Pulsars, Truth and Science

First it has to be understood there is a difference between theory and reality, and a model or explanation and actual facts. There is a difference between deduction and observations.

Theory and Reality

The problem with scientific investigations of outer space is things are explained in a way that often you simply can't prove them wrong you can come up with anything of speculation fantasy and magic. The weird and wonderful.

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Typically in a journal article it seems a model is presented and soon, a page or two later insidiously accepted and treated as truth. More as a result of carelessness and laziness really. Physical observation and measurements are completely reliable it is in the interpretation and explanations where the problem lies. Guesswork comes in. Information only relating to quality and kind not amounts and numbers, not reliably expressible in quantities and measurements.

It comes down to the fact you cannot do any real scientific experiments far out in the cosmos. As science you can come up with the most weird and wonderful it can go through because no-one can prove you wrong. I'm very doubtful and amazed at the confidence I feel we should always keep this in mind so we don't come to misleading conclusions.

It is as democracy. In effect a given theory is put to the vote. It looks like truth is established by consensus.

Pulsars

Pulsars are believed to be rotating magnetic “neutron stars”. The word pulsar is short for pulsating radio source, they can can be observed and the spin rate measured as a description of extremely regular pulses like a cosmic lighthouse or gigantic atom clock.

They are thought to be rapidly spinning magnetic neutron stars and the pulses caused by enormously powerful fast rotating magnetic fields that beam radio waves around the area around their magnetic poles. The pulses can be measured through astronomical observation. The rotational speed varies from revolving once every few seconds to almost a thousand times a second.

Occasionally a phenomenon has been observed where the pulsar suddenly spins faster and then slows again relaxing to the original usual value Such an occurrence is called a “glitch”.

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We are investigating highly simplified models. Ultimately we hope to explain the cause of glitches in pulsar spin. There are other interesting things that could measured for example observed spin rate distance and the doppler effect.

Of course you must be observing a pulsar at the exact time to see an actual glitch. I don't know how many pulsars are known, observing them must be very hard you would have to basically watch all pulsars and all the time and perhaps in vain since a glitch is not predictable, brief, and appear sporadic but there have been recordings and measured occurrences.

Neutron Stars

A neutron star would be an hypothetical small but massive object in space of immense density comparable to an atomic nucleus and consisting mostly as neutrons as some unknown form of matter. Typically it would be a sphere about 20km across and three times mass of the sun. Neutron stars are believed to be the imploded cores of massive stars that became supernovas.

This would then be a pulsar given intense magnetic fields and rapid rotation. It is believed this is a neutron star but not all neutron stars are pulsars.

At such terrifically high internal pressure atoms might break up in particles and merging to neutron and the interior thus a incredibly dense “sea of neutrons”. In the commonly accepted model a neutron star consists of an solid crust, a superfluid outer shell and inner core.

In more detailed models the “static state” is not stable and considers the coupling between the core of superfluid and a solid crust. Superfluids don't rotate uniformly instead a vortex forms in the core and may be only weakly coupled to the crust so a gradual exchange of angular momentum of the two follows. As a further simplification the stars are cylindrical

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The most obvious weakness in current studies is that general relativity is ignored for convenience, and such extremes such as rapid rotation, terrific densities and gravitation fields all cannot really be ignored and it must make crucial difference. One should bring quantum mechanics in too, more particle physics and the unknown state of matter. What we believe now must be far from the truth I feel for this our understanding is very limited.

In general in astrophysics thus is scope for serious scientific investigation and there have been actual experiments. The (physical) laboratory model of  the Tsakadze's is an experiment with a small glass cylinder of slowly rotating Helium II at 1.46 Kelvin as a physical model of a neutron star. The glass would be the crust and interior the He II superfluid. Such experiments must be very expensive.

Calculations

For the neutron star we used the simplified model as in Alpar et al and Epstein & Link. I didn't go into the detail and derivation of the mathematics it can be found in the articles and is now taken as correct including their data. Therefore assuming the actual equations as already derived and from there begin our calculations.

Thus we are concerned here only with the mathematical model and not a “physical” description as in the references. It is a non-linear PDE with a dynamic boundary condition. I don't know how all the data is obtained such as temperature and mass of an actual pulsar but for the analysis will take it in the examples in literature as given.

For that there is a possibility of shock waves, in effect discontinuities in speed. It is drastic. I hoped to show for certain parameters the characteristic lines could intersect in such a way. The idea is not hard to understand in effect you are drawing contours as on a map. The work involves numerical analysis and plotting graphs.

Equipped with data and PDE system mathematical model complete all now is numerically graphing the characteristics with different parameters and see what happens. I was trying trial and error with estimated values and plotting the curves but didn't get far with this it would probably help to have a descent computer mathematics package they can be expensive.

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If there are no shock-waves even still the analysis will be of value such as characteristic curves may heap up very close to each other with very sudden velocity increase at places. Perhaps we could learn which pulsars are more likely to glitch it would help a lot.

Such “shock waves” do occur, in such things as supersonic flight, powerful explosions and lightning and such as effects of the solar wind on the magnetosphere. The phenomenon is well known there are many examples in physics. They talk of star quakes it could be the crust breaks and reforms. One also wonders about detecting gravitational waves.

This analysis may help in understanding our model and perhaps even making unexpected  discoveries. My approach for the calculations is as for an engineering problem although one would need more explanations to understand the mathematics.

References

MA Alpar, PW Anderson, D Pines, J Shaham, Vortex creep and the internal temperature of Neutron Stars, 1.General Theory, The Astrophysical Journal, 276 (1984), pp. 325–334.

RI Epstein & B Link, Thermally driven Neutron star glitches, The Astrophysical Journal, 457 (1996), pp. 844–854.

JS Tsakadze & SJ Tsakadze, Properties of slowly rotating He II and the superfluidity of pulsars, Journal of low temperature Physics, 39 Nr’s 5&6 (1980), pp. 649–688.

R Bowers & T Deeming, Astrophysics I,  Publisher Arthur Bartlett (1984).

(Also see www.ska.ac.za)