# Logical Proof of the NS-Capture Theory

The purpose of this web site is to present, explain, discuss, and prove the Neutron Star Capture Theory (NS-Capture Theory), which claims that neutron star pulsars “cause” supernova explosions, as opposed to neutron star pulsars being “created” by supernova explosions. This page begins the language structuring for the logical proof.

The alternative theory is the Neutron Star Creation Theory (NS-Creation Theory), which says that a giant star explodes, and the corresponding implosion is what creates a neutron star. For example, the following describes NS-Creation:
https://www.space.com/22180-neutron-stars.html

In order to create a logical proof, we need a taxonomy of definitions of the critical entities and events that comprise the theory.

To start, we will provide a few definitions to be used in the logical analysis. These definitions are constructed in order to express evolution of stars and pulsars

• Entities:
• GS = Giant Star
• RS = Regular Star (generally any star incl giants)
• SNE = SuperNova Explosion
• SNR = SuperNova Remnants (all the stuff left over after the SNE)
• NS = Neutron Star (generic NS)
• NS(0) = Neutron Star (generic non-pulsing NS)
• FP = Fast Pulsar (generic fast pulsing NS)
• FP(-) = Fast Pulsar (FP where pulses/sec is decreasing (spin-down)
• FP(+) = Fast Pulsar (FP where pulses/sec is increasing (spin-up))
• FP(=) = Fast Pulsar (FP where pulses/sec reached max and spin-down begins)
• SP = Slow Pulsar (generic slow pulsing NS)
• SP = Slow Pulsar (SP where pulses/sec is increasing (spin-up))
• SP = Slow Pulsar (PS where pulses/sec is decreasing (spin-down))
• Events:
• sne = SuperNova Explosion
• sd = Spin Down  (pulsar slowing down)
• su = Spin Up  (pulsar speeding up)
• si =  Spiral In  (pulsar spiraling in toward the core of its companion)
• bc = Binding Collision (Capture: a GS “capturing” a nearby passing NS)

In order to represent the NS-Creation theory view of supernovae and pulsars, we can assert the following:

[ GS ]   =>   [ FP(=) + SNE ]  =>   [ FP(-) + SNR ]        (1a): NS-Creation

The above states that:

• a giant star: ([GS]),
• spontaneously explodes in a supernova explosion (SNE), accompanied by an FP at its maximum spin rate (FP(=))
• which becomes
• a fast spinning-down pulsar ([FP(-)])
• plus a giant cloud of supernova remnants (+[SNR]).

The process above, (1a), is theoretical. i.e. it is not truly known that a giant star (GS), by itself, can produce a fast spinning pulsar (FP).

An alternative explanation would be that the fast spinning-up pulsar (FP(+)), already existed inside the atmosphere of the giant star (GS), at the time of the supernova explosion as follows:

[ FP(+) + GS ]   =>   [ FP(=) + SNE ]  =>   [ FP(-) + SNR ]        (1b): NS-Capture

One may regard the brackets “[…]” as enclosing a “system” in a particular state, described by the contents within the brackets.In addition, we have labelled the above sequence as “(1b)”, so it may easily be referenced.

One may also regard the  arrow “=>” as representing an event that may take place suddenly or over a period of time, that has the effect of transitioning the system in brackets from one state to another state.

In addition, we can also extend the sequence as follows:

[ GS ] => [FP(=) + SNE] => [FP(-) + SNR] => [SP(-)]  => [NS(0)]    (2a): NS-Creation

This extension to the first process, (1a), says that

• the process then has the fast pulsar (FP(=)) begin to spin down (FP(-)) among the supernova remnants (SNR)
• to become a slow pulsar spinning down (SP(-)),
• while, during the same time period, the supernova remnants (SNR)
have dispersed and no longer appear in the formulation.
• The slow pulsar (SP(-)) then spins down further
• and becomes a non-visible, non-pulsing, neutron star (NS(0)).

So, for example, the Crab Supernova that occurred in 1054 AD is an example of the first stage of the process, where we currently can observe the Crab Nebula (SNR) accompanied by the fast (33-ms) Crab Pulsar (FP(-)) which was “Discovered in 1968, the pulsar was the first to be connected with a supernova remnant.”

From 1968, through the present, it has been generally accepted that the Crab Pulsar was created by the supernova (NS-Creation). However, evidence first discovered in 1971, the Cen X-3 Binary X-ray Pulsarcan and will be shown here to disprove the NS-Creation theory.

By contrast, in fact, we will show that the NS-Capture theory, which says that the Crab Supernova was caused by a neutron star that collided with the giant star that existed before the supernova, became bound to it in a binary system. spun up to become a fast pulsar and subsequently destroyed its companion in a supernova explosion.

This process may be represented as follows:

{ GS, NS }  =>  [ GS + NS(0) ]  =>  [ GS + SP(+) ]  =>  [ GS + FP(+) ]   (3): NS-Capture

The above process, (3) says:

• a hither-to unrelated giant star and neutron star {GS,NS}
• have a close encounter, which results in a binding collision {a,b} => {a+b}
• that produces a giant star + neutron star binary system (GS+NS(0))
• whereby the neutron star (NS) begins to spin up
• whereby the NS becomes a slow pulsar (SP(+)) in the binary system (GS+SP(+))
• whereby the SP(+) continues to spin up,
• becoming a fast pulsar (FP(+) in the binary system (GS+FP(+))

The above process is observed in the case of Cen X-3, where for over 45 years the slow pulsar (4.8 sec) has been spinning up, while in close binary orbit with a giant star, while being in the  [ GS + SP(+) ] state..

The question now becomes whether the NS-Creation theory can explain the existence of a system such as [ NS + SP(+) ].

In order to do this, we would need to start with a binary pair of giant stars that undergo the following process:

[ GS + GS ] => [ GS + FP(=)+SNE ] => [ GS + FP(-)+SNR] => [ GS + SP(-) ]  (4): NS-Creation

i.e. the [ GS + FP(=) ]  resulting from the supernova (sne) would  have to have the fast pulsar (FP(-)) slow down and become a slow pulsar (SP(-)).

However, as in the observed process, (3), we already know that a [ GS + SP(+) ] will spin up to become a { GS + FP(+) ]. Therefore, the 2 final states in (4) are impossible to reach because the GS can only spin up the FP(+) further to make it a very fast pulsar (VFP).

So, if we use the NS-Creation theory to create the NS in the { GS + FP(-) + SNR] system, we have a contradiction, because you can’t go [ GS + FP(=)+SNE ] => [ GS + FP(-)+SNR], and therefore NS-Creation theory must be regarded as false.

The above logic is the core of the NS-Capture Theory, and the purpose of this web site is to further reinforce the conclusion that the NS-Creation Theory must be false if it used to try to explain the neutron stars found in the pulsed X-ray binary systems.

i.e. either the NS-Caputre theory OR the NS-Creation theory must be true, but not both.

Therefore, if the NS-Creation theory is shown to be false, then the NS-Capture Theory must be true.