Long troughs observed in the z > 5.5 Lycx and Ly,3 forests are thought to be caused by the last remaining neutral patches during the end phases of reionization - termed neutral islands. If this is true, then the longest troughs mark locations where we are most likely to observe the reionizing intergalactic medium (IGM). A key feature of the neutral islands is that they are bounded by ionization fronts (I-fronts) which emit Lyman series lines. In this paper, we explore the possibility of directly imaging the outline of neutral islands with a narrowband survey targeting Lycx. In a companion paper, we quantified the intensity of I-front Lycx emissions during reionization and its dependence on the spectrum of incident ionizing radiation and I-front speed. Here we apply those results to reionization simulations to model the emissions from neutral islands. We find that neutral islands would appear as diffuse structures that are tens of comoving Mpc across, with surface brightnesses in the range approximate to 1 - 5 x 10(-21) erg s(-1) cm(-2) arcsec(-2). The islands are brighter if the spectrum of ionizing radiation driving the I-fronts is harder, and/or if the I-fronts are moving faster. We develop mock observations for current and futuristic observatories and find that, while extremely challenging, detecting neutral islands is potentially within reach of an ambitious observing program with wide-field narrowband imaging. Our results demonstrate the potentially high impact of low-surface brightness observations for studying reionization.

During reionization, intergalactic ionization fronts (I-fronts) are sources of Ly$\alpha$ line radiation produced by collisional excitation of hydrogen atoms within the fronts. In principle, detecting this emission could provide direct evidence for a reionizing intergalactic medium (IGM). In this paper, we use a suite of high-resolution one-dimensional radiative transfer simulations run on cosmological density fields to quantify the parameter space of I-front Ly$\alpha$ emission. We find that the Ly$\alpha$ production efficiency -- the ratio of emitted Ly$\alpha$ flux to incident ionizing flux driving the front -- depends mainly on the I-front speed and the spectral index of the ionizing radiation. IGM density fluctuations on scales smaller than the typical I-front width produce scatter in the efficiency, but they do not significantly boost its mean value. The Ly$\alpha$ flux emitted by an I-front is largest if 3 conditions are met simultaneously: (1) the incident ionizing flux is large; (2) the incident spectrum is hard, consisting of more energetic photons; (3) the I-front is traveling through a cosmological over-density, which causes it to propagate more slowly. We present a convenient parameterization of the efficiency in terms of I-front speed and incident spectral index. We make these results publicly available as an interpolation table and we provide a simple fitting function for a representative ionizing background spectrum. Our results can be applied as a sub-grid model for I-front Ly$\alpha$ emissions in reionization simulations with spatial and/or temporal resolutions too coarse to resolve I-front structure. In a companion paper, we use our results to explore the possibility of directly imaging Ly$\alpha$ emission around neutral islands during the last phases of reionization.

Recent JWST observations at z > 6 may imply galactic ionizing photon production above prior expectations. Under observationally motivated assumptions about escape fractions, these suggest a z ~ 8–9 end to reionization, in tension with the z < 6 end required by the Ly α forest. In this work, we use radiative transfer simulations to understand what different observations tell us about when reionization ended and when it started. We consider a model that ends too early ( z _end ≈ 8) alongside two more realistic scenarios with z _end ≈ 5: one starting late ( z ~ 9) and another early ( z ~ 13). We find that the latter requires up to an order-of-magnitude evolution in galaxy ionizing properties at 6 < z < 12, perhaps in tension with measurements of ξ _ion by JWST, which indicate little evolution. We study how these models compare to recent measurements of the Ly α forest opacity, mean free path, intergalactic medium thermal history, visibility of z > 8 Ly α emitters, and the patchy kSZ signal from the cosmic microwave background (CMB). We find that neither of the late-ending scenarios is strongly disfavored by any single data set. However, a majority of observables, spanning several distinct types of observations, prefer a late start. Not all probes agree with this conclusion, hinting at a possible lack of concordance arising from deficiencies in observations and/or theoretical modeling. Observations by multiple experiments (including JWST, Roman, and CMB-S4) in the coming years will establish a concordance picture of reionization's beginning or uncover such deficiencies.

Detection of the faint 21 cm line emission from the Cosmic Dawn and Epoch of Reionisation will require not only exquisite control over instrumental calibration and systematics to achieve the necessary dynamic range of observations but also validation of analysis techniques to demonstrate their statistical properties and signal loss characteristics. A key ingredient in achieving this is the ability to perform high-fidelity simulations of the kinds of data that are produced by the large, many-element, radio interferometric arrays that have been purpose-built for these studies. The large scale of these arrays presents a computational challenge, as one must simulate a detailed sky and instrumental model across many hundreds of frequency channels, thousands of time samples, and tens of thousands of baselines for arrays with hundreds of antennas. In this paper, we present a fast matrix-based method for simulating radio interferometric measurements (visibilities) at the necessary scale. We achieve this through judicious use of primary beam interpolation, fast approximations for coordinate transforms, and a vectorised outer product to expand per-antenna quantities to per-baseline visibilities, coupled with standard parallelisation techniques. We validate the results of this method, implemented in the publicly-available matvis code, against a high-precision reference simulator, and explore its computational scaling on a variety of problems.

The kinetic Sunyaev–Zel’dovich effect (kSZ) and patchy screening effect are two complementary cosmic microwave background (CMB) probes of the reionization era. The kSZ effect is a relatively strong signal, but is difficult to disentangle from other sources of temperature anisotropy, whereas patchy screening is weaker but can be reconstructed using the cleaner polarization channel. Here, we explore the potential of using upcoming CMB surveys to correlate a reconstructed map of patchy screening with (the square of) the kSZ map, and what a detection of this cross correlation would mean for reionization science. To do this, we use simulations and theory to quantify the contributions to this signal from different redshifts. We then use the expected survey properties for CMB-S4 and CMB-HD to make detection forecasts. We find that, for our fiducial reionization scenario, CMB-S4 will obtain a hint of this signal at up to 1.8 σ , and CMB-HD will detect it at up to 14 σ . We explore the physical interpretation of the signal and find that it is uniquely sensitive to the first half of reionization and to the bispectrum of the ionized gas distribution.

ABSTRACT Recent measurements of the ionizing photon mean free path (MFP) based on composite quasar spectra may point to reionization ending at z < 6. These measurements are challenging because they rely on assumptions about the proximity zones of the quasars. For example, some quasars might have been close to neutral patches where reionization was still ongoing (‘neutral islands’), and it is unclear how they would affect the measurements. We address this question with mock MFP measurements from radiative transfer simulations. We find that, even in the presence of neutral islands, our mock MFP measurements agree to within $30~{{\ \rm per\ cent}}$ with the true spatially averaged MFP in our simulations, which includes opacity from both the ionized medium and the islands. The inferred MFP is sensitive at the $\lt ~50~{{\ \rm per\ cent}}$ level to assumptions about quasar environments and lifetimes for realistic models. We demonstrate that future analyses with improved data may require explicitly modelling the effects of neutral islands on the composite spectra, and we outline a method for doing this. Lastly, we quantify the effects of neutral islands on Lyman-series transmission, which has been modelled with optically thin simulations in previous MFP analyses. Neutral islands can suppress transmission at λrest < 912 Å significantly, up to a factor of 2 for zqso = 6 in a plausible reionization scenario, owing to absorption by many closely spaced lines as quasar light redshifts into resonance. However, the suppression is almost entirely degenerate with the spectrum normalization and thus does not significantly bias the inferred MFP.

The wealth of high-quality observational data from the epoch of reionization that will become available in the next decade motivates further development of modeling techniques for their interpretation. Among the key challenges in modeling reionization are (1) its multi-scale nature, (2) the computational demands of solving the radiative transfer (RT) equation, and (3) the large size of reionization's parameter space. In this paper, we present and validate a new RT code designed to confront these challenges. FLExRT (Flexible Radiative Transfer) combines adaptive ray tracing with a highly flexible treatment of the intergalactic ionizing opacity. This gives the user control over how the intergalactic medium (IGM) is modeled, and provides a way to reduce the computational cost of a FLExRT simulation by orders of magnitude while still accounting for small-scale IGM physics. Alternatively, the user may increase the angular and spatial resolution of the algorithm to run a more traditional reionization simulation. FLExRT has already been used in several contexts, including simulations of the Lyman-alpha forest of high-z quasars, the redshifted 21cm signal from reionization, as well as in higher resolution reionization simulations in smaller volumes. In this work, we motivate and describe the code, and validate it against a set of standard test problems from the Cosmological Radiative Transfer Comparison Project. We find that FLExRT is in broad agreement with a number of existing RT codes in all of these tests. Lastly, we compare FLExRT to an existing adaptive ray tracing code to validate FLExRT in a cosmological reionization simulation.

The relationship between Lyα forest opacity and local galaxy density (the opacity-density relation) is a key observational test of late reionization models. Using narrow-band surveys of z=5.7 Lyα emitters centered on quasar sight lines, Christenson et al. (2023) showed that two of the most transmissive forest segments at this redshift intersect galaxy underdensities. This is in tension with models of a strongly fluctuating ionizing background, including some late reionization models, which predict that the vast majority of these segments should intersect overdensities where the ionizing intensity is strongest. We use radiative transfer simulations to explore in detail the opacity-density relation in late reionization models. Fields like the one toward quasar PSO J359-06 – the more underdense of the two transmissive sight lines in Christenson et al. (2023) – typically contain recently reionized gas in cosmic voids where the hot temperatures and low densities enhance Lyα transmission. The opacity-density relation's transmissive end is sensitive to the amount of neutral gas in voids, and its morphology, set by the reionization source clustering. These effects are, however, degenerate. We demonstrate that models with very different source clustering can yield similar opacity-density relations when their reionization histories are calibrated to match Lyα forest mean flux measurements at z<6. In models with fixed source clustering, a lower neutral fraction increases the likelihood of intersecting hot, recently reionized gas in voids, increasing the likelihood of observing PSO J359-06. For instance, the probability of observing this field is 15 neutral fraction x_ HI=5% at z=5.7, three times more likely than in a model with x_ HI=15%. The opacity-density relation may thus provide a complementary probe of reionization's end.

Observations with radio arrays that target the 21-cm signal originating from the early Universe suffer from a variety of systematic effects. An important class of these are reflections and spurious couplings between antennas. We apply a Hamiltonian Monte Carlo sampler to the modelling and mitigation of these systematics in simulated Hydrogen Epoch of Reionisation Array (HERA) data. This method allows us to form statistical uncertainty estimates for both our models and the recovered visibilities, which is an important ingredient in establishing robust upper limits on the Epoch of Reionisation (EoR) power spectrum. In cases where the noise is large compared to the EoR signal, this approach can constrain the systematics well enough to mitigate them down to the noise level for both systematics studied. Where the noise is smaller than the EoR, our modelling can mitigate the majority of the reflections with there being only a minor level of residual systematics, while cross-coupling sees essentially complete mitigation. Our approach performs similarly to existing filtering/fitting techniques used in the HERA pipeline, but with the added benefit of rigorously propagating uncertainties. In all cases it does not significantly attenuate the underlying signal.

We report the discovery of a unique quasar-dusty star-forming galaxy (DSFG) system at z = 5.63, consisting of the bright quasar J1133+1603 (M_ UV = -27.42) and its compact, dust-obscured companion, J1133c. ALMA observations reveal a prominent [C II] bridge connecting the quasar and DSFG, indicating ongoing interaction at a projected separation of 1.8 arcsec (∼10 proper kpc). J1133c exhibits unusually bright and broad [C II] emission (L_ [CII] > 10^43 erg s^-1, FWHM > 500 km s^-1), with a [C II] luminosity five times that of the quasar, suggesting intense star formation or potential AGN activity. The inferred star formation rate from [C II] is approximately 10^3 M_⊙ yr^-1. The remarkable properties of this pair strongly suggest that galaxy interactions may simultaneously trigger both starburst and quasar activity, driving rapid evolution in the early universe.

The thermal history and structure of the intergalactic medium (IGM) at z ≥ 4 is a key boundary condition for reionization, which has been measured using the Lyα forest of high-redshift quasars. It is also a key input for studies that use the forest to constrain the particle masses of alternative dark matter candidates. Most such inferences rely on simulations that lack the spatial resolution to fully resolve the hydrodynamic response of IGM filaments and minihalos caused by HI reionization heating. In this letter, we use high-resolution hydrodynamic+radiative transfer simulations to study the impact of these on the IGM thermal structure. We find that the adiabatic heating and cooling driven by the expansion of initially cold gas filaments and minihalos drives significant temperature fluctuations on small scales. These likely persist in much of the IGM until at least z = 4. Capturing this effect requires resolving the characteristic clumping scale of cold, pre-ionized gas, which demands spatial resolutions of at least 2 h^-1kpc. Pre-heating of the IGM by X-Ray sources can slightly reduce the effect. Our preliminary estimate of the effect on the Lyα forest finds that, at log(k /[ km^-1 s]) = -1.0, the forest flux power (at fixed mean flux) can increase by 10-20% when going from 8 and 2 h^-1kpc resolution at z = 4-5 for gas ionized at z < 7. These findings motivate a more careful analysis of how temperature fluctuations driven by pressure smoothing from reionization affect the Lyα forest.

Quasar absorption spectra measurements suggest that reionization proceeded rapidly, ended late at $z \sim 5.5$, and was followed by a flat evolution of the ionizing background. Simulations that can reproduce this behavior often rely on a fine-tuned galaxy ionizing emissivity, which peaks at $z \sim 6 - 7$ and drops by a factor of $1.5-2.5$ by $z \sim 5$. This is puzzling since the abundance of galaxies has been observed to grow monotonically during this period. Explanations for this include effects such as dust obscuration of ionizing photon escape and feedback due to photo-heating of the IGM. We explore the possibility that this drop in emissivity is instead an artifact of one or more modeling deficiencies in reionization simulations. These include possibly incorrect assumptions about the ionizing spectrum and/or inaccurate modeling of the clumpiness of the IGM. Our results suggest that the need for a drop could be alleviated if simulations are underestimating the IGM opacity from massive, star-forming halos. Other potential modeling issues either have a small effect or require a steeper drop when remedied. We construct an illustrative model in which the emissivity is nearly flat at the end of reionization, evolving only $\sim 0.05$ dex at $5 < z < 7$. More realistic scenarios, however, require a $\sim 0.1-0.3$ dex drop. We also study the evolution of the Ly$\alpha$ effective optical depth distribution in these scenarios and compare them to recent measurements. We find models that feature a hard ionizing spectrum and/or are driven by faint, low-bias sources can most easily reproduce the mean transmission and optical depth distribution of the forest simultaneously. Lastly, we show that the reduced speed of light approximation and low spatial resolution in the forest can lead to erroneous conclusions about the end of reionization.

The reduced speed of light approximation (RSLA) has been employed to speed up radiative transfer simulations of reionization by a factor of ≳ 5-10. However, it has been shown to cause significant errors in the HI-ionizing background near reionization's end in simulations of representative cosmological volumes. We show that using the RSLA is, to a good approximation, equivalent to re-scaling the global ionizing emissivity in a redshift-dependent way. We derive this re-scaling and show that it can be used to “correct” the emissivity in RSLA simulations. This method requires the emissivity to be re-scaled after the simulation has been run, which limits its applicability to situations where the emissivity is set “by hand” or determined by free parameters. We test our method by running full speed of light simulations using these re-scaled emissivities and comparing them with their RSLA counterparts. We find that for reduced speeds of light c̃≥ 0.2, the 21 cm power spectrum at 0.1 ≤ k /[h Mpc^-1] ≤ 0.2 and key Lyα forest observables agree to within 20%, and often within 10%, throughout reionization. Position-dependent time-delay effects cause inaccuracies in reionization's morphology on large scales at the factor of 2 level for c̃≤ 0.1. Our method allows for up to a factor of 5 speedup in studies that express the emissivity in terms of free parameters, including efforts to constrain the emissivity using observations. This is a crucial step towards constraining the ionizing properties of high-redshift galaxies using efficient radiative transfer simulations.

Recent quasar absorption line observations suggest that reionization may end as late as z ≈ 5.3. As a means to search for large neutral hydrogen islands at z<6, we revisit long dark gaps in the Lyβ forest in VLT/X-Shooter and Keck/ESI quasar spectra. We stack the Lyα forest corresponding to the edges of these Lyβ dark gaps and identify a damping wing-like extended absorption profile. The average redshift of the stacked forest is z=5.8. By comparing these observations with reionization simulations, we infer that such a damping wing-like feature can be naturally explained if these gaps are at least partially created by neutral islands. Conversely, simulated dark gaps lacking neutral hydrogen struggle to replicate the observed damping wing features. Furthermore, this damping wing-like profile implies that the volume-averaged neutral hydrogen fraction must be ⟨ x_ HI⟩≥ 6.1 ± 3.9% at z = 5.8. Our results offer robust evidence that reionization extends below z=6.

The mean free path of ionizing photons, $λ_{\rm mfp}$, is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements of $λ_{\rm mfp}$ from QSO spectra over the redshift range $5

ABSTRACT A recent measurement of the Lyman-limit mean free path at z = 6 suggests it may have been very short, motivating a better understanding of the role that ionizing photon sinks played in reionization. Accurately modelling the sinks in reionization simulations is challenging because of the large dynamic range required if ∼104−108M⊙ gas structures contributed significant opacity. Thus, there is no consensus on how important the sinks were in shaping reionization’s morphology. We address this question with a recently developed radiative transfer code that includes a dynamical sub-grid model for the sinks based on radiative hydrodynamics simulations. Compared to assuming a fully pressure-smoothed intergalactic medium, our dynamical treatment reduces ionized bubble sizes by $10-20~{{\ \rm per\ cent}}$ under typical assumptions about reionization’s sources. Near reionization’s midpoint, the 21 cm power at k ∼ 0.1 hMpc−1 is similarly reduced. These effects are more modest than the $30-60~{{\ \rm per\ cent}}$ suppression resulting from the higher recombination rate if pressure smoothing is neglected entirely. Whether the sinks played a significant role in reionization’s morphology depends on the nature of its sources. For example, if reionization was driven by bright (MUV < −17) galaxies, the sinks reduce the large-scale 21 cm power by at most 20 per cent, even if pressure smoothing is neglected. Conveniently, when bright sources contribute significantly, the morphology in our dynamical treatment can be reproduced accurately with a uniform sub-grid clumping factor that yields the same ionizing photon budget. By contrast, if MUV ∼ −13 galaxies drove reionization, the uniform clumping model can err by up to 40 per cent.

The mean free path of ionizing photons, λ mfp, is a critical parameter for modeling the intergalactic medium (IGM) both during and after reionization. We present direct measurements of λ mfp from QSO spectra over the redshift range 5 < z < 6, including the first measurements at z ≃ 5.3 and 5.6. Our sample includes data from the XQR-30 VLT large program, as well as new Keck/ESI observations of QSOs near z ∼ 5.5, for which we also acquire new [C ii] 158 μm redshifts with ALMA. By measuring the Lyman continuum transmission profile in stacked QSO spectra, we find λmfp=9.33−1.80+2.06 , 5.40−1.40+1.47 , 3.31−1.34+2.74 , and 0.81−0.48+0.73 pMpc at z = 5.08, 5.31, 5.65, and 5.93, respectively. Our results demonstrate that λ mfp increases steadily and rapidly with time over 5 < z < 6. Notably, we find that λ mfp deviates significantly from predictions based on a fully ionized and relaxed IGM as late as z = 5.3. By comparing our results to model predictions and indirect λ mfp constraints based on IGM Lyα opacity, we find that the evolution of λ mfp is consistent with scenarios wherein the IGM is still undergoing reionization and/or retains large fluctuations in the ionizing UV background well below redshift 6.

Recently, the mean free path of ionizing photons in the z = 6 intergalactic medium (IGM) was measured to be very short, presenting a challenge to existing reionization models. At face value, the measurement can be interpreted as evidence that the IGM clumps on scales M ≲ 10 8 M ⊙ , a key but largely untested prediction of the cold dark matter (CDM) paradigm. Motivated by this possibility, we study the role that the underlying dark matter cosmology plays in setting the z > 5 mean free path. We use two classes of models to contrast against the standard CDM prediction: (1) thermal relic warm dark matter (WDM), representing models with suppressed small-scale power; (2) an ultralight axion exhibiting a white noise-like power enhancement. Differences in the mean free path between the WDM and CDM models are subdued by pressure smoothing and the possible contribution of neutral islands to the IGM opacity. For example, comparing late reionization scenarios with a fixed volume-weighted mean neutral fraction of 20% at z = 6, the mean free path is 19 (45)% longer in a WDM model with m x = 3 (1) keV. The enhanced power in the axion-like model produces better agreement with the short mean free path measured at z = 6. However, drawing robust conclusions about cosmology is hampered by large uncertainties in the reionization process, extragalactic ionizing background, and thermal history of the Universe. This work highlights some key open questions about the IGM opacity during reionization.

Recent measurements of the ionizing photon mean free path ( λ912mfp ) at 5 < z < 6 suggest that the IGM was rapidly evolving at those times. We use radiative transfer simulations to explore the implications for reionization, with a focus on the short value of λ912mfp=3.57−2.14+3.09 cMpc h −1 at z = 6. We introduce a model for subresolution ionizing photon sinks based on radiative hydrodynamics simulations of small-scale IGM clumping. We argue that the rapid evolution in λ912mfp at z = 5 − 6, together with constraints on the metagalactic ionizing background, favors a late reionization process in which the neutral fraction evolved rapidly in the latter half. We also argue that the short λ912mfp(z=6) points to faint galaxies as the primary drivers of reionizaton. Our preferred model, with λ912mfp(z=6)=6.5 Mpc h −1, has a midpoint of z = 7.1 and ends at z = 5.1. It requires three ionizing photons per H atom to complete reionization and a LyC photon production efficiency of log(fesceffξion/[erg−1Hz])=24.8 at z > 6. Recovering λ912mfp(z=6) as low as the measured central value may require an increase in IGM clumpiness beyond predictions from simulations, with a commensurate increase in the photon budget.

Becker et al. measured the mean free path of Lyman-limit photons in the intergalactic medium (IGM) at z = 6. The short value suggests that absorptions may have played a prominent role in reionization. Here we study physical properties of ionizing photon sinks in the wake of ionization fronts (I-fronts) using radiative hydrodynamic simulations. We quantify the contributions of gaseous structures to the Lyman-limit opacity by tracking the column-density distributions in our simulations. Within Δ t = 10 Myr of I-front passage, we find that self-shielding systems ( N H I > 10 17.2 cm −2 ) are comprised of two distinct populations: (1) overdensity Δ ∼ 50 structures in photoionization equilibrium with the ionizing background, and (2) Δ ≳ 100 density peaks with fully neutral cores. The self-shielding systems contribute more than half of the opacity at these times, but the IGM evolves considerably in Δ t ∼ 100 Myr as structures are flattened by pressure smoothing and photoevaporation. By Δ t = 300 Myr, they contribute ≲10% to the opacity in an average 1 Mpc 3 patch of the universe. The percentage can be a factor of a few larger in overdense patches, where more self-shielding systems survive. We quantify the characteristic masses and sizes of self-shielding structures. Shortly after I-front passage, we find M = 10 4 –10 8 M ⊙ and effective diameters d eff = 1–20 ckpc h −1 . These scales increase as the gas relaxes. The picture herein presented may be different in dark matter models with suppressed small-scale power.