Reionization is thought to have occurred in the redshift range of 6 < z < 9, which is now being probed by both deep galaxy surveys and CMB observations. Using halo abundance matching over the ...redshift range 5 < z < 8 and assuming smooth, continuous gas accretion, we develop a model for the star formation efficiency f
⋆ of dark matter haloes at z > 6 that matches the measured galaxy luminosity functions at these redshifts. We find that f
⋆ peaks at ∼30 per cent at halo masses M ∼ 1011–1012 M⊙, in qualitative agreement with its behaviour at lower redshifts. We then investigate the cosmic star formation histories and the corresponding models of reionization for a range of extrapolations to small halo masses. We use a variety of observations to further constrain the characteristics of the galaxy populations, including the escape fraction of UV photons. Our approach provides an empirically calibrated, physically motivated model for the properties of star-forming galaxies sourcing the epoch of reionization. In the case where star formation in low-mass haloes is maximally efficient, an average escape fraction ∼0.1 can reproduce the optical depth reported by Planck, whereas inefficient star formation in these haloes requires either about twice as many UV photons to escape, or an escape fraction that increases towards higher redshifts. Our models also predict how future observations with James Webb Space Telescope can improve our understanding of these galaxy populations.
We present a new determination of the ultraviolet (UV) galaxy luminosity function (LF) at redshift z 7 and 8, and a first estimate at z 9. An accurate determination of the form and evolution of the ...galaxy LF during this era is of key importance for improving our knowledge of the earliest phases of galaxy evolution and the process of cosmic reionization. Our analysis exploits to the full the new, deepest Wide Field Camera 3/infrared imaging from our Hubble Space Telescope (HST) Ultra-Deep Field 2012 (UDF12) campaign, with dynamic range provided by including a new and consistent analysis of all appropriate, shallower/wider area HST survey data. Our new measurement of the evolving LF at z 7 to 8 is based on a final catalogue of 600 galaxies, and involves a step-wise maximum-likelihood determination based on the photometric redshift probability distribution for each object; this approach makes full use of the 11-band imaging now available in the Hubble Ultra-Deep Field (HUDF), including the new UDF12 F140W data, and the latest Spitzer IRAC imaging. The final result is a determination of the z 7 LF extending down to UV absolute magnitudes M
1500 = −16.75 (AB mag) and the z 8 LF down to M
1500 = −17.00. Fitting a Schechter function, we find M1500
* = −19.90+0.23
−0.28, log φ* = −2.96+0.18
−0.23 and a faint-end slope α = −1.90+0.14
−0.15 at z 7, and M1500* = −20.12+0.37
−0.48, log φ* = −3.35+0.28
−0.47 and α = −2.02+0.22
+0.23 at z 8. These results strengthen previous suggestions that the evolution at z > 7 appears more akin to 'density evolution' than the apparent 'luminosity evolution' seen at z 5 − 7. We also provide the first meaningful information on the LF at z 9, explore alternative extrapolations to higher redshifts, and consider the implications for the early evolution of UV luminosity density. Finally, we provide catalogues (including derived z
phot, M
1500 and photometry) for the most robust z ∼ 6.5-11.9 galaxies used in this analysis. We briefly discuss our results in the context of earlier work and the results derived from an independent analysis of the UDF12 data based on colour-colour selection.
We use the new ultra-deep, near-infrared imaging of the Hubble Ultra-Deep Field (HUDF) provided by our UDF12 Hubble Space Telescope (HST) Wide Field Camera 3/IR campaign to explore the rest-frame ...ultraviolet (UV) properties of galaxies at redshifts z > 6.5. We present the first unbiased measurement of the average UV power-law index, 〈β〉, (f
λ ∝ λβ) for faint galaxies at z 7, the first meaningful measurements of 〈β〉 at z 8, and tentative estimates for a new sample of galaxies at z 9. Utilizing galaxy selection in the new F140W (J
140) imaging to minimize colour bias, and applying both colour and power-law estimators of β, we find 〈β〉 = −2.1 ± 0.2 at z 7 for galaxies with M
UV −18. This means that the faintest galaxies uncovered at this epoch have, on average, UV colours no more extreme than those displayed by the bluest star-forming galaxies at low redshift. At z 8 we find a similar value, 〈β〉 = −1.9 ± 0.3. At z 9, we find 〈β〉 = −1.8 ± 0.6, essentially unchanged from z 6 to 7 (albeit highly uncertain). Finally, we show that there is as yet no evidence for a significant intrinsic scatter in β within our new, robust z 7 galaxy sample. Our results are most easily explained by a population of steadily star-forming galaxies with either solar metallicity and zero dust, or moderately sub-solar ( 10-20 per cent) metallicity with modest dust obscuration (A
V
0.1-0.2). This latter interpretation is consistent with the predictions of a state-of-the-art galaxy-formation simulation, which also suggests that a significant population of very-low metallicity, dust-free galaxies with β −2.5 may not emerge until M
UV > −16, a regime likely to remain inaccessible until the James Webb Space Telescope.
We consider the evolution of the sky-averaged 21-cm background during the early phases of structure formation. Using simple analytic models, we calculate the thermal and ionization histories, ...assuming that stellar photons dominate the radiation background. The resulting 21-cm spectra can constrain the properties of the first generations of stars and quasars. If Population II stars dominate, Lyα coupling renders the intergalactic medium (IGM) visible before it is heated by X-rays and long before reionization. Thus the 21-cm background has a strong absorption epoch followed by weaker emission that fades during reionization. The harder spectra of very massive Population III stars compress these transitions into a shorter time interval and decreases the signal amplitude. However, the reionization epoch will remain visible except in extreme cases. The global 21-cm signal will be challenging to observe because of astronomical foregrounds, but it offers an exciting opportunity to study the first sources of light. It also fixes the overall amplitude of the fluctuating background whose detection is a major goal of several next-generation low-frequency radio interferometers.
A number of radio interferometers are currently being planned or constructed to observe 21 cm emission from reionization. Not only will such measurements provide a detailed view of that epoch, but, ...since the 21 cm emission also traces the distribution of matter in the universe, this signal can be used to constrain cosmological parameters. The sensitivity of an interferometer to the cosmological information in the signal may depend on how precisely the angular dependence of the 21 cm three-dimensional power spectrum can be measured. Using an analytic model for reionization, we quantify all the effects that break the spherical symmetry of the three-dimensional 21 cm power spectrum. We find that upcoming observatories will be sensitive to the 21 cm signal over a wide range of scales, from larger than 100 to as small as 1 comoving Mpc. Next, we consider three methods to measure cosmological parameters from the signal: (1) direct fitting of the density power spectrum to the signal, (2) using only the velocity field fluctuations in the signal, and (3) looking at the signal at large enough scales that all fluctuations trace the density field. With the foremost method, the first generation of 21 cm observations should moderately improve existing constraints on cosmological parameters for certain low-redshift reionization scenarios, and a 2 yr observation with the second-generation interferometer MWA5000 in combination with the CMB telescope Planck could improve constraints on sub(w), sub(m)h super(2), sub(b)h super(2), sub(v), n sub(s), and a sub(s). If the universe is substantially ionized by z 6 12 or if spin temperature fluctuations are important, we show that it will be difficult to place competitive constraints on cosmological parameters with any of the considered methods.
We present results from a large volume simulation of hydrogen reionization. We combine 3D radiative transfer calculations and an N-body simulation, describing structure formation in the intergalactic ...medium, to detail the growth of H II regions around high-redshift galaxies. Our simulation tracks 1024 super(3) dark matter particles, in a box of comoving side length 65.6 Mpc h super(-1). This large volume allows us to accurately characterize the size distribution of H II regions throughout most of the reionization process. At the same time, our simulation resolves many of the small galaxies likely responsible for reionization. It confirms a picture anticipated by analytic models: H II regions grow collectively around highly clustered sources and have a well-defined characteristic size, which evolves from a sub-Mpc scale at the beginning of reionization to R > 10 Mpc toward the end. We present a detailed statistical description of our results and compare them with a numerical scheme based on the analytic model by Furlanetto and coworkers. We find that the analytic calculation reproduces the size distribution of H II regions and the 21 cm power spectrum of the radiative transfer simulation remarkably well. The ionization field from the simulation, however, has more small-scale structure than the analytic calculation, owing to Poisson scatter in the simulated abundance of galaxies on small scales. We propose and validate a simple scheme to incorporate this scatter into our calculations. Our results suggest that analytic calculations are sufficiently accurate to aid in predicting and interpreting the results of future 21 cm surveys. In particular, our fast numerical scheme is useful for forecasting constraints from future 21 cm surveys and in constructing mock surveys to test data analysis procedures.
ABSTRACT
We examine the effect of Lyman‐continuum photons on the 21‐cm background in the high‐redshift Universe. The brightness temperature of this transition is determined by the spin temperature ...Ts, which describes the relative populations of the singlet and triplet hyperfine states. Once the first luminous sources appear, Ts is set by the Wouthuysen–Field effect, in which Lyman‐series photons mix the hyperfine levels. Here we consider coupling through n > 2 Lyman photons. We first show that coupling (and heating) from scattering of Lyn photons is negligible, because they rapidly cascade to lower‐energy photons. These cascades can result in either a Lyα photon – which will then affect Ts according to the usual Wouthuysen–Field mechanism – or photons from the 2 s → 1 s continuum, which escape without scattering. We show that a proper treatment of the cascades delays the onset of strong Wouthuysen–Field coupling and affects the power spectrum of brightness fluctuations when the overall coupling is still relatively weak (i.e., around the time of the first stars). Cascades damp fluctuations on small scales because only ∼1/3 of Lyn photons cascade through Lyα, but they do not affect the large‐scale power because that arises from those photons that redshift directly into the Lyα transition. We also comment on the utility of Lyn transitions in providing ‘standard rulers’ with which to study the high‐redshift unvierse.
During the epoch of reionization, local variations in the ionized fraction (patchiness) imprint arcminute-scale temperature anisotropies in the CMB through the kinetic Sunyaev-Zel'dovich (kSZ) ...effect. We employ an improved version of an analytic model of reionization devised by Furlanetto and coworkers to calculate the kSZ anisotropy from patchy reionization. This model uses extended Press-Schechter theory to determine the distribution and evolution of H II bubbles and produces qualitatively similar reionization histories to those seen in recent numerical simulations. We find that the angular power spectrum of the kSZ anisotropies depends strongly on the size distribution of the H II bubbles and on the duration of reionization. In addition, we show that upcoming measurements of the kSZ effect should be able to distinguish between several popular reionization scenarios. In particular, the amplitude of the patchy power spectrum for reionization scenarios in which the IGM is significantly ionized by Population III stars (or by miniquasars/decaying particles) can be larger (or smaller) by over a factor of 3 than the amplitude in more traditional reionization histories (with temperature anisotropies that range between 0.5 and 3 kK at l = 5000). We highlight the differences in the kSZ signal between many possible reionization morphologies and discuss the constraints that future observations of the kSZ will place on this epoch.
We re-examine scattering of photons near the Lyα resonance in the intergalactic medium (IGM). We first derive a general integral solution for the radiation field around resonance within the usual ...Fokker–Planck approximation. Our solution shows explicitly that recoil and spin diffusivity source an absorption feature, whose magnitude increases with the relative importance of recoil compared to Doppler broadening. This spectrum depends on the Lyα line profile, but approximating it with the absorption profile appropriate to the Lorentzian wings of natural broadening accurately reproduces the results for a full Voigt profile so long as the IGM temperature is less than ∼1000 K. This approximation allows us to obtain simple analytic formulae for the total scattering rate of Lyα photons and the accompanying energy exchange rate. Our power series solutions converge rapidly for photons that redshift into the Lyα resonance as well as for photons injected at line centre. We confirm previous calculations showing that heating through this mechanism is quite slow and probably negligible compared to other sources. We then show that energy exchange during the scattering of higher-order Lyman-series photons can be much more important than naively predicted by recoil arguments. However, the resulting heating is still completely negligible.
ABSTRACT
We present an analytical model for the sizes of voids in the galaxy distribution. Peebles and others have recently emphasized the possibility that the observed characteristics of voids may ...point to a problem in galaxy formation models, but testing these claims has been difficult without any clear predictions for their properties. In order to address such questions, we build a model to describe the distribution of galaxy underdensities. Our model is based on the ‘excursion set formalism’, the same technique used to predict the dark matter halo mass function. We find that, because of bias, galaxy voids are typically significantly larger than dark matter voids and should fill most of the Universe. We show that voids selected from catalogues of luminous galaxies should be larger than those selected from faint galaxies: the characteristic radii range from ∼5 to 10 h−1 Mpc for galaxies with absolute r‐band magnitudes Mr− 5 log h < −16 to −20. These are reasonably close to, although smaller than, the observed sizes. The discrepancy may result from the void selection algorithm or from their internal structure. We also compute the halo populations inside voids. We expect small haloes (M≲ 1011 M⊙) to be up to a factor of 2 less underdense than the haloes of normal galaxies. Within large voids, the mass function is nearly independent of the size of the underdensity, but finite‐size effects play a significant role in small voids (≲7 h−1 Mpc).
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