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J. M. Solanes

Publications and source records attributed to J. M. Solanes.

At least 19 recordsLinked to original sources

Tracing the evolution of brightest galaxies and diffuse light in galaxy groups

We present a suite of 100 cosmologically motivated, controlled N-body simulations designed to advance the understanding of the role of purely gravitational dynamics in the early formation of low-mass galaxy groups (~ 1-5 x 10^13 M_sun). In this work, we investigate the temporal evolution of key indicators of dynamical relaxation, with particular emphasis on the secular growth of the diffuse intragroup light (IGL), the four major group galaxies, and the mass distributions of their progenitors. We also assess the diagnostic power of several magnitude gaps between top-ranked galaxies as proxies for dynamical age. As in our previous study, we compare outcomes from three group classes defined by the number of brightest group galaxies (BGGs) present at the end of the simulations. The early assembly of galaxy groups is consistent with a stochastic Poisson process at an approximately constant merger rate. Various dynamical diagnostics - including galaxy pairwise separations, velocity dispersions, and the offset of the first-ranked galaxy from the group barycentre - indicate that single-BGG groups evolve more rapidly towards virialisation than double- and especially non-BGG systems. We further find that first-ranked group members and the IGL, follow distinct growth histories, with the IGL assembled from a more numerous and systematically lower-mass population than the central object. This distinction is particularly pronounced in non-BGG systems, where about one third of the IGL originates from small galaxies, each contributing less than 5% to this component. Among the tested magnitude gaps, the difference between the first- and fourth-ranked galaxies, $ΔM4-1$, proves a more robust indicator of dynamical age for low-mass groups than the conventional $ΔM2-1$ gap. The $ΔM5-1$ and $ΔM6-1$ gaps also perform well and may be preferable in certain contexts.

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The distribution of lenticular galaxies in the phase space of present-day galaxy cluster regions

We investigate the environmental impact of cluster regions on the evolution of nearby S0 galaxies, focusing on their distinct quiescent and star-forming (SF) subpopulations. We select a sample of clusters by crossmatching optical and X-ray data and extract a subset of 14 systems with maximally relaxed cores by applying strict virialization and substructure tests. A projected phase space (PPS) diagram is generated from the stack of relaxed clusters up to 3 virial radii to assess the locations of quiescent and SF S0s and their cluster infall histories. Additionally, we compare the radial line-of-sight velocity dispersion (VDLOS) and specific star-formation rate (SSFR) profiles for the different S0 subpopulations, using other Hubble types as benchmarks. Our study shows that quiescent S0s, the dominant class in the entire cluster region, concentrate preferentially at low radii in the PPS diagram, while SF S0s are more abundant in the outskirts. Despite this segregation, both subpopulations show similar VDLOS profiles in the cluster core -indicating an advanced stage of dynamical relaxation-, but that resemble those of late-type galaxies beyond the virial radius. This finding, combined with the distinct PPS distributions of both S0 subpopulations, which lead to mean infall times $\sim 1$ Gyr longer for quiescent S0s but that are shorter than those expected for ancient infallers, suggests that a substantial fraction of S0s present in the core region arrive via secondary infall. We also find evidence in the SSFR profiles that star formation in S0s begins to decline beyond the virialized core, likely due to preprocessing in infalling groups. Our results support a delayed-then-rapid quenching scenario for SF S0s in cluster regions, where their centrally concentrated star formation persists for an extended period before abruptly ending ($\lesssim 0.1$ Gyr) after their first pericenter passage.

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MeerKAT view of Hickson Compact Groups: II. HI deficiency in the core and surrounding regions

Hickson compact groups (HCGs) offer an ideal environment for investigating galaxy transformation as a result of interactions. It has been established that the evolutionary sequence of HCGs is marked by an intermediate stage characterised by a substantial amount of HI in their intragroup medium (IGrM) in the form of tidal tails and bridges (Phase 2), rapidly followed by a final stage where no IGrM gas is found and where their member galaxies are highly HI-deficient (Phase 3). Despite numerous single-dish and interferometric HI studies on the HCGs, a clear HI picture of the groups within their large-scale environment still remains to be uncovered. Taking advantage of the MeerKAT's high column density sensitivity and large field-of-view, we aim to investigate the rapid transformation of HCGs from the intermediate to late phases, and establish a picture of their gas content variations in the context of their large-scale environments. We performed MeerKAT observations of six HCGs selected to represent the intermediate and late phases of the proposed evolutionary sequence. Combining the HI observations with data from recent wide-field optical surveys, we evaluated the HI deficiencies of galaxies in a ~30' radius of the HCGs. We find that galaxies surrounding both phases exhibit similar distributions in their gas content. Similarly, galaxies making up the cores of Phase 2 HCGs are comparable to their neighbours in terms of HI deficiencies. However, Phase 3 groups are over an order of magnitude more deficient than their surroundings, supporting previous findings that late-phase HCG galaxies are more evolved than their large-scale environments.

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Growth of Ex-situ Diffuse Intragroup Light in Simulated Galaxy Groups

Deep surface photometry reveals a faint, diffuse baryonic component in a significant fraction of galaxy groups, permeating the intragroup space. This intragroup light (IGL) is primarily formed by stars removed from their host galaxies through gravitational interactions and now drifting freely, unbound to any galaxy. We conduct a detailed analysis to investigate how various physical parameters of galaxy groups influence the formation of ex-situ IGL during the earliest stages of group assembly, and to explore their correlations with this component. Additionally, we evaluate the potential of the IGL as a luminous tracer of the total mass distribution in galaxy groups, with particular focus on systems that are far from being dynamically relaxed. We use controlled numerical simulations of 100 low-mass galaxy groups spanning a range of masses and numbers of constituent galaxies. We show that the IGL typically begins to form in significant amounts after the turnaround epoch (redshift ~ 0.85), increasing steadily thereafter. We observe a sublinear relationship between the masses of this component and the brightest group galaxy, indicating intertwined formation histories but differing growth rates, which suggests that other group members may also significantly contribute to the diffuse light. Additionally, we observe indications that IGL formation is enhanced in groups with lower internal velocity dispersions, suggesting that gravitational interactions among member galaxies become more effective when their relative velocities are reduced. Two-thirds of our groups reveal significant alignment between the radial surface density profiles of the total and IGL mass, with fractional discrepancies below 25%. This supports the notion that this diffuse and faint baryonic component serves as a reliable tracer of the total gravitational potential in galaxy aggregations, regardless of their dynamical state.

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MeerKAT view of Hickson Compact Groups:I. Data description and release

Context: Hickson Compact Groups (HCGs) are dense gravitationally-bound collections of 4-10 galaxies ideal for studying gas and star formation quenching processes. Aims: We aim to understand the transition of HCGs from possessing complex HI tidal structures (so-called phase 2 groups) to a phase where galaxies have lost most or all their HI (phase 3). We also seek to detect diffuse H i gas that was previously missed by the Very Large Array (VLA). Methods: We observed three phase 2 and three phase 3 HCGs with MeerKAT and reduced the data using the Containerized Automated Radio Astronomy Calibration (CARACal) pipeline. We produced data cubes, moment maps, integrated spectra, and compared our findings with previous VLA and Green Bank Telescope (GBT) observations. Results: Compared with previous VLA observations, MeerKAT reveals much more extended tidal features in phase 2 and some new high surface brightness features in phase 3 groups. However, no diffuse HI component was found in phase 3 groups. We also detected many surrounding galaxies for both phase 2 and phase 3 groups, most of which are normal disk galaxies. Conclusions: The difference between phase 2 and phase 3 groups is still substantial, supporting previous findings that the transition between the two phases must be abrupt.

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Growth of Diffuse Intragroup Light in Simulated Galaxy Groups

The diffuse intragroup light (IGL) is a pervasive feature of galaxy groups consisting of an extended low-surface-brightness component that permeates the intergalactic medium of these galaxy associations. It is primarily formed by stars separated from their host galaxies and now drift freely, unbound to any particular galaxy. We used controlled numerical simulations to investigate the formation and evolution of IGL in galaxy groups during the pre-virialization phase. Our study reveals that the emergence of this diffuse luminous component typically begins to form in significant amounts around the turnaround epoch, increasing steadily thereafter. We analyzed the correlation between the mass and fraction of IGL and other group properties. We found a sublinear relationship between the IGL mass and the brightest group galaxy, suggesting intertwined formation histories but with potentially differing growth rates and distinct driving mechanisms. Additionally, we observed a negative correlation between the IGL fraction and the group's velocity dispersion, indicating that a lower velocity dispersion may enhance IGL formation through increased gravitational interaction effectiveness. Furthermore, our comparative analysis of the density profiles of IGL and total system mass revealed significant similarities, suggesting that the intragroup light serves as a reliable tracer of the gravitational potential of host groups, even when these galaxy aggregations are far from dynamic equilibrium.

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Fully comprehensive diagnostic of galaxy activity using principal components of visible spectra: implementation on nearby S0s

We introduce a novel galaxy classification methodology based on the visible spectra of a sample of over 68,000 nearby ($z\leq 0.1$) Sloan Digital Sky Survey lenticular (S0) galaxies. Unlike traditional diagnostic diagrams, which rely on a limited set of emission lines and class dividers to identify ionizing sources, our approach provides a comprehensive framework for characterizing galaxies regardless of their activity level. By projecting galaxies into the 2D latent space defined by the first three principal components (PCs) of their entire visible spectra, our method remains robust even when data from individual emission lines are missing. We employ Gaussian kernel density estimates of the classical Baldwin-Phillips-Terlevich (BPT) activity classes in the new classification subspace, adjusted according to their relative abundance in our S0 sample, to generate probability maps for star-forming, Seyfert, composite, and LINER galaxies. These maps closely mirror the canonical distribution of BPT classes shown by the entire galaxy population, demonstrating that our PC-based taxonomy effectively predicts the dominant ionizing mechanisms through a probabilistic approach that provides a realistic reflection of galaxy activity and allows for refined class membership. Our analysis further reveals that flux-limited BPT-like diagrams are inherently biased against composite and star-forming galaxies due to their weaker [OIII] emission. Besides, it suggests that although most low-activity galaxies excluded from these diagnostics exhibit visual spectra with LINER-like characteristics, their remaining activity is likely driven by mechanisms unrelated to either star formation or supermassive black hole accretion. A machine-readable catalogue listing BPT-class probabilities for the galaxies analysed is available online at the CDS website.

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The local Universe in the era of large surveys -- III. Radial activity profiles of S0 galaxies

Spatially resolved MaNGA's optical spectra of 1072 present-day lenticular (S0) galaxies, dimensionally reduced from a principal component analysis (PCA), are used to determine their radial activity structure shaped by any possible nebular ionization source. Activity profiles within $1.5\,R_{\mathrm e}$ are examined in tandem with the mass, age, ellipticity and kinematics of the stars, as well as environmental density. Among the results of this comparison, we find that the sign of the radial activity gradient of S0s is tightly related to their PCA classification, BPT designation, and star formation status. PCA-passive lenticulars often show low-level, flat activity profiles, although there is also a significant number of systems with positive gradients, while their less common active counterparts generally have negative gradients, usually associated with high SSFRs and, sometimes, moderate Seyfert emission. A fraction of the latter also shows radial activity profiles with positive gradients, which become more abundant with increasing stellar mass regardless of environmental density. Our analysis also reveals that the subset of active S0s with negative gradients experiences at all galactocentric radii a systematic reduction in its median activity level with stellar mass, consistent with expectations for main sequence galaxies. In contrast, passive S0s with positive gradients show the opposite behaviour. Furthermore, systems whose activity is dominated by star formation are structurally rounder than the rest of S0s, while those classified as Seyfert exhibit higher rotational support. The possibility that negative and positive activity gradients in S0s may result from rejuvenation by two distinct types of minor mergers is raised.

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The origin of star-forming rings in S0 galaxies

Spatially resolved integral field spectroscopic maps in a sample of $532$ S0 galaxies from the MaNGA survey have unveiled the existence of inner rings ($\langle R\rangle\sim 1\,R_\mathrm{e}$) betraying ongoing star formation in a number of these objects. Activity gradients averaged over bins of galactocentric radius up to $\sim 1.5\,R_\mathrm{e}$ have been measured in the subspace defined by the first two principal components of the optical spectra of these galaxies. We find that the sign of the gradients is closely related to the presence of such rings in the spectral maps, which are especially conspicuous in the equivalent width of the H$α$ emission line, EW(H$α$), with a fractional abundance $\unicode{x2014}21\unicode{x2013}34\%\unicode{x2014}$ notably larger than that inferred from optical images. While the numbers of S0s with positive, negative, and flat activity gradients are comparable, star-forming rings are largely found in objects for which quenching proceeds from the inside out, in good agreement with predictions from cosmological simulations studying S0 buildup. Assessment of these ringed structures indicates that their frequency increases with the mass of their hosts, that they have shorter lifetimes in galaxies with ongoing star formation, that they may feed on gas from the disks, and that the local environment does not play a relevant role in their formation. We conclude that the presence of inner rings in the EW(H$α$) is a common phenomenon in fully formed S0s, possibly associated with annular disk resonances driven by weakly disruptive mergers preferentially involving a relatively massive primary galaxy and a tiny satellite strongly bound to the former.

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The local Universe in the era of large surveys -- II. Multi-wavelength characterisation of activity in nearby S0 galaxies

This is the second paper in a series using data from tens of thousands S0 galaxies of the local Universe ($z\lesssim 0.1$) retrieved from the NASA-Sloan Atlas. It builds on the outcomes of the previous work, which introduced a new classification scheme for these objects based on the principal component analysis (PCA) of their optical spectrum and its projections on to the first two eigenvectors or principal components (the PC1$\unicode{x2013}$PC2 diagram). We provide a comprehensive characterization of the activity of present-day S0s throughout both the broad-band PC1$\unicode{x2013}$PC2 spectral classifier and the conventional narrow-line BPT/WHAN ones, contrasting the different types of activity classes they define, and present an alternative diagram that exploits the concordance between WHAN and PCA demarcations. The analysis is extended to the mid-infrared, radio and X-ray wavelengths by crossmatching our core sample with data from the WISE, FIRST, XMM$\unicode{x2013}$Newton, and Chandra surveys. This has allowed us to carry out a thorough comparison of the most important activity diagnostics in the literature over different wavebands, discuss their similarities and differences, and explore the connections between them and with parameters related to star formation and black hole accretion. In particular, we find evidence that the bulk of nebular emission from radio and X-ray detected S0$\unicode{x2013}$Seyfert and LINER systems is not driven by star birth, while the dominant ionising radiation for a number of LINERs might come from post-AGB stars. These and other outcomes from the present work should be transferable to other morphologies.

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The local universe in the era of large surveys. I. Spectral classification of S0 galaxies

This is the first paper in a series devoted to review the main properties of galaxies designated S0 in the Hubble classification system. Our aim is to gather abundant and, above all, robust information on the most relevant physical parameters of this poorly-understood morphological type and their possible dependence on the environment that could later be used to assess their possible formation channel(s). The adopted approach combines the characterisation of the fundamental features of the optical spectra of $68{,}043$ S0 with heliocentric $z\lesssim 0.1$ with the exploration of a comprehensive set of their global attributes. A principal component analysis is used to reduce the huge number of dimensions of the spectral data to a low-dimensional space facilitating a bias-free machine-learning-based classification of the galaxies. This procedure has revealed that objects bearing the S0 designation consist, despite their similar morphology, of two separate sub-populations with statistically inconsistent physical properties. Compared to the absorption-dominated S0, those with significant nebular emission are, on average, somewhat less massive, more luminous with less concentrated light profiles, have a younger, bluer and metal-poorer stellar component, and avoid high-galaxy-density regions. Noteworthy is the fact that the majority of members of this latter class, which accounts for at least a quarter of the local S0 population, show star formation rates and spectral characteristics entirely similar to those seen in late spirals. Our findings suggest that star-forming S0 might be less rare than hitherto believed and raise the interesting possibility of identifying them with plausible progenitors of their quiescent counterparts.

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A statistical method for the identification of stars enriched in neutron-capture elements from medium-resolution spectra

We present an automated statistical method that uses medium-resolution spectroscopic observations of a set of stars to select those that show evidence of possessing significant amounts of neutron-capture elements. Our tool was tested against a sample of $\sim 70,000$ F- and G-type stars distributed among $215$ plates from the Galactic Understanding and Exploration (SEGUE) survey, including $13$ that were directed at stellar Galaxy clusters. Focusing on five spectral lines of europium in the visible window, our procedure ranked the stars by their likelihood of having enhanced content of this atomic species and identifies the objects that exhibit signs of being rich in neutron-capture elements as those scoring in the upper $2.5\%$. We find that several of the cluster plates contain relatively large numbers of stars with significant absorption around at least three of the five selected lines. The most prominent is the globular cluster M3, where we measured a fraction of stars that are potentially rich in heavy nuclides, representing at least $15\%$.

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Intrinsic and observed dual AGN fractions from major mergers

A suite of 432 collisionless simulations of bound pairs of spiral galaxies with mass ratios 1:1 and 3:1, and global properties consistent with the $Λ$CDM paradigm, is used to test the conjecture that major mergers fuel the dual AGN (DAGN) of the local volume. Our analysis is based on the premise that the essential aspects of this scenario can be captured by replacing the physics of the central BH with restrictions on their relative separation in phase space. We introduce several estimates of the DAGN fraction and infer predictions for the activity levels and resolution limits usually involved in surveys of these systems, assessing their dependence on the parameters controlling the length of both mergers and nuclear activity. Given a set of constraints, we find that the values adopted for some of the latter factors often condition the outcomes from individual experiments. Still, the results do not reveal, in general, very tight correlations, being the tendency of the frequencies normalized to the merger time to anticorrelate with the orbital circularity the clearest effect. In agreement with other theoretical studies, our simulations predict intrinsic abundances of these systems that range from $\sim$few to $15\%$ depending on the maximum level of nuclear activity achieved. At the same time, we show that these probabilities are reduced by about an order of magnitude when they are filtered with the typical constraints applied by observational studies of the DAGN fraction at low redshift. As a whole, the results of the present work prove that the consideration of the most common limitations involved in the detection of close active pairs at optical wavelengths is sufficient by itself to reconcile the intrinsic frequencies envisaged in a hierarchical universe with the small fractions of double-peaked narrow-line systems which are often reported at kpc-scales.

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Forming first-ranked early-type galaxies through hierarchical dissipationless merging

We have developed a computationally competitive N-body model of a previrialized aggregation of galaxies in a flat LambdaCDM universe to assess the role of the multiple mergers that take place during the formation stage of such systems in the configuration of the remnants assembled at their centres. An analysis of a suite of 48 simulations of low-mass forming groups (of about 1E13 solar masses) demonstrates that the gravitational dynamics involved in their hierarchical collapse is capable of creating realistic first-ranked galaxies without the aid of dissipative processes. Our simulations indicate that the brightest group galaxies (BGGs) constitute a distinct population from other group members, sketching a scenario in which the assembly path of these objects is dictated largely by the formation of their host system. We detect significant differences in the distribution of Sersic indices and total magnitudes, as well as a luminosity gap between BGGs and the next brightest galaxy that is positively correlated with the total luminosity of the parent group. Such gaps arise from both the grow of BGGs at the expense of lesser companions and the decrease in the relevance of second-ranked objects in equal measure. This results in a dearth of intermediate-mass galaxies which explains the characteristic central dip detected in their luminosity functions in dynamically young galaxy aggregations. The fact that the basic global properties of our BGGs define a thin mass fundamental plane strikingly similar to that followed giant early-type galaxies in the local universe reinforces confidence in the results obtained.

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HI Content and Optical Properties of Field Galaxies from the ALFALFA Survey. I.Selection of a Control Sample

We report results from a study of the HI content and stellar properties of nearby galaxies detected by the Arecibo Legacy Fast ALFA blind 21-cm line survey and the Sloan Digital Sky Survey in two declination strips covering a total area of 9 hr X 16 deg. Our analysis seeks to assemble a control sample of galaxies suitable for providing absolute measures of the HI content of gaseous objects. From a database of ~15,000 HI detections, we have assembled three samples of gas-rich galaxies expected to show little or no evidence of interaction with their surroundings that could provide adequate HI standards. The most reliable results are obtained with a sample of 5647 sources found in low density environments, as defined by a nearest neighbor approach. The other two samples contain several hundred relatively isolated galaxies each, as determined from standard isolation algorithms. We find that isolated objects are not particularly gas-rich compared to their low-density-environment counterparts, while they suffer from selection bias and span a smaller dynamic range. All this makes them less suitable for defining a reference for HI content. We have explored the optical morphology of gaseous galaxies in quiet environments finding that, within the volume surveyed, the vast majority of them display unequivocal late-type galaxy features. In contrast, bona fide gas-rich early-type systems account only for a negligible fraction of the 21-cm detections. We argue that HI emission provides the most reliable way to determine the morphological population to which a galaxy belongs. We have also observed that the color distribution of flux-limited samples of optically-selected field HI emitters does not vary significantly with increasing distance, while that of non-detections becomes notably redder. This result suggests that the colors and HI masses of gas-rich galaxies cannot be very closely related.

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HI Content and Optical Properties of Field Galaxies from the ALFALFA Survey. II. Multivariate Analysis of a Galaxy Sample in Low Density Environments

This is the second paper of two reporting results from a study of the HI content and stellar properties of nearby galaxies detected by the Arecibo Legacy Fast ALFA blind 21-cm line survey and the Sloan Digital Sky Survey in a 2160 deg^2 region covered by both surveys. We apply strategies of multivariate data analysis to a complete HI flux-limited subset of 1624 objects extracted from the control sample of HI emitters assembled by Toribio et al. (2011a) in order to: i) investigate the correlation structure of the space defined by an extensive set of observables describing gas-rich systems; ii) identify the intrinsic parameters that best define their HI content; and iii) explore the scaling relations arising from the joint distributions of the quantities most strongly correlated with the HI mass. The principal component analysis performed over a set of five galaxy properties reveals that they are strongly interrelated, supporting previous claims that nearby HI emitters show a high degree of correlation. The best predictors for the expected value of MHI are the diameter of the stellar disk, D25r, followed by the total luminosity (both in the r-band), and the maximum rotation speed, while morphological proxies such as color show only a moderately strong correlation with the gaseous content attenuated by observational error. The simplest and most accurate prescription is log(MHI/Msun)= 8.72 + 1.25*log(D25r/kpc). We find a slope of $-8.2 \pm 0.5$ for the relation between optical magnitude and log rotation speed, in good agreement with Tully-Fisher studies, and a log slope of $1.55 \pm 0.06$ for the HI mass-optical galaxy size relation. Given the homogeneity of the measurements and the completeness of our dataset, the latter outcome suggests that the constancy of the average (hybrid) HI surface density advocated by some authors for the spiral population is a crude approximation.

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The GALEX Ultraviolet Virgo Cluster Survey (GUViCS). I: The UV luminosity function of the central 12 sq.deg

The GALEX Ultraviolet Virgo Cluster Survey (GUViCS) is a complete blind survey of the Virgo cluster covering about 40 sq. deg. in the far UV (FUV, lambda_eff=1539A, Delta-lambda=442A) and about 120 sq. deg. in the near UV (NUV, lambda_eff=2316A, Delta-lambda=1060A). The goal of the survey is to study the ultraviolet (UV) properties of galaxies in a rich cluster environment, spanning a wide luminosity range from giants to dwarfs, and regardless of prior knowledge of their star formation activity. The UV data will be combined with those in other bands (optical: NGVS; far-infrared - submm: HeViCS; HI: ALFALFA) and with our multizone chemo-spectrophotometric models of galaxy evolution to make a complete and exhaustive study of the effects of the environment on the evolution of galaxies in high density regions. We present here the scientific objectives of the survey, describing the observing strategy and briefly discussing different data reduction techniques. Using UV data already in-hand for the central 12 sq. deg. we determine the FUV and NUV luminosity functions of the Virgo cluster core for all cluster members and separately for early- and late-type galaxies and compare it to the one obtained in the field and other nearby clusters (Coma, A1367). This analysis shows that the FUV and NUV luminosity functions of the core of the Virgo clusters are flatter (alpha about -1.1) than those determined in Coma and A1367. We discuss the possible origin of this difference

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Fitting functions for a disk-galaxy model with different LCDM-halo profiles

We present an adaptation of the standard scenario of disk-galaxy formation to the concordant LCDM cosmology aimed to derive analytical expressions for the scale length and rotation speed of present-day disks that form within four different, cosmologically motivated protogalactic dark matter halo-density profiles. We invoke a standard galaxy-formation model that includes virial equilibrium of spherical dark halos, specific angular momentum conservation during gas cooling, and adiabatic halo response to the gas inflow. The mean mass-fraction and mass-to-light ratio of the central stellar disk are treated as free parameters whose values are tuned to match the zero points of the observed size-luminosity and circular speed-luminosity relations of galaxies. We supply analytical formulas for the characteristic size and rotation speed of disks built inside Einasto r^{1/6}, Hernquist, Burkert, and Navarro-Frenk-White dark matter halos. These expressions match simultaneously the observed zero points and slopes of the different correlations that can be built in the RVL space of disk galaxies from plausible values of the galaxy- and star-formation efficiencies.

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