On Earth the distances between magnetic poles and poles of rotation are complicated by structural factors.
In a neutron star the structure should be fairly uniform. But the most outstanding examples of nonaligned axes occur in the pulsars. A reason should be discovered for displacement of the magnetic poles from the poles of rotation.
In other threads and private correspondence I have suggested that the magnetic fields are repelled by gravity and attracted by kinetic energy of rotation which is largest far from the spin axis. If this was not true then it seems that the magnetic axis of a neutron star would align with the rotation axis, and pulsars would not pulsate.
Why does the magnetic axis of a pulsar not align with the axis of rotation?
A number of studies have been done with different results.
http://adsabs.harvard.edu/full/1983A%26A...127..259N
Flowers and Ruderman 1977 concluded that young neutron stars had a close alignment early zero angle between magnetic pole and spin axis, but in older neutron stars the angle approached 90 degrees. Jones 1975, 1976 concluded just the opposite.
One of these or the other is likely to be true. In terms of stress energy in GR, gravity must either attract or repell magnetic fields. Referring to Lagrangian methods, the repulsion seems to be indicated, favoring Flowers and Rudman over Jones.
Jerry
My mathematics Self-Field Theory has an interesting side to it in terms of this angle you are talking about. If you read what I've written at my website www.unifiedphysics.com about 'gravitational structure of the universe' you will see there's different (fractal) levels of gravitation where the angles between the 'electric' component and the 'magnetic' component change in a similar (quantum-like) fashion with a 90 degrees shift between the fractal levels. It could be the young neutron star starts off with a gravity different to the older neutron stars. Maybe the young star is essentially nuclear where its gravity is galactic-like, while the old star burns out its nuclear energy and becomes mainly like our Sun and mainly solar-system-like with a bit of residual nuclear energy.
In terms of this fractal-like series for gravity note that Newton's gravitation is still correct as the main component of gravity at all fractal levels and hence it can still be useful as 'an engineering approximation' while GR is 'more accurate' but is still a sub-component of the full fractal series of gravity within the universe. At each level there is another form of spinor introduced into the full mathematics.
At the solar system level the gravity is a differential of the ordinary EM fields; in other words the differentiated magnetic field spins about the gyroscopic motion of Earth and Sun; this is the reason why Einstein's GR worked for the perihelion of Mercury. At the galactic level of gravitation the magnetic component shift by 90 degrees.
This is a short excerpt from my book on self-field theory "A New Mathematical Description of Physics" A.H.J. Fleming (Pan Stanford 2012) :
"The E- and H-fields form a cyclic stream of photons that move in two orthogonal planes. The fields can be separated into two coupled spatial coordinate systems (Fig. 2.5). In terms of these coordinates, a radial E-field spinor rotates in rho0; this spinor and its time derivatives form a discrete cyclic set (of period 4 as with the phase shifts) in the rho0-phi0 plane (Fig. 2.5). An H-field spinor derivative also rotates in phi0; the H-field spinor and its derivatives also form a discrete cyclic set of period 4 in the rho0-phi0 plane causing the electron to perform a cyclotron motion in the rho0-theta0 plane. The H-field cyclotron field spinor rotates in theta0 Only four of the six spatial coordinates are independent, as in space–time coordinate systems.
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Figure 2.6 Time and space derivatives of the EM field form geometric series n = 0, 1, 2, 3, that return to the initial direction after a cycle of period 4. E-field series lies in the r-phi plane."
Raul it may be the angle between the two may be related to the component of solar system gravity compared with the galactic gravity. So each planet may actually be a combination of nuclear and EM gravitational fields in a ratio that defines the angle between the solar system plane and the galactic plane.
Thierry I just got your answer and so give me a few hours to think about my answer. But in brief yes I agree. The force(s) you talk about are NOT simply photons as with an EM application but there are now photon 'differentials' including the radial component. This is the 'gravitomagnetic' analogue of EM forces (I call this a 'differo-electromagnetic' DEM field). The difference between Newton's forces, GR forces, and SFT forces is, in part, that we now introduce the relative dielectric permittivity and relative magnetic permeability of say the Sun and the Earth at all points within each mass (or atomic conglomerate). So each gravitating object must be defined as an inhomogeneous body of revolution.
Polarization in radio emissions from relativistic electrons that spiral around the field lines allows modeling of the distant magnetic fields.
http://www.lofar.org/astronomy/cosmic-magnetism/measuring-cosmic-magnetic-fields/measuring-cosmic-magnetic-fields
Hi Thierry
Very nice presentation, thank you. I came across Magnetogravitism some decades ago (in the early 1990's) . It was at this time I was working on my mathematics (self-field theory) that turns out to be a deterministic version of quantum theory; SFT appears to be an evolution of the earlier quantum theories like QFT, QCD, QED and QM. It is similar to Bohr's original work of 1914. One main difference with the quantum theories is the metric which in SFT is NOT Pythagorean unlike QT and GR. It also sets up the problem as two masses interacting. So it impacts not only QT, but GR as well since both QT and GR are based on a single mass and its field. It is based on the Maxwell-Lorentz eqns and spinorial field forms (exp(j*omega*r). So very similar to the classical theory of differential equations except that the bosons are quantum and emitted by all masses and act as binding energy between the masses; this is also the case in gravitational applications, for example the Sun and the Earth have a stream of photons (and other bosons) that are swapped between the masses in a periodic fashion.
https://www.researchgate.net/publication/290542834_Self-field_theory_general_relativity_and_quantum_theory
https://www.researchgate.net/publication/267775069_Self-field_Theory_and_General_Physical_Uncertainty_Relations
It may be interesting for you to read a paper on the actual application to galaxies
https://www.researchgate.net/publication/266410528_Self-field_Theory_-_A_Possible_Gravitational_Structure_for_Galaxies
If this is correct then this should give us a way to detect high nuclear content planets. And it gives us a much more direct means of telling us our place in the Galaxy