[Paper Review] Reconstructing the redshift evolution of escaped ionizing flux from early galaxies with Planck and HST observations

Layne C. Price, Hy Trac+1 more|arXiv (Cornell University)|May 12, 2016

Galaxies: Formation, Evolution, Phenomena16 references18 citations

TL;DR

This study reconstructs the redshift evolution of ionizing photon escape fractions ($f_{\mathrm{esc}}$) and photon production rates ($\dot{n}_{\gamma}$) from early galaxies using Planck 2015 and 2016 CMB data, HST galaxy observations, and BAO constraints. It finds strong evidence for redshift evolution in $f_{\mathrm{esc}}(z)$, with $f_{\mathrm{esc}} \lesssim 0.5$ at $z=8$ and a power-law slope $\beta \gtrsim 2.0$, while model-independent $\dot{n}_{\gamma}(z)$ suggests a sharper reionization period with suppressed flux at $z=9$ under Planck 2016 data.

ABSTRACT

While galaxies at $6 \lesssim z \lesssim 10$ are believed to dominate the epoch of cosmic reionization, the escape fraction of ionizing flux $f_\mathrm{esc}$ and the photon production rate $\dot n_γ$ from these galaxies must vary with redshift to simultaneously match CMB and low-redshift observations. We constrain $f_\mathrm{esc}(z)$ and $\dot n_γ(z)$ with Planck 2015 measurements of the Thomson optical depth $τ$, recent low multipole E-mode polarization measurements from Planck 2016, SDSS BAO data, and $3 \lesssim z \lesssim 10$ galaxy observations. We compare different galaxy luminosity functions that are calibrated to HST observations, using both parametric and non-parametric statistical methods that marginalize over the effective clumping factor $C_\mathrm{HII}$, the LyC production efficiency $ξ_\mathrm{ion}$, and the time-evolution of the UV limiting magnitude $dM_\mathrm{SF}/dz$. Using a power-law model, we find $f_\mathrm{esc} \lesssim 0.5$ at $z=8$ with slope $β\gtrsim 2.0$ at $68\%$ confidence with little dependence on the galaxy luminosity function or data, although there is non-negligible probability for no redshift evolution $β\sim 0$ or small escape fraction $f_\mathrm{esc} \sim 10^{-2}$. A non-parametric form for $f_\mathrm{esc}(z)$ evolves significantly with redshift, yielding $f_\mathrm{esc} \sim 0.2, 0.3, 0.6$ at $z=6,9,12$, respectively. However, a model-independent reconstruction of $\dot n_γ(z)$ predicts a suppressed escaped photon production rate at $z=9$ for the latest Planck data compared to the other models, implying a quicker period of reionization. We find evidence for redshift evolution in the limiting magnitude of the galaxy luminosity function for empirical models of the galaxy luminosity function.

Motivation & Objective

• To constrain the redshift evolution of the escape fraction $f_{\mathrm{esc}}(z)$ and ionizing photon production rate $\dot{n}_{\gamma}(z)$ from early galaxies during the Epoch of Reionization.
• To test whether $f_{\mathrm{esc}}(z)$ must evolve with redshift to reconcile CMB optical depth measurements with low-redshift galaxy observations.
• To assess the impact of galaxy luminosity function (GLF) assumptions, limiting magnitude evolution, and LyC production efficiency $\xi_{\mathrm{ion}}$ on $f_{\mathrm{esc}}(z)$ and $\dot{n}_{\gamma}(z)$.
• To compare parametric and non-parametric reconstructions of $f_{\mathrm{esc}}(z)$ and $\dot{n}_{\gamma}(z)$ to assess model independence and robustness.
• To determine whether redshift evolution in the UV luminosity function's faint-end magnitude limit $M_{\mathrm{SF}}$ is required to match observational constraints.

Proposed method

• Uses Planck 2015 and 2016 CMB measurements of the Thomson optical depth $\tau$ as the primary constraint on $\dot{n}_{\gamma}(z)$, which is model-independent and sensitive to the total escaped ionizing flux.
• Employs HST-based galaxy luminosity functions (GLFs), including the Scorch and Bouwens et al. (2015b) models, to link UV luminosity to ionizing photon production.
• Applies both parametric (power-law) and non-parametric statistical methods to reconstruct $f_{\mathrm{esc}}(z)$ and $\dot{n}_{\gamma}(z)$, marginalizing over uncertain parameters like $C_{\mathrm{HII}}$, $\xi_{\mathrm{ion}}$, and $dM_{\mathrm{SF}}/dz$.
• Incorporates SDSS Baryon Acoustic Oscillation (BAO) data to break degeneracies in cosmological parameters and improve constraints on reionization history.
• Uses Bayesian inference with log-prior for $\xi_{\mathrm{ion}}$ and uniform prior for $f_{\mathrm{esc}}(z)$ to assess sensitivity of results to prior assumptions.
• Performs model-independent reconstruction of $\dot{n}_{\gamma}(z)$ to avoid bias from assumed functional forms, enabling comparison with parametric models.

Experimental results

Research questions

• RQ1 Does the escape fraction $f_{\mathrm{esc}}(z)$ from early galaxies require redshift evolution to reconcile CMB optical depth measurements with galaxy observations?
• RQ2 How does the choice of galaxy luminosity function (GLF) affect the inferred $f_{\mathrm{esc}}(z)$ and $\dot{n}_{\gamma}(z)$?
• RQ3 What is the impact of assuming a power-law or non-parametric form for $f_{\mathrm{esc}}(z)$ on the reconstructed ionizing photon production rate?
• RQ4 Is there evidence for redshift evolution in the faint-end magnitude limit $M_{\mathrm{SF}}$ of the UV luminosity function?
• RQ5 How do different CMB datasets (Planck 2015 vs. 2016 lowE) affect the inferred $\dot{n}_{\gamma}(z)$ and the required $f_{\mathrm{esc}}(z)$?

Key findings

• A power-law model for $f_{\mathrm{esc}}(z)$ yields $f_{\mathrm{esc}} \lesssim 0.5$ at $z=8$ with a slope $\beta \gtrsim 2.0$ at 68% confidence, indicating strong redshift evolution.
• Non-parametric reconstruction of $f_{\mathrm{esc}}(z)$ yields $f_{\mathrm{esc}} \sim 0.2, 0.3, 0.6$ at $z=6, 9, 12$, respectively, showing significant evolution across the reionization era.
• The model-independent $\dot{n}_{\gamma}(z)$ reconstruction predicts a suppressed photon production rate at $z=9$ when using Planck 2016 lowE data, implying a sharper reionization period.
• The limiting magnitude $M_{\mathrm{SF}}$ of the UV GLF must evolve with redshift, with $dM_{\mathrm{SF}}/dz \lesssim -0.05$ at 68% confidence, to avoid overproduction of ionizing photons.
• The variation in $\tau$ between Planck 2015 and 2016 datasets is better fit by adjusting $\xi_{\mathrm{ion}}$ than by changing $f_{\mathrm{esc}}(z)$, though this depends on prior assumptions.
• Both parametric and non-parametric methods yield consistent constraints on $\dot{n}_{\gamma}(z)$, validating the robustness of the model-independent approach to reconstructing reionization history.