  We implement the hydro-PM (HPM) technique (Gnedin & Hui 1998) in the
hydrodynamical simulation code GADGET-II and quantify the differences between
this approximate method and full hydrodynamical simulations of the Lyman-alpha
forest in a concordance LCDM model. At redshifts z=3 and z=4, the differences
between the gas and dark matter (DM) distributions, as measured by the
one-point distribution of density fluctuations, the density power spectrum and
the flux power spectrum, systematically decrease with increasing resolution of
the HPM simulqation. However, reducing these differences to less than a few
percent requires a significantly larger number of grid-cells than particles,
with a correspondingly larger demand for memory. Significant differences in the
flux decrement distribution remain even for very high resolution hydro-PM
simulations, particularly at low redshift. At z=2, the differences between the
flux power spectra obtained from HPM simulations and full hydrodynamical
simulations are generally large and of the order of 20-30 %, and do not
decrease with increasing resolution of the HPM simulation. This is due to the
presence of large amounts of shock-heated gas, a situation which is not
adequately modelled by the HPM approximation. We confirm the results of Gnedin
& Hui (1998) that the statistical properties of the flux distribution are
discrepant by > 5-20 % when compared to full hydrodynamical simulations. The
discrepancies in the flux power spectrum are strongly scale- and
redshift-dependent and extend to large scales. Considerable caution is needed
in attempts to use calibrated HPM simulations for quantitative predictions of
the flux power spectrum and other statistical properties of the Lyman-alpha
forest.
