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Let ${\cal K}_1(G)$ denote the inverse subsemigroup of ${\cal K}(G)$ consisting of all right cosets of all non-trivial subgroups of $G$. This paper concentrates on the study of the group $\Sigma({\cal K}_1(G))$ of all units of the completion of ${\cal K}_1(G)$. The characterizations and the representations of $\Sigma({\cal K}_1(G))$ are given when $G$ is a periodic group whose minimal subgroups permute with each other. Based on these, for such groups $G$ except some special $p$-groups, it is shown that $G$ and its coset semigroup ${\cal K}_1(G)$ are uniquely determined by each other, up to isomorphism. This extends the related results obtained by Schein in 1973.

In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids with semilattice $E$ of idempotents and the group $G$ of units such that the natural connection $\theta$ is a dual isomorphism from $E$ to a sublattice of $L(G)$, then any two composition subcentral (resp., central) idempotent series in $S$ are isomorphic. It may be considered as an appropriate analogue in semigroup theory of Jordan-H\"{o}lder Theorem in group theory. Based on this,$G$-nilpotent and $G$-solvable inverse monoids are also introduced and studies. Some characterizations of the coset monoid of nilpotent groups and solvable groups are given. This extends the main result in Semigroup Forum 20: 255-267, 1980 and also provides another effective approach for the study of nilpotent and solvable groups. Finally, some open problems related to nilpotent and solvable groups are translated to semigroup theory, which may be helpful for us to solve these open problems.

The process of galaxy cluster formation likely leaves an imprint on the properties of its individual member galaxies. Understanding this process is essential for uncovering the evolutionary connections between galaxies and cosmic structures. Here we study a sample of ten protoclusters at z~2-3 in different dynamical states that we estimate based on spectroscopic data of their members. We combine the dynamical information with HST imaging to measure galaxy sizes and pair fractions. Our analysis reveals a clear anti-correlation between the velocity dispersion of the protocluster and its galaxy pair fractions (indicative of merger rates). The velocity dispersion also anti-correlates with the dispersion in size among of the member galaxies. These correlations may be explained by protoclusters in colder dynamical states maintaining a velocity dispersion and galaxy number density that boosts galaxy mergers, which in turn contributes to the structural expansion and compaction of galaxies. Our findings offer constraints for cosmological models regarding the evolution of galaxy morphology across different stages in the assembly of protoclusters., Comment: 11 pages, 8 figures, 1 table. Accepted for publication in MNRAS

Thanks to the rapidly increasing time-domain facilities, we are entering a golden era of research on gamma-ray bursts (GRBs). In this Letter, we report our observations of GRB 240529A with the Burst Optical Observer and Transient Exploring System, the 1.5-meter telescope at Observatorio Sierra Nevada, the 2.5-meter Wide Field Survey Telescope of China, the Large Binocular Telescope, and the Telescopio Nazionale Galileo. The prompt emission of GRB 240529A shows two comparable energetic episodes separated by a quiescence time of roughly 400 s. Combining all available data on the GRB Coordinates Network, we reveal the simultaneous apparent X-ray plateau and optical re-brightening around $10^3-10^4$ s after the burst. Rather than the energy injection from the magnetar as widely invoked for similar GRBs, the multi-wavelength emissions could be better explained as two shocks launched from the central engine separately. The optical peak time and our numerical modeling suggest that the initial bulk Lorentz factor of the later shock is roughly 50, which indicates that the later jet should be accretion-driven and have a higher mass loading than a typical one. The quiescence time between the two prompt emission episodes may be caused by the transition between different accretion states of a central magnetar or black hole, or the fall-back accretion process. A sample of similar bursts with multiple emission episodes in the prompt phase and sufficient follow-up could help to probe the underlying physics of GRB central engines., Comment: Resubmitted to ApJL after addressing the referee's comments; comments are welcome

Chinese Space Station Telescope (CSST) has the capability to conduct slitless spectroscopic survey simultaneously with photometric survey. The spectroscopic survey will measure slitless spectra, potentially providing more accurate estimations of galaxy properties, particularly redshifts, compared to using broadband photometry. CSST relies on these accurate redshifts to perform baryon acoustic oscilliation (BAO) and other probes to constrain the cosmological parameters. However, due to low resolution and signal-to-noise ratio of slitless spectra, measurement of redshifts is significantly challenging.} In this study, we employ a Bayesian neural network (BNN) to assess the accuracy of redshift estimations from slitless spectra anticipated to be observed by CSST. The simulation of slitless spectra is based on real observational data from the early data release of the Dark Energy Spectroscopic Instrument (DESI-EDR) and the 16th data release of the Baryon Oscillation Spectroscopic Survey (BOSS-DR16), combined with the 9th data release of the DESI Legacy Survey (DESI LS DR9). The BNN is constructed employing transfer learning technique, by appending two Bayesian layers after a convolutional neural network (CNN), leveraging the features learned from the slitless spectra and corresponding redshifts. Our network can provide redshift estimates along with corresponding uncertainties, achieving an accuracy of $\sigma_{\rm NMAD} = 0.00063$, outlier percentage $\eta=0.92\%$ and weighted mean uncertainty $\bar{E} = 0.00228$. These results successfully fulfill the requirement of $\sigma_{\rm NMAD} < 0.005$ for BAO and other studies employing CSST slitless spectroscopic surveys., Comment: 14 pages, 12 figures, accepted for publication in ApJ

We present confusion-limited SCUBA-2 450-$\mu$m observations in the COSMOS-CANDELS region as part of the JCMT Large Program, SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES). Our maps at 450 and 850 $\mu$m cover an area of 450 arcmin$^2$. We achieved instrumental noise levels of $\sigma_{\mathrm{450}}=$ 0.59 mJy beam$^{-1}$ and $\sigma_{\mathrm{850}}=$ 0.09 mJy beam$^{-1}$ in the deepest area of each map. The corresponding confusion noise levels are estimated to be 0.65 and 0.36 mJy beam$^{-1}$. Above the 4 (3.5) $\sigma$ threshold, we detected 360 (479) sources at 450 $\mu$m and 237 (314) sources at 850 $\mu$m. We derive the deepest blank-field number counts at 450 $\mu$m, covering the flux-density range of 2 to 43 mJy. These are in agreement with other SCUBA-2 blank-field and lensing-cluster observations, but are lower than various model counts. We compare the counts with those in other fields and find that the field-to-field variance observed at 450 $\mu$m at the $R=6^\prime$ scale is consistent with Poisson noise, so there is no evidence of strong 2-D clustering at this scale. Additionally, we derive the integrated surface brightness at 450 $\mu$m down to 2.1 mJy to be $57.3^{+1.0}_{-6.2}$~Jy deg$^{-2}$, contributing to (41$\pm$4)\% of the 450-$\mu$m extragalactic background light (EBL) measured by COBE and Planck. Our results suggest that the 450-$\mu$m EBL may be fully resolved at $0.08^{+0.09}_{-0.08}$~mJy, which extremely deep lensing-cluster observations and next-generation submillimeter instruments with large aperture sizes may be able to achieve., Comment: 29 pages, 14 figures, accepted for publication in ApJ

The measurements of morphological indicators of galaxies are often influenced by a series of observational effects. In this study, we utilize a sample of over 800 TNG50 simulated galaxies with log($M_*$/M$_\odot$)$>9$ at $0.51$\,$\mu$m. The morphological indicators of star-forming galaxies (SFGs) and quiescent galaxies (QGs) are significantly different. The morphologies of QGs exhibit a higher sensitivity to rest-frame wavelength than SFGs. After analyzing the evolution of morphological indicators in the rest-frame V-band (0.5-0.7\,$\mu$m) and rest-frame J-band (1.1-1.4\,$\mu$m), we find that the morphologies of QGs evolve substantially with both redshift and stellar mass. For SFGs, the $C$, $Gini$ and $M_{\rm 20}$ show a rapid evolution with stellar mass at log($M_*$/M$_\odot$)$\geq10.5$, while the $A_{\rm O}$, $D_{\rm O}$ and $A$ evolve with both redshift and stellar mass. Our comparison shows that TNG50 simulations effectively reproduce the morphological indicators we measured from {\it JWST} observations when the impact of dust attenuation is considered., Comment: 21 pages, 14 figures, 1 table. Accepted for publication in ApJ

The Chinese Space Station Telescope (CSST) slitless spectroscopic survey will observe objects to a limiting magnitude of ~ 23 mag (5$\sigma$, point sources) in U, V, and I over 17500 deg$^2$. The spectroscopic observations are expected to be highly efficient and complete for mapping galaxies over 0 < z < 1 with secure redshift measurements at spectral resolutions of R ~ 200, providing unprecedented data sets for cosmological studies. To quantitatively examine the survey potential, we develop a software tool, namely the CSST Emulator for Slitless Spectroscopy (CESS), to quickly generate simulated 1D slitless spectra with limited computing resources. We introduce the architecture of CESS and the detailed process of creating simulated CSST slitless spectra. The extended light distribution of a galaxy induces the self-broadening effect on the 1D slitless spectrum. We quantify the effect using morphological parameters: S\'ersic index, effective radius, position angle, and axis ratio. Moreover, we also develop a module for CESS to estimate the overlap contamination rate for CSST grating observations of galaxies in galaxy clusters. Applying CESS to the high-resolution model spectra of a sample of ~ 140 million galaxies with m_z < 21 mag selected from the Dark Energy Spectroscopic Instrument LS DR9 catalogue, we obtain the simulated CSST slitless spectra. We examine the dependence of measurement errors on different types of galaxies due to instrumental and observational effects and quantitatively investigate the redshift completeness for different environments out to z ~ 1. Our results show that the CSST spectroscopy is able to provide secure redshifts for about one-quarter of the sample galaxies., Comment: 14 pages, 15 figures, 2 tables, accepted for publication in MNRAS

Dust attenuation in star-forming galaxies (SFGs), as parameterized by the infrared excess (IRX $\equiv L_{\rm IR}/L_{\rm UV}$), is found to be tightly correlated with star formation rate (SFR), metallicity and galaxy size, following a universal IRX relation up to $z=3$. This scaling relation can provide a fundamental constraint for theoretical models to reconcile galaxy star formation, chemical enrichment, and structural evolution across cosmic time. We attempt to reproduce the universal IRX relation over $0.1\leq z\leq 2.5$ using the EAGLE hydrodynamical simulations and examine sensitive parameters in determining galaxy dust attenuation. Our findings show that while the predicted universal IRX relation from EAGLE approximately aligns with observations at $z\leq 0.5$, noticeable disparities arise at different stellar masses and higher redshifts. Specifically, we investigate how modifying various galaxy parameters can affect the predicted universal IRX relation in comparison to the observed data. We demonstrate that the simulated gas-phase metallicity is the critical quantity for the shape of the predicted universal IRX relation. We find that the influence of the infrared luminosity and infrared excess is less important while galaxy size has virtually no significant effect. Overall, the EAGLE simulations are not able to replicate some of the observed characteristics between IRX and galaxy parameters of SFGs, emphasizing the need for further investigation and testing for our current state-of-the-art theoretical models., Comment: 19 pages, 15 figures, accepted for publication in MNRAS

Aiming at improving the survey efficiency of the Wide Field Survey Telescope, we have developed a basic scheduling strategy that takes into account the telescope characteristics, observing conditions, and weather conditions at the Lenghu site. The sky area is divided into rectangular regions, referred to as `tiles', with a size of 2.577 deg * 2.634 deg slightly smaller than the focal area of the mosaic CCDs. These tiles are continuously filled in annulars parallel to the equator. The brightness of the sky background, which varies with the moon phase and distance from the moon, plays a significant role in determining the accessible survey fields. Approximately 50 connected tiles are grouped into one block for observation. To optimize the survey schedule, we perform simulations by taking into account the length of exposures, data readout, telescope slewing, and all relevant observing conditions. We utilize the Greedy Algorithm for scheduling optimization. Additionally, we propose a dedicated dithering pattern to cover the gaps between CCDs and the four corners of the mosaic CCD array, which are located outside of the 3 deg field of view. This dithering pattern helps to achieve relatively uniform exposure maps for the final survey outputs., Comment: 14 pages, 7 figures, 1 table. Accepted for pubulication in Research in Astronomy and Astrophysics

We revisit the evolution of galaxy morphology in the COSMOS field over the redshift range $0.2\leq z \leq 1$, using a large and complete sample of 33,605 galaxies with a stellar mass of log($M_{\ast}$/M$_{\odot} )>9.5$ with significantly improved redshifts and comprehensive non-parametric morphological parameters. Our sample has 13,881 ($\sim41.3\%$) galaxies with reliable spectroscopic redshifts and has more accurate photometric redshifts with a $\sigma_{\rm NMAD} \sim 0.005$. This paper is the first in a series that investigates merging galaxies and their properties. We identify 3,594 major merging galaxies through visual inspection and find 1,737 massive galaxy pairs with log($M_\ast$/M$_\odot$)$>10.1$. Among the family of non-parametric morphological parameters including $C$, $A$, $S$, $Gini$, $M_{\rm 20}$, $A_{\rm O}$, and $D_{\rm O}$, we find that the outer asymmetry parameter $A_{\rm O}$ and the second-order momentum parameter $M_{\rm 20}$ are the best tracers of merging features than other combinations. Hence, we propose a criterion for selecting candidates of violently star-forming mergers: $M_{\rm 20}> -3A_{\rm O}+3$ at $0.2 -6A_{\rm O}+3.7$ at $0.6

Expected to be of the highest survey power telescope in the northern hemisphere, the Wide Field Survey Telescope (WFST) will begin its routine observations of the northern sky since 2023. WFST will produce a lot of scientific data to support the researches of time-domain astronomy, asteroids and the solar system, galaxy formation and cosmology and so on. We estimated that the 5 $\sigma$ limiting magnitudes of WFST with 30 second exposure are $u=22.31$ mag, $g=23.42$ mag, $r=22.95$ mag, $i=22.43$ mag, $z=21.50$ mag, $w=23.61$ mag. The above values are calculated for the conditions of $airmass=1.2$, seeing = 0.75 arcsec, precipitable water vapour (PWV) = 2.5 mm and Moon-object separation = $45^{\circ}$ at the darkest New Moon night of the Lenghu site (V=22.30 mag, Moon phase $\theta=0^{\circ}$). The limiting magnitudes in different Moon phase conditions are also calculated. The calculations are based on the empirical transmittance data of WFST optics, the vendor provided CCD quantum efficiency, the atmospherical model transmittance and spectrum of the site. In the absence of measurement data such as sky transmittance and spectrum, we use model data., Comment: Figure 5 (a,b,c) has been updated in this latest version. 12 pages, 5 figures, published in RAA (Research in Astronomy and Astrophysics)

We present an analysis of physical properties of 34 [O III] emission-line galaxies (ELGs) at z=3.254$\pm$0.029 in the Extended Chandra Deep Field South (ECDFS). These ELGs are selected from deep narrow H2S(1) and broad Ks imaging of 383 arcmin$^{2}$ obtained with CFHT/WIRCam. We construct spectral energy distributions (SEDs) from U to Ks to derive the physical properties of ELGs. These [O III] ELGs are identified as starburst galaxies with strong [O III] lines of L([O III]) ~ 10$^{42.6}$ - 10$^{44.2}$ erg s$^{-1}$, and have stellar masses of M* ~ 10$^{9.0}$-10$^{10.6}$ M$_\odot$ and star formation rates of ~ 10-210 M$_\odot$ yr$^{-1}$. Our results show that 24% of our sample galaxies are dusty with Av > 1 mag and EW(OIII)$_{rest}$ ~ 70-500 $\AA$, which are often missed in optically selected [O III] ELG samples. Their rest-frame UV and optical morphologies from HST/ACS and HST/WFC3 deep imaging reveal that these [O III] ELGs are mostly multiple-component systems (likely mergers) or compact. And 20% of them are nearly invisible in the rest-frame UV owing to heavy dust attenuation. Interestingly, we find that our samples reside in an overdensity consisting of two components: one southeast (SE) with an overdensity factor of $\delta_{gal}$ ~ 41 over a volume of 13$^{3}$ cMpc$^{3}$ and the other northwest (NW) with $\delta_{gal}$ ~ 38 over a volume of 10$^{3}$ cMpc$^{3}$. The two overdense substructures are expected to be virialized at z=0 with a total mass of ~ 1.1 x 10$^{15}$ M$_\odot$ and ~ 4.8 x 10$^{14}$ M$_\odot$, and probably merge into a Coma-like galaxy cluster., Comment: 22 pages, 11 figures, 3 tables. Accepted for publication in ApJ

We report the first spatially resolved measurements of gas-phase metallicity radial gradients in star-forming galaxies in overdense environments at $z\gtrsim2$. The spectroscopic data are acquired by the \mg\ survey, a Hubble Space Telescope (HST) cycle-28 medium program. This program is obtaining 45 orbits of WFC3/IR grism spectroscopy in the density peak regions of three massive galaxy protoclusters (BOSS 1244, BOSS 1542 and BOSS 1441) at $z=2-3$. Our sample in the BOSS 1244 field consists of 20 galaxies with stellar-mass ranging from $10^{9.0}$ to $10^{10.3}$ \Msun\ , star formation rate (SFR) from 10 to 240 \Msun\,yr$^{-1}$, and global gas-phase metallicity (\oh) from 8.2 to 8.6. At $1\sigma$ confidence level, 2/20 galaxies in our sample show positive (inverted) gradients -- the relative abundance of oxygen increasing with galactocentric radius, opposite the usual trend. Furthermore, 1/20 shows negative gradients and 17/20 are consistent with flat gradients. This high fraction of flat/inverted gradients is uncommon in simulations and previous observations conducted in blank fields at similar redshifts. To understand this, we investigate the correlations among various observed properties of our sample galaxies. We find an anticorrelation between metallicity gradient and global metallicity of our galaxies residing in extreme overdensities, and a marked deficiency of metallicity in our massive galaxies as compared to their coeval field counterparts. We conclude that the cold-mode gas accretion plays an active role in shaping the chemical evolution of galaxies in the protocluster environments, diluting their central chemical abundance, and flattening/inverting their metallicity gradients., Comment: 13 pages, 6 figures, 1 table. Accepted for publication in ApJL

Submillimetre galaxies represent a rapid growth phase of both star formation and massive galaxies. Mapping SMGs in galaxy protoclusters provides key insights into where and how these extreme starbursts take place in connections with the assembly of the large-scale structure in the early Universe. We search for SMGs at 850$\,\mu m$ using JCMT/SCUBA-2 in two massive protoclusters at $z=2.24$, BOSS1244 and BOSS1542, and detect 43 and 54 sources with $S_{850}>4\,$mJy at the $4\sigma$ level within an effective area of 264$\,$arcmin$^2$, respectively. We construct the intrinsic number counts and find that the abundance of SMGs is $2.0\pm0.3$ and $2.1\pm0.2$ times that of the general fields, confirming that BOSS1244 and BOSS1542 contain a higher fraction of dusty galaxies with strongly enhanced star formation. The volume densities of the SMGs are estimated to be $\sim15-$30 times the average, significantly higher than the overdensity factor ($\sim 6$) traced by H$\alpha$ emission-line galaxies (HAEs). More importantly, we discover a prominent offset between the spatial distributions of the two populations in these two protoclusters -- SMGs are mostly located around the high-density regions of HAEs, and few are seen inside these regions. This finding may have revealed for the first time the occurrence of violent star formation enhancement in the outskirts of the HAE density peaks, likely driven by the boosting of gas supplies and/or starburst triggering events. Meanwhile, the lack of SMGs inside the most overdense regions at $z\sim2$ implies a transition to the environment disfavouring extreme starbursts., Comment: 16pages, 11figures, accepted for publication in MNRAS

While the slope of the dust attenuation curve ($\delta$) is found to correlate with effective dust attenuation ($A_V$) as obtained through spectral energy distribution (SED) fitting, it remains unknown how the fitting degeneracies shape this relation. We examine the degeneracy effects by fitting SEDs of a sample of local star-forming galaxies (SFGs) selected from the Galaxy And Mass Assembly survey, in conjunction with mock galaxy SEDs of known attenuation parameters. A well-designed declining starburst star formation history is adopted to generate model SED templates with intrinsic UV slope ($\beta_0$) spanning over a reasonably wide range. The best-fitting $\beta_0$ for our sample SFGs shows a wide coverage, dramatically differing from the limited range of $\beta_0<-2.2$ for a starburst of constant star formation. Our results show that strong degeneracies between $\beta_0$, $\delta$, and $A_V$ in the SED fitting induce systematic biases leading to a false $A_V$--$\delta$ correlation. Our simulation tests reveal that this relationship can be well reproduced even when a flat $A_V$--$\delta$ relation is taken to build the input model galaxy SEDs. The variations in best-fitting $\delta$ are dominated by the fitting errors. We show that assuming a starburst with constant star formation in SED fitting will result in a steeper attenuation curve, smaller degeneracy errors, and a stronger $A_V$--$\delta$ relation. Our findings confirm that the $A_V$--$\delta$ relation obtained through SED fitting is likely driven by the systematic biases induced by the fitting degeneracies between $\beta_0$, $\delta$, and $A_V$., Comment: 21 pages, 13 figures, accepted for publication in the MNRAS, Comments welcome!