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By P. Monaco

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This was noted especially in the case of the transverse 3c term; however, it has been verified that this term can be safely neglected in the calculation; this is again in agreement with Buchert et al. (1994). The interpretation of this fact is simple: the 3c term, being purely rotational, is not expected to influence much the density of the mass element. The following collapse times bc have been calculated for every point: spherical (hereafter SPH), Zel’dovich (ZEL), second-order (2ND) third-order (3RD) and ellipsoidal (ELL) ones.

Then, tides are the relevant dynamical interaction neglected by spherical collapse. An important remark has to be made at this point. The equations just presented describe the behavior of a vanishing mass element in a smooth density field; any conclusion, including the calculation of collapse times, is relative to mass elements; in Monaco (1996a) this has been called punctual interpretation of collapse times. 4). 3 can be used: a mass element accreting on a perfectly spherical peak, which is not a top-hat, experiences spindle collapse (two axes collapse, one axis is shrunk to infinity).

The homogeneous ellipsoid collapse model has been used in the cosmological context, besides Bond & Myers (1996a,b,c), by White & Silk (1979), Peebles (1980), Barrow & Silk (1981), Hoffman (1986), and, more recently, by Bartlemann, Ehlers & Shneider (1993), who used it to estimate collapse times, by Eisenstein & Loeb (1995a), who modeled a collapsing structure by means of an ellipsoid, in order to calculate its angular momentum acquired in the mildly non-linear regime, and by Audit & Alimi (1996).

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