The growth of the angular momentum { \bf L } of protogalaxies induced by tidal torques is reconsidered .
We adopt White ’ s formalism and study the evolution of { \bf L } in Lagrangian coordinates ; the motion of the fluid elements is described by the Zel ’ dovich approximation .
We obtain a general expression for the ensemble expectation value of the square of { \bf L } in terms of the first and second invariant of the inertia tensor of the Lagrangian volume \Gamma enclosing the protoobject ’ s collapsing mass .
We then specialize the formalism to the particular case in which \Gamma is centred 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 probability distribution for the rms final angular momentum \langle { \bf L } _ { f } ^ { 2 } \rangle ^ { 1 / 2 } on the scales corresponding to common bright galaxies , M \approx 10 ^ { 11 } M _ { \odot } , is centred on a value of \approx 10 ^ { 67 } { kg } { m } ^ { 2 } { s } ^ { -1 } , for any cosmologically relevant power spectrum , in line with previous theoretical and observational estimates for L _ { f } .
Other astrophysical consequences are discussed .
In particular , we find that typical values \langle \lambda ^ { 2 } \rangle ^ { 1 / 2 } \approx 0.1 of the dimensionless spin parameter for peaks smoothed on galactic scales and of height \nu \sim 1 , usually associated with late type galaxies , may be recovered in the framework of the Gaussian peak formalism .
This partially relaxes the importance attributed to dissipative processes in generating such high values of centrifugal support for spiral galaxies .
In addition , the values of the specific angular momentum versus mass – as deduced from observations of rotational velocities and photometric radii of spiral galaxies – 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 can not be accounted for within our linear regime investigation , highlighting the importance of strongly non-linear phenomena to explain the spin of such objects .