arXiv subjects

Satoshi Yamanaka

Publications and source records attributed to Satoshi Yamanaka.

At least 19 recordsLinked to original sources

arXiv2026

An alternative proof of Miyashita's theorem in a skew polynomial ring II

Y. Miyashita gave characterizations of a separable polynomial and a Hirata separable polynomial in skew polynomial rings. In the previous paper, the author and S. Ikehata gave direct and elementary proofs of Miyashita's theorems in skew polynomial rings of automorphism type $B[X;ρ]$ and derivation type $B[X;D]$, respectively. The purpose of this paper is to give proofs for them in the general skew polynomial ring $B[X;ρ,D]$.

math.RA↗

arXiv2026

Note on Morita equivalence in ring extensions

It seems that Morita invariance is a useful criterion for judging the importance of the classes of ring extensions concerned. Y. Miyashita introduced the notion of Morita equivalence in ring extensions, and he showed that the classes of $G$-Galois extensions and Frobenius extensions are Morita invariant. After that, S. Ikehata showed that the classes of separable extensions, Hirata separable extensions, symmetric extensions, and QF-extensions are Morita invariant. In this paper, we shall prove that the classes of several extensions are Morita invariant. Further, we will give an example of the class of ring extensions which is not Morita invariant.

math.RA↗

arXiv2026

On weakly separable polynomials and weakly quasi-separable polynomials over rings

Separable extensions of noncommutative rings have already been studied extensively. Recently, N. Hamaguchi and A. Nakajima introduced the notions of weakly separable extensions and weakly quasi-separable extensions. They studied weakly separable polynomials and weakly quasi-separable polynomials in the case that the coefficient ring is commutative. The purpose of this paper is to give some improvements and generalizations of Hamaguchi and Nakajima's results. We shall characterize a weakly separable polynomial f(X) over a commutative ring by using its derivative f'(X) and its discriminant δ(f(X)). Further, we shall try to give necessary and sufficient conditions for weakly separable polynomials in skew polynomial rings in the case that the coefficient ring is noncommutative.

math.RA↗

arXiv2026

On Weakly Separable Polynomials in Skew Polynomial Rings

The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type.

math.RA↗

arXiv2025

The first direct imaging of the silhouette of a damped Lyman $α$ system along the line-of-sight to a background galaxy

The H~{\sc i} gas distribution in damped Lyman $α$ absorbers (DLAs) has remained elusive due to the point-source nature of background quasar emission. Observing DLAs against spatially extended background galaxies provides a new method for constraining their size and structure. Using the Keck Cosmic Web Imager, we present the first ``silhouette'' image of a DLA at $z=3.34$, identified in the spectrum of a background galaxy at $z=3.61$. Although the silhouette remains unresolved due to limited spatial resolution, this represents a successful proof-of-concept for studying DLA morphology using extended background sources. Possible residual emission in the DLA trough suggests an optical depth contrast exceeding $10^7$ in the internal structure, implying a sharp edge or patchy structure. A Lyman $α$ emitter (LAE) at $z_{\rm LAE}=3.3433\pm0.0005$, consistent with the DLA redshift, is detected at an angular separation of $1.''73\pm0.''28$ ($12.9\pm2.1$ kpc). The DLA is surrounded by three galaxies within 140 kpc in projected distance and 500 km s$^{-1}$ in line-of-sight velocity, indicating that it resides in the circumgalactic medium of the LAE or within a galaxy group/protocluster environment. An O~{\sc i} $\lambda1302$ absorption at $z_{\rm OI}=3.3288\pm0.0004$ is also detected along the line of sight. This absorber may trace metal-enriched outflow from the LAE or a gas-rich galaxy exhibiting the highest star formation activity among the surrounding galaxies. Future large spectroscopic surveys of galaxies will expand such a DLA sample, and three-dimensional spectroscopy for it will shed new light on the role of intergalactic dense gas in galaxy formation and evolution.

astro-ph.CO↗

arXiv2024

JWST, ALMA, and Keck Spectroscopic Constraints on the UV Luminosity Functions at z~7-14: Clumpiness and Compactness of the Brightest Galaxies in the Early Universe

We present the number densities and physical properties of the bright galaxies spectroscopically confirmed at $z\sim7-14$. Our sample is composed of 60 galaxies at $z_\mathrm{spec}\sim7-14$, including recently-confirmed galaxies at $z_\mathrm{spec}=12.34-14.32$ with JWST, as well as new confirmations at $z_\mathrm{spec}=6.583-7.643$ with $-24< M_\mathrm{UV}< -21$ mag using ALMA and Keck. Our JWST/NIRSpec observations have also revealed that very bright galaxy candidates at $z\sim10-13$ identified from ground-based telescope images before JWST are passive galaxies at $z\sim3-4$, emphasizing the necessity of strict screening and spectroscopy in the selection of the brightest galaxies at $z>10$. The UV luminosity functions derived from these spectroscopic results are consistent with a double power-law function, showing tensions with theoretical models at the bright end. To understand the origin of the overabundance of bright galaxies, we investigate their morphologies using JWST/NIRCam high-resolution images obtained in various surveys including PRIMER and COSMOS-Web. We find that $\sim70\%$ of the bright galaxies at $z\sim7$ exhibit clumpy morphologies with multiple sub-components, suggesting merger-induced starburst activity, which is consistent with SED fitting results showing bursty star formation histories. At $z\gtrsim10$, bright galaxies are classified into two types of galaxies; extended ones with weak high-ionization emission lines, and compact ones with strong high-ionization lines including NIV]$λ$1486, indicating that at least two different processes (e.g., merger-induced starburst and compact star formation/AGN) are shaping the physical properties of the brightest galaxies at $z\gtrsim10$ and are responsible for their overabundance.

astro-ph.GA↗

arXiv2024

JWST/NIRSpec spectroscopy of intermediate-mass quiescent galaxies at $z \sim 3-4$

We present the analysis of three intermediate-mass quiescent galaxies (QGs) with stellar masses of $\sim10^{10}M_{\rm \odot}$ at redshifts $z\sim 3 - 4$ using NIRSpec low-resolution spectroscopy. Utilising the SED fitting code BAGPIPES, we confirm these target galaxies are consistent with quiescent population, with their specific star formation rates (sSFR) falling below 2-dex the star-forming main sequence at the same redshifts. Additionally, we identify these QGs to be less massive than those discovered in previous works, particularly prior to the JWST era. Two of our target galaxies exhibit the potentially-blended H$α$+[NII] emission line within their spectra with $S/N>5$. We discuss whether this feature comes from an Active Galactic Nucleus (AGN) or star formation although future high-resolution spectroscopy is required to reach a conclusion. One of the target galaxies is covered by JWST/NIRCam imaging of the PRIMER survey. Using the 2D profile fitting code Galfit, we examine its morphology, revealing a disc-like profile with a Sérsic index of $n=1.1 \pm 0.1$. On the size-mass relation, we find a potential distinction between less-massive ($\log_{10}{(M_*/M_\odot)}<10.3$) and massive ($\log_{10}{(M_*/M_\odot)}>10.3$) QGs in their evolutionary pathways. The derived quenching timescales for our targets are less than 1 Gyr. This may result from these galaxies being quenched by AGN feedback, supporting the AGN scenario of the emission line features.

astro-ph.GA↗

arXiv2024

Gas conditions of a star-formation selected sample in the first billion years

We present Atacama Large Millimetre/submillimetre Array (ALMA) observations of the [O$_{\rm III}$] 88 $μ$m emission of a sample of thirteen galaxies at $z$ = 6 to 7.6 selected as [C$_{\rm II}$]-emitting companion sources of quasars. To disentangle the origins of the luminous Oxygen line in the $z$ > 6 Universe, we looked at emission-line galaxies that are selected through an excellent star-formation tracer [C$_{\rm II}$] with star-formation rates between 9 and 162 M$_{\odot}$/yr. Direct observations reveal [O$_{\rm III}$] emission in just a single galaxy (L$_{\rm [O_{\rm III}]}$/L$_{\rm [C_{\rm II}]}$ = 2.3), and a stacked image shows no [O$_{\rm III}$] detection, providing deep upper limits on the L$_{\rm [O_{\rm III}]}$/L$_{\rm [C_{\rm II}]}$ ratios in the $z > 6$ Universe (L$_{\rm [O_{\rm III}]}$/L$_{\rm [C_{\rm II}]}$ < 1.2 at 3$σ$). While the fidelity of this sample is high, no obvious optical/near-infrared counterpart is seen in the JWST imaging available for four galaxies. Additionally accounting for low-redshift CO emitters, line stacking shows that our sample-wide result remains robust: The enhanced L$_{\rm [O_{\rm III}]}$/L$_{\rm [C_{\rm II}]}$ reported in the first billion years of the Universe is likely due to the selection towards bright, blue Lyman-break galaxies with high surface star-formation rates or young stellar populations. The deep upper limit on the rest-frame 90 $μ$m continuum emission (< 141 $μ$Jy at 3$σ$), implies a low average dust temperature (T$_{\rm dust}$ < 30K) and high dust mass (M$_{\rm dust}$ ~ 10$^8$ M$_{\odot}$). As more normal galaxies are explored in the early Universe, synergy between JWST and ALMA is fundamental to further investigate the ISM properties of the a broad range of samples of high-$z$ galaxies.

astro-ph.GA↗

arXiv2023

SILVERRUSH. XIII. A Catalog of 20,567 Ly$α$ Emitters at $z=2-7$ Identified in the Full-depth Data of the Subaru/HSC-SSP and CHORUS Surveys

We present 20,567 Ly$α$ emitters (LAEs) at $z=2.2-7.3$ that are photometrically identified by the SILVERRUSH program in a large survey area up to 25 deg$^2$ with deep images of five broadband filters (grizy) and seven narrowband filters targeting Ly$α$ lines at $z=2.2$, $3.3$, $4.9$, $5.7$, $6.6$, $7.0$, and $7.3$ taken by the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) and the Cosmic HydrOgen Reionization Unveiled with Subaru (CHORUS) survey. We select secure $>5σ$ sources showing narrowband color excesses via Ly$α$ break screening, taking into account the spatial inhomogeneity of limiting magnitudes. After removing spurious sources by careful masking and visual inspection of coadded and multi-epoch images obtained over the 7 yr of the surveys, we construct LAE samples consisting of 6995, 4641, 726, 6124, 2058, 18, and 5 LAEs at $z=2.2$, 3.3, 4.9, 5.7, 6.6, 7.0, and 7.3, respectively, although the $z=7.3$ candidates are tentative. Our LAE catalogs contain 241 spectroscopically confirmed LAEs at the expected redshifts from previous work. We demonstrate that the number counts of our LAEs are consistent with previous studies with similar LAE selection criteria. The LAE catalogs will be made public on our project webpage with detailed descriptions of the content and ancillary information about the masks and limiting magnitudes.

astro-ph.GA↗

arXiv2023

Big Three Dragons: Molecular Gas in a Bright Lyman-Break Galaxy at $z=7.15$

We report ALMA Band 3 observations of CO(6-5), CO(7-6), and [CI](2-1) in B14-65666 (``Big Three Dragons''), one of the brightest Lyman-Break Galaxies at $z>7$ in the rest-frame ultraviolet continuum, far-infrared continuum, and emission lines of [OIII] 88 $μ$m and [CII] 158 $μ$m. CO(6-5), CO(7-6), and [CI](2-1), whose $3σ$ upper limits on the luminosities are approximately 40 times fainter than the [CII] luminosity, are all not detected. The $L_{\rm [CII]}$/$L_{\rm CO(6-5)}$ and $L_{\rm [CII]}$/$L_{\rm CO(7-6)}$ ratios are higher than the typical ratios obtained in dusty star-forming galaxies or quasar host galaxies at similar redshifts, and they may suggest a lower gas density in the photodissociated region in B14-65666. By using the (1) [CII] luminosity, (2) dust mass-to-gas mass ratio, and (3) a dynamical mass estimate, we find that the molecular gas mass ($M_{\rm{mol}}$) is $(0.05-11)\times10^{10}$ $M_{\rm \odot}$. This value is consistent with the upper limit inferred from the nondetection of mid-$J$ CO and [CI](2-1). Despite the large uncertauinty in $M_{\rm mol}$, we estimate a molecular gas-to-stellar mass ratio ($μ_{\rm{gas}}$) of $0.65-140$ and a gas depletion time ($τ_{\rm dep}$) of $2.5-550$ Myr; these values are broadly consistent with those of other high-redshift galaxies. B14-65666 could be an ancestor of a passive galaxy at $z\gtrsim4$ if no gas is fueled from outside the galaxy.

astro-ph.GA↗

arXiv2023

Detections of [C II] 158 $μ$m and [O III] 88 $μ$m in a Local Lyman Continuum Emitter, Mrk 54, and its Implications to High-redshift ALMA Studies

We present integral field, far-infrared (FIR) spectroscopy of Mrk 54, a local Lyman Continuum Emitter (LCE), obtained with FIFI-LS on the Stratospheric Observatory for Infrared Astronomy. This is only the second time, after Haro 11, that [C II] 158 $μ$m and [O III] 88 $μ$m spectroscopy of the known LCEs have been obtained. We find that Mrk 54 has a strong [C II] emission that accounts for $\sim1$% of the total FIR luminosity, whereas it has only moderate [O III] emission, resulting in the low [O III]/[C II] luminosity ratio of $0.22\pm0.06$. In order to investigate whether [O III]/[C II] is a useful tracer of $f_{\rm esc}$ (LyC escape fraction), we examine the correlations of [O III]/[C II] and (i) the optical line ratio of $\rm O_{32} \equiv$ [O III] 5007 Å/[O II] 3727 Å, (ii) specific star formation rate, (iii) [O III] 88 $μ$m/[O I] 63 $μ$m ratio, (iv) gas phase metallicity, and (v) dust temperature based on a combined sample of Mrk 54 and the literature data from the Herschel Dwarf Galaxy Survey and the LITTLE THINGS Survey. We find that galaxies with high [O III]/[C II] luminosity ratios could be the result of high ionization (traced by $\rm O_{32}$), bursty star formation, high ionized-to-neutral gas volume filling factors (traced by [O III] 88 $μ$m/[O I] 63 $μ$m), and low gas-phase metallicities, which is in agreement with theoretical predictions. We present an empirical relation between the [O III]/[C II] ratio and $f_{\rm esc}$ based on the combination of the [O III]/[C II] and $\rm O_{32}$ correlation, and the known relation between $\rm O_{32}$ and $f_{\rm esc}$. The relation implies that high-redshift galaxies with high [O III]/[C II] ratios revealed by ALMA may have $f_{\rm esc}\gtrsim0.1$, significantly contributing to the cosmic reionization.

astro-ph.GA↗

arXiv2023

The SSA22 HI Tomography Survey (SSA22-HIT). I. Data Set and Compiled Redshift Catalog

We conducted a deep spectroscopic survey, named SSA22-HIT, in the SSA22 field with the DEep Imaging MultiObject Spectrograph (DEIMOS) on the Keck telescope, designed to tomographically map high-z HI gas through analysis of Lya absorption in background galaxies' spectra. In total, 198 galaxies were spectroscopically confirmed at 2.5 < z < 6 with a few low-z exceptions in the 26 x 15 arcmin^2 area, of which 148 were newly determined in this study. Our redshift measurements were merged with previously confirmed redshifts available in the 34 x 27 arcmin^2 area of the SSA22 field. This compiled catalog containing 730 galaxies of various types at z > 2 is useful for various applications, and it is made publicly available. Our SSA22-HIT survey has increased by approximately twice the number of spectroscopic redshifts of sources at z > 3.2 in the observed field. From a comparison with publicly available redshift catalogs, we show that our compiled redshift catalog in the SSA22 field is comparable to those among major extragalactic survey fields in terms of a combination of wide area and high surface number density of objects at z > 2. About 40 % of the spectroscopically confirmed objects in SSA22-HIT show reasonable quality of spectra in the wavelengths shorter than Lya when a sufficient amount of smoothing is adopted. Our data set enables us to make the HI tomographic map at z > 3, which we present in a parallel study.

astro-ph.GA↗

arXiv2022

Bridging Optical and Far-Infrared Emission-Line Diagrams of Galaxies from Local to the Epoch of Reionization: Characteristic High [O III] 88 $\mathrm{μm}$/SFR at $z > 6$

We present photoionization modeling of galaxy populations at $z\sim0$, $2$, and $> 6$ to bridge optical and far-infrared (FIR) emission-line diagrams. We collect galaxies with measurements of optical and/or FIR ([O III] 88 $\mathrm{μm}$ and [C II] 158 $\mathrm{μm}$) emission line fluxes and plot them on the [O III]$\lambda5007/\mathrm{Hβ}$--[N II]$\lambda6585/\mathrm{Hα}$ (BPT) and L([O III]88)/SFR--L([C II]158)/SFR diagrams, where SFR is the star-formation rate and L([O III]88) and L([C II]158) are the FIR line luminosities. We aim to explain the galaxy distributions on the two diagrams with photoionization models that employ three nebular parameters: the ionization parameter $U$, hydrogen density $n_\text{H}$, and gaseous metallicity $Z_\text{gas}$. Our models successfully reproduce the nebular parameters of local galaxies, and then predict the distributions of the $z\sim0$, $2$, and $> 6$ galaxies on the diagrams. The predicted distributions illustrate the redshift evolution on all the diagrams; e.g., [O III]$/\mathrm{Hβ}$ and [O III]88/[C II]158 ratios continuously decrease from $z > 6$ to $0$. Specifically, the $z > 6$ galaxies exhibit $\sim\!0.5$ dex higher $U$ than low-redshift galaxies at a given $Z_\text{gas}$ and show predicted flat distributions on the BPT diagram at $\log{\mathrm{[O III]/Hβ}} = 0.5$-$0.8$. We find that some of the $z > 6$ galaxies exhibit high L([O III]88)/SFR ratios. To explain these high ratios, our photoionization models require a low stellar-to-gaseous metallicity ratio or bursty/increasing star-formation history at $z > 6$. The James Webb Space Telescope will test the predictions and scenarios for the $z > 6$ galaxies proposed by our photoionization modeling.

astro-ph.GA↗

arXiv2022

Possible Systematic Rotation in the Mature Stellar Population of a $z=9.1$ Galaxy

We present new observations with the Atacama Large Millimeter/submillimeter Array for a gravitationally-lensed galaxy at $z=9.1$, MACS1149-JD1. [O III] 88-$μ$m emission is detected at 10$σ$ with a spatial resolution of $\sim0.3$ kpc in the source plane, enabling the most distant morpho-kinematic study of a galaxy. The [O III] emission is distributed smoothly without any resolved clumps and shows a clear velocity gradient with $ΔV_{\rm obs}/2σ_{\rm tot}=0.84\pm0.23$, where $ΔV_{\rm obs}$ is the observed maximum velocity difference and $σ_{\rm tot}$ is the velocity dispersion measured in the spatially-integrated line profile, suggesting a rotating system. Assuming a geometrically thin self-gravitating rotation disk model, we obtain $V_{\rm rot}/σ_V=0.67_{-0.26}^{+0.73}$, where $V_{\rm rot}$ and $σ_V$ are the rotation velocity and velocity dispersion, respectively, still consistent with rotation. The resulting disk mass of $0.65_{-0.40}^{+1.37}\times10^{9}$ M$_\odot$ is consistent with being associated with the stellar mass identified with a 300 Myr-old stellar population independently indicated by a Balmer break in the spectral energy distribution. We conclude that the most of the dynamical mass is associated with the previously-identified mature stellar population that formed at $z\sim15$.

astro-ph.GA↗

arXiv2022

A Search for H-Dropout Lyman Break Galaxies at z~12-16

We present two bright galaxy candidates at z~12-13 identified in our H-dropout Lyman break selection with 2.3 deg2 near-infrared deep imaging data. These galaxy candidates, selected after careful screening of foreground interlopers, have spectral energy distributions showing a sharp discontinuity around 1.7 um, a flat continuum at 2-5 um, and non-detections at <1.2 um in the available photometric datasets, all of which are consistent with z>12 galaxy. An ALMA program targeting one of the candidates shows a tentative 4sigma [OIII]88um line at z=13.27, in agreement with its photometric redshift estimate. The number density of the z~12-13 candidates is comparable to that of bright z~10 galaxies, and is consistent with a recently proposed double power-law luminosity function rather than the Schechter function, indicating little evolution in the abundance of bright galaxies from z~4 to 13. Comparisons with theoretical models show that the models cannot reproduce the bright end of rest-frame ultraviolet luminosity functions at z~10-13. Combined with recent studies reporting similarly bright galaxies at z~9-11 and mature stellar populations at z~6-9, our results indicate the existence of a number of star-forming galaxies at z>10, which will be detected with upcoming space missions such as James Webb Space Telescope, Nancy Grace Roman Space Telescope, and GREX-PLUS.

astro-ph.GA↗

arXiv2022

CHORUS IV: Mapping the Spatially Inhomogeneous Cosmic Reionization with Subaru HSC

The spatial inhomogeneity is one of the important features for understanding the reionization process; however, it has not yet been fully quantified. To map this inhomogeneous distribution, we simultaneously detect Ly$α$ emitters (LAEs) and Lyman break galaxies (LBGs) at $z \sim 6.6$ from the Subaru/Hyper Suprime-Cam (HSC) large-area ($\sim1.5\,\mathrm{ deg}^2 = 34000\,\mathrm{cMpc}^2$) deep survey. We estimate the neutral fraction, $x_\mathrm{HI}$, from the observed number density ratio of LAEs to LBGs, $n(\mathrm{LAE})/n(\mathrm{LBG})$ based on numerical radiative transfer simulation, in which model galaxies are selected to satisfy the observed selection function. While the average $x_\mathrm{HI}$ within the field of view is found to be $x_\mathrm{HI} < 0.4$, which is consistent with previous studies, the variation of $n(\mathrm{LAE})/n(\mathrm{LBG})$ within the field of view for each $140\,\mathrm{pMpc}^2$ is found to be as large as a factor of three. This may suggest a spatially inhomogeneous topology of reionization, but it also leaves open the possibility that the variation is based on the inherent large-scale structure of the galaxy distribution. Based on the simulations, it may be difficult to distinguish between the two from the current survey. We also find that LAEs in the high LAE density region are more populate high $\mathrm{EW}_0$, supporting that the observed $n(\mathrm{LAE})/n(\mathrm{LBG})$ is more or less driven by the neutral fraction, though the statistical significance is not high.

astro-ph.GA↗

arXiv2021

A Morphological Study on Galaxies Hosting Optical Variability-Selected AGNs in the COSMOS Field

The morphological study is crucial to investigate the connections between active galactic nuclei (AGN) activities and the evolution of galaxies. Substantial studies have found that radiative-mode AGNs primarily reside in disk galaxies, questioning the merger-driven mechanism of AGN activities. In this study, through S{é}rsic profile fitting and non-parametric morphological parameter measurements, we investigated the morphology of host galaxies of 485 optical variability-selected low luminosity AGNs at $z\lesssim4.26$ in the COSMOS field. We analyzed high-resolution images of the Hubble Space Telescope to measure these morphological parameters. We only successfully measured the morphological parameters for 76 objects and most AGN hosts ($\sim70\%$) were visually compact point-like sources. We examined the obtained morphological information as a function of redshift and compared them with literature data. We found that these AGN host galaxies showed no clear morphological preference. However, the merger rate increased with the higher hosts' SFRs and AGN luminosity. Interestingly, we found ongoing star formation consistent with the typical star forming populations in both elliptical and spiral galaxies while these two types of galaxies were more symmetric than normal star forming galaxies. These results suggested that optical variability-selected AGNs have} higher probabilities to reside in elliptical galaxies than infrared-selected AGNs (IR-AGNs), whose host galaxies had a strong disk-dominance, and supported recent studies that the AGN feedback could enhance star forming activities in host galaxies.

astro-ph.GA↗

arXiv2021

SILVERRUSH XI: Constraints on the Ly$α$ luminosity function and cosmic reionization at $z=7.3$ with Subaru/Hyper Suprime-Cam

The Ly$α$ luminosity function (LF) of Ly$α$ emitters (LAEs) has been used to constrain the neutral hydrogen fraction in the intergalactic medium (IGM) and thus the timeline of cosmic reionization. Here we present the results of a new narrow-band imaging survey for $z=7.3$ LAEs in a large area of $\sim 3\ \mathrm{deg}^2$ with Subaru/Hyper Suprime-Cam. No LAEs are detected down to $L_{\mathrm{Ly}α}\simeq 10^{43.2}\ \mathrm{erg\ s^{-1}}$ in an effective cosmic volume of $\sim 2\times 10^6$ Mpc$^3$, placing an upper limit to the bright part of the $z=7.3$ Ly$α$ LF for the first time and confirming a decrease in bright LAEs from $z=7.0$. By comparing this upper limit with the Ly$α$ LF in the case of the fully ionized IGM, which is predicted using an observed $z=5.7$ Ly$α$ LF on the assumption that the intrinsic Ly$α$ LF evolves in the same way as the UV LF, we obtain the relative IGM transmission $T^\mathrm{IGM}_{\mathrm{Ly}α}(7.3)/T^\mathrm{IGM}_{\mathrm{Ly}α}(5.7)<0.77$, and then the volume-averaged neutral fraction $x_\mathrm{HI}(7.3)>0.28$. Cosmic reionization is thus still ongoing at $z=7.3$, being consistent with results from other $x_\mathrm{HI}$ estimation methods. A similar analysis using literature Ly$α$ LFs finds that at $z=6.6$ and 7.0 the observed Ly$α$ LF agrees with the predicted one, consistent with full ionization.

astro-ph.GA↗