Testing Ansatze for quasi-non-linear clustering: The linear APM power spectrum

We compare the accuracy of published formulae that transform the linear perturbation theory power spectrum into the non-linear regime against the results of an ensemble of large N-body simulations, paying attention to scales on which the density fluctuations are linear and quasi-linear. The inverse transformation to obtain the linear power spectrum is applied to the APM Galaxy Survey power spectrum measured by Baugh & Efstathiou. The resulting linear spectrum is used to generate the initial density fluctuations in an N-body simulation, which is evolved to match the measured APM amplitude on large scales. We find very good agreement between the final power spectrum of the simulation and the measured APM power spectrum. However, the higher moments for the particle distribution match the ones recovered from the APM Survey only on large scales, R greater than or similar to 10 h(-1) Mpc. On small scales, R < 10 h(-1) Mpc, the APM estimations give smaller amplitudes, indicating that non-gravitational effects, such as biasing, are important on those scales. Our approach can be used to constrain a model of how light from galaxies traces the underlying mass distribution.