# Empirical Proof: Population Analysis

It is important to understand that if the NS-Creation theory is proved to be false, that the NS-Capture theory then must be true, which will be explained further below. Our initial focus is to prove NS-Creation false for the use case of Giant Stars and their association with x-ray pulsars.

There are on the order of 100 High Mass X-ray Binaries (HMXB’s) that have been observed to exist in the Milky Way Galaxy (MWG). The life expectancy of any one of the HMXB’s is on the order of 10 million years (10**7 yrs).

Since the HMXB’s contain pulsars that are spinning up at rates ~ 10**-11 sec/sec, their spin up rate is comparable to that of the spin down rate of radio pulsars, which is typically on the order of 10**-12 -> 10**-13 sec/sec, as shown in the P/P-dot diagram. That diagram also shows that the spin-down time for a pulsar from the time of the SNE until the radio pulsar is rotating too slow is on the order of 10 million years (10**7 yrs), which is roughly the same time span as the life expectancy of the HMXB’s.

That means that every 10**7 years a new batch of 100 HMXB’s needs to be produced in order to sustain the population of HMXB’s

This then means that 100 neutron stars need to be produced every 10 million years and placed in orbit around 100 giant stars in order to create the HMXB’s.

Therefore according to the NS-Creation theory there must be 100:

[GS+GS] => [GS+SNE] => [GS+FP(-)] => [GS+NS(0)]    (1)

transitions each 10 million years.

SInce the FP(-) pulsars must be created in the proximity of the GS’s, this mean that each FP(-) must slow down to become a non-rotating NS(0) within 10 million years.

It is questionable whether that can happen in the presence of a GS (because accretion between the GS and FP(-) will prevent FP spin-down), however, let us assume for the moment that it actually does happen.

If that slowdown does occur then, in radio wavelengths,  we should be able to observe ~100 [GS+FP(-) or [GS+SP(-)] systems that would appear as binaries on the P/P-dot diagram. However, zero such high mass radio spin-down binaries are observed. Therefore we must conclude that the [GS+GS]=>[GS+NS(0)] evolutionary transitions do not exist, which makes it impossible for NS-Creation to create the neutron stars found in the HMXB systems.

i.e. NS-Creation is the only theoretical mechanism that is capable of creating a neutron star, and therefore it must be the mechanism for creating the NS’s in HMXB’s. However, such NS’s must be FP(-) neutron stars to be consistent with the Supernova remnants observed such as the Crab. If NS-Creation cannot explain the NS’s in HMXB’s, then the only possibility is that the NS’s have been introduced by some other mechanism than SNE which produces FP(-)’s.

Therefore, we must conclude that the origin of the HMXB == [GS+SP(+)] systems are created by NS-Capture, which can then explain the full life cycle of:

[GS, NS(0)] => [GS+NS(0)] => [GS+SP(+)] => [GS+FP(+)] => [SNE+FP(=)] => [FP(-)] => [NS(0]   (2)

i.e. (2) states that

1. a neutron star (NS(0)) has a close encounter and binds to a GS
2. the NS(0) spins up to become SP(+), then FP(+) by accreting material from the GS
3. the FP(+) causes the GS to explode in a SNE + FP(=)
4. the SNE leaves behind a FP(-) and SNR
5. the FP(-) spins down to a NS(0) in about 10 million years

Basically the NS comes along, becomes a FP and destroys the GS, then spins back down to become a plain old NS(0) again.

i.e.: [GS+NS(0)] => [NS(0)]

Very simple: the NS destroys the GS and leaves the scene, itself intact.

Thus, we have again shown, using population analysis that NS-Creation fails and again requires NS-Capture to explain the HMXB’s and associated SNE’s.

Interestingly, by proving the theory for Giant Stars, alone, implicitly proves the theory for Regular Stars, as well, because the proof for Giant Stars provides all the Neutron Stars necessary for those Neutron Stars to interact both with Giant Stars and Regular Stars.

QED (empirical)

Note: the original impetus for the NS-Capture theory in 1974 was the realization that a neutron star in close orbit around a giant star could not slow down. This led to the main argument that the slow pulsars in the x-ray binaries must have come from some other origin, which could only be an external population of neutron stars that could be captured and start with their rotation rate at zero. That was the analytical aspect of the proof of the NS-Capture theory.

What we are discussing on this page, however, is the experimental evidence that supports the main argument of NS-Capture that neutron stars in binaries with a giant star cannot slow down. The NS-Creation theory argues that this slowdown can occur. One can argue the pluses and minuses of each of those claims, however, it is difficult to come to a 100% solid conclusion on either side.

Now, by analyzing the empirical evidence, particularly, the lack of binary radio pulsars in the island on the P/P-dot diagram, we can see that the NS-Creation theory is refuted by the evidence. The NS-Capture theory predicts that such binary data in the island will not be found.

Therefore, we have both strong analytical and strong empirical evidence that the NS-Capture theory is the only plausible explanation of the complete set of evidence known about radio and x-ray pulsars.