Evolution of the angular momentum of protogalaxies from tidal torques: Zel'dovich approximation

The growth of the angular momentum L of protogalaxies induced by tidaltorques is reconsidered within the Zel'dovich approximation. We obtain ageneral expression for the ensemble expectation value of the square of L interms of the first and second invariant of the inertia tensor of the Lagrangianvolume enclosing the protoobject's collapsing mass. We then specialize theformalism to the particular case in which this volume is centered on a peak ofthe smoothed Gaussian density field and approximated by an isodensityellipsoid. The result is the appropriate analytical estimate for the rmsangular momentum of peaks to be compared against simulations that make use ofthe Hoffman-Ribak algorithm to set up a constrained density field that containsa peak with given shape. Extending the work of Heavens & Peacock, we calculatethe joint probability distribution function for several spin parameters andpeak mass M using the distribution of peak shapes, for different initial powerspectra. The values of observed specific angular momentum versus mass are wellfitted by our theoretical isoprobability contours. In contrast, the observedlower values for the specific angular momentum for ellipticals of the same masscannot be accounted for within our linear regime investigation, highlightingthe importance of strongly non-linear phenomena to explain the spin of suchobjects.Comment: 25 pages, latex (mn.sty), 13 figures, to be published by MNRA