Neutron Stars

Neutron Stars are the result of the gravitational collapse of the core of a dead star, after supernova.
Live stars prevented from gravitational collapse because of pressure from thermonuclear processes
Without these, gravity asserts itself and the stellar core collapses inwards

Depending on the mass, can reach different sizes.
Small stars form white dwarfs; collapse stopped by electrostatic forces.
Neutron stars heavier, collapse until they have the same density as atomic nuclei!
The collapse causes the matter in the interior to convert to be mostly neutrons, releasing a wave of neutrinos in a supernova.

What is a Neutron Star?

Extremely dense sphere, 20 km across
Proposed mass range about 1-3 Solar Masses. Anything smaller becomes a white dwarf, anything bigger collapses further.
Very intense density, gravity
Outer layer is a plasma crust, ~1km thick.

• nuclei form "a solid network", surrounded by an electron gas that flows between the atoms. Some debate over whether this is solid or more fluid.

• Some models suggest it is not homogenous, made of many intermediate mass elements. Other models suggest it is mostly hydrogen and helium.

• A solid heterogeneous crus allows structures analogous to molecules, made of nuclei in a particular configuration.

• Spins very fast due to conservation of angular momentum.

Magnetic Atoms on the Surface

Neutron stars have staggeringly intense mgnetism
The magnetic field of the earth is of order 10^-5
The magnetic field of our sun ranges from order 10^-4 to order 10^-1
The magnetic field of neutron stars ranges from order 10^4 to 10^11

Under these conditions, strange electron behaviour; electron orbitals are squished and flat (diagrams on F&S pp 371, 372).
F&S term these "Magnetic Atoms". I don't know if this particular physical model is still well regarded; however this paper by Dong Lai from 2000 ( 10.1103/RevModPhys.73.629 ) appears to examine the general proposal in detail. Only read it if you really like the Hamiltonian.
The electrons would all have spin oriented perpendicular to the magnetic field, allowing for very unusual behaviour.
Atoms with these electron configurations can interact to form long chains, analogous to polymers. They are surrounded by an electron sheath. The magnetic field of a neutron star is sufficient that these polymers would point out perpendicular to the surface.
F & S suggest these could interact with each other to clump together, and Lai suggests the long chains would be able to have quadripole-quadripole interactions.
The chains could have variable lengths, and could be made up of variable elements.
This gives us a form of matter that can vary, and that can interact with other matter in the same form, analogous to molecules. This could provide a mechanism for storing order, which could provide a vessel for life.

F & S propose that in order to replicate this order, a collection of polymer chains would need to be able to either assemble new chains, or to break apart existing chains and reassemble them in a suitable configuration.

Neutron stars are constantly bombarded with ions from space, so this provides a source of material to build new chains.
High energy particles are ejected from deeper within the neutron star, and these have sufficient energy to knock atoms out of old chains, allowing them to be reassembled.

Hence, possibility for complexity, order, change. Yay, life!