  The growth of the angular momentum L of protogalaxies induced by tidal
torques is reconsidered within the Zel'dovich approximation. We obtain a
general expression for the ensemble expectation value of the square of L in
terms of the first and second invariant of the inertia tensor of the Lagrangian
volume enclosing the protoobject's collapsing mass. We then specialize the
formalism to the particular case in which this volume is centered on a peak of
the smoothed Gaussian density field and approximated by an isodensity
ellipsoid. The result is the appropriate analytical estimate for the rms
angular momentum of peaks to be compared against simulations that make use of
the Hoffman-Ribak algorithm to set up a constrained density field that contains
a peak with given shape. Extending the work of Heavens & Peacock, we calculate
the joint probability distribution function for several spin parameters and
peak mass M using the distribution of peak shapes, for different initial power
spectra. The values of observed specific angular momentum versus mass are well
fitted by our theoretical isoprobability contours. In contrast, the observed
lower values for the specific angular momentum for ellipticals of the same mass
cannot be accounted for within our linear regime investigation, highlighting
the importance of strongly non-linear phenomena to explain the spin of such
objects.
