Testing the accuracy of the Hydro-PM approximation in numerical simulations of the Lyman-alpha forest

TL;DR

This study tests the Hydro-PM (HPM) approximation by implementing it in GADGET-2 and benchmarking it against full hydrodynamical simulations of the Lyman-$\alpha$ forest in a concordance LCDM universe across $z=2$–$4$. It finds that DM and gas density fields converge to full hydrodynamics when the PM grid is sufficiently refined, but flux statistics reveal persistent, redshift- and scale-dependent discrepancies, driven largely by differences in the thermal state and shock heating not captured by HPM. The flux power spectrum shows only modest, scale-dependent offsets at $z=3$ and $z=4$ for high PM resolution, while at $z=2$ the differences can be large (20–30% and non-convergent), casting doubt on the quantitative reliability of calibrated HPM for precise flux-power predictions. The results emphasize the need for careful calibration against full hydrodynamics and potentially introducing scatter in the temperature–density relation to improve HPM's applicability for Lyman-$\alpha$ forest analyses, particularly at low redshift and for strong absorption regions.

Abstract

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.

Figures (10)

• Figure 1: Power spectrum of the gas density field of the HPM simulations run with GADGET-2 at $z=3$, at two different resolutions and for several different values of the parameter $N_{\rm grid}$. The power spectrum of the full hydrodynamical simulation is represented by the filled triangles.
• Figure 2: Left: differences in the probability distribution functions of the dark matter density field between GADGET-2 (G2) and the Gnedin & Hui (GH) code. Both of them have been run in the PM mode with a grid of $200^3$ for GH and $400^3$ for G2. Right: Fractional differences in the 3D matter power spectrum. The results are shown at three different redshifts $z=2,3,4$ as dashed, continuous and dotted curves, respectively.
• Figure 3:
• Figure 4: Left: differences in the probability distribution functions of the dark matter density field between simulations run with GADGET-2 in its HPM and in its TreePM mode (the PM grid for the TreePM run is fixed to the value $N_{\rm grid}=200$). Right: Fractional differences in the 3D matter power spectrum. The results are shown at $z=3$ and for three different values of $N_{\rm grid}$ (400,600,1200) as continuous, dashed and dot-dashed curves, respectively.
• Figure 5: Left: differences in the probability distribution functions of the gas density field between simulations run with GADGET-2 in its HPM and in its TreePM mode (the PM grid for the TreePM run is fixed to the value 200). Right: Fractional differences in the 3D matter power spectrum. The results are shown at $z=3$ and for three different values of $N_{\rm grid}$ (400,600,1200) as continuous, dashed and dot-dashed curves, respectively.