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2.5. Where, and to what extent could magnetic forces compete with gravity in galaxy systems?

Nelson (1987) and Battaner et a1 (1991) have called attention to the consequences, not yet widely considered, of the fact that interstellar magnetic field strengths in nearby spiral galaxy disks appear to decline much more slowly with galactocentric radius than the average disk matter density. Estimates of the magnetic field strength are made from a combination of measurements of the synchrotron emissivity (equation (1.1)) over the galaxy disk, the assumption of equipartition between the cosmic ray particle and magnetic field energy densities, Faraday rotation, and estimates of the ionized interstellar gas density. Whereas the rotationa1 energy density varepsilonrot near the co-rotation radius is approx 400 times the magnetic energy density, varepsilonm, the ratio varepsilonrot / varepsilonm decreases in the outer disk to the point where magnetic stresses become comparable with gravity, and possibly even dominate. In other words, in the RHS of equation (2.6), the third term becomes comparable to, or greater than the first term.

Significant magnetic stresses could pose a challenge to conventional theories of outer galaxy dynamics. The relative prominence of magnetic stresses at large galactocentric radii can also more naturally account for the observed `flaring' of galactic disks at those radii (cf Binney 1992), a phenomenon which has been difficult to understand on pure gravitational dynamics. To the extent that magnetic stresses of the (largely azimuthal) disk fields extend to Parge radii, the result will be to increase the rotational velocity (Vr) at the larger r, relative to the quasi-Keplerian velocity which would be expected in the absence of, e.g., a dark matter halo (Nelson 1987). It is precisely the flat, i.e. non-Keplerian, (Vr) against r relation which has been taken as one of the key pieces of evidence for dark matter around galaxies. Thus it appears conceivable that magnetic forces can `compete' with gravitational forces, and might help provide the explanation for the flatness of galaxy rotation curves at the larger galactocentric radii. The relative importance of varepsilonm in outer galaxy disk regions is supported (though not proven) by the recent finding that the magnetic field strengths appear to correlate with neutral hydrogen column densities in galaxy disks and in a molecular clouds (Han and Qiao 1993); we could infer that since the vertical H I column density in galaxy disks is relatively insensitive to galactocentric radius beyond a few kpc, and since H I extends to large radii in spiral galaxies, a significantly strong (and probably ordered) magnetic field also exists at these large radii.

This possibility puts a premium on definitive observational tests for differences between (Vr) against r curves for matter whose motion is purely gravitational (e.g. old stars), as distinct from that which could be influenced by both the gravitational and large scale magnetic forces in equation (2.6) (namely the interstellar gas, and the newly formed, bright stars which will move with it). Unfortunately, virtually all of the V against r data on galaxies come from transitions in the interstellar gas (the 21 cm line of H I and recombination lines of H II), or from spectra of young stars. Since the age of these (conveniently bright) stars is typically << 108 years, they have moved only a fraction of a galactic rotation (approx 3 × 108 yr at r = 12 kp) since they formed out of the interstellar gas, and may therefore not be purely ballistic probes of the galactic gravitational potential. Better probes of galactic gravitational potentials at large galactocentric radii would be the oldest disk stars - e.g. main sequence dwarfs - which are unfortunately very faint. They would be best detected by observation of their collective absorption spectra, and only with the largest optical telescopes. If such objects have a different V against r curve from the interstellar gas, a magnetic influence on galactic rotation would be inferred. Unfortunately very few such measurements on old (> 109 yr) stars have been undertaken to date.

Another case in point is the magnetic energy in the intracluster medium of clusters of galaxies: As we discuss in section 4 below, widespread, µG-level fields are also found to exist in the intracluster medium (ICM) of some galaxy clusters. In some cooling flow clusters, ICM field values approach 10-40 µG locally (section 4.1.3). The corresponding magnetic energy density of the latter is greater than for galaxy disk fields (which exhibit ordering on comparable scales). This revelation of widespread, and sometimes strong localized (relative to a galaxy cluster size) cluster ICM fields suggests that galaxy fields merge with those of the intracluster medium. If so, our conventional ideas of magnetic field amplification in galaxies, and the role of magnetic as well as gravitational forces in galaxy formation are just beginning to be explored.

Small galaxies like the Magellanic Clouds and other dwarf galaxies have less mass, but are gas and dust-rich, and have cosmic ray electrons and organized magnetic fields of comparable magnitude to large spirals (cf section 2.4 above). Thus, they too may be `connected' with the surrounding IGM as mentioned above, and subjected to magnetic drag which could cause angular momentum exchange with the surrounding IGM. The consequence could be a non-negligible magnetic force contribution to their global dynamics. The rotational velocity in the outer regions of these low-mass galaxies is likely to be even more susceptible to magnetic tension than large spirals, due to their lower mass.

Dwarf galaxies are particularly interesting in this context, especially if normal large galaxies formed originally from the merging of smaller sub-galaxies. Galactic `building blocks' of this type would almost certainly have been rich in at least partly ionized gas, which would therefore have been well coupled to organized, galaxy-scale, magnetic fields. If they already had microgauss-level fields at this stage, magnetic drag effects (to say nothing of thermal conductivity effects) would likely have provided a significant force component in the merging process.

On the contrary, the motions of satellite galaxies whose orbital motions are purely gravitational (e.g. Kulessa and Lynden-Bell 1992) supports the existence of an unseen matter component associated with the Milky Way. It seems unlikely that magnetism in general could be used to completely eliminate hypothesized dark matter distributions around galaxies. The point of the foregoing discussion is to emphasize that large scale magnetic forces must be accounted for, or ruled out before galaxy mass distributions can be confidently calculated. This applies especially to small, gas-rich galaxies.

Although magnetic forces are probably not the only factor connected to the ultimate amount and distribution of dark matter, the bets would seem open at this point on whether there are links between magnetic forces and the amount of dark matter. This in turn is linked to the question of the overall matter density in the universe and whether we live in an open, and older universe q0 << 1/2 (or Omega << 1), or a closed `flat' Omega = 1 universe, for which large amounts of dark matter seem essential in `conventional' Friedmann cosmological models having Lambda = 0. An interesting question is therefore whether magnetic fields could help `alleviate' the currently problematic `cosmic time crunch' in Friedmann Universe models with Omega = 1 - which require the heavier elements to be produced, and galaxies to form, in an uncomfortably short proper time.

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