Diagrammatic Proof of NS-Capture

Summary of Diagram

Diagram 0, above, represents the full analysis of the NS-Capture vs the NS-Creation theories.

We will initially summarize the contents of the diagram with further detail to follow.

But first, we will quickly show how the proof works based on the diagram:

• NS-Creation requires the scenario in columns 1 and 2 in order to produce the observations in column 3. However, the theoretical column 2 is in direct contradiction with the observations in column 3. In addition there are no observations of the states in column 2
• Therefore we conclude that column 2 is false and that in order to explain column 3, we need to introduce a random binding collision in cell (5,3) that creates the binary in cell (4,3).
• Finally, since we have a mechanism to create column 3 that agrees with observations, we no longer need the isolated column 5.
• Therefore, columns 3 and 4, which represent NS-Capture must be true.
• And, columns 1, 2, and 5, which represent NS-Creation are superfluous and must be considered false.

The diagram consists of 5 processes, represented by the 5 columns:

1. Column 1 (dark blue cells) is a process that goes up the column, starting with a pair of Giant Stars (GS), and at the top of the column one of the GS’s explodes in a SuperNova Explosion (SNE), which produces both an explosion of stellar material into space (SuperNova Remnants (SNR)), and an implosion that creates a fast-spinning neutron star pulsar (FP).
   This is a theoretical process that has not actually been observed.
   This process (col 1) is a critical assumption of NS-Creation theory, but is not needed in NS-Creation theory and furthermore will be shown to be logically inconsistent with a detailed analysis of the complete set of pulsar data, which is represented by the complete 5 columns of the diagram above.
2. Column 2 (dark blue cells) is a process that goes down the column, starting with the remains from column 1. It initially starts with a GS and a Fast Pulsar (FP) and as the system evolves down the column, the FP spins down and eventually becomes a non-spinning Neutron Star (NS), still accompanied by the 2nd GS that did not explode from column 1.
   This is also a theoretical process that has not been observed.
3. Column 3 (green cells + red cells) is a process that goes up the column, starting with a non-spinning NS plus a GS, and the NS spins up to become a FP at the top of column 3.
   This is an observed process, for which there are many examples that have been discovered using X-ray Astronomy.
4. Column 4 (green cells + red cells) is a process that goes down the column, starting with a Fast Pulsar amongst the remnants of an exploded star. The FP slows down as it goes down the column, eventually becoming a non-spinning isolated neutron star.
   This is also an observed process, of which there are many examples that have been observed primarily using Radio Astronomy.
5. Finally, column 5 (light blue cells) is a process that goes up the column and consists of an isolated giant star that evolves to the point where it explodes and creates a fast pulsar.
   This is a theoretical process and has not been directly observed.

In summary, there are 5 processes in the 5 columns:

• 3 of them move up the column and correspond to the creation of a fast pulsar (columns 1,3,5).
• 2 of them move down the column and correspond to the appearance of a fast pulsar, which subsequently spins down as it goes down the column (columns 2,4).

As mentioned above, two of the columns, 3 and 4, are primarily “observed” processes (green cells) for which there is much physical data that has been accumulated since the discovery of the first pulsar in 1967.

Three of the columns, 1, 2, and 5, (dark and light blue cells) are purely theoretical and represent what we call on this site to be “NS-Creation Theory”, because they describe the commonly accepted theory that Giant Stars can spontaneously blow up and “create” a Fast Pulsar.

The discussion below will demonstrate why NS-Creation Theory is actually totally inconsistent with the observations in columns 3 and 4.

Finally, we will show that there is another theory, described on this web site, called NS-Capture Theory, that is completely explained within the observed columns 3 and 4 (red cells), and renders NS-Creation theory unnecessary to explain the behavior of pulsars.

NS-Capture Theory says that there are pre-existing Neutron Stars in the Galaxy that can interact with normal stars and become bound in a binary system as a result of the interaction. i.e. the NS is “captured” by the regular star (cells: (3,1)->(3,2). After being captured by the regular star the NS then proceeds to totally destroy the regular star eventually leaving nothing behind except itself and the blown away remnants of the regular star.

The logic of the analysis below actually proves that NS-Capture Theory MUST be the correct explanation to the behavior of pulsars, because the observed data is inconsistent with the NS-Creation Theory, that leaves only the NS-Capture theory to explain the observations.

Terminology used in the diagrams

The content of this page explains how Diagram 0 was constructed, what all the elements in it mean, plus sub-diagrams representing specific sub-processes in the analysis. The diagram will be repeated below upon its logical completion from the analysis.

The cells in the diagram are referred to by row number and the column number of the cell being referred to:

( <row-number>, <column-number> ).

So, for example, “cell (3,2)” (or “(row 3, col 2)”), refers to row 3, column 2 in the diagram, which contains a box with a label “GS+SP(-)” in it.

Note that the box also has an arrow pointing into it from above, and an arrow pointing out of it from below, indicating the direction of evolution of the system.

The neutron star/pulsar icons on the diagram represent:

• fast spinning pulsars (FP),
• slow spinning pulsars (SP) and
• general non-spinning neutron stars (NS).

In addition, other entities that enter the analysis are:

• supernova explosions (SNE),
• supernova remnants (SNR),
• giant star (GS),
• giant star explosion (GSE),
• giant star remnants (GSR), and
• indicators of spin acceleration direction (in parentheses):
  • spin-up (+),
  • spin-down (-), and
  • steady or non-spin (0).

Finally a standalone “+” sign usually indicates a binary system, although it is also used to represent association between a FP and SNR or GSR.
An arrow “->” within a box is used to represent an event. Examples are:

1. a supernova event causing a fast pulsar to be created (SNE->FP), and the opposite:
2. a fast pulsar causes a supernova event to occur (FP->SNE).

One of the major points of this analysis is to determine whether (FP->SNE) is true, or if (SNE->FP) is true.  As will be shown below in the diagrammatic proof, it will be shown that the “fast pulsar (FP) causing (->) the supernova event (SNE)” is capable of explaining the full set of pulsar observations, while the “SNE causing the FP” cannot explain the binary pulsars and is unnecessary to explain the isolated pulsars.

The discovery of pulsars

The first pulsar was discovered in November 1967. It emitted pulses every 1.33 sec, and it still does. The most important early pulsar discovery was the Crab Pulsar found in the center of the remnants of a supernova explosion:

“The discovery of the Crab pulsar later in 1968 seemed to provide confirmation of the rotating neutron star model of pulsars.
The Crab pulsar has a 33-millisecond pulse period, which was too short to be consistent with other proposed models for pulsar emission.”

In addition to the above properties it was found that the Crab pulsar is slowing down and eventually the pulses will be too long and weak to be observed. The time of the slow-down to obscurity is on the order of 1 million years.

Therefore, observational evidence provided a model for pulsar behavior which basically says that a pulsar first appears in the midst of the remnants of a supernova explosion and eventually the remnants dissipate and the pulsar slows down until it is no longer visible.

Given that a pulsar is well understood to be a rotating neutron star that emits a radio pulse with each rotation, and that it uses up rotational energy with each pulse, we can assume that eventually it will end up as a non-rotating neutron star (at least having no observable rotation properties).

Detailed description of the Diagrammatic Proof

Diagram 1, which is a part of the diagram at the top of this page (Diagram 0), shows the observed pulsar process. The icons in this process are colored green to indicate that these states are observed, or at least predicted without any doubt.

The observed process (row 2,col 4) -> (row 5, col 4) is therefore:

FP(-)+SNR -> SP(-) -> NS(0) -> NS
(2,4) -> (3,4) -> (4,4) -> (5,4)

which can be read as:

1. A fast pulsar that is slowing down is observed within a nebula of supernova remnants (SNR) (row 2, col 4).
2. At a later time the remnants will have dissipated and the pulsar will have become an isolated slowing-down-pulsar SP(-) (row 3,col 4).
3. At a still later time the pulsar will no longer be observable, yet it will still exists an isolated NS(0), with no observable rotation properties (row 4, col 4).
4. Finally, millions of years later, the isolated NS will simply be floating through space with no observable characteristics, nor any historical evidence of its prior experiences (row 5,col 4).

 

Early theories of neutron stars and supernovae

Given the above observations, theoretical physicists embarked on developing theories of something that could explain the observations of these supernova events and pulsars.

The primary theory that quickly gained acceptance was that a massive giant star (GS) evolved to the point where it experienced a gravitational core collapse implosion which created a rapidly rotating neutron star (FP), and with an equally energetic explosion blowing up the rest of the GS into an observable cloud of supernova remnants (SNR).

We represent this theory in the main diagram (diagram 0, above) with the light blue cells in columns 5 and 4.

In Diagram 2, below, we add the theory (light blue boxes) to the observations (green boxes) of the previous diagram. The new cells are:

GS -> (FP->SNE) -> (FP + SNR)

which says:

1. A giant star (GS) evolves to the point just prior to core-collapse (row 2,col 5).
2. As a part of the core-collapse event a supernova explosion (SNE) is observed and creates a fast pulsar (FP) (row 1, col 5). Note that this is represented as SNE->FP in order to indicate that the SNE is what caused the FP to be created.
3. Immediately after the event the system moves to the top of column 4, where it will begin a new phase of its existence, becoming observable as a fast pulsar rotating within the supernova remnants (FP+SNR) (row 1, col 4).

These 3 (light blue) cells are what we refer to on this web site as NS-Creation Theory. i.e. this theory states the neutron stars are created in supernova explosions as fast pulsars, which eventually slow down to become isolated neutron stars floating through the cosmos. (By “cosmos” we are referring to the interstellar regions of the Milky Way Galaxy (MWG).)
We may also refer to this theory as “radio pulsar theory” since it is primarily based on observations done in radio wavelengths on earth-based radio telescopes.

Note: Row 1 may be thought of as a row that contains either an “event“, that completes the process that has evolved upward in the column below it, or the “initial state“, which is the starting point for the column that evolves downward, below it. i.e. in row 1 events occur (namely supernova explosions (SNE) that cause the system that had been evolving in which the event occurred at the top of the column, which then immediately becomes a new initial system state at the top of the adjacent column, which then proceeds to evolve down the column.

So, in this case we have the NS-Creation theory of the cause of SuperNova Explosion (SNE) event in (row 1,col 5), being the end of the evolution of the Giant Star (GS) (row 2, col 5).

That SNE event that created the Fast Pulsar (FP) plus the SuperNova Remnants (SNR) then becomes the initial state in the adjacent column (row 1, col 4).

X-ray Astronomy Observations

In December 1970, an x-ray satellite, named Uhuru,  was launched from Kenya, which would prove to be the beginning of a whole new era of our understanding of the universe. The effects of the discoveries from this satellite are still being understood and revealing the answers to many mysteries, with explanations that were never expected. In short, X-ray astronomy has been a scientific revolution that forces us to completely re-examine much of what has previously been the standard astronomical interpretation of the observations of the stars.

Almost four years to the day, after the discovery of the first pulsar in November 1967, a discovery was made in November 1971, that would change our understanding of the universe forever.

That discovery was that Cen X-3 is a pulsar in a binary system, and that unlike all previous pulsars that had been spinning down, the Cen X-3 pulsar is actually spinning up: as time goes by it is spinning faster and faster!

The purpose of this web site is to explain and understand this revolutionary discovery and how it changes our view of the Galaxy, and, by extension, the Universe.

The whole explanation is contained in the diagram at the top of this page, but we need to continue building the diagram, one step at a time, in order to understand its significance.

The first step is to add the x-ray observations to the diagram. We have added 3 new cells in column 3 of diagram 3 below that we are continuing to build on diagram 1 and diagram 2.

In diagram 3, if we look in column 3, we see that three new cells have been filled in the correspond to observations of x-ray pulsars.

NS(0)+GS -> SP(+)+GS -> FP(+)+GS
(r4, c3) -> (r3, c3) -> (r2, c3)

What this diagram says is that the following process is observed in the measurements of the X-rays detected by an X-ray satellite, such as Uhuru:

1. A non-spinning neutron star (NS) is found orbiting a giant star (GS), and x-rays are emitted because the NS is gravitationally and magnetically interacting with the atmosphere of the GS. The orbit tends to be highly elliptical with the NS-GS interactions only emitting x-rays in the part of the orbit around the distance of closest approach. (4,3)
2. After many orbits of the NS around the GS, the NS starts to noticeably spin-up and becomes a slow spinning-up pulsar (SP(+)), where the “+” indicates spinning up. The orbit is still elliptical but the eccentricity of the orbit decreases with each cycle of the orbit, with the distance of closest approach slightly decreasing as well, and the distance of furthest approach having major decreases. (3,3)
3. After many orbits of the slow pulsar, the orbit circularizes and the SP(+) has become a fast spinning-up pulsar (FP(+)), and is constantly emitting x-rays that are generated by material being gravitationally pulled from the atmosphere of the GS and causing the spin-rate to accelerate, and the circular orbit begins to shrink in radius as the FP(+) burrows its way deeper and deeper into the atmosphere of the GS. (2,3)

Note that all 3 boxes are green, indicating that these are observations directly derived from the observed X-ray data. The only theoretical aspect associated with these observations is that the pulsars are in binary systems. That determination was made by applying well-known mathematical principles of Simple Harmonic Oscillators, ellipses, circles, and Newtonian mechanics. These principles are applied in a standard manner and mathematics described in those principles exactly matches the data, resulting in an unquestioned representation of a binary system, consisting of a rotating NS (pulsar) around a giant star (GS) companion.

Notice that unlike the post supernova cells in the earlier diagram of column 4, where the arrows point down indicating the pulsar is spinning down, in the binary system the arrows in column 3 point up indicating that the pulsar is spinning up. i.e.

•  a lone pulsar spins down emitting radio waves and
• a binary pulsar with GS companion spins up emitting x-rays.

At this point our diagram has 2 observed (green cell) processes, column 3 evolving vertically upward ( (row 4, col 3) -> (row 2, col 3) ), and column 4, evolving vertically downward ( (row 2, col 4) -> (row 5, col 4) ) , along with the NS-Creation radio theory (light blue cells), column 5,  that is intended by NS-Creation Theory to explain the spin-down process in column 4.

What remains to be done is to develop a theory that, in addition to explaining the observations of the spin-down process in column 4, also explains the observations of the spin-up process in column 3.

i.e. we need a theory that explains both the spinning down and the spinning up of the pulsars observed to be experiencing these processes.

The Attempt to Apply NS-Creation Theory to Binary X-ray Pulsars

As described in the previous section, X-ray observations resulted in the discovery of the first binary x-ray pulsars (1971-1972), which were discovered to be in close binary systems, where the neutron star pulsar was gravitationally drawing in material from the companion’s atmosphere along the pulsar’s magnetic field lines. By directing the inflow along the magnetic poles, a specific torque is created that acts like a long lever causing the neutron star to rotate with a spin axis perpendicular to its magnetic pole axis. In this manner the magnetic poles rotate around the equator of the spin axis, and, as a result, with each rotation, we observe a “pulse” as the magnetic axis sweeps through our line of sight, thus being a “pulsar”.

The result of this process is a spinning-up x-ray pulsar in a close binary system, where the companion is a giant star. The first known example of this phenomenon was discovered in November 1971, when it was found that the Cen X-3 pulsar was in a close binary system with a giant star. (Note: Cen X-3 was the first pulsar of any kind discovered in a binary system.)

In addition to being in a close binary, it was also discovered that Cen X-3 is spinning up. i.e. its rotation rate is increasing and its rotation period is decreasing.

When compared to the other pulsars that had been discovered, Cen X-3 had the following properties that distinguished it from the isolated radio pulsars that had been discovered in the previous 4 years:

1. Cen X-3 pulsar is in binary system; radio pulsars are isolated
2. Cen X-3 pulsar is spinning up; radio pulsars are spinning down
3. Cen X-3 emits high energy x-rays; radio pulsars emit low energy radio waves

In the sections above it was stated that theorists developed the NS-Creation core collapse theory to explain the creation of fast spinning, spinning-down, isolated radio pulsars.

Since this mechanism is used to explain how a neutron star (NS) can be created out of a giant star (GS), it was assumed that one could apply this mechanism to explain the presence of the NS in the Cen X-3 binary system.

Basically, using NS-Creation Theory to create a pulsar in a close binary system with a giant star (GS), one must begin with a system consisting of 2 GS’s, where one of them explodes in a SNE in order to create the NS that is found in the Cen X-3 system. Since Cen X-3 is a GS, and a GS is also required to create a FP, the original system had to have been 2 GS’s, as shown in cell (2,1).

Diagram 4 shows how NS-Creation theory is used to explain the x-ray binaries.

The following statements are equivalent to what is shown in diagram 4:

GS+GS -> GS+(SNE->FP) ->
(2,1) -> (1,1) ->
GS+(FP+SNR) -> GS+FP(-) -> GS+SP(-) -> GS+NS(0)
(1,2) -> (2,2) -> (3,2) -> (4,2)

The above statements are shown as dark blue icons in Diagram 4, which represent the NS-Creation Theory of the creation of x-ray binary systems:

The above statements basically say:

1. Originally there was a binary system comprised of 2 GS’s (row 2, col1).
2. One of the GS’s experienced a SNE producing a fast spinning pulsar  (SNE -> FP), that would continue orbiting around the other GS (row 1, col 1).
3. The resulting system would be a GS plus a FP, surrounded by supernova remnants (SNR) (row 1, col 2)).
4. Similar to the isolated radio pulsars, it was assumed that this FP(-) would also spin down, while continuing to orbit its GS companion (row 2,col 2).
5. The FP(-) would continue to slow down to become a SP(-) (row 3, col 2).
6. And eventually the pulsar rotation would become too weak to be observed, which would result in a GS+NS(0) binary (row 4, col 2).

NS-Creation theory vs X-ray Observations

Diagram 5, below, shows the NS-Creation binary theory (dark blue icons) from Diagram 4 in the previous section along with the x-ray observations (green icons) as shown in Diagram 3.
For completeness we also include the NS-Creation isolated pulsar theory that was also included in Diagram 3.

The cell sequences for diagram 5 are the following:

NS-Creation Theory: Binary pulsar spinning down in column 2,
then spinning up in column 3
Col 1:  GS+GS  -> GS+(SNE->FP) ->
Col 2:  GS+(FP+SNR) -> GS+FP(-) -> GS+SP(-) -> GS+NS(0) ->
Col 3:  GS+NS(0) -> GS+SP(+)  -> GS+FP(+) -> ??? ->

NS-Creation Theory: Isolated fast pulsar created in column 5,
then spinnng down in column 4.
Col 5:  GS -> (SNE->FP) ->
Col 4:  FP+SNR -> FP(-) -> SP(-) -> NS(0) -> NS

Note: the sequences above show the states in the order that they occur in the two processes.

Col 1 -> Col 2 are the NS-Creation binary pulsar theoretical states (dark blue)
Col 3 is the X-ray pulsar observed states (green)
Col 5: is the NS-Creation isolated pulsar theoretical states (light blue)
Col 4: is the radio pulsar observed states (green)

Note: we have never actually “seen” an isolated GS explode and produce a FP + SNR. However, we do observe the after-effects of a GS explosion, namely, FP(-)+SNR, as in cell (2,4). However, its origin in cells (2,5) -> (1,5) -> (1,4), is purely theoretical.
However, one could say we have observed a before and after scenario in the SNE: SN1987A. In that reference, it is stated that:

“it is now widely understood that blue supergiants are natural progenitors of some supernovae, although there is still speculation that the evolution of such stars could require mass loss involving a binary companion”

If, indeed, there originally was a binary companion before the SNE, then this would not be an isolated GS exploding. It would be a close binary similar to the x-ray pulsars such as Cen X-3, which also orbits a blue supergiant.

In addition, the identification of SN1987A with a blue supergiant was described in the above reference:

“Four days after the event was recorded, the progenitor star was tentatively identified as Sanduleak −69 202 (Sk -69 202), a blue supergiant.
After the supernova faded, that identification was definitely confirmed by Sk −69 202 having disappeared.”

Note: the theories in blue, generally precede the observations in green. This is expected as the theory’s intent is to explain how the observations came into existence.
Note: at the end of the process in Col 3 there is a “???”. This indicates that there is not much that has been said about the end state of the GS-Xray Binaries. However, we shall address that below.
Note: there is no connection yet between columns 3 and 4. This will also be addressed below.

Analysis

This section is the most important section of this page. It contains the fundamental reason that the NS-Creation theory does not work for binary x-ray pulsars.

In diagram 5 above, note the following cells:

(2,2): GS+FP(-)
(2,3): GS+FP(+)

(3,2): GS+SP(-)
(3,3): GS+SP(+)

(4,2): GS+NS(0)
(4,3): GS+NS(0)

Note that (row 4, col 2) => (row 4, col 3). This indicates that the same state that is the endpoint of evolving down col 2 is also the starting point for evolving up col 3. This should be read as:

After the NS has spun down, it accompanies its companion for a long time, until finally the conditions change enabling the NS to spin up again.

This is an assumption of the NS-Creation theory that there is a way to explain the contradiction of the cells in rows 2 and 3.

• The cells (row 2, col 2) and (row 2, col 3) contradict each other.
  NS-Creation claims that a FP can spin down in the presence of a GS.
  The only observations of a FP in the presence of a GS have the FP spinning up.
• The cells (row 3, col 2) and (row 3,col 3) also contradict each other, and just represent slower spin-rates than row 2.

Therefore the theoretical predictions of NS-Creation theory are in direct contradiction with the observations of binary x-ray pulsars with GS companions.

There are 2 ways to resolve this contradiction:

1. Make observations that show the spin-down states in col 2.
2. Conclude that NS-Creation cannot be used to explain binary x-ray pulsars.

No observations have been made of radio pulsars with GS companions that are slowing down.

Hundreds of observations have been made of isolated pulsars that are slowing down.

In order to maintain a population of GS-binary x-ray pulsars, there needs to be a mechanism to produce these binary systems on a steady basis in order to explain the population of the short-lived GS-binary x-ray pulsars which have an expected observable life of only about 1 million years.

Therefore we should see dozens of GS-binary radio pulsars to support the NS-Creation theory. However, there are no such observations. Therefore we must conclude that NS-Creation theory fails for GS-binary x-ray pulsars.

Introducing the NS-Capture Theory

Since there is no known mechanism to create a slow x-ray pulsar in a GS-binary x-ray system using stellar evolutionary processes, we must conclude that the neutron stars found in these systems must have come from some external origin.
i.e. the model that one member of a binary system experiences a SNE and then slows down in the presence of its companion is simply not observed, and if it was a feasible mechanism it should be observed.

We therefore conclude that the neutron star (NS) that is the companion of a giant star (GS) in a binary x-ray system must have originated from elsewhere in interstellar space and had a binding collision with the GS resulting in a GS+NS(0) system as in cell (4,3).

How can neutron stars originate in interstellar space?

The only feasible mechanism is that they have always been there, and with our observing capabilities we simply have not yet seen them except in these extreme situations where one of them encounters a normal star and in the course of a few million years simply destroys that star, spins down, and resumes what was its original quiet journey through space.

We have done preliminary calculations to estimate the number of neutron stars (NS) required to provide the collision rate necessary to produce the observed population of GS-binary x-ray systems, and, by extension, any binary x-ray system regardless of the size of the companion.

Those preliminary calculations indicate that in order to create the observed population of x-ray binaries, there would need to be somewhere in the range of 5->50 times the number of NS’s as regular stars (RS’s).

i.e. in a 4 light year sphere with the Sun at the center and the closest star, Alpha Centauri, on the surface of that sphere, then within the 4 light year sphere around the Sun there must exist  somewhere in the range of 5 to 50 neutron stars.

We can represent this in Diagram 6, where we simply add one new cell, (row 5, col 3), that shows an isolated NS and an isolated GS coming within range of each other for the first time and colliding in a manner such that they will remain bound, resulting in the GS+NS(0) cell in (row 4, col 3).

We color the entities in (row 5, col 3) red in order to indicate that they are part of the NS-Capture theory, as opposed to the NS-Creation theory (blue), or the observed states (green). The following is a textual representation of the capture and spin-up process shown in column 3.

Col 3:  ([GS] [NS]) -> GS+NS(0) -> GS+SP(+)  -> GS+FP(+) -> ??? ->

For a textual representation of the isolated NS and GS in cell (5,3) we have chosen to show the [GS] and [NS] in square brackets to show they are isolated from each other and in red to show they are part of NS-Capture Theory. At the same time, we have enclosed the 2 isolated entities in parentheses in order to indicate that these two isolated entities are in the same state box on the diagram, and have come within significant gravitational contact with each other.

One might consider another possibility that the NS created as a FP in (row 1, col 1) is actually created as a non-spinning NS, which would make it immediately jump down to (row 4, col 2).
However, this is contradicted by the P/P-dot diagram which shows that all pulsars are created in the upper left in SNE’s and subsequently slow down. Therefore there is no evidence that a NS can be created as anything other than a fast pulsar (FP).

NS-Capture Theory: Part 2

Diagram 6, above, is almost complete except for the fact that there is still a gap between columns 3 and 4. These are the two “observation” columns. In column 3, we have an observed process that spins a neutron star up to become a fast pulsar. In column 4, we have an observed process that spins a fast pulsar down to become a non-observable neutron star.

In Diagram 7 we show that the fast pulsar in (row 2,col 3) is continuing to spin up, while accreting from its GS companion, there must be an end to this process that results in the destruction of the GS leaving only the FP amidst the remnants of the destroyed GS. This is shown in (row 1,col 3). i.e. the FP(+) will continue to orbit through the atmosphere of the GS companion in (row 2, col 3) until the point of destruction in (row 1, col 3).

We now assert that the result of the state (row 1, col 3) will immediately change the behavior of the system to that of (row 1, col 4). i.e. instead of a GS+FP(+), we now have a GSR+FP(-), shown as (row 1, col 4) immediately starts behaving as any pulsar amidst remnants in (row 2, col 4).

The above diagram is the completed NS-Capture and NS-Creation diagram that was introduced at the top of this page. The red cells are the NS-Capture theory:

1. At the bottom of column 3 (row 5, col 3), the cell shows a NS and GS encountering each other, which results in a binding collision to form the x-ray binary, GS+NS(0), shown in cell (row 4, col 3). This is the heart of the NS-Capture Theory, namely that there are huge numbers of neutron stars in interstellar space. The number is so huge that there must be, in fact, at least 5-100 NS’s for every RS (regular star).
2. The two new red  cells in the top row (row 1, col 3)->(row 1,col 4) shows the NS-Capture Theory of Supernova Explosions, namely that the end result a capture such as described in item 1, above, is the explosion of a Giant Star, leaving a fast pulsar (FP) amidst the giant star remnants (GSR), which may, in fact, be exactly what Supernova Remnants (SNR) appear to be.

The bottom line is that the red cells  (row 5 col,3), representing the capture part of the NS-Capture Theory, and the two red cells (row 1, col 3) -> (row 1, col 4), representing the Supernova (SNE) part of NS-Capture Theory, together represent a complete theory that is both necessary and sufficient to explain all the known major properties of all known pulsars.

Impact of the NS-Capture Theory on the Diagram

Since observations have forced us to discard the NS-Creation theory as a possible source of the NS found in cell (row 4, col 3), and replaced that theory with the NS-Capture theory resulting in the addition of cell (row 5, col 3) to the process, there is no longer any need to retain the entries in col 1 and col 2 in diagram 7, which we remove in diagram 8, below.

Diagram 8, above, now shows the complete NS-Capture Theory (cols 3->4) plus the single pulsar NS-Creation Theory (cols 5->4).

We now have to introduce the second main prediction of the NS-Capture theory, which is that the GS+NS(0) system in cell (4,3), resulting from the capture from cell (5,3), will evolve up the column to cell (2,3), where it is a fast pulsar that is continuing to spin-up while in a close binary circular orbit around the GS companion.

It is the assertion of NS-Capture theory that eventually cell (2,3) must totally destroy the GS in a giant star explosion (GSE) in cell (1,3), which then becomes a fast pulsar spinning down in the midst of giant star remnants (GSR) in cell (1,4). The portion of these 2 cells that are part of the NS-Capture theory are shown in red.

From a more logical perspective, we must consider that we have a choice between two proposed mechanisms to create a SuperNova Explosion (SNE) with a Fast Pulsar spinning down among the remnants.

Basically the choice is between:

1. (row 2, col 3) which contains a Giant Star on the verge of destruction plus a Fast Pulsar observed to be the cause of the destruction.
2. (row 2, col 5) which contains a Giant Star that theoretically has evolved to a point where it will self-destruct and create a Fast Pulsar in the process.

The big advantage to choice 1, obviously, is the fact that a Fast Pulsar is already in place and causing the destruction, and this situation is observed in many x-ray binary sources, and therefore this is the assertion of NS-Capture Theory.

Therefore, NS-Capture provides us with a complete theory of pulsars and supernova events, and removes any need to use the process of NS-Creation to explain any aspect of the complete theory, which will be explained in more detail in the next section.

NS-Capture theory vs NS-Creation theory

The result of this analysis so far is shown in the previous diagram, which shows the NS-Capture theory in red plus the NS-Creation single pulsar theory in light blue.

However, we must now consider whether we must retain both theories of isolated pulsars that converge in cell (1,4).

Thus we now have the full NS-Capture theory process represented on the diagram in columns 3 and 4, as well as the full NS-Creation theory: isolated pulsar process represented on the diagram in columns 5 and 4, and all textually by the following statements.

Col 3:  ([GS] [NS]) -> GS+NS(0) -> GS+SP(+)  -> GS+FP(+) -> (FP->GSE) ->
Col 4a:  FP+GSR -> FP(-) -> SP(-) -> NS(0) -> NS

Col 5:  GS -> (SNE->FP) ->
Col 4b:  FP+SNR -> FP(-) -> SP(-) -> NS(0) -> NS

Note that we now have two theories of how to create a fast slowing-down pulsar, which are:

• the NS-Capture theory in col 3 that results in the FP+GSR in col 4a
• the NS-Creation theory in col 5 that results in the FP+SNR in col 4b

It is actually only the top cell in col 4: (1,4) that has two possible entry points, one from col 3 and the other from col 5. We have designated those 2 entry points as col 4a and 4b above. i.e. both entry points are shown in cell (1,4), one in red and one in blue, to account for the two theories, but the rest of column 4 is a common set of observations shown in green.

Our necessary conclusion that the origin of GS-binary x-ray systems must be from a pre-existing population of what has preliminarily been calculated to be a population of size 5->25 times the population of regular stars in the Milky Way Galaxy (MWG), puts us in the situation where there must already be billions upon billions of NS’s existing in the MWG.

It is clear that the rate of SNE’s observed in the MWG, given the age of the MWG of around 15 billion years, would not be sufficient to produce even a tiny fraction of the NS’s required for NS-Capture theory.

Therefore, we conclude that there is no necessity for the NS-Creation theory to be used to create neutron stars, because there are already more than enough NS’s in existence based on the necessity to provide them for NS-Capture theory.

We can therefore remove the light blue cells from col 5, and the light blue item in cell (1,4) to produce our final Diagram 9 representing NS-Capture theory as the only possible explanation of both the existence of GS-binary x-ray systems, as well as the mechanism to explain the phenomenon of SuperNova Explosions (SNE) as the result of a NS-Capture.

We are also asserting that this analysis results in a “QED” for NS-Capture and welcome any relevant discussion to further understand the phenomenon of pulsars.

General Considerations of the Quality of the Above “Proof”

On the “proof”, there are 3 main items or sections involved that need to be viewed in sequence and apply to 3 different parts of the diagram.

1. The most important is the contradiction between cols 2 and col 3, as previously shown in diagram 5, with the thoeretical GS+FP(-) being compared to the observed GS+FP(+), which forces the introduction of NS-Capture theory in diagram 6.
   This may be viewed as a theoretical contradiction based on observation. i.e. spin-up is observed in col 2 and there is theoretical support for that observation based on the notion of accretion.
   It also may be seen as a common sense contradiction since one has to come up with a method for the FP to spin down in col 2.
   The above points combined make a fairly strong case that an FP created by SNE->FP in GS+FP cannot slow down.In addition to the “theoretical” case, there is the fact that there are no pulsars w GS companions observed spinning down. There really should be 10’s of them. i.e. we see hundreds of isolated pulsars spinning down, but all the pulsars seen in GS+FP or GS+SP systems are spinning up.
   That is the core of the proof, where the “proof” is the combo of the observations of GS+spin-up, the theory, and the corresponding lack of observations of GS+spin-down.
2. The next part of the “proof” is the assertion that cell (2,3) will blow up into cell (1,3). i.e. the event “FP->GSE” is a common sense conclusion based on the fact that the NS is pumping 10**39 ergs/sec into its companion and that is never going to stop because there is no way for the NS to go away.
3. The final part of the proof is the equating of GSE==SNE and GSR==SNR.
   We are not saying that we “know” that a GSE as it’s portrayed in the NS-Capture scenario will blow up in a way that is exactly like observations like the Crab Nebula.
   All we are asserting is that the GSE will actually take place, and that the FP will subsequently blow the GSR away.

The value of diagram 10 (which is a repeat of diagrams 0 and 7, and placed here, again, for convenience) is that it allows us to look at these 3 aspects of the whole story in isolation from each other.

The first main item, Item 1, above, is viewed as a direct challenge to the current GS+GS theory of binaries represented by col 1 and col 2.

Item 2, above, is viewed as providing an observed path to a NS turning into a FP exploding a captured star.

Item 3, above, is viewed as kind of an open question: mainly it seems obvious to me that based on item 2, that item 3 would be a logical next step, however by keeping these 3 issues separate, we can deal with them separately but in the common context of the whole diagram.