What does an isolated neutron star look like?

A neutron star, all by itself, that is not interacting with any other matter would probably be invisible, except possibly as a gravitational lensing event which would occur if it passed through the observer’s line of sight of some other visible object.

We will assume an isolated neutron star has a strong magnetic field (explained further below) and that if the NS is rotating at all that the rotation axis is aligned with the magnetic field axis, which is exactly the opposite of the case that exists when the NS has been turned into a pulsar, where its magnetic field specifically not aligned with the rotation axis. i.e. these neutron stars have not had any interaction with a normal star and therefore have not been through an accretion phase that would have spun them up to become a pulsar.

So, what we have is a 1.4 solar mass object that is about 20 km in diameter, that has a strong magnetic field floating through interstellar space.

As the NS floats along for millions, probably billions of years, it gathers material from the interstellar medium that forms clouds around the NS. In particular, it is likely that there are 2 main types of clouds:

1. Clouds of material that collect high above the magnetic poles, consisting of ionized particles that are rotating around the magnetic pole lines while also being pulled down by the gravitational field. The clouds are kind of a balance point between the rotational velocity around the magnetic field lines which provides a centrifugal force that resists the gravitational pull toward the NS. i.e. material is balanced between magnetic and gravitational forces and forms a “lobe” high above the actual magnetic pole of the NS.
2. A larger cloud of material will also collect in a torus or ring around the magnetic field axis of the NS. This is probably a larger accumulation of matter that primarily behaves as a gravity-supported ring around the neutron star. If there was no magnetic field, it would probably just be a spherical cloud completely surrounding the NS, but because of the activity of the magnetic field, holes are punched through the spherical cloud along the magnetic pole lines, and the result is a toroidal-shaped cloud of material with the NS at the center of the torus.

Therefore, the overall picture can be visualized as a donut-shaped cloud with two more spherical shaped clouds, one above and one below the donut hole. At the center of the donut hole is the NS.

The clouds above and below the torus will contain much hotter material than the torus. This is because as material from the upper and lower clouds are pulled toward the surface of the NS, the material will emit x-rays as bremsstrahlung, which will generally be directed toward the clouds from which it came and heat the ionized clouds.

On the other hand, x-rays that are emitted into the torus will generally be absorbed by the material in the torus and absorption lines may appear in the spectrum of the heated torus.

We will make some assumptions about the neutron stars, based on the premises of the NS-Capture theory that these isolated NS’s are progenitors for the binary systems in which they are occasionally captured, particularly that they should have a strong magnetic field on the order of 10**14 Gauss or more. This is because NS-Capture theory says that neutron stars are pre-cursors to all pulsars, and because some pulsars have extremely strong magnetic fields, such as magnetars, then we assume every neutron star upon capture must be capable of generating any observed outcome on the P/P-dot diagram. Therefore, the core physical assumption here is that after capture, the neutron star’s magnetic field progressively weakens as it is spun up by its companion. Companions that explode early in the process will leave slowly spinning pulsars with strong magnetic fields. Companions that do not explode at all and are accreted down to their core, as in the case of millisecond pulsars will have pulsars that have very weak magnetic fields because they have been accreting matter since their capture until they are fully spun up (100’s of rotations per second) and the magnetic field will continuously weaken through that process.