## 1. General equationsIn Paper I, we presented the basic equations governing the evolution of the large scale energy density structure in the prerecombination universe, when the effect of magnetic fields cannot be ignored. In the linear regime, the magnetic field configuration remains time-independent throughout this era, only growing with the expansion. The degree and the way this field structure affects the evolution of density inhomogeneities would depend on the particular pattern of the magnetic field lines. We will consider here a small cell in which the magnetic field has the simplest structure: a magnetic flux tube. Different sizes of the flux tube will be considered, for small, intermediate and large scales. We will deal with the integration of Eq. (86) of Paper I where:
is the relative energy density contrast, defined
as
, where
is the energy density and
the difference between its value within the
inhomogeneity and its mean value in the Universe. As we are
considering relativistic particles, we also have
where is the second derivative with respect to the time-like variable . is defined as
where is the Laplacian operator, when the spatial coordinates are instead of , the usual comoving coordinates. is defined as
, where
would be the present magnetic field if no source and no loss other than expansion had taken place after the time period considered here. Because the post-recombination epoch is probably very complicated, concerning the evolution of magnetic fields, has in practice no relation with present magnetic fields. is exactly defined as . We measure magnetic field strengths in , with the equivalence being 1 Gauss = . is the relativistic particle hydrostatic pressure at present. It is defined as and we have chosen the value .
where To integrate our basic equation it is then necessary to specify the field. In this paper we analyze the influence of a magnetic tube flux, i.e. is given by where In the particular case of a flux tube: where and For integrating, it is better to define another time-like variable as Using this dimensionless time the basic equation becomes: where now and are first and second derivatives with respect to . From now on we will write simply © European Southern Observatory (ESO) 1997 Online publication: April 8, 1998 |