Proof of the Neutron Star Capture Theory

Description of proof:

At a high level, the problem we are trying to solve is what is the cause of SuperNova Explosions (SNE’s) and the origin of the neutron star pulsars associated with several of these SNE’s.

The fundamental approach to proving the NS-Capture Theory is to disprove the NS-Creation Theory. We can make an assertion that given the existence of a fast-spinning NS  pulsar amidst a giant cloud of SuperNova Remnants (SNR), that one and only one of the following must be true:

  1. EITHER (NS-Creation): the neutron star did not exist before the Supernova explosion, and it was an isolated giant star that exploded, leaving the SNR and neutron star behind, which means the neutron star was “created” by and during  the Supernova explosion, thus the term “NS-Creation Theory”,
  2. OR (NS-Capture): the neutron star was present before the Supernova explosion and most probably caused the supernova explosion, which means that the neutron star must have come from somewhere else and had an encounter with the star, and become bound to the star, and remained bound to the star until the star exploded in a Supernova explosion, thus the term “NS-Capture Theory”.

We observe two situations to consider:

  1. We have observations of fast pulsars spinning down in the aftermath of an SNE.
  2. We have observations of slow pulsars spinning up in the context of a close binary system where the pulsar’s orbit at distance of closest approach creates interaction with a giant star companion.

What we think on this site is that: the spinning-up close pulsar system in item 2 is going to cause the GS companion to blow up in an SNE after the pulsar has  spun up to become a fast pulsar, and after heating up the companion, the fast pulsar destroys its giant star companion leaving remnants behind that are consistent with item 2.

Since neutron stars that are known to be present in X-ray binary systems (i.e. NS is there before any observed explosion), and it is known that the companion star in these X-ray binary systems can only survive for about one million years with the neutron star present (because of the heat that the NS adds to its companion), this means the neutron star must have somehow been introduced to its companion in the last million years or so.
Thus the neutron star must have had its first encounter with the companion within the last million years, and as a result of that encounter, then became part of a new X-ray binary system.

The above statement can be reduced to the following:

  1. EITHER the neutron star (in the GS+NS binary) was created by a supernova explosion of a previously existing GS companion in a binary GS pair converting one of the GS’s into a neutron star pulsar (GS+GS => GS+SNE(FP(=)) => GS+SNR(FP(=)) => GS+FP(-),
  2. OR: the neutron star was introduced by some other mechanism, such as NS-Capture: GS,NS => GS+NS and then the NS spun up and caused the GS to blow up in a supernova explosion.

Both these statements cannot be true, yet one of them MUST be true, otherwise there would not be neutron stars associated with supernova explosions. What we are saying is that the NS in an NS+GS system had to have been introduced within the last million years. And the only 2 ways it could have been introduced:

  1. A pre-existing GS+GS binary had one of its GS’s blow up in an SNE leaving the NS behind, thus creating the GS+NS system that we are trying to explain (NS-Creation).
  2. Or, if 1 is false, then the NS must have come from somewhere else and been captured by the GS within the last million years, thus creating the GS+NS system we are trying to explain (NS-Capture).

Therefore, if we can prove that the NS-Creation theory is false, then the NS-Capture theory MUST be true.

That is the intention of the initial proof of the NS-Capture theory: i.e. to prove its truth by proving the falsehood of the NS-Creation theory.

Context for Proof based on the Crab

The Crab was one of the first pulsars discovered (1968). It pulses at 33 pulses per second in the low energy radio wavelengths. It was found in the midst of a supernova remnant (SNR) that was observed by Chinese astronomers in 1054 AD. They observed the SNE that produced the SNR. Also, it has since been determined that the pulsar was traveling through the supernova remnants at a high speed, and its trajectory could be traced back to the center of the supernova remnants indicating it was right at the star when the star exploded.

Because of the high rotation speed, it was determined that the pulsar must be a neutron star, which until that moment had only been a theoretical concept: no one had ever observed anything that there was any reason to believe was a neutron star, but observations of the Crab pulsar “proved” that it is a neutron star.

Naturally, scientists started coming up with theories of how this neutron star came into existence, and the popular theory that was agreed upon (NS-Creation), was that the original star that exploded as a supernova, simultaneously imploded as well, leaving a neutron star in the remnants.

This NS-Creation theory is what this web site is disproving, which will force us to accept the only alternative: NS-Capture.

However, there are some problems with the NS-Creation theory, such as:

  1. Why is the neutron star traveling through the supernova remnants? If the explosion was symmetric in all directions, the neutron star would remain near the center. In order to explain its post-explosion motion, it became necessary to assert that the explosion was highly asymmetric. After all, to give a 1.4 solar mass a velocity of hundreds of miles per second requires a pretty good kick.
  2. Why is the neutron star pulsing? We know it is pulsing because it has a huge magnetic field that has its polar axis perpendicular to its rotation axis. But why would the initial explosion create such a situation. Nobody really knows what exactly would happen in the several seconds that it took the neutron star to be created by gravitational collapse.
  3. Why is it rotating so fast? i.e. if it is 30 rotations per second now, it must have been 100 or more rotations per second when it was created in 1054 AD, based on the rate that it is slowing down.
  4. Why does a star explode in a supernova?
    Is it internally caused by natural evolution of the star (NS-Creation Theory),
    or is it externally caused (NS-Capture Theory)?
    (for example, because a neutron star collided with it, became bound in a close binary orbit, and actually caused the star to explode by pumping so much energy into it via X-rays, that the star effectively becomes gravitationally unbound (NS-Capture Theory)

Some reasonable answers (which we refer to as NS-Creation Theory) had been suggested to explain the above phenomena in the years following the 1968 discovery, but those conjectures have been shown to be inadequate and contradictory to the new set of questions that arose when the Cen X-3 pulsar was discovered in 1971, just 3 years after the Crab pulsar was discovered.

Context for Proof Based on Cen X-3

The proof that is going to be presented is an empirical proof. It is based on the 1974-proof, which was published in the Meta Research Bulletin edited by Tom van Flandern in 1993:
(see also: “Dark Matter, Missing Planets & New Comets” by Tom van Flandern: The Secret of the Pulsars listed on p484, as appearing in Meta Research Bulletin, Volume II, p30-38.)

Unfortunately, the above site appears to be inactive, but I will put a copy of the paper on this site in the near future. Be that as it may, we shall push forward and continue with the proof in basically a self-contained manner on this page.

First, given the context of the Crab above, we must talk a bit about what Cen X-3 is, and then put that together with the Crab.

The properties of Cen X-3 will give us our empirical proof that the NS-Creation theory falls short and leads to self-contradiction, which as described above forces us to choose the NS-Capture theory, which implies there are 25 times as many neutron stars as there are regular stars in the galaxy, which means there are 5 trillion neutron stars in the Milky Way Galaxy. Enough with the preliminaries, now, let’s get right into the meat of the proof.

Cen X-3 was first discovered to be an X-ray source in 1967 as a result of a sounding rocket study, which simply determined that there were X-rays coming from a specific location in the constellation Centaurus.

Then, in May 1971, this X-ray source was examined by the Uhuru satellite, and discovered to be pulsing in X-rays, once every 4.8 seconds. This represented the first time a pulsar had been discovered at wavelengths other than radio waves. X-rays are much stronger than radio waves, in fact, X-rays contain 100,000 times as much energy as visible light waves, which, in turn, contain 1 million or more times as much energy as radio waves. Therefore, an X-ray pulsar is a much more powerful emitter of radiation than a normal radio pulsar.

Then, in December 1971, an even more remarkable discovery was made about Cen X-3. It was indisputably disputably to be in a close binary system, such that it was determined to be a neutron star orbiting in the upper atmosphere of a companion star every 2.1 days. The source of X-rays was therefore determined to be the result of material from the atmosphere of the companion star being accelerated in the huge magnetic and gravitational fields of the neutron star 4.8 second X-ray pulsar. It was known that Cen X-3 was right in its companion’s atmosphere, because it pulsar was eclipsed of 90 degrees or one quarter of the orbit, plus the spectrum showed absorption when the pulsar was just entering and just leaving the eclipse.

In addition, one more amazing fact was determined about the Cen X-3 4.8 second pulsar in Dec 1971:

  • All the radio pulsars that had been discovered, as isolated pulsars were not in binary systems and their spin rate was slowing down.
  • However, measurements on the Cen X-3 pulsar determined that its spin rate was speeding up! And, ongoing measurements for the last 48 years have shown that it continues to spin up.

It was determined that the reason the Cen X-3 pulsar was speeding up was that the material falling into Cen X-3’s huge gravitational field was exerting a torque on it, causing it to spin faster, much the way when an figure skater spins faster when they pull their arms in.

To complete the Cen X-3 contextual framework, there was one more discovery made in 1974, the companion star to the Cen X-3 pulsar was determined to be an O-type supergiant, called Krzeminski’s star. This O-type supergiant is 20.5 times the mass of the Sun, and 12 times the radius of the Sun.

That means that the circumference of the Cen X-3 orbit around the supergiant is approximately 30 million miles, which means that for it to have a 2-day orbit, that it must be travelling about 200 miles per second (calculated to be 339 km/sec).

Proof of the NS-Capture Theory

Now that we have sufficient context (facts related to the situation, at hand), we can show the actual proof that the NS-Capture Theory MUST be true, because the NS-Creation Theory MUST be false.

What we are going to show is that while the NS-Creation theory was acceptable to explain the radio pulsars alone, the facts of Cen X-3 determined that the NS-Creation theory could NOT explain the Cen X-3 pulsar, and therefore, another explanation was required, which could only be the NS-Capture theory. The requirement to use the NS-Capture theory then renders to NS-Creation theory moot and not necessary to explain the radio pulsars. For more detailed proof the reader is suggested to go to the diagrammatic proof page.

Theorem I: X-ray Binaries are formed by neutron star capture

The essence of the proof is the following:

  • Based on the Crab, when a pulsar is created, it has a rapid rotation rate and a high observed velocity with respect to the supernova remnants in which it is immersed.
  • Based on Cen X-3 observations, if the Cen X-3 pulsar was created in the same way as the Crab pulsar, then it would have been created with a rapid rotation rate. However, Cen X-3 has a slow rotation rate, 100 times slower than the Crab pulsar.
  • In addition, the Cen X-3 pulsar system [GS+SP(+)] is speeding up, as opposed to the Crab pulsar, which is slowing down.
  • Therefore, since the Cen X-3 pulsar is slow and speeding up, then it could not have been created as a fast pulsar that was slowing down, like the Crab, because the Cen X-3 pulsar is in an environment where it is speeding up! i.e. how could it have slowed down?

This is the fundamental contradiction that is created by assuming that a pulsar is created by a supernova explosion. i.e. if the Cen X-3 pulsar was created as a fast pulsar, how did it spin down to become a slow pulsar, in an environmental one way street for spinning up.

The fundamental question that must be answered is how does one create a rapidly rotating neutron star that is traveling through supernova remnants of a star that recently exploded?

The solution can be one of two possibilities:

  1. EITHER, the neutron star was created as a result of the supernova explosion, and in the process of creation was given a rapid rotation rate with its magnetic poles perpendicular to it rotation axis, plus it was given an asymmetric kick to give it a large velocity with respect to the explosion remnants that created it,
  2. OR, the neutron star existed prior to the supernova explosion and, in fact, caused the supernova explosion using the NS-Capture method for its initial conditions. i.e. use capture to create a GS+NS binary, spin the NS up to GS+FP(+), blow the GS away: SNE+FP(+).

All by itself, the fact that supernova explosion results in a rapidly rotating neutron star pulsar, is sufficient to logically prove that the pulsar in Cen X-3 could not have been created in a supernova explosion. The reason is that the Cen X-3 pulsar is slow and speeding up, and the fact that it is speeding up means that it is in an environment where it could not have slowed down, and as a result we must conclude that the Cen X-3 pulsar could not have been created by a supernova explosion, because NS-Creation would require the state chain:

[GS+FP(+)] => [GS+SP(+)]           NS-Creation (physically impossible)

which is inconsistent with the observed state chain:

[GS+SP(+) => [GS+FP(+)]            NS-Capture (physically observed)

This fundamental contradiction is only the beginning of the analysis, however, it leads us directly to a completely different set of conclusions as to how pulsars are created and how supernova explosions occur.


Next we will look at the implications of the pulsar spin contradiction. i.e. we will examine more precisely what the contradiction means in terms of the constraints that resolving puts on the evolution of Cen X-3 and similar systems.