Magnetic fields may explain rotation curves if a) there is a sub-critical strength gradient and b) they have a sufficient order of magnitude. The next step is to deduce the existence of these fields theoretically and to identify the mechanisms that produce them.
A first simple model with this objective was presented by Battaner, Lesch and Florido (1999), in which a mechanism is responsible for a critical slope, B B* R-1. A highly convective disk in the vertical direction maintains a highly turbulent magnetic diffusivity, establishing a connection and equilibrium between extragalactic and galactic fields. The origin of galactic fields is extragalactic and they are amplified and ordered by differential rotation. The problem of the origin of magnetic fields is then shifted to the intergalactic medium, a topic that will be addressed in the next section.
With this model, we depart from the classical approach, basically consisting of the dynamo or similar models. We can allow ourselves this liberty because the classical dynamo theory (summarized, for instance, in the review by Wielebinski and Krause, 1993) has been subject to severe criticism and does not offer a clear scenario. The standard dynamo approach does not take into account the back reaction of the turbulence on the amplified magnetic field, which is very strong at small scales (Kulsrud, 1986; Kulsrud and Anderson, 1992). Another important shortcoming of the standard dynamo theory lies in the following fact: The dynamo exponentially amplifies a preexisting seed field up to the present, with strengths of the order of 1-10 G. The field is amplified e-times in each rotation. Suppose that the galaxy has rotated about 20 times since its birth. Then, the field has been amplified by a factor of about e20 5 × 108. Therefore, the initial strength would have been about 10-15G. This is in contradiction with the G fields measured in 3C295 (with z = 0.395) (Kronberg, Perry and Zukowski, 1992). Moreover Perley and Taylor (1991) detected such large fields at z=0.461. Absorption Line Systems of quasar spectra, usually interpreted as pregalactic structures, also have G fields (Kronberg and Perry, 1982; Watson and Perry, 1991). Observations of Lyman- clouds at z 2 also show 3G-fields (Wolfe, Lanzetta and Oren, 1992), similar to other highly redshifted disks (Wolfe, 1988; Kronberg et al., 1992). If new-born galaxies were so highly magnetized, the dynamo would have amplified these initial fields to a present value of about 500 G, in astonishing disagreement with observations. Even if, before reaching this value, some saturation mechanism had appeared, the classical dynamo is incompatible with pregalactic G-strengths. Therefore, the topic is now free for speculation and the search for alternative scenarios.
This argument not only invalidates the classical dynamo theory but also many hypotheses about the origin of primordial magnetic fields that were conceived as providing 10-15G at the epoch of galaxy formation. Galaxies were probably formed out of an already strongly magnetized medium, with an equivalent-to-present 1G field, the same order of magnitude as the present intergalactic medium field.