arXiv subjects

Chiara Mazzucchelli

Publications and source records attributed to Chiara Mazzucchelli.

At least 91 records · Page 5Linked to original sources

arXiv2020

Pōniuā'ena: A Luminous $z=7.5$ Quasar Hosting a 1.5 Billion Solar Mass Black Hole

We report the discovery of a luminous quasar, J1007+2115 at $z=7.515$ ("Pōniuā'ena"), from our wide-field reionization-era quasar survey. J1007+2115 is the second quasar now known at $z>7.5$, deep into the reionization epoch. The quasar is powered by a $(1.5\pm0.2)\times10^9$ $M_{\odot}$ supermassive black hole (SMBH), based on its broad MgII emission-line profile from Gemini and Keck near-IR spectroscopy. The SMBH in J1007+2115 is twice as massive as that in quasar J1342+0928 at $z=7.54$, the current quasar redshift record holder. The existence of such a massive SMBH just 700 million years after the Big Bang significantly challenges models of the earliest SMBH growth. Model assumptions of Eddington-limited accretion and a radiative efficiency of 0.1 require a seed black hole of $\gtrsim 10^{4}$ $M_{\odot}$ at $z=30$. This requirement suggests either a massive black hole seed as a result of direct collapse or earlier periods of rapid black hole growth with hyper-Eddington accretion and/or a low radiative efficiency. We measure the damping wing signature imprinted by neutral hydrogen absorption in the intergalactic medium (IGM) on J1007+2115's Ly$α$ line profile, and find that it is weaker than that of J1342+0928 and two other $z\gtrsim7$ quasars. We estimate an IGM volume-averaged neutral fraction $\langle x\rm_{HI}\rangle=0.39^{+0.22}_{-0.13}$. This range of values suggests a patchy reionization history toward different IGM sightlines. We detect the 158 $μ$m [C II] emission line in J1007+2115 with ALMA; this line centroid yields a systemic redshift of $z=7.5149\pm0.0004$ and indicates a star formation rate of $\sim210$ $M_{\odot}$ yr$^{-1}$ in its host galaxy.

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arXiv2020

A metal-poor damped Ly-alpha system at redshift 6.4

We identify a strong Ly-alpha damping wing profile in the spectrum of the quasar P183+05 at z=6.4386. Given the detection of several narrow metal absorption lines at z=6.40392, the most likely explanation for the absorption profile is that it is due to a damped Ly-alpha system. However, in order to match the data a contribution of an intergalactic medium 5-38% neutral or additional weaker absorbers near the quasar is also required. The absorption system presented here is the most distant damped Ly-alpha system currently known. We estimate an HI column density ($10^{20.68\pm0.25}\,$cm$^{-2}$), metallicity ([O/H]$=-2.92\pm 0.32$), and relative chemical abundances of a system consistent with a low-mass galaxy during the first Gyr of the universe. This object is among the most metal-poor damped Ly-alpha systems known and, even though it is observed only ~850 Myr after the big bang, its relative abundances do not show signatures of chemical enrichment by Population III stars.

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arXiv2019

X-ray Observations of a $z\sim6.2$ Quasar/Galaxy Merger

Quasars at early redshifts ($z > 6$) with companion galaxies offer unique insights into the growth and evolution of the first supermassive black holes. Here, we report on a 150 ks Chandra observation of PSO J308.0416$-$21.2339, a $z=6.23$ quasar with a merging companion galaxy identified in [C II] and rest-frame UV emission. With $72.3^{+9.6}_{-8.6}$ net counts, we find that PSO J308.0416$-$21.2339 is powerful ($L_X = 2.31^{+1.14}_{-0.76} \times 10^{45}\ \textrm{erg}\,\textrm{s}^{-1}\,\textrm{cm}^{-2}$ in rest-frame $2.0-10.0$ keV) yet soft (spectral power-law index $Γ=2.39^{+0.37}_{-0.36}$ and optical-to-X-ray slope $α_{\rm OX} = -1.41 \pm 0.11$). In addition, we detect three hard-energy photons $2.''0$ to the west of the main quasar, cospatial with the brightest UV emission of the merging companion. As no soft-energy photons are detected in the same area, this is potentially indicative of a highly-obscured source. With conservative assumptions, and accounting for both background fluctuations and the extended wings of the quasar's emission, these photons only have a probability $P=0.021$ of happening by chance. If confirmed by deeper observations, this system is the first high redshift quasar and companion individually detected in X-rays and is likely a dual AGN.

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arXiv2019

The REQUIEM Survey I: A Search for Extended Ly-Alpha Nebular Emission Around 31 z>5.7 Quasars

The discovery of quasars few hundred megayears after the Big Bang represents a major challenge to our understanding of black holes and galaxy formation and evolution. Their luminosity is produced by extreme gas accretion onto black holes, which already reached masses of 10$^9$ M$_\odot$ by z ~ 6. Simultaneously, their host galaxies form hundreds of stars per year, using up gas in the process. To understand which environments are able to sustain the rapid formation of these extreme sources we started a VLT/MUSE effort aimed at characterizing the surroundings of a sample of 5.7 < z < 6.6 quasars dubbed: the Reionization Epoch QUasar InvEstigation with MUSE (REQUIEM) survey. We here present results of our searches for extended Ly-Alpha halos around the first 31 targets observed as part of this program. Reaching 5-sigma surface brightness limits of 0.1-1.1 x 10$^{-17}$ erg/s/cm$^2$/arcsec$^2$ over a 1 arcsec$^2$ aperture, we were able to unveil the presence of 12 Ly-Alpha nebulae, 8 of which are newly discovered. The detected nebulae show a variety of emission properties and morphologies with luminosities ranging from 8 x 10$^{42}$ to 2 x 10$^{44}$ erg/s, FWHMs between 300 and 1700 km/s, sizes < 30 pkpc, and redshifts consistent with those of the quasar host galaxies. As the first statistical and homogeneous investigation of the circum-galactic medium of massive galaxies at the end of the reionization epoch, the REQUIEM survey enables the study of the evolution of the cool gas surrounding quasars in the first 3 Gyr of the Universe. A comparison with the extended Ly-Alpha emission observed around bright (M$_{1450}$ < -25 mag) quasars at intermediate redshift indicates little variations on the properties of the cool gas from z ~ 6 to z ~ 3 followed by a decline in the average surface brightness down to z ~ 2.

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arXiv2019

The z=7.54 Quasar ULAS J1342+0928 Is Hosted by a Galaxy Merger

We present ALMA 0.28"x0.20" (1.4kpc x 1.0kpc) resolution observations of the [CII] 158um line and underlying dust continuum in the host galaxy of the most distant quasar currently known, ULAS J1342+0928 at z=7.5413. Both the [CII] and continuum are detected and spatially resolved. The [CII] line is ~1.5 times more extended than the continuum emission, showing an elongated and complex structure of approximately 3.2kpc x 6.4kpc. Two separate peaks are clearly seen (>6sigma each) in three 100 km/s width [CII] channel maps. The velocity field of the [CII] gas does not show evidence of a coherent rotation field but rather chaotic motion, reminiscent of an on-going merger.

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arXiv2019

Resolved [CII] Emission from z>6 Quasar Host -- Companion Galaxy Pairs

We report on ~0.35"(~2 kpc) resolution observations of the [CII] and dust continuum emission from five z>6 quasar host-companion galaxy pairs obtained with the Atacama Large Millimeter/submillimeter Array. The [CII] emission is resolved in all galaxies, with physical extents of 3.2-5.4 kpc. The dust continuum is on-average 40% more compact, which results in larger [CII] deficits in the center of the galaxies. However, the measured [CII] deficits are fully consistent with those found at lower redshifts. Four of the galaxies show [CII] velocity fields that are consistent with ordered rotation, while the remaining six galaxies show no clear velocity gradient. All galaxies have high (~80-200 km/s) velocity dispersions, consistent with the interpretation that the interstellar medium (ISM) of these high redshift galaxies is turbulent. By fitting the galaxies with kinematic models, we estimate the dynamical mass of these systems, which range between (0.3 -> 5.4) x 1E10 Msun. For the three closest separation galaxy pairs, we observe dust and [CII] emission from gas in between and surrounding the galaxies, which is an indication that tidal interactions are disturbing the gas in these systems. Although gas exchange in these tidal interactions could power luminous quasars, the existence of quasars in host galaxies without nearby companions suggests that tidal interactions are not the only viable method for fueling their active centers. These observations corroborate the assertion that accreting supermassive black holes do not substantially contribute to the [CII] and dust continuum emission of the quasar host galaxies, and showcase the diverse ISM properties of galaxies when the universe was less than one billion years old.

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arXiv2019

Discovery of the first heavily obscured QSO candidate at $z>6$ in a close galaxy pair

While theoretical arguments predict that most of the early growth of supermassive black holes (SMBHs) happened during heavily obscured phases of accretion, current methods used for selecting $z>6$ quasars (QSOs) are strongly biased against obscured QSOs, thus considerably limiting our understanding of accreting SMBHs during the first Gyr of the Universe from an observational point of view. We report the $Chandra$ discovery of the first heavily obscured QSO candidate in the early universe, hosted by a close ($\approx5$ kpc) galaxy pair at $z=6.515$. One of the members is an optically classified type 1 QSO, PSO167-13. The companion galaxy was first detected as a [C II] emitter by ALMA. An X-ray source is significantly ($P=0.9996$) detected by $Chandra$ in the 2-5 keV band, with $<1.14$ net counts in the 0.5-2 keV band, although the current positional uncertainty does not allow a conclusive association with either PSO167-13 or its companion galaxy. From X-ray photometry and hardness-ratio arguments, we estimated an obscuring column density of $N_H>2\times10^{24}\,\mathrm{cm^{-2}}$ and $N_H>6\times10^{23}\,\mathrm{cm^{-2}}$ at $68\%$ and $90\%$ confidence levels, respectively. Thus, regardless of which of the two galaxies is associated with the X-ray emission, this source is the first heavily obscured QSO candidate at $z>6$.

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arXiv2019

An ALMA multi-line survey of the interstellar medium of the redshift 7.5 quasar host galaxy J1342+0928

We use ALMA observations of the host galaxy of the quasar ULAS-J1342+0928 at z=7.54 to study the dust continuum and far infrared lines emitted from its interstellar medium. The Rayleigh-Jeans tail of the dust continuum is well sampled with eight different spectral setups, and from a modified black body fit we obtain an emissivity coefficient of beta=1.85+-0.3. Assuming a standard dust temperature of 47 K we derive a dust mass of Mdust=0.35x10^8 Msol and a star formation rate of 150+-30 Msol/yr. We have >4sigma detections of the [CII]_158, [OIII]_88 and [NII]_122 atomic fine structure lines and limits on the [CI]_369, [OI]_146 and [NII]_205 emission. We also report multiple limits of CO rotational lines with Jup >= 7, as well as a tentative 3.3sigma detection of the stack of four CO lines (Jup=11, 10, 8, 7). We find line deficits that are in agreement with local ultra luminous infrared galaxies. Comparison of the [NII]_122 and [CII]_158 lines indicates that the [CII]_158 emission arises predominantly from the neutral medium, and we estimate that the photo-disassociation regions in J1342+0928 have densities <~5x10^4cm^-3. The data suggest that ~16% of hydrogen is in ionized form and that the HII regions have high electron densities of n_e>180 cm^-3. Our observations favor a low gas-to-dust ratio of <100 and a metallicity of the interstellar medium comparable to the Solar value. All the measurements presented here suggest that the host galaxy of J1342+0928 is highly enriched in metal and dust, despite being observed just 680 Myr after the Big Bang.

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arXiv2019

Ly$α$ Halos Around $z\sim6$ Quasars

We present deep MUSE observations of five quasars within the first Gyr of the Universe ($z\gtrsim6$), four of which display extended Ly$α$ halos. After PSF-subtraction, we reveal halos surrounding two quasars for the first time, as well as confirming the presence of two more halos for which tentative detections exist in long-slit spectroscopic observations and narrow-band imaging. The four Ly$α$ halos presented here are diverse in morphology and size, they each display spatial asymmetry, and none are centred on the position of the quasar. Spectra of the diffuse halos demonstrate that none are dramatically offset in velocity from the systemic redshift of the quasars ($Δ$ v $< 200$ kms$^{-1}$), however each halo shows a broad Ly$α$ line, with a velocity width of order $\sim1000$ kms$^{-1}$. Total Ly$α$ luminosities range between $\sim$ $2 \times 10^{43}$ erg s$^{-1}$ and $\sim$ $2 \times 10^{44}$ erg s$^{-1}$, reaching maximum radial extents of $13 - 30$ pkpc from the quasar positions. We find larger sizes and higher Ly$α$ luminosities than previous literature results at this redshift, but find no correlation between the quasar properties and the Ly$α$ halo, suggesting that the detected emission is most closely related to the physical properties of the circum-galactic medium

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arXiv2019

ALMA and HST kiloparsec-scale imaging of a quasar-galaxy merger at $z\approx 6.2$

We present kpc-scale ALMA and HST imaging of the quasar PJ308-21 at $z$=$6.2342$, tracing dust, gas (via the [CII] 158 $μ$m line) and young stars. At a resolution of $\sim0.3''$ ($\approx1.7$ kpc), the system is resolved over $>4''$ ($>$20 kpc). In particular, it features a main component, identified to be the quasar host galaxy, centered on the accreting supermassive black hole; and two other extended components on the West and East side, one redshifted and the other blueshifted relative to the quasar. The [CII] emission of the entire system stretches over $>$1500 km/s along the line of sight. All the components of the system are observed in dust, [CII], and rest-frame UV emission. The inferred [CII] luminosities [(0.9-4.6)$\times 10^9$ L$_\odot$], dust luminosities [(0.15-2.6)$\times10^{12}$ L$_\odot$], and rest-frame UV luminosities [(6.6-15)$\times10^{10}$ L$_\odot$], their ratios, and the implied gas/dust masses and star formation rates [11-290 M$_\odot$ yr$^{-1}$] are typical of high-redshift star-forming galaxies. A toy model of a single satellite galaxy that is tidally stripped by the interaction with the quasar host galaxy can account for the observed velocity and spatial extent of the two extended components. An outflow interpretation of the unique features in PJ308-21 is not supported by the data. PJ308-21 is thus one of the earliest galaxy mergers imaged at cosmic dawn.

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arXiv2019

The First Luminous Quasars and Their Host Galaxies

The discovery of luminous quasars at redshifts up to 7.5 demonstrates the existence of several billion M_sun supermassive black holes (SMBHs) less than a billion years after the Big Bang. They are accompanied by intense star formation in their host galaxies, pinpointing sites of massive galaxy assembly in the early universe, while their absorption spectra reveal an increasing neutral intergalactic medium (IGM) at the epoch of reionization. Extrapolating from the rapid evolution of the quasar density at z=5-7, we expect that there is only one luminous quasar powered by a billion M_sun SMBH in the entire observable universe at z~9. In the next decade, new wide-field, deep near-infrared (NIR) sky surveys will push the redshift frontier to the first luminous quasars at z~9-10; the combination with new deep X-ray surveys will probe fainter quasar populations that trace earlier phases of SMBH growth. The identification of these record-breaking quasars, and the measurements of their BH masses and accretion properties require sensitive spectroscopic observations with next generation of ground-based and space telescopes at NIR wavelengths. High-resolution integral-field spectroscopy at NIR, and observations at millimeter and radio wavelengths, will together provide a panchromatic view of the quasar host galaxies and their galactic environment at cosmic dawn, connecting SMBH growth with the rise of the earliest massive galaxies. Systematic surveys and multiwavelength follow-up observations of the earliest luminous quasars will strongly constrain the seeding and growth of the first SMBHs in the universe, and provide the best lines of sight to study the history of reionization.

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arXiv2019

A Quasar Discovered at redshift 6.6 from Pan-STARRS1

Luminous high-redshift quasars can be used to probe of the intergalactic medium (IGM) in the early universe because their UV light is absorbed by the neutral hydrogen along the line of sight. They help us to measure the neutral hydrogen fraction of the high-z universe, shedding light on the end of reionization epoch. In this paper, we present a discovery of a new quasar (PSO J006.1240+39.2219) at redshift $z=6.61\pm0.02$ from Panoramic Survey Telescope & Rapid Response System 1. Including this quasar, there are nine quasars above $z>6.5$ up to date. The estimated continuum brightness is $M_\text{1450}$=$-25.96\pm0.08$. PSO J006.1240+39.2219 has a strong Ly~$α$ emission compared with typical low-redshift quasars, but the measured near-zone region size is $R_\text{NZ}=3.2\pm1.1$ proper megaparsecs, which is consistent with other quasars at z$\sim$6.

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arXiv2018

No evidence for enhanced [OIII] 88um emission in a z~6 quasar compared to its companion starbursting galaxy

We present ALMA band 8 observations of the [OIII] 88um line and the underlying thermal infrared continuum emission in the z=6.08 quasar CFHQS J2100-1715 and its dust-obscured starburst companion galaxy (projected distance: ~60 kpc). Each galaxy hosts dust-obscured star formation at rates > 100 M_sun/yr, but only the quasar shows evidence for an accreting 10^9 M_sun black hole. Therefore we can compare the properties of the interstellar medium in distinct galactic environments in two physically associated objects, ~1 Gyr after the Big Bang. Bright [OIII] 88um emission from ionized gas is detected in both systems; the positions and line-widths are consistent with earlier [CII] measurements, indicating that both lines trace the same gravitational potential on galactic scales. The [OIII] 88um/FIR luminosity ratios in both sources fall in the upper range observed in local luminous infrared galaxies of similar dust temperature, although the ratio of the quasar is smaller than in the companion. This suggests that gas ionization by the quasar (expected to lead to strong optical [OIII] 5008A emission) does not dominantly determine the quasar's FIR [OIII] 88um luminosity. Both the inferred number of photons needed for the creation of O++ and the typical line ratios can be accounted for without invoking extreme (top-heavy) stellar initial mass functions in the starbursts of both sources.

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arXiv2018

The Discovery of A Luminous Broad Absorption Line Quasar at A Redshift of 7.02

Despite extensive efforts, only two quasars have been found at $z>7$ to date due to a combination of low spatial density and high contamination from more ubiquitous Galactic cool dwarfs in quasar selection. This limits our current knowledge of the super-massive black hole (SMBH) growth mechanism and reionization history. In this letter, we report the discovery of a luminous quasar at $z=7.021$, DELS J003836.10$-$152723.6 (hereafter J0038$-$1527), selected using photometric data from DESI Legacy imaging Survey (DELS), Pan-STARRS1 (PS1) imaging Survey, as well as Wide-field Infrared Survey Explore ($WISE$) mid-infrared all-sky survey. With an absolute magnitude of $M_{1450}$=$-$27.1 and bolometric luminosity of $L_{\rm Bol}$=5.6$\times$10$^{13}$ $L_\odot$, J0038$-$1527 is the most luminous quasar known at $z>7$. Deep optical to near infrared spectroscopic observations suggest that J0038-1527 hosts a 1.3 billion solar mass BH accreting at the Eddington limit, with an Eddington ratio of 1.25$\pm$0.19. The CIV broad emission line of J0038$-$1527 is blue-shifted by more than 3000 km s$^{-1}$ to the systemic redshift. More detailed investigations of the high quality spectra reveal three extremely high velocity CIV broad absorption lines (BALs) with velocity from 0.08 to 0.14 times the speed of light and total balnicity index of more than 5000 km s$^{-1}$, suggesting the presence of relativistic outflows. J0038$-$1527 is the first quasar found at the epoch of reionization (EoR) with such strong outflows and provides a unique laboratory to investigate AGN feedback on the formation and growth of the most massive galaxies in the early universe.

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arXiv2018

Dust emission in an accretion-rate-limited sample of z>6 quasars

We present Atacama Large Millimeter Array 1mm observations of the rest-frame far-infrared (FIR) dust continuum in 27 quasars at redshifts 6.0 < z < 6.7. We detect FIR emission at >3sigma in all quasar host galaxies with flux densities at ~1900GHz in the rest-frame of 0.12 < S_rest,1900GHz < 5.9mJy, with a median (mean) flux density of 0.88mJy (1.59mJy). The implied FIR luminosities range from L_FIR = (0.27-13)x10^12 L_sun, with 74% of our quasar hosts having L_FIR > 10^12 L_sun. The estimated dust masses are M_dust = 10^7-10^9 M_sun. If the dust is heated only by star formation, then the star formation rates in the quasar host galaxies are between 50 and 2700 M_sun/yr. In the framework of the host galaxy-black hole coevolution model a correlation between ongoing black hole growth and star formation in the quasar host galaxy would be expected. However, combined with results from the literature to create a luminosity-limited quasar sample, we do not find a strong correlation between quasar UV luminosity (a proxy for ongoing black hole growth) and FIR luminosity (star formation in the host galaxy). The absence of such a correlation in our data does not necessarily rule out the coevolution model, and could be due to a variety of effects (including different timescales for black hole accretion and FIR emission).

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arXiv2018

No Evidence for Millimeter Continuum Source Overdensities in the Environments of $z\gtrsim6$ Quasars

Bright high-redshift quasars ($z>6$), hosting supermassive black holes ($\rm M_{BH} > 10^8 M_{\odot}$), are expected to reside in massive host galaxies embedded within some of the earliest and most massive galaxy overdensities. We analyze 1.2\,mm ALMA dust continuum maps of 35 bright quasars at $6<z<7$ and search the primary beam for excess dust continuum emission from sources with L$_{\rm IR} \gtrsim{ 10^{12}}$\,L$_{\odot}$ as evidence for early protoclusters. We compare the detection rates of continuum sources at $\geq5σ$ significance in the fields surrounding the quasars (A$_{\rm eff}$ = 4.3\,arcmin$^2$) with millimeter number counts in blank field surveys. We discover 15 millimeter sources in the fields excluding the quasars themselves, corresponding to an overdensity $δ_{\rm gal} \equiv (N_{\rm gal} - N_{\rm exp})/N_{\rm exp} = -0.07\pm0.56$, consistent with no detected overdensity of dusty galaxies within 140 physical kpc of the quasars. However, the apparent lack of continuum overdensity does not negate the hypothesis that quasars live in overdense environments, as evidenced by strong [CII] overdensities found on the same scales to similarly-selected quasars. The small field of view of ALMA could miss a true overdensity if it exists on scales larger than 1\,cMpc, if the quasar is not centered in the overdensity, or if quasar feedback plays a role close to the quasar, but it is most likely that the large line of sight volume probed by a continuum survey will wash out a true overdensity signal. We discuss the necessary factors in determining the bias with which dusty star-forming galaxies trace true dark matter overdensities in order to improve upon overdensity searches in dust continuum.

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arXiv2018

A powerful radio-loud quasar at the end of cosmic reionization

We present the discovery of the radio-loud quasar PSO J352.4034-15.3373 at z=5.84 pm 0.02. This quasar is the radio brightest source known, by an order of magnitude, at z~6 with a flux density in the range of 8-100 mJy from 3GHz to 230MHz and a radio loudness parameter R>~1000. This source provides an unprecedented opportunity to study powerful jets and radio-mode feedback at the highest redshifts, and presents the first real chance to probe deep into the neutral intergalactic medium by detecting 21 cm absorption at the end of cosmic reionization.

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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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