Hydrogen reionization is the epoch when ultraviolet photons produced by the first galaxies ionized almost all of the hydrogen in the Universe. (The vast majority of the atoms in the Universe are hydrogen.) Astrophysicists think that this process happened when the Universe was several hundred million to a billion years old, but exactly when and how it happened is something that we are struggling to answer.  This era is the least understood of any after the Universe was a mere second old.  I have worked on modeling this epoch (the adjacent image is from one of my simulations of this process) as well as on developing different observational methods that can be used to study it.  For an old review of  different techniques to study hydrogen reionization see this link.  Click here for movies generated from reionization simulations from my grad student days.

There aren't many ideas for directly studying the very first stars, which we think were more massive than subsequent ones.  The cosmic microwave background (CMB) is one of our only hopes for probing the first stars, with the main idea to measure  (via CMB polarization) the high redshift tail of reionization that these stars may have driven. Graduate student Xiaohan Wu led a paper that concluded, despite the significant uncertainties in when and how many of these stars formed, any plausible model cannot give a large enough ionization tail to be detected.  This result was partly driven by the small optical depth that the CMB has constrained reionization to have -- it is difficult to generate a measurably-large tail in the ionization history without overshooting the optical depth the CMB already measures.    Too bad....

Radiative transfer during reionization is a hard problem, as each point in space has streams of radiation moving in many different directions.  To make radiative transfer tractable, most cosmological simulations of reionization approximate the radiation field by only its monopole and dipole moments, making some ansatz for the quadrupole moments to close the system of equations.  It was unclear how these approximations affect their results.  In another study led by Xiaohan Wu, we were the first to investigate the standard approximate algorithms' accuracy by comparing their solutions with the exact solution on test problems.  The results were mostly positive regarding these algorithms -- these test problems point to the biggest inaccuracies occurring during the overlap phase and just after reionization.  However, these times are also the ones where we have the most detailed observations via the Lyman-alpha forest, and so more accurate methods may be needed.

This was a very long-term project that Anson D'Aloisio started when he was beginning as a postdoc at UW in 2014.  We got sidetracked, and finished when he was a few years into his professorship at UC Riverside.  We simulated what happens to cosmic gas as it is violently heated during reionization.  The movies, like shown on the left, are beautiful!  Before reionization, the cosmic gas clumps down to scales as small as ~10^4 Msun.  This heating causes it to dramatically readjust, smoothing out over ~10^9 Msun.  As it becomes less clumpy over hundreds of millions of years, it recombines less quickly and there are fewer self-shielding regions in which the gas can remain neutral.  This is the process we wanted to understand as this small-scale physics -- which is not resolved in reionization simulations -- affects the duration and structure of reionization.  

In 2022, UC Riverside graduate student Chris Cain led a study that took these small simulations and used them to develop a subgrid model to understand the back reaction on reionization.

Observations of redshifted 21cm emission targeting reionization are most sensitive to the power spectrum of this signal.  Indeed, the power spectrum should be detected well before any other statistic is measured.  The power spectrum is fairly far removed from imaging large patches of neutral gas -- what we would most want to measure, but lack the sensitivity.  A 21cm power spectrum measurement will result in a large interpretational challenge.  It is not clear what information about reionization such a measurement constrains. Motivated by the fact that the cross correlation coefficient between the linear density field and the 21cm signal in simulations is not small on many of the scales potentially probed by 21cm instrumental efforts, we developed an effective perturbation theory (or, equivalently, a bias expansion) for the inhomogeneous 21cm radiation field from reionization.   

This result provides an understanding of the potential signal shapes that had been missing. We find that the predicted signal in radiative transfer simulations of reionization can often be described with a few bias coefficients that can be interpreted in terms of the source galaxy’s bias, the average neutral fraction, and the characteristic size of ionized regions.  

Subsequent work by others has reproduced our exciting result.

This project felt like a capstone to a lot of studies we performed on the effect of temperature fluctuations on the Lyman-alpha forest (some described below).   Graduate student Xiaohan Wu ran several AREPO radiation-hydrodynamics simulations of reionization, which we used to calculate in detail how these temperature fluctuations shape the power spectrum of the Lyman-alpha forest.   The images on the left show slices through these simulations. 

Unfortunately, we found that their imprint would be challenging to detect at high wavenumbers, but they could be detectable if the power is measured at smaller wavenumbers.  This study is also relevant for warm/fuzzy dark matter constraints, as we thought that temperature effects would compromise previous limits....our conclusion was that this was not really the case and that the bounds seemed to stand up.  

Observations of the z >5 Lyman-alpha forest show large-scale spatial variations in the intergalactic Lyman-alpha opacity that grow rapidly with increasing redshift. Previous studies have attempted to explain this excess with spatial fluctuations in the ionizing background, but found that this required either extremely rare sources or problematically low values for the mean free path of ionizing photons.  In collaboration with Anson D’Aloisio [this study’s lead] and Hy Trac, we showed that opacity fluctuations could arise from residual spatial variations in temperature that are an inevitable byproduct of a patchy and extended reionization process.  (Click here for the paper link.)  We showed that if the entire excess is due to temperature variations alone, the observed fluctuation amplitude favors a late-ending but extended reionization process that was half complete by z~9 and that ended at z~6. In this scenario, the highest opacities occur in regions that were reionized earliest, since they have had the most time to cool, while the lowest opacities occur in the warmer regions that reionized most recently. This correspondence potentially opens a new observational window into patchy reionization.  Below is an illustration of a model for the distribution of reionization redshifts (left panel), and skewers through this model showing the reionization redshift and the transmission in the Lyman-alpha forest (right panel).  Regions reionized more recently are hotter (~104K), which results in more neutral hydrogen and more transmission, than regions ionized much earlier on (which can be a factor of five or so times cooler).  The size of the fluctuations in this model turn out to explain very well the observed opacity fluctuations and their redshift evolution, despite this model having essentially no freedom in describing the post-reionization evolution.

The competing explanation for these fluctuations is that they owe to spatial inhomogeneities in the hydrogen ionizing background. Fluctuating ionizing background models require either extremely rare sources (quasars to dominate the ionizing background) or for the mean free path of ionizing photons to be smaller than expected.  We also examined the plausibility of these alternatives (here and here).