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1.
A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ωb= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α2≃−1.6  . At masses below  ∼108.5 M⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α2≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼1011 M⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.  相似文献   

2.
Using the spectroscopic sample of the Sloan Digital Sky Survey Data Release 1 (SDSS DR1), we measure how gas was transformed into stars as a function of time and stellar mass: the baryonic conversion tree (BCT). There is a clear correlation between early star formation activity and present-day stellar mass: the more massive galaxies have formed approximately 80 per cent of their stars at   z > 1  , while for the less massive ones the value is only approximately 20 per cent. By comparing the BCT with the dark matter merger tree, we find indications that star formation efficiency at   z > 1  had to be approximately a factor of two higher than today (∼10 per cent) in galaxies with present-day stellar mass larger than  2 × 1011 M⊙  , if this early star formation occurred in the main progenitor. Therefore, the λ cold dark matter (LCDM) paradigm can accommodate a large number of red objects. On the other hand, in galaxies with present-day stellar mass less than  1011 M⊙  , efficient star formation seems to have been triggered at   z ∼ 0.2  . We show that there is a characteristic mass  ( M *∼ 1010 M⊙)  for feedback efficiency (or lack of star formation). For galaxies with masses lower than this, feedback (or star formation suppression) is very efficient while for higher masses it is not. The BCT, determined here for the first time, should be an important observable with which to confront theoretical models of galaxy formation.  相似文献   

3.
We present a semi-analytic treatment of galactic winds within high-resolution, large-scale cosmological N -body simulations of a Λ cold dark matter (ΛCDM) universe. The evolution of winds is investigated by following the expansion of supernova-driven superbubbles around the several hundred thousand galaxies that form in an approximately spherical region of space with diameter 52  h −1 Mpc and mean density close to the mean density of the universe. We focus our attention on the impact of winds on the diffuse intergalactic medium. Initial conditions for mass loss at the base of winds are taken from Shu, Mo & Mao. Results are presented for the volume filling factor and the mass fraction of the intergalactic medium (IGM) affected by winds, and their dependence on the model parameters is carefully investigated. The mass-loading efficiency of bubbles is a key factor to determine the evolution of winds and their global impact on the IGM: the higher the mass loading, the later the IGM is enriched with metals. Galaxies with 109 < M ★ < 1010 M⊙ are responsible for most of the metals ejected into the IGM at   z = 3  , while galaxies with   M ★ < 109 M⊙   give a non-negligible contribution only at higher redshifts, when larger galaxies have not yet assembled. We find a higher mean IGM metallicity than Lyα forest observations suggest, and we argue that the discrepancy may be explained by the high temperatures of a large fraction of the metals in winds, which may not leave detectable imprints in absorption in the Lyα forest.  相似文献   

4.
In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a  106–109 M⊙  supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a  105–107 M⊙  nuclear star cluster. To date, few galaxies have been found with both types of nuclei coexisting and even less have had the masses determined for both central components. Here, we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei – which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range  108–1011 M⊙  , we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few per cent to ∼0.3 per cent such that  log[( M BH+ M NC)/ M sph]=−(0.39 ± 0.07) log[ M sph/1010 M⊙]− (2.18 ± 0.07)  . Once dry merging commences and the nuclear star clusters disappear, this ratio is expected to become a constant value.
As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters is well approximated with Sérsic functions having a range of indices from ∼0.5 to ∼3, the latter index describing the Milky Way's nuclear star cluster.  相似文献   

5.
Using cosmological hydrodynamic simulations, we measure the mean transmitted flux in the Lyα forest for quasar sightlines that pass near a foreground quasar. We find that the trend of absorption with pixel quasar separation distance can be fitted using a simple power-law form including the usual correlation function parameters r 0 and γ, so that     . From the simulations, we find the relation between r 0 and quasar host mass, and formulate this as a way to estimate quasar host dark matter halo masses, quantifying uncertainties due to cosmological and IGM parameters, and redshift errors. With this method, we examine data for ∼9000 quasars from the Sloan Digital Sky Survey (SDSS) Data Release 5, assuming that the effect of ionizing radiation from quasars (the so-called transverse proximity effect) is unimportant (no evidence for it is seen in the data). We find that the best-fitting host halo mass for SDSS quasars with mean redshift z = 3 and absolute G -band magnitude −27.5 is  log  M /M⊙= 12.68+0.81−0.67  . We also use the Lyman-Break Galaxy (LBG) and Lyα forest data of Adelberger et al. in a similar fashion to constrain the halo mass of LBGs to be  log10  M /M⊙= 11.41+0.54−0.59  , a factor of ∼20 lower than the bright quasars. In addition, we study the redshift distortions of the Lyα forest around quasars, using the simulations. We use the quadrupole to monopole ratio of the quasar Lyα forest correlation function as a measure of the squashing effect. We find its dependence on halo mass difficult to measure, but find that it may be useful for constraining cosmic geometry.  相似文献   

6.
Using the combined capabilities of the large near-infrared Palomar/DEEP-2 survey, and the superb resolution of the Advanced Camera for Surveys HST camera, we explore the size evolution of 831 very massive galaxies  ( M ⋆≥ 1011 h −270 M⊙)  since   z ∼ 2  . We split our sample according to their light concentration using the Sérsic index n . At a given stellar mass, both low  ( n < 2.5)  and high  ( n > 2.5)  concentrated objects were much smaller in the past than their local massive counterparts. This evolution is particularly strong for the highly concentrated (spheroid like) objects. At   z ∼ 1.5  , massive spheroid-like objects were a factor of 4 (±0.4) smaller (i.e. almost two orders of magnitudes denser) than those we see today. These small sized, high-mass galaxies do not exist in the nearby Universe, suggesting that this population merged with other galaxies over several billion years to form the largest galaxies we see today.  相似文献   

7.
We present discovery images, together with follow-up imaging and spectroscopy, of two large-separation gravitational lenses found by our survey for wide arcs [the CAmbridge Sloan Survey Of Wide ARcs in the skY (CASSOWARY)]. The survey exploits the multicolour photometry of the Sloan Digital Sky Survey to find multiple blue components around red galaxies. CASSOWARY 2 (or 'the Cheshire Cat') is composed of two massive early-type galaxies at   z = 0.426  and 0.432, respectively, lensing two background sources, the first a star-forming galaxy at   z = 0.97  and the second a high -redshift galaxy  ( z > 1.4)  . There are at least three images of the former source and probably four or more of the latter, arranged in two giant arcs. The mass enclosed within the larger arc of radius ∼11 arcsec is  ∼33 × 1012 M⊙  . CASSOWARY 3 comprises an arc of three bright images of a   z = 0.725  source, lensed by a foreground elliptical at   z = 0.274  . The radius of the arc is ∼4 arcsec and the enclosed mass is  ∼2.5 × 1012 M⊙  . Together with earlier discoveries like the Cosmic Horseshoe and the 8 o'clock Arc, these new systems, with separations intermediate between the arcsecond-separation lenses of typical strong galaxy lensing and arcminute-separation cluster lenses, probe the very high end of the galaxy mass function.  相似文献   

8.
It has recently been shown that galaxy formation models within the Λ cold dark matter cosmology predict that, compared to the observed population, small galaxies (with stellar masses  <1011 M⊙  ) form too early, are too passive since   z ∼ 3  and host too old stellar populations at   z = 0  . We then expect an overproduction of small galaxies at   z ≳ 4  that should be visible as an excess of faint Lyman-break galaxies. To check whether this excess is present, we use the morgana galaxy formation model and grasil spectrophotometric  +  radiative transfer code to generate mock catalogues of deep fields observed with Hubble Space Telescope Advanced Camera for Surveys. We add observational noise and the effect of Lyman α emission, and perform colour–colour selections to identify Lyman-break galaxies. The resulting mock candidates have plausible properties that closely resemble those of observed galaxies. We are able to reproduce the evolution of the bright tail of the luminosity function of Lyman-break galaxies (with a possible underestimate of the number of the brightest i -dropouts), but uncertainties and degeneracies in dust absorption parameters do not allow to give strong constraints to the model. Besides, our model shows a clear excess with respect to observations of faint Lyman-break galaxies, especially of   z 850∼ 27 V   -dropouts at   z ∼ 5  . We quantify the properties of these 'excess' galaxies and discuss the implications: these galaxies are hosted in dark matter haloes with circular velocities in excess of 100 km s−1, and their suppression may require a deep rethinking of stellar feedback processes taking place in galaxy formation.  相似文献   

9.
We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ≃100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  −1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ∗=(2.6±0.7)×1022 W Hz−1  and density   φ ∗=(4.8±1.1)×10−4 Mpc−3.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×1019 W Hz−1 Mpc−3  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ∼2 times larger than the Gallego et al. H α estimate, i.e.   ρ 1.4 GHz=(2.10±0.45±0.04)×10−2 M⊙ yr−1 Mpc−3  for a Salpeter initial mass function from  0.1–125 M⊙  and Hubble constant of 50 km s−1 Mpc−1. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.  相似文献   

10.
We investigate the role that dry mergers play in the build-up of massive galaxies within the cold dark matter paradigm. Implementing an empirical shut-off mass scale for star formation, we find a nearly constant dry merger rate of  ∼6 × 10−5 Mpc−3 Gyr−1  at   z ≤ 1  and a steep decline at larger z . Less than half of these mergers are between two galaxies that are morphologically classified as early-types, and the other half is mostly between an early- and late-type galaxy. Latter are prime candidates for the origin of tidal features around red elliptical galaxies. The introduction of a transition mass scale for star formation has a strong impact on the evolution of galaxies, allowing them to grow above a characteristic mass scale of   M *, c ∼ 6.3 × 1010 M⊙  by mergers only. As a consequence of this transition, we find that around   M *, c   , the fraction of 1:1 mergers is enhanced with respect to unequal mass major mergers. This suggests that it is possible to detect the existence of a transition mass scale by measuring the relative contribution of equal mass mergers to unequal mass mergers as a function of galaxy mass. The evolution of the high-mass end of the luminosity function is mainly driven by dry mergers at low z . We however find that only 10–20 per cent of galaxies more massive than   M *, c   experience dry major mergers within their last Gyr at any given redshift   z ≤ 1  .  相似文献   

11.
We present the results of Australia Telescope Compact Array (ATCA) H  i line and 20-cm radio continuum observations of the galaxy quartet NGC 6845. The H  i emission extends over all four galaxies but can only be associated clearly with the two spiral galaxies, NGC 6845A and B, which show signs of strong tidal interaction. We derive a total H  i mass of at least  1.8 × 1010 M⊙  , most of which is associated with NGC 6845A, the largest galaxy of the group. We investigate the tidal interaction between NGC 6845A and B by studying the kinematics of distinct H  i components and their relation to the known H  ii regions. No H  i emission is detected from the two lenticular galaxies, NGC 6845C and D. A previously uncatalogued dwarf galaxy, ATCA  J2001−4659  , was detected 4.4 arcmin NE from NGC 6845B and has an H  i mass of  ∼5 × 108 M⊙  . No H  i bridge is visible between the group and its newly detected companion. Extended 20-cm radio continuum emission is detected in NGC 6845A and B as well as in the tidal bridge between the two galaxies. We derive star formation rates of  15–40 M⊙ yr−1  .  相似文献   

12.
The first spectroscopic census of active galactic nuclei (AGNs) associated with late-type galaxies in the Virgo cluster was carried out by observing 213 out of a complete set of 237 galaxies more massive than   M dyn > 108.5 M⊙  . Among them, 77 are classified as AGNs [including 21 transition objects, 47 low-ionization nuclear emission regions (LINERs) and nine Seyferts] and comprise 32 per cent of the late-type galaxies in Virgo. Due to spectroscopic incompleteness, at most 21 AGNs are missed in the survey, so that the fraction would increase up to 41 per cent. Using corollary near-infrared observations that enable us to estimate galaxy dynamical masses, it is found that AGNs are hosted exclusively in massive galaxies, i.e.   M dyn≳ 1010 M⊙  . Their frequency increases steeply with the dynamical mass from zero at   M dyn≈ 109.5 M⊙  to virtually 1 at   M dyn > 1011.5 M⊙  . These frequencies are consistent with those of low-luminosity AGNs found in the general field by the Sloan Digital Sky Survey. Massive galaxies that harbour AGNs commonly show conspicuous r -band star-like nuclear enhancements. Conversely, they often, but not necessarily, contain massive bulges. A few well-known AGNs (e.g. M61, M100, NGC 4535) are found in massive Sc galaxies with little or no bulge. The AGN fraction seems to be only marginally sensitive to galaxy environment. We infer the black hole masses using the known scaling relations of quiescent black holes. No black holes lighter than  ∼106 M⊙  are found active in our sample.  相似文献   

13.
Photometric redshifts are used to determine the rest-frame luminosity function (LF) of both early- and late-type galaxies to  MB∼−17.6  for the cluster Cl 1601+42 at  z=0.54  . The total LF shows a steep faint-end slope   α ∼−1.4  , indicating the existence of a population of numerous dwarf galaxies. Luminous galaxies, with  MB≲−19.5  are mostly red, early-type galaxies, with a LF best described by a Gaussian. Faint galaxies are predominantly blue, late-type galaxies, well fitted by a Schechter function with   α ∼−1.7  . Compared with clusters at lower redshift, the steepening of the faint end starts at brighter magnitudes for Cl 1601+42, which may indicate a brightening of the present-day dwarf population relative to the giant population with increasing redshift. Early-type galaxies are centrally concentrated, and dominate the core region, implying that the radial gradient of early-type galaxies seen in local clusters is already established at  z∼0.5  . Bright, late-type galaxies are rare, consistent with a decrease in star formation in field galaxies as they are accreted on to the cluster, while faint, blue galaxies are evenly distributed across the cluster, except for a depletion in the core region. The blue fraction is  fB∼0.15  , which is somewhat lower than the Butcher–Oemler average at  z∼0.5  . The value of f B is found to increase with limiting magnitude and with radius from the centre.  相似文献   

14.
We present 21-cm H  i line observations of the blue compact dwarf galaxy NGC 1705. Previous optical observations show a strong outflow powered by an ongoing starburst dominating the H  ii morphology and kinematics. In contrast, most of the H  i lies in a rotating disc. An extraplanar H  i spur accounts for ∼8 per cent of the total H  i mass, and is possibly associated with the H  ii outflow. The inferred mass loss rate out of the core of the galaxy is significant, ∼0.2 − 2 M⊙ yr−1, but does not dominate the H  i dynamics. Mass model fits to the rotation curve show that the dark matter (DM) halo is dominant at nearly all radii and has a central density ρ0 ≈ 0.1 M⊙ pc−3: ten times higher than typically found in dwarf irregular galaxies, but similar to the only other mass-modelled blue compact dwarf, NGC 2915. This large difference strongly indicates that there is little evolution between dwarf irregular and blue compact dwarf types. Instead, dominant DM haloes may regulate the morphology of dwarf galaxies by setting the critical surface density for disc star formation. Neither our data nor catalogue searches reveal any likely external trigger to the starburst in NGC 1705.  相似文献   

15.
We use deep Hubble Space Telescope photometry of the rich, young (∼20- to 45-Myr old) star cluster NGC 1818 in the Large Magellanic Cloud to derive its stellar mass function (MF) down to  ∼0.15 M⊙  . This represents the deepest robust MF thus far obtained for a stellar system in an extragalactic, low-metallicity  ([Fe/H]≃−0.4 dex)  environment. Combining our results with the published MF for masses above  1.0 M⊙  , we obtain a complete present-day MF. This is a good representation of the cluster's initial MF (IMF), particularly at low masses, because our observations are centred on the cluster's uncrowded half-mass radius. Therefore, stellar and dynamical evolution of the cluster will not have affected the low-mass stars significantly. The NGC 1818 IMF is well described by both a lognormal and a broken power-law distribution with slopes of  Γ= 0.46 ± 0.10  and  Γ≃−1.35  (Salpeter-like) for masses in the range from 0.15 to  0.8 M⊙  and greater than  0.8 M⊙  , respectively. Within the uncertainties, the NGC 1818 IMF is fully consistent with both the Kroupa solar neighbourhood and the Chabrier lognormal mass distributions.  相似文献   

16.
Deep inside the core of Abell 1795: the Chandra view   总被引：1，自引：0，他引：1  
We present X-ray spatial and spectral analysis of the Chandra data from the central     of the cluster of galaxies Abell 1795. The plasma temperature rises outwards by a factor of 3, whereas the iron abundance decreases by a factor of 4. The spatial distribution of oxygen, neon, sulphur, silicon and iron shows that supernovae Type Ia dominate the metal enrichment process of the cluster plasma within the inner 150 kpc. Resolving both the gas density and temperature in nine radial bins, we recover the gravitational mass density profile and show that it flattens within 100 kpc as   ρ DM∝ r -0.6  with a power-law index flatter than −1 at >3 σ level. The observed motion of the central galaxy and the presence of excesses and deficits along the north–south direction in the brightness distribution indicate that the central cluster region is not relaxed. In the absence of any non-gravitational heating source, the data from the inner ∼200 kpc indicate the presence of a cooling flow with an integrated mass deposition rate of about 100 M⊙ yr−1. Over the same cluster region, the observed rate of 74 M⊙ yr−1 is consistent with the recent XMM-Newton Reflection Grating Spectrometer limit of 150 M⊙ yr−1.  相似文献   

17.
We report the result of a search for Lyα emission from the host galaxies of the gamma-ray bursts  (GRBs) 030226 ( z = 1.986), 021004 ( z = 2.335)  and  020124 ( z = 3.198)  . We find that the host galaxy of GRB 021004 is an extended (around 8 kpc) strong Lyα emitter with a rest-frame equivalent width (EW) of 68+12−11Å, and a star formation rate of  10.6 ± 2.0 M⊙ yr−1  . We do not detect the hosts of GRB 030226 and GRB 020124, but the upper limits on their Lyα fluxes do not rule out large rest-frame EWs. In the fields of GRB 021004 and GRB 030226 we find seven and five other galaxies, respectively, with excess emission in the narrow-band filter. These galaxies are candidate Lyα-emitting galaxies in the environment of the host galaxies. We have also compiled a list of all   z ≳ 2  GRB hosts, and demonstrate that a scenario where they trace star formation in an unbiased way is compatible with current observational constraints. Fitting the   z = 3  luminosity function (LF) under this assumption results in a characteristic luminosity of   R *= 24.6  and a faint-end slope of  α=−1.55  , consistent with the LF measured for Lyman-break galaxies.  相似文献   

18.
The evolution of number density, size and intrinsic colour is determined for a volume-limited sample of visually classified early-type galaxies selected from the Hubble Space Telescope /Advanced Camera for Surveys images of the Great Observatories Origins Deep Survey (GOODS) North and South fields (version 2). The sample comprises 457 galaxies over 320 arcmin2 with stellar masses above  3 × 1010 M⊙  in the redshift range  0.4 < z < 1.2  . Our data allow a simultaneous study of number density, intrinsic colour distribution and size. We find that the most massive systems  (≳3 × 1011 M⊙)  do not show any appreciable change in comoving number density or size in our data. Furthermore, when including the results from 2dF galaxy redshift survey, we find that the number density of massive early-type galaxies is consistent with no evolution between   z = 1.2  and 0, i.e. over an epoch spanning more than half of the current age of the Universe. We find large discrepancies between the predictions of semi-analytic models. Massive galaxies show very homogeneous intrinsic colour distributions, with nearly flat radial colour gradients, but with a significant negative correlation between stellar mass and colour gradient, such that red cores appear predominantly in massive galaxies. The distribution of half-light radii – when compared to   z ∼ 0  and   z > 1  samples – is compatible with the predictions of semi-analytic models relating size evolution to the amount of dissipation during major mergers.  相似文献   

19.
We present a possible star formation and chemical evolutionary history for two early-type galaxies NGC 1407 and NGC 1400. They are the two brightest galaxies of the NGC 1407 (or Eridanus-A) group, one of the 60 groups studied as part of the Group Evolution Multi-wavelength Study.
Our analysis is based on new high signal-to-noise ratio spatially resolved integrated spectra obtained at the ESO 3.6-m telescope, out to ∼0.6 (NGC 1407) and ∼1.3 (NGC 1400) effective radii. Using Lick/IDS indices, we estimate luminosity-weighted ages, metallicities and α-element abundance ratios. Colour radial distributions from HST /ACS and Subaru Suprime-Cam multiband wide-field imaging are compared to colours predicted from spectroscopically determined ages and metallicities using single stellar population (SSP) models. The galaxies formed over half of their mass in a single short-lived burst of star formation  (≥100 M⊙ yr−1)  at redshift z ≥ 5. This likely involved an outside–in mechanism with supernova-driven galactic winds, as suggested by the flatness of the α-element radial profiles and the strong negative metallicity gradients. Our results support the predictions of the revised version of the monolithic collapse model for galaxy formation and evolution. We speculate that, since formation, the galaxies have evolved quiescently and that we are witnessing the first infall of NGC 1400 in the group.  相似文献   

20.
Transformation of discs into spheroids via mergers is a well-accepted element of galaxy formation models. However, recent simulations have shown that the bulge formation is suppressed in increasingly gas-rich mergers. We investigate the global implications of these results in a cosmological framework, using independent approaches: empirical halo-occupation models (where galaxies are populated in haloes according to observations) and semi-analytic models. In both, ignoring the effects of gas in mergers leads to the overproduction of spheroids: low- and intermediate-mass galaxies are predicted to be bulge-dominated (   B / T ∼ 0.5  at  <1010 M⊙  , with almost no 'bulgeless' systems), even if they have avoided major mergers. Including the different physical behaviour of gas in mergers immediately leads to a dramatic change: bulge formation is suppressed in low-mass galaxies, observed to be gas-rich (giving   B / T ∼ 0.1  at  <1010 M⊙  , with a number of bulgeless galaxies in good agreement with observations). Simulations and analytic models which neglect the similarity-breaking behaviour of gas have difficulty reproducing the strong observed morphology–mass relation. However, the observed dependence of gas fractions on mass, combined with suppression of bulge formation in gas-rich mergers, naturally leads to the observed trends. Discrepancies between observations and models that ignore the role of gas increase with redshift; in models that treat gas properly, galaxies are predicted to be less bulge-dominated at high redshifts, in agreement with the observations. We discuss implications for the global bulge mass density and future observational tests.  相似文献   

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