The reionization of the intergalactic medium (IGM) was driven by the first stars, galaxies, and accreting black holes. However, the relative importance of these sources and the efficiency by which ionizing photons escape into the IGM remain poorly understood. Most reionization modelling frameworks assume idealized, isotropic emissions. We investigate this assumption by examining a suite of simulations incorporating directed, anisotropic photon emissions. We find that such anisotropic emissions of ionizing photons yield a different reionization geometry compared to the standard, isotropic, case. During the early stages of reionization (when less than 30 per cent of the Universe is ionized), simulations with narrow photon leakage channels produce smaller ionized bubbles on average. However, these bubbles grow to similar sizes during the middle stages of reionization. This anisotropy not only produces a distinctive evolution of the size distribution of the ionized regions, but also imprints a feature onto the spherically averaged power spectra of the 21-cm signal throughout reionization. We observe a suppression in power by about 10–40 per cent at scales corresponding to wavenumbers ⁠k=0.1−1 h Mpc⁻¹, corresponding to the range in which current radio interferometers are most likely to measure the power spectrum. The simulation with the narrowest channel of ionization emission shows the strongest suppression. However, this anisotropic emission process does not introduce any measurable anisotropy in the 21-cm signal.

Context. Galaxies may suffer some starburst and quenched periods in their history due to galaxy mergers and feedback. However, semi-numerical simulations of the Epoch of Reionization (EoR) do not accurately model the effects of the star formation history (SFH) of galaxies.

Aims. Keeping the same total ionizing photon budget from galaxies, we investigate how the ionization and heating of the intergalactic medium (IGM), as well as the associated 21 cm signal during the EoR, depend on the variations in modeling the SFH of galaxies.

Methods. We adopted the JIUTIAN-300 N-body dark matter simulation and the semi-analytic model L-GALAXIES 2020 to model galaxy formation. Using the galaxy catalog from L-GALAXIES 2020 as input, we post-processed the JIUTIAN-300 density field with the 1D radiative transfer code GRIZZLY to model the reionization process and the 21 cm signal.

Results. We find that the ionized regions produced by galaxies with a SFH derived from L-GALAXIES 2020 are slightly larger and warmer than the ones obtained with a constant star formation rate. For a fixed stellar mass, galaxies produce smaller ionized regions with increasing stellar-mass-weighted stellar age τ_age. This results in a different topology and timing of the IGM ionization and heating obtained from GRIZZLY.

Conclusions. The SFH of galaxies is highly dependent on τ_age and redshift. Different models of the galactic SFH affect the gas heating and ionizing processes during the EoR and, as a consequence, also affect the 21 cm global signal and power spectrum.

Context. While many astrophysical plasmas can be modelled successfully assuming ionisation and thermal equilibrium, in some cases this is not appropriate and a non-equilibrium approach is required. In nebulae around evolved stars, the local elemental abundances may also strongly vary in space and time. Aims. Here we present a non-equilibrium multi-ion module developed for the fluid-dynamics code PION, describing the physical processes included and demonstrating its capabilities with some test calculations. Methods. A non-equilibrium ionisation solver is developed that allows arbitrary elemental abundances for neutral and ionised (but not molecular) gas, for the elements H, He, C, N, O, Ne, Si, S, and Fe. Collisional ionisation and recombination, photoionisation and charge-exchange reactions are included, and ion-by-ion non-equilibrium radiative cooling is calculated based on the instantaneous ion fractions of each element. Element and ion mass-fractions are advected using passive scalars, operator-split from the microphysical processes. Results. The module is validated by comparing with equilibrium and non-equilibrium calculations in the literature. Effects of charge exchange on ion abundances in cooling plasmas are discussed. Application to modelling shocks and photo-ionised H II regions is demonstrated. The time-dependent expansion of a WR nebula is studied, including photoionisation and collisional processes, and spectral-line luminosities calculated for non-equilibrium and equilibrium plasma states. Conclusions. The multi-ion module enables simulation of ionised plasmas with spatially varying elemental abundances using self-consistent ion abundances and thermal evolution. This allows prediction of spectral lines in UV, optical, IR, and X-ray even in cases where the plasma is out of ionisation equilibrium.

The power spectra of the redshifted 21 cm signal from the Epoch of Reionization (EoR) contain information about the ionization and thermal states of the intergalactic medium (IGM) and depend on the properties of the sources that existed during that period. Recently, the LOFAR-EoR Key Science Project team has analysed ten nights of LOFAR high-band data and estimated upper limits on the 21 cm power spectrum at redshifts 8.3, 9.1, and 10.1. Here, we used these upper limit results to constrain the properties of the IGM at those redshifts. We focus on the properties of the ionized and heated regions where the temperature is larger than that of the cosmic microwave background (CMB). We modelled the power spectrum of the 21 cm signal with the code GRIZZLY and used a Bayesian inference framework to explore the source parameters for uniform priors on their ranges. The framework also provides information about the IGM properties in the form of derived parameters. We do not include constraints from other observables except for some very conservative limits on the maximum ionization fraction at those redshifts, which we estimated from the CMB Thomson scattering optical depth. In a model that includes a radio background in excess of the CMB, the 95% (68%) credible intervals of disfavoured models at redshift 9.1 for the chosen priors correspond to IGM states with an averaged ionization and heated fraction below 0.46 (≲ 0.05), an average gas temperature below 44 K (4 K), and a characteristic size of the heated region of ≲14 h⁻¹ Mpc (≲3 h⁻¹ Mpc). The 68% credible interval suggests an excess radio background that is more than 100% of the CMB at 1.42 GHz, while the 95% credible interval of the radio background efficiency parameter spans the entire prior range. The behaviour of the credible intervals is similar at all redshifts. The models disfavoured by the LOFAR upper limits are extreme, as they are mainly driven by rare and large ionized or heated regions. We find that the inclusion of upper limits from other radio interferometric observations in the Bayesian analysis significantly increases the number of disfavoured EoR models, thus enhancing the disfavoured credible intervals of the IGM parameters, especially those related to the average gas temperature and size distribution of the heated regions. While our constraints are not yet very strong, more stringent upcoming results from 21 cm observations together with the detection of many high-z galaxies, for example with the James Webb Space Telescope, will strengthen understanding of this crucial phase of the Universe.

We present new upper limits on the 21 cm signal power spectrum from the epoch of reionisation (EoR), at redshifts z ∼ 10.1,9.1, and 8.3, based on reprocessed observations from the Low-Frequency Array (LOFAR). The analysis incorporates significant enhancements in calibration methods, sky model subtraction, radio-frequency interference (RFI) mitigation, and an improved signal separation technique using machine learning to develop a physically motivated covariance model for the 21 cm signal. These advancements have markedly reduced previously observed excess power due to residual systematics, bringing the measurements closer to the theoretical thermal noise limit across the entire k-space. Using comparable observational data, we achieve a two- to fourfold improvement over our previous LOFAR limits, with best upper limits of I 212 < (68.7 mK)2 at k=0.076 h cMpc1, I212 < (54.3 mK)2 at k=0.076 h cMpc 1, and I212 < (65.5a mK)2 at k=0.083 h cMpc 1 at redshifts z ∼ 10.1,9.1, and 8.3, respectively. These new multi-redshift upper limits provide new constraints that can be used to refine our understanding of the astrophysical processes during the EoR. Comprehensive validation tests, including signal injection, were performed to ensure the robustness of our methods. The remaining excess power is attributed to residual foreground emissions from distant sources, beam model inaccuracies, and low-level RFI. We discuss ongoing and future improvements to the data processing pipeline aimed at further reducing these residuals, thereby enhancing the sensitivity of LOFAR observations in the quest to detect the 21 cm signal from the EoR.

A detection of the 21-cm signal power spectrum from the Epoch of Reionization is imminent, thanks to consistent advancements from telescopes such as LOFAR, MWA, and HERA, along with the development of SKA. In light of this progress, it is crucial to expand the parameter space of simulations used to infer astrophysical properties from this signal. In this work, we explore the role of cosmological parameters such as the Hubble constant H0 and the matter clustering amplitude σ8, whose values as provided by measurements at different redshifts are in tension. We run N-body simulations using gadget-4, and post-process them with the reionization simulation code polar, that uses L-Galaxies to include galaxy formation and evolution properties and grizzly to execute 1D radiative transfer of ionizing photons in the intergalactic medium (IGM). We compare our results with the latest James Webb Space Telescope (JWST) observations and explore which astrophysical properties for different cosmologies are necessary to match the observed UV luminosity functions at redshifts z = 10 and 9. Additionally, we explore the impact of these parameters on the observed 21-cm signal power spectrum upper limits, focusing on the redshifts within the range of LOFAR 21-cm signal observations (z ≈ 8.5-10). Despite differences in cosmological and astrophysical parameters, our models cannot be ruled out by the current upper limits. This suggests the need for broader physical parameter spaces for inference modeling to account for all models that agree with observations. However, we also propose stronger constraining power by using a combination of galactic and IGM observables.

Neutral hydrogen serves as a crucial probe for the Cosmic Dawn and the Epoch of Reionization (EoR). Actual observations of the 21 cm signal often encounter challenges such as thermal noise and various systematic effects. To overcome these challenges, we simulate SKA-Low-depth images in the South Celestial Pole field and process them with a deep learning method. We utilized foreground residuals acquired by LOFAR during actual North Celestial Pole field observations, thermal and excess variances calculated via Gaussian process regression, and 21 cm signals generated with 21cmFAST for signal extraction tests. Our approach to overcome these foreground, thermal noise, and excess variance components employs a 3D U-Net neural network architecture for image analysis. When considering thermal noise corresponding to 1752 hr of integration time, U-Net provides reliable 2D power spectrum predictions, and robustness tests ensure that we get realistic EoR signals. Adding foreground residuals, however, causes inconsistencies below the horizon delay line. Lastly, evaluating both thermal noise and excess variances with observations up to 4380 hr and 13,140 hr ensures reliable power spectrum estimations within the EoR window and across nearly all scales, respectively. The incoherence of excess variances in the frequency direction can greatly affect deep learning to extract 21 cm signals.

The redshifted 21-cm signal of neutral hydrogen from the epoch of reionization (EoR) can potentially be detected using low-frequency radio instruments such as the Low-Frequency Array (LOFAR). So far, LOFAR upper limits on the 21-cm signal power spectrum have been published using a single target field: the North Celestial Pole (NCP). In this work, we analyse and provide upper limits for the 3C 196 field, observed by LOFAR, with a strong ≈80 Jy source in the centre. This field offers advantages such as higher sensitivity due to zenith-crossing observations and reduced geostationary radio-frequency interference, but also poses challenges due to the presence of the bright central source. After constructing a wide-field sky model, we process a single 6-h night of 3C 196 observations using direction-independent and direction-dependent calibration, followed by a residual foreground subtraction with a machine learning Gaussian process regression (ML-GPR). A bias correction is necessary to account for signal suppression in the GPR step. Still, even after this correction, the upper limits are a factor of 2 lower than previous single-night NCP results, with a lowest 2σ upper limit of (146.61 mK)² at redshift z = 9.16 and wavenumber k = 0.078 h cMpc⁻¹ (with ⁠dk/k ≈ 0.3). The results also reveal an excess power, different in behaviour from that observed in the NCP field, suggesting a potential residual foreground origin. In future work, the use of multiple nights of 3C 196 observations combined with improvements to sky modelling and ML-GPR to avoid the need for bias correction should provide tighter constraints per unit observing time than the NCP.

The high redshift 21-cm signal promises to be a crucial probe of the state of the intergalactic medium (IGM). Understanding the connection between the observed 21-cm power spectrum and the physical quantities intricately associated with the IGM is crucial to fully understand the evolution of our Universe. In this study, we develop an emulator using artificial neural network (ANN) to predict the 21-cm power spectrum from a given set of IGM properties, namely, the bubble size distribution and the volume averaged ionization fraction. This emulator is implemented within a standard Bayesian framework to constrain the IGM parameters from a given 21-cm power spectrum. We compare the performance of the Bayesian method to an alternate method using ANN to predict the IGM parameters from a given input power spectrum, and find that both methods yield similar levels of accuracy, while the ANN is significantly faster. We also use this ANN method of parameter estimation to predict the IGM parameters from a test set contaminated with noise levels expected from the SKA-LOW instrument after 1000 hours of observation. Finally, we train a separate ANN to predict the source parameters from the IGM parameters directly, at a redshift of z = 9.1, demonstrating the possibility of a non-analytic inference of the source parameters from the IGM parameters for the first time. We achieve high accuracies, with R2-scores ranging between 0.898-0.978 for the ANN emulator and between 0.966-0.986 and 0.817-0.981 for the predictions of IGM parameters from 21-cm power spectrum and source parameters from IGM parameters, respectively. The predictions of the IGM parameters from the Bayesian method incorporating the ANN emulator leads to tight constraints on the IGM parameters.

Radiation pressure from Lyman-α (Lyα) scattering is a potentially dominant form of early stellar feedback, capable of injecting up to ∼ 100 × more momentum into the interstellar medium (ISM) than ultraviolet continuum radiation pressure and stellar winds. Lyα feedback is particularly strong in dust-poor environments and is thus especially important during the formation of the first stars and galaxies. As upcoming galaxy formation simulations incorporate Lyα feedback, it is crucial to consider processes that can limit it to avoid placing Lambda-cold dark matter in apparent tension with recent JWST observations indicating efficient star formation at Cosmic Dawn. We study Lyα feedback using a novel analytical Lyα radiative transfer solution that includes the effects of continuum absorption, gas velocity gradients, Lyα destruction (e.g. by 2p → 2s transitions), ISM turbulence, and atomic recoil. We verify our solution for uniform clouds using extensive Monte Carlo radiative transfer (MCRT) tests, and resolve a previous discrepancy between analytical and MCRT predictions. We then study the sensitivity of Lyα feedback to the aforementioned effects. While these can dampen Lyα feedback by a factor ≤ few × 10, we find it remains ≥ 5 − 100 × stronger than direct radiation pressure and therefore cannot be neglected. We provide an accurate fit for the Lyα force multiplier MF, suitable for implementation in subgrid models for galaxy formation simulations. Our findings highlight the critical role of Lyα feedback in regulating star formation at Cosmic Dawn, and underscore the necessity of incorporating it into simulations to accurately model early galaxy evolution.