arXiv subjects

Nicolas Gillet

Publications and source records attributed to Nicolas Gillet.

At least 19 recordsLinked to original sources

arXiv2026

Joint Bayesian inference of Earth's magnetic field and core surface flow on millennial timescales

Understanding Earth's core dynamics over millennial timescales requires models that jointly describe the evolution of the geomagnetic field and core surface flow, while accommodating the sparse, irregular, and uncertain nature of archaeomagnetic and palaeomagnetic data. We present a new Bayesian core field and core flow modelling framework that utilises archaeo/palaeomagnetic data directly, combining a reduced stochastic representation of core surface dynamics derived from numerical geodynamo statistics with a probabilistic treatment of observational and chronological uncertainties. A key innovation is an efficient discrete marginalisation of age uncertainties, which avoids the convergence difficulties associated with co-estimating ages in high-dimensional Hamiltonian Monte Carlo inversions. The framework aims to reconstruct the coupled evolution of the geomagnetic field and core surface flow over the past 9000 years while preserving dynamical correlations implied by the prior geodynamo time series. Tests using synthetic data generated from an Earth-like geodynamo demonstrate that the method reliably recovers large-scale geomagnetic field variations and key aspects of core dynamics, including long-term westward drift and the evolution of planetary-scale eccentric gyres. These results show that, when combined with physically informed priors, archaeo/palaeomagnetic data can constrain millennial-scale core flow, paving the way for reconstructions based on real data.

physics.geo-ph↗

arXiv2023

Contributions to the geomagnetic secular variation from a reanalysis of core surface dynamics

We invert for motions at the surface of Earth's core under spatial and temporal constraints that depart from the mathematical smoothings usually employed to ensure spectral convergence of the flow solutions. Our spatial constraints are derived from geodynamo simulations. The model is advected in time using stochastic differential equations coherent with the occurrence of geomagnetic jerks. Together with a Kalman filter, these spatial and temporal constraints enable the estimation of core flows as a function of length and time-scales. From synthetic experiments, we find it crucial to account for subgrid errors to obtain an unbiased reconstruction. This is achieved through an augmented state approach. We show that a significant contribution from diffusion to the geomagnetic secular variation should be considered even on short periods, because diffusion is dynamically related to the rapidly changing flow below the core surface. Our method, applied to geophysical observations over the period 1950-2015, gives access to reasonable solutions in terms of misfit to the data. We highlight an important signature of diffusion in the Eastern equatorial area, where the eccentric westward gyre reaches low latitudes, in relation with important up/down-wellings. Our results also confirm that the dipole decay, observed over the past decades, is primarily driven by advection processes. Our method allows us to provide probability densities for forecasts of the core flow and the secular variation.

physics.geo-ph↗

arXiv2023

Assimilation of ground and satellite magnetic measurements: inference of core surface magnetic and velocity field changes

We jointly invert for magnetic and velocity fields at the core surface over the period 1997-2017, directly using ground-based observatory time series and measurements from the CHAMP and Swarm satellites. Satellite data are reduced to the form of virtual observatory time series distributed on a regular grid in space. Such a sequential storage helps incorporate voluminous modern magnetic data into a stochastic Kalman filter, whereby spatial constraints are incorporated based on a norm derived from statistics of a numerical geodynamo model. Our algorithm produces consistent solutions both in terms of the misfit to the data and the estimated posterior model uncertainties. We retrieve core flow features previously documented from the analysis of spherical harmonic field models, such as the eccentric anti-cyclonic gyre. We find enhanced diffusion patterns under both Indonesia and Africa. In contrast to a steady flow that is strong under the Atlantic hemisphere but very weak below the Pacific, interannual motions appear evenly distributed over the two hemispheres. Recovered interannual to decadal flow changes are predominantly symmetrical with respect to the equator outside the tangent cylinder. In contrast, under the Northern Pacific we find an intensification of a high latitude jet, but see no evidence for a corresponding feature in the Southern hemisphere. The largest flow accelerations that we isolate over the studied era are associated with meanders, attached to the equatorward meridional branch of the planetary gyre in the Eastern hemisphere, that is l

physics.geo-ph↗

arXiv2023

Reionisation time fields reconstruction from 21 cm signal maps

During the Epoch of reionisation, the intergalactic medium is reionised by the UV radiation from the first generation of stars and galaxies. One tracer of the process is the 21 cm line of hydrogen that will be observed by the Square Kilometre Array (SKA) at low frequencies, thus imaging the distribution of ionised and neutral regions and their evolution. To prepare for these upcoming observations, we investigate a deep learning method to predict from 21 cm maps the reionisation time field (treion(r)), i.e. the time at which each location has been reionised. treion(r) encodes the propagation of ionisation fronts in a single field, gives access to times of local reionisation or to the extent of the radiative reach of early sources. Moreover it gives access to the time evolution of ionisation on the plane of sky, when such evolution is usually probed along the line-of-sight direction. We trained a convolutional neural network (CNN) using simulated 21 cm maps and reionisation times fields produced by the simulation code 21cmFAST . We also investigate the performance of the CNN when adding instrumental effects. Globally, we find that without instrumental effects the 21 cm maps can be used to reconstruct the associated reionisation times field in a satisfying manner: the quality of the reconstruction is dependent on the redshift at which the 21 cm observation is being made and in general it is found that small scale (<10cMpc/h) features are smoothed in the reconstructed field, while larger scale features are well recovered. When instrumental effects are included, the scale dependance of reconstruction is even further pronounced, with significant smoothing on small and intermediate scales.

astro-ph.CO↗

arXiv2023

Topology of Reionisation times: concepts, measurements and comparisons to gaussian random field predictions

In the next decade, radio telescopes like the Square Kilometer Array (SKA) will explore the Universe at high redshift, and particularly during the Epoch of Reionisation (EoR). The first structures emerged during this epoch, and their radiations have reionised the previously cold and neutral gas of the Universe creating ionised bubbles that percolate at the end of the EoR (at a redshift of approximately 6). SKA will produce 2D images of the distribution of the neutral gas at many redshifts, pushing us to develop tools and simulations to understand its properties. This paper aims at measuring topological statistics of the EoR in the "reionisation times" fields from both cosmological and semi-analytical simulations. This field informs us about the time of reionisation of the gas at each position, is used to probe the inhomogeneities of reionisation histories and can possibly be extracted from 21 cm maps. We also compare these measurements with analytical predictions from the gaussian random field (GRF) theory. The GRF theory allows us to compute many statistics of a field: PDFs of the field or its gradient, isocontour length, critical point distributions, and skeleton length. We compare these theoretical predictions to measurements made on reionisation time fields extracted from an EMMA and a 21cmFAST simulations at 1 a cMpc/h resolution. We also compared our results to GRFs generated from the fitted power spectra of the simulation maps. Both EMMA and 21cmFAST reionisation time fields (treion(r)) are close to be gaussian fields, in contrast with the 21 cm, density or ionisation fraction that are all proven to be non-gaussian. Only accelerating ionisation fronts at the end of the EoR seem to be a cause of small non-gaussianities in treion(r). Overall our results indicate that an analytical description of the reionisation percolation can be reasonably made within the framework of GRF theory.

astro-ph.CO↗

arXiv2023

DUSTiER (DUST in the Epoch of Reionization): dusty galaxies in cosmological radiation-hydrodynamical simulations of the Epoch of Reionization with RAMSES-CUDATON

In recent years, interstellar dust has become a crucial topic in the study of the high and very high redshift Universe. Evidence points to the existence of high dust masses in massive star forming galaxies already during the Epoch of Reionization, potentially affecting the escape of ionising photons into the intergalactic medium. Moreover, correctly estimating dust extinction at UV wavelengths is essential for precise ultra-violet luminosity function (UVLF) prediction and interpretation. In this paper, we investigate the impact of dust on the observed properties of high redshift galaxies, and cosmic reionization. To this end, we couple a physical model for dust production to the fully coupled radiation-hydrodynamics cosmological simulation code RAMSES-CUDATON, and perform a $16^3$, $2048^3$, simulation, that we call DUSTiER for DUST in the Epoch of Reionization. It yields galaxies with dust masses and UV slopes compatible with constraints at z $\geq 5$. We find that extinction has a dramatic impact on the bright end of the UVLF, even as early as $\rm z=8$, and our dusty UVLFs are in better agreement with observations than dust-less UVLFs. The fraction of obscured star formation rises up to 45% at $\rm z=5$, in agreement with some of the latest results from ALMA. Finally, we find that dust reduces the escape of ionising photons from galaxies more massive than $10^{10} M_\odot$ (brighter than $\approx -18$ MAB1600) by >10%, and possibly up to 80-90% for our most massive galaxies. Nevertheless, we find that the ionising escape fraction is first and foremost set by neutral Hydrogen in galaxies, as the latter produces transmissions up to 100 times smaller than through dust alone.

astro-ph.GA↗

arXiv2022

Minimum size of 21-cm simulations

Cosmic 21cm interferometry is set to revolutionize our understanding of the Epoch of Reionization (EoR) and the Cosmic Dawn (CD). However, the signal has structure on a huge range of scales, requiring large simulation boxes to statistically capture the relevant fields. In this work we quantify the minimum box size for simulating the power spectrum (PS) of the cosmic 21cm signal. We perform multiple realizations of the initial conditions, for a range of box sizes. We quantify convergence with respect to a mock observation of box length 1.1 Gpc, with thermal noise computed for a 1000h observation with SKA1-low. We find that simulations of box lengths 200-300 Mpc underestimate the large-scale power during the CD by ~7-9 % on average. We conclude that box lengths of $L\gtrsim250$ Mpc are needed to converge at the level of <~1$σ$ of the total noise.

astro-ph.CO↗

arXiv2022

Machine learning astrophysics from 21 cm lightcones: impact of network architectures and signal contamination

Imaging the cosmic 21 cm signal will map out the first billion years of our Universe. The resulting 3D lightcone (LC) will encode the properties of the unseen first galaxies and physical cosmology. Here, we build on previous work using neural networks (NNs) to infer astrophysical parameters directly from 21 cm LC images. We introduce recurrent neural networks (RNNs), capable of efficiently characterizing the evolution along the redshift axis of 21 cm LC images. Using a large database of simulated cosmic 21 cm LCs, we compare the relative performance in parameter estimation of different network architectures. These including two types of RNNs, which differ in their complexity, as well as a more traditional convolutional neural network (CNN). For the ideal case of no instrumental effects, our simplest and easiest to train RNN performs the best, with a mean squared parameter estimation error (MSE) that is lower by a factor of $\ge 2$ compared with the other architectures studied here, and a factor of $\ge 8$ lower than the previously-studied CNN. We also corrupt the cosmic signal by adding noise expected from a 1000 h integration with the Square Kilometre Array, as well as excising a foreground-contaminated 'horizon wedge'. Parameter prediction errors increase when the NNs are trained on these contaminated LC images, though recovery is still good even in the most pessimistic case (with $R^2 \ge 0.5-0.95$). However, we find no notable differences in performance between network architectures on the contaminated images. We argue this is due to the size of our data set, highlighting the need for larger data sets and/or better data augmentation in order to maximize the potential of NNs in 21 cm parameter estimation.

astro-ph.CO↗

arXiv2021

A first look at the topology of reionization redshifts in models of the Epoch of the Reionization

During the EoR, the first stars and galaxies appear while creating ionized bubbles that will eventually percolate near z=6. These ionized bubbles and percolation process are nowadays under a lot of scrutiny since observations of the HI gas will be carried on in the next decade with e.g. the SKA radiotelescope. Studies of the EoR are performed on semi-analytical and fully numerical cosmological simulations to investigate e.g. the topology of the process. We analyse the topology of EoR models through regions that are under the radiative influence of ionization sources. They are associated with peak patches of reionization redshift (zreion) field, for which we measure their general properties (e.g. number, size, shape, orientation). We aim at gaining insights on the geometry of the reionization process and how it relates to the matter distribution for example. We also assess how such measurements can be used to quantify the influence of physical parameters on the reionization models or the differences between fully numerical simulations and semi-analytical models. We use the DisPerSE framework (which applies the Morse theory and the persistent homology) on different EoR scenarios through gas density and zreion maps. We find that we can distinguish between EoR models with different sources using simple analyses on the number, shape and size distributions of the peak patches. For every model, we statistically show that they are rather prolate and aligned with the gas filaments. We briefly highlight that the percolation process can be followed studying zreion fields with different persistence thresholds. We show that fully numerical EMMA simulations can be made consistent with 21cmFAST models in this topological framework as long as the source distribution is diffuse enough.

astro-ph.CO↗

arXiv2021

Lyman-alpha opacities at z=4-6 require low mass, radiatively-suppressed galaxies to drive cosmic reionization

The high redshift Lyman-alpha forest, in particular the Gunn-Peterson trough, is the most unambiguous signature of the neutral to ionized transition of the intergalactic medium (IGM) taking place during the Epoch of Reionization (EoR). Recent studies, e.g. Kulkarni et al. (2019a) and Keating et al. (2019), showed that reproducing the observed Lyman-alpha opacities after overlap required a non-monotonous evolution of cosmic emissivity: rising, peaking at z=6, and then decreasing onwards to z=4. Such an evolution is puzzling considering galaxy build-up and the cosmic star formation rate are still continously on the rise at these epochs. Here, we use new RAMSES-CUDATON simulations to show that such a peaked evolution may occur naturally in a fully coupled radiation-hydrodynamical framework. In our fiducial run, cosmic emissivity at z>6 is dominated by a low mass (M$_{\rm DM}<2.10^9$ M$_{\odot}$), high escape fraction halo population, driving reionization, up to overlap. Approaching z=6, this population is radiatively suppressed due to the rising ionizing UV background, and its emissivity drops. In the meantime, the high mass halo population builds up and its emissivity rises, but not fast enough to compensate the dimming of the low mass haloes, because of low escape fractions. The combined ionizing emissivity of these two populations therefore naturally results in a rise and fall of the cosmic emissivity, from z=12 to z=4, with a peak at z=6. An alternative run, which features higher escape fractions for the high mass haloes and later suppression at low mass, leads to overshooting the ionizing rate, over-ionizing the IGM and therefore too low Lyman-alpha opacities.

astro-ph.CO↗

arXiv2021

Constraints on warm dark matter from UV luminosity functions of high-z galaxies with Bayesian model comparison

The number density of small dark matter (DM) halos hosting faint high-redshift galaxies is sensitive to the DM free-streaming properties. However, constraining these DM properties is complicated by degeneracies with the uncertain baryonic physics governing star formation. In this work, we use a flexible astrophysical model and a Bayesian inference framework to analyse ultra-violet (UV) luminosity functions (LFs) at z=6-8. We vary the complexity of the galaxy model (single vs double power law for the stellar -- halo mass relation) as well as the matter power spectrum (cold DM vs thermal relic warm DM), comparing their Bayesian evidences. Adopting a conservatively wide prior range for the WDM particle mass, we show that the UV LFs at z=6-8 only weakly favour CDM over WDM. We find that particle masses of $\lesssim$2 keV are rejected at a 95% credible level in all models that have a WDM-like power spectrum cutoff. This bound should increase to ~2.5 keV with the James Webb Space Telescope (JWST).

astro-ph.CO↗

arXiv2021

The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions

Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual time scale range where Earth's core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth's core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis. Three classes of hydrodynamic and hydromagnetic waves are identified in the model output, all with propagation velocity largely exceeding that of convective advection: axisymmetric, geostrophic Alfvén torsional waves, and non-axisymmetric, quasi-geostrophic Alfvén and Rossby waves. The contribution of these waves to the geomagnetic acceleration amounts to an enrichment and flattening of its energy density spectral profile at decadal time scales, thereby providing a constraint on the extent of the $f^{-4}$ range observed in the geomagnetic frequency power spectrum. The flow and magnetic acceleration energies carried by waves both linearly increase with the ratio of the magnetic diffusion time scale to the Alfvén time scale, highlighting the dominance of Alfvén waves in the signal and the stabilising control of magnetic dissipation at non-axisymmetric scales. Extrapolation of the results to Earth's core conditions supports the detectability of Alfvén waves in geomagnetic observations, either as axisymmetric torsional oscillations or through the geomagnetic jerks caused by non-axisymmetric waves. In contrast, Rossby waves appear to be too fast and carry too little magnetic energy to be detectable in geomagnetic acceleration signals of limited spatio-temporal resolution.

physics.geo-ph↗

arXiv2019

A deep learning model to emulate simulations of cosmic reionization

We present a deep learning model trained to emulate the radiative transfer during the epoch of cosmological reionization. CRADLE (Cosmological Reionization And Deep LEarning) is an autoencoder convolutional neural network that uses two-dimensional maps of the star number density and the gas density field at z=6 as inputs and that predicts 3D maps of the times of reionization $\mathrm{t_{reion}}$ as outputs. These predicted single fields are sufficient to describe the global reionization history of the intergalactic medium in a given simulation. We trained the model on a given simulation and tested the predictions on another simulation with the same paramaters but with different initial conditions. The model is successful at predicting $\mathrm{t_{reion}}$ maps that are in good agreement with the test simulation. We used the power spectrum of the $\mathrm{t_{reion}}$ field as an indicator to validate our model. We show that the network predicts large scales almost perfectly but is somewhat less accurate at smaller scales. While the current model is already well-suited to get average estimates about the reionization history, we expect it can be further improved with larger samples for the training, better data pre-processing and finer tuning of hyper-parameters. Emulators of this kind could be systematically used to rapidly obtain the evolving HII regions associated with hydro-only simulations and could be seen as precursors of fully emulated physics solvers for future generations of simulations.

astro-ph.CO↗

arXiv2019

Properties of reionization-era galaxies from JWST luminosity functions and 21-cm interferometry

Next generation observatories will enable us to study the first billion years of our Universe in unprecedented detail. Foremost among these are 21-cm interferometry with the HERA and the SKA, and high-$z$ galaxy observations with the James Webb Space Telescope (JWST). Taking a basic galaxy model, in which we allow the star formation rates and ionizing escape fractions to have a power-law dependence on halo mass with an exponential turnover below some threshold, we quantify how observations from these instruments can be used to constrain the astrophysics of high-$z$ galaxies. For this purpose, we generate mock JWST LFs, based on two different hydrodynamical cosmological simulations; these have intrinsic luminosity functions (LFs) which turn over at different scales and yet are fully consistent with present-day observations. We also generate mock 21-cm power spectrum observations, using 1000h observations with SKA1 and a moderate foreground model. Using only JWST data, we predict up to a factor of 2-3 improvement (compared with HST) in the fractional uncertainty of the star formation rate to halo mass relation and the scales at which the LFs peak (i.e. turnover). Most parameters regulating the UV galaxy properties can be constrained at the level of $\sim 10$% or better, if either (i) we are able to better characterize systematic lensing uncertainties than currently possible; or (ii) the intrinsic LFs peak at magnitudes brighter than $M_{\rm UV} \lesssim -13$. Otherwise, improvement over HST-based inference is modest. When combining with upcoming 21-cm observations, we are able to significantly mitigate degeneracies, and constrain all of our astrophysical parameters, even for our most pessimistic assumptions about upcoming JWST LFs. The 21-cm observations also result in an order of magnitude improvement in constraints on the EoR history.

astro-ph.CO↗

arXiv2019

Spatial And Temporal Changes Of The Geomagnetic Field: Insights From Forward And Inverse Core Field Models

Observational constraints on geomagnetic field changes from interannual to millenial periods are reviewed, and the current resolution of field models (covering archeological to satellite eras) is discussed. With the perspective of data assimilation, emphasis is put on uncertainties entaching Gauss coefficients, and on the statistical properties of ground-based records. These latter potentially call for leaving behind the notion of geomagnetic jerks. The accuracy at which we recover interannual changes also requires considering with caution the apparent periodicity seen in the secular acceleration from satellite data. I then address the interpretation of recorded magnetic fluctuations in terms of core dynamics, highlighting the need for models that allow (or pre-suppose) a magnetic energy orders of magnitudes larger than the kinetic energy at large length-scales, a target for future numerical simulations of the geodynamo. I finally recall the first attempts at implementing geomagnetic data assimilation algorithms.

physics.geo-ph↗

arXiv2019

Deep learning from 21-cm tomography of the Cosmic Dawn and Reionization

The 21-cm power spectrum (PS) has been shown to be a powerful discriminant of reionization and cosmic dawn astrophysical parameters. However, the 21-cm tomographic signal is highly non-Gaussian. Therefore there is additional information which is wasted if only the PS is used for parameter recovery. Here we showcase astrophysical parameter recovery directly from 21-cm images, using deep learning with convolutional neural networks (CNN). Using a database of 2D images taken from 10,000 21-cm lightcones (each generated from different cosmological initial conditions), we show that a CNN is able to recover parameters describing the first galaxies: (i) Tvir , their minimum host halo virial temperatures (or masses) capable of hosting efficient star formation; (ii) ζ , their typical ionizing efficiencies; (iii) LX/SFR , their typical soft-band X-ray luminosity to star formation rate; and (iv) E0 , the minimum X-ray energy capable of escaping the galaxy into the IGM. For most of their allowed ranges, log Tvir and log LX/SFR are recovered with < 1% uncertainty, while ζ and E0 are recovered within 10% uncertainty. Our results are roughly comparable to the accuracy obtained from Monte Carlo Markov Chain sampling of the PS with 21CMMC for the two mock observations analyzed previously, although we caution that we do not yet include noise and foreground contaminants in this proof-of-concept study.

astro-ph.CO↗

arXiv2019

Inferring the astrophysics of reionization and cosmic dawn from galaxy luminosity functions and the 21-cm signal

The properties of the first galaxies, expected to drive the Cosmic Dawn (CD) and the Epoch of Reionization (EoR), are encoded in the 3D structure of the cosmic 21-cm signal. Parameter inference from upcoming 21-cm observations promises to revolutionize our understanding of these unseen galaxies. However, prior inference was done using models with several simplifying assumptions. Here we introduce a flexible, physically-motivated parametrization for high-$z$ galaxy properties, implementing it in the public code 21cmFAST. In particular, we allow their star formation rates and ionizing escape fraction to scale with the masses of their host dark matter halos, and directly compute inhomogeneous, sub-grid recombinations in the intergalactic medium. Combining current Hubble observations of the rest-frame UV luminosity function (UV LFs) at high-$z$ with a mock 1000h 21-cm observation using the Hydrogen Epoch of Reionization Arrays (HERA), we constrain the parameters of our model using a Monte Carlo Markov Chain sampler of 3D simulations, 21CMMC. We show that the amplitude and scaling of the stellar mass with halo mass is strongly constrained by LF observations, while the remaining galaxy properties are constrained mainly by 21-cm observations. The two data sets compliment each other quite well, mitigating degeneracies intrinsic to each observation. All eight of our astrophysical parameters are able to be constrained at the level of $\sim 10\%$ or better. The updated versions of 21cmFAST and 21CMMC used in this work are publicly available.

astro-ph.GA↗

arXiv2018

Suppression of Star Formation in Low-Mass Galaxies Caused by the Reionization of their Local Neighborhood

Photoheating associated with reionization suppressed star formation in low-mass galaxies. Reionization was inhomogeneous, however, affecting different regions at different times. To establish the causal connection between reionization and suppression, we must take this local variation into account. We analyze the results of CoDa (`Cosmic Dawn') I, the first fully-coupled radiation-hydrodynamical simulation of reionization and galaxy formation in the Local Universe, in a volume large enough to model reionization globally but with enough resolving power to follow all atomic-cooling galactic halos in that volume. For every halo identified at a given time, we find the redshift at which the surrounding IGM reionized, along with its instantaneous star formation rate (`SFR') and baryonic gas-to-dark matter ratio ($M_\text{gas}/M_\text{DM}$). The average SFR per halo with $M < 10^9 \text{ M}_\odot$ was steady in regions not yet reionized, but declined sharply following local reionization. For $M > 10^{10} \text{ M}_\odot$, this SFR continued through local reionization, increasing with time, instead. For $10^9 < M < 10^{10} \text{ M}_\odot$, the SFR generally increased modestly through reionization, followed by a modest decline. In general, halo SFRs were higher for regions that reionized earlier. A similar pattern was found for $M_\text{gas}/M_\text{DM}$, which declined sharply following local reionization for $M < 10^9 \text{ M}_\odot$. Local reionization time correlates with local matter overdensity, which determines the local rates of structure formation and ionizing photon consumption. The earliest patches to develop structure and reionize ultimately produced more stars than they needed to finish and maintain their own reionization, exporting their `surplus' starlight to help reionize regions that developed structure later.

astro-ph.CO↗