Exact hierarchical clustering in one dimension

We present the results of a series of one-dimensional simulations of gravitational clustering based on the adhesion model, which is exact in the one-dimensional case. The catalogues of bound objects resulting from these simulations are used as a test of analytical approaches to cosmological structure formation. We consider mass functions of the Press–Schechter type, together with modifications to this formalism based on density-peak theories, and also the two-point correlation function estimated from peak theory. With suitable choices of filter function for the linear density field, these techniques can give an excellent fit to the data. However, there are some restrictions: for a one-dimensional spectral index, n > 3, the characteristic mass scale grows faster than expected in the standard clustering hierarchy, and the multiplicity function has a shape quite different from the Press–Schechter form. For $$n\gtrsim 0$$, the correlation-function method also gives less satisfactory results as dynamical contributions to the correlations tend to dominate statistical ones in this case. Finally, we test to what extent the locations of individual collapsed objects can be predicted via linear theory. This turns out to be possible only for objects near the characteristic non-linear mass: results such as the low-mass slope of the multiplicity function can only be correct in a statistical sense.