Adding long-wavelength power to N-body simulations

Tormen and Bertschinger have presented an algorithm which allows the dynamic range of N-body simulations to be extended by adding long-wavelength power to an evolved N-body simulation. This procedure is of considerable interest as it will enable mock galaxy catalogues to be constructed with volumes as larger as those of the next generation of galaxy redshift surveys. Their algorithm, however, neglects the coupling between long-wavelength linear modes and short-wavelength non-linear modes. The growth of structure on small scales is coupled to the amplitude of long-wavelength density perturbations via their effect on the local value of the density parameter Omega_0. The effect of neglecting this coupling is quantified using a set of specially tailored N-body simulations. It is shown that the large-scale clustering of objects defined in the evolved density field such as galaxy clusters is strongly underestimated by their algorithm. An adpatation to their algorithm is proposed that, at the expense of additional complexity, should remedy the shortcomings of the original one. Methods of constructing biased mock galaxy catalogues which utilise the basic algorithm of Tormen and Bertschinger, but avoid the pitfalls are discussed