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R. M. González Delgado

Publications and source records attributed to R. M. González Delgado.

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Nearby supernova host galaxies from the CALIFA Survey: II. SN environmental metallicity

The metallicity of a supernova (SN) progenitor, together with its mass, is one of the main parameters that rules their outcome. We present a metallicity study of 115 nearby SN host galaxies (0.005 10 dex) by targeted searches. We also found no evidence that the metallicity at the SN location differs from the average metallicity at the GCD of the SNe. By extending our SN sample with published metallicities at the SN location, we studied the metallicity distributions for all SN subtypes split into SN discovered in targeted and untargeted searches. We confirm a bias toward higher host masses and metallicities in the targeted searches. Combining data from targeted and untargeted searches we found a sequence from higher to lower local metallicity: SN Ia, Ic, and II show the highest metallicity, which is significantly higher than SN Ib, IIb, and Ic-BL. Our results support the picture of SN Ib resulting from binary progenitors and, at least part of, SN Ic being the result of single massive stars stripped of their outer layers by metallicity driven winds. We studied several proxies of the local metallicity frequently used in the literature and found that the total host metallicity allows for the estimation of the metallicity at the SN location with an accuracy better than 0.08 dex and very small bias. In addition, weak AGNs not seen in total spectra may only weakly bias (by 0.04 dex) the metallicity estimate from integrated spectra. (abridged)

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Star formation along the Hubble sequence: Radial structure of the star formation of CALIFA galaxies

The aim of this paper is to characterize the radial structure of the star formation rate (SFR) in galaxies in the nearby Universe as represented by the CALIFA survey. The sample under study contains 416 galaxies observed with IFS, covering a wide range of Hubble types and stellar masses. Spectral synthesis techniques are applied to obtain radial profiles of the intensity of the star formation rate in the recent past, and the local sSFR. To emphasize the behavior of these properties for galaxies that are on and off the main sequence of star formation (MSSF) we stack the individual radial profiles in bins of galaxy morphology and stellar masses. Our main results are: a) The intensity of SFR shows declining profiles that exhibit very little differences between spirals. The dispersion between the profiles is significantly smaller in late type spirals. This confirms that the MSSF is a sequence of galaxies with nearly constant intensity of SFR b) sSFR values scale with Hubble type and increase radially outwards, with a steeper slope in the inner 1 HLR. This behavior suggests that galaxies are quenched inside-out, and that this process is faster in the central, bulge-dominated part than in the disks. c) As a whole, and at all radii, E and S0 are off the MSSF. d) Applying the volume-corrections for the CALIFA sample, we obtain a density of star formation in the local Universe of 0.0105 Msun/yr/Mpc^{-3}. Most of the star formation is occurring in the disks of spirals. e) The volume averaged birthrate parameter, b'=0.39, suggests that the present day Universe is forming stars at 1/3 of its past average rate. E, S0, and the bulge of early type spirals contribute little to the recent SFR of the Universe, which is dominated by the disks of later spirals. f) There is a tight relation between the intensity of the SFR and stellar mass, defining a local MSSF relation with a logarithmic slope of 0.8.

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Spatially-Resolved Star Formation Main Sequence of Galaxies in the CALIFA Survey

The "main sequence of galaxies" $-$ defined in terms of the total star formation rate $ψ$ vs. the total stellar mass $M_*$ $-$ is a well-studied tight relation that has been observed at several wavelengths and at different redshifts. All earlier studies have derived this relation from integrated properties of galaxies. We recover the same relation from an analysis of spatially-resolved properties, with integral field spectroscopic (IFS) observations of 306 galaxies from the CALIFA survey. We consider the SFR surface density in units of log(M$_{\odot}$ yr$^{-1}$ Kpc$^{-2}$) and the stellar mass surface density in units of log(M$_{\odot}$ Kpc$^{-2}$) in individual spaxels which probe spatial scales of 0.5-1.5 Kpc. This local relation exhibits a high degree of correlation with small scatter ($σ= 0.23$ dex), irrespective of the dominant ionisation source of the host galaxy or its integrated stellar mass. We highlight: $(i)$ the integrated star formation main sequence formed by galaxies whose dominant ionisation process is related to star formation, for which we find a slope of 0.81 $\pm 0.02$; (ii) the spatially-resolved relation obtained with the spaxel analysis, we find a slope of 0.72 $\pm 0.04$; (iii) for the integrated main sequence we identified also a sequence formed by galaxies that are dominated by an old stellar population, which we have called the retired galaxies sequence.

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Simultaneous spectroscopic and photometric analysis of galaxies with STARLIGHT: CALIFA $+$ GALEX

We present an extended version of the spectral synthesis code STARLIGHT designed to incorporate both $λ$-by-$λ$ spectra and photometric fluxes in the estimation of stellar population properties of galaxies. The code is tested with simulations and data for 260 galaxies culled from the CALIFA survey, spatially matching the 3700--7000 Å optical datacubes to GALEX near and far UV images. The sample spans E--Sd galaxies with masses from $10^9$ to $10^{12} M_\odot$ and stellar populations all the way from star-forming to old, passive systems. Comparing results derived from purely optical fits with those which also consider the NUV and FUV data we find that: (1) The new code is capable of matching the input UV data within the errors while keeping the quality of the optical fit essentially unchanged. (2) Despite being unreliable predictors of the UV fluxes, purely optical fits yield stellar population properties which agree well with those obtained in optical+UV fits for nearly 90% of our sample. (3) The addition of UV constraints has little impact on properties such as stellar mass and dust optical depth. Mean stellar ages and metallicities also remain nearly the same for most galaxies, the exception being low-mass, late-type galaxies, which become older and less enriched due to rearrangements of their youngest populations. (4) The revised ages are better correlated with observables such as the 4000 Å break index, and the $NUV - r$ and $u - r$ colours, an empirical indication that the addition of UV constraints helps mitigating the effects of age-metallicity-extinction degeneracies.

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The ALHAMBRA survey: evolution of galaxy spectral segregation

We study the clustering of galaxies as a function of spectral type and redshift in the range $0.35 < z < 1.1$ using data from the Advanced Large Homogeneous Area Medium Band Redshift Astronomical (ALHAMBRA) survey. The data cover 2.381 deg$^2$ in 7 fields, after applying a detailed angular selection mask, with accurate photometric redshifts [$σ_z < 0.014(1+z)$] down to $I_{AB} < 24$. From this catalog we draw five fixed number density, redshift-limited bins. We estimate the clustering evolution for two different spectral populations selected using the ALHAMBRA-based photometric templates: quiescent and star-forming galaxies. For each sample, we measure the real-space clustering using the projected correlation function. Our calculations are performed over the range $[0.03,10.0] h^{-1}$ Mpc, allowing us to find a steeper trend for $r_p \lesssim 0.2 h^{-1}$ Mpc, which is especially clear for star-forming galaxies. Our analysis also shows a clear early differentiation in the clustering properties of both populations: star-forming galaxies show weaker clustering with evolution in the correlation length over the analysed redshift range, while quiescent galaxies show stronger clustering already at high redshifts, and no appreciable evolution. We also perform the bias calculation where similar segregation is found, but now it is among the quiescent galaxies where a growing evolution with redshift is clearer. These findings clearly corroborate the well known colour-density relation, confirming that quiescent galaxies are mainly located in dark matter halos that are more massive than those typically populated by star-forming galaxies.

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No direct coupling between bending of galaxy disc stellar age and light profiles

We study the stellar properties of 44 face-on spiral galaxies from the Calar Alto Legacy Integral Field Area survey via full spectrum fitting techniques. We compare the age profiles with the surface brightness distribution in order to highlight differences between profile types (type I, exponential profile; and II, down-bending profile). We observe an upturn ("U-shape") in the age profiles for 17 out of these 44 galaxies with reliable stellar information up to their outer parts. This "U-shape" is not a unique feature for type II galaxies but can be observed in type I as well. These findings suggest that the mechanisms shaping the surface brightness and stellar population distributions are not directly coupled. This upturn in age is only observable in the light-weighted profiles while it flattens out in the mass-weighted profiles. Given recent results on the outer parts of nearby systems and the results presented in this Letter, one of the most plausible explanations for the age upturn is an early formation of the entire disc ($\sim$~10~Gyr ago) followed by an inside-out quenching of the star formation.

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The warm ionized gas in CALIFA early-type galaxies: 2D emission-line patterns and kinematics for 32 galaxies

The morphological, spectroscopic and kinematical properties of the warm interstellar medium (wim) in early-type galaxies (ETGs) hold key observational constraints to nuclear activity and the buildup history of these massive, quiescent systems. High-quality integral field spectroscopy (IFS) data with a wide spectral and spatial coverage, such as those from the CALIFA survey, offer an unprecedented opportunity for advancing our understanding of the wim in ETGs. This article centers on a 2D investigation of the wim component in 32 nearby (<~150Mpc) ETGs from CALIFA, complementing a previous 1D analysis of the same sample (Papaderos et al. 2013; P13). We include here Hα intensity and equivalent width (EW) maps and radial profiles, diagnostic emission-line ratios, besides ionized-gas and stellar kinematics. This study is supplemented by τ-ratio maps as an efficient means to quantify the role of photoionization by pAGB stars, as compared to other mechanisms (e.g., AGN, low-level star formation). Additionally, we extend the tentative classification proposed in P13 by the type i+, which is assigned to a subset of type i ETGs exhibiting ongoing low-level star-formation (SF) in their periphery. This finding along with faint traces of localized SF in the extranuclear component of several of our sample ETGs points to a non-negligible contribution by OB stars to the total ionizing budget. We also demonstrate that, at the typical emission-line detection threshold of ~2Åin previous studies, most of the extranuclear wim emission in an ETG may evade detection, which could in turn prompt its classification as an entirely gas-devoid system. This study adds further observational evidence for a considerable heterogeneity among ETGs with regard to the physical properties and 2D kinematics of the wim component, and underscores the importance of IFS studies over their entire optical extent.

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Spectroscopic aperture biases in inside-out evolving early-type galaxies from CALIFA

Integral field spectroscopy studies based on CALIFA data have recently revealed the presence of ongoing low-level star formation (SF) in the periphery of ~10% of local early-type galaxies (ETGs), witnessing a still ongoing inside-out galaxy growth process. A distinctive property of the nebular component in these ETGs, classified i+, is a two-radial-zone structure, with the inner zone displaying LINER emission with a Hαequivalent width EW~1Å, and the outer one (3Å<EW<~20Å) showing HII-region characteristics. Using CALIFA IFS data, we empirically demonstrate that the confinement of nebular emission to the galaxy periphery leads to a strong aperture (or, redshift) bias in spectroscopic single-fiber studies of type i+ ETGs: At low redshift (<~0.45), SDSS spectroscopy is restricted to the inner (SF-devoid LINER) zone, thereby leading to their erroneous classification as "retired" galaxies (systems lacking SF and whose faint emission is powered by pAGB stars). Only at higher z's the SDSS aperture can encompass the outer SF zone, permitting their unbiased classification as "composite SF/LINER". We also demonstrate that the principal effect of a decreasing aperture on the classification of i+ ETGs via standard BPT emission-line ratios consists in a monotonic up-right shift precisely along the upper-right wing of the "seagull" distribution. Motivated by these insights, we also investigate theoretically these biases in aperture-limited studies of inside-out growing galaxies as a function of z. To this end, we devise a simple model, which involves an outwardly propagating SF process, that reproduces the radial extent and two-zone EW distribution of i+ ETGs. By simulating on this model the spectroscopic SDSS aperture, we find that SDSS studies at z<~1 are progressively restricted to the inner LINER-zone, and miss an increasingly large portion of the Hα-emitting periphery.

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Spiral-like star-forming patterns in CALIFA early-type galaxies

Based on a combined analysis of SDSS imaging and CALIFA integral field spectroscopy data, we report on the detection of faint (24 < μ$_r$ mag/arcsec$^2$ < 26) star-forming spiral-arm-like features in the periphery of three nearby early-type galaxies (ETGs). These features are of considerable interest because they document the still ongoing inside-out growth of some local ETGs and may add valuable observational insight into the origin and evolution of spiral structure in triaxial stellar systems. A characteristic property of the nebular component in the studied ETGs, classified i+, is a two-radial-zone structure, with the inner zone that displays faint (EW(Hα)$\simeq$1Å) low-ionization nuclear emission-line region (LINER) properties, and the outer one (3Å<EW(Hα)<~20Å) HII-region characteristics. This spatial segregation of nebular emission in two physically distinct concentric zones calls for an examination of aperture effects in studies of type i+ ETGs with single-fiber spectroscopic data.

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Outer-disk reddening and gas-phase metallicities: The CALIFA connection

We study, for the first time in a statistically significant and well-defined sample, the relation between the outer-disk ionized-gas metallicity gradients and the presence of breaks in the surface brightness profiles of disk galaxies. SDSS g'- and r'-band surface brightness, (g'- r') color, and ionized-gas oxygen abundance profiles for 324 galaxies within the CALIFA survey are used for this purpose. We perform a detailed light-profile classification finding that 84% of our disks show down- or up-bending profiles (Type II and Type III, respectively) while the remaining 16% are well fitted by one single exponential (Type I). The analysis of the color gradients at both sides of this break shows a U-shaped profile for most Type II galaxies with an average minimum (g'- r') color of ~0.5 mag and a ionized-gas metallicity flattening associated to it only in the case of low-mass galaxies. More massive systems show a rather uniform negative metallicity gradient. The correlation between metallicity flattening and stellar mass results in p-values as low as 0.01. Independently of the mechanism having shaped the outer light profiles of these galaxies, stellar migration or a previous episode of star formation in a shrinking star-forming disk, it is clear that the imprint in their ionized-gas metallicity was different for low- and high-mass Type II galaxies. In the case of Type III disks, a positive correlation between the change in color and abundance gradient is found (the null hypothesis is ruled out with a p-value of 0.02), with the outer disks of Type III galaxies with masses $\leq$10$^{10}$ M$_{\odot}$ showing a weak color reddening or even a bluing. This is interpreted as primarily due to a mass down-sizing effect on the population of Type III galaxies having recently experienced an enhanced inside-out growth.

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The ALHAMBRA survey : Estimation of the clustering signal encoded in the cosmic variance

The relative cosmic variance ($σ_v$) is a fundamental source of uncertainty in pencil-beam surveys and, as a particular case of count-in-cell statistics, can be used to estimate the bias between galaxies and their underlying dark-matter distribution. Our goal is to test the significance of the clustering information encoded in the $σ_v$ measured in the ALHAMBRA survey. We measure the cosmic variance of several galaxy populations selected with $B-$band luminosity at $0.35 \leq z < 1.05$ as the intrinsic dispersion in the number density distribution derived from the 48 ALHAMBRA subfields. We compare the observational $σ_v$ with the cosmic variance of the dark matter expected from the theory, $σ_{v,{\rm dm}}$. This provides an estimation of the galaxy bias $b$. The galaxy bias from the cosmic variance is in excellent agreement with the bias estimated by two-point correlation function analysis in ALHAMBRA. This holds for different redshift bins, for red and blue subsamples, and for several $B-$band luminosity selections. We find that $b$ increases with the $B-$band luminosity and the redshift, as expected from previous work. Moreover, red galaxies have a larger bias than blue galaxies, with a relative bias of $b_{\rm rel} = 1.4 \pm 0.2$. Our results demonstrate that the cosmic variance measured in ALHAMBRA is due to the clustering of galaxies and can be used to characterise the $σ_v$ affecting pencil-beam surveys. In addition, it can also be used to estimate the galaxy bias $b$ from a method independent of correlation functions.

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The impact from survey depth and resolution on the morphological classification of galaxies

We consistently analyse for the first time the impact of survey depth and spatial resolution on the most used morphological parameters for classifying galaxies through non-parametric methods: Abraham and Conselice-Bershady concentration indices, Gini, M20 moment of light, asymmetry, and smoothness. Three different non-local datasets are used, ALHAMBRA and SXDS (examples of deep ground-based surveys), and COSMOS (deep space-based survey). We used a sample of 3000 local, visually classified galaxies, measuring their morphological parameters at their real redshifts (z ~ 0). Then we simulated them to match the redshift and magnitude distributions of galaxies in the non-local surveys. The comparisons of the two sets allow to put constraints on the use of each parameter for morphological classification and evaluate the effectiveness of the commonly used morphological diagnostic diagrams. All analysed parameters suffer from biases related to spatial resolution and depth, the impact of the former being much stronger. When including asymmetry and smoothness in classification diagrams, the noise effects must be taken into account carefully, especially for ground-based surveys. M20 is significantly affected, changing both the shape and range of its distribution at all brightness levels.We suggest that diagnostic diagrams based on 2 - 3 parameters should be avoided when classifying galaxies in ground-based surveys, independently of their brightness; for COSMOS they should be avoided for galaxies fainter than F814 = 23.0. These results can be applied directly to surveys similar to ALHAMBRA, SXDS and COSMOS, and also can serve as an upper/lower limit for shallower/deeper ones.

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Star Formation in the Local Universe from the CALIFA sample. I. Calibrating the SFR using IFS data

The Star Formation Rate (SFR) is one of the main parameters used to analyze the evolution of galaxies through time. The need for recovering the light reprocessed by dust commonly requires the use of low spatial resolution far-infrared data. Recombination-line luminosities provide an alternative, although uncertain dust-extinction corrections based on narrow-band imaging or long-slit spectroscopy have traditionally posed a limit to their applicability. Integral Field Spectroscopy (IFS) is clearly the way to overcome such limitation. We obtain integrated Hα, ultraviolet (UV) and infrared (IR)-based SFR measurements for 272 galaxies from the CALIFA survey at 0.005 < z < 0.03 using single-band and hybrid tracers. We provide updated calibrations, both global and split by properties (including stellar mass and morphological type), referred to Hα. The extinction-corrected Hα luminosity agrees with the updated hybrid SFR estimators based on either UV or Hα plus IR luminosity over the full range of SFRs (0.03-20 M$_{\odot}$ yr$^{-1}$). The coefficient that weights the amount of energy produced by newly-born stars that is reprocessed by dust on the hybrid tracers, a$_{IR}$, shows a large dispersion. However, it does not became increasingly small at high attenuations, as expected if significant highly-obscured H$α$ emission would be missed. Lenticulars, early-type spirals and type-2 AGN host galaxies show smaller coefficients due to the contribution of optical photons and AGN to dust heating. In the Local Universe the Hα luminosity derived from IFS observations can be used to measure SFR, at least in statistically-significant, optically-selected galaxy samples. The analysis of the SFR calibrations by galaxies properties could be potentially used by other works to study the impact of different selection criteria in the SFR values derived.

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The CALIFA survey across the Hubble sequence: Spatially resolved stellar population properties in galaxies

This paper characterizes the radial structure of stellar population properties of galaxies in the nearby universe, based on 300 galaxies from the CALIFA survey. The sample covers a wide range of Hubble types, and galaxy stellar mass. We apply the spectral synthesis techniques to recover the stellar mass surface density, stellar extinction, light and mass-weighted ages, and mass-weighted metallicity, for each spatial resolution element in our target galaxies. To study mean trends with overall galaxy properties, the individual radial profiles are stacked in seven bins of galaxy morphology. We confirm that more massive galaxies are more compact, older, more metal rich, and less reddened by dust. Additionally, we find that these trends are preserved spatially with the radial distance to the nucleus. Deviations from these relations appear correlated with Hubble type: earlier types are more compact, older, and more metal rich for a given mass, which evidences that quenching is related to morphology, but not driven by mass. Negative gradients of ages are consistent with an inside-out growth of galaxies, with the largest ages gradients in Sb-Sbc galaxies. Further, the mean stellar ages of disks and bulges are correlated, with disks covering a wider range of ages, and late type spirals hosting younger disks. The gradients in stellar mass surface density depend mostly on stellar mass, in the sense that more massive galaxies are more centrally concentrated. There is a secondary correlation in the sense that at the same mass early type galaxies have steeper gradients. We find mildly negative metallicity gradients, shallower than predicted from models of galaxy evolution in isolation. The largest gradients occur in Sb galaxies. Overall we conclude that quenching processes act in manners that are independent of mass, while metallicity and galaxy structure are influenced by mass-dependent processes.

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Tracing kinematic (mis)alignments in CALIFA merging galaxies: Stellar and ionized gas kinematic orientations at every merger stage

We present spatially resolved stellar and/or ionized gas kinematic properties for a sample of 103 interacting galaxies, tracing all merger stages: close companions, pairs with morphological signatures of interaction, and coalesced merger remnants. We compare our sample with 80 non-interacting galaxies. We measure for the stellar and the ionized gas components the major (projected) kinematic position angles (PA$_{\mathrm{kin}}$, approaching and receding) directly from the velocity fields with no assumptions on the internal motions. This method allow us to derive the deviations of the kinematic PAs from a straight line ($δ$PA$_{\mathrm{kin}}$). Around half of the interacting objects show morpho-kinematic PA misalignments that cannot be found in the control sample. Those misalignments are present mostly in galaxies with morphological signatures of interaction. Alignment between the kinematic sides for both samples is similar, with most of the galaxies displaying small misalignments. Radial deviations of the kinematic PA from a straight line in the stellar component measured by $δ$PA$_{\mathrm{kin}}$ are large for both samples. However, for a large fraction of interacting galaxies the ionized gas $δ$PA$_{\mathrm{kin}}$ is larger than typical values derived from isolated galaxies (48%), making this parameter a good indicator to trace the impact of interaction and mergers in the internal motions of galaxies. By comparing the stellar and ionized gas kinematic PA, we find that 42% (28/66) of the interacting galaxies have misalignments larger than 16 degrees, compared to 10% from the control sample. Our results show the impact of interactions in the internal structure of galaxies as well as the wide variety of their velocity distributions. This study also provides a local Universe benchmark for kinematic studies in merging galaxies at high redshift.

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The CALIFA survey across the Hubble sequence: How galaxies grow their bulges and disks

We characterize in detail the radial structure of the stellar population properties of 300 galaxies in the nearby universe, observed with integral field spectroscopy in the CALIFA survey. The sample covers a wide range of Hubble types, from spheroidal to spiral galaxies, ranging in stellar masses from $M_\star \sim 10^9$ to $7 \times 10^{11}$ $M_\odot$. We derive the stellar mass surface density ($μ_\star$), light-weighted and mass-weighted ages ($\langle {\rm log}\,age\rangle _L$, $\langle {\rm log}\,age\rangle _M$), and mass-weighted metallicity ($\langle {\rm log}\,Z_\star\rangle _M$), applying the spectral synthesis technique. We study the mean trends with galaxy stellar mass, $M_\star$, and morphology (E, S0, Sa, Sb, Sbc, Sc and Sd). We confirm that more massive galaxies are more compact, older, more metal rich, and less reddened by dust. Additionally, we find that these trends are preserved spatially with the radial distance to the nucleus. Deviations from these relations appear correlated with Hubble type: earlier types are more compact, older, and more metal rich for a given M$_\star$, which evidences that quenching is related to morphology, but not driven by mass.

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High redshift galaxies in the ALHAMBRA survey: I. selection method and number counts based on redshift PDFs

Context. Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using the so called dropout technique or Ly-alpha selection. However, the availability of multifilter data allows now replacing the dropout selections by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the population of high redshift galaxies in the ALHAMBRA survey data. Aims. Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies in ALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing in the study of the brightest, less frequent, high redshift galaxies. Methods. The methodology is based on redshift probability distribution functions (zPDFs). It is shown how a clean galaxy sample can be obtained by selecting the galaxies with high integrated probability of being within a given redshift interval. However, reaching both a complete and clean sample with this method is challenging. Hence, a method to derive statistical properties by summing the zPDFs of all the galaxies in the redshift bin of interest is introduced. Results. Using this methodology we derive the galaxy rest frame UV number counts in five redshift bins centred at z=2.5, 3.0, 3.5, 4.0, and 4.5, being complete up to the limiting magnitude at m_UV(AB)=24. With the wide field ALHAMBRA data we especially contribute in the study of the brightest ends of these counts, sampling well the surface densities down to m_UV(AB)=21-22. Conclusions. We show that using the zPDFs it is easy to select a clean sample of high redshift galaxies. We also show that statistical analysis of the properties of galaxies is better done using a probabilistic approach, which takes into account both the incompleteness and contamination in a natural way.

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Bar pattern speeds in CALIFA galaxies: I. Fast bars across the Hubble sequence

The bar pattern speed ($Ω_{\rm b}$) is defined as the rotational frequency of the bar, and it determines the bar dynamics. Several methods have been proposed for measuring $Ω_{\rm b}$. The non-parametric method proposed by Tremaine \& Weinberg (1984; TW) and based on stellar kinematics is the most accurate. This method has been applied so far to 17 galaxies, most of them SB0 and SBa types. We have applied the TW method to a new sample of 15 strong and bright barred galaxies, spanning a wide range of morphological types from SB0 to SBbc. Combining our analysis with previous studies, we investigate 32 barred galaxies with their pattern speed measured by the TW method. The resulting total sample of barred galaxies allows us to study the dependence of $Ω_{\rm b}$ on galaxy properties, such as the Hubble type. We measured $Ω_{\rm b}$ using the TW method on the stellar velocity maps provided by the integral-field spectroscopy data from the CALIFA survey. Integral-field data solve the problems that long-slit data present when applying the TW method, resulting in the determination of more accurate $Ω_{\rm b}$. In addition, we have also derived the ratio $\cal{R}$ of the corotation radius to the bar length of the galaxies. According to this parameter, bars can be classified as fast ($\cal{R}$ $< 1.4$) and slow ($\cal{R}$>1.4). For all the galaxies, $\cal{R}$ is compatible within the errors with fast bars. We cannot rule out (at 95$\%$ level) the fast bar solution for any galaxy. We have not observed any significant trend between $\cal{R}$ and the galaxy morphological type. Our results indicate that independent of the Hubble type, bars have been formed and then evolve as fast rotators. This observational result will constrain the scenarios of formation and evolution of bars proposed by numerical simulations.

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