A Gravitationally Powered Oscillatory Pulsar Model

The pulsars are generally believed to be rapidly rotating neutron stars. However, because it is extraordinarily difficult to observationally distinguish between rotating and oscillating point-like radiators, certain of the pulsars might actually be electrograv oscillators.

The pulsars are thought to be simultaneously near the Dirac critical magnetic field and the Schwarzschild gravitational limit. Under these conditions there is not good cause for supposing the still-unknown relationships between the electrical and gravitational fields can be neglected. Until the gravitational and electrical fields are unified, it is doubtful that a satisfactory theoretical basis exists for explaining the pulsars.

Vela pulsar Chandra X-ray image of the outer jets of the Vela pulsar, from [53]. The jet on the right extends to about 0.45 light-year from the pulsar. The blobs in the jet move outward at 0.3 to 0.6 c. The pulsar is moving at a velocity of 97 km/s toward the right jet, which probably explains the asymmetry between the poles. The second image shows the Crab pulsar's jets [25].

The magnetic force between the poles of a magnetized sphere is attractive. The force at the equator is repulsive, so the magnetic field causes an equatorial bulge. Centrifugal force also causes an equatorial bulge. The energetically preferred orientation of the magnetic field is therefore parallel to the spin axis.

Crab pulsar Charged particles tend to move parallel to the lines of magnetic flux, so if the magnetic and rotational axes were not aligned the jets should be cone shaped. A rotationally powered pulsar becomes disabled when the axes are aligned.

In the most general case mathematically possible, the distance between two infinitesimally spaced points has both symmetric and antisymmetric components. It is the conventional conclusion that the antisymmetric terms do not occur in nature, but there is the consideration that the general theory is not a theory of electricity. The Maxwell equations are accommodated by the theory; they are not obtainable from the asymptotic limits of it.

There have been many investigations into the possibility that the antisymmetric terms play a role [42], even by Einstein himself, but none of them has led to an established theory. It is suggested that some of the difficulty is due to the lack of observational data of an appropriate form, and that pulsar observations may be able to supply it.

sprites This 1995 time-lapse movie taken by the [Hubble Space Telescope] shows sprites dancing (and being blown away) above the polar regions of the Crab pulsar. Each frame represents an interval of several weeks. The sprites are at a distance of about two light-months from the pulsar, and are probably shock fronts caused by an invisible relativistic beam of charged particles. The pulsar itself is the star at bottom center. It looks like an ordinary star in a time exposure, but the optical emission is actually in the form of 30 Hz flashes.

The situation is something of a predicament. The existing nonsymmetric gravitational theories are not well enough developed that they can be used to obtain a persuasive pulsar solution, while without observational evidence that the pulsars are oscillators there is no compelling need to develop them. The theoretical and observational consequences of discovering that the pulsars are oscillators are so enormous that a further analysis of the observational data seems justified. Some observational tests are discussed below in Section 5.

A fully developed derivation of the pulsar solution will be a formidable exercise, since the symmetric and antisymmetric terms uncouple in linearized solutions. See Moffat [41], for example. There appears to be a simpler way of obtaining the essential characteristics of the solution. The method is not very accurate, but the solution obtained should be sufficient for the initial evaluations, and if the pulsars are found to be oscillators then a substantial amount of theoretical work in the literature will be brought to bear on the problem.

The electrical and gravitational fields appear to be coupled in dynamic solutions. One consequence of the coupling is that a dense magnetized sphere has a specific resonant frequency that decreases to about 0.4 Hz as the radius shrinks to the Schwarzschild radius. Planck's constant is one of the quantities in the equation for the resonant frequency. The limiting frequency is independent of the mass of the object and all other parameters. It is a constant of physics. In being nonlinearly coupled to the gravitational potential energy of the source, gravitational contraction can supply energy to the resonant system, causing it to break into oscillation.

One reason that oscillatory pulsar models have not received much attention is that the resonant frequency must decrease as the radius decreases if gravitational contraction is to supply the energy. The oscillator developed here is probably the only one in existence with that characteristic.

M87 [Hubble Space Telescope] view of the M87 jet. The galaxy is thought to contain a massive black hole. Could it actually be a monstrous pulsar?

When applied to the 7.47 second isolated X-ray pulsar SGR 1806-20 the oscillatory model overestimates the observed power output of the full system, including the nebula, by a factor of 105. The rotational pulsar model fares no better, as it underestimates the total power output by a factor of 103 if the pulsar radius is 10 km. The most commonly accepted explanation for the energy deficit is that the pulsar is powered by the decay of an unusually intense magnetic field rather than by rotational kinetic energy [7]. The magnetar field estimates exceed the critical field of the Dirac equations by up to a factor of 20 [28]. That may be possible, but the field strength estimates do not appear to be reliable. The spindown rate of SGR 1900+14 doubled for 80 days following the August 1998 outburst, suggesting that magnetic braking is not the spindown mechanism for this pulsar, since the field strength would have had to increase by a factor of two in a short time, which is not plausible [29].

The oscillatory power calculation is based only on basic energy relationships, so the energy discrepancy in this model may be due to mass ejection. In this model the pulsar has an intense E field so that when infalling material becomes ionized half the particles are ejected from the system. The other half collides with the pulsar, creating more charged particles. At high energies a relatively small mass flow could account for the computed energy transfer, but a more likely explanation is that the equation badly overestimates the actual power output if the pulsar ejects its own mass, which can happen in an electrostatic field. The computed power output must therefore be taken as only an upper limit until observational data on the pulsar's mass flow become available. Infrared observations show that the pulsar is surrounded by a dust cloud [14], which may be relevant to the energy flow equation.

Knot The inner knot of the Crab pulsar [34]. The knot is on the spin axis at a distance of about one light-week. It is a stable feature. Polarization measurements show that the knot's magnetic field is perpendicular to the spin axis, implying that the field is toroidal.

   Section 1  A nonsymmetric metric
   Section 2  The electrical field limits of the vacuum
   Section 3  The conservation of charge in the intense field    
   Section 4  Derivation of the pulsar resonance frequency
   Section 5  Observational tests
   Section 6  Gamma ray bursts

Gary Osborn
Anaheim, California
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Last update August 2013      Revision History

An earlier version of the paper is archived at http://arxiv.org/abs/astro-ph/9901425.  Some of the material is obsolete, but the equations are the same.