The Effect of Large-Scale Power on Simulated Spectra of the Lyα forest

We explore the effects of size of the box that we use for simulations of the intergalactic medium (IGM) at redshift two. We examine six simulations from the hydrodynamic code ENZO using the same cosmological and astrophysical input parameters and cell size, but different box size. We study the CDM distribution and many statistics of the Lyα forest absorption from the IGM. Larger boxes have fewer pixels with significant absorption (flux < 0.96), more pixels in longer stretches with little or no absorption, and they have wider Lyα lines. The larger boxes differ only because they include power from long wavelength modes that do not fit inside the periodic conditions of the smaller boxes. The long modes change the density, velocity and temperature fields and these increase in the gas temperature. Small simulations are too cold compared to larger ones. When we deliberately increase the heat we put into the IGM, we can approximate the Lyα forest in a simulation of twice the size. When we double the box size, the difference of most statistics from their value in our largest 76.8 Mpc box is reduced by approximately a factor of two. Most of the statistics converge towards their value in the simulation with the largest box size, though line widths are not yet converged and the most common value of the CDM density shows no sign of converging, because the larger boxes include places with ever higher densities. These regions are not in the IGM, but they may produce the strongest of Lyα lines. When we double the box size from 38.4 Mpc to 76.8 Mpc, the mean Lyα absorption decreases 0.5%, the frequency with which we encounter different common CDM densities changes by 2%, typical Lyα line widths, the frequency of flux values and the power spectrum of the flux all change by 4–7%, and the column density distribution changes by up to 15%. When we compare to the errors in data, we find that our 76.8 Mpc box is larger than we need for the mean flux, barely large enough for the column density distribution and the power spectrum of the flux, and too small for the line widths that increase by 1 km s when we increase the box from 38.4 Mpc to 76.8 Mpc, which is approximately the error in data. We can most readily see the effects of the long wavelength modes in measurement on the smallest scales in the Lyα forest, the line widths, because they are easier to measure than the long wavelength power. Our optically thin simulations have a factor of several too few lines with H I column densities > 10 cm. Reducing the cell size from 75 to 18.75 kpc is not a solution. Our simulated spectra have 20% less power than data on small scales and 50% less on large scales, and their Lyα lines are 2.6 km s too wide. We do not see how our simulations might match all data at z = 2. Reducing the cell size to 18.75 kpc lowers the Lyα line widths by 1.8 km s, but radiative transfer effects can increase them by as much as 1.3 km s at z=2.5. We might reduce line widths using a softer ionizing spectrum to reduce heating, or we could use σ8 > 0.9 that has the additional benefit of increasing the large scale power. It is hard to see how simulations using popular cosmological and astrophysical parameters can match the Lyα forest data at z = 2.