1.3. Magnetic fields and structure formation

The idea that cosmic magnetic fields may have played some role in the formation of galaxies is not new. Some early work has been done on this subject, e.g. by Peblees [23], Rees and Rheinhardt [24] and especially by Wasserman [25]. A considerable amount of recent papers testify the growing interest around this issue. A detailed review of this particular aspect of cosmology is, however, beyond the purposes of this report. We only summarize here few main points with the hope to convince the reader of relevance of this subject.

Large scale magnetic fields modify standard equations of linear density perturbations in a gas of charged particles by adding the effect of the Lorentz force. In the presence of the field the set of Euler, continuity and Poisson equations become respectively [25]

	(1.11)
	(1.12)
	(1.13)

Here a is the scale factor and other symbols are obvious. This set of equations is completed by the Faraday equation

(1.14)

and

(1.15)

The term due to the Lorentz force is clearly visible in the right hand side of the Euler equation. It is clear that, due to this term, an inhomogeneous magnetic field becomes itself a source of density, velocity and gravitational perturbations in the electrically conducting fluid. It has been estimated [25] that the magnetic field needed to produce a density contrast ~ 1, as required to induce structure formation on a scale l, is

(1.16)

In his recent book Peebles Ref. [26] pointed-out a significabt coincidence: the primordial magnetic field required to explain galactic fields without invoking dynamo amplification (see Eq. 10) would also play a relevant dynamical role in the galaxy formation process.

The reader may wonder if such a dynamical role of magnetic fields is really required. To assume that magnetic fields were the dominant dynamical factor at the time of galaxy formation and that they were the main source of initial density perturbations is perhaps too extreme and probably incompatible with recent measurements of the CMBR anisotropies. A more reasonable possibility is that magnetic fields are an important missing ingredient in the current theories on large scale structure formation (for a recent review on this subject see Ref. [27]). It has been argued by Coles [28] that an inhomogeneous magnetic field could modulate galaxy formation in the cold dark matter picture (CDM) by giving the baryons a streaming velocity relative to the dark matter. In this way, in some places the baryons may be prevented from falling into the potential wells and the formation of luminous galaxies on small scales may be inhibited. Such an effect could help to reconcile the well know discrepancy of the CDM model with clustering observations without invoking more exotic scenarios.

Such a scenario received some support from a paper by Kim, Olinto and Rosner [29] which extended Wasserman's [25] pioneering work. Kim et al. determined the power spectrum of density perturbation due to a primordial inhomogeneous magnetic field. They showed that a present time rms magnetic field of 10^-10 G may have produced perturbations on galactic scale which should have entered the non-linear grow stage at z ~ 6, which is compatible with observations. Although, Kim et al. showed that magnetic fields alone cannot be responsible of the observed galaxy power spectrum on large scales, according to the authors it seems quite plausible that in a CDM scenario magnetic fields played a not minor role by introducing a bias for the formation of galaxy sized objects.

A systematic study of the effects of magnetic fields on structure formation was recently undertaken by Battaner, Florido and Jimenez-Vicente [30], Florido and Battaner [31], and Battaner, Florido and Garcia-Ruiz [32]. Their results show that primordial magnetic fields with strength B₀ 10^-9 in the pre-recombination era are able to produce significant anisotropic density inhomogeneities in the baryon-photon plasma and in the metric. In particular, Battaner at al. showed that magnetic fields tend to organize themselves and the ambient plasma into filamentary structures. This prediction seems to be confirmed by recent observations of magnetic fields in galaxy clusters [6]. Battaner et al. suggest that such a behavior may be common to the entire Universe and be responsible for the very regular spider-like structure observed in the local supercluster [33] as for the filaments frequently observed in the large scale structure of the Universe [27]. Araujo and Opher [34] have considered the formation of voids by the magnetic pressure.

An interesting hypothesis has been recently rised by Totani [35]. He suggested that spheroidal galaxy formation occurs has a consequence of starbursts triggered by strong magnetic fields. Totani argument is based on two main observational facts. The first is that magnetic fields strengths observed in spiral galaxies sharply concentrate at few microgauss (see Sec. 1.1), quite independently on the galaxy luminosity and morphology. The second point on which Totani based his argument, is that star formation activity has been observed to be correlated to the strength of local magnetic field [36]. A clear example is given by the spiral galaxy M82, which has an abnormally large magnetic field of ~10 µG and is known as an archetypal starburst galaxy. Such a correlation is theoretical motivated by the so-called magnetic braking [19]: in order for a protostellar gas cloud to collapse into a star a significant amount of angular moment must be transported outwards. Magnetic fields provide a way to fulfill this requirement by allowing the presence of Alfvén waves (see Sec. 2.2) which carry away the excess of angular moment. Whereas it is generally agreed that galaxy bulges and elliptical galaxies have formed by intense starburst activity at high redshift, the trigger mechanism leading to this phenomenon is poorly known. According to Totani, starbursts, hence massive galaxy formation, take place only where the magnetic field is stronger of a given threshold, which would explain the apparent uniformity in the magnetic field amplitude in most of the observed galaxies. The value of the threshold field depends on the generation mechanism of the galactic magnetic field. Totani assumed that a seed field may have been produced by a battery mechanism followed by a dynamo amplification period. Such an assumption, however, looks not necessary and a primordial field may very well have produced the same final effect.