The shape of galactic rotation curves (i.e. the galactic rotation velocity as a function of the distance from the galactic center), has led astronomers to the conclusion that galaxies must be surrounded by an invisible massive halo of 'dark matter' which exceeds the visible mass by up to 10 times (see detailed review of this and related theories
The underlying assumption with this model is that gravity is the only force determining the dynamics of the galaxy. However, practically all rotation curves indicating the existence of dark matter have been obtained by observing the Doppler shift of gas (usually the 21 cm line of hydrogen) rather than of stars. It is generally assumed that the gas provides a tracer for the motion of the stars, but this assumption neglects the fact that ionized atoms are very much affected by electromagnetic forces: it is easy to show that with the generally assumed galactic magnetic field of 10-6
Gauss, the Lorentz force on a thermal proton is about 10 orders of magnitude stronger than the gravitational force (assuming a galaxy of the mass and size of the Milky Way) and should therefore completely determine the dynamics of the plasma, which in turn should also have an impact on the neutral gas because of recombination. Even a large additional amount of dark matter would therefore not exclusively determine the galactic gas dynamics.
Note: It is surprising that the dark matter theory has not been challenged yet on grounds of general scientific implausibility alone: as the mass of the dark matter is usually many times the normal mass of the galaxy, it would be bizarre to assume that the formation of the dark matter halo has been triggered by the normal matter (one might as well assume that the planets are responsible for the formation of the sun). One would have to conclude therefore that, on the contrary, the dark matter has led to the formation of the visible galaxy. This however would mean that all galaxies should show evidence for dark matter, which is clearly not the case
Magnetic Field Lines and Lorentz Force
A magnetic field line is an imaginary line along which the Lorentz force FL
= 0. This condition effectively defines the direction of the magnetic field B
. However, the Lorentz force is not only zero if v
is parallel to B
, but also if v
is zero. As velocities are by definition relative, a preferred reference frame defining v
and therefore FL
uniquely has to be specified. It is obvious that this can only be given by the physical object producing the magnetic field (a circumstance commonly neglected in electrodynamics). For a magnetic field produced dynamically by a plasma current (dynamo), the velocity v
in the Lorentz force has therefore to be referred to the average velocity of the plasma ions in the dynamo region (as these constitute the main mass of the current system).
Plasma- and Gas Dynamics in the Galactic Magnetic Field
The galactic magnetic field can be assumed to be produced by a rotating plasma (dynamo region) in the more central region of the galaxy, i.e. the velocity v
in the Lorentz force term has to be referred to the rotational velocity vD
of this region (vD
itself refers obviously to the center of the galaxy).
is not constant throughout the dynamo region, one would in principle have to perform an average over the whole volume, but since the magnetic field strength produced by each sub-region decreases with distance, one can assume as a first order approximation that vD
is determined by the dynamo region closest to the point in question.
Only charged particles with a velocity v
will therefore not experience any Lorentz force, i.e. this is the speed with which the plasma will be dragged along by the magnetic field. Because the condition v
is independent of the distance from the dynamo region, the rotation curve of the plasma is consequently constant in the outer regions of the galaxy, as observed (see illustration below). The neutral gas is of course not immediately affected by the magnetic field, but once an atom becomes ionized, it will be imparted the velocity vD
by the magnetic field. If the ion recombines it will maintain the tangential speed despite not being trapped anymore by the magnetic field. If this speed exceeds the gravitational escape velocity, the atom will then escape from the galaxy. The ionization rate of the neutral gas varies obviously quite strongly throughout the galaxy, but one can estimate that a neutral atom in interstellar space is ionized after 106
years, which is smaller or at least about equal to the dynamical time scale of the galaxy, so that most of the neutral gas should appear to co-rotate with the plasma. Because of the conservation laws of mechanics, the dynamo region must therefore continuously lose energy as well as angular momentum. This circumstance could well explain the slightly increasing rotation curve for some galaxies if one assumes a more extended dynamo region. Furthermore, the ejection of gas due to the magnetic field rotation could be an explanation for the hot intergalactic gas observed in galaxy clusters. In a different context, this mechanism could also account for the apparent loss of angular momentum in the process of star formation. On the other hand, rotation curves decreasing with distance could indicate that the (rotating) galactic magnetic field blends into the (near-stationary) intergalactic magnetic field.
The plasma dynamics in the magnetic field of galaxies could in this sense explain most of the rotation curves seen as an evidence for dark matter.
Schematic representation of galactic gas rotation:
the plasma at the rim of the central dynamo region rotates with velocity vD. Therefore the magnetic field lines outside the dynamo region rotate with the same velocity (v=vD), dragging the plasma with them.
However, even if the velocity of stars (rather than gas) is apparently not consistent with the galaxy mass (it is for instance claimed that the observed velocity of globular clusters indicates the presence of dark matter), one could ask the question if the 'known' visible mass of stars is actually correct. Since this mass is derived from the luminosity of the galaxy over the mass-luminosity relationship, it is obvious that any errors in the latter will have a crucial influence (according to the mass-luminosity relationship, a star with half the mass has only 1/10 of the luminosity, so with 10 times as many stars of half the mass, one would have the same overall brightness but 5 times the overall mass, which might dispense with the need for dark matter). Looking at the publication about the MASSIF project
to improve the accuracy of the mass-luminosity relationship , one finds indeed that the luminosities for stars less than 1 solar mass are uncertain by about 2-3 magnitudes (i.e. up to about a factor 10). It is quite remarkable that the mass luminosity relationship, which a) is quite uncertain for low mass stars, b) obtained only in the solar neighbourhood and c) obtained only from double stars, is applied to all stars in our or other galaxies regardless. I don't think that all these points have been sufficiently examined to justify the conclusion of dark matter from the dynamics of galactic objects.