arXiv subjects

Frederick B. Davies

Publications and source records attributed to Frederick B. Davies.

126 records · Page 7Linked to original sources

arXiv2018

Exploring Reionization-Era Quasars III: Discovery of 16 Quasars at $6.4\lesssim z \lesssim 6.9$ with DESI Legacy Imaging Surveys and UKIRT Hemisphere Survey and Quasar Luminosity Function at $z\sim6.7$

This is the third paper in a series aims at finding reionzation-era quasars with the combination of DESI Legacy imaging Surveys (DELS) and near-infrared imaging surveys, such as the UKIRT Hemisphere Survey (UHS), as well as the Wide-field Infrared Survey Explore ($WISE$) mid-infrared survey. In this paper, we describe the updated quasar candidate selection procedure, report the discovery of 16 quasars at $6.4\lesssim z \lesssim6.9$ from area of $\sim$13,020 deg$^2$, and present the quasar luminosity function (QLF) at $z\sim6.7$. The measured QLF follows $Φ(L_{1450})\propto L_{1450}^{-2.35}$ in the magnitude range $27.6<M_{1450}<-25.5$. We determine the quasar comoving spatial density at $\langle z \rangle$=6.7 and $M_{1450}<-26.0$ to be $\rm 0.39\pm0.11 Gpc^{-3}$ and find that the exponential density evolution parameter to be $k=-0.78\pm0.18$ from $z\sim6$ to $z\sim6.7$, corresponding to a rapid decline by a factor of $\sim 6$ per unit redshift towards earlier epoch, a rate significantly faster than that at $z\sim 3- 5$. The cosmic time between $z\sim6$ and $z\sim6.7$ is only 121 Myrs. The quasar density declined by a factor of more than three within such short time requires that SMBHs must grow rapidly or they are less radiatively efficient at higher redshifts. We measured quasar comoving emissivity at $z\sim6.7$ which indicate that high redshift quasars are highly unlikely to make a significant contribution to hydrogen reionization. The broad absorption line (BAL) quasar fraction at $z\gtrsim6.5$ is measured to be $\gtrsim$22%. In addition, we also report the discovery of additional five quasars at $z\sim6$ in the appendix.

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arXiv2018

The Opacity of the Intergalactic Medium Measured Along Quasar Sightlines at $z\sim 6$

We publicly release a new sample of $34$ medium resolution quasar spectra at $5.77\leq z_{\rm em}\leq6.54$ observed with the Echellette Spectrograph and Imager (ESI) on the Keck telescope. This quasar sample represents an ideal laboratory to study the intergalactic medium (IGM) during the end stages of the epoch of reionization, and constrain the timing and morphology of the phase transition. For a subset of $23$ of our highest signal-to-noise ratio spectra (S/N$>7$, per $10\,{\rm km\,s^{-1}}$ pixel), we present a new measurement of the Lyman-$α$ (Ly$α$) forest opacity spanning the redshift range $4.8\lesssim z\lesssim6.3$. We carefully eliminate spectral regions that could be causing biases in our measurements due to additional transmitted flux in the proximity zone of the quasars, or extra absorption caused by strong intervening absorption systems along the line of sight. We compare the observed evolution of the IGM opacity with redshift to predictions from a hydrodynamical simulation with uniform ultraviolet background (UVB) radiation, as well as two semi-numerical patchy reionization models, one with a fluctuating UVB and another with a fluctuating temperature field. Our measurements show a steep rise in opacity at $z\gtrsim5.0$ and an increased scatter and thus support the picture of a spatially inhomogeneous reionization process, consistent with previous work. However, we measure significantly higher optical depths at $5.3\lesssim z\lesssim5.7$ than previous studies, which reduces the contrast between the highest opacity Gunn-Peterson troughs and the average opacity trend of the IGM, which may relieve some of the previously noted tension between these measurements and reionization models.

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arXiv2018

First Spectroscopic Study of a Young Quasar

The quasar lifetime $t_{\rm\,Q}$ is one of the most fundamental quantities for understanding quasar evolution and the growth of supermassive black holes (SMBHs), but remains uncertain by several orders of magnitude. In a recent study we uncovered a population of very young quasars ($t_{\rm Q}\lesssim10^4-10^5$ yr), based on the sizes of their proximity zones, which are regions of enhanced Ly$α$ forest transmission near the quasar resulting from its own ionizing radiation. The presence of such young objects poses significant challenges to models of SMBH formation, which already struggle to explain the existence of SMBHs at such early cosmic epochs. We conduct the first comprehensive spectroscopic study of the youngest quasar known, $\rm SDSS\,J1335+3533$ at $z=5.9012$, whose lifetime is $t_{\rm Q}<10^4$ yr ($95\%$ confidence). A careful search of our deep optical and near-infrared spectra for HI and metal absorption lines allows us to convincingly exclude that its small proximity zone results from an associated absorption system rather than a short lifetime. We use the MgII emission line to measure its black hole mass $M_{\rm BH}=(4.09\pm0.58)\times 10^9 M_{\odot}$, implying an Eddington ratio of $0.30\pm0.04$ -- comparable to other co-eval quasars. We similarly find that the relationship between its black hole mass and dynamical mass are consistent with other $z\sim6$ quasars. The only possible anomaly associated with youth are its weak emission lines, but larger samples are needed to shed light on a potential causal connection. We discuss the implications of short lifetimes for various SMBH growth scenarios, and argue that future observations of young quasars with JWST could distinguish between them.

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arXiv2018

Evidence for Large-Scale Fluctuations in the Metagalactic Ionizing Background Near Redshift Six

The observed scatter in intergalactic Lyman-$α$ opacity at $z \lesssim 6$ requires large-scale fluctuations in the neutral fraction of the intergalactic medium (IGM) after the expected end of reionization. Post-reionization models that explain this scatter invoke fluctuations in either the ionizing ultraviolet background (UVB) or IGM temperature. These models make very different predictions, however, for the relationship between Lyman-$α$ opacity and local density. Here we test these models using Lyman-$α$ emitting galaxies (LAEs) to trace the density field surrounding the longest and most opaque known Lyman-$α$ trough at $z < 6$. Using deep Subaru Hyper Suprime-Cam narrow-band imaging, we find a highly significant deficit of $z \simeq 5.7$ LAEs within 20 Mpc/$h$ of the trough. The results are consistent with a model in which the scatter in Lyman-$α$ opacity near $z \sim 6$ is driven by large-scale UVB fluctuations, and disfavor a scenario in which the scatter is primarily driven by variations in IGM temperature. UVB fluctuations at this epoch present a boundary condition for reionization models, and may help shed light on the nature of the ionizing sources.

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arXiv2018

Large Fluctuations in the High-Redshift Metagalactic Ionizing Background

Recent observations have shown that the scatter in opacities among coeval segments of the Lyman-alpha forest increases rapidly at z > 5. In this paper, we assess whether the large scatter can be explained by fluctuations in the ionizing background in the post-reionization intergalactic medium. We find that matching the observed scatter at z ~ 5.5 requires a short spatially averaged mean free path of < 15 comoving Mpc/h, a factor of > 3 shorter than direct measurements at z ~ 5.2. We argue that such rapid evolution in the mean free path is difficult to reconcile with our measurements of the global H I photoionization rate, which stay approximately constant over the interval z ~ 4.8 - 5.5. However, we also show that measurements of the mean free path at z > 5 are likely biased towards higher values by the quasar proximity effect. This bias can reconcile the short values of the mean free path that are required to explain the large scatter in opacities. We discuss the implications of this scenario for cosmological reionization. Finally, we investigate whether other statistics applied to the z > 5 Lyman-alpha forest can shed light on the origin of the scatter. Compared to a model with a uniform ionizing background, models that successfully account for the scatter lead to enhanced power in the line-of-sight flux power spectrum on scales k < 0.1 h/Mpc. We find tentative evidence for this enhancement in observations of the high-redshift Lyman-alpha forest.

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arXiv2018

The Structure and Dynamics of the Sub-parsec Scale Jet in M87 Based on 50 VLBA Observations Over 17 Years at 43 GHz

The central radio source in M87 provides the best opportunity to study jet formation because it has a large angular size for the gravitational radius of the black hole and has a bright jet that is well resolved by VLBI observations. We present intensive monitoring observations from 2007 and 2008, plus roughly annual observations that span 17 years, all made with the the Very Long Baseline Array at 43 GHz with a resolution of about 30 by 60 Rs. Our high-dynamic-range images clearly show the wide-opening-angle structure and the counter-jet. The jet and counter-jet are nearly symmetric in the inner 1.5 milli-arcseconds (mas; 0.12 pc in projection) with both being edge brightened. Both show deviations from parabolic shape in the form of an initial rapid expansion and subsequent contraction followed by further rapid expansion and, beyond the visible counter-jet, subsequent collimation. Proper motions and counter-jet/jet intensity ratios both indicate acceleration from apparent speeds of $\lesssim 0.5c$ to $\gtrsim 2c$ in the inner about 2 mas and suggest a helical flow. The jet displays a sideways shift with an approximately 8 to 10 year quasi-periodicity. The shift propagates outwards non-ballistically and significantly more slowly than the flow speed revealed by the fastest moving components. Polarization data show a systematic structure with magnetic field vectors that suggest a toroidal field close to the core.

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arXiv2018

Quantitative Constraints on the Reionization History from the IGM Damping Wing Signature in Two Quasars at z > 7

During reionization, neutral hydrogen in the intergalactic medium (IGM) imprints a damping wing absorption feature on the spectrum of high-redshift quasars. A detection of this signature provides compelling evidence for a significantly neutral Universe, and enables measurements of the hydrogen neutral fraction $x_{\rm HI}(z)$ at that epoch. Obtaining reliable quantitative constraints from this technique, however, is challenging due to stochasticity induced by the patchy inside-out topology of reionization, degeneracies with quasar lifetime, and the unknown unabsorbed quasar spectrum close to rest-frame Ly$α$. We combine a large-volume semi-numerical simulation of reionization topology with 1D radiative transfer through high-resolution hydrodynamical simulations of the high-redshift Universe to construct models of quasar transmission spectra during reionization. Our state-of-the-art approach captures the distribution of damping wing strengths in biased quasar halos that should have reionized earlier, as well as the erosion of neutral gas in the quasar environment caused by its own ionizing radiation. Combining this detailed model with our new technique for predicting the quasar continuum and its associated uncertainty, we introduce a Bayesian statistical method to jointly constrain the neutral fraction of the Universe and the quasar lifetime from individual quasar spectra. We apply this methodology to the spectra of the two highest redshift quasars known, ULAS J1120+0641 and ULAS J1342+0928, and measured volume-averaged neutral fractions $\langle x_{\rm HI} \rangle(z=7.09)=0.48^{+0.26}_{-0.26}$ and $\langle x_{\rm HI} \rangle(z=7.54)=0.60^{+0.20}_{-0.23}$ (posterior medians and 68% credible intervals) when marginalized over quasar lifetimes of $10^3 \leq t_{\rm q} \leq 10^8$ years.

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arXiv2018

Predicting Quasar Continua Near Lyman-$α$ with Principal Component Analysis

Measuring the proximity effect and the damping wing of intergalactic neutral hydrogen in quasar spectra during the epoch of reionization requires an estimate of the intrinsic continuum at rest-frame wavelengths $λ_{\rm rest}\sim1200$-$1260$ Å. In contrast to previous works which used composite spectra with matched spectral properties or explored correlations between parameters of broad emission lines, we opted for a non-parametric predictive approach based on principal component analysis (PCA) to predict the intrinsic spectrum from the spectral properties at redder (i.e. unabsorbed) wavelengths. We decomposed a sample of $12764$ spectra of $z\sim2$-$2.5$ quasars from SDSS/BOSS into 10 red-side ($1280$ Å $<λ_{\rm rest}<2900$ Å) and 6 blue-side ($1180$ Å $<λ_{\rm rest}<1280$ Å) PCA basis spectra, and constructed a projection matrix to predict the blue-side coefficients from a fit to the red-side spectrum. We found that our method predicts the blue-side continuum with $\sim6$-$12\%$ precision and $\lesssim1\%$ bias by testing on the full training set sample. We then computed predictions for the blue-side continua of the two quasars currently known at $z>7$: ULAS J1120+0641 ($z=7.09$) and ULAS J1342+0928 ($z=7.54$). Both of these quasars are known to exhibit extreme emission line properties, so we individually calibrated the precision of the continuum predictions from similar quasars in the training set. We find that both $z>7$ quasars, and in particular ULAS J1342+0928, show signs of damping wing-like absorption at wavelengths redward of Ly$α$.

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arXiv2017

Modeling the HeII Transverse Proximity Effect: Constraints on Quasar Lifetime and Obscuration

The HeII transverse proximity effect - enhanced HeII Lyα transmission in a background sightline caused by the ionizing radiation of a foreground quasar - offers a unique opportunity to probe the emission properties of quasars, in particular the emission geometry (obscuration, beaming) and the quasar lifetime. Building on the foreground quasar survey published in Schmidt+2017, we present a detailed model of the HeII transverse proximity effect, specifically designed to include light travel time effects, finite quasar ages, and quasar obscuration. We post-process outputs from a cosmological hydrodynamical simulation with a fluctuating HeII UV background model, plus the added effect of the radiation from a single bright foreground quasar. We vary the age $t_\mathrm{age}$ and obscured sky fractions $Ω_\mathrm{obsc}$ of the foreground quasar, and explore the resulting effect on the HeII transverse proximity effect signal. Fluctuations in IGM density and the UV background, as well as the unknown orientation of the foreground quasar, result in a large variance of the HeII Lyα transmission along the background sightline. We develop a fully Bayesian statistical formalism to compare far UV HeII Lyα transmission spectra of the background quasars to our models, and extract joint constraints on $t_\mathrm{age}$ and $Ω_\mathrm{obsc}$ for the six Schmidt+2017 foreground quasars with the highest implied HeII photoionization rates. Our analysis suggests a bimodal distribution of quasar emission properties, whereby one foreground quasar, associated with a strong HeII transmission spike, is relatively old $(22\,\mathrm{Myr})$ and unobscured $Ω_\mathrm{obsc}<35\%$, whereas three others are either younger than $(10\,\mathrm{Myr})$ or highly obscured $(Ω_\mathrm{obsc}>70\%)$.

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arXiv2017

Determining the Nature of Late Gunn-Peterson Troughs with Galaxy Surveys

Recent observations have discovered long (up to ~110 Mpc/h), opaque Gunn-Peterson troughs in the z ~ 5.5 Lyman-alpha forest, which are challenging to explain with conventional models of the post-reionization intergalactic medium. Here we demonstrate that observations of the galaxy populations in the vicinity of the deepest troughs can distinguish two competing models for these features: deep voids where the ionizing background is weak due to fluctuations in the mean free path of ionizing photons would show a deficit of galaxies, while residual temperature variations from extended, inhomogeneous reionization would show an overdensity of galaxies. We use large (~550 Mpc/h) semi-numerical simulations of these competing explanations to predict the galaxy populations in the largest of the known troughs at z ~ 5.7. We quantify the strong correlation of Lyman-alpha effective optical depth and galaxy surface density in both models and estimate the degree to which realistic surveys can measure such a correlation. While a spectroscopic galaxy survey is ideal, we also show that a relatively inexpensive narrowband survey of Lyman-alpha-emitting galaxies is ~90% likely to distinguish between the competing models.

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arXiv2017

Small-scale Intensity Mapping: Extended Halos as a Probe of the Ionizing Escape Fraction and Faint Galaxy Populations during Reionization

We present a new method to quantify the value of the escape fraction of ionizing photons, and the existence of ultra-faint galaxies clustered around brighter objects during the epoch of cosmic reionization, using the diffuse Ly$α$, continuum and H$α$ emission observed around galaxies at $z\sim6$. We model the surface brightness profiles of the diffuse halos considering the fluorescent emission powered by ionizing photons escaping from the central galaxies, and the nebular emission from satellite star-forming sources, by extending the formalisms developed in Mas-Ribas & Dijkstra (2016) and Mas-Ribas et al. (2017). The comparison between our predicted profiles and Ly$α$ observations at $z=5.7$ and $z=6.6$ favors a low ionizing escape fraction, $f_{\rm esc}^{\rm ion}\sim5\%$, for galaxies in the range $-19\gtrsim M_{\rm UV} \gtrsim -21.5$. However, uncertainties and possible systematics in the observations do not allow for firm conclusions. We predict H$α$ and rest-frame visible continuum observations with JWST, and show that JWST will be able to detect extended (a few tens of kpc) fluorescent H$α$ emission powered by ionizing photons escaping from a bright, $L\gtrsim 5L^*$, galaxy. Such observations can differentiate fluorescent emission from nebular emission by satellite sources. We discuss how observations and stacking of several objects may provide unique constraints on the escape fraction for faint galaxies and/or the abundance of ultra-faint radiation sources.

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arXiv2017

Implications of $z \sim 6$ Quasar Proximity Zones for the Epoch of Reionization and Quasar Lifetimes

We study quasar proximity zones in the redshift range $5.77 \leq z \leq 6.54$ by homogeneously analyzing $34$ medium resolution spectra, encompassing both archival and newly obtained data, and exploiting recently updated systemic redshift and magnitude measurements. Whereas previous studies found strong evolution of proximity zone sizes with redshift, and argued that this provides evidence for a rapidly evolving intergalactic medium (IGM) neutral fraction during reionization, we measure a much shallower trend $\propto(1+z)^{-1.44}$. We compare our measured proximity zone sizes to predictions from hydrodynamical simulations post-processed with one-dimensional radiative transfer, and find good agreement between observations and theory irrespective of the ionization state of the ambient IGM. This insensitivity to IGM ionization state has been previously noted, and results from the fact that the definition of proximity zone size as the first drop of the smoothed quasar spectrum below the $10\%$ flux transmission level probes locations where the ionizing radiation from the quasar is an order of magnitude larger than the expected ultraviolet ionizing background that sets the neutral fraction of the IGM. Our analysis also uncovered three objects with exceptionally small proximity zones (two have $R_p < 1$proper Mpc), which constitute outliers from the observed distribution and are challenging to explain with our radiative transfer simulations. We consider various explanations for their origin, such as strong absorption line systems associated with the quasar or patchy reionization, but find that the most compelling scenario is that these quasars have been shining for $\lesssim 10^5$yr.

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arXiv2017

A self-consistent 3D model of fluctuations in the helium-ionizing background

Large variations in the effective optical depth of the He II Ly$α$ forest have been observed at $z\gtrsim2.7$, but the physical nature of these variations is uncertain: either the Universe is still undergoing the process of He II reionization, or the Universe is highly ionized but the He II-ionizing background fluctuates significantly on large scales. In an effort to build upon our understanding of the latter scenario, we present a novel model for the evolution of ionizing background fluctuations. Previous models have assumed the mean free path of ionizing photons to be spatially uniform, ignoring the dependence of that scale on the local ionization state of the intergalactic medium (IGM). This assumption is reasonable when the mean free path is large compared to the average distance between the primary sources of He II-ionizing photons, $\gtrsim L_\star$ quasars. However, when this is no longer the case, the background fluctuations become more severe, and an accurate description of the average propagation of ionizing photons through the IGM requires additionally accounting for the fluctuations in opacity. We demonstrate the importance of this effect by constructing 3D semi-analytic models of the helium ionizing background from $z=2.5$-$3.5$ that explicitly include a spatially varying mean free path of ionizing photons. The resulting distribution of effective optical depths at large scales in the He II Ly$α$ forest is very similar to the latest observations with HST/COS at $2.5 \lesssim z \lesssim 3.5$.

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arXiv2017

A New Method to Measure the Post-Reionization Ionizing Background from the Joint Distribution of Lyman-$α$ and Lyman-$β$ Forest Transmission

The amplitude of the ionizing background that pervades the intergalactic medium (IGM) at the end of the epoch of reionization provides a valuable constraint on the emissivity of the sources which reionized the Universe. While measurements of the ionizing background at lower redshifts rely on a simulation-calibrated mapping between the photoionization rate and the mean transmission of the Ly$α$ forest, at $z\gtrsim6$ the IGM becomes increasingly opaque, and transmission arises solely in narrow spikes separated by saturated Gunn-Peterson troughs. In this regime, the traditional approach of measuring the average transmission over large $\sim 50$ Mpc$/h$ regions is less sensitive and sub-optimal. Additionally, the five times smaller oscillator strength of the Ly$β$ transition implies the Ly$β$ forest is considerably more transparent at $z\gtrsim6$, even in the presence of contamination by foreground $z\sim 5$ Ly$α$ forest absorption. In this work we present a novel statistical approach to analyze the joint distribution of transmission spikes in the co-spatial $z\sim 6$ Ly$α$ and Ly$β$ forests. Our method relies on Approximate Bayesian Computation (ABC), which circumvents the necessity of computing the intractable likelihood function describing the highly correlated Ly$α$ and Ly$β$ transmission. We apply ABC to mock data generated from a large-volume hydrodynamical simulation combined with a state-of-the-art model of ionizing background fluctuations in the post-reionization IGM, and show that it is sensitive to higher IGM neutral hydrogen fractions than previous techniques. As a proof of concept, we apply this methodology to a real spectrum of a $z=6.54$ quasar and measure the ionizing background from $5.4\leq z \leq 6.4$ along this sightline with $\sim0.2$ dex statistical uncertainties.

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arXiv2015

The Flatness and Sudden Evolution of the Intergalactic Ionizing Background

The ionizing background of cosmic hydrogen is an important probe of the sources and absorbers of ionizing radiation in the post-reionization universe. Previous studies show that the ionization rate should be very sensitive to changes in the source population: as the emissivity rises, absorbers shrink in size, increasing the ionizing mean free path and, hence, the ionizing background. By contrast, observations of the ionizing background find a very flat evolution from z~2-5, before falling precipitously at z~6. We resolve this puzzling discrepancy by pointing out that, at z~2-5, optically thick absorbers are associated with the same collapsed halos that host ionizing sources. Thus, an increasing abundance of galaxies is compensated for by a corresponding increase in the absorber population, which moderates the instability in the ionizing background. However, by z~5-6, gas outside of halos dominates the absorption, the coupling between sources and absorbers is lost, and the ionizing background evolves rapidly. Our halo based model reproduces observations of the ionizing background, its flatness and sudden decline, as well as the redshift evolution of the ionizing mean free path. Our work suggests that, through much of their history, both star formation and photoelectric opacity in the universe track halo growth.

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arXiv2015

Large fluctuations in the hydrogen-ionizing background and mean free path following the epoch of reionization

Extremely large opaque troughs in the Lyman-alpha forest have been interpreted as a sign of an extended reionization process below z~6. Such features are impossible to reproduce with simple models of the intergalactic ionizing background that assume a uniform mean free path of ionizing photons. We build a self-consistent model of the ionizing background that includes fluctuations in the mean free path due to the varying strength of the ionizing background and large-scale density field. The dominant effect is the suppression of the ionizing background in large-scale voids due to "self-shielding" by an enhanced number of optically thick absorbers. Our model results in a distribution of 50 Mpc/h Lyman-alpha forest effective optical depths that significantly improves agreement with the observations at z~5.6. Extrapolation to z~5.4 and z~5.8 appears promising, but matching the mean background evolution requires evolution in the absorber population beyond the scope of the present model. We also demonstrate the need for extremely large volumes (>400 Mpc on a side) to accurately determine the incidence of rare large-scale features in the Lyman-alpha forest.

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arXiv2014

Quasar Ionization Front Lyα Emission in an Inhomogeneous Intergalactic Medium

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 current and near-future instruments. Past work calculated the Lyman-alpha emission from a quasar ionization front in a homogeneous medium with a clumping factor approximation to account for inhomogeneities. We find using 1D radiative transfer calculations that this approximation overestimates the emission by a factor of >3. Our calculations model the propagation of ionizing photons and compute the Lyman-alpha emission from quasar ionization fronts on sightlines from a hydrodynamic cosmological simulation at z = 7.1. To better understand the physical properties of the emission, we also develop an analytic model that accurately describes the results of the full radiative transfer calculation.

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arXiv2013

The Effect of Fluctuations on the Helium-Ionizing Background

Interpretation of He II Lyα absorption spectra after the epoch of He II reionization requires knowledge of the He II ionizing background. While past work has modelled the evolution of the average background, the standard cosmological radiative transfer technique assumes a uniform radiation field despite the discrete nature of the (rare) bright quasars that dominate the background. We implement a cosmological radiative transfer model that includes the most recent constraints on the ionizing spectra and luminosity function of quasars and the distribution of IGM absorbers. We also estimate, for the first time, the effects of fluctuations on the evolving continuum opacity in two ways: by incorporating the complete distribution of ionizing background amplitudes into the standard approach, and by explicitly treating the quasars as discrete -- but isolated -- sources. Our model results in a He II ionization rate that evolves steeply with redshift, increasing by a factor ~2 from z=3.0 to z=2.5. This causes rapid evolution in the mean He II Lyα optical depth -- as recently observed -- without appealing to the reionization of He II. The observed behaviour could instead result from rapid evolution in the mean free path of ionizing photons as the helium in higher H I column density absorbers becomes fully ionized.

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