Modeling of the High Column Density systems in The Lyman-Alpha Forest

TL;DR

This work tackles the challenge of modeling high-column-density systems (HCDs) in the Lyman-α forest, which damps radial power-spectrum modes and induces a scale-dependent bias. It develops and tests a physically motivated Voigt-profile HCD model, relating the damping to the HI column-density distribution and halo biases, and compares it to the traditional exponential (Exp) phenomenology. Using mocks with known HCD content, the Voigt model generally recovers the HCD bias around $b_{ m HCD} oughly 2$, while Lyα bias parameters remain stable and BAO measurements remain consistent with unity, validating the approach in a controlled setting. When applied to real eBOSS DR16 data, the inferred HCD bias appears larger than in mocks, signaling potential additional smoothing effects or uncertainties in HCD content and masking; nonetheless, BAO constraints remain robust, underscoring the need for careful HCD modeling in future DESI analyses and offering guidance on strategies to handle DLA masking and f(n) uncertainties.

Abstract

The Lyman-$α$ forests observed in the spectra of high-redshift quasars can be used as a tracer of the cosmological matter density to study baryon acoustic oscillations (BAO) and the Alcock-Paczynski effect. Extraction of cosmological information from these studies requires modeling of the forest correlations. While the models depend most importantly on the bias parameters of the intergalactic medium (IGM), they also depend on the numbers and characteristics of high-column-density systems (HCDs) ranging from Lyman-limit systems with column densities $\log_{10}\!\bigl(N_{\mathrm{HI}}/\mathrm{cm}^{-2}\bigr)>17$ to damped Lyman-$α$ systems (DLAs) with $\log_{10}\!\bigl(N_{\mathrm{HI}}/\mathrm{cm}^{-2}\bigr)>20.2$. These HCDs introduce broad damped absorption characteristic of a Voigt profile. Consequently they imprint a component on the power spectrum whose modes in the radial direction are suppressed, leading to a scale-dependent bias. Using mock data sets of known HCD content, we test a model that describes this effect in terms of the distribution of column densities of HCDs, the Fourier transforms of their Voigt profiles and the bias of the halos containing the HCDs. Our results show that this physically well-motivated model describes the effects of HCDs with an accuracy comparable to that of the ad-hoc models used in published forest analyses. We also discuss the problems of applying the model to real data, where the HCD content and their bias is uncertain.

Figures (15)

• Figure 1: A flux spectrum, $f_q(\lambda)$, for a mock quasar, with $z_{\text{QSO}}=2.86$. The Ly$\alpha$ emission line is present at 4685Å and a DLA with $N_{\text{HI}}=10^{20.72}\text{cm}^{-2}$ at redshift $z_{\text{DLA}}=2.57$ is present at 4339.9Å. The red line shows the estimated mean spectrum, $\overline{F}(\lambda)C_q(\lambda)$, about which the fluctuations are measured. The red dotted line indicates the region that is masked in the standard picca analysis. The black line shows the fitted Voigt profile fit to this DLA.
• Figure 2: The Voigt transmission profile, $V(\lambda)$ and the Fourier transform, $W(k)$ of $W(\lambda)=1-V(\lambda)$ for HCDs with $N_{\text{HI}}=10^{20}\text{cm}^{-2}$ (black) and $10^{21}\text{cm}^{-2}$ (red) at a redshift of 2.35. The distance and $k_{\parallel}$ scales are derived from the wavelength scale using the fiducial cosmological model.
• Figure 3: Illustration of the flux-flux auto-correlations and quasar-flux cross-correlations. The top two lines of sight illustrate flux-flux auto-correlation for two forests in front of quasars $q$ and $q'$. The bottom two lines of sight illustrate the quasar-flux cross-correlation. Flux measurements $f_q(\lambda)$ along the LOS to quasar $q$ and the associated flux-transmission field $\delta_q(\lambda)$ are measured on "pixels" of width $\Delta\log\lambda=0.0001$ (BOSS and eBOSS) or $\Delta\lambda=0.8$Å (DESI) as represented by the dots and indexed by $j$. On the bottom plot a HCD is centered on a wavelength indexed by $j_{HCD}$. Correlations of $\delta_q(\lambda)$ with a neighboring pixel or quasar are measured as a function of $(r_{\perp},r_{\parallel})$ calculated from the pixel wavelength separation and angular separation of the two lines-of-sight assuming a fiducial cosmological model.
• Figure 4: The $N_{\text{HI}}$ distribution $f(n=\log N_{\rm{HI}}/{1\rm{cm}^{-2}})$ that is used in our analysis. The orange curve shows the distribution of pyigmprochaska2017pyigm, and the blue points give the HCD distribution in our mocks.
• Figure 5: The function $F_{\rm HCD}^{\rm Voigt}$ (equation \ref{['Equa:Fhcd']}) based on integration of HCDs with the distribution of $\text{N}_{\text{HI}}$ over the ranges as labeled and assuming $\rho_{\rm HCD}=0.00158$Å$^{-1}$. The solid green line gives the complete $F_{\rm HCD}^{\rm Voigt}$ if no DLAs are masked and the solid gray line the complete $F_{\rm HCD}^{\rm Voigt}$ if all DLAs with $\log N_{\rm{HI}}/{1\rm{cm}^{-2}}>20.3$ are masked.