Maximal representations of complex hyperbolic lattices in SU(m,n)

Let $\Gamma$ denote a lattice in $SU(1,p)$, with $p$ greater than 1. We show that there exists no Zariski dense maximal representation with target $SU(m,n)$ if $n>m>1$. The proof is geometric and is based on the study of the rigidity properties of the geometry whose points are isotropic $m$-subspaces of a complex vector space $V$ endowed with a Hermitian metric $h$ of signature $(m,n)$ and whose lines correspond to the $2m$ dimensional subspaces of $V$ on which the restriction of $h$ has signature $(m,m)$.Comment: 41 pages, 2 figures, accepted for pubblication in GAF

Deep Galaxy Counts, Extragalactic Background Light, and the Stellar Baryon Budget

We assess the constraints imposed by the observed extragalactic background light (EBL) on the cosmic history of star formation and the stellar mass density today. The logarithmic slope of the galaxy number-magnitude relation from the Southern Hubble Deep Field} imaging survey is flatter than 0.4 in all seven UBVIJHK optical bandpasses, i.e. the light from resolved galaxies has converged from the UV to the near-IR. We find a lower limit to the surface brightness of the optical extragalactic sky of about 15 nW/m^2/sr, comparable to the intensity of the far-IR background from COBE data. Assuming a Salpeter initial mass function with a lower cutoff consistent with observations of M subdwarf disk stars, we set a lower limit of Omega_g+s h^2>0.0013 I_50 to the visible (processed gas + stars) mass density required to generate an EBL at a level of 50 I_50 nW/m^2/sr; our `best-guess' value is Omega_g+s h^2=0.003 I_50. Motivated by the recent microlensing results of the MACHO collaboration, we consider the possibility that massive dark halos around spiral galaxies are composed of faint white dwarfs, and show that only a small fraction (<5%) of the nucleosynthetic baryons can be locked in the remnants of intermediate-mass stars forming at z_F<5, as the bright early phases of such halos would otherwise overproduce the observed EBL.Comment: LaTeX, 17 pages, 5 figures, revised version accepted for publication in the MNRA

zCOSMOS – 10k-bright spectroscopic sample : The bimodality in the galaxy stellar mass function: exploring its evolution with redshift

We present the galaxy stellar mass function (GSMF) to redshift z ≃ 1, based on the analysis of about 8500 galaxies with I < 22.5 (AB mag) over 1.4 deg^2, which are part of the zCOSMOS-bright 10k spectroscopic sample. We investigate the total GSMF, as well as the contributions of early- and late-type galaxies (ETGs and LTGs, respectively), defined by different criteria (broad-band spectral energy distribution, morphology, spectral properties, or star formation activities). We unveil a galaxy bimodality in the global GSMF, whose shape is more accurately represented by 2 Schechter functions, one linked to the ETG and the other to the LTG populations. For the global population, we confirm a mass-dependent evolution (“mass-assembly downsizing”), i.e., galaxy number density increases with cosmic time by a factor of two between z = 1 and z = 0 for intermediate-to-low mass (log(M/M_⊙) ~ 10.5) galaxies but less than 15% for log(M/M_⊙) > 11.We find that the GSMF evolution at intermediate-to- low values of M(log(M/M_⊙) < 10.6) is mostly explained by the growth in stellar mass driven by smoothly decreasing star formation activities, despite the redder colours predicted in particular at low redshift. The low residual evolution is consistent, on average, with ~0.16 merger per galaxy per Gyr (of which fewer than 0.1 are major), with a hint of a decrease with cosmic time but not a clear dependence on the mass. From the analysis of different galaxy types, we find that ETGs, regardless of the classification method, increase in number density with cosmic time more rapidly with decreasing M, i.e., follow a top-down building history, with a median “building redshift” increasing with mass (z > 1 for log(M/M_⊙) > 11), in contrast to hierarchical model predictions. For LTGs, we find that the number density of blue or spiral galaxies with log(M/M_⊙) > 10 remains almost constant with cosmic time from z ~ 1. Instead, the most extreme population of star-forming galaxies (with high specific star formation), at intermediate/high-mass, rapidly decreases in number density with cosmic time. Our data can be interpreted as a combination of different effects. Firstly, we suggest a transformation, driven mainly by SFH, from blue, active, spiral galaxies of intermediate mass to blue quiescent and subsequently (1−2 Gyr after) red, passive types of low specific star formation. We find an indication that the complete morphological transformation, probably driven by dynamical processes, into red spheroidal galaxies, occurred on longer timescales or followed after 1−2 Gyr. A continuous replacement of blue galaxies is expected to be accomplished by low-mass active spirals increasing their stellar mass. We estimate the growth rate in number and mass density of the red galaxies at different redshifts and masses. The corresponding fraction of blue galaxies that, at any given time, is transforming into red galaxies per Gyr, due to the quenching of their SFR, is on average ~25% for log(M/M_⊙) < 11. We conclude that the build-up of galaxies and in particular of ETGs follows the same downsizing trend with mass (i.e. occurs earlier for high-mass galaxies) as the formation of their stars and follows the converse of the trend predicted by current SAMs. In this scenario, we expect there to be a negligible evolution of the galaxy baryonic mass function (GBMF) for the global population at all masses and a decrease with cosmic time in the GBMF for the blue galaxy population at intermediate-high masses

On the Luminosity Function of Early--Type Galaxies

In a recent paper Loveday et al. (1992) have presented new results on the luminosity function for a sample of galaxies with $b_J \le 17.15$. After having morphologically classified each galaxy (early--type, late--type, merged or uncertain), they have estimated the parameters of a Schechter luminosity function for early-- and late--type galaxies. However, in their sample there is a bias against identifying early--type galaxies at large distances and/or faint magnitudes: in fact, many of the early--type galaxies at faint magnitudes have probably been classified as ``uncertain". As discussed in Loveday et al., the existence of such a bias is indicated by the fact that for these galaxies $=0.32$. In this paper we show, both theoretically and through the use of simulated samples, that this incompleteness strongly biases the derived parameters of the luminosity function for early--type galaxies. If no correction for such incompleteness is applied to the data (as done by Loveday et al.), one obtains a flatter slope $\alpha$ and a brighter $M^*$ with respect to the real parameters.Comment: accepted for publication on MNRAS, Standard TeX, for tables and figures contact [email protected] BAP 03-1994-04-IR

Search Instructions for Globular Clusters in Formation at High Redshifts

The formation of globular clusters (GC), with their multiple stellar generations, is still an unsolved puzzle. Thus, interest is rising on the possibility to detect their precursors at high redshift, hence directly witnessing their formation. A simple set of assumptions are empirically justified and then used to predict how many such precursors formed between redshift 3 and 10 could actually be detected by the NIRCam instrument on board of JWST. It is shown that the near power-law shape of the rest-frame UV continuum of young globular cluster precursors (GCP) implies that both colours and luminosities in NIRCam long-wavelength passbands depend remarkably weakly on formation redshift. Thus, the predicted number counts depend only little on the actual formation redshifts in the mentioned range, with the exception of the bluest passbands for which counts can be strongly suppressed by intergalactic absorption along the line of sight. Instead, counts depend strongly on the actual mass of GCPs, in such a way that one NIRCam pointing should detect of the order of 10 GCPs to mag$\sim 30$ if their mass distribution was the same of today GCs, or over 1,000 if their mass was 10 times higher. Therefore, GCP number counts will set fairly tight constraints on the initial mass of GCs. An encouraging agreement with the number density of candidate GCPs at $z=6-8$, revealed by the Hubble Frontier Fields (HFF) program, suggests that their initial mass could be at least 4 times higher than that of their local descendants if all were to end up as GCs.Comment: MNRAS accepte

Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces

We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type we show that there cannot be Zariski-dense maximal representations, and whenever the existence of a boundary map can be guaranteed, the representation preserves a finite dimensional totally geodesic subspace on which the action is maximal. In the opposite direction we construct examples of geometrically dense maximal representation in the infinite dimensional Hermitian symmetric space of tube type and finite rank. Our approach is based on the study of boundary maps, that we are able to construct in low ranks or under some suitable Zariski-density assumption, circumventing the lack of local compactness in the infinite dimensional setting.Comment: Comments are welcome! The maximality assumption was unfortunately missing in Theorem 1.1 and 1.4 of the first versio

On the robustness of the Hβ\beta Lick index as a cosmic clock in passive early-type galaxies

We examine the H$\beta$ Lick index in a sample of $\sim 24000$ massive ($\rm log(M/M_{\odot})>10.75$) and passive early-type galaxies extracted from SDSS at z<0.3, in order to assess the reliability of this index to constrain the epoch of formation and age evolution of these systems. We further investigate the possibility of exploiting this index as "cosmic chronometer", i.e. to derive the Hubble parameter from its differential evolution with redshift, hence constraining cosmological models independently of other probes. We find that the H$\beta$ strength increases with redshift as expected in passive evolution models, and shows at each redshift weaker values in more massive galaxies. However, a detailed comparison of the observed index with the predictions of stellar population synthesis models highlights a significant tension, with the observed index being systematically lower than expected. By analyzing the stacked spectra, we find a weak [NII]$\lambda6584$ emission line (not detectable in the single spectra) which anti-correlates with the mass, that can be interpreted as a hint of the presence of ionized gas. We estimated the correction of the H$\beta$ index by the residual emission component exploiting different approaches, but find it very uncertain and model-dependent. We conclude that, while the qualitative trends of the observed H$\beta$-z relations are consistent with the expected passive and downsizing scenario, the possible presence of ionized gas even in the most massive and passive galaxies prevents to use this index for a quantitative estimate of the age evolution and for cosmological applications.Comment: 20 pages, 11 figures, 1 table. Accepted for publication in MNRAS Main Journa

Pure Luminosity Evolution models for faint field galaxy samples

We have examined a set of pure luminosity evolution (PLE) models in order to explore up to what extent the rapidly increasing observational constraints from faint galaxy samples can be understood in this simple framework. We find that a PLE model, in which galaxies evolve mildly in time even in the rest frame UV, can reproduce most of the observed properties of faint galaxies assuming an open ($\Omega\sim0$) universe. In particular, such a model is able to fit reasonably well the number counts in the $U,~b_j,~r_f,~I$, and $K$ bands, as well as the colour and redshift distributions derived from most of the existing samples. The most significant discrepancy between the predictions of this model and the data is the $z$ distribution of faint $K$-selected galaxies. Significantly worse fits are obtained with PLE models for the theoretically attractive value of $\Omega = 1$, although a simple number luminosity evolution model with a significant amount of merger events fits the data also in this cosmology.Comment: 15 pages, plain tex (insert encapsulated postscript figures), plus an extra figure Fig3c.ps and the tex-macro mn.tex uuencoded, gzipp'ed tar file -- accepted by MNRA

Extending higher dimensional quasi-cocycles

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We prove that, in degree 3, the bounded cohomology of G with real coefficients is infinite-dimensional. Our proof is based on an extension to higher degrees of a recent result by Hull and Osin. Namely, we prove that, if H is a hyperbolically embedded subgroup of G and V is any G-module, then any n-quasi cocycle on H with values in V may be extended to G. Also, we show that our extensions detect the geometry of the embedding of hyperbolically embedded subgroups, in a suitable sense.Comment: Minor revisions. This version has been accepted for publication by the Journal of Topolog