crust is composed of material, mostly iron, with degenerate electron pressure maintaining its hydrostatic equilibrium. The next layer is this pasta, which is a sort of nuclear plasma. The next layer is the neutron lattice. If the body is massive enough there may be a deeper hyperon region composed of $\Xi^0$, $\Sigma^0$ and $\Delta^0$ in the baryon decuplet. Then if the body is really massive the core might be composed of a quark-gluon plasma. There is some attempt to use these models to understand the physics of the neutron star exterior, such as its magnetic field.

• There are many ways to test understanding of neutron star interiors - the mass-radius relation, cooling curves, evolutiin of rotation and magnetic fields and perhaps one day pulsations, neutrinos and gravitational waves. – Rob Jeffries Aug 21 '16 at 19:40
• What is a neutron lattice? Immediately interior to the pasta phase is an n,p,e fluid. – Rob Jeffries Aug 21 '16 at 19:42
• The neutron star has from my understanding been traditionally thought of as a sphere packing of neutrons in a Kepler problem tetrahedral configuration. The neutron star is in a sense a giant nucleus. – Lawrence B. Crowell Aug 22 '16 at 1:54
• Immediately interior to the pasta is an n,p,e fluid, which makes up the bulk of the mass of the neutron star. Indeed the neutrons and protons are thought to be in a superfluid state. – Rob Jeffries Aug 22 '16 at 7:54