arXiv subjects

C. J. Walcher

Publications and source records attributed to C. J. Walcher.

At least 73 records · Page 4Linked to original sources

arXiv2014

Large scale kinematics and dynamical modelling of the Milky Way nuclear star cluster

Within the central 10pc of our Galaxy lies a dense nuclear star cluster (NSC), and similar NSCs are found in most nearby galaxies. Studying the structure and kinematics of NSCs reveals the history of mass accretion of galaxy nuclei. Because the Milky Way (MW) NSC is at a distance of only 8kpc, we can spatially resolve the MWNSC on sub-pc scales. This makes the MWNSC a reference object for understanding the formation of all NSCs. We have used the NIR long-slit spectrograph ISAAC (VLT) in a drift-scan to construct an integral-field spectroscopic map of the central 9.5 x 8pc of our Galaxy. We use this data set to extract stellar kinematics both of individual stars and from the unresolved integrated light spectrum. We present a velocity and dispersion map from the integrated light and model these kinematics using kinemetry and axisymmetric Jeans models. We also measure CO bandhead strengths of 1,375 spectra from individual stars. We find kinematic complexity in the NSCs radial velocity map including a misalignment of the kinematic position angle by 9 degree counterclockwise relative to the Galactic plane, and indications for a rotating substructure perpendicular to the Galactic plane at a radius of 20" or 0.8pc. We determine the mass of the NSC within r = 4.2pc to 1.4 x 10^7 Msun. We also show that our kinematic data results in a significant underestimation of the supermassive black hole (SMBH) mass. The kinematic substructure and position angle misalignment may hint at distinct accretion events. This indicates that the MWNSC grew at least partly by the mergers of massive star clusters. Compared to other NSCs, the MWNSC is on the compact side of the r_eff - M_NSC relation. The underestimation of the SMBH mass might be caused by the kinematic misalignment and a stellar population gradient. But it is also possible that there is a bias in SMBH mass measurements obtained with integrated light.

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arXiv2014

CALIFA: a diameter-selected sample for an integral field spectroscopy galaxy survey

We describe and discuss the selection procedure and statistical properties of the galaxy sample used by the Calar Alto Legacy Integral Field Area Survey (CALIFA), a public legacy survey of 600 galaxies using integral field spectroscopy. The CALIFA "mother sample" was selected from the Sloan Digital Sky Survey (SDSS) DR7 photometric catalogue to include all galaxies with an r-band isophotal major axis between 45" and 79.2" and with a redshift 0.005 < z < 0.03. The mother sample contains 939 objects, 600 of which will be observed in the course of the CALIFA survey. The selection of targets for observations is based solely on visibility and thus keeps the statistical properties of the mother sample. By comparison with a large set of SDSS galaxies, we find that the CALIFA sample is representative of galaxies over a luminosity range of -19 > Mr > -23.1 and over a stellar mass range between 10^9.7 and 10^11.4Msun. In particular, within these ranges, the diameter selection does not lead to any significant bias against - or in favour of - intrinsically large or small galaxies. Only below luminosities of Mr = -19 (or stellar masses < 10^9.7Msun) is there a prevalence of galaxies with larger isophotal sizes, especially of nearly edge-on late-type galaxies, but such galaxies form < 10% of the full sample. We estimate volume-corrected distribution functions in luminosities and sizes and show that these are statistically fully compatible with estimates from the full SDSS when accounting for large-scale structure. We also present a number of value-added quantities determined for the galaxies in the CALIFA sample. We explore different ways of characterizing the environments of CALIFA galaxies, finding that the sample covers environmental conditions from the field to genuine clusters. We finally consider the expected incidence of active galactic nuclei among CALIFA galaxies.

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arXiv2014

Insights on the stellar mass-metallicity relation from the CALIFA survey

We use spatially and temporally resolved maps of stellar population properties of 300 galaxies from the CALIFA integral field survey to investigate how the stellar metallicity (Z*) relates to the total stellar mass (M*) and the local mass surface density ($μ$*) in both spheroidal and disk dominated galaxies. The galaxies are shown to follow a clear stellar mass-metallicity relation (MZR) over the whole 10$^9$ to 10$^{12}$ M$_{\odot}$ range. This relation is steeper than the one derived from nebular abundances, which is similar to the flatter stellar MZR derived when we consider only young stars. We also find a strong relation between the local values of $μ$* and Z* (the $μ$ZR), betraying the influence of local factors in determining Z*. This shows that both local ($μ$*-driven) and global (M*-driven) processes are important in determining the metallicity in galaxies. We find that the overall balance between local and global effects varies with the location within a galaxy. In disks, $μ$* regulates Z*, producing a strong $μ$ZR whose amplitude is modulated by M*. In spheroids it is M* who dominates the physics of star formation and chemical enrichment, with $μ$* playing a minor, secondary role. These findings agree with our previous analysis of the star formation histories of CALIFA galaxies, which showed that mean stellar ages are mainly governed by surface density in galaxy disks and by total mass in spheroids.

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arXiv2014

Kinematic alignment of non-interacting CALIFA galaxies: Quantifying the impact of bars on stellar and ionised gas velocity field orientations

We present 80 stellar and ionised gas velocity maps from the Calar Alto Legacy Integral Field Area (CALIFA) survey in order to characterize the kinematic orientation of non-interacting galaxies. The study of galaxies in isolation is a key step towards understanding how fast-external processes, such as major mergers, affect kinematic properties in galaxies. We derived the global and individual (projected approaching and receding sides) kinematic position angles (PAs) for both the stellar and ionised gas line-of-sight velocity distributions. When compared to the photometric PA, we find that morpho-kinematic differences are smaller than 22 degrees in 90% of the sample for both components; internal kinematic misalignments are generally smaller than 16 degrees. We find a tight relation between the global stellar and ionised gas kinematic PA consistent with circular-flow pattern motions in both components. This relation also holds generally in barred galaxies across the bar and galaxy disk scales. Our findings suggest that even in the presence of strong bars, both the stellar and the gaseous components tend to follow the gravitational potential of the disk. As a result, kinematic orientation can be used to assess the degree of external distortions in interacting galaxies.

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arXiv2013

A characteristic oxygen abundance gradient in galaxy disks unveiled with CALIFA

We present the largest and most homogeneous catalog of HII regions and associations compiled so far. The catalog comprises more than 7000 ionized regions, extracted from 306 galaxies observed by the CALIFA survey. We describe the procedures used to detect, select, and analyse the spectroscopic properties of these ionized regions. In the current study we focus on the characterization of the radial gradient of the oxygen abundance in the ionized gas, based on the study of the deprojected distribution of HII regions. We found that all galaxies without clear evidence of an interaction present a common gradient in the oxygen abundance, with a characteristic slope of alpha = -0.1 dex/re between 0.3 and 2 disk effective radii, and a scatter compatible with random fluctuations around this value, when the gradient is normalized to the disk effective radius. The slope is independent of morphology, incidence of bars, absolute magnitude or mass. Only those galaxies with evidence of interactions and/or clear merging systems present a significant shallower gradient, consistent with previous results. The majority of the 94 galaxies with H ii regions detected beyond 2 disk effective radii present a flattening in the oxygen abundance. The flattening is statistically significant. We cannot provide with a conclusive answer regarding the origin of this flattening. However, our results indicate that its origin is most probably related to the secular evolution of galaxies. Finally, we find a drop/truncation of the oxygen abundance in the inner regions for 26 of the galaxies. All of them are non-interacting, mostly unbarred, Sb/Sbc galaxies. This feature is associated with a central star-forming ring, which suggests that both features are produced by radial gas flows induced by resonance processes.

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arXiv2013

The effects of spatial resolution on Integral Field Spectrograph surveys at different redshifts. The CALIFA perspective

Over the past decade, 3D optical spectroscopy has become the preferred tool for understanding the properties of galaxies and is now increasingly used to carry out galaxy surveys. Low redshift surveys include SAURON, DiskMass, ATLAS3D, PINGS and VENGA. At redshifts above 0.7, surveys such as MASSIV, SINS, GLACE, and IMAGES have targeted the most luminous galaxies to study mainly their kinematic properties. The on-going CALIFA survey ($z\sim0.02$) is the first of a series of upcoming Integral Field Spectroscopy (IFS) surveys with large samples representative of the entire population of galaxies. Others include SAMI and MaNGA at lower redshift and the upcoming KMOS surveys at higher redshift. Given the importance of spatial scales in IFS surveys, the study of the effects of spatial resolution on the recovered parameters becomes important. We explore the capability of the CALIFA survey and a hypothetical higher redshift survey to reproduce the properties of a sample of objects observed with better spatial resolution at lower redshift. Using a sample of PINGS galaxies, we simulate observations at different redshifts. We then study the behaviour of different parameters as the spatial resolution degrades with increasing redshift.

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arXiv2013

The star formation history of CALIFA galaxies: Radial structures

We study the radial structure of the stellar mass surface density ($μ$) and stellar population age as a function of the total stellar mass and morphology for a sample of 107 galaxies from the CALIFA survey. We use the fossil record to recover the star formation history (SFH) in spheroidal and disk dominated galaxies with masses from 10$^9$ to 10$^{12}$ M$_\odot$. We derive the half mass radius, and we find that galaxies are on average 15% more compact in mass than in light. HMR/HLR decreases with increasing mass for disk galaxies, but is almost constant in spheroidal galaxies. We find that the galaxy-averaged stellar population age, stellar extinction, and $μ$ are well represented by their values at 1 HLR. Negative radial gradients of the stellar population ages support an inside-out formation. The larger inner age gradients occur in the most massive disk galaxies that have the most prominent bulges; shallower age gradients are obtained in spheroids of similar mass. Disk and spheroidal galaxies show negative $μ$ gradients that steepen with stellar mass. In spheroidal galaxies $μ$ saturates at a critical value that is independent of the galaxy mass. Thus, all the massive spheroidal galaxies have similar local $μ$ at the same radius (in HLR units). The SFH of the regions beyond 1 HLR are well correlated with their local $μ$, and follow the same relation as the galaxy-averaged age and $μ$; suggesting that local stellar mass surface density preserves the SFH of disks. The SFH of bulges are, however, more fundamentally related to the total stellar mass, since the radial structure of the stellar age changes with galaxy mass even though all the spheroid dominated galaxies have similar radial structure in $μ$. Thus, galaxy mass is a more fundamental property in spheroidal systems while the local stellar mass surface density is more important in disks.

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arXiv2013

The O3N2 and N2 abundance indicators revisited: improved calibrations based on CALIFA and Te-based literature data

The use of IFS is since recently allowing to measure the emission line fluxes of an increasingly large number of star-forming galaxies both locally and at high redshift. The main goal of this study is to review the most widely used empirical oxygen calibrations, O3N2 and N2, by using new direct abundance measurements. We pay special attention to the expected uncertainty of these calibrations as a function of the index value or abundance derived and the presence of possible systematic offsets. This is possible thanks to the analysis of the most ambitious compilation of Te-based HII regions to date. This new dataset compiles the Te-based abundances of 603 HII regions extracted from the literature but also includes new measurements from the CALIFA survey. Besides providing new and improved empirical calibrations for the gas abundance, we also present here a comparison between our revisited calibrations with a total of 3423 additional CALIFA HII complexes with abundances derived using the ONS calibration by Pilyugin et al. (2010). The combined analysis of Te-based and ONS abundances allows us to derive their most accurate calibration to date for both the O3N2 and N2 single-ratio indicators, in terms of all statistical significance, quality and coverage of the space of parameters. In particular, we infer that these indicators show shallower abundance dependencies and statistically-significant offsets compared to those of Pettini and Pagel (2004), Nagao et al. (2006) and Pérez-Montero and Contini (2009). The O3N2 and N2 indicators can be empirically applied to derive oxygen abundances calibrations from either direct abundance determinations with random errors of 0.18 and 0.16, respectively, or from indirect ones (but based on a large amount of data) reaching an average precision of 0.08 and 0.09 dex (random) and 0.02 and 0.08 dex (systematic; compared to the direct estimations),respectively.

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arXiv2013

Resolving galaxies in time and space: II: Uncertainties in the spectral synthesis of datacubes

In a companion paper we have presented many products derived from the application of the spectral synthesis code STARLIGHT to datacubes from the CALIFA survey, including 2D maps of stellar population properties and 1D averages in the temporal and spatial dimensions. Here we evaluate the uncertainties in these products. Uncertainties due to noise and spectral shape calibration errors and to the synthesis method are investigated by means of a suite of simulations based on 1638 CALIFA spectra for NGC 2916, with perturbations amplitudes gauged in terms of the expected errors. A separate study was conducted to assess uncertainties related to the choice of evolutionary synthesis models. We compare results obtained with the Bruzual & Charlot models, a preliminary update of them, and a combination of spectra derived from the Granada and MILES models. About 100k CALIFA spectra are used in this comparison. Noise and shape-related errors at the level expected for CALIFA propagate to 0.10-0.15 dex uncertainties in stellar masses, mean ages and metallicities. Uncertainties in A_V increase from 0.06 mag in the case of random noise to 0.16 mag for shape errors. Higher order products such as SFHs are more uncertain, but still relatively stable. Due to the large number statistics of datacubes, spatial averaging reduces uncertainties while preserving information on the history and structure of stellar populations. Radial profiles of global properties, as well as SFHs averaged over different regions are much more stable than for individual spaxels. Uncertainties related to the choice of base models are larger than those associated with data and method. Differences in mean age, mass and metallicity are ~ 0.15 to 0.25 dex, and 0.1 mag in A_V. Spectral residuals are ~ 1% on average, but with systematic features of up to 4%. The origin of these features is discussed. (Abridged)

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arXiv2013

Resolving galaxies in time and space: I: Applying STARLIGHT to CALIFA data cubes

Fossil record methods based on spectral synthesis techniques have matured over the past decade, and their application to integrated galaxy spectra fostered substantial advances on the understanding of galaxies and their evolution. Yet, because of the lack of spatial resolution, these studies are limited to a global view, providing no information about the internal physics of galaxies. Motivated by the CALIFA survey, which is gathering Integral Field Spectroscopy over the full optical extent of 600 galaxies, we have developed an end-to-end pipeline which: (i) partitions the observed data cube into Voronoi zones in order to, when necessary and taking due account of correlated errors, increase the S/N, (ii) extracts spectra, including propagated errors and bad-pixel flags, (iii) feeds the spectra into the STARLIGHT spectral synthesis code, (iv) packs the results for all galaxy zones into a single file, (v) performs a series of post-processing operations, including zone-to-pixel image reconstruction and unpacking the spectral and stellar population properties into multi-dimensional time, metallicity, and spatial coordinates. This paper provides an illustrated description of this whole pipeline and its products. Using data for the nearby spiral NGC 2916 as a show case, we go through each of the steps involved, presenting ways of visualizing and analyzing this manifold. These include 2D maps of properties such as the v-field, stellar extinction, mean ages and metallicities, mass surface densities, star formation rates on different time scales and normalized in different ways, 1D averages in the temporal and spatial dimensions, projections of the stellar light and mass growth (x,y,t) cubes onto radius-age diagrams, etc. The results illustrate the richness of the combination of IFS data with spectral synthesis, providing a glimpse of what is to come from CALIFA and future surveys. (Abridged)

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arXiv2013

The Mass-Metallicity relation explored with CALIFA: I. Is there a dependence on the star formation rate?

We present the results on the study of the global and local M-Z relation based on the first data available from the CALIFA survey (150 galaxies). This survey provides integral field spectroscopy of the complete optical extent of each galaxy (up to 2-3 effective radii), with enough resolution to separate individual HII regions and/or aggregations. Nearly $\sim$3000 individual HII regions have been detected. The spectra cover the wavelength range between [OII]3727 and [SII]6731, with a sufficient signal-to-noise to derive the oxygen abundance and star-formation rate associated with each region. In addition, we have computed the integrated and spatially resolved stellar masses (and surface densities), based on SDSS photometric data. We explore the relations between the stellar mass, oxygen abundance and star-formation rate using this dataset. We derive a tight relation between the integrated stellar mass and the gas-phase abundance, with a dispersion smaller than the one already reported in the literature ($σ_{Δ{\rm log(O/H)}}=$0.07 dex). Indeed, this dispersion is only slightly larger than the typical error derived for our oxygen abundances. However, we do not find any secondary relation with the star-formation rate, other than the one induced due to the primary relation of this quantity with the stellar mass. We confirm the result using the $\sim$3000 individual HII regions, for the corresponding local relations. Our results agree with the scenario in which gas recycling in galaxies, both locally and globally, is much faster than other typical timescales, like that of gas accretion by inflow and/or metal loss due to outflows. In essence, late-type/disk dominated galaxies seem to be in a quasi-steady situation, with a behavior similar to the one expected from an instantaneous recycling/closed-box model.

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arXiv2013

Aperture corrections for disk galaxy properties derived from the CALIFA survey. Balmer emission lines in spiral galaxies

This work investigates the effect of the aperture size on derived galaxy properties for which we have spatially-resolved optical spectra. We focus on some indicators of star formation activity and dust attenuation for spiral galaxies that have been widely used in previous work on galaxy evolution. We have used 104 spiral galaxies from the CALIFA survey for which 2D spectroscopy with complete spatial coverage is available. From the 3D cubes we have derived growth curves of the most conspicuous Balmer emission lines (Halpha, Hbeta) for circular apertures of different radii centered at the galaxy's nucleus after removing the underlying stellar continuum. We find that the Halpha flux (f(Halpha)) growth curve follows a well defined sequence with aperture radius showing low dispersion around the median value. From this analysis, we derive aperture corrections for galaxies in different magnitude and redshift intervals. Once stellar absorption is properly accounted for, the f(Halpha)/f(Hbeta) ratio growth curve shows a smooth decline, pointing towards the absence of differential dust attenuation as a function of radius. Aperture corrections as a function of the radius are provided in the interval [0.3,2.5]R_50. Finally, the Halpha equivalent width (EW(Halpha)) growth curve increases with the size of the aperture and shows a very large dispersion for small apertures. This large dispersion prevents the use of reliable aperture corrections for this quantity. In addition, this result suggests that separating star-forming and quiescent galaxies based on observed EW(Halpha) through small apertures is likely to result in low EW(Halpha) star-forming galaxies begin classified as quiescent.

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arXiv2012

Integral field spectroscopy of a sample of nearby galaxies: II. Properties of the H ii regions

In this work we analyze the spectroscopic properties of a large number of H ii regions, \sim2600, located in 38 galaxies. The sample of galaxies has been assembled from the face-on spirals in the PINGS survey and a sample described in Mármol-Queraltó (2011, henceforth Paper I). All the galaxies were observed using Integral Field Spectroscopy with a similar setup, covering their optical extension up to \sim2.4 effective radii within a wavelength range from \sim3700 to \sim6900Å. We develop a new automatic procedure to detect H ii regions, based on the contrast of the Hα intensity maps. Once detected, the procedure provides us with the integrated spectra of each individual segmented region. A well-tested automatic decoupling procedure has been applied to remove the underlying stellar population, deriving the main proper- ties of the strongest emission lines in the considered wavelength range (covering from [O ii] λ3727 to [S ii] λ6731). A final catalogue of the spectroscopic properties of these regions has been created for each galaxy. In the current study we focused on the understanding of the average properties of the H ii regions and their radial distributions. We find that the gas-phase oxygen abundance and the Hα equivalent width present negative and positive gradient, respectively. The distribution of slopes is statistically compatible with a random Gaussian distribution around the mean value, if the radial distances are measured in units of the respective effective radius. No difference in the slope is found for galaxies of different morphologies: barred/non-barred, grand-design/flocculent. Therefore, the effective radius is a universal scale length for gradients in the evolution of galaxies. Other properties have a larger variance across each object.

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arXiv2011

CALIFA, the Calar Alto Legacy Integral Field Area survey: I. Survey presentation

We present here the Calar Alto Legacy Integral Field Area (CALIFA) survey, which has been designed to provide a first step in this direction.We summarize the survey goals and design, including sample selection and observational strategy.We also showcase the data taken during the first observing runs (June/July 2010) and outline the reduction pipeline, quality control schemes and general characteristics of the reduced data. This survey is obtaining spatially resolved spectroscopic information of a diameter selected sample of $\sim600$ galaxies in the Local Universe (0.005< z <0.03). CALIFA has been designed to allow the building of two-dimensional maps of the following quantities: (a) stellar populations: ages and metallicities; (b) ionized gas: distribution, excitation mechanism and chemical abundances; and (c) kinematic properties: both from stellar and ionized gas components. CALIFA uses the PPAK Integral Field Unit (IFU), with a hexagonal field-of-view of $\sim1.3\sq\arcmin'$, with a 100% covering factor by adopting a three-pointing dithering scheme. The optical wavelength range is covered from 3700 to 7000 Å, using two overlapping setups (V500 and V1200), with different resolutions: R\sim850 and R\sim1650, respectively. CALIFA is a legacy survey, intended for the community. The reduced data will be released, once the quality has been guaranteed. The analyzed data fulfill the expectations of the original observing proposal, on the basis of a set of quality checks and exploratory analysis. We conclude from this first look at the data that CALIFA will be an important resource for archaeological studies of galaxies in the Local Universe.

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arXiv2010

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.

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arXiv2009

Differential stellar population models: how to reliably measure [Fe/H] and [alpha/Fe] in galaxies

We present differential stellar population models, which allow improved determinations of the ages, iron and alpha-element abundances of old stellar populations from spectral fitting. These new models are calibrated at solar abundances using the predictions from classical, semi-empirical stellar population models. We then use the predictive power of fully synthetic models to compute predictions for different [Fe/H] and [alpha/Fe]. We show that these new differential models provide remarkably accurate fits to the integrated optical spectra of the bulge globular clusters NGC6528 and NGC6553, and that the inferred [Fe/H] and [alpha/Fe] agree with values derived elsewhere from stellar photometry and spectroscopy. The analysis of a small sample of SDSS early-type galaxies further confirms that our alpha-enhanced models provide a better fit to the spectra of massive ellipticals than the solar-scaled ones. Our approach opens new opportunities for precision measurements of abundance ratios in galaxies.

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arXiv2009

The Vimos VLT Deep Survey: Stellar mass segregation and large-scale galaxy environment in the redshift range 0.2<z<1.4

Hierarchical models of galaxy formation predict that the properties of a dark matter halo depend on the large-scale environment surrounding the halo. As a result of this correlation, we expect massive haloes to be present in larger number in overdense regions than in underdense ones. Given that a correlation exists between a galaxy stellar mass and the hosting dark matter halo mass, the segregation in dark matter halo mass should then result in a segregation in the distribution of stellar mass in the galaxy population. In this work we study the distribution of galaxy stellar mass and rest-frame optical color as a function of the large-scale galaxy distribution using the VLT VIMOS Deep Survey sample, in order to verify the presence of segregation in the properties of the galaxy population. We use the VVDS redshift measurements and multi-band photometric data to derive estimates of the stellar mass, rest-frame optical color, and of the large-scale galaxy density, on a scale of approximately 8 Mpc, for a sample of 5619 galaxies in the redshift range 0.2 0.7. However, when we consider only galaxies in narrow bins of stellar mass, in order to exclude the effects of the stellar mass segregation on the galaxy properties, we do not observe any more any significant color segregation.

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arXiv2008

Testing gravity on large scales. The skewness of the galaxy distribution at z~1

We study the evolution of the low-order moments of the galaxy overdensity distribution over the redshift interval 0.7<z<1.5. We find that the variance and the normalized skewness evolve over this redshift interval in a way that is remarkably consistent with predictions of first- and second-order perturbation theory. This finding confirms the standard gravitational instability paradigm over nearly 9 Gyrs of cosmic time and demonstrates the importance of accounting for the non-linear component of galaxy biasing to avoid disagreement between theory and observations.

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