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At least 181 records · Page 10

The Palomar Transient Factory Core-collapse Supernova Host-galaxy Sample. I. Host-galaxy Distribution Functions and Environment Dependence of Core-collapse Supernovae

Several thousand core-collapse supernovae (CCSNe) of different flavors have been discovered so far. However, identifying their progenitors has remained an outstanding open question in astrophysics. Studies of SN host galaxies have proven to be powerful in providing constraints on the progenitor populations. In this paper, we present all CCSNe detected between 2009 and 2017 by the Palomar Transient Factory. This sample includes 888 SNe of 12 distinct classes out to redshift z ≈ 1. We present the photometric properties of their host galaxies from the far-ultraviolet to the mid-infrared and model the host-galaxy spectral energy distributions to derive physical properties. The galaxy mass function of Type Ic, Ib, IIb, II, and IIn SNe ranges from 105 to 1011.5 M o˙, probing the entire mass range of star-forming galaxies down to the least-massive star-forming galaxies known. Moreover, the galaxy mass distributions are consistent with models of star-formation-weighted mass functions. Regular CCSNe are hence direct tracers of star formation. Small but notable differences exist between some of the SN classes. Type Ib/c SNe prefer galaxies with slightly higher masses (i.e., higher metallicities) and star formation rates than Type IIb and II SNe. These differences are less pronounced than previously thought. H-poor superluminous supernovae (SLSNe) and SNe Ic-BL are scarce in galaxies above 1010 M o˙. Their progenitors require environments with metallicities of < 0.4 and < 1 solar, respectively. In addition, the hosts of H-poor SLSNe are dominated by a younger stellar population than all other classes of CCSNe. Our findings corroborate the notion that low metallicity and young age play an important role in the formation of SLSN progenitors.

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Formation of S0s in extreme environments Ⅲ: the role of environment in the formation pathways

It is well established that there are at least two main channels to form lenticular (or S0) galaxies. The first, which we name ‘faded spiral’ scenario, includes quenching events that led to consumption or removal of gas from a spiral progenitor. The second, which we call ‘merger’ scenario, includes merger-like events and interactions between galaxies. Each scenario leaves characteristic signatures in the newly formed lenticular galaxy. However, the conditions that trigger one mechanism over another are still unknown. This paper is the third of a series aimed at understanding the role of the environment in the formation of lenticular galaxies. In this study, we combine the kinematics, morphology, and properties of the stellar populations of 329 S0s from the SAMI and MaNGA surveys in order to highlight the role of the environment in the process. We divide the S0s into two classes (A and B) according to their global properties, that we can associate to the products of a faded spiral scenario (class A) or a merger scenario (class B). Here we then study how the various classes are distributed within different environments. Our study reveals that the ‘faded spiral’ pathway is the most efficient channel to produce S0s, and it becomes more efficient as the mass of the group or cluster or local density of galaxies increase. The merger pathway is also a viable channel, and its efficiency becomes higher with decreasing local density or environment mass.

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New Conductive Opacities for White Dwarf Envelopes

Thanks to their continuous cooling and relative simplicity, white dwarf stars are routinely used to measure the ages of stellar populations. The usefulness of white dwarfs as cosmochronometers depends on the availability of accurate cooling models. A key ingredient of those models is conductive opacities, which largely govern the cooling rate. In this work, we present improved conductive opacities for the regime of moderate coupling and moderate degeneracy that characterizes an important portion of the envelopes of DA and DB white dwarfs. Here, we find differences of up to a factor of 3 between our calculations and the commonly used opacities of Cassisi et al., which we attribute to an improved account of electron–electron scattering. The cooling models are strongly affected by those changes in the conductive opacities: the age of a 4000 K white dwarf can be reduced by as much as 2 Gyr. We provide analytical fits to our new opacities to facilitate the implementation of this important effect in white dwarf evolution codes.

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Substructure in the stellar halo near the Sun: II. Characterisation of independent structures

In an accompanying paper, we present a data-driven method for clustering in ‘integrals of motion’ space and apply it to a large sample of nearby halo stars with 6D phase-space information. The algorithm identified a large number of clusters, many of which could tentatively be merged into larger groups. The goal here is to establish the reality of the clusters and groups through a combined study of their stellar populations (average age, metallicity, and chemical and dynamical properties) to gain more insights into the accretion history of the Milky Way. To this end, we developed a procedure that quantifies the similarity of clusters based on the Kolmogorov–Smirnov test using their metallicity distribution functions, and an isochrone fitting method to determine their average age, which is also used to compare the distribution of stars in the colour–absolute magnitude diagram. Also taking into consideration how the clusters are distributed in integrals of motion space allows us to group clusters into substructures and to compare substructures with one another. We find that the 67 clusters identified by our algorithm can be merged into 12 extended substructures and 8 small clusters that remain as such. The large substructures include the previously known Gaia-Enceladus, Helmi streams, Sequoia, and Thamnos 1 and 2. We identify a few over-densities that can be associated with the hot thick disc and host a small metal-poor population. Especially notable is the largest (by number of member stars) substructure in our sample which, although peaking at the metallicity characteristic of the thick disc, has a very well populated metal-poor component, and dynamics intermediate between the hot thick disc and the halo. We also identify additional debris in the region occupied by Sequoia with clearly distinct kinematics, likely remnants of three different accretion events with progenitors of similar masses. Although only a small subset of the stars in our sample have chemical abundance information, we are able to identify different trends of [Mg/Fe] versus [Fe/H] for the various substructures, confirming our dissection of the nearby halo. We find that at least 20% of the halo near the Sun is associated to substructures. When comparing their global properties, we note that those substructures on retrograde orbits are not only more metal-poor on average but are also older. We provide a table summarising the properties of the substructures, as well as a membership list that can be used for follow-up chemical abundance studies for example.

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Quantifying radial migration in the Milky Way: inefficient over short time-scales but essential to the very outer disc beyond ∼15 kpc

ABSTRACT Stellar radial migration plays an important role in reshaping a galaxy’s structure and the radial distribution of stellar population properties. In this work, we revisit reported observational evidence for radial migration and quantify its strength using the age–[Fe/H] distribution of stars across the Milky Way with APOGEE data. We find a broken age–[Fe/H] relation in the Galactic disc at r > 6 kpc, with a more pronounced break at larger radii. To quantify the strength of radial migration, we assume stars born at each radius have a unique age and metallicity, and then decompose the metallicity distribution function (MDF) of mono-age young populations into different Gaussian components that originated from various birth radii at rbirth < 13 kpc. We find that, at ages of 2 and 3 Gyr, roughly half the stars were formed within 1 kpc of their present radius, and very few stars (<5 per cent) were formed more than 4 kpc away from their present radius. These results suggest limited short-distance radial migration and inefficient long-distance migration in the Milky Way during the last 3 Gyr. In the very outer disc beyond 15 kpc, the observed age–[Fe/H] distribution is consistent with the prediction of pure radial migration from smaller radii, suggesting a migration origin of the very outer disc. We also estimate intrinsic metallicity gradients at ages of 2 and 3 Gyr of −0.061 and −0.063 dex kpc−1, respectively.

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Emission line predictions for mock galaxy catalogues: a new differentiable and empirical mapping from DESI

ABSTRACT We present a simple, differentiable method for predicting emission line strengths from rest-frame optical continua using an empirically determined mapping. Extensive work has been done to develop mock galaxy catalogues that include robust predictions for galaxy photometry, but reliably predicting the strengths of emission lines has remained challenging. Our new mapping is a simple neural network implemented using the JAX Python automatic differentiation library. It is trained on Dark Energy Spectroscopic Instrument Early Release data to predict the equivalent widths (EWs) of the eight brightest optical emission lines (including H α, H β, [O ii], and [O iii]) from a galaxy’s rest-frame optical continuum. The predicted EW distributions are consistent with the observed ones when noise is accounted for, and we find Spearman’s rank correlation coefficient ρs > 0.87 between predictions and observations for most lines. Using a non-linear dimensionality reduction technique, we show that this is true for galaxies across the full range of observed spectral energy distributions. In addition, we find that adding measurement uncertainties to the predicted line strengths is essential for reproducing the distribution of observed line-ratios in the BPT diagram. Our trained network can easily be incorporated into a differentiable stellar population synthesis pipeline without hindering differentiability or scalability with GPUs. A synthetic catalogue generated with such a pipeline can be used to characterize and account for biases in the spectroscopic training sets used for training and calibration of photo-z’s, improving the modelling of systematic incompleteness for the Rubin Observatory LSST and other surveys.

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Identifying RR Lyrae Variable Stars in Six Years of the Dark Energy Survey

We present a search for RR Lyrae stars using the full six-year data set from the Dark Energy Survey covering ∼5000 deg2 of the southern sky. Using a multistage multivariate classification and light-curve template-fitting scheme, we identify RR Lyrae candidates with a median of 35 observations per candidate. We detect 6971 RR Lyrae candidates out to ∼335 kpc, and we estimate that our sample is >70% complete at ∼150 kpc. We find excellent agreement with other wide-area RR Lyrae catalogs and RR Lyrae studies targeting the Magellanic Clouds and other Milky Way satellite galaxies. We fit the smooth stellar halo density profile using a broken-power-law model with fixed halo flattening (q = 0.7), and we find strong evidence for a break at with an inner slope of and an outer slope of . We use our catalog to perform a search for Milky Way satellite galaxies with large sizes and low luminosities. Using a set of simulated satellite galaxies, we find that our RR Lyrae-based search is more sensitive than those using resolved stellar populations in the regime of large (r h ≳ 500 pc), low-surface-brightness dwarf galaxies. A blind search for large, diffuse satellites yields three candidate substructures. The first can be confidently associated with the dwarf galaxy Eridanus II. The second has a distance and proper motion similar to the ultrafaint dwarf galaxy Tucana II but is separated by ∼5 deg. The third is close in projection to the globular cluster NGC 1851 but is ∼10 kpc more distant and appears to differ in proper motion.

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Final Targeting Strategy for the SDSS-IV APOGEE-2S Survey

APOGEE is a high-resolution (R ~ 22,000), near-infrared, multi-epoch, spectroscopic survey of the Milky Way. The second generation of the APOGEE project, APOGEE-2, includes an expansion of the survey to the Southern Hemisphere called APOGEE-2S. This expansion enabled APOGEE to perform a fully panoramic mapping of all of the main regions of the Milky Way; in particular, by operating in the H band, APOGEE is uniquely able to probe the dust-hidden inner regions of the Milky Way that are best accessed from the Southern Hemisphere. In this paper we present the targeting strategy of APOGEE-2S, with special attention to documenting modifications to the original, previously published plan. The motivation for these changes is explained as well as an assessment of their effectiveness in achieving their intended scientific objective. In anticipation of this being the last paper detailing APOGEE targeting, we present an accounting of all such information complete through the end of the APOGEE-2S project; this includes several main survey programs dedicated to exploration of major stellar populations and regions of the Milky Way, as well as a full list of programs contributing to the APOGEE database through allocations of observing time by the Chilean National Time Allocation Committee and the Carnegie Institution for Science. This work was presented along with a companion article, Beaton et al. (2021), presenting the final target selection strategy adopted for APOGEE-2 in the Northern Hemisphere.

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photoD with Rubin ’s Data Preview 1: First stellar photometric distances and faint blue star deficits

Aims. We investigate the utility of Rubin’s Data Preview 1 (DP1) for estimating stellar number density profiles across the Milky Way halo. Methods. We used stellar broad-band near-UV to near-IR ugrizy photometry released in Rubin’s DP1 to estimate distance and metallicity for blue main sequence stars brighter than r = 24 in three ~1.1 sq. deg. fields at southern Galactic latitudes. Results. Compared to TRILEGAL simulations of the Galaxy’s stellar content, we found a likely deficit of blue main sequence turn-off stars with 22 < r < 24. We interpreted this discrepancy as a signature of a steeper halo number density profile at galactocentric distances 10–50 kpc than the canonical ~1/r 3 profile assumed in TRILEGAL simulations. Conclusions. This interpretation is consistent with earlier suggestions based on observations of more luminous, but much less numerous, evolved stellar populations, along with a few pencil beam surveys of blue main sequence stars in the northern sky. These results bode well for the future Galactic halo exploration with Rubin’s Legacy Survey of Space and Time (LSST).

Galaxy: fundamental parameters↗

The use of double-mode RR Lyrae stars as robust distance and metallicity indicators

Abstract RR Lyrae stars are one of the primary distance indicators for old stellar populations such as globular clusters, dwarf galaxies and galaxies. Typically, fundamental-mode RR Lyr stars are used for distance measurements, and their accuracy is strongly limited by the dependence of absolute magnitudes on metallicity, in both the optical and infrared bands. Here, we report the discovery of a period–(period ratio)–metallicity relation for double-mode RR Lyr stars, which can predict metallicity as accurately as the low-resolution spectra. With theoretical and observational evidence, we propose that the period–luminosity relation of double-mode RR Lyr stars is not affected by the metallicity. Combining the Large Magellanic Cloud distance and Gaia parallaxes, we calibrate the zero point of the period–luminosity relation to an error of 0.022 mag, which means that in the best case double-mode RR Lyr stars can anchor galaxy distances to an accuracy of 1.0%. For four globular clusters and two dwarf galaxies, we obtain distances using double-mode RR Lyr stars with a distance accuracy of 2–3% and 1–2%, respectively. With future telescopes such as the China Space Station Telescope and the Vera C. Rubin Observatory, double-mode RR Lyr stars will be established as an independent distance ladder in the near-field universe.

Astronomy & Astrophysics↗

Spectroscopic confirmation of a mature galaxy cluster at a redshift of 2

Galaxy clusters are the most massive virialized structures in the Universe and are formed through the gravitational accretion of matter over cosmic time. The discovery of an evolved galaxy cluster at redshift z = 2, corresponding to a look-back time of 10.4 billion years, provides an opportunity to study its properties. The galaxy cluster XLSSC 122 was originally detected as a faint, extended X-ray source in the XMM Large Scale Structure survey and was revealed to be coincident with a compact over-density of galaxies with photometric redshifts of 1.9 ± 0.2. Subsequent observations at millimetre wavelengths detected a Sunyaev–Zel’dovich decrement along the line of sight to XLSSC 122, thus confirming the existence of hot intracluster gas, while deep imaging spectroscopy from the European Space Agency’s X-ray Multi-Mirror Mission (XMM-Newton) revealed an extended, X-ray-bright gaseous atmosphere with a virial temperature of 60 million Kelvin, enriched with metals to the same extent as are local clusters. Here we report optical spectroscopic observations of XLSSC 122 and identify 37 member galaxies at a mean redshift of 1.98, corresponding to a look-back time of 10.4 billion years. We use photometry to determine a mean, dust-free stellar age of 2.98 billion years, indicating that star formation commenced in these galaxies at a mean redshift of 12, when the Universe was only 370 million years old. The full range of inferred formation redshifts, including the effects of dust, covers the interval from 7 to 13. These observations confirm that XLSSC 122 is a remarkably mature galaxy cluster with both evolved stellar populations in the member galaxies and a hot, metal-rich gas composing the intracluster medium.

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Toward precision cosmochronology

The continuous cooling of a white dwarf is punctuated by events that affect its cooling rate. The most significant of these events is the crystallization of its core, a phase transition that occurs once the C/O interior has cooled down below a critical temperature. This transition releases latent heat, as well as gravitational energy due to the redistribution of the C and O ions during solidification, thereby slowing down the evolution of the white dwarf. The unambiguous observational signature of core crystallization–a pile-up of objects in the cooling sequence–was recently reported. However, existing evolution models struggle to quantitatively reproduce this signature, casting doubt on their accuracy when used to measure the ages of stellar populations. The timing and amount of the energy released during crystallization depend on the exact form of the C/O phase diagram. Using the advanced Gibbs–Duhem integration method and state-of-the-art Monte Carlo simulations of the solid and liquid phases, we obtained a very accurate version of this phase diagram that allows a precise modeling of the phase transition. Despite this improvement, the magnitude of the crystallization pile-up remains underestimated by current evolution models. We conclude that latent heat release and O sedimentation alone are not sufficient to explain the observations, and that other unaccounted physical mechanisms, possibly 22 Ne phase separation, play an important role.

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The dependence of the gradients of oxygen and nitrogen-to-oxygen on stellar age in MaNGA galaxies

For this work, we derived the oxygen abundance (O/H), the nitrogen-to-oxygen (N/O) abundance ratio, and their corresponding radial gradients for a sample of 1431 galaxies from the MaNGA DR15 survey using two different realisations of the strong line method: empirical R calibration and the Bayesian model-based HII-CHI-MISTRY (HCM) code. We find that both abundance calculation methods reveal a correlation between the O/H gradient and the stellar mass of a galaxy. This relation is non-linear, with the steepest average gradients in the intermediate mass range and flatter average gradients for high- and low-mass galaxies. The relation between the N/O gradient and the stellar mass is, on average, non-linear with the steepest gradients in the intermediate mass range (log(M/M ⊙ )~10), flatter gradients for high-mass galaxies, and the flattest gradients for low-mass galaxies. However, the general trend of steepening N/O gradients for higher masses, as reported in previous studies, remains evident. We find a dependence between the O/H and N/O gradients and the galaxy mean stellar age traced by the D(4000) index. For galaxies of lower masses, both gradients are, generally, steeper for intermediate values of D(4000) and flatter for low and high values of D(4000). Only the most massive galaxies do not show this correlation. We interpret this behaviour as an evolution of the metallicity gradients with the age of stellar population. Though the galaxies with a positive slope of the D(4000) radial gradient tend to have flatter O/H and N/O gradients, as compared to those with a negative D(4000) gradient.

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Star formation in outer rings of S0 galaxies: IV. NGC 254: A double-ringed S0 with gas counter-rotation

Although S0 galaxies are usually considered “red and dead”, they often demonstrate star formation organized into ring structures. We aim to clarify the nature of this phenomenon and how it differs from star formation in spiral galaxies. We investigated the nearby, moderate-luminosity S0 galaxy NGC 254 using long-slit spectroscopy taken with the South African Large Telescope and publicly available imaging data. Applying a full spectral fitting, we analyzed gaseous and stellar kinematics as well as ionized gas excitation and metallicity and stellar population properties resolved by radius. An advanced approach of simultaneously fitting spectra and photometric data allowed us to quantify the fraction of hidden counter-rotating stars in this galaxy. We find that the ionized gas is counter-rotating with respect to the stars throughout NGC 254 disk, indicating an external origin of the gas. We argue the gas-rich galaxy merger from retrograde orbit as a main source of counter-rotating material. The star formation fed by this counter-rotating gas occurs within two rings: an outer ring at R = 55' - 70" and an inner ring at R = 18". The star formation rate is weak, 0.02 solar mass per year in total, and the gas metallicity is slightly subsolar. We estimated that the accretion of the gas occurred about 1 Gyr ago, and about 1% of all stars have formed in situ from counter-rotating gas.

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The chemical composition of globular clusters in the Local Group

We present detailed chemical abundance measurements for 45 globular clusters (GCs) associated with galaxies in (and, in one case, beyond) the Local Group. The measurements are based on new high-resolution integrated-light spectra of GCs in the galaxies NGC 185, NGC 205, M 31, M 33, and NGC 2403, combined with reanalysis of previously published observations of GCs in the Fornax dSph, WLM, NGC 147, NGC 6822, and the Milky Way. The GCs cover the range -2.8 < [Fe/H] < -0.1 and we determined abundances for Fe, Na, Mg, Si, Ca, Sc, Ti, Cr, Mn, Ni, Cu, Zn, Zr, Ba, and Eu. Corrections for non local thermodynamic equilibrium effects are included for Na, Mg, Ca, Ti, Mn, Fe, Ni, and Ba, building on a recently developed procedure. For several of the galaxies, our measurements provide the first quantitative constraints on the detailed composition of their metal-poor stellar populations. Overall, the GCs in different galaxies exhibit remarkably uniform abundance patterns of the α, iron-peak, and neutron-capture elements, with a dispersion of less than 0.1 dex in [α/Fe] for the full sample. There is a hint that GCs in dwarf galaxies are slightly less α-enhanced (by ~0.04 dex on average) than those in larger galaxies. One GC in M 33 (HM33-B) resembles the most metal-rich GCs in the Fornax dSph (Fornax 4) and NGC 6822 (SC7) by having α-element abundances closer to scaled-solar values, possibly hinting at an accretion origin. A principal components analysis shows that the α-element abundances strongly correlate with those of Na, Sc, Ni, and Zn. Several GCs with [Fe/H] < -1.5 are deficient in Mg compared to other α-elements. We find no GCs with strongly enhanced r-process abundances as reported for metal-poor stars in some ultra-faint dwarfs and the Magellanic Clouds. The similarity of the abundance patterns for metal-poor GCs in different environments points to similar early enrichment histories and only allow for minor variations in the initial mass function.

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Stragglers of the thick disc

Young alpha-rich (YAR) stars have been detected in the past as outliers to the local age - [α/Fe] relation. These objects are enhanced in α-elements, but they are apparently younger than typical thick disc stars. Here, we study the global kinematics and chemical properties of YAR giant stars in the APOGEE DR17 survey and show that they have properties similar to those of the standard thick disc stellar population. This leads us to conclude that YAR are rejuvenated thick disc objects, and the most likely explanation is that they are evolved blue stragglers. This is confirmed by their position in the Hertzsprung–Russel diagram (HRD). Extending our selection to dwarfs allowed us to obtain the first general straggler distribution in an HRD of field stars. We also compared the elemental abundances of our sample with those of standard thick disc stars and found that our YAR stars are shifted in oxygen, magnesium, sodium, and the slow neutron-capture element cerium. Although we detected no sign of binarity for most objects, the enhancement in cerium may be a signature of a mass transfer from an asymptotic giant branch companion. The most massive YAR stars suggest that mass transfer from an evolved star may not be the only plausible formation pathway and that other scenarios, such as collision or coalescence, should be considered.

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Heavy dark matter in rapidly evolving massive stars

We study the impact of heavy dark matter (DM) captured in massive stars via scattering(s) with the star constituents. We focus on the first stars and use stellar evolution simulations to track down how DM capture evolves over time from the zero-age main sequence to the late metal-rich stages of stellar evolution. During the early hydrogen-helium-dominated phase, the capture process is well described by scattering with two targets. As a star evolves, metal production leads to the formation of a dense core surrounded by a lighter envelope. The core significantly enhances the capture of ultra-heavy DM; in this case, three distinct nuclear species are required to accurately describe multiple-scattering capture. We use the Eddington inversion method to obtain a realistic DM velocity distribution, better suited when the star is near the center of a halo, than the widely used Maxwell-Boltzmann distribution. We find that heavy DM would be able to thermalize and achieve capture-annihilation equilibrium within a massive star's lifetime for regions of the parameter space not excluded by direct detection. For non-annihilating DM, because of the high amount of targets available for capture and despite massive stars being short-lived, it would even be possible for DM to achieve self-gravitation and collapse to a black hole, which eventually could swallow the star from within before the expected end of the star's life, for non-excluded regions of the parameter space. Our results highlight the dependence of DM capture on the stellar evolutionary stage, composition, and halo location, demonstrating that accurate modeling of massive stars is essential for constraining heavy DM with primordial stellar populations.

dark matter theory↗

Photometric Redshifts and Galaxy Clusters for DES DR2, DESI DR9, and HSC-SSP PDR3 Data

Photometric redshift (photoz) is a fundamental parameter for multi-wavelength photometric surveys, while galaxy clusters are important cosmological probes and ideal objects for exploring the dense environmental impact on galaxy evolution. We extend our previous work on estimating photoz and detecting galaxy clusters to the latest data releases of the Dark Energy Spectroscopic Instrument (DESI) imaging surveys, Dark Energy Survey (DES) and Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) imaging surveys and make corresponding catalogs publicly available for more extensive scientific applications. The photoz catalogs include accurate measurements of photoz and stellar mass for about 320, 293 and 134 million galaxies with r < 23, i < 24 and i < 25 in DESI DR9, DES DR2 and HSC-SSP PDR3 data, respectively. The photoz accuracy is about 0.017, 0.024 and 0.029 and the general redshift coverage is z < 1, z < 1.2 and z < 1.6, respectively for those three surveys. Furthermore, the uncertainty of the logarithmic stellar mass that is inferred from stellar population synthesis fitting is about 0.2 dex. With the above photoz catalogs, galaxy clusters are detected using a fast cluster-finding algorithm. A total of 532,810, 86,963 and 36,566 galaxy clusters with the number of members larger than 10 is discovered for DESI, DES and HSC-SSP, respectively. Their photoz accuracy is at the level of 0.01. The total mass of our clusters is also estimated by using the calibration relations between the optical richness and the mass measurement from X-ray and radio observations. The photoz and cluster catalogs are available at ScienceDB (https://www.doi.org/10.11922/sciencedb.o00069.00003) and PaperData Repository (https://doi.org/10.12149/101089).

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