BIASED POWER SPECTRUM AND BISPECTRUM FOR AN ENSEMBLE OF 3-DIMENSIONALSCALE-FREE NUMERICAL SIMULATIONS

We examine the effect of a threshold bias on the power spectrum and th e bispectrum in an ensemble of numerical simulations (Gaussian initial perturbations with power-law spectra P(k)similar to k(n), n = + 1, 0, -1, -2) and compare our results with theoretical predictions. Our sim ulations are evolved sufficiently that on the scale where we apply the threshold the rms fluctuation has developed significantly into the no n-linear regime. Thus predictions based on perturbation theory do not necessarily apply. Nevertheless, we find that our results for the powe r spectrum, biased power simply amplified by a numerical factor, follo w predicted trends, far beyond the regime where perturbation theory is expected to be valid. We find that the biased bispectrum continues to follow the so-called hierarchical form, with reduced three-point ampl itude Q approximate to 1 in the strongly non-linear regime, independen t of the initial spectrum. In the quasi-linear perturbative regime the three point amplitude depends on configuration shape, a behaviour tha t is found to give useful information about the amount of bias without information, either direct or inferred from velocities, on the unbias ed matter distribution.