An improved model for the effect of correlated Si-III absorption on the one-dimensional Lyman-$α$ forest power spectrum

TL;DR

This work addresses the impact of correlated Si III absorption on the 1D Lyα forest power spectrum, revealing a notable small-scale power enhancement not captured by the canonical McDonald 2006 model. By leveraging Sherwood-Relics hydrodynamical simulations, the authors derive a physically motivated four-parameter template that accounts for narrower Si III line profiles and a pixel-dependent Si III/Lyα optical-depth ratio, yielding a practical fit for $\frac{P_{ m tot}(k)}{P_{ m Lyα}(k)}$ across $2.2 \le z \le 5.0$ and $k \lesssim 0.2\,\mathrm{s\,km^{-1}}$. The model shows good agreement with simulations, with residuals typically at the percent level, and its redshift evolution is described by explicit forms tied to the IGM temperature and silicon abundance. While the Si III contamination modestly affects warm dark matter constraints under physically motivated priors, it is essential for interpreting future high-precision Lyα forest measurements and can inform constraints on low-density IGM metal enrichment.

Abstract

We present an analysis of Si III absorption and its effect on the 1D Ly$α$ forest power spectrum using the Sherwood-Relics hydrodynamical simulation suite. In addition to oscillations from the Ly$α$--Si III cross correlation that are damped toward smaller scales, we find an enhancement in small-scale power that has been ignored in previous studies. We therefore develop a new analytical fitting function that captures two critical effects that have previously been neglected: distinct Ly$α$ and Si III line profiles, and a variable ratio for coeval Ly$α$ and Si III optical depths. In contrast to earlier work, we also predict amplitudes for the Si III power spectrum and Ly$α$--Si III cross power spectrum that decrease toward lower redshift due to the hardening metagalactic UV background spectrum at $z\lesssim 3.5$. The fitting function is validated by comparison against multiple simulated datasets at redshifts $2.2\leq z \leq 5.0$ and wavenumbers $k < 0.2\rm\,s\,km^{-1}$. Our model has little effect on existing warm dark matter constraints from the Ly$α$ forest when adopting a physically motivated prior on the silicon abundance. It will, however, be an essential consideration for future, high precision Ly$α$ forest power spectrum measurements.

Figures (12)

• Figure 1: Left panel: The solid black contours show the volume weighted temperature-density plane at $z=3$ for the Sherwood-Relics hydrodynamical simulation used in this work. The number density of points increases by $0.5$ dex within each contour level. Note the horizontal axis is given in terms of both the logarithm of the gas overdensity, $\log_{10}\Delta$, and the logarithm of the hydrogen number density, $\log_{10}(n_{\rm H}/\rm cm^{-3})$. The overlaid colour scale shows the logarithm of the Si III fraction, $\log_{10}x_{\rm SiIII}$, predicted by the photo-ionisation code Cloudy Ferland1998Chatzikos2023 using the UV background synthesis model from Puchwein2019. Right panel: The redshift evolution of silicon ion fractions for gas with density $\log_{10}(n_{\rm H}/\rm cm^{-3})=-3.4$ and temperature $\log_{10}(T/\rm K)=4.5$. The decline in the Si II, Si III and Si IV fractions at $z\lesssim 3.5$ is driven by the hardening of the UV background spectrum due to ionising photons emitted by quasars.
• Figure 2: The transmitted flux for the Ly$\alpha$ forest (grey) and Si III absorption (red) for a random simulated sightline at $z \sim 3$. The upper panel shows the results from our direct calculation of the Si III spectrum from the hydrodynamical simulation described in Section \ref{['sec:method']}. The lower panel compares this to the Si III absorption obtained by a rescaling of the Ly$\alpha$ optical depths. This is similar to the approach often used in the literature when modelling the contribution of correlated metal absorption to the 1D Ly$\alpha$ forest power spectrum. In this example the scaling is chosen so that the mean Si III transmission in both panels is equal. Note the narrower widths for the Si III absorption in the direct calculation. The Ly$\alpha$ absorption is identical in both panels.
• Figure 3: A comparison of the total Ly$\alpha$ forest power spectrum including the contamination by correlated Si III absorption ($P_{\rm tot}(k)$, grey dashed curves) and its constituent terms (see Eq. \ref{['eqn:Pclm_old']}) at $z=3$, where the Si III absorption has been computed either by a linear rescaling of the Ly$\alpha$ optical depths (left column) or from a direct simulation following the procedure described in Section \ref{['sec:method']} (right column). Additional curves show the power spectrum for Ly$\alpha$ absorption only ($P_{\rm Ly\alpha}(k)$, black solid curve), Si III absorption only ($P_{\rm Si\,\textsc{III}}(k)$, red solid curve), and the cross term between Ly$\alpha$ and Si III ($P_{\rm Ly\alpha-Si\,\textsc{III}}(k)$, blue solid curve). The bottom panels show the ratio of $P_{\text{Si-III}}(k)$ and $P_{\rm Ly\alpha-Si\,\textsc{III}}(k)$ to $P_{\rm Ly\alpha}(k)$. In the left column, the value for the linear rescaling parameter $A$, where $\tau_{\rm Si\,\textsc{III}}(v)=A\tau_{\rm Ly\alpha}(v+\Delta v)$, was chosen so that the amplitude of $P_{\rm Si\,\textsc{III}}(k)$ is similar to the direct simulation on large scales.
• Figure 4: Stacked absorption line profiles for different Si III absorbers as a function of column density, $N_{\rm Si\,\textsc{III}}$, at $z=3.0$. Solid curves represent the stacked Si III absorption profiles, while dashed curves show the coeval Ly$\alpha$ absorption profiles. The line colours correspond the $N_{\rm Si\,\textsc{III}}$ in each stack. For most strong Si III systems, the Ly$\alpha$ absorption is saturated. This decorrelates the two tracers and leads to a suppression of the oscillation amplitude in the Ly$\alpha$--Si III cross power spectrum toward smaller scales.
• Figure 5: Comparison of analytical fits for $P_{\rm tot}(k)/P_{\rm Ly\alpha}(k)$ to the results from a hydrodynamical simulation drawn from the Sherwood-Relics suite (black circles with error bars). Each panel shows a different redshift, spanning the range $2.2\leq z \leq 5.0$. The binning with wavenumber in the top row follows the eBOSS 1D power spectrum Chabanier2019, while the bottom row follows the 1D power spectrum measurement from Boera2019 obtained from high resolution Keck/HIRES and VLT/UVES spectra. The error bars give the 68 per cent confidence interval and represent the variance in the 5000 sight-lines of length $40\,h^{-1}\rm\,cMpc$ used to construct the Ly$\alpha$ and Si III absorption spectra. The red and blue curves respectively show the best fit using the function proposed in this work, Eq. (\ref{['eq:model']}), and the original M06 ansatz. At large scales, $k\lesssim 0.02\rm\,s\,km^{-1}$, both models provide an excellent fit to the simulation. However, at smaller scales Eq. (\ref{['eq:model']}) performs much better because the contribution from the Si III power spectrum, $P_{\rm Si\,\textsc{III}}(k)$, becomes significant.