The Be X-ray Binary Spin Orbit Data

Probably the most dramatic prediction of the NS-Capture Theory that was conceived in 1974 has been the realization of the existence of pre-Cen X-3 and pre-Her X-1 systems that have been discovered in the form of the Be X-Ray Binary Pulsar systems.

These systems consist of relatively slow spinning X-ray pulsars in eccentric orbits around individual Be stars that are each surrounded by a rapidly rotating circumstellar disc of material that is periodically disrupted by the X-ray pulsar when the pulsar passes through the periastron of its orbit. When this occurs there is a huge burst of x-rays emitted, which have been observed by x-ray observatory satellites for the last 50 years.

Much data has been collected by these x-ray observatories and a collection of references has been assembled on this site to enable visitor access.

What we are going to focus on here is a view of data that was first published in Corbet (1984) which showed a log-log graph of spin vs orbit data for the known Be X-ray binaries at the time.


Corbet, “Be/neutron star binaries: a relationship between orbital period and neutron star spin period.”, Astron. & Astronphys. 141, 91–93 (1984)


The above diagram shows a clear trend of long orbital period and spin period to short orbital period and spin period that goes from the upper right of the diagram to the lower left.

This trend has persisted in the data that has been collected since that time, although the data has a wider spread, but we will show that is not really a significant concern.


F. Haberl and R. Sturm, “High-mass X-ray binaries in the Small Magellanic Cloud”, A&A 586, A81 (2016)


The above diagram shows additional data from 2016 which retains that same trend as the previous data from 1984. In the 2016 diagram, a single point in the lower left was plotted to show a more highly evolved x-ray binary, SMC X-1, that is in the same general Small Magellanic Cloud region. If we were to add Her X-1 (1.7 days, 1.24 sec) and Cen X-3 (2.09 days, 4.84 sec) to the graph, they would also appear in the lower left corner.

The important physical forces that are at work in this diagram are accretion (which, in general, forces the spin period to become shorter and shorter) and orbital energy loss of the x-ray pulsar during the collision at periastron (which, in general, causes the x-ray pulsar to be unable to reach its previous apastron (furthest distance from the Be star)).

The net result of these ongoing collisions is that the orbit will shrink, because the pulsar will return to its distance of closest approach each time, but fall short of its previous distance of maximum separation (apastron). i.e. the orbit will become shorter and the orbital period will become shorter. In addition, as the orbit ellipse continues to have its major axis shrink, the orbit will eventually circularize, similar to Cen X-3 and Her X-1.

Therefore in addition to the data showing a pattern from the upper right to the lower left, there is a physical force arrow pointing from the upper right to the lower left, which indicates there is time evolution to shorter orbital period (from the energy loss of collision) and shorter pulse period (from the angular momentum increase to the pulsar due to accretion of material at periastron).

This exact process is shown in the simulation of NS-Capture demo on this site.

The significance of this data is that it shows the complete NS-Capture theory from initial capture of the NS in a highly elliptical orbit to later evolution to a close binary circular orbit.

In addition, it should be noted that, the NS-Capture Theory originally discovered and conceived in 1974, which was based only on the analysis of Cen X-3 and Her X-1 spin data, plus the context of the Crab pulsar spin-down data, was enough to predict that the existence of the whole Be X-Ray Binary phenomenon should be observable! The fact that it has been observed during the last 50 years is empirical support for the validity of the NS-Capture Theory.