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, ${\left<n^2\right>/\left<n\right>^2}$, 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.
Estimating the intergalactic medium ionization level of a region needs proper treatment of the reionization process for a large representative volume of the universe. The clumping factor, a parameter which accounts for the effect of recombinations in unresolved, small-scale structures, aids in achieving the required accuracy for the reionization history even in simulations with low spatial resolution. In this paper, we study for the first time the redshift evolution of clumping factors of different ionized species of H and He in a small but very high resolution simulation of the reionization p…
We discuss the role of recombinations in the IGM, and the related concept of the clumping factor, during cosmic reionization. The clumping factor is, in general, a local quantity that depends on the local over-density and the scale below which the baryon density field can be assumed smooth. That scale, called the filtering scale, is itself depended on over-density and local thermal history. We present a method for building a self-consistent analytical model of inhomogeneous reionization assuming the linear growth rate of the density fluctuation, which accounts for these effects simultaneously.…
Small-scale density fluctuations can significantly affect reionization but are typically modelled quite crudely. Unresolved fluctuations in numerical simulations and analytical calculations are included using a gas clumping factor, typically assumed to be independent of the local environment. In Paper I, we presented an improved, local density-dependent model for the sub-grid gas clumping. Here we extend this using an empirical stochastic model based on the results from high-resolution numerical simulations which fully resolve all relevant fluctuations. Our model reproduces well both the mean …
We use fully self-consistent numerical simulations of cosmic reionization, completed under the Cosmic Reionization On Computers (CROC) project, to explore how well the recombinations in the ionized IGM can be quantified by the effective "clumping factor." The density distribution in the simulations (and, presumably, in a real universe) is highly inhomogeneous and more-or-less smoothly varying in space. However, even in highly complex and dynamic environments the concept of the IGM remains reasonably well-defined; the largest ambiguity comes from the unvirialized regions around galaxies that ar…
In the Simulations and Constructions of the Reionization of Cosmic Hydrogen (SCORCH) project, we compare analytical models of the hydrogen ionization fraction with radiation-hydrodynamic simulations. We derive analytical models of the mass-weighted hydrogen ionization fraction from the local ionization balance equations as a more accurate alternative to the widely adopted model based on the volume filling factor. In particular, our model has a recombination term quadratic in the ionization fraction, which is consistent with the two-body interaction nature of recombination. Then, we use the rad…
An ionization front expanding into a neutral medium can be slowed-down significantly by recombinations. In cosmological numerical simulations the recombination rate is often computed using a 'clumping factor', that takes into account that not all scales in the simulated density field are resolved. Here we demonstrate that using a single value of the clumping factor significantly overestimates the recombination rate, and how a local estimate of the clumping factor is both easy to compute, and gives significantly better numerical convergence. We argue that this lower value of the recombination r…
In this first of several application papers, we investigate the mechanics of reionization from stellar sources in high-z galaxies, the utility of various clumping factors on estimating the recombination time in the IGM, and the photon budget required to achieve reionization. We test the accuracy of the static and time-dependent models of Madau et al. as predictors of reionization completion/maintenance. We simulate a WMAP7 LCDM cosmological model in a 20 Mpc comoving cube with 800^3 uniform fluid cells and dark matter particles. By tuning our star formation to approximately match the observed …
The density contrast of the Universe, parametrized in terms of the matter power spectrum and its variance, can amplify the signal of the free-free process in the plasma. The damping of fluctuations on scales smaller than the DM particle free streaming scale corresponds to a suppression of the total matter power spectrum on large wave numbers k. We derive the time evolution of the variance of the matter power spectrum for various cosmological models and parameters by numerically computing the power spectrum with a modified version of the Boltzmann code CAMB, for different values of the cut-off …
The intergalactic medium is expected to clump on scales down to $10^4-10^8$ M$_{\odot}$ before the onset of reionization. The impact of these small-scale structures on reionization is poorly understood despite the modern understanding that gas clumpiness limits the growth of H II regions. We use a suite of radiation-hydrodynamics simulations that capture the $\sim 10^4$ $M_\odot$ Jeans mass of unheated gas to study density fluctuations during reionization. Our simulations track the complex ionization and hydrodynamical response of gas in the wake of ionization fronts. The clumping factor of io…
We examine the impact of baryon-dark matter relative velocities on intergalactic small-scale structure and the 21 cm signal during reionization. Streaming velocities reduced clumping in the intergalactic medium (IGM) on mass scales of $\sim 10^4 - 10^8$ M$_{\odot}$. This effect produced a distinct baryon acoustic oscillation (BAO) feature in the 21 cm power spectrum at wave numbers $k\sim 0.1$ h/Mpc, near which forthcoming surveys will be most sensitive. In contrast to the highly uncertain impact of streaming velocities on star formation, the effect on clumping is better constrained because it…
We assess the probable redshift (z_rei ~ 7) for full reionization of the intergalactic medium (IGM) using a prescription for the co-moving star-formation-rate (SFR) density (rho_SFR) required to maintain photoionization against recombination. Our newly developed on-line reionization simulator allows users to assess the required SFR and ionization histories, using a variety of assumptions for galactic and stellar populations, IGM clumping factor and temperature, and LyC escape fraction. The decline in high-redshift galaxy candidates and Lya emitters at z = 6-8 suggests a rising neutral fraction…
The Lumina Project: Intergalactic Clumping and Recombination Sinks
The University of Texas at Dallas（德克萨斯大学达拉斯分校）；Institute for Basic Science（韩国基础科学研究所）；Massachusetts Institute of Technology（麻省理工学院）；York University（约克大学）；Max Planck Institute for Astrophysics（马克斯·普朗克天体物理学研究所）
Cosmic Dawn II (CoDa II) is a new, fully-coupled radiation-hydrodynamics simulation of cosmic reionization and galaxy formation and their mutual impact, to redshift $z < 6$. With $4096^3$ particles and cells in a 94 Mpc box, it is large enough to model global reionization and its feedback on galaxy formation while resolving all haloes above $10^8$ M$_{\odot}$. Using the same hybrid CPU-GPU code RAMSES-CUDATON as CoDa I in Ocvirk et al. (2016), CoDa II modified and re-calibrated the subgrid star-formation algorithm, making reionization end earlier, at $z \gtrsim 6$, thereby better matching the …
By depleting the ionizing photon budget available to expand cosmic HII regions, recombining systems (or Lyman limit systems) can have a large impact during (and following) cosmic reionization. Unfortunately, directly resolving such structures in large-scale reionization simulations is computationally impractical. Instead, here we implement a sub-grid prescription for tracking inhomogeneous recombinations in the intergalactic medium. Building on previous work parameterizing photo-heating feedback on star-formation, we present large-scale, semi-numeric reionization simulations which self-consist…
I present a simple calculation of the expected mean CO brightness temperature from the large scale distribution of galaxies during cosmic reionization. The calculation is based on the cosmic star formation rate density required to reionize, and keep ionized, the intergalactic medium, and uses standard relationships between star formation rate, IR luminosity, and CO luminosity derived for star forming galaxies over a wide range in redshift. I find that the mean CO brightness temperature resulting from the galaxies that could reionize the Universe at $z = 8$ is $T_B \sim 1.1 (C/5) (f_{esc}/0.1)^…
Reionization in HESTIA: Studying reionization in the LG through zoom simulations
University of Sussex（萨塞克斯大学）；The University of Nottingham（诺丁汉大学）；Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦阿基米德天体物理研究所）；P.N. Lebedev Physical Institute（列别捷夫物理研究所）；Eastern Kentucky University（东肯塔基大学）
Upcoming galaxy surveys and 21-cm experiments targeting high redshifts $z\gtrsim 6$ are highly complementary probes of galaxy formation and reionization. However, in order to expedite the large volume simulations relevant for 21-cm observations, many models of galaxies within reionization codes are entirely subgrid and/or rely on halo abundances only. In this work, we explore the extent to which resolving and modeling individual galaxy formation histories affects predictions both for the galaxy populations detectable by upcoming surveys and the signatures of reionization accessible to upcoming…
At cosmic recombination, there was supersonic relative motion between baryons and dark matter, which originated from the baryonic acoustic oscillations in the early universe. This motion has been considered to have a negligible impact on the late stage of cosmic reionization because the relative velocity quickly decreases. However, recent studies have suggested that the recombination in gas clouds smaller than the local Jeans mass ($\lesssim$ $10^8~M_\odot$) can affect the reionization history by boosting the number of ultraviolet photons required for ionizing the intergalactic medium. Motivat…
Thomson optical depth tau measurements from Planck provide new insights into the reionization of the universe. In pursuit of model-independent constraints on the properties of the ionising sources, we determine the empirical evolution of the cosmic ionizing emissivity. We use a simple two-parameter model to map out the evolution in the emissivity at z>~6 from the new Planck optical depth tau measurements, from the constraints provided by quasar absorption spectra and from the prevalence of Ly-alpha emission in z~7-8 galaxies. We find the redshift evolution in the emissivity dot{N}_{ion}(z) req…
Density inhomogeneity in the intergalactic medium (IGM) can boost the recombination rate of ionized gas substantially, affecting the growth of HII regions during reionization. Previous attempts to quantify this effect typically failed to resolve down to the Jeans scale in the pre-ionization IGM, which is important in establishing this effect, along with the hydrodynamical back-reaction of reionization on it. Towards that end, we perform a set of fully-coupled, radiation-hydrodynamics simulations from cosmological initial conditions, extending the mass resolution of previous work to the scale o…
Recent measurements of the ionizing photon mean free path ($λ_{912}^{\rm mfp}$) 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 $λ_{912}^{\rm mfp} = 3.57^{+3.09}_{-2.14}$ cMpc/$h$ at $z=6$. We introduce a model for sub-resolution ionizing photon sinks based on radiative hydrodynamics simulations of small-scale IGM clumping. We argue that the rapid evolution in $λ_{912}^{\rm mfp}$ at $z=5-6$, together with constraints on the metagalactic ionizing backgr…
An emulator for the ionizing photon mean free path in ultra-high resolution simulations: the implications of mean free path measurements for the reionization history
University of Washington（华盛顿大学）；Arizona State University（亚利桑那州立大学）；University of California Riverside（加州大学河滨分校）
Understanding cosmic reionization requires the identification and characterization of early sources of hydrogen-ionizing photons. The 2012 Hubble Ultra Deep Field (UDF12) campaign has acquired the deepest infrared images with the Wide Field Camera 3 aboard Hubble Space Telescope and, for the first time, systematically explored the galaxy population deep into the era when cosmic microwave background (CMB) data indicates reionization was underway. The UDF12 campaign thus provides the best constraints to date on the abundance, luminosity distribution, and spectral properties of early star-forming…
We describe an extension of the Enzo code to enable fully-coupled radiation hydrodynamical simulation of inhomogeneous reionization in large $\sim (100 Mpc)^3$ cosmological volumes with thousands to millions of point sources. We solve all dynamical, radiative transfer, thermal, and ionization processes self-consistently on the same mesh, as opposed to a postprocessing approach which coarse-grains the radiative transfer. We do, however, employ a simple subgrid model for star formation which we calibrate to observations. Radiation transport is done in the grey flux-limited diffusion (FLD) approx…
The conditions within the ionization front of a quasar during reionization (T ~ 30,000 K, neutral hydrogen fraction ~ 0.5) are ideal for producing Lyman-alpha emission via collisional excitation of hydrogen atoms. Observations of this emission, which could subtend >10 arcmin$^2$ on the sky, would definitively demonstrate the presence of a neutral intergalactic medium at the observed epoch, placing valuable constraints on the progress of reionization. We find that the expected Lyman-alpha surface brightness is significantly weaker than previously determined and may be impossible to observe with…
We present a set of cosmological simulations with radiative transfer in order to model the reionization history of the Universe. Galaxy formation and the associated star formation are followed self-consistently with gas and dark matter dynamics using the RAMSES code, while radiative transfer is performed as a post-processing step using a moment-based method with M1 closure relation in the ATON code. The latter has been ported to a multiple Graphics Processing Units (GPU) architecture using CUDA + MPI, resulting in an overall acceleration (x80) that allows us to tackle radiative transfer proble…
We have searched for star-forming galaxies at z~7 by applying the Lyman-break technique to newly-released 1.1micron Y-band images from WFC3 on HST. By comparing these images of the Hubble Ultra Deep Field with the ACS z'-band (0.85micron), we identify objects with red colours, (z'-Y)_AB>1.3), consistent with the Ly-alpha forest absorption at z~6.7-8.8. We identify 12 of these z'-drops down to a limiting magnitude Y_AB<28.5 (equivalent to a star formation rate of 1.3M_sun/yr at z=7.1), which are undetected in the other ACS filters. We use the WFC3 J-band image to eliminate contaminant low mass …
