arXiv subjects

M. A. Dopita

Publications and source records attributed to M. A. Dopita.

At least 19 recordsLinked to original sources

arXiv2019

IFU spectroscopy of Southern PNe: VII Photo-ionization modelling of intermediate excitation class objects

We present integral field unit spectroscopic observations of southern Galactic planetary nebulae (PNe), IC 2501, Hen 2-7, and PB4. The goal of studying these objects together is that, although they have roughly similar intermediate excitation and evolution of central stars (CSs), they display very different evolution in their nebular structure which needs to be understood. The morphologies and ionisation structures of the objects are investigated using a set of emission-line maps representative of the different ionisation zones. We use those in order to construct two-zone self-consistent photoionisation models for each nebula to determine new model-dependent distances, progenitor luminosities, effective temperatures and CS masses. The physical conditions, chemical compositions, and expansion velocities and ages of these nebulae are derived. In Hen 2-7 we discover a strong poleward-directed jet from the presumed binary CS. Oxygen and nitrogen abundances derived from both collisionally excited and recombination lines reveal that PB4 displays an extreme abundance discrepancy factor, and we present evidence that this is caused by uorescent pumping of the OII ion by the EUV continuum of an interacting binary CS, rather than by recombination of the OIII ion. Both IC 2501 and PB4 were classified by others as Weak Emission Line Stars (WELS). However, our emission line maps show that their recombination lines are spatially extended in both objects, and are therefore of nebular rather than CS origin. Given that we have found this result in a number of other PNe, this result casts further doubt on the reliability, or even the reality, of the WELS classification.

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arXiv2019

Identification of the Central Compact Object in the young supernova remnant 1E0102.2-7219

Oxygen-rich young supernova remnants are valuable objects for probing the outcome of nucleosynthetic processes in massive stars, as well as the physics of supernova explosions. Observed within a few thousand years after the supernova explosion, these systems contain fast-moving oxygen-rich and hydrogen-poor filaments visible at optical wavelengths: fragments of the progenitor's interior expelled at a few 1000 km/s during the supernova explosion. Here we report the first identification of the compact object in 1E0102.2-7219 in reprocessed Chandra X-ray Observatory data, enabled via the discovery of a ring-shaped structure visible primarily in optical recombination lines of Ne I and O I. The optical ring, discovered in integral field spectroscopy observations from the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope, has a radius of $(2.10\pm0.35)$ arcsec = $(0.63\pm0.11)$ pc, and is expanding at a velocity of $90.5_{-30}^{+40}$ km/s. It surrounds an X-ray point source with an intrinsic X-ray luminosity $L_{i}$ (1.2--2.0 keV)= $(1.4\pm0.2)\times10^{33}$ erg/s. The energy distribution of the source indicates that this object is an isolated neutron star: a Central Compact Object akin to those present in the Cas A and Puppis A supernova remnants, and the first of its kind to be identified outside of our Galaxy.

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arXiv2018

Near-identical star formation rate densities from H$α$ and FUV at redshift zero

For the first time both H$α$ and far-ultraviolet (FUV) observations from an HI-selected sample are used to determine the dust-corrected star formation rate density (SFRD: $\dotρ$) in the local Universe. Applying the two star formation rate indicators on 294 local galaxies we determine log($\dotρ$$ _{Hα}) = -1.68~^{+0.13}_{-0.05}$ [M$_{\odot} $ yr$^{-1} $ Mpc$^{-3}]$ and log($\dotρ_{FUV}$) $ = -1.71~^{+0.12}_{-0.13}$ [M$_\odot $ yr$^{-1} $ Mpc$^{-3}]$. These values are derived from scaling H$α$ and FUV observations to the HI mass function. Galaxies were selected to uniformly sample the full HI mass (M$_{HI}$) range of the HI Parkes All-Sky Survey (M$_{HI} \sim10^{7}$ to $\sim10^{10.7}$ M$_{\odot}$). The approach leads to relatively larger sampling of dwarf galaxies compared to optically-selected surveys. The low HI mass, low luminosity and low surface brightness galaxy populations have, on average, lower H$α$/FUV flux ratios than the remaining galaxy populations, consistent with the earlier results of Meurer. The near-identical H$α$- and FUV-derived SFRD values arise with the low H$α$/FUV flux ratios of some galaxies being offset by enhanced H$α$ from the brightest and high mass galaxy populations. Our findings confirm the necessity to fully sample the HI mass range for a complete census of local star formation to include lower stellar mass galaxies which dominate the local Universe.

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arXiv2017

IFU spectroscopy of southern PN VI: The extraordinary chemo-dynamics of Hen 2-111

In this paper we present integral field spectroscopy of the extraordinary Type I bipolar planetary nebula Hen 2-111. In the lobes we map fast moving knots of material with [N II]$λ6584$/H$α$ ratios up to 12, and with radial velocities relative to systemic from -340 km/s up to +390 km/s. We find evidence of a bipolar ejection event at a velocity $\sim 600$ km/s from the central star (assumed to be a binary), which occurred about 8000yr ago. The fast moving material is chemically quite distinct from the lower velocity gas in the bipolar lobes., and displays very high N abundances. We show that the fast moving N-rich knots are not photoionised by the central star, and have constructed detailed shock models for the brightest knot. We find a pre-shock density $\sim 6$cm$^{-3}$, and a shock velocity $\sim150$ km/s. The shock is not fully radiative, being only $\sim 600$yr old. This shocked gas is partially H-burnt, with a helium abundance by mass exceeding that of hydrogen, and is interacting with partially H-burnt material ejected in an earlier episode of mass loss. We conclude that the high-velocity material and the bipolar shell must have originated during the late stages of evolution of a common-envelope phase in a close binary system.

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arXiv2017

Spatially-resolved spectroscopy of narrow-line Seyfert 1 host galaxies

We present optical integral field spectroscopy for five $z<0.062$ narrow-line Seyfert 1 galaxies (NLS1s) host galaxies, probing their host galaxies at $\gtrsim 2-3$ kpc scales. Emission lines in the nuclear AGN spectra and the large-scale host galaxy are analyzed separately, based on an AGN-host decomposition technique. The host galaxy gas kinematics indicates large-scale gas rotation in all five sources. At the probed scales of $\gtrsim 2-3$ kpc, the host galaxy gas is found to be predominantly ionized by star formation without any evidence of a strong AGN contribution. None of the five objects shows specific star formation rates exceeding the main sequence of low-redshift star forming galaxies. The specific star formation rates for MCG-05-01-013 and WPVS 007 are roughly consistent with the main sequence, while ESO 399-IG20, MS 22549-3712, and TON S180 show lower specific star formation rates, intermediate to the main sequence and red quiescent galaxies. The host galaxy metallicities, derived for the two sources with sufficient data quality (ESO 399-IG20 and MCG-05-01-013), indicate central oxygen abundances just below the low-redshift mass-metallicity relation. Based on this initial case study, we outline a comparison of AGN and host galaxy parameters as a starting point for future extended NLS1 studies with similar methods.

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arXiv2017

IFU spectroscopy of Southern Planetary Nebulae V: Low-ionization structures

In this 5th paper of the series, we examine the spectroscopy and morphology of four southern Galactic planetary nebulae Hen 2-141, NGC5307, IC 2553, and PB6 using new integral field spectroscopy data. The morphologies and ionization structures of the sample are given as a set of emission-line maps. In addition, the physical conditions, chemical compositions, and kinematical characteristics of these objects are derived. The results show that PB6 and Hen 2-141 are of very high excitation classes and IC 2553 and NGC5307 are mid to high excitation objects. The elemental abundances reveal that PB6 is of Type I, Hen 2-141 and IC 2553 are of Type IIa, and NGC5307 of Type IIb/III. The observations unveil the presence of well- defined low-ionization structures or \knots" in all objects. The diagnostic diagrams reveal that the excitation mechanism of these knots is probably by photo-ionization of dense material by the nebular central stars. The physical analysis of six of these knots show no significant differences with their surrounding nebular gas, except their lower electron densities. In spite of the enhancement of the low-ionization emission lines of these knots, their chemical abundances are nearly comparable to their surrounding nebulae, with the exception of perhaps slightly higher nitrogen abundances in the NGC5307 knots. The integrated spectrum of IC 2553 reveals that nearly all key lines that have led researchers to characterize its central star as a weak-emission line star type are in fact of nebular origin.

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arXiv2017

[Fe XIV] and [Fe XI] reveal the forward shock in SNR 1E0102.2-7219

Aims. We study the forward shock in the oxygen-rich young supernova remnant (SNR) 1E0102.2-7219 (1E0102 in short) via optical coronal emission from [Fe XIV] and [Fe XI]: emission lines which offer an alternative method to X-rays to do so. Methods. We have used the Multi-Unit Spectroscopic Explorer (MUSE) optical integral field spectrograph at the Very Large Telescope (VLT) on Cerro Paranal to obtain deep observations of SNR 1E0102 in the Small Magellanic Cloud. Our observations cover the entire extent of the remnant with a seeing limited spatial resolution of 0.7" = 0.2 pc at the distance of 1E 0102. Results. Our MUSE observations unambiguously reveal the presence of [Fe XIV] and [Fe XI] emission in 1E0102. The emission largely arises from a thin, partial ring of filaments surrounding the fast moving O-rich ejecta in the system. The brightest [Fe XIV] and [Fe XI] emission is found along the eastern and north-western sides of 1E0102, where shocks are driven into denser ISM material, while fainter emission along the northern edge reveals the location of the forward shock in lower density gas, possibly the relic stellar wind cavity. Modeling of the eastern shocks and the photoionization precursor surrounding 1E0102, we derive a pre-shock density $n_H$ = (7.4 +-1.5) cm$^{-3}$, and a shock velocity 330 km/s < $v_s$ < 350 km/s.

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arXiv2017

IFU spectroscopy of Southern Planetary Nebulae IV: A Physical Model for IC 418

We describe high spectral resolution, high dynamic range integral field spectroscopy of IC418 covering the spectral range 3300-8950Å and compare with earlier data. We determine line fluxes, derive chemical abundances, provide a spectrum of the central star, and determine the shape of the nebular continuum. Using photoionisation models, we derive the reddening function from the nebular continuum and recombination lines. The nebula has a very high inner ionisation parameter. Consequently, radiation pressure dominates the gas pressure and dust absorbs a large fraction of ionising photons. Radiation pressure induces increasing density with radius. From a photoionisation analysis we derive central star parameters; $\log T_{\mathrm eff} = 4.525$K, $\log L_*/L_{\odot} = 4.029$, $\log g = 3.5$ and using stellar evolutionary models we estimate an initial mass of $2.5 < M/M_{\odot} < 3.0$. The inner filamentary shell is shocked by the rapidly increasing stellar wind ram pressure, and we model this as an externally photoionised shock. In addition, a shock is driven into the pre-existing Asymptotic Giant Branch stellar wind by the strong D-Type ionisation front developed at the outer boundary of the nebula. From the dynamics of the inner mass-loss bubble, and from stellar evolutionary models we infer that the nebula became ionised in the last $100-200$\,yr, but evolved structurally during the $\sim 2000$ yr since the central star evolved off the AGB. The estimated current mass loss rate ($\dot M = 3.8\times 10^{-8} M_{\odot}$yr$^{-1}$) and terminal velocity ($v_{\infty} \sim 450$ km/s) is sufficient to excite the inner mass-loss bubble. While on the AGB, the central star lost mass at $\dot M = 2.1\times 10^{-5} M_{\odot}$yr$^{-1}$ with outflow velocity $\sim 14$ km/s.

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arXiv2017

Evidence for azimuthal variations of the oxygen abundance gradient tracing the spiral structure of the galaxy HCG91c

Context. The distribution of elements in galaxies forms an important diagnostic tool to characterize the system's formation and evolution. This tool is however complex to use in practice, as galaxies are subject to a range of simultaneous physical processes active from pc to kpc scales. This renders observations of the full optical extent of galaxies down to sub-kpc scales essential. Aims. Using the WiFeS integral field spectrograph, we previously detected abrupt and localized variations in the gas-phase oxygen abundance of the spiral galaxy HCG91c. Here, we follow-up on these observations to map HCG91c's disk out to ~2Re at a resolution of 600pc, and characterize the non-radial variations of the gas-phase oxygen abundance in the system. Methods. We obtained deep MUSE observations of the target under ~0.6 arcsec seeing conditions. We perform both a spaxel-based and aperture-based analysis of the data to map the spatial variations of 12+log(O/H) across the disk of the galaxy. Results. We confirm the presence of rapid variations of the oxygen abundance across the entire extent of the galaxy previously detected with WiFeS, for all azimuths and radii. The variations can be separated in two categories: a) localized and associated with individual HII regions, and b) extended over kpc scales, and occurring at the boundaries of the spiral structures in the galaxy. Conclusions. Our MUSE observations suggest that the enrichment of the interstellar medium in HGC91c has proceeded preferentially along spiral structures, and less efficiently across them. Our dataset highlights the importance of distinguishing individual star-forming regions down to scales of a few 100pc when using integral field spectrographs to spatially resolve the distribution of oxygen abundances in a given system, and accurately characterize azimuthal variations and intrinsic scatter.

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arXiv2016

Linking the X3D pathway to integral field spectrographs: YSNR 1E0102.2-7219 in the SMC as a case study

The concept of the X3D pathway was introduced by Vogt et al. (2016) as a new approach to sharing and publishing 3-D structures interactively in online scientific journals. The core characteristics of the X3D pathway are that: 1) it does not rely on specific software, but rather a file format (X3D), 2) it can be implemented using fully open-source tools, and 3) article readers can access the interactive models using most main stream web browsers without the need for any additional plugins. In this article, we further demonstrate the potential of the X3D pathway to visualize datasets from optical integral field spectrographs. We use recent observations of the oxygen-rich young supernova remnant 1E0102.2-7219 in the Small Magellanic Cloud to implement additional X3DOM tools & techniques and expand the range of interactions that can be offered to article readers. In particular, we present a set of javascript functions allowing the creation and interactive handling of clip planes, effectively allowing users to take measurements of distances and angles directly from the interactive model itself.

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arXiv2016

IFU spectroscopy of southern PNe: III

In this paper we describe integral field spectroscopic observations of four southern Galactic Planetary Nebulae (PNe), M3-4, M3-6, Hen2-29 and Hen2-37 covering the spectral range, 3400-7000 A. We derive the ionisation structure, the physical conditions, the chemical compositions and the kinematical characteristics of these PNe and find good agreement with previous studies that relied upon the long-slit technique in their co-spatial area. From their chemical compositions as well as their spatial and kinematic characteristics, we determined that Hen2-29 is of the Peimbert Type I (He and N rich), while the other three are of Type II. The strength of the nebular He II line reveals that M3-3, Hen2-29 and Hen2-37 are of mid to high excitation classes while M3-6 is a low excitation planetary nebula (PN). A series of emission-line maps extracted from the data cubes were constructed for each PN to describe its overall structure. These show remarkable morphological diversity. Spatially resolved spectroscopy of M3-6, shows that the recombination lines of CII, CIII, CIV and NIII are of nebular origin, rather than arising from the central star as had been previously proposed. This result increases doubts regarding the weak emission-line star (WELS) classification raised by Basurah et al. (2016). In addition, they reinforce the probability that most genuine cases of WELS are arise from irradiation effects in close binary central stars (Miszalski 2009).

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arXiv2016

Shapley Supercluster Survey: Ram-Pressure Stripping vs. Tidal Interactions in the Shapley Supercluster

We present two new examples of galaxies undergoing transformation in the Shapley supercluster core. These low-mass (stellar mass from 0.4E10 to 1E10 Msun) galaxies are members of the two clusters SC-1329-313 (z=0.045) and SC-1327-312 (z=0.049). Integral-field spectroscopy complemented by imaging in ugriK bands and in Halpha narrow-band are used to disentangle the effects of tidal interaction (TI) and ram-pressure stripping (RPS). In both galaxies, SOS-61086 and SOS-90630, we observe one-sided extraplanar ionized gas extending respectively 30kpc and 41kpc in projection from their disks. The galaxies' gaseous disks are truncated and the kinematics of the stellar and gas components are decoupled, supporting the RPS scenario. The emission of the ionized gas extends in the direction of a possible companion for both galaxies suggesting a TI. The overall gas velocity field of SOS-61086 is reproduced by ad hoc N-body/hydrodynamical simulations of RPS acting almost face-on and starting about 250Myr ago, consistent with the age of the young stellar populations. A link between the observed gas stripping and the cluster-cluster interaction experienced by SC-1329-313 and A3562 is suggested. Simulations of ram pressure acting almost edge-on are able to fully reproduce the gas velocity field of SOS-90630, but cannot at the same time reproduce the extended tail of outflowing gas. This suggests that an additional disturbance from a TI is required. This study adds a piece of evidence that RPS may take place in different environments with different impacts and witnesses the possible effect of cluster-cluster merger on RPS.

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arXiv2015

Star Formation Suppression in Compact Group Galaxies: A New Path to Quenching?

We present CO(1-0) maps of 12 warm H$_2$-selected Hickson Compact Groups (HCGs), covering 14 individually imaged warm H$_2$ bright galaxies, with CARMA. We found a variety of molecular gas distributions within the HCGs, including regularly rotating disks, bars, rings, tidal tails, and possibly nuclear outflows, though the molecular gas morphologies are more consistent with spirals and early-type galaxies than mergers and interacting systems. Our CO-imaged HCG galaxies show star formation suppression of $\langle$S$\rangle$=10$\pm$5, distributed bimodally, with five objects exhibiting suppressions of S$\gtrsim$10 and depletion timescales $\gtrsim$10Gyr. This star formation inefficiency is also seen in the efficiency per freefall time. We investigate the gas-to-dust ratios of these galaxies to determine if an incorrect conversion caused the apparent suppression and find that HCGs have normal ratios. It is likely that the cause of the suppression in these objects is associated with shocks injecting turbulence into the molecular gas. Galaxies with high star formation suppression (S$\gtrsim$10) also appear to be those in the most advanced stages of transition across optical and infrared color space. This supports the idea that some galaxies in HCGs are transitioning objects, where a disruption of the existing molecular gas in the system suppresses star formation by inhibiting the molecular gas from collapsing and forming stars efficiently. These observations, combined with recent work on poststarburst galaxies with molecular reservoirs, indicates that galaxies do not need to expel their molecular reservoirs prior to quenching star formation and transitioning from blue spirals to red early-type galaxies. This may imply that star formation quenching can occur without the need to starve a galaxy of cold gas first.

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arXiv2015

Galaxy Mergers Drive Shocks: an Integral Field Study of GOALS galaxies

We present an integral field spectroscopic study of radiative shocks in 27 nearby ultraluminous and luminous infrared galaxies (U/LIRGs) from the Great Observatory All-sky LIRG Survey, a subset of the Revised Bright Galaxy Sample. Our analysis of the resolved spectroscopic data from the Wide Field Spectrograph (WiFeS) focuses on determining the detailed properties of the emission line gas, including a careful treatment of multi- component emission line profiles. The resulting information obtained from the spectral fits are used to map the kinematics of the gas, sources of ionizing radiation and feedback present in each system. The resulting properties are tracked as a function of merger stage. Using emission line flux ratios and velocity dispersions, we find evidence for widespread, extended shock excitation in many local U/LIRGs. These low-velocity shocks become an increasingly important component of the optical emission lines as a merger progresses. We find that shocks may account for as much as half of the Hα luminosity in the latest-stage mergers in our sample. We discuss some possible implications of our result and consider the presence and effects of AGN on the spectra in our sample.

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arXiv2015

The physics and kinematics of the evolved, interacting planetary nebula PN G342.0-01.7

Here we aim to study the physical and kinematical characteristics of the unstudied old planetary nebula (PN) PN G342.0-01.7, which shows evidence of interaction with its surrounding interstellar medium. We used Integral Field Spectra from the Wide Field Spectrograph on the ANU 2.3 m telescope to provide spectroscopy across the whole object covering the spectral range 3400-7000 Å. We formed narrow-band images to investigate the excitation structure. The spectral analysis shows that the object is a distant Peimbert Type I PN of low excitation, formally of excitation class of 0.5. The low electron density, high dynamical age, and low surface brightness of the object confirm that it is observed fairly late in its evolution. It shows clear evidence for dredge-up of CN-processed material characteristic of its class. In addition, the low peculiar velocity of 7 km s$^{-1}$ shows it to be a member of the young disk component of our Galaxy. We built a self-consistent photoionisation model for the PNe matching the observed spectrum, the H$β$ luminosity, and the diameter. On the basis of this we derive an effective temperature $\log T_{\rm eff} \sim 5.05$ and luminosity $1.85 < \log L < 2.25$. The temperature is much higher than might have been expected using the excitation class, proving that this can be misleading in classifying evolved PNe. PN G342.0-01.7 is in interaction with its surrounding interstellar medium through which the object is moving in the south-west direction. This interaction drives a slow shock into the outer PN ejecta. A shock model suggests that it only accounts for about 10\% of the total luminosity, but has an important effect on the global spectrum of the PN.

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arXiv2015

The WiFeS S7 AGN survey: Current status and recent results on NGC 6300

The Siding Spring Southern Seyfert Spectroscopic Snapshot Survey (S7) is a targeted survey probing the narrow-line regions (NLRs) of a representative sample of ~140 nearby (z<0.02) Seyfert galaxies by means of optical integral field spectroscopy. The survey is based on a homogeneous data set observed using the Wide Field Spectrograph WiFeS. The data provide a 25x38 arcsec$^2$ field-of-view around the galaxy centre at typically ~1.5 arcsec spatial resolution and cover a wavelength range between ~3400 - 7100 $Å$ at spectral resolutions of ~100 km s$^{-1}$ and ~50 km s$^{-1}$ in the blue and red parts, respectively. The survey is primarily designed to study gas excitation and star formation around AGN, with a special focus on the shape of the AGN ionising continuum, the interaction between radio jets and the NLR gas, and the nature of nuclear LINER emission. We provide an overview of the current status of S7-based results and present new results for NGC 6300.

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arXiv2015

Galaxy Interactions in Compact Groups II: abundance and kinematic anomalies in HCG 91c

Galaxies in Hickson Compact Group 91 (HCG 91) were observed with the WiFeS integral field spectrograph as part of our ongoing campaign targeting the ionized gas physics and kinematics inside star forming members of compact groups. Here, we report the discovery of HII regions with abundance and kinematic offsets in the otherwise unremarkable star forming spiral HCG 91c. The optical emission line analysis of this galaxy reveals that at least three HII regions harbor an oxygen abundance ~0.15 dex lower than expected from their immediate surroundings and from the abundance gradient present in the inner regions of HCG 91c. The same star forming regions are also associated with a small kinematic offset in the form of a lag of 5-10 km/s with respect to the local circular rotation of the gas. HI observations of HCG 91 from the Very Large Array and broadband optical images from Pan-STARRS suggest that HCG 91c is caught early in its interaction with the other members of HCG 91. We discuss different scenarios to explain the origin of the peculiar star forming regions detected with WiFeS, and show that evidence point towards infalling and collapsing extra-planar gas clouds at the disk-halo interface, possibly as a consequence of long-range gravitational perturbations of HCG 91c from the other group members. As such, HCG 91c provides evidence that some of the perturbations possibly associated with the early phase of galaxy evolution in compact groups impact the star forming disk locally, and on sub-kpc scales.

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arXiv2014

Shapley Supercluster Survey (ShaSS): Galaxy Evolution from Filaments to Cluster Cores

We present an overview of a multi-wavelength survey of the Shapley supercluster (SSC; z~0.05) covering a contiguous area of 260 h^-2_70 Mpc^2 including the supercluster core. The project main aim is to quantify the influence of cluster-scale mass assembly on galaxy evolution in one of the most massive structures in the local Universe. The Shapley supercluster survey (ShaSS) includes nine Abell clusters (A3552, A3554, A3556, A3558, A3559, A3560, A3562, AS0724, AS0726) and two poor clusters (SC1327- 312, SC1329-313) showing evidence of cluster-cluster interactions. Optical (ugri) and near-infrared (K) imaging acquired with VST and VISTA allow us to study the galaxy population down to m*+6 at the supercluster redshift. A dedicated spectroscopic survey with AAOmega on the Anglo-Australian Telescope provides a magnitude-limited sample of supercluster members with 80% completeness at ~m*+3. We derive the galaxy density across the whole area, demonstrating that all structures within this area are embedded in a single network of clusters, groups and filaments. The stellar mass density in the core of the SSC is always higher than 9E09 M_sun Mpc^-3, which is ~40x the cosmic stellar mass density for galaxies in the local Universe. We find a new filamentary structure (~7 Mpc long in projection) connecting the SSC core to the cluster A3559, as well as previously unidentified density peaks. We perform a weak-lensing analysis of the central 1 sqdeg field of the survey obtaining for the central cluster A3558 a mass of M_500=7.63E14 M_sun, in agreement with X-ray based estimates.

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