## 2. Tidal torquesThe explanation of galaxies spins gain through tidal torques was
pioneered by Hoyle (1949) in the context of a collapsing protogalaxy.
Peebles (1969) considered the process in the context of an expanding
world model showing that the angular momentum gained by the matter in
a random comoving More recent analytic computations (White 1984; Hoffman 1986 and
R88a) and numerical simulations (Barnes & Efstathiou 1987) have
re-investigated the role of tidal torques in originating galaxies
angular momentum. In particular White (1984) considered an analysis by
Doroshkevich (1970) that showing as the angular momentum of galaxies
grows to first order in proportion to Hoffman (1986) has been much more involved in the analysis of the correlation of the growth of angular momentum with the density perturbation . He found an angular momentum-density anticorrelation: high density peaks acquire less angular momentum than low density peaks. One way to study the variation of angular momentum with radius in a galaxy is that followed by R88a. In this approach the protogalaxy is divided into a series of mass shells and the torque on each mass shell is computed separately. The density profile of each proto-structure is approximated by the superposition of a spherical profile, , and a random CDM distribution, , which provides the quadrupole moment of the protogalaxy. To the first order, the initial density can be represented by: where is the background density and is given by: being the power spectrum, while the density profile is (Ryden & Gunn 1987): where is the height of a density peak,
is the two-point correlation function,
and are two spectral
parameters (BBKS, Eq. 4.6a, 4.6d) while is a
function given in BBKS (Eq. 6.14). As shown by R88a the net rms torque
on a mass shell centered on the origin of internal radius where , the multipole moments of the shell and , the tidal moments, are given by: where is the mass of the shell, and are the spherical Bessel function of first and second order while the power spectrum is given by: (Ryden & Gunn 1987). The normalization constant where the functions , are given by R88a (Eq. 31) while the mean over-density inside the shell, , is given by (R88a): In Fig. 1 we show the variation of with the
distance
This is the angular momentum-density anticorrelation showed by Hoffman (1986). This effect arises because the angular momentum is proportional to the gain at turn around time, , which in turn is proportional to . © European Southern Observatory (ESO) 1998 Online publication: August 6, 1998 |