arXiv subjects

Ilian T. Iliev

Publications and source records attributed to Ilian T. Iliev.

At least 55 records · Page 3Linked to original sources

arXiv2019

The impact of inhomogeneous subgrid clumping on cosmic reionization

Cosmic reionization was driven by the imbalance between early sources and sinks of ionizing radiation, both of which were dominated by small-scale structure and are thus usually treated in cosmological reionization simulations by subgrid modelling. The recombination rate of intergalactic hydrogen is customarily boosted by a subgrid clumping factor, ${\left /\left ^2}$, which corrects for unresolved fluctuations in gas density ${n}$ on scales below the grid-spacing of coarse-grained simulations. We investigate in detail the impact of this inhomogeneous subgrid clumping on reionization and its observables, as follows: (1) Previous attempts generally underestimated the clumping factor because of insufficient mass resolution. We perform a high-resolution $N$-body simulation that resolves haloes down to the pre-reionization Jeans mass to derive the time-dependent, spatially-varying local clumping factor and a fitting formula for its correlation with local overdensity. (2) We then perform a large-scale $N$-body and radiative transfer simulation that accounts for this inhomogeneous subgrid clumping by applying this clumping factor-overdensity correlation. Boosting recombination significantly slows the expansion of ionized regions, which delays completion of reionization and suppresses 21 cm power spectra on large scales in the later stages of reionization. (3) We also consider a simplified prescription in which the globally-averaged, time-evolving clumping factor from the same high-resolution $N$-body simulation is applied uniformly to all cells in the reionization simulation, instead. Observables computed with this model agree fairly well with those from the inhomogeneous clumping model, e.g. predicting 21 cm power spectra to within 20% error, suggesting it may be a useful approximation.

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arXiv2019

Modelling the stochasticity of high-redshift halo bias

A very large dynamic range with simultaneous capture of both large- and small-scales in the simulations of cosmic structures is required for correct modelling of many cosmological phenomena, particularly at high redshift. This is not always available, or when it is, it makes such simulations very expensive. We present a novel sub-grid method for modelling low-mass ($10^5\,M_\odot\leq M_{\rm halo}\leq 10^9\,M_\odot$) haloes, which are otherwise unresolved in large-volume cosmological simulations limited in numerical resolution. In addition to the deterministic halo bias that captures the average property, we model its stochasticity that is correlated in time. We find that the instantaneous binned distribution of the number of haloes is well approximated by a log-normal distribution, with overall amplitude modulated by this "temporal correlation bias". The robustness of our new scheme is tested against various statistical measures, and we find that temporally correlated stochasticity generates mock halo data that is significantly more reliable than that from temporally uncorrelated stochasticity. Our method can be applied for simulating processes that depend on both the small- and large-scale structures, especially for those that are sensitive to the evolution history of structure formation such as the process of cosmic reionization. As a sample application, we generate a mock distribution of medium-mass ($ 10^{8} \leq M/M_{\odot} \leq 10^{9}$) haloes inside a 500 Mpc$\,h^{-1}$, $300^3$ grid simulation box. This mock halo catalogue bears a reasonable statistical agreement with a halo catalogue from numerically-resolved haloes in a smaller box, and therefore will allow a very self-consistent sets of cosmic reionization simulations in a box large enough to generate statistically reliable data.

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arXiv2019

Neutral island statistics during reionization from 21-cm tomography

We present the prospects of extracting information about the Epoch of Reionization by identifying the remaining neutral regions, referred to as islands, in tomographic observations of the redshifted 21-cm signal. Using simulated data sets we show that at late times the 21-cm power spectrum is fairly insensitive to the details of the reionization process but that the properties of the neutral islands can distinguish between different reionization scenarios. We compare the properties of these islands with those of ionized bubbles. At equivalent volume filling fractions, neutral islands tend to be fewer in number but larger compared to the ionized bubbles. In addition, the evolution of the size distribution of neutral islands is found to be slower than that of the ionized bubbles and also their percolation behaviour differs substantially. Even though the neutral islands are relatively rare, they will be easier to identify in observations with the low-frequency component of the Square Kilometre Array (SKA-Low) due to their larger size and the lower noise levels at lower redshifts. The size distribution of neutral islands at the late stages of reionization is found to depend on the source properties, such as the ionizing efficiency of the sources and their minimum mass. We find the longest line of sight through a neutral region to be more than 100 comoving Mpc until very late stages (90-95 per cent reionized), which may have relevance for the long absorption trough at $z=5.6-5.8$ in the spectrum of quasar ULAS J0148+0600.

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arXiv2019

Evaluating the QSO contribution to the 21-cm signal from the Cosmic Dawn

The upcoming radio interferometer Square Kilometre Array (SKA) is expected to directly detect the redshifted 21-cm signal from the neutral hydrogen present during the Cosmic Dawn. Temperature fluctuations from X-ray heating of the neutral intergalactic medium can dominate the fluctuations in the 21-cm signal from this time. This heating depends on the abundance, clustering, and properties of the X-ray sources present, which remain highly uncertain. We present a suite of three new large-volume, 349\,Mpc a side, fully numerical radiative transfer simulations including QSO-like sources, extending the work previously presented in Ross et al. (2017). The results show that our QSOs have a modest contribution to the heating budget, yet significantly impact the 21-cm signal. Initially, the power spectrum is boosted on large scales by heating from the biased QSO-like sources, before decreasing on all scales. Fluctuations from images of the 21-cm signal with resolutions corresponding to SKA1-Low at the appropriate redshifts are well above the expected noise for deep integrations, indicating that imaging could be feasible for all the X-ray source models considered. The most notable contribution of the QSOs is a dramatic increase in non-Gaussianity of the signal, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. However, in the case of late Lyman-$α$ saturation, this non-Gaussianity could be dramatically decreased particularly when heating occurs earlier. We conclude that increased non-Gaussianity is a promising signature of rare X-ray sources at this time, provided that Lyman-$α$ saturation occurs before heating dominates the 21-cm signal.

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arXiv2018

A method to determine the evolution history of the mean neutral Hydrogen fraction

The light-cone (LC) effect imprints the cosmological evolution of the redshifted 21-cm signal $T_{\rm b} ({\hat{\bf{n}}}, ν)$ along the frequency axis which is the line of sight (LoS) direction of an observer. The effect is particularly pronounced during the Epoch of Reionization (EoR) when the mean hydrogen neutral fraction ${\bar{x}_{\rm HI}}(ν)$ falls rapidly as the universe evolves. The multi-frequency angular power spectrum (MAPS) ${{\mathcal C}_{\ell}}(ν_1,ν_2)$ quantifies the entire second-order statistics of $T_{\rm b} ({\hat{\bf{n}}}, ν)$ considering both the systematic variation along $ν$ due to the cosmological evolution and also the statistically homogeneous and isotropic fluctuations along all the three spatial directions encoded in ${\hat{\bf{n}}}$ and $ν$. Here we propose a simple model where the systematic frequency $(ν_1,ν_2)$ dependence of ${{\mathcal C}_{\ell}}(ν_1,ν_2)$ arises entirely due to the evolution of ${\bar{x}_{\rm HI}}(ν)$. This provides a new method to observationally determine the reionization history. Considering a LC simulation of the EoR 21-cm signal, we use the diagonal elements $ν_1=ν_2$ of ${{\mathcal C}_{\ell}}(ν_1,ν_2)$ to validate our model. We demonstrate that it is possible to recover the reionization history across the entire observational bandwidth provided we have the value ${\bar{x}_{\rm HI}}$ at a single frequency as an external input.

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arXiv2018

The 21cm bispectrum as a probe of non-Gaussianities due to X-ray heating

We present analysis of the normalised 21-cm bispectrum from fully-numerical simulations of intergalactic-medium heating by stellar sources and high-mass X-ray binaries (HMXB) during the cosmic dawn. Lyman-$α$ coupling is assumed to be saturated, we therefore probe the nature of non-Gaussianities produced by X-ray heating processes. We find the evolution of the normalised bispectrum to be very different from that of the power spectrum. It exhibits a turnover whose peak moves from large to small scales with decreasing redshift, and corresponds to the typical separation of emission regions. This characteristic scale reduces as more and more regions move into emission with time. Ultimately, small-scale fluctuations within heated regions come to dominate the normalised bispectrum, which at the end of the simulation is almost entirely driven by fluctuations in the density field. To establish how generic the qualitative evolution of the normalised bispectrum we see in the stellar + HMXB simulation is, we examine several other simulations - two fully-numerical simulations that include QSO sources, and two with contrasting source properties produced with the semi-numerical simulation 21cmFAST. We find the qualitative evolution of the normalised bispectrum during X-ray heating to be generic, unless the sources of X-rays are, as with QSOs, less numerous and so exhibit more distinct isolated heated profiles. Assuming mitigation of foreground and instrumental effects are ultimately effective, we find that we should be sensitive to the normalised bispectrum during the epoch of heating, so long as the spin temperature has not saturated by $z \approx 19$.

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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.

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arXiv2018

The Inhomogeneous Reionization Times of Present-day Galaxies

Today's galaxies experienced cosmic reionization at different times in different locations. For the first time, reionization ($50\%$ ionized) redshifts, $z_R$, at the location of their progenitors are derived from new, fully-coupled radiation-hydrodynamics simulation of galaxy formation and reionization at $z > 6$, matched to N-body simulation to z = 0. Constrained initial conditions were chosen to form the well-known structures of the local universe, including the Local Group and Virgo, in a (91 Mpc)$^3$ volume large enough to model both global and local reionization. Reionization simulation CoDa I-AMR, by CPU-GPU code EMMA, used (2048)$^3$ particles and (2048)$^3$ initial cells, adaptively-refined, while N-body simulation CoDa I-DM2048, by Gadget2, used (2048)$^3$ particles, to find reionization times for all galaxies at z = 0 with masses $M(z=0)\ge 10^8 M_\odot$. Galaxies with $M(z=0) \gtrsim 10^{11} M_\odot$ reionized earlier than the universe as a whole, by up to $\sim$ 500 Myrs, with significant scatter. For Milky-Way-like galaxies, $z_R$ ranged from 8 to 15. Galaxies with $M(z=0) \lesssim 10^{11} M_\odot$ typically reionized as late or later than globally-averaged $50\%$ reionization at $\langle z_R\rangle =7.8$, in neighborhoods where reionization was completed by external radiation. The spread of reionization times within galaxies was sometimes as large as the galaxy-to-galaxy scatter. The Milky Way and M31 reionized earlier than global reionization but later than typical for their mass, neither dominated by external radiation. Their most massive progenitors at $z>6$ had $z_R$ = 9.8 (MW) and 11 (M31), while their total masses had $z_R$ = 8.2 (both).

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arXiv2017

Bubble size statistics during reionization from 21-cm tomography

The upcoming SKA1-Low radio interferometer will be sensitive enough to produce tomographic imaging data of the redshifted 21-cm signal from the Epoch of Reionization. Due to the non-Gaussian distribution of the signal, a power spectrum analysis alone will not provide a complete description of its properties. Here, we consider an additional metric which could be derived from tomographic imaging data, namely the bubble size distribution of ionized regions. We study three methods that have previously been used to characterize bubble size distributions in simulation data for the hydrogen ionization fraction - the spherical-average, mean-free-path and friends-of-friends methods - and apply them to simulated 21-cm data cubes. Our simulated data cubes have the (sensitivity-dictated) resolution expected for the SKA1-Low reionization experiment and we study the impact of both the light-cone and redshift space distortion effects. To identify ionized regions in the 21-cm data we introduce a new, self-adjusting thresholding approach based on the K-Means algorithm. We find that the fraction of ionized cells identified in this way consistently falls below the mean volume-averaged ionized fraction. From a comparison of the three bubble size methods, we conclude that all three methods are useful, but that the mean-free-path method performs best in terms of tracking the progress of reionization and separating different reionization scenarios. The light-cone effect is found to affect data spanning more than about 10~MHz in frequency ($Δz\sim0.5$). We find that redshift space distortions only marginally affect the bubble size distributions.

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arXiv2017

Recovering the HII region size statistics from 21-cm tomography

We introduce a novel technique, called "granulometry", to characterize and recover the mean size and the size distribution of HII regions from 21-cm tomography. The technique is easy to implement, but places the previously not very well defined concept of morphology on a firm mathematical foundation. The size distribution of the cold spots in 21-cm tomography can be used as a direct tracer of the underlying probability distribution of HII region sizes. We explore the capability of the method using large-scale reionization simulations and mock observational data cubes while considering capabilities of SKA1-low and a future extension to SKA2. We show that the technique allows the recovery of the HII region size distribution with a moderate signal-to-noise ratio from wide-field imaging ($\rm SNR\lesssim3$), for which the statistical uncertainty is sample variance dominated. We address the observational requirements on the angular resolution, the field-of-view, and the thermal noise limit for a successful measurement. To achieve a full scientific return from 21-cm tomography and to exploit a synergy with 21-cm power spectra, we suggest an observing strategy using wide-field imaging (several tens of square degrees) by an interferometric mosaicking/multi-beam observation with additional intermediate baselines (~2-4 km).

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arXiv2017

Using Artificial Neural Networks to Constrain the Halo Baryon Fraction during Reionization

Radiative feedback from stars and galaxies has been proposed as a potential solution to many of the tensions with simplistic galaxy formation models based on $Λ$CDM, such as the faint end of the UV luminosity function. The total energy budget of radiation could exceed that of galactic winds and supernovae combined, which has driven the development of sophisticated algorithms that evolve both the radiation field and the hydrodynamical response of gas simultaneously, in a cosmological context. We probe self-feedback on galactic scales using the adaptive mesh refinement, radiative transfer, hydrodynamics, and $N$-body code. Unlike previous studies which assume a homogeneous UV background, we self-consistently evolve both the radiation field and gas to constrain the halo baryon fraction during cosmic reionization. We demonstrate that the characteristic halo mass with mean baryon fraction half the cosmic mean, $M_{\mathrm{c}}(z)$, shows very little variation as a function of mass-weighted ionization fraction. Furthermore, we find that the inclusion of metal cooling and the ability to resolve scales small enough for self-shielding to become efficient leads to a significant drop in $M_{\mathrm{c}}$ when compared to recent studies. Finally, we develop an Artificial Neural Network that is capable of predicting the baryon fraction of haloes based on recent tidal interactions, gas temperature, and mass-weighted ionization fraction. Such a model can be applied to any reionization history, and trivially incorporated into semi-analytical models of galaxy formation.

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arXiv2017

Simulating the Impact of X-ray Heating during the Cosmic Dawn

Upcoming observations of the 21-cm signal from the Epoch of Reionization will soon provide the first direct detection of this era. This signal is influenced by many astrophysical effects, including long range X-ray heating of the intergalactic gas. During the preceding Cosmic Dawn era the impact of this heating on the 21-cm signal is particularly prominent, especially before spin temperature saturation. We present the largest-volume (349\,Mpc comoving=244~$h^{-1}$Mpc) full numerical radiative transfer simulations to date of this epoch that include the effects of helium and multi-frequency heating, both with and without X-ray sources. We show that X-ray sources contribute significantly to early heating of the neutral intergalactic medium and, hence, to the corresponding 21-cm signal. The inclusion of hard, energetic radiation yields an earlier, extended transition from absorption to emission compared to the stellar-only case. The presence of X-ray sources decreases the absolute value of the mean 21-cm differential brightness temperature. These hard sources also significantly increase the 21-cm fluctuations compared the common assumption of temperature saturation. The 21-cm differential brightness temperature power spectrum is initially boosted on large scales, before decreasing on all scales. Compared to the case of the cold, unheated intergalactic medium, the signal has lower rms fluctuations and increased non-Gaussianity, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. Images of the 21-cm signal with resolution around 11~arcmin still show fluctuations well above the expected noise for deep integrations with the SKA1-Low, indicating that direct imaging of the X-ray heating epoch could be feasible.

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arXiv2017

Reionization of the Milky Way, M31, and their satellites I: reionization history and star formation

Observations of the Milky Way (MW), M31, and their vicinity, known as the Local Group (LG), can provide clues about the sources of reionization. We present a suite of radiative transfer simulations based on initial conditions provided by the Constrained Local UniversE Simulations (CLUES) project that are designed to recreate the Local Universe, including a realistic MW-M31 pair and a nearby Virgo. Our box size (91 Mpc) is large enough to incorporate the relevant sources of ionizing photons for the LG. We employ a range of source models, mimicking the potential effects of radiative feedback for dark matter haloes between $10^{8}-10^{9}$ M$_{\odot}$. Although the LG mostly reionizes in an inside-out fashion, the final 40 per cent of its ionization shows some outside influence. For the LG satellites, we find no evidence that their redshift of reionization is related to the present-day mass of the satellite or the distance from the central galaxy. We find that less than 20 per cent of present-day satellites for MW and M31 have undergone any star formation prior to the end of global reionization. Approximately five per cent of these satellites could be classified as fossils, meaning the majority of star formation occurred at these early times. The more massive satellites have more cumulative star formation prior to the end of global reionization, but the scatter is significant, especially at the low-mass end. Present-day mass and distance from the central galaxy are poor predictors for the presence of ancient stellar populations in satellite galaxies.

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arXiv2016

Cosmic Dawn (CoDa): the First Radiation-Hydrodynamics Simulation of Reionization and Galaxy Formation in the Local Universe

Cosmic reionization by starlight from early galaxies affected their evolution, thereby impacting reionization, itself. Star formation suppression, for example, may explain the observed underabundance of Local Group dwarfs relative to N-body predictions for Cold Dark Matter. Reionization modelling requires simulating volumes large enough [~(100Mpc)^3] to sample reionization "patchiness", while resolving millions of galaxy sources above ~10^8 Msun , combining gravitational and gas dynamics with radiative transfer. Modelling the Local Group requires initial cosmological density fluctuations pre-selected to form the well-known structures of the local universe today. Cosmic Dawn ("CoDa") is the first such fully-coupled, radiation-hydrodynamics simulation of reionization of the local universe. Our new hybrid CPU-GPU code, RAMSES-CUDATON, performs hundreds of radiative transfer and ionization rate-solver timesteps on the GPUs for each hydro-gravity timestep on the CPUs. CoDa simulated (91Mpc)^3 with 4096^3 particles and cells, to redshift 4.23, on ORNL supercomputer Titan, utilizing 8192 cores and 8192 GPUs. Global reionization ended slightly later than observed. However, a simple temporal rescaling which brings the evolution of ionized fraction into agreement with observations also reconciles ionizing flux density, cosmic star formation history, CMB electron scattering optical depth and galaxy UV luminosity function with their observed values. Photoionization heating suppressed the star formation of haloes below ~2 x 10^9 Msun , decreasing the abun- dance of faint galaxies around MAB_1600 = [-10,-12]. For most of reionization, star formation was dominated by haloes between 10^10 - 10^11 Msun , so low-mass halo suppression was not reflected by a distinct feature in the global star formation history. (Abridged)

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arXiv2016

Systematic biases in low frequency radio interferometric data due to calibration: the LOFAR EoR case

The redshifted 21 cm line of neutral hydrogen is a promising probe of the Epoch of Reionization (EoR). However, its detection requires a thorough understanding and control of the systematic errors. We study two systematic biases observed in the LOFAR EoR residual data after calibration and subtraction of bright discrete foreground sources. The first effect is a suppression in the diffuse foregrounds, which could potentially mean a suppression of the 21 cm signal. The second effect is an excess of noise beyond the thermal noise. The excess noise shows fluctuations on small frequency scales, and hence it can not be easily removed by foreground removal or avoidance methods. Our analysis suggests that sidelobes of residual sources due to the chromatic point spread function and ionospheric scintillation can not be the dominant causes of the excess noise. Rather, both the suppression of diffuse foregrounds and the excess noise can occur due to calibration with an incomplete sky model containing predominantly bright discrete sources. We show that calibrating only on bright sources can cause suppression of other signals and introduce an excess noise in the data. The levels of the suppression and excess noise depend on the relative flux of sources which are not included in the model with respect to the flux of modeled sources. We discuss possible solutions such as using only long baselines to calibrate the interferometric gain solutions as well as simultaneous multi-frequency calibration along with their benefits and shortcomings.

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arXiv2016

The Effects of Lyman-Limit Systems on the Evolution and Observability of the Epoch of Reionization

We present the first large-scale, full radiative transfer simulations of the reionization of the intergalactic medium in the presence of Lyman-limit systems (LLSs). To illustrate the impact of LLS opacity, possibly missed by previous simulations, we add either a uniform or spatially-varying hydrogen bound-free opacity. This opacity, implemented as the mean free path (mfp) of the ionizing photons, extrapolates the observed, post-reionization redshift dependence into the epoch of reionization. In qualitative agreement with previous studies, we find that at late times the presence of LLSs slows down the ionization fronts, and alters the size distribution of H II regions. We quantitatively characterize the size distribution and morphological evolution of H II regions and examine the effects of the LLSs on the redshifted 21-cm signal from the patchy reionization. The presence of LLSs extends the ionization history by $Δz \sim 0.8$. The LLS absorbers significantly impede the late-time growth of the H II regions. The position dependent LLS distribution slows reionization further and additionally limits the late growth of the ionized regions. However, there is no "freeze out" of the H II regions and the largest regions grow to the size of the simulation volume. The 21-cm power spectra show that at large scales the power drops by a factor of 2 for 50% and 75% ionization stages (at $k = 0.1$ $\text{h} \, \text{Mpc}^{-1} $) reflecting the limiting effect of the LLSs on the growth of ionized patches. The statistical observables such as the RMS of the brightness temperature fluctuations and the peak amplitudes of the 21-cm power spectra at large-scales ($k = 0.05 - 0.1$ $\text{h} \, \text{Mpc}^{-1} $) are diminished by the presence of LLS.

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arXiv2015

The Large-Scale Observational Signatures of Low-Mass Galaxies During Reionization

Observations of the epoch of reionization give us clues about the nature and evolution of the sources of ionizing photons, or early stars and galaxies. We present a new suite of structure formation and radiative transfer simulations from the PRACE4LOFAR project designed to investigate whether the mechanism of radiative feedback, or the suppression of star formation in ionized regions from UV radiation, can be inferred from these observations. Our source halo mass extends down to $10^8 M_\odot$, with sources in the mass range $10^8$ to $10^9 M_\odot$ expected to be particularly susceptible to feedback from ionizing radiation, and we vary the aggressiveness and nature of this suppression. Not only do we have four distinct source models, we also include two box sizes (67 Mpc and 349 Mpc), each with two grid resolutions. This suite of simulations allows us to investigate the robustness of our results. All of our simulations are broadly consistent with the observed electron-scattering optical depth of the cosmic microwave background and the neutral fraction and photoionization rate of hydrogen at $z\sim6$. In particular, we investigate the redshifted 21-cm emission in anticipation of upcoming radio interferometer observations. We find that the overall shape of the 21-cm signal and various statistics are robust to the exact nature of source suppression, the box size, and the resolution. There are some promising model discriminators in the non-Gaussianity and small-scale power spectrum of the 21-cm signal.

astro-ph.CO↗

arXiv2015

Effects of the sources of reionization on 21-cm redshift-space distortions

The observed 21-cm signal from the epoch of reionization will be distorted along the line-of-sight by the peculiar velocities of matter particles. These redshift-space distortions will affect the contrast in the signal and will also make it anisotropic. This anisotropy contains information about the cross-correlation between the matter density field and the neutral hydrogen field, and could thus potentially be used to extract information about the sources of reionization. In this paper, we study a collection of simulated reionization scenarios assuming different models for the sources of reionization. We show that the 21-cm anisotropy is best measured by the quadrupole moment of the power spectrum. We find that, unless the properties of the reionization sources are extreme in some way, the quadrupole moment evolves very predictably as a function of global neutral fraction. This predictability implies that redshift-space distortions are not a very sensitive tool for distinguishing between reionization sources. However, the quadrupole moment can be used as a model-independent probe for constraining the reionization history. We show that such measurements can be done to some extent by first-generation instruments such as LOFAR, while the SKA should be able to measure the reionization history using the quadrupole moment of the power spectrum to great accuracy.

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