Scale-dependent bias in the BAO-scale intergalactic neutral hydrogen

TL;DR

This work addresses how inhomogeneous, clustered UV sources imprint a scale-dependent bias on intergalactic HI at $z\simeq 2.3$, affecting the Lyman-α forest and the BAO signal. It develops a linear, monochromatic radiative-transfer framework that couples diffuse HI, self-shielded clumps, recombination emission, and biased emissivity fluctuations, yielding a central result $b_{\mathrm{HI}}(k) = \frac{b_{\mathrm{HI,u}} - b_{j,\mathrm{eff}}\,S(k)}{1 - \beta_{\mathrm{HI}}\,S(k)}$ with the kernel $S(k) = \frac{a\kappa_{\mathrm{tot},0}}{k} \arctan\left(\frac{k}{a\kappa_{\mathrm{tot},0}}\right)$. The analysis predicts a distinctive imprint on the HI power spectrum and a distortion of the correlation function at BAO scales that depends on the source bias, mean-free-path, and source density, offering a pathway to constrain UV-source properties from Lyman-α data. The results motivate new simulations and careful treatment of observational effects to leverage BOSS-like surveys for astrophysical inferences about the cosmic UV background. Overall, the paper clarifies how radiative-transfer physics can reshape large-scale structure probes and highlights the potential for using BAO-scale Lyman-α measurements to learn about ionizing sources in the near future.

Abstract

I discuss fluctuations in the neutral hydrogen (HI) density of the z~2.3 intergalactic medium and show that their relation to cosmic overdensity is strongly scale-dependent. This behaviour arises from a linearized version of the well-known "proximity effect", in which bright sources suppress atomic hydrogen density. Using a novel, systematic and detailed linear-theory radiative transfer calculation, I demonstrate how HI density consequently anti-correlates with total matter density when averaged on scales exceeding the Lyman-limit mean-free-path. The radiative transfer thumbprint is highly distinctive and should be measurable in the Lyman-alpha forest. Effects extend to sufficiently small scales to generate significant distortion of the correlation function shape around the baryon acoustic oscillation peak, although the peak location shifts only by 1.2 percent for a mean source bias of b_j=3. The distortion changes significantly with b_j and other astrophysical parameters; measuring it should provide a helpful observational constraint on the nature of ionizing photon sources in the near future.

Figures (8)

• Figure 1: In the linear approximation, the radiative transfer consists of convolving an effective source function (including emission, absorption and re-radiation terms) with a kernel S, equation \ref{['eq:radiation-equation']}. The kernel is shown here in Fourier space (upper panel) as a function of wavenumber divided by $\kappa_{\mathrm{tot},0}$. On large scales (toward the left) $S(k)$ is $\approx 1$, meaning fluctuations in the effective source function are tracked by fluctuations in the number density of ionizing photons. On small scales (toward the right), $S(k)$ decays towards zero; fluctuations in the photon density are suppressed and the uniform UV approximation will apply. The lower panel shows the same kernel transformed into real space; the horizontal axis is an inverse distance, so the two panels read in the same direction.
• Figure 2: ( Upper panel) the calculated bias of intergalactic H i at $z=2.3$ as function of comoving wavenumber. The dashed line shows the bias in the uniform-radiation case; the solid line shows the bias calculated with radiative transfer. On small scales (towards the right), the calculated bias agrees with that of the uniform case. On large scales, the H i is negatively biased because overdensities imply high emissivity, high radiation density and hence net H i under-density. Dotted lines show the effect of changing the source bias $b_j$; from top to bottom, $b_j=1.5$, $2.0$, $\cdots$, $4.0$. ( Lower panel) the corresponding power spectrum, $P_{\mathrm{HI}}(k)$, defined by equation \ref{['eq:PHI']}, has a strong feature where $b_{\mathrm{HI}}$ passes through zero (near to $k=\kappa_{\mathrm{tot},0}^{-1}$).
• Figure 3: The correlation function of intergalactic H i at $z=2.3$, as defined by the Legendre transform \ref{['eq:legendre']} of the power spectrum shown in Figure \ref{['fig:bk']}. As before, dashed lines show the constant bias case, whereas the solid line shows the calculated bias for inhomogeneous radiation (in the default case, $b_j=3.0$). The dotted lines show a series of different source biases ($b_j=1.5$, nearest the dashed line; then $2.0$, $2.5$, $3.5$ and $4.0$). The result of cross-correlating the H i against a tracer population with fixed bias is shown by the dash-dotted line.
• Figure 4: The effect of varying the mean H i opacity on the power spectrum (upper panel) and correlation function (lower panel). Other parameters are held fixed. The dashed and solid lines show the uniform-radiation and reference case respectively, so agreeing with the same lines in Figures \ref{['fig:bk']} and \ref{['fig:xi']}. Dotted lines show the results for an H i opacity $0.25$, $0.5$, $2$ and $4$ times that of the default case. As the opacity increases, the mean-free-path decreases, meaning that the "dip" feature in the H i power spectrum moves to shorter wavenumbers. Consequently small-scale power is increasingly suppressed, whereas large-scale power is enhanced.
• Figure 5: The effect of source shot-noise on the power spectrum (upper panel) and correlation function (lower panel). Other parameters are held fixed. The dashed and solid lines show the uniform-radiation and reference case respectively, so agreeing with the same lines in Figures \ref{['fig:bk']} and \ref{['fig:xi']}. The dotted lines show the results for (top to bottom) $\bar{n}=10^{-5}$, $5 \times 10^{-5}$, $10^{-4}$, $5 \times 10^{-4}$ (solid line), $10^{-3}$ and $5\times 10^{-3}\,h^3\,\mathrm{Mpc}^{-3}$. As the effective source density $\bar{n}$ decreases, the amplitude of shot-noise increases, confusing the H i signal. The changes are strongest on large scales for the reasons discussed in the text.