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George D. Becker

Publications and source records attributed to George D. Becker.

At least 55 records · Page 3Linked to original sources

The Sherwood-Relics simulations: overview and impact of patchy reionization and pressure smoothing on the intergalactic medium

We present the Sherwood-Relics simulations, a new suite of large cosmological hydrodynamical simulations aimed at modelling the intergalactic medium (IGM) during and after the cosmic reionization of hydrogen. The suite consists of over 200 simulations that cover a wide range of astrophysical and cosmological parameters. It also includes simulations that use a new lightweight hybrid scheme for treating radiative transfer effects. This scheme follows the spatial variations in the ionizing radiation field, as well as the associated fluctuations in IGM temperature and pressure smoothing. It is computationally much cheaper than full radiation hydrodynamics simulations and circumvents the difficult task of calibrating a galaxy formation model to observational constraints on cosmic reionization. Using this hybrid technique, we study the spatial fluctuations in IGM properties that are seeded by patchy cosmic reionization. We investigate the relevant physical processes and assess their impact on the z > 4 Lyman-alpha forest. Our main findings are: (i) Consistent with previous studies patchy reionization causes large scale temperature fluctuations that persist well after the end of reionization, (ii) these increase the Lyman-alpha forest flux power spectrum on large scales, and (iii) result in a spatially varying pressure smoothing that correlates well with the local reionization redshift. (iv) Structures evaporated or puffed up by photoheating cause notable features in the Lyman-alpha forest, such as flat-bottom or double-dip absorption profiles.

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The XQR-30 Metal Absorber Catalog: 778 Absorption Systems Spanning 2 < z < 6.5

Intervening metal absorption lines in the spectra of z > 6 quasars are fundamental probes of the ionization state and chemical composition of circumgalactic and intergalactic gas near the end of the reionization epoch. Large absorber samples are required to robustly measure typical absorber properties and to refine models of the synthesis, transport, and ionization of metals in the early Universe. The "Ultimate XSHOOTER legacy survey of quasars at z~5.8-6.6" (XQR-30) has obtained high signal-to-noise spectra of 30 luminous quasars, nearly quadrupling the existing sample of 12 high quality z~6 quasar spectra. We use this unprecedented sample to construct a catalog of 778 systems showing absorption in one or more of MgII (360 systems), FeII (184), CII (46), CIV (479), SiIV (127), and NV (13) which span 2 < z < 6.5. This catalog significantly expands on existing samples of z > 5 absorbers, especially for CIV and SiIV which are important probes of the ionizing photon background at high redshift. The sample is 50% (90%) complete for rest-frame equivalent widths W > 0.03AA (0.09AA). We publicly release the absorber catalog along with completeness statistics and a Python script to compute the absorption search path for different ions and redshift ranges. This dataset is a key legacy resource for studies of enriched gas from the era of galaxy assembly to cosmic noon, and paves the way for even higher redshift studies with the James Webb Space Telescope and 30m-class telescopes.

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Long Dark Gaps in the Ly$β$ Forest at $z<6$: Evidence of Ultra Late Reionization from XQR-30 Spectra

We present a new investigation of the intergalactic medium (IGM) near reionization using dark gaps in the Lyman-$β$ (Ly$β$) forest. With its lower optical depth, Ly$β$ offers a potentially more sensitive probe to any remaining neutral gas compared to commonly used Ly$α$ line. We identify dark gaps in the Ly$β$ forest using spectra of 42 QSOs at $z_{\rm em}>5.5$, including new data from the XQR-30 VLT Large Programme. Approximately $40\%$ of these QSO spectra exhibit dark gaps longer than $10h^{-1}{\rm Mpc}$ at $z\simeq5.8$. By comparing the results to predictions from simulations, we find that the data are broadly consistent both with models where fluctuations in the Ly$α$ forest are caused solely by ionizing ultraviolet background (UVB) fluctuations and with models that include large neutral hydrogen patches at $z<6$ due to a late end to reionization. Of particular interest is a very long ($L=28h^{-1}{\rm Mpc}$) and dark ($τ_{\rm eff} \gtrsim 6$) gap persisting down to $z\simeq 5.5$ in the Ly$β$ forest of the $z_{\rm}=5.85$ QSO PSO J025$-$11. This gap may support late reionization models with a volume-weighted average neutral hydrogen fraction of $ \langle x_{\rm HI}\rangle \gtrsim 5\%$ by $z=5.6$. Finally, we infer constraints on $\langle x_{\rm HI}\rangle$ over $5.5 \lesssim z \lesssim 6.0$ based on the observed Ly$β$ dark gap length distribution and a conservative relationship between gap length and neutral fraction derived from simulations. We find $\langle x_{\rm HI}\rangle \leq 0.05$, 0.17, and 0.29 at $z\simeq 5.55$, 5.75, and 5.95, respectively. These constraints are consistent with models where reionization ends significantly later than $z = 6$.

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Hydrogen reionisation ends by $z=5.3$: Lyman-$α$ optical depth measured by the XQR-30 sample

The presence of excess scatter in the Ly-$α$ forest at $z\sim 5.5$, together with the existence of sporadic extended opaque Gunn-Peterson troughs, has started to provide robust evidence for a late end of hydrogen reionisation. However, low data quality and systematic uncertainties complicate the use of Ly-$α$ transmission as a precision probe of reionisation's end stages. In this paper, we assemble a sample of 67 quasar sightlines at $z>5.5$ with high signal-to-noise ratios of $>10$ per $\leq 15$ km s$^{-1}$ spectral pixel, relying largely on the new XQR-30 quasar sample. XQR-30 is a large program on VLT/X-Shooter which obtained deep (SNR $>20$ per pixel) spectra of 30 quasars at $z>5.7$. We carefully account for systematics in continuum reconstruction, instrumentation, and contamination by damped Ly-$α$ systems. We present improved measurements of the mean Ly-$α$ transmission over $4.9 3.5 σ$). Our results indicate that reionisation-related fluctuations, whether in the UVB, residual neutral hydrogen fraction, and/or IGM temperature, persist in the intergalactic medium until at least $z=5.3$ ($t=1.1$ Gyr after the Big Bang). This is further evidence for a late end to reionisation.

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Measuring the Density Fields around Bright Quasars at $z\sim 6$ with XQR-30 Spectra

Measuring the density of the intergalactic medium using quasar sightlines in the epoch of reionization is challenging due to the saturation of Lyman-$α$ absorption. Near a luminous quasar, however, the enhanced radiation creates a proximity zone observable in the quasar spectra where the Lyman-$α$ absorption is not saturated. In this study, we use $10$ high-resolution ($R\gtrsim 10,000$) $z\sim 6$ quasar spectra from the extended XQR-30 sample to measure the density field in the quasar proximity zones. We find a variety of environments within $3$ pMpc distance from the quasars. We compare the observed density cumulative distribution function (CDF) with models from the $\textit{Cosmic Reionization on Computers}$ simulation, and find a good agreement between $1.5$ to $3$pMpc from the quasar. This region is far away from the quasar hosts and hence approaching the mean density of the universe, which allows us to use the CDF to set constraints on the cosmological parameter $σ_8=0.6\pm0.3$. The uncertainty is mainly due to the limited number of high-quality quasar sightlines currently available. Utilizing the more than $>200$ known quasars at $z\gtrsim 6$, this method will allow us in the future to tighten the constraint on $σ_8$ to the percent level. In the region closer to the quasar within $1.5$ pMpc, we find the density is higher than predicted in the simulation by $1.23 \pm 0.17$, suggesting the typical host dark matter halo mass of a bright quasar ($M_{\rm 1450}<-26.5$) at $z\sim 6$ is $\log_{\rm 10} (M/M_\odot)=12.5^{+0.4}_{-0.7}$.

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Constraints on the End of Reionization from the Density Fields Surrounding Two Highly Opaque Quasar Sightlines

The observed large-scale scatter in Lyman $α$ opacity of the intergalactic medium at $z<6$ implies large fluctuations in the neutral hydrogen fraction that are unexpected long after reionization has ended. A number of models have emerged to explain these fluctuations that make testable predictions for the relationship between Ly$α$ opacity and density. We present selections of $z=5.7$ Ly$α$-emitting galaxies (LAEs) in the fields surrounding two highly opaque quasar sightlines with long Ly$α$ troughs. The fields lie towards the $z=6.0$ quasar ULAS J0148+0600, for which we re-analyze previously published results using improved photometric selection, and towards the $z=6.15$ quasar SDSS J1250+3130, for which results are presented here for the first time. In both fields, we report a deficit of LAEs within 20 $h^{-1}$ Mpc of the quasar. The association of highly opaque sightlines with galaxy underdensities in these two fields is consistent with models in which the scatter in Ly$α$ opacity is driven by large-scale fluctuations in the ionizing UV background, or by an ultra-late reionization that has not yet concluded at $z=5.7$.

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SDSS J1059+4251, a highly magnified z ~ 2.8 star-forming galaxy: ESI observations of the rest-frame UV spectrum

Detailed analyses of high-redshift galaxies are challenging due to their faintness, but this difficulty can be overcome with gravitational lensing, in which the magnification of the flux enables high signal-to-noise ratio (S/N) spectroscopy. We present the rest-frame ultraviolet (UV) Keck Echellette Spectrograph and Imager (ESI) spectrum of the newly discovered z = 2.79 lensed galaxy SDSS J1059+4251. With an observed magnitude F814W = 18.8 and a magnification factor μ= 31 \pm 3, J1059+4251 is both highly magnified and intrinsically luminous, about two magnitudes brighter than M* at z ~ 2-3. With stellar mass M* = (3.22 \pm 0.20) \times 10^10 M_sun, UV star formation rate SFR=50 \pm 7 M_sun yr^-1, and stellar metallicity Z*~ 0.15-0.5 Z_sun, J1059+4251 is typical of bright star-forming galaxies at similar redshifts. Thanks to the high S/N and the spectral resolution of the ESI spectrum, we are able to separate the interstellar and stellar features and derive properties that would be inaccessible without the aid of the lensing. We find evidence of a gas outflow with speeds up to -1000 km s^-1, and of an inflow that is probably due to accreting material seen along a favorable line of sight. We measure relative elemental abundances from the interstellar absorption lines and find that alpha-capture elements are overabundant compared to iron-peak elements, suggestive of rapid star formation. However, this trend may also be affected by dust depletion. Thanks to the high data quality, our results represent a reliable step forward in the characterization of typical galaxies at early cosmic epochs.

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A short mean free path at $z=6$ favors late and rapid reionization by faint galaxies

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 background, favors a late reionization process in which the neutral fraction evolved rapidly in the latter half. We also argue that the short $λ_{912}^{\rm mfp}(z=6)$ points to faint galaxies as the primary drivers of reionizaton. Our preferred model, with $λ_{912}^{\rm mfp}(z=6) = 6.5$ Mpc/$h$, has a midpoint of $z= 7.1$ and ends at $z= 5.1$. It requires 3 ionizing photons per H atom to complete reionization and a LyC photon production efficiency of $\log(f^{\rm eff}_{\rm esc} ξ_{\rm ion}/[\mathrm{erg}^{-1} \mathrm{Hz}]) = 24.8$ at $z>6$. Recovering $λ_{912}^{\rm mfp}(z=6)$ as low as the measured central value may require an increase in IGM clumpiness beyond predictions from simulations, with a commensurate increase in the photon budget.

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The mean free path of ionizing photons at 5 < z < 6: evidence for rapid evolution near reionization

The mean free path of ionizing photons, $λ_{\rm mfp}$, is a key factor in the photoionization of the intergalactic medium (IGM). At $z \gtrsim 5$, however, $λ_{\rm mfp}$ may be short enough that measurements towards QSOs are biased by the QSO proximity effect. We present new direct measurements of $λ_{\rm mfp}$ that address this bias and extend up to $z \sim 6$ for the first time. Our measurements at $z \sim 5$ are based on data from the Giant Gemini GMOS survey and new Keck LRIS observations of low-luminosity QSOs. At $z \sim 6$ we use QSO spectra from Keck ESI and VLT X-Shooter. We measure $λ_{\rm mfp} = 9.09^{+1.62}_{-1.28}$ proper Mpc and $0.75^{+0.65}_{-0.45}$ proper Mpc (68% confidence) at $z = 5.1$ and 6.0, respectively. The results at $z = 5.1$ are consistent with existing measurements, suggesting that bias from the proximity effect is minor at this redshift. At $z = 6.0$, however, we find that neglecting the proximity effect biases the result high by a factor of two or more. Our measurement at $z = 6.0$ falls well below extrapolations from lower redshifts, indicating rapid evolution in $λ_{\rm mfp}$ over $5 < z < 6$. This evolution disfavors models in which reionization ended early enough that the IGM had time to fully relax hydrodynamically by $z = 6$, but is qualitatively consistent with models wherein reionization completed at $z = 6$ or even significantly later. Our mean free path results are most consistent with late reionization models wherein the IGM is still 20% neutral at $z=6$, although our measurement at $z = 6.0$ is even lower than these models prefer.

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Chasing the Tail of Cosmic Reionization with Dark Gap Statistics in the Ly$α$ Forest over $5 < z < 6$

We present a new investigation of the intergalactic medium (IGM) near the end of reionization using "dark gaps" in the Lyman-alpha (Ly$α$) forest. Using spectra of 55 QSOs at $z_{\rm em}>5.5$, including new data from the XQR-30 VLT Large Programme, we identify gaps in the Ly$α$ forest where the transmission averaged over 1 comoving $h^{-1}\,{\rm Mpc}$ bins falls below 5%. Nine ultra-long ($L > 80~h^{-1}\,{\rm Mpc}$) dark gaps are identified at $z<6$. In addition, we quantify the fraction of QSO spectra exhibiting gaps longer than $30~h^{-1}\,{\rm Mpc}$, $F_{30}$, as a function of redshift. We measure $F_{30} \simeq 0.9$, 0.6, and 0.15 at $z = 6.0$, 5.8, and 5.6, respectively, with the last of these long dark gaps persisting down to $z \simeq 5.3$. Comparing our results with predictions from hydrodynamical simulations, we find that the data are consistent with models wherein reionization extends significantly below redshift six. Models wherein the IGM is essentially fully reionized that retain large-scale fluctuations in the ionizing UV background at $z \lesssim 6$ are also potentially consistent with the data. Overall, our results suggest that signature of reionization in the form of islands of neutral hydrogen and/or large-scale fluctuations in the ionizing background remain present in the IGM until at least $z \simeq 5.3$.

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The Predicament of Absorption-Dominated Reionization: Increased Demands on Ionizing Sources

The reionization epoch concludes when ionizing photons reach every corner of the Universe. Reionization has generally been assumed to be limited primarily by the rate at which galaxies produce ionizing photons, but the recent measurement of a surprisingly short ionizing photon mean free path of $0.75^{+0.65}_{-0.45}$ proper Mpc at $z = 6$ by Becker et al. (2021) suggests that absorption by residual neutral hydrogen in the otherwise ionized intergalactic medium may play a much larger role than previously expected. Here we show that consistency between this short mean free path and the coeval dark pixel fraction in the Ly$α$ forest requires a cumulative output of $6.1^{+11}_{-2.4}$ ionizing photons per baryon by reionization's end. This represents a dramatic increase in the ionizing photon budget over previous estimates, greatly exacerbating the tension with measurements of the ionizing output from galaxies at later times. Translating this constraint into the instantaneous ionizing production from galaxies in our model, we find $\log_{10}f_{\rm esc}ξ_{\rm ion}/\text{(erg/Hz)}^{-1} =25.02_{-0.21}^{+0.45}$ at $z\sim6$. Even with optimistic assumptions about the ionizing production efficiency of early stellar populations, and assuming the galaxy luminosity function extends to extremely faint sources ($M_{\text{UV}}\leq-11$), complete reionization requires the escape fraction of ionizing photons to exceed $20\%$ across the galaxy population. This is far larger than observed in any galaxy population at lower redshifts, requiring rapid evolution in galaxy properties after the first billion years of cosmic time. This tension cannot be completely relieved within existing observational constraints on the hydrogen neutral fraction and mean free path.

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Sub-damped Lyman alpha systems in the XQ-100 survey II -- Chemical evolution at 2.4<z<4.3

We present the measured gas-phase metal column densities in 155 sub-damped Lyman alpha systems (subDLAs) with the aim to investigate the contribution of subDLAs to the chemical evolution of the Universe. The sample was identified within the absorber-blind XQ-100 quasar spectroscopic survey over the redshift range 2.4<=z<=4.3. Using all available column densities of the ionic species investigated (mainly CIV, SiII, MgII, SiIV, AlII, FeII, CII, and OI; in order of decreasing detection frequency), we estimate the ionization-corrected gas-phase metallicity of each system using Markov Chain Monte Carlo techniques to explore a large grid of Cloudy ionization models. Without accounting for ionization and dust depletion effects, we find that the HI-weighted gas-phase metallicity evolution of subDLAs are consistent with damped Lyman alpha systems (DLAs). When ionization corrections are included, subDLAs are systematically more metal-poor than DLAs (between ~0.5 sigma and ~3 sigma significance) by up to ~1.0 dex over the redshift range 3<=z<=4.3. The correlation of gas-phase [Si/Fe] with metallicity in subDLAs appears to be consistent with that of DLAs, suggesting that the two classes of absorbers have a similar relative dust depletion pattern. As previously seen for Lyman limit systems, the gas-phase [C/O] in subDLAs remains constantly solar for all metallicities indicating that both subDLAs and Lyman limit systems could trace carbon-rich ejecta, potentially in circumgalactic environments.

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Probing the thermal state of the intergalactic medium at $z>5$ with the transmission spikes in high-resolution Ly$α$ forest spectra

We compare a sample of five high-resolution, high S/N Ly$α$ forest spectra of bright $6 5$ with those obtained from mock absorption spectra from the Sherwood and Sherwood-Relics suites of hydrodynamical simulations of the intergalactic medium (IGM). We use a profile fitting procedure for the inverted transmitted flux, $1-F$, similar to the widely used Voigt profile fitting of the transmitted flux $F$ at lower redshifts, to characterise the transmission spikes that probe predominately underdense regions of the IGM. We are able to reproduce the width and height distributions of the transmission spikes, both with optically thin simulations of the post-reionization Universe using a homogeneous UV background and full radiative transfer simulations of a late reionization model. We find that the width of the fitted components of the simulated transmission spikes is very sensitive to the instantaneous temperature of the reionized IGM. The internal structures of the spikes are more prominant in low temeperature models of the IGM. The width distribution of the observed transmission spikes, which require high spectral resolution ($\leq $ 8 km/s) to be resolved, is reproduced for optically thin simulations with a temperature at mean density of $T_0= (11000 \pm 1600,10500\pm 2100,12000 \pm 2200)$ K at $z= (5.4,5.6,5.8)$. This is weakly dependent on the slope of the temperature-density relation, which is favoured to be moderately steeper than isothermal. In the inhomogeneous, late reionization, full radiative transfer simulations where islands of neutral hydrogen persist to $z\sim5.3$, the width distribution of the observed transmission spikes is consistent with the range of $T_0$ caused by spatial fluctuations in the temperature-density relation.

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Sub-damped Lyman alpha systems in the XQ-100 survey I -- Identification and contribution to the cosmological HI budget

Sub-damped Lyman alpha systems (subDLAs; HI column densities of 19.0<=logN(HI)<20.3) are rarely included in the cosmic HI census performed at redshifts z>=1.5, yet are expected to contribute significantly to the overall HI mass budget of the Universe. In this paper, we present a blindly selected sample of 155 subDLAs found along 100 quasar sightlines (with a redshift path length X=475) in the XQ-100 survey to investigate the contribution of subDLAs to the HI mass density of the Universe. The impact of X-Shooter's spectral resolution on sub-DLA identification is evaluated, and found to be sufficient for reliably finding absorbers with logN(HI)>=18.9. We compared the implications of searching for subDLAs solely using HI absorption versus the use of additional metal lines to confirm the identification, and found that metal-selection techniques would have missed 75 subDLAs. Using a bootstrap-Monte Carlo simulation, we computed the column density distribution function (f(N,X)) and the cosmological HI mass density of subDLAs and compared with our previous work based on the XQ-100 damped Lyman alpha systems. We do not find any significant redshift evolution in f(N,X) or cosmological HI mass density for subDLAs. However, subDLAs contribute 10-20 per cent of the total cosmological HI mass density measured at redshifts 2<z<5 (agreeing with previous measurements), and thus have a small but significant contribution to the HI budget of the Universe.

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The Evolution of O I over 3.2 < z < 6.5: Reionization of the Circumgalactic Medium

We present a survey for metal absorption systems traced by neutral oxygen over $3.2 < z < 6.5$. Our survey uses Keck/ESI and VLT/X-Shooter spectra of 199 QSOs with redshifts up to 6.6. In total we detect 74 O I absorbers, of which 57 are separated from the background QSO by more than 5000 km/s. We use a maximum likelihood approach to fit the distribution of O I $λ$1302 equivalent widths in bins of redshift, and from this determine the evolution in number density of absorbers with $W_{1302} > 0.05$ angstroms. We find that the number density does not monotonically increase with decreasing redshift, as would naively be expected from the buildup of metal-enriched circumgalactic gas with time. The number density over $4.9 < z < 5.7$ is a factor of 1.7--4.1 lower (68% confidence) than over $5.7 < z < 6.5$, with a lower value at $z < 5.7$ favored with 99% confidence. This decrease suggests that the fraction of metals in a low-ionization phase is larger at $z \sim 6$ than at lower redshifts. Absorption from highly ionized metals traced by C IV is also weaker in higher-redshift O I systems, supporting this picture. The evolution of O I absorbers implies that metal-enriched circumgalactic gas at $z \sim 6$ is undergoing an ionization transition driven by a strengthening ultraviolet background. This in turn suggests that the reionization of the diffuse intergalactic medium may still be ongoing at or only recently ended by this epoch.

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Studying the Reionization Epoch with QSO Absorption Lines

Absorption signatures in the spectra of QSOs are one of our most powerful tools for studying galactic and intergalactic environments at high redshifts. With the discovery of QSOs out to z > 7, QSO absorption lines are now tracing the end stages of reionization on multiple fronts using the hydrogen Lyman-$α$ forest and heavy element absorbers. Next-generation QSO absorption line studies with large optical/IR telescopes will reveal in detail how the first galaxies emerged form the cosmic web, transformed their circum- and inter-galactic environments, and completed the last major phase transition of the Universe. These efforts will complement other upcoming studies of reionization, such as those with JWST, ALMA, and redshifted 21cm experiments.

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Revealing reionization with the thermal history of the intergalactic medium: new constraints from the Lyman-$α$ flux power spectrum

We present a new investigation of the thermal history of the intergalactic medium (IGM) during and after reionization using the Lyman-$α$ forest flux power spectrum at $4.0\lesssim z\lesssim5.2$. Using a sample of 15 high-resolution spectra, we measure the flux power down to the smallest scales ever probed at these redshifts ($-1\lesssim \log(k/$km$^{-1}$s)$\lesssim -0.7$). These scales are highly sensitive to both the instantaneous temperature of the IGM and the total energy injected per unit mass during and after reionization. We measure temperatures at the mean density of $T_{0}\sim7000$-8000 K, consistent with no significant temperature evolution for redshifts $4.2\lesssim z\lesssim5.0$. We also present the first observational constraints on the integrated IGM thermal history, finding that the total energy input per unit mass increases from $u_{0}\sim4.6$ ${\rm eV}$ $m_{\rm p}^{-1}$ to 7.3 eV $m_{\rm p}^{-1}$ from $z\sim 6$ to $4.2$ assuming a $Λ$-CDM cosmology. We show how these results can be used simultaneously to obtain information on the timing and the sources of the reionization process. Our first proof of concept using simplistic models of instantaneous reionization produces results comparable to and consistent with the recent Planck constraints, favoring models with $z_{\rm rei}\sim 8.5^{+1.1}_{-0.8}$.

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New Constraints on the free-streaming of warm dark matter from intermediate and small scale Lyman-$α$ forest data

We present new measurements of the free-streaming of warm dark matter (WDM) from Lyman-$α$ flux-power spectra. We use data from the medium resolution, intermediate redshift XQ-100 sample observed with the X-shooter spectrograph ($z=3 - 4.2$) and the high-resolution, high-redshift sample used in Viel et al. (2013) obtained with the HIRES/MIKE spectrographs ($z=4.2 - 5.4$). Based on further improved modelling of the dependence of the Lyman-$α$ flux-power spectrum on the free-streaming of dark matter, cosmological parameters, as well as the thermal history of the intergalactic medium (IGM) with hydrodynamical simulations, we obtain the following limits, expressed as the equivalent mass of thermal relic WDM particles. The XQ-100 flux power spectrum alone gives a lower limit of 1.4 keV, the re-analysis of the HIRES/MIKE sample gives 4.1 keV while the combined analysis gives our best and significantly strengthened lower limit of 5.3 keV (all 2$σ$ C.L.). The further improvement in the joint analysis is partly due to the fact that the two data sets have different degeneracies between astrophysical and cosmological parameters that are broken when the data sets are combined, and more importantly on chosen priors on the thermal evolution. These results all assume that the temperature evolution of the IGM can be modelled as a power law in redshift. Allowing for a non-smooth evolution of the temperature of the IGM with sudden temperature changes of up to 5000K reduces the lower limit for the combined analysis to 3.5 keV. A WDM with smaller thermal relic masses would require, however, a sudden temperature jump of $5000\,K$ or more in the narrow redshift interval $z=4.6-4.8$, in disagreement with observations of the thermal history based on high-resolution resolution Lyman-$α$ forest data and expectations for photo-heating and cooling in the low density IGM at these redshifts.

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