In the excursion set approach to structure formation initially spherical regions of the linear density field collapse if the average density contrast within them exceeds some critical value , \delta _ { c } .
This model allows one to make predictions for several fundamental aspects of structure formation such as the mass function of dark matter halos , their merger histories and clustering properties .
The value of \delta _ { c } is often calculated from the spherical or ellipsoidal collapse model , which provide well-defined predictions given auxiliary properties of the linear tidal field at a given point .
We use two cosmological simulations of structure growth in a LCDM cosmology to test a key assumption used in calculating \delta _ { c } : that the shapes of the initial Lagrangian patches that eventually collapse ( or proto-haloes ) are spherical .
Our results indicate that the vast majority of dark matter proto-haloes are non-spherical , and have minor-to-major axis ratios that vary from \langle a _ { 3 } / a _ { 1 } \rangle \sim 0.4 at the galaxy mass scale to \sim 0.65 for rich galaxy clusters .
We show that this non-sphericity likely originates from the asymmetry of the linear tidal field which pushes material onto , or away from , local density maxima in the linear density field .
We study the implications of these results for the collapse barriers for CDM halo formation inferred from the classic ellipsoidal collapse model .
Our results indicate that the “ standard ” ellipsoidal collapse model commonly adopted in the literature does not provide a full account of the possible collapse thresholds for halo formation , since the model predictions depend sensitively on the assumed shape of the primordial perturbation .
We show that an improved model , which accounts for the intrinsic shapes of proto-haloes , provides a much more accurate description of their measured minimum overdensities .