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We introduce a holographic dark energy model that incorporates the first-order approximate Kaniadaski entropy, utilizing the Hubble horizon, $1/H$, as the infrared cutoff. We investigate the cosmological evolution within this framework. The model introduces an extra parameter relative to the $\Lambda$CDM model. It posits a Universe that is initially dominated by dark matter, which then evolves to a phase where dark energy becomes the predominant component, with this transition occurring at a redshift of approximately $z \sim 0.419$. The energy density of dark energy is ultimately expected to become constant, thereby circumventing the potential issue of a "big rip". Employing the most recent Type Ia supernova and Hubble parameter data, we constrain the model's parameters and find a Hubble constant of $H_0=72.8$ km/s/Mpc, thereby resolving the Hubble tension issue. The estimated age of the Universe, based on the best-fit parameter values, is $14.2$ Gyr. Furthermore, we predict the number of strong gravitational lenses and conduct statefinder and $Om$ diagnostic analyses to validate and characterize the model., Comment: 9 pages, 5 figures

Accurate photometric redshift (photo-$z$) estimation requires support from multi-band observational data. However, in the actual process of astronomical observations and data processing, some sources may have missing observational data in certain bands for various reasons. This could greatly affect the accuracy and reliability of photo-$z$ estimation for these sources, and even render some estimation methods unusable. The same situation may exist for the upcoming Chinese Space Station Telescope (CSST). In this study, we employ a deep learning method called Generative Adversarial Imputation Networks (GAIN) to impute the missing photometric data in CSST, aiming to reduce the impact of data missing on photo-$z$ estimation and improve estimation accuracy. Our results demonstrate that using the GAIN technique can effectively fill in the missing photometric data in CSST. Particularly, when the data missing rate is below 30\%, the imputation of photometric data exhibits high accuracy, with higher accuracy in the $g$, $r$, $i$, $z$, and $y$ bands compared to the $NUV$ and $u$ bands. After filling in the missing values, the quality of photo-$z$ estimation obtained by the widely used Easy and Accurate Zphot from Yale (EAZY) software is notably enhanced. Evaluation metrics for assessing the quality of photo-$z$ estimation, including the catastrophic outlier fraction ($f_{out}$), the normalized median absolute deviation ($\rm {\sigma_{NMAD}}$), and the bias of photometric redshift ($bias$), all show some degree of improvement. Our research will help maximize the utilization of observational data and provide a new method for handling sample missing values for applications that require complete photometry data to produce results.

Accurate estimation of photometric redshifts (photo-$z$) is crucial in studies of both galaxy evolution and cosmology using current and future large sky surveys. In this study, we employ Random Forest (RF), a machine learning algorithm, to estimate photo-$z$ and investigate the systematic uncertainties affecting the results. Using galaxy flux and color as input features, we construct a mapping between input features and redshift by using a training set of simulated data, generated from the Hubble Space Telescope Advanced Camera for Surveys (HST-ACS) and COSMOS catalogue, with the expected instrumental effects of the planned China Space Station Telescope (CSST). To improve the accuracy and confidence of predictions, we incorporate inverse variance weighting and perturb the catalog using input feature errors. Our results show that weighted RF can achieve a photo-$z$ accuracy of $\rm \sigma_{NMAD}=0.025$ and an outlier fraction of $\rm \eta=2.045\%$, significantly better than the values of $\rm \sigma_{NMAD}=0.043$ and $\rm \eta=6.45\%$ obtained by the widely used Easy and Accurate Zphot from Yale (EAZY) software which uses template-fitting method. Furthermore, we have calculated the importance of each input feature for different redshift ranges and found that the most important input features reflect the approximate position of the break features in galaxy spectra, demonstrating the algorithm's ability to extract physical information from data. Additionally, we have established confidence indices and error bars for each prediction value based on the shape of the redshift probability distribution function, suggesting that screening sources with high confidence can further reduce the outlier fraction.

The nucleus of almost all massive galaxies contains a supermassive black hole (BH). The feedback from the accretion of these BHs is often considered to have crucial roles in establishing the quiescence of massive galaxies, although some recent studies show that even galaxies hosting the most active BHs do not exhibit a reduction in their molecular gas reservoirs or star formation rates. Therefore, the influence of BHs on galaxy star formation remains highly debated and lacks direct evidence. Here, based on a large sample of nearby galaxies with measurements of masses of both BHs and atomic hydrogen (HI), the main component of the interstellar medium, we show that the HI gas mass to stellar masses ratio ($\mu_{\rm HI} = M_{\rm HI}/M_{\star}$) is more strongly correlated with BH masses ($M_{\rm BH}$) than with any other galaxy parameters, including stellar mass, stellar mass surface density and bulge masses. Moreover, once the $\mu_{\rm HI}-M_{\rm BH}$ correlation is considered, $\mu_{\rm HI}$ loses dependence on other galactic parameters, demonstrating that $M_{\rm BH}$ serves as the primary driver of $\mu_{\rm HI}$. These findings provide important evidence for how the accumulated energy from BH accretion regulates the cool gas content in galaxies, by ejecting interstellar medium gas and/or suppressing gas cooling from the circumgalactic medium., Comment: Published in Nature. Updated to match the accepted version

With mock strong gravitational lensing images, we investigate the performance of the broken power-law (BPL) model proposed by \citet{2020ApJ...892...62D} on the mass reconstruction of galaxy-scale lenses. An end-to-end test is carried out, including the creation of mock strong lensing images, the subtraction of lens light, and the reconstruction of lensed images, where the lenses are selected from the galaxies in the Illustris-1 simulation. We notice that, regardless of the adopted mass models (the BPL model or its special cases), the Einstein radius can be robustly determined from imaging data alone, and the median bias is typically less than $1\%$. Away from the Einstein radius, the lens mass distribution tends to be harder to measure, especially at radii where there are no lensed images detected. We find that, with rigid priors, the BPL model can clearly outperform the single power-law models by achieving $<5\%$ median bias on the radial convergence profile within the Einstein radius. As for the source light reconstructions, they are found to be sensitive to both lens light contamination and lens mass models, where the BPL model with rigid priors still performs best when there is no lens light contamination. We show that, by correcting for the projection effect, the BPL model can estimate the aperture and luminosity weighted line-of-sight velocity dispersions to an accuracy of $\sim6\%$ scatter. These results highlight the great potential of the BPL model in strong lensing related studies., Comment: Accepted for publication in ApJ, 24 pages, 13 figures, 2 tables

To investigate the properties of dust in the nuclear region of quasars, we explored the extinction curves of the iron low-ionization broad absorption line (FeLoBAL) quasar SDSS J163004.29+311957.6 and its two analogues. The parameterized extinction curves indicated the Milky Way-like 2175 \AA~ bump features in underlying extinction, which are similar to those seen in the Local Group and a subset of high-redshift star-forming galaxies. Compared to the bump features in the Large Magellanic Clouds (LMC), the detections in this work are much closer to those in the Milky Way (MW). These bump features, as well as those in the high- and low-ionization broad absorption line (BAL) quasars of Zhang et al., are probably the counterpart of the 2175 \AA~ bump features in the quasar environment. This type of dust grain is generally small, easily disrupted by high-energy photons and has difficulty surviving in the radiation field of the active galactic nucleus (AGN). However, due to the presence of absorption-line outflows, the 2175 \AA~ bump feature in quasars, which should be rare, is seen many times in BAL quasars. The shielding effect of outflow clouds allows the MW-like dust grains to be assembled or extends the survival period in the quasar nuclear region. The process, and physical and chemical conditions deserve further observational study and investigation., Comment: 13 pages, 10 figures. Accepted by Astronomy & Astrophysics

We investigate the cosmological evolution of the power law K-essence dark energy (DE) model $F(X)= -\sqrt{X} + X$ with a new interaction $Q = \alpha\rho _m\rho _{\phi }H^{-1}$ in FRWL spacetime. The evolution behavior of dark energy under this interaction is analyzed by using dynamical systems method, and ten critical points are obtained. Among those critical points, a new stable point, which we called Scaling-like dark energy(DE) solution, is very important and interesting. The cosmological meaning of this attractor is different from the Scaling solution and dark energy dominated solution. For some value of model parameters, the universe will evolve to the attractor solution with the dark energy density parameter $\Omega_{\phi}=0.682946$ and the the equation of state $w_{\phi}=-0.99$, which can be in good agreement with the observed data, and alleviate the Coincidence Problem.

Existing models of galaxy formation have not yet explained striking correlations between structure and star-formation activity in galaxies, notably the sloped and moving boundaries that divide star-forming from quenched galaxies in key structural diagrams. This paper uses these and other relations to ``reverse-engineer'' the quenching process for central galaxies. The basic idea is that star-forming galaxies with larger radii (at a given stellar mass) have lower black-hole masses due to lower central densities. Galaxies cross into the green valley when the cumulative effective energy radiated by their black hole equals $\sim4\times$ their halo-gas binding energy. Since larger-radii galaxies have smaller black holes, one finds they must evolve to higher stellar masses in order to meet this halo-energy criterion, which explains the sloping boundaries. A possible cause of radii differences among star-forming galaxies is halo concentration. The evolutionary tracks of star-forming galaxies are nearly parallel to the green-valley boundaries, and it is mainly the sideways motions of these boundaries with cosmic time that cause galaxies to quench. BH-scaling laws for star-forming, quenched, and green-valley galaxies are different, and most BH mass growth takes place in the green valley. Implications include: the radii of star-forming galaxies are an important second parameter in shaping their black holes; black holes are connected to their halos but in different ways for star-forming, quenched, and green-valley galaxies; and the same BH-halo quenching mechanism has been in place since $z \sim 3$. We conclude with a discussion of black hole-galaxy co-evolution, the origin and interpretation of BH scaling laws., Comment: 45 pages, 20 figures, 2 tables, accepted for publication in ApJ

As the second paper of a series on studying galaxy-galaxy lensing signals using the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our measurement and modelling of the lensing signals around groups of galaxies. We divide the groups into four halo mass bins, and measure the signals around four different halo-center tracers: brightest central galaxy (BCG), luminosity-weighted center, number-weighted center and X-ray peak position. For X-ray and SDSS DR7 cross identified groups, we further split the groups into low and high X-ray emission subsamples, both of which are assigned with two halo-center tracers, BCGs and X-ray peak positions. The galaxy-galaxy lensing signals show that BCGs, among the four candidates, are the best halo-center tracers. We model the lensing signals using a combination of four contributions: off-centered NFW host halo profile, sub-halo contribution, stellar contribution, and projected 2-halo term. We sample the posterior of 5 parameters i.e., halo mass, concentration, off-centering distance, sub halo mass, and fraction of subhalos via a MCMC package using the galaxy-galaxy lensing signals. After taking into account the sampling effects (e.g. Eddington bias), we found the best fit halo masses obtained from lensing signals are quite consistent with those obtained in the group catalog based on an abundance matching method, except in the lowest mass bin. Subject headings: (cosmology:) gravitational lensing, galaxies: clusters: general, Comment: 12 pages, 7 figures, submitted to ApJ

After thirty years of the discovery of the fundamental plane, explanations to the tilt of the fundamental plane with respect to the virial plane still suffer from the need of fine-tuning. In this paper, we try to explore the origin of this tilt from the perspective of modified Newtonian dynamics (MOND) by applying the 16 Coma galaxies available in Thomas et al.[1]. Based on the mass models that can reproduce de Vaucouleurs' law closely, we find that the tilt of the traditional fundamental plane is naturally explained by the simple form of the MONDian interpolating function, if we assume a well motivated choice of anisotropic velocity distribution, and adopt the Kroupa or Salpeter stellar mass-to-light ratio. Our analysis does not necessarily rule out a varying stellar mass-to-light ratio., Comment: The paper is accepted for Physical Review D

As the first paper in a series on the study of the galaxy-galaxy lensing from Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our image processing pipeline that corrects the systematics primarily introduced by the Point Spread Function (PSF). Using this pipeline, we processed SDSS DR7 imaging data in $r$ band and generated a background galaxy catalog containing the shape information of each galaxy. Based on our own shape measurements of the galaxy images from SDSS DR7, we extract the galaxy-galaxy (GG) lensing signals around foreground spectroscopic galaxies binned in different luminosity and stellar mass. The overall signals are in good agreement with those obtained by \citet{Mandelbaum2005, Mandelbaum2006} from the SDSS DR4. The results in this paper with higher signal to noise ratio is due to the larger survey area than SDSS DR4, confirm that more luminous/massive galaxies bear stronger GG lensing signal. We also divide the foreground galaxies into red/blue and star forming/quenched subsamples and measured their GG lensing signals, respectively. We find that, at a specific stellar mass/luminosity, the red/quenched galaxies have relatively stronger GG lensing signals than their counterparts especially at large radii. These GG lensing signals can be used to probe the galaxy-halo mass relations and their environmental dependences in the halo occupation or conditional luminosity function framework., Comment: 19pages, 12 figures ApJ submitted

$f(R)$ gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasi-static approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in $f(R)$ models, some studies have suggested that this method is not valid for all $f(R)$ models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, $\Psi$, and the curvature potential, $\Phi$. Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasi-static behaviours in $f(R)$ gravity. In addition, regardless the validity of quasi-static approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable $f(R)$ gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to $k=10 c^{-1} \mathcal{H}_0$.

We give a full investigation on the dynamics of power-law kinetic quintessence $L(X, \phi)=V(\phi)(-X+X^2)$ by considering the potential related parameter $\Gamma$($=\frac{V V''}{V'^2}$) as a function of another potential parameter $\lambda$($=\frac{V'}{\kappa V^{3/2}}$), which correspondingly extends the analysis of the dynamical system of our universe from two-dimension to three-dimension. Beside the critical points found in previous papers, we find a new de-Sitter-like dominant attractor(\textit{cp$6$}) and give its stable condition using the center manifold theorem. For the dark energy dominant solution(\textit{cp$6$} and \textit{cp$7$}), it could be distinguished from canonical quintessence and tachyon models since the sound speed $c_s^2=0$ or $c_s^2\ll 1$. For the scaling solution (\textit{cp$8$}), it is very interesting that the sound speed $c_s^2=1/5$ while it behaves as ordinary matter. We therefore point out that the power-law kinetic quintessence should have different signatures on cold dark matter power spectrum and cosmic microwave background both at early time when this scalar field is an early dark energy with $\Omega_\phi$ being non-negligible at high redshift and at late time when it drives the accelerating expansion. We even do not know whether there are any degeneracies of the impacts between these two epoches. They are expected to be investigated in future., Comment: 17 pages, 4 figures, accepted by Physical Review D, in press

We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models, change the dynamical variables from variables $(x, y, \lambda)$ to observable related variables $(w_{\phi}, \Omega_{\phi}, \lambda)$, and show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that, it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in $(w_{\phi}, \Omega_{\phi}, \lambda)$ instead of variables $(x, y, \lambda)$ and to investigate the dynamical system in 3-Dimension instead of 2-Dimension. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter., Comment: 20 pages, 8 figures,some references added. Minor changes according to the suggestions from referees

The Tully-Fisher relation of spiral galaxies shows notable dependence on morphological types, with earlier type spirals having systematically lower luminosity at fixed maximum rotation velocity $V_{max}$. This decrement of luminosity is more significant in shorter wavelengths. By modeling the rotation curve and stellar population of different morphological type spiral galaxies in combination, we find the $V_{max}$ of spiral galaxies is weakly dependent on the morphological type, whereas the difference of the stellar population originating from the bulge disk composition effect mainly account for the morphological type dependence of the Tully-Fisher relation., Comment: 8 pages, 3 figures, ApJ accepted

While both isothermal and NFW-based mass models for galaxy clusters are widely adopted in strong-lensing studies, they cannot easily be distinguished based solely on observed positions of arcs and arclets. We compare the magnifications predicted for giant arcs obtained from isothermal and NFW profiles, taking axially-symmetric and asymmetric mass distributions into account. We find that arc magnifications can differ strongly between the two types of density profiles even if the image morphology is well reproduced. Magnifications by lenses with NFW density profiles are usually larger than those for lenses with singular or nearly singular isothermal density profiles, unless the latter have large cores. Asymmetries play an important role. We illustrate our results with the two well-studied clusters MS 2137 and A~370. We confirm earlier results showing that both isothermal and NFW mass models can very well reproduce the observed arcs, radial arcs and other arclets. While the mass model for MS 2137 is not very well constrained, the two types of mass models produce strongly differing critical curves and caustics for A~370. We find that the NFW mass profile is preferred for A~370. We identify new arclet candidates in the field of A~370. Redshift estimates allowed by the lens model are consistent with results in the literature, where available. Three newly found counter-images are suggested to arise from an active, dust-enshrouded star-forming galaxy at $z\approx1.1$., Comment: 11 pages, 15 figures; accepted for publication in ApJ

We use a large sample of galaxies drawn from the Sloan Digital Sky Survey (SDSS) and Two Micro All Sky Survey (2MASS) to present Color-Magnitude Relations (CMRs) for late-type galaxies in both optical and optical-infrared bands. A sample from SDSS Data Release 4 (DR4) is selected to investigate the optical properties. Optical-infrared colors are estimated from a position matched sample of DR4 and 2MASS, in which the photometric aperture mismatch between these two surveys is carefully corrected. It is shown that, after correcting the dust attenuation, the optical colors for faint galaxies (i.e. $M_r > -21$) have very weak correlation with the luminosity, while the optical colors for bright galaxies (i.e. $M_r < -21$) are redder for more luminous galaxies. All (optical, optical-infrared and infrared) colors show similar but stronger correlations with stellar mass than with absolute magnitude. The optical colors correlate more strongly with stellar mass surface density than with stellar mass, while optical-infrared and infrared colors show stronger correlations with stellar mass. By comparing the observed colors of our sample galaxies with the colors predicted by stellar population synthesis model, we find that massive late-type galaxies have older and higher metallicity stellar population than less massive galaxies. This suggests that CMRs for late-type galaxies are trends defined by the combination of stellar mean age and metallicity. Moreover, our results suggest that the stellar mean metallicity of late-type galaxy is mainly determined by its stellar mass, while the star formation history is mainly regulated by the stellar mass surface density., Comment: 16 pages, 8 figures, accepted by MNRAS

Galactic winds and mass outflows are observed both in nearby starburst galaxies and in high-redshift star-forming galaxies. In this paper we develop a simple analytic model to understand the observed superwind phenomenon. Our model is built upon the model of McKee & Ostriker (1977) for the interstellar medium. It allows one to predict how properties of a superwind, such as wind velocity and mass outflow rate, are related to properties of its star-forming host galaxy, such as size, gas density and star formation rate. The model predicts a threshold of star formation rate density for the generation of observable galactic winds. Galaxies with more concentrated star formation produce superwinds with higher velocities. The predicted mass outflow rates are comparable to (or slightly larger than) the corresponding star formation rates. We apply our model to both local starburst galaxies and high-redshift Lyman break galaxies, and find its predictions to be in good agreement with current observations. Our model is simple, and so can be easily incorporated into numerical simulations and semi-analytical models of galaxy formation., Comment: 26 pages, 10 figures, submitted to MNRAS

Current theory of disk galaxy formation is used to study fundamental-plane (FP) type of relations for disk galaxies. We examine how the changes in model parameters affect these relations and explore the possibility of using such relations to constrain theoretical models. The distribution of galaxy disks in the space of their fundamental properties are predicted to be concentrated in a plane, with the Tully-Fisher (TF) relation (a relation between luminosity $L$ and maximum rotation velocity $V_m$) being an almost edge-on view. Using rotation velocities at larger radii generally leads to larger TF scatter. In searching for a third parameter, we find that both the disk scale-length $R_d$ (or surface brightness) and the rotation-curve shape are correlated with the TF scatter. The FP relation in the $(\Log L, \Log V_m, \Log R_d)$-space obtained from the theory is $L\propto R_d^{\alpha'} V_m^{\beta'}$, with ${\alpha'}\sim 0.50$ and ${\beta'}\sim 2.60$, consistent with the preliminary result we obtain from observational data. Among the model parameters we probe, variation in any of them can generate significant scatter in the TF relation, but the effects of the spin parameter and halo concentration can be reduced significantly by introducing $R_d$ while the scatter caused by varying $m_d$ (the ratio between disk mass and halo mass) is most effectively reduced by introducing the parameters which describes the rotation-curve shape. The TF and FP relations combined should therefore provide useful constraints on models of galaxy formation., Comment: 25 pages, 11 figures, 4 tables; submitted to MNRAS

We use the observed sizes and star formation rates of Lyman-break galaxies (LBGs) to understand their properties expected in the hierarchical scenario of galaxy formation. The observed size distribution constrains the masses of the host haloes of LBGs from below, while the observed star-formation distribution constrains the masses from above. Assuming a flat CDM model with a cosmological constant ($\Omega_\Lambda=0.7$), we find that consistency with observations requires the circular velocities of LBG host haloes to be in the range 100--$300 {\rm km s^{-1}}$. The predicted comoving correlation length of these objects is $\sim 3 h^{-1}{\rm Mpc}$, and the predicted velocity dispersion of their stellar contents is typically $70 {\rm km s^{-1}}$. The same prescription applied to larger haloes in the CDM cosmogony predicts the existence of galaxies with star formation rates $\sim 1000 {\rm M_\odot yr^{-1}}$ at redshift $z\sim 3$. We explore the possibility of identifying these galaxies to be the bright sub-millimeter (sub-mm) sources detected by SCUBA. The model predicts that the host haloes of these sub-mm sources are massive. These galaxies are predicted to be strongly correlated, with a comoving correlation length of $\sim 7 h^{-1}{\rm Mpc}$. The descendants of the bright sub-mm sources should reside in clusters of galaxies at the present time, and it is likely that these objects are the progenitors of giant ellipticals. The model predicts the existence of a relatively bright and red population of galaxies at $z\sim 3$, which may be observed in the K-band., Comment: 27 pages, 14 figures, submitted to MNRAS

This paper presents some statistical correlations of 72 northern spiral galaxies. The results show that early-type spirals that are brighter, and thicker, and the axis ratios ($H_{z}/H_r$) of the disk tend to be smaller along the Hubble sequence. We also find that $H_{z}/H_r$ correlates strongly with the galaxy's color, and early-type spirals have larger values of $H_{z}/H_r$. The inclinations obtained by fitting the pattern of a spiral structure with a logarithmic spiral form are nearly the same as those obtained by using the formulas of Aaronson et al. (1980). Finally, the mean measured pitch angles for the different Hubble sequences in the Third Catalogue of Bright Galaxies by de Vaucouleurs et al. (1991) are derived., Comment: 8 pages, LaTex, 7 figures

The normalized inclination distributions are presented for the spiral galaxies in RC3. The results show that, except for the bin of $81^{\circ}$-$90^{\circ}$, in which the apparent minor isophotal diameters that are used to obtain the inclinations, are affected by the central bulges, the distributions for Sa, Sab, Scd and Sd are well consistent with the Monte-Carlo simulation of random inclinations within 3-$\sigma$, and Sb and Sbc almost, but Sc is different. One reason for the difference between the real distribution and the Monte-Carlo simulation of Sc may be that some quite inclined spirals, the arms of which are inherently loosely wound on the galactic plane and should be classified to Sc galaxies, have been incorrectly classified to the earlier ones, because the tightness of spiral arms which is one of the criteria of the Hubble classification in RC3 is different between on the galactic plane and on the tangent plane of the celestial sphere. Our result also implies that there might exist biases in the luminosity functions of individual Hubble types if spiral galaxies are only classified visually., Comment: 5 pages + 8 figures, LaTex

The number density and clustering properties of Lyman-break galaxies (LBGs) observed at redshift $z\sim 3$ are best explained by assuming that they are associated with the most massive haloes at $z\sim 3$ predicted in hierarchical models of structure formation. In this paper we study, under the same assumption, how star formation and chemical enrichment may have proceeded in the LBG population. A consistent model, in which the amount of cold gas available for star formation must be regulated, is suggested. It is found that gas cooling in dark haloes provides a natural regulation process. In this model, the star formation rate in an LBG host halo is roughly constant over about 1 Gyr. The predicted star formation rates and effective radii are consistent with observations. The metallicity of the gas associated with an LBG is roughly equal to the chemical yield, or about the order of $1 Z_{\odot}$ for a Salpeter IMF. The contribution to the total metals of LBGs is roughly consistent with that obtained from the observed cosmic star formation history. The model predicts a marked radial metallicity gradient in a galaxy, with the gas in the outer region having much lower metallicity. As a result, the metallicities for the damped Lyman-alpha absorption systems expected from the LBG population are low. Since LBG halos are filled with hot gas in this model, their contributions to the soft X-ray background and to the UV ionization background are calculated and discussed., Comment: 21 pages, 7 figures, to appear in A&A