Characterizing Lyman alpha emission from high-redshift galaxies

TL;DR

The paper develops a forward-modeling, data-driven empirical model for the emergent Ly$\alpha$ spectrum from high-redshift galaxies to enable robust interpretation of IGM damping-wing signatures during the EoR. It treats the emergent properties $x_{\alpha}=\{\log_{10}L_{\rm Ly\alpha},\;\Delta v,\;\log_{10}L_{\rm H\alpha}\}$ as a multivariate Gaussian conditioned on ${\rm M}_{\rm UV}$ with a linear mean $\mu({\rm M}_{\rm UV})=m\cdot{\rm M}_{\rm UV}+b$ and fixed covariance $\Sigma$, while forward-modeling survey selection as sigmoid functions. Calibrated on the $z\sim5$ Tang et al. sample combining VLT MUSE Ly$\alpha$ and JWST NIRCam H$\alpha$ observations, the model reproduces the Subaru-based Ly$\alpha$ EW PDF and the Ly$\alpha$ luminosity function, and yields extended distributions for $W_{\rm emerg}^{\rm Ly\alpha}$ and $\Delta v$ as functions of ${\rm M}_{\rm UV}$. The framework enables conditional inferences (e.g., about $P(\Delta v|W_{\rm emerg}^{\rm Ly\alpha},{\rm M}_{\rm UV})$), identifies GN-z11-like outliers, and supports redshift evolution studies, with fitting functions and code publicly available to help constrain IGM neutrality and EoR morphology.

Abstract

The Lyman $α$ (Ly$α$) line from high-redshift galaxies is a powerful probe of the Epoch of Reionization (EoR). Neutral hydrogen in the intergalactic medium (IGM) can significantly attenuate the emergent Ly$α$ line, even in the damping wing of the cross-section. However, interpreting this damping wing imprint relies on our prior knowledge of the spectrum that escapes from the galaxy and its environs into the IGM. This emergent spectrum is highly sensitive to the composition and geometry of the interstellar and circumgalactic media, and so exhibits a large galaxy to galaxy scatter. Characterizing this scatter is further complicated by non-trivial selection effects introduced by observational surveys. Here we build a flexible, empirical model for the emergent Ly$α$ spectra. Our model characterizes the emergent Ly$α$ luminosity, the velocity offset of the Ly$α$ line with respect to the systemic redshift, and the H$α$ luminosity, with multivariate probability distributions conditioned on the UV magnitude. We constrain these distributions using $z\sim5-6$ galaxy observations with VLT MUSE and JWST NIRCam, forward-modeling observational selection functions together with galaxy parameters. Our model results in Ly$α$ equivalent width distributions that are a better match to (independent) Subaru observations than previous empirical models. The extended distributions of Ly$α$ equivalent widths and velocity offsets we obtain could facilitate Ly$α$ transmission during the early stages of the EoR. We also illustrate how our model can be used to identify GN-z11-like outliers, potentially originating from merging systems. We publish fitting functions and make our model publicly available.

Figures (12)

• Figure 1: Toy model illustrating the impact of observational selection bias on the inferred $\log_{10}W_{\rm emerg}^{\rm Ly\alpha}$--${\rm M}_{\rm UV}$ relation. The black dashed lines show the completeness limits of a realistic Ly$\alpha$ survey (taken from debarros17). The blue curve traces the mean of a fiducial normal $\log_{10}W_{\rm emerg}^{\rm Ly\alpha}$--${\rm M}_{\rm UV}$ relation. $1250$ samples drawn from this distribution are shown with black dots (observed) and grey x's (non-observed). The green stars and line show the relation one obtains by linear regression to the observed samples. The red stars and line show the relation one obtains by linear regression on the observed samples, corrected for $W_{\rm emerg}^{Ly\alpha}$ completeness using the method of schenker14. The pink dashed curve shows the mean relation one obtains by the fitting procedure of mason2018.
• Figure 2: Schematic overview of our model. We model $P(x_\alpha|{\rm M}_{\rm UV})$ as a multivariate Gaussian distribution conditioned on ${\rm M}_{\rm UV}$, and fit the parameters of this distribution, along with the parameters related to selection, labeled ${\rm obs}$, to the measured distribution of the data $P(x_\alpha|{\rm obs},{\rm M}_{\rm UV})$. We bin the data in ${\rm M}_{\rm UV}$ to take advantage of the Schechter fit to the measured UV luminosity function of bouwens21. All observational selection functions are modeled as sigmoids, varying from $0$ to $1$, whose inflection points are free parameters.
• Figure 3: The fraction of galaxies in the observation field observed in both Ly$\alpha$ and H$\alpha$ as a function of ${\rm M}_{\rm UV}$, shown in orange for T24-Deep and red for T24-Wide. Points with error bars are estimated from the T24 data, while dotted lines show the same statistic computed from a realization of our model.
• Figure 4: Scalings between select Ly$\alpha$ parameters in our model. For better visualization of the trends at the rare/bright end, this figure was generated by uniformly sampling ${\rm M}_{\rm UV}$ over the range shown. The Ly$\alpha$ luminosity, H$\alpha$ luminosity, and velocity offset of the Ly$\alpha$ line all increase with increasing UV continuum luminosity (bottom row) whereas the Ly$\alpha$ emergent equivalent width and escape fraction increase for decreasing UV continuum luminosity (top row).
• Figure 5: The distribution of Ly$\alpha$ properties predicted by our model (red-orange probability density function) and measured by tang24 (black points). The top row applies the flux completeness limits of MUSE-Deep and the JWST FRESCO survey, the second row applies that of MUSE-Wide and the JWST FRESCO survey, and the third row applies no selection effects. The PDF in each panel is normalized independently for visibility.