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We have learnt in the last decades that the majority of galaxies belong to high density regions interconnected in a sponge-like fashion. This large-scale structure is characterised by clusters, filaments, walls, where most galaxies concentrate, but also under-dense regions, called voids. The void regions and the galaxies within represent an ideal place for the study of galaxy formation and evolution as they are largely unaffected by the complex physical processes that transform galaxies in high-density environments. These void galaxies can hold the key as well to answer current challenges to the $\Lambda$CDM paradigm. The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a Legacy project approved by the Calar Alto Observatory to obtain spatially resolved spectroscopic information of $\sim300$ void galaxies in the Local Universe (0.005 < z < 0.050) covering from -17.0 to -21.5 in $\rm r$ band absolute magnitude. It officially started in January 2021 and has been awarded 110 useful dark observing nights at the 3.5 m telescope using the PMAS spectrograph. Complementary follow-up projects including deep optical imaging, integrated, as well as resolved CO data, and integrated HI spectra, have joint the PMAS observations and naturally complete the scientific aim of characterising galaxies in cosmic voids. The extension data has been denominated CAVITY+. The data will be available to the whole community in different data releases, the first of which is planned for July 2024, and it will provide the community with PMAS data cubes for around 100 void galaxies through a user friendly, and well documented, database platform. We present here the survey, sample selection, data reduction, quality control schemes, science goals, and some examples of the scientific power of the CAVITY and CAVITY+ data., Comment: 19 pages, 11 figures. Accepted for publication in A&A - Replacement after A&A minor language edition

Galaxies in the Universe are distributed in a web-like structure characterised by different large-scale environments: dense clusters, elongated filaments, sheetlike walls, and under-dense regions, called voids. The low density in voids is expected to affect the properties of their galaxies. Indeed, previous studies have shown that galaxies in voids are on average bluer and less massive, and have later morphologies and higher current star formation rates than galaxies in denser large-scale environments. However, it has never been observationally proved that the star formation histories (SFHs) in void galaxies are substantially different from those in filaments, walls, and clusters. Here we show that void galaxies have had, on average, slower SFHs than galaxies in denser large-scale environments. We also find two main SFH types present in all the environments: 'short-timescale' galaxies are not affected by their large-scale environment at early times but only later in their lives; 'long-timescale' galaxies have been continuously affected by their environment and stellar mass. Both types have evolved slower in voids than in filaments, walls, and clusters., Comment: Published in Nature. 27 pages, 4 Figures, 7 Extended Data Figures, and 1 Extended Data Table

Context. The present study addresses a key question related to our understanding of the relation between void galaxies and their environment: the relationship between luminous and dark matter in and around voids. Aims. To explore the extent to which local Universe voids are empty of matter, we study the full (dark+luminous) matter content of seven nearby cosmic voids that are fully contained within the CosmicFlows-3 volume. Methods. We obtained the matter-density profiles of seven cosmic voids using two independent methods. These were built from the galaxy redshift space two-point correlation function in conjunction with peculiar velocity gradients from the CosmicFlows-3 dataset. Results. The results are striking, because when the redshift survey is used, all voids show a radial positive gradient of galaxies, while based on the dynamical analysis, only three of these voids display a clear underdensity of matter in their center. Conclusions. This work constitutes the most detailed observational analysis of voids conducted so far, and shows that void emptiness should be derived from dynamical information. From this limited study, the Hercules void appears to be the best candidate for a local Universe pure "pristine volume", expanding in three directions with no dark matter located in that void., Comment: Submitted A\&A Nov 29, 2022 - AA/2022/45578 / Accepted March 3rd, 2023

We present the first molecular gas mass survey of void galaxies. We compare these new data together with data for the atomic gas mass and star formation rate ($\rm SFR$) from the literature to those of galaxies in filaments and walls in order to better understand how molecular gas and star formation are related to the large-scale environment. We observed at the IRAM 30 m telescope the CO(1-0) and CO(2-1) emission of 20 void galaxies selected from the Void Galaxy Survey (VGS), with a stellar mass range from $\rm 10^{8.5}$ to $\rm 10^{10.3}M_{\odot}$. We detected 15 objects in at least one CO line. We compared the molecular gas mass ($M_{\rm H_2}$), the star formation efficiency ($\rm SFE =SFR/M_{\rm H_2}$), the atomic gas mass, the molecular-to-atomic gas mass ratio, and the specific star formation rate (sSFR) of the void galaxies with two control samples of galaxies in filaments and walls, selected from xCOLD GASS and EDGE-CALIFA, for different stellar mass bins and taking the star formation activity into account. The results for the molecular gas mass for a sample of 20 voids galaxies allowed us to make a statistical comparison to galaxies in filaments and walls for the first time., Comment: 24 pages, 15 figures, accepted in A&A, language corrected version

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics., Comment: 22 pages, 1 figure, to appear in General Relativity and Gravitation

We introduce the 4-metre Multi-Object Spectroscopic Telescope (4MOST), a new high-multiplex, wide-field spectroscopic survey facility under development for the four-metre-class Visible and Infrared Survey Telescope for Astronomy (VISTA) at Paranal. Its key specifications are: a large field of view (FoV) of 4.2 square degrees and a high multiplex capability, with 1624 fibres feeding two low-resolution spectrographs ($R = \lambda/\Delta\lambda \sim 6500$), and 812 fibres transferring light to the high-resolution spectrograph ($R \sim 20\,000$). After a description of the instrument and its expected performance, a short overview is given of its operational scheme and planned 4MOST Consortium science; these aspects are covered in more detail in other articles in this edition of The Messenger. Finally, the processes, schedules, and policies concerning the selection of ESO Community Surveys are presented, commencing with a singular opportunity to submit Letters of Intent for Public Surveys during the first five years of 4MOST operations., Comment: Part of the 4MOST issue of The Messenger, published in preparation of 4MOST Community Workshop, see http://www.eso.org/sci/meetings/2019/4MOST.html

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology. In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE is designed as a near-ultimate CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation scienceand cannot be obtained by any other means than a dedicated space mission., Comment: 79 pages, 14 figures

We examine the cosmological constraints that can be achieved with a galaxy cluster survey with the future CORE space mission. Using realistic simulations of the millimeter sky, produced with the latest version of the Planck Sky Model, we characterize the CORE cluster catalogues as a function of the main mission performance parameters. We pay particular attention to telescope size, key to improved angular resolution, and discuss the comparison and the complementarity of CORE with ambitious future ground-based CMB experiments that could be deployed in the next decade. A possible CORE mission concept with a 150 cm diameter primary mirror can detect of the order of 50,000 clusters through the thermal Sunyaev-Zeldovich effect (SZE). The total yield increases (decreases) by 25% when increasing (decreasing) the mirror diameter by 30 cm. The 150 cm telescope configuration will detect the most massive clusters ($>10^{14}\, M_\odot$) at redshift $z>1.5$ over the whole sky, although the exact number above this redshift is tied to the uncertain evolution of the cluster SZE flux-mass relation; assuming self-similar evolution, CORE will detect $\sim 500$ clusters at redshift $z>1.5$. This changes to 800 (200) when increasing (decreasing) the mirror size by 30 cm. CORE will be able to measure individual cluster halo masses through lensing of the cosmic microwave background anisotropies with a 1-$\sigma$ sensitivity of $4\times10^{14} M_\odot$, for a 120 cm aperture telescope, and $10^{14} M_\odot$ for a 180 cm one. [abridged], Comment: 35 pages, 15 figures, to be submitted to JCAP

We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE, that has been submitted in response to ESA's call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high-z galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high-z galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively., Comment: 40 pages, 9 figures, text expanded, co-authors added, to be submitted to JCAP

We analyze photometry from deep B-band images of 59 void galaxies in the Void Galaxy Survey (VGS), together with their near-infrared 3.6$\mu$m and 4.5$\mu$m Spitzer photometry. The VGS galaxies constitute a sample of void galaxies that were selected by a geometric-topological procedure from the SDSS DR7 data release, and which populate the deep interior of voids. Our void galaxies span a range of absolute B-magnitude from $\rm{M_B=-15.5}$ to $\rm{M_B=-20}$, while at the 3.6$\mu$m band their magnitudes range from $\rm{M_{3.6}=-18}$ to $\rm{M_{3.6}=-24}$. Their B-[3.6] colour and structural parameters indicate these are star forming galaxies. A good reflection of the old stellar population, the near-infrared band photometry also provide a robust estimate of the stellar mass, which for the VGS galaxies we confirm to be smaller than $3 \times 10^{10}$ M$_\odot$. In terms of the structural parameters and morphology, our findings align with other studies in that our VGS galaxy sample consists mostly of small late-type galaxies. Most of them are similar to Sd-Sm galaxies, although a few are irregularly shaped galaxies. The sample even includes two early-type galaxies, one of which is an AGN. Their S\'{e}rsic indices are nearly all smaller than $n=2$ in both bands and they also have small half-light radii. In all, we conclude that the principal impact of the void environment on the galaxies populating them mostly concerns their low stellar mass and small size., Comment: Accepted for publication in MNRAS, 16 pages, 11 figures

We study the star formation properties of 59 void galaxies as part of the Void Galaxy Survey (VGS). Current star formation rates are derived from $\rm{H\alpha}$ and recent star formation rates from near-UV imaging. In addition, infrared 3.4 $\rm{\mu m}$, 4.6 $\rm{\mu m}$, 12 $\rm{\mu m}$ and 22 $\rm{\mu m}$ WISE emission is used as star formation and mass indicator. Infrared and optical colours show that the VGS sample displays a wide range of dust and metallicity properties. We combine these measurements with stellar and HI masses to measure the specific SFRs ($\rm{SFR/M_{*}}$) and star formation efficiencies ($\rm{SFR/M_{HI}}$). We compare the star formation properties of our sample with galaxies in the more moderate density regions of the cosmic web, 'the field'. We find that specific SFRs of the VGS galaxies as a function of stellar and HI mass are similar to those of the galaxies in these field regions. Their $\rm{SFR\alpha}$ is slightly elevated than the galaxies in the field for a given total HI mass. In the global star formation picture presented by Kennicutt-Schmidt, VGS galaxies fall into the regime of low average star formation and correspondingly low HI surface density. Their mean $\rm{SFR\alpha/M_{HI}}$ and $\rm{SFR\alpha/M_{*}}$ are of the order of $\rm{10^{-9.9}}$ $\rm{yr^{-1}}$. We conclude that while the large scale underdense environment must play some role in galaxy formation and growth through accretion, we find that even with respect to other galaxies in the more mildly underdense regions, the increase in star formation rate is only marginal., Comment: 18 pages, 17 figures, accepted for publication in MNRAS

We present the structural and star formation properties of 59 void galaxies as part of the Void Galaxy Survey (VGS). Our aim is to study in detail the physical properties of these void galaxies and study the effect of the void environment on galaxy properties. We use Spitzer 3.6 $\rm{\mu m}$ and B-band imaging to study the morphology and color of the VGS galaxies. For their star formation properties, we use Halpha and GALEX near-UV imaging. We compare our results to a range of galaxies of different morphologies in higher density environments. We find that the VGS galaxies are in general disk dominated and star forming galaxies. Their star formation rates are, however, often less than 1 $\rm{M_{\odot}}$ $\rm{yr^{-1}}$. There are two early-type galaxies in our sample as well. In $\rm{r_{e}}$ versus $\rm{M_{B}}$ parameter space, VGS galaxies occupy the same space as dwarf irregulars and spirals., Comment: Conference proceeding

The current Lambda CDM cosmological model predicts that galaxy evolution proceeds more slowly in lower density environments, suggesting that voids are a prime location to search for relatively pristine galaxies that are representative of the building blocks of early massive galaxies. To test the assumption that void galaxies are more pristine, we compare the evolutionary properties of a sample of dwarf galaxies selected specifically to lie in voids with a sample of similar isolated dwarf galaxies in average density environments. We measure gas-phase oxygen abundances and gas fractions for eight dwarf galaxies (M_r > -16.2), carefully selected to reside within the lowest density environments of seven voids, and apply the same calibrations to existing samples of isolated dwarf galaxies. We find no significant difference between these void dwarf galaxies and the isolated dwarf galaxies, suggesting that dwarf galaxy chemical evolution proceeds independent of the large-scale environment. While this sample is too small to draw strong conclusions, it suggests that external gas accretion is playing a limited role in the chemical evolution of these systems, and that this evolution is instead dominated mainly by the internal secular processes that are linking the simultaneous growth and enrichment of these galaxies., Comment: 6 pages, 3 figures, accepted for publication in ApJ Letters

Cosmological voids provide a unique environment for the study of galaxy formation and evolution. The galaxy population in their interior have significantly different properties than average field galaxies. As part of our Void Galaxy Survey (VGS), we have found a system of three interacting galaxies (VGS_31) inside a large void. VGS_31 is a small elongated group whose members are embedded in a common HI envelope. The HI picture suggests a filamentary structure with accretion of intergalactic cold gas from the filament onto the galaxies. We present deep optical and narrow band H_alpha data, optical spectroscopy, near-UV and far-UV GALEX and CO(1-0) data. We find that one of the galaxies, a Markarian object, has a ring-like structure and a tail evident both in optical and HI. While all three galaxies form stars in their central parts, the tail and the ring of the Markarian object are devoid of star formation. We discuss these findings in terms of a gravitational interaction and ongoing growth of galaxies out of a filament. VGS_31 is one of the first observed examples of a filamentary structure in a void. It is an important prototype for understanding the formation of substructure in a void. This system also shows that the galaxy evolution in voids can be as dynamic as in high density environments., Comment: 17 pages, 8 figures, accepted for publication in AJ

We have carefully selected a sample of 60 galaxies that reside in the deepest underdensities of geometrically identified voids within the SDSS. HI imaging of 55 galaxies with the WSRT reveals morphological and kinematic signatures of ongoing interactions and gas accretion. We probe a total volume of 485 Mpc^3 within the voids, with an angular resolution of 8 kpc at an average distance of 85 Mpc. We reach column density sensitivities of 5 x 10^19 cm^-2, corresponding to an HI mass limit of 3 x 10^8 M_sun. We detect HI in 41 galaxies, with total masses ranging from 1.7 x 10^8 to 5.5 x 10^9 M_sun. The upper limits on the 14 non-detections are not inconsistent with their luminosities, given their expected HI mass to light ratios. We find that the void galaxies are generally gas rich, low luminosity, blue disk galaxies, with optical and HI properties that are not unusual for their luminosity and morphology. The sample spans a range of absolute magnitudes (-16.1 > M_r > -20.4) and colors (0.06 < g-r < 0.87), and includes disk and irregular galaxies. We also identify three as early type galaxies, all of which are not detected in HI. All galaxies have stellar masses less than 3 x 10^10 M_sun, and many have kinematic and morphological signs of ongoing gas accretion, suggesting that the void galaxy population is still in the process of assembling. The small scale clustering in the void, within 600 kpc and 200 km/s, is similar to that in higher density regions, and we identify 18 HI rich neighboring galaxies in the voids. Most are within 100 kpc and 100 km/s of the targeted galaxy, and we find no significant population of HI rich low luminosity galaxies filling the voids, contrary to what is predicted by simulations., Comment: 34 pages, 33 figures (including Atlas in Appendix), accepted for publication in AJ

We have found that KK 246, the only confirmed galaxy located within the nearby Tully Void, is a dwarf galaxy with an extremely extended H I disk and signs of an H I cloud with anomalous velocity. It also exhibits clear misalignment between the kinematical major and minor axes, indicative of an oval distortion, and a general misalignment between the H I and optical major axes. We measure a H I mass of 1.05 +- 0.08 x 10^8 M_sun, and a H I extent 5 times that of the stellar disk, one of the most extended H I disks known. We estimate a dynamical mass of 4.1 x 10^9 M_sun, making this also one of the darkest galaxies known, with a mass-to-light ratio of 89. The relative isolation and extreme underdense environment make this an interesting case for examining the role of gas accretion in galaxy evolution., Comment: 15 pages, 8 figures, 2 tables, accepted for publication in AJ

The Void Galaxy Survey (VGS) is a multi-wavelength program to study $\sim$60 void galaxies. Each has been selected from the deepest interior regions of identified voids in the SDSS redshift survey on the basis of a unique geometric technique, with no a prior selection of intrinsic properties of the void galaxies. The project intends to study in detail the gas content, star formation history and stellar content, as well as kinematics and dynamics of void galaxies and their companions in a broad sample of void environments. It involves the HI imaging of the gas distribution in each of the VGS galaxies. Amongst its most tantalizing findings is the possible evidence for cold gas accretion in some of the most interesting objects, amongst which are a polar ring galaxy and a filamentary configuration of void galaxies. Here we shortly describe the scope of the VGS and the results of the full analysis of the pilot sample of 15 void galaxies., Comment: 9 pages, 6 figures. This is an extended version of a paper to appear in "Environment and the Formation of Galaxies: 30 years later", Proceedings of Symposium 2 of JENAM 2010, eds. I. Ferreras, A. Pasquali, ASSP, Springer. Version with highres figures at http://www.astro.rug.nl/~weygaert/vgs_jenam_weygaert.col.pdf

Void galaxies, residing within the deepest underdensities of the Cosmic Web, present an ideal population for the study of galaxy formation and evolution in an environment undisturbed by the complex processes modifying galaxies in clusters and groups, as well as provide an observational test for theories of cosmological structure formation. We have completed a pilot survey for the HI imaging aspects of a new Void Galaxy Survey (VGS), imaging 15 void galaxies in HI in local (d < 100 Mpc) voids. HI masses range from 3.5 x 10^8 to 3.8 x 10^9 M_sun, with one nondetection with an upper limit of 2.1 x 10^8 M_sun. Our galaxies were selected using a structural and geometric technique to produce a sample that is purely environmentally selected and uniformly represents the void galaxy population. In addition, we use a powerful new backend of the Westerbork Synthesis Radio Telescope that allows us to probe a large volume around each targeted galaxy, simultaneously providing an environmentally constrained sample of fore- and background control sample of galaxies while still resolving individual galaxy kinematics and detecting faint companions in HI. This small sample makes up a surprisingly interesting collection of perturbed and interacting galaxies, all with small stellar disks. Four galaxies have significantly perturbed HI disks, five have previously unidentified companions at distances ranging from 50 to 200 kpc, two are in interacting systems, and one was found to have a polar HI disk. Our initial findings suggest void galaxies are a gas-rich, dynamic population which present evidence of ongoing gas accretion, major and minor interactions, and filamentary alignment despite the surrounding underdense environment., Comment: 53 pages, 18 figures, accepted for publication in AJ. High resolution available at http://www.astro.columbia.edu/~keejo/kreckel2010.pdf

We present a framework for the hierarchical identification and characterization of voids based on the Watershed Void Finder. The Hierarchical Void Finder is based on a generalization of the scale space of a density field invoked in order to trace the hierarchical nature and structure of cosmological voids. At each level of the hierarchy, the watershed transform is used to identify the voids at that particular scale. By identifying the overlapping regions between watershed basins in adjacent levels, the hierarchical void tree is constructed. Applications on a hierarchical Voronoi model and on a set of cosmological simulations illustrate its potential., Comment: 5 pages, 2 figures

We have completed a pilot survey imaging 15 SDSS selected void galaxies in HI in local (d=50 to 100 Mpc) voids. This small sample makes up a surprisingly interesting collection of galaxies, consisting of galaxies with asymmetric and perturbed HI disks, previously unidentified companions, and ongoing interactions. One was found to have a polar HI disk with no stellar counterpart. While our small number statistics so far are limiting, results support past findings that most void galaxies are typically late type galaxies with gas rich disks and small scale clustering similar to field galaxies despite their large scale underdense environment., Comment: 4 pages, to be published in the proceedings of the conference "Galaxies in Isolation" (12-15 May 2009; Granada, Spain)

We have found an isolated polar disk galaxy in what appears to be a cosmological wall situated between two voids. This void galaxy is unique as its polar disk was discovered serendipitously in an HI survey of SDSS void galaxies, with no optical counterpart to the HI polar disk. Yet the HI mass in the disk is comparable to the stellar mass in the galaxy. This suggests slow accretion of the HI material at a relatively recent time. There is also a hint of a warp in the outer parts of the HI disk. The central, stellar disk appears relatively blue, with faint near UV emission, and is oriented (roughly) parallel to the surrounding wall, implying gas accretion from out of the voids. The considerable gas mass and apparent lack of stars in the polar disk, coupled with the general underdensity of the environment, supports recent theories of cold flow accretion as an alternate formation mechanism for polar disk galaxies., Comment: 5 pages, 5 figures, accepted for publication in ApJ Letters

We study the clustering properties of the recently compiled HIPASS neutral hydrogen (HI) sources catalogue using the two point correlation function in redshift space. If the two point correlation is modelled as a power law, $\xi(r)=(r_{0}/r)^{\gamma}$, then the best-fitting parameters for the HI selected galaxies are $r_{0}=4.3 \pm 0.3 h^{-1}$ Mpc with $\gamma=1.42 \pm 0.14$. Fixing the slope to its universal value $\gamma=1.8$, we obtain $r_{0}= 4.1^{+0.2}_{-0.3} h^{-1}$ Mpc. Comparing the measured two point correlation function with the predictions of the concordance cosmological model, we find that at the present epoch the HI selected galaxies are anti-biased with respect to the underline matter fluctuation field with bias value being $b_{0}\simeq 0.63$. Also, we investigate the evolution of the linear bias factor, $b(z)$, and we find to be a strongly dependent function of redshift. Finally, we estimate the HI selected galaxies redshift space distortion parameter $\beta \simeq \Omega_{\rm m}^{0.6}/b_{0}$ in order to correct the correlation function for the peculiar motions and we find $\beta\simeq 0.77$. Taking into account the corrections for the redshift space distortions the HI correlation length in real space is $r^{\rm re}_{0}=3^{+0.4}_{-0.3}h^{-1}$Mpc for $\gamma=1.42$ while using $\gamma=1.8$ we get $r^{\rm re}_{0}= 3.1 \pm 0.3 h^{-1}$Mpc., Comment: The definitive version of this manuscript will be submitted in a few weeks time after the authors have fixed a few omissions

We present the results of a study confronting density maps reconstructed by the Delaunay Tessellation Field Estimator (DTFE) and by regular SPH kernel-based techniques. The comparison between the two methods clearly demonstrates the superior performance of the DTFE with respect to conventional SPH methods, in particular at locations where SPH appears to fail. The DTFE is a fully self-adaptive technique for reconstructing continuous density fields from discrete particle distributions, and is based upon the corresponding Delaunay tessellation. Its principal asset is its complete independence of arbitrary smoothing functions and parameters specifying the properties of these. As a result it manages to faithfully reproduce the anisotropies of the local particle distribution and through its adaptive and local nature proves to be optimally suited for uncovering the full structural richness in the density distribution. Through the improvement in local density estimates, calculations invoking the DTFE will yield a much better representation of physical processes which depend on density. The presented results form an encouraging step towards the application and insertion of the DTFE in astrophysical hydrocodes. We describe an outline for the construction of a particle hydrodynamics code in which the DTFE replaces kernel-based methods. Further discussion addresses the issue and possibilities for a moving grid based hydrocode invoking the DTFE, and Delaunay tessellations, in an attempt to combine the virtues of the Eulerian and Lagrangian approaches., Comment: 11 pages, 2 figures, accepted for publication in A&A, author info corrected (email addresses added)

We assess the extent to which the flux-limited PSCz redshift sample is capable of accounting for the major share of mass concentrations inducing the external tidal forces affecting the peculiar velocities within the Local Supercluster (LS). The investigation is based upon a comparison of the ``true'' velocities in 2 large N-body simulations and their reconstruction from ``observation-mimicking'' mock catalogues. The mildly nonlinear ``mock'' LS and PSCz velocities are analyzed by means of the Least Action Principle technique in its highly optimized implementation of Nusser & Branchini's Fast Action Method (FAM). For both model N-body Universes, we conclude that the dipolar and quadrupolar force field implied by the PSCz galaxy distribution would indeed be sufficiently representing the full external tidal force field., Comment: 2 pages, 1 figure, contribution to ``Where's the Matter? Tracing Dark and Bright Matter with the New Generation of Large Scale Surveys'', June 2001, Treyer & Tresse Eds, Frontier Group

Optimally resolved one-dimensional density and velocity profiles through cosmological N-body simulations are constructed by means of the Voronoi-Delaunay tessellation reconstruction technique. In a fully self-adaptive fashion a strikingly detailed view of the density features and the corresponding cosmic motions is recovered., Comment: 2 pages, 1 figure, contribution to ``Statistical Challenges in Modern Astronomy III'', Eds. G.J. Babu & E.D. Feigelson, 2002, Springer-Verlag

Astronomical observations, physical experiments as well as computer simulations often involve discrete data sets supposed to represent a fair sample of an underlying smooth and continuous field. Reconstructing the underlying fields from a set of irregularly sampled data is therefore a recurring key issue in operations on astronomical data sets. Conventional methods involve artificial filtering through a grid or a smoothing kernel and fail to achieve an optimal result. Here we describe a fully self-adaptive geometric method which does not make use of artificial filtering, and which makes optimal use of the available information., Comment: 2 pages, 2 figures, contribution to ``Where's the Matter? Tracing Dark and Bright Matter with the New Generation of Large Scale Surveys'', Eds. Treyer & Tresse, 2001, Frontier Group

Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields from a set of irregularly sampled data is a recurring key issue in operations on astronomical data sets, both in an observational context as well as in the context of numerical simulations. Our technique is based upon the stochastic geometric concept of the Delaunay tessellation generated by the point set. We shortly describe the method, and illustrate its virtues by means of an application to an N-body simulation of cosmic structure formation. The presented technique is a fully adaptive method: automatically it probes high density regions at maximum possible resolution, while low density regions are recovered as moderately varying regions devoid of the often irritating shot-noise effects. Of equal importance is its capability to sharply and undilutedly recover anisotropic density features like filaments and walls. The prominence of such features at a range of resolution levels within a hierarchical clustering scenario as the example of the standard CDM scenario is shown to be impressively recovered by our scheme., Comment: 4 pages, 2 figures, accepted for publication in Astronomy & Astrophysics Letters

Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter Omega in the quasi-linear regime. This dependence is particularly interesting as it does not involve the possible bias between the galaxy spatial distribution and the underlying mass distribution. This implies a new and promising method for determining a bias-independent value of Omega based on a reliable determination of the velocity divergence PDF. In this paper we study the Omega dependence of the velocity divergence PDF and its first moments in a set of N-body simulations, using the so-called Voronoi and Delaunay methods. We show that this dependence is in agreement with the theoretical prediction, even while the number density of velocity field tracers has been diluted to a value comparable to that available in current galaxy catalogues. In addition, we demonstrate that a sufficiently reliable determination of these statistical quantities is also possible when the measurement of the galaxy peculiar velocities is restricted to the one component along the line-of-sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Omega., Comment: 12 pages, LaTex file, 5 figures. Revised version with significant extensions of the numerical studies, accepted for publication in MNRAS