Classification of the Pulsars

Note: the image at the top of this page (called a P/P-dot diagram as described below) is copied from the book: “Essential Radio Astronomy” (scroll down a tad from where the link navigates to).

We have discussed two types of binary pulsars, associated with giant stars:

• pulsars found with super-giants (that have a neutron star companion in a close binary circular orbit) and
• pulsars found with Be X-ray binaries (that have a slow x-ray neutron star pulsar companion in an elliptical orbit)

The companions of these two types of pulsars, are, in general, large giant stars.
Giant stars represent only about 1/10th of 1 percent of all stars, however, they also represent approximately one half of the progenitors (pre-cursors) of supernova events that are observed.

We have already asserted in the NS-Capture theory that these supernova events are generally all caused as the result of these giant stars having originally experienced a binding collision with a neutron star, which then proceeded to spin up as a pulsar while, simultaneously having its orbit spiraling deep into the atmosphere of the giant star, ultimately culminating in a supernova explosion, that destroys the giant star.

We will return to this point about the giant vs normal stars later, but for the present, we shall discuss “the rest of the pulsars”, the progenitors, for which, are more ordinary run-of-the-mill stars that are around the size of the Sun and have neutron star companions.

The “rest of the pulsars” fall into 4 basic classes:

1. Pulsars with a non-giant normal star companion.
2. Pulsars with no companion.
3. Milli-second pulsars (msp’s), most of which have some kind of white dwarf companion.
4. Pulsars in globular clusters, most of which have a normal star or white dwarf companion.

The above breakdown might be a bit confusing, so let us look at the pulsars from another perspective.

According to the NS-Capture theory all pulsars fall into one of the following 2 classes:

• binary pulsars that are precursors to a supernova explosion
• isolated pulsars that are part of the remnants of a supernova explosion

In the precursor class, we have 3 subclasses which the pulsars can fall in (typically x-ray pulsars):

1. Pulsars with a super-giant companion (eg. Cen X-3 with circular orbit)
2. Pulsars with a Be-star giant companion (slow pulsar with elliptical orbit)
3. Pulsars with a normal companion (eg. Her X-1, with circular orbit)

In the remants class, we have the following sub-classes (typically radio pulsars, either slowing down, or millisecond pulsars that may or may not be slowing down):

1. Isolated radio pulsars that are slowing down (possibly within recent supernova remnants like the Crab) (most radio pulsars fall in this sub-class)
2. Milli-second pulsars (typically have a white dwarf companion) (pulsar may be slightly slowing down or slightly speeding up)
3. Milli-second pulsars in globular clusters (typically have a white dwarf companion) (pulsar may be slightly slowing down or slightly speeding up)

Pre-cursor class pulsars

So far, we have discussed the first two sub-classes of the precursor class (supergiants and Be X-ray binaries). Briefly, let us consider the 3rd precursor subclass: an x-ray pulsar with a normal star companion.

The only real difference between the two precursor giant star sub-classes and the normal star sub-class is the size of the x-ray pulsar’s companion.

The reason the size of the companion is important is that the remnants phase is generally dependent on the size of the star that experiences the supernova.

The giant stars (GS’s) generally produce type II supernova explosions and completely destroy the giant, leaving no companion behind in the remnants.

The normal (regular) stars (RS’s) generally produce a type I supernova explosion and often leave a white dwarf companion behind in the remnants, and can remain bound to the white dwarf.

Remnants class pulsars

With that explanation of the 3 sub-classes of precursor pulsars, we can now turn to the sub-classes of the remnants pulsars.

In order to understand the remnants classification, an extremely useful framework is the P/P-dot diagram, where P is the spin rate of the pulsar and P-dot is the rate at which the spin rate of the pulsar is slowing down. These are generally radio pulsars.

Broadly speaking: precursors are x-ray pulsars, and remnants are radio pulsars. This will be explained in a subsequent page in more detail.

A great reference for pulsars is in the book “Essential Radio Astronomy” by James J. Condon and Scott M. Ransom (2016). In particular, Chapter 6 Pulsars is a great explanation of the Neutron Star Creation Theory view of pulsars, NS-Creation, which is the current standard theory of pulsar evolution.
However on this site we focus on an alternate view of pulsars, which is pulsar creation as a result of NS-Capture.

The neutron star capture theory, NS-Capture, (this site) uses the same data as the NS-Creation theory, but applies a much different interpretation to the data.

In particular, the NS-Capture theory says:

“The Neutron Star causes the supernova explosion.”,

while the NS-Creation theory says:

“The Neutron Star is created by the supernova explosion.”

The difference between these two theories is extreme, because the NS-Creation theory requires zero neutron stars to pre-exist and the cause of a supernova explosion is normal stellar evolution, and regards the neutron star as a by-product of the supernova explosion.

Whereas the NS-Capture theory requires on the order of 5 trillion neutron stars to pre-exist, any one of which can cause a supernova explosion by encountering any kind of normal (regular) star (RS), and is generally unrelated to the state of evolution that the RS is in.

(The encounter is a binding collision between the RS and the NS, where, after the binding, through the process of accretion, the NS spins up to become a fast pulsar (FP) which disrupts and heats up the companion prior to causing the actual supernova explosion (SNE).)

The P/P-dot diagram

There is a great example of a P/P-dot diagram in the Essential Astronomy book, which is copied at the top of this page for reference.

The diagram basically contains information about most of the known radio pulsars as well as a few X-ray pulsars. The common property of all these pulsars is that they are all slowing down. The vertical P-dot axis represents the rate at which a plotted pulsar is slowing down. The higher on the graph means the faster the pulsar is slowing down.

Note: P-dot stands for dP/dt (often represented by “P” with a dot “.” over it), where P is the time period of between pulses, which increases as the pulsar slows down and is thus a positive value. For pulsars that are spinning up, dP/dt is a negative value, and not shown on current P/P-dot diagrams.

The horizontal axis is the spin period of the pulsar. Pulsars with a longer spin period are on the right and a shorter spin period on the left.

Therefore, if we were to take another reading of these pulsars some time in the future, say 20 years from now, we would see all of the pulsars would have shifted a bit to the right: i.e. they would have a slightly slower rotation period. In general the pulsars at the top of the diagram will have moved further to the right than those at the bottom, because the pulsars at the top are slowing down faster than those at the bottom, according to the vertical P-dot axis.

Basically, there are 3 major sub-classes of the radio pulsars shown on the diagram:

1. Pulsars within supernova remnants, shown by a star, mostly near the upper/center, and upper/right-of-center, of the diagram.
2. Isolated pulsars, shown by a single gray dot, mostly collected near the middle/right-of-center of the diagram.
3. Pulsars that are in a binary system, shown by a gray dot with a circle around it, mostly in the lower/left-of-center section of the diagram.

It is generally considered that the pulsars at the top of the diagram are recently created and therefore are found within supernova remnants that have not yet dissipated. (Supernova remnants are indicated by a “star icon” on the diagram as shown in the legend box on the lower right.)

Most pulsars (single gray dot) are in the middle of the diagram (and represent pulsars that were created in supernova explosions from long ago, which have since dissipated and the remnants are no longer visible. These pulsars have longer periods, in general, because they have slowing down longer than those in recent visible supernova remnants. This large section of gray dots is often referred to as the pulsar island in the P/P-dpt diagram.

Finally there are the pulsars in the lower left which have extremely high rotation rates and are found most often in binary systems. These are the so-called “millisecond pulsars”, so- named because their rotation rates can be up to almost 1,000 times per second. IN addition, their P-dot values are very small, meaning they will take hundreds of millions of years to slow down. This conclusion is disputed on this site, because the NS-Capture view is that any binary companion, no matter how small, can provide enough accretion fuel to the pulsar to prevent it from slowing down.

Imagine a 1.4 solar mass, 5 mile radius neutron star rotating anywhere from 100 times per second up to 500->700 times per second. The surface of the star is actually rotating at about 2*pi*5miles*rate ~ 6*5*500 ~ 15,000 miles per second!

What is even more incredible is that material is caught up in the magnetic field of the neutron star, at say 50 miles from the center, will be rotating at 6*50*500 ~150,000 miles per second! Remember, the speed of light is 186,000 miles per second, so things really can’t go much faster than that.

i.e. these neutron stars that are in binary systems that are collecting mass from their binary companions bring in that mass at close to the speed of light.

One really needs to spend some time thinking about this in order to appreciate what is going on. And remember: these are “observed properties”, as opposed to some theoretical notion that may not have yet been proven to exist. It exists.

Additional comments on the P/P-dot diagram

There is a major omission from the P/P-dot diagram. It is the omission of the pulsars in binary systems that are spinning up, which would have a negative P-dot and would thus be located below the “Spin Period (s)” axis.

In order to graphically show this we would need values on the P-dot axis starting at -10^-21 and increasing down the axis as -10^-20, -10^-19, etc. i.e. the further down on the negative P-dot axis, would mean a faster spin-up rate, just as on the positive P-dot axis as you go further up the axis you get a greater spin-down rate.

Therefore, if the pulsars that are spinning up were plotted, we would see at least 2 sections:

• a section in the upper left corner of the negative values with binary millisecond pulsars clustered together. These binary pulsars have very slow P-dot value, meaning their spin-up time appears to be hundreds of millions of years.
• a section below and to the right of the millisecond cluster in the upper left. Basically, below the island of pulsars on the positive side. These are the binary x-ray pulsars, such as Cen X-3 that have much longer periods, and much faster spin-up rates than the millisecond pulsars in the upper left negative corner.

In addition, the binary pulsars on the negative side of the P-dot axis are spinning up, meaning the period of the pulses is decreasing with time. This means that the pulsars in the lower negative half of the diagram would be moving to the left with time.

With this view of the diagram, NS-Capture tells us that for the spinning up pulsars in the middle, like, Cen X-3, there will at some point be a supernova explosion and the pulsar in the remnants will begin to slow down. Therefore from an evolution point of view, we would draw and arrow from the bottom half of the chart to the top half of the chart to show that after the SNE occurs, the pulsar begins to slow down.

Another interesting suggestion is that the millisecond binary pulsars in the upper left negative corner and the lower left positive corner are kind of “hovering” with their companion. When material flows from the small companion to the pulsar, there would be a slight spin up, and the pulsar would be in the upper left negative corner. When the material flow temporarily stopped, the pulsar would jump to the lower left positive corner, We could represent this hovering by a two-headed arrow that crossed the axis from the negative side to the positive side.

The point is that we do not need to extend the P-dot axis below observed values on the spin-down side, nor above observed values on the spin up side.

The evolution of pulsars would then look like a side-ways horse shoe or a “C” shape, where evolution can follow all the way around the “C” like a millisecond pulsar, or jump from the lower part of the “C” to the upper part for giant SNE’s. The path of evolution is moving to the left at the bottom of the “C”, and to the right on the top of the “C”.

A discussion of this modification of the P/P-dot diagram is at “How NS-Capture explains the P/P-dot Diagram“.

The empirical proof of the NS-Capture boils down to this:

• if NS-Creation is true, then we would need to see giant binaries in the positive island that are slowing down from their initial more rapid spin rate.
• no giant binaries are observed in the positive half of the P/P-dot diagram. Therefore NS-Creation must be false for the x-ray binaries. That then forces us to assert that NS-Capture must be true.
• once NS-Capture for giants is proven to be true, that forces the assertion of the presence of trillions of isolated NS’s in the galaxy. Under such conditions there really is no need to assert that new NS’s are created by SNE’s of giant stars (GS’s).