Analytic Model for Scattered Ly$\boldsymbolα$ Emission in the Post-reionization Intergalactic Medium

TL;DR

This work addresses the challenge of interpreting Lyα intensity mapping by resonant radiative transfer in the post-reionization IGM. It develops a fast analytic prescription that exploits a near-spherical last-scattering surface, with the scattering location governed by $r_s = - (v_{\alpha,i} + v_{\rm pe,r})/(aH(z))$, and negligible damping-wing opacity. The authors derive closed-form expressions for the scattered emissivity $\epsilon_{\rm scat}(\mathbf{r})$ and projected surface brightness $S_{\rm scat}(\mathbf{r}_\perp)$ that depend on the source spectrum $L_\lambda(\lambda_i)$, HI density, and peculiar velocity field, enabling efficient generation of Lyα maps. Validation against MCRT in a Nyx-based mock IGM shows good agreement on Mpc scales, with small deviations near halos due to strong infall but sub-10% accuracy in angle-averaged SB beyond ~3 $h^{-1}$ Mpc, and roughly 37% of photons scattered in both approaches. The analytic framework offers a computationally efficient path for forward-modeling Lyα LIM data and inferring cosmological and astrophysical parameters from future observations.

Abstract

Ly$α$ intensity mapping is emerging as a new probe of faint galaxies consisting the cosmic web that elude traditional surveys. However, the resonant nature of Ly$α$ radiative transfer complicates the interpretation of observed data. In this study, we develop a fast and accurate analytic prescription for computing the Ly$α$ intensity field on Mpc scales in the post-reionization Universe. Motivated by insights from Monte Carlo radiative transfer (MCRT) experiments, we exploit the fact that in a highly ionized intergalactic medium (IGM) with negligible damping-wing opacity, cosmological redshifting quickly drives Ly$α$ photons out of resonance, terminating the scattering process and simplifying their large-scale behavior. Photons emitted blueward of the Ly$α$ line center tend to scatter on a thin, nearly spherical surface of last scattering, with a radius determined by the redshifting distance to resonance. Based on this behavior, we derive closed-form expressions for the scattered emissivity and projected surface brightness that depend only on the source spectrum, the HI density, and the peculiar velocity field. When applied to a source in a realistically simulated IGM at $z = 3$, our model shows mild discrepancies with MCRT results within a physical Mpc of the host halo, where strong gravitational infall redistributes the scattered photons, but achieves better than 5% accuracy beyond that distance in angle-averaged radial surface brightness profile. Our prescription offers a computationally efficient alternative to MCRT for forward-modeling Ly$α$ intensity maps from cosmological simulations, enabling the inference of underlying cosmological and astrophysical parameters from future observations

Figures (8)

• Figure 1: Trajectories of photons initially emitted 4.06Å blueward of Ly$\alpha$ ($v_{\alpha,{\rm i}} = -1000~{\rm km}{\rm s}^{-1}$; $\Delta\lambda_{\alpha,{\rm i}} = -4.06~{\rm Å}$) in the $+x$ direction, projected onto the $xy$ plane. The IGM is assumed to be static and to have uniform neutral hydrogen densities of $10^{-8}$, $10^{-9}$, and $10^{-10}~{\rm cm}^{-3}$, corresponding to Ly$\alpha$ optical depths (Eq. \ref{['eq:tau_star']}) of $\tau_* = 133$, 13.3, and 1.33 in the upper, middle, and lower panels, respectively. The star symbol marks the photon source, and the black dashed circle in the left panels indicates the last-scattering distance $r_{\rm s}$ as described in Section \ref{['sec:LSS']}. For each HI density, the trajectories of seven photons are shown as solid and dotted lines, with the dotted lines marking the final paths taken by the photons as they escape. The right panels provide zoomed-in views of the regions where most scatterings occur. In the lower-left corner of each right panel, we report the average number of scatterings, $\left<N_{\rm scat}\right>$, and the average separation between the first and last scattering, $\left<d_{\rm scat}\right>$.
• Figure 2: Location of last scattering events projected on the $xy$ plane for photons emitted isotropically in the static, uniform IGM with $n_{\rm HI}=10^{-9}~{\rm cm}^{-3}$. The results are shown for initial velocity offset of $v_{\alpha,{\rm i}}=-500$ (left), $-1000$ (middle), and $-1500~{\rm km}~{\rm s}^{-1}$ (right panel), corresponding to wavelength offset of $\Delta \lambda_{\alpha,i}=-2.03,~ -4.06$, and $-6.08~{\rm Å}$, respectively. The dashed circle in each panel indicates the scattering distance $r_{\rm s}$ from the source corresponding to the respective initial wavelength at emission given by Equation (\ref{['eq:r_s']}).
• Figure 3: Radial surface brightness profile (left) and cumulative distribution (right) of the scattered Ly$\alpha$ photons as a function of projected distance from an isotropic monochromatic source. We assume a source luminosity of $L_{\rm tot}=10^{44}~{\rm erg}~{\rm s}^{-1}$ and an HI density of $n_{\rm HI}=10^{-9}~{\rm cm}^{-3}$. Simulation results are shown as histograms outlined by solid lines, while the analytic model from Equation (\ref{['eq:SBmono']}) is shown as dashed lines. The upper, middle, and lower curves correspond to $v_{\alpha,{\rm i}}=-500$, $-1000$, and $-1500~{\rm km}~{\rm s}^{-1}$, respectively.
• Figure 4: Scattering fraction at the Ly$\alpha$ resonance, $1-e^{-\tau_*}$, on a slice of IGM through the center of Nyx simulation at $z=3$. The scattering fraction decreases from 1 to 0 as the color transitions from black to white. The ionizing source at the center is marked with a star symbol.
• Figure 5: Comparison of surface brightness maps constructed from the analytic model (left) versus the MCRT simulation (right) from Sec. \ref{['sec:test']}. The maps are generated by projecting the Ly$\alpha$ intensity distribution along the $z$-axis, with the $xy$ plane representing the sky.