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Astron. Astrophys. 326, 13-22 (1997)

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8. Conclusions

As previously mentioned, the implications of various individual magnetic patterns and of a cosmological magnetic spatial spectrum in the formation of structures will be studied in forthcoming papers. In particular, we will examine in Paper II the effects of a magnetic flux tube, the simplest structure with cylindrical symmetry. Our basic results will be confirmed with this simple particular case. We will now examine the general results obtainable from the differential equation (86).

The primordial magnetic field spatial spectrum remains time independent in the linear approximation considered here, being diluted just by the general expansion but conserving patterns and relative values. Therefore, present large scale magnetic field patterns in the intergalactic medium, if we are eventually able to observe them, could reveal very early processes concerning magnetogenesis. Complementary to the standard methods reviewed by Kronberg (1994), the measurement of the highest energy cosmic rays (Lee, Olinto, & Siegl, 1996) and other indirect methods (Plaga 1995; Kronberg 1995; Battaner et al. 1991) are promising in the future. There is even the possibility of measuring magnetic fields at the last scattering surface (Kosowsky & Loeb 1996).

The fact that magnetic inhomogeneities are conserved until recent epochs in the history of the Universe supports the works by Wasserman(1978) and by Kim et al. (1994) in which a preexisting magnetic configuration determines the evolution of density inhomogeneities. The influence of this primordial magnetic field spectrum on the formation of large-scale structures, clusters and superclusters, as well as of galaxies, is very important.

If magnetic fields have enough strength they can have a clear influence on the origin and evolution of density inhomogeneities. For very early times, with very large [FORMULA], or equivalently for very large scale structures, the last two terms in Eq. (86) would become smaller and the resulting equation would be easily integrated to give


This equation will be analyzed in detail in Paper II. We now see that for very large [FORMULA], [FORMULA] would become very large unless [FORMULA]. For large [FORMULA] we would then have [FORMULA].

Observe that when [FORMULA] this equation is just the solution in the absence of magnetic fields, expressing the growth of the compressional mode as summarized in the classic book by Weinberg (1972), giving [FORMULA].

Then, magnetic fields may provide an alternative mechanism to generate the promordial spectrum of density inhomogeneities, which are then amplified by gravitational instabilities. Other primordial mechanisms, such as quantum fluctuations at Inflation, or exotic discontinuities produced by phase transitions, cannot be rejected, but magnetism is a very interesting additional possibility as, if [FORMULA] were null initially, and only the homogeneous Universe were perturbed by random magnetic fields, [FORMULA] would have been created.

On the other hand, not only are primordial magnetic fields able to originate density structures at very early epochs, but they have a direct influence on the evolution of structures at [FORMULA]. The effect of this direct influence may be of a very different nature, depending on the initial conditions and on the type of the magnetic field pattern, producing concentrations of photons which would eventually be the site of baryon concentrations.

The term X only depends on the magnetic field energy density, but the last term, including m, depends on the magnetic field as a vector, thus producing anisotropies in the evolution of density inhomogeneities. This anisotropic evolution would be more important at relative recent times, close to Equality, and for small scale structures. Later on, heat conduction and viscosity would eliminate small scale structures and, after Recombination, non-linear effects would complicate the initial structure, but the primordial distribution of magnetic fields and that of the density at the epoch of Equality would probably still be recognizable at present.

It is important to obtain the order of magnitude of the field strength able to affect the evolution of the density inhomogeneities. The magnitude of X must be at least of the same order than [FORMULA], which can have typical values of [FORMULA] in the period of time considered. If X were unity, we would have equipartition between magnetic and radiative energy densities and we would have [FORMULA]. But if [FORMULA], we see from its definition (X depends on [FORMULA]) that [FORMULA]. Therefore, magnetism affects the evolution of the density pattern if [FORMULA]. Higher fields are not expected as they would produce a very fast density evolution, incompatible with present observations. The magnetic field may not differ very much from [FORMULA].

This is an equivalent-to-present value. Real magnetic fields at any time are calculated taking into account [FORMULA]. It is important to calculate B at the epoch of nucleosynthesis. With [FORMULA] at the end of nucleosynthesis, we have [FORMULA], perfectly compatible with the limits of Grasso and Rubinstein (1995) of [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998