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Rob Sharp

Publications and source records attributed to Rob Sharp.

At least 37 records · Page 2Linked to original sources

LZIFU: an emission-line fitting toolkit for integral field spectroscopy data

We present LZIFU (LaZy-IFU), an IDL toolkit for fitting multiple emission lines simultaneously in integral field spectroscopy (IFS) data. LZIFU is useful for the investigation of the dynamical, physical and chemical properties of gas in galaxies. LZIFU has already been applied to many world-class IFS instruments and large IFS surveys, including the Wide Field Spectrograph, the new Multi Unit Spectroscopic Explorer (MUSE), the Calar Alto Legacy Integral Field Area (CALIFA) survey, the Sydney-Australian-astronomical-observatory Multi-object Integral-field spectrograph (SAMI) Galaxy Survey. Here we describe in detail the structure of the toolkit, and how the line fluxes and flux uncertainties are determined, including the possibility of having multiple distinct kinematic components. We quantify the performance of LZIFU, demonstrating its accuracy and robustness. We also show examples of applying LZIFU to CALIFA and SAMI data to construct emission line and kinematic maps, and investigate complex, skewed line profiles presented in IFS data. The code is made available to the astronomy community through github. LZIFU will be further developed over time to other IFS instruments, and to provide even more accurate line and uncertainty estimates.

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Using an Artificial Neural Network to Classify Multi-component Emission Line Fits

We present The Machine, an artificial neural network (ANN) capable of differentiating between the numbers of Gaussian components needed to describe the emission lines of Integral Field Spectroscopic (IFS) observations. Here we show the preliminary results of the S7 first data release (Siding Spring Southern Seyfert Spectro- scopic Snapshot Survey, Dopita et al. 2015) and SAMI Galaxy Survey (Sydney-AAO Multi-object Integral Field Unit, Croom et al. 2012) to classify whether the emission lines in each spatial pixel are composed of 1, 2, or 3 different Gaussian components. Previously this classification has been done by individual people, taking an hour per galaxy. This time investment is no longer feasible with the large spectroscopic surveys coming online.

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Discovery of a z=0.65 Post-Starburst BAL Quasar in the DES Supernova Fields

We present the discovery of a z=0.65 low-ionization broad absorption line (LoBAL) quasar in a post-starburst galaxy in data from the Dark Energy Survey (DES) and spectroscopy from the Australian Dark Energy Survey (OzDES). LoBAL quasars are a minority of all BALs, and rarer still is that this object also exhibits broad FeII (an FeLoBAL) and Balmer absorption. This is the first BAL quasar that has signatures of recently truncated star formation, which we estimate ended about 40 Myr ago. The characteristic signatures of an FeLoBAL require high column densities, which could be explained by the emergence of a young quasar from an early, dust-enshrouded phase, or by clouds compressed by a blast wave. The age of the starburst component is comparable to estimates of the lifetime of quasars, so if we assume the quasar activity is related to the truncation of the star formation, this object is better explained by the blast wave scenario.

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The SAMI Galaxy Survey: extraplanar gas, galactic winds, and their association with star formation history

We investigate a sample of 40 local, main-sequence, edge-on disc galaxies using integral field spectroscopy with the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey to understand the link between properties of the extraplanar gas and their host galaxies. The kinematics properties of the extraplanar gas, including velocity asymmetries and increased dispersion, are used to differentiate galaxies hosting large-scale galactic winds from those dominated by the extended diffuse ionized gas. We find rather that a spectrum of diffuse gas-dominated to wind dominated galaxies exist. The wind-dominated galaxies span a wide range of star formation rates ($-1 \lesssim \log({\rm SFR/M_{\odot} yr^{-1}}) \lesssim 0.5$) across the whole stellar mass range of the sample ($8.5 \lesssim \log({\rm M_{*}/M_{\odot}}) \lesssim 11$). The wind galaxies also span a wide range in SFR surface densities ($10^{-3} \textrm{--} 10^{-1.5}\rm~M_{\odot} ~yr^{-1}~kpc^{-2}$) that is much lower than the canonical threshold of $\rm0.1~M_{\odot} ~yr^{-1}~kpc^{-2}$. The wind galaxies on average have higher SFR surface densities and higher $\rm Hδ_A$ values than those without strong wind signatures. The enhanced $\rm Hδ_A$ indicates that bursts of star formation in the recent past are necessary for driving large-scale galactic winds. We demonstrate with Sloan Digital Sky Survey data that galaxies with high SFR surface density have experienced bursts of star formation in the recent past. Our results imply that the galactic winds revealed in our study are indeed driven by bursts of star formation, and thus probing star formation in the time domain is crucial for finding and understanding galactic winds.

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The WiggleZ Dark Energy Survey: Probing the Epoch of Radiation Domination using Large Scale Structure

We place the most robust constraint to date on the scale of the turnover in the cosmological matter power spectrum using data from the WiggleZ Dark Energy Survey. We find this feature to lie at a scale of $k_0=0.0160^{+0.0041}_{-0.0035}$ [h/Mpc] (68% confidence) for an effective redshift of 0.62 and obtain from this the first-ever turnover-derived distance and cosmology constraints: a measure of the cosmic distance-redshift relation in units of the horizon scale at the redshift of radiation-matter equality (r_H) of D_V(z=0.62)/r_H=18.3 (+6.3/-3.3) and, assuming a prior on the number of extra relativistic degrees of freedom $N_{eff}=3$, constraints on the matter density parameter $Ω_Mh^2=0.136^{+0.026}_{-0.052}$ and on the redshift of matter-radiation equality $z_{eq}=3274^{+631}_{-1260}$. All results are in excellent agreement with the predictions of standard LCDM models. Our constraints on the logarithmic slope of the power spectrum on scales larger than the turnover is bounded in the lower limit with values only as low as -1 allowed, with the prediction of standard LCDM models easily accommodated by our results. Lastly, we generate forecasts for the achievable precision of future surveys at constraining $k_0$, $Ω_Mh^2$, $z_{eq}$ and $N_{eff}$. We find that BOSS should substantially improve upon the WiggleZ turnover constraint, reaching a precision on $k_0$ of $\pm$9% (68% confidence), translating to precisions on $Ω_Mh^2$ and $z_{eq}$ of $\pm$10% (assuming a prior $N_{eff}=3$) and on $N_{eff}$ of (+78/-56)% (assuming a prior $Ω_Mh^2=0.135$). This is sufficient precision to sharpen the constraints on $N_{eff}$ from WMAP, particularly in its upper limit. For Euclid, we find corresponding attainable precisions on $(k_0, Ω_Mh^2, N_eff)$ of (3,4,+17/-21)%. This represents a precision approaching our forecasts for the Planck Surveyor.

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The SAMI Galaxy Survey: Can we trust aperture corrections to predict star formation?

In the low redshift Universe (z<0.3), our view of galaxy evolution is primarily based on fibre optic spectroscopy surveys. Elaborate methods have been developed to address aperture effects when fixed aperture sizes only probe the inner regions for galaxies of ever decreasing redshift or increasing physical size. These aperture corrections rely on assumptions about the physical properties of galaxies. The adequacy of these aperture corrections can be tested with integral-field spectroscopic data. We use integral-field spectra drawn from 1212 galaxies observed as part of the SAMI Galaxy Survey to investigate the validity of two aperture correction methods that attempt to estimate a galaxy's total instantaneous star formation rate. We show that biases arise when assuming that instantaneous star formation is traced by broadband imaging, and when the aperture correction is built only from spectra of the nuclear region of galaxies. These biases may be significant depending on the selection criteria of a survey sample. Understanding the sensitivities of these aperture corrections is essential for correct handling of systematic errors in galaxy evolution studies.

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Simulations of the OzDES AGN Reverberation Mapping Project

As part of the OzDES spectroscopic survey we are carrying out a large scale reverberation mapping study of $\sim$500 quasars over five years in the 30 deg$^2$ area of the Dark Energy Survey (DES) supernova fields. These quasars have redshifts ranging up to 4 and have apparent AB magnitudes between $16.8<r<22.5$ mag. The aim of the survey is to measure time lags between fluctuations in the quasar continuum and broad emission line fluxes of individual objects in order to measure black hole masses for a broad range of AGN and constrain the radius-luminosity ($R-L$) relationship. Here we investigate the expected efficiency of the OzDES reverberation mapping campaign and its possible extensions. We expect to recover lags for $\sim$35-45\% of the quasars. AGN with shorter lags and greater variability are more likely to yield a lag, and objects with lags $\lesssim$6 months or $\sim$1 year are expected be recovered the most accurately. The baseline OzDES reverberation mapping campaign is predicted to produce an unbiased measurement of the $R-L$ relationship parameters for H$β$, Mg II $λ$2798, and C IV $λ$1549. However, extending the baseline survey by either increasing the spectroscopic cadence, extending the survey season, or improving the emission line flux measurement accuracy will significantly improve the $R-L$ parameter constraints for all broad emission lines.

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The SAMI Pilot Survey: The Fundamental and Mass Planes in Three Low-Redshift Clusters

Using new integral field observations of 106 galaxies in three nearby clusters we investigate how the intrinsic scatter of the Fundamental Plane depends on the way in which the velocity dispersion and effective radius are measured. Our spatially resolved spectroscopy, combined with a cluster sample with negligible relative distance errors allows us to derive a Fundamental Plane with minimal systematic uncertainties. From the apertures we tested, we find that velocity dispersions measured within a circular aperture with radius equal to one effective radius minimises the intrinsic scatter of the Fundamental Plane. Using simple yet powerful Jeans dynamical models we determine dynamical masses for our galaxies. Replacing luminosity in the Fundamental Plane with dynamical mass, we demonstrate that the resulting Mass Plane has further reduced scatter, consistent with zero intrinsic scatter. Using these dynamical models we also find evidence for a possibly non-linear relationship between dynamical mass-to-light ratio and velocity dispersion.

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The accretion histories of brightest cluster galaxies from their stellar population gradients

We analyse the spatially-resolved stellar populations of 9 local ($z<0.1$) Brightest Cluster Galaxies (BCGs) observed with VIMOS in IFU mode. Our sample is composed of 7 slow-rotating and 2 fast-rotating BCGs. We do not find a connection between stellar kinematics and stellar populations in this small sample. The BCGs have shallow metallicity gradients (median $Δ$[Fe/H] $= -0.11\pm0.1$), high central metallicities (median $[$Fe/H]$_{[α/Fe]=0} = 0.13\pm0.07$), and a wide range of central ages (from 5 to 15 Gyr). We propose that the reason for this is diverse evolutionary paths in BCGs. 67 per cent of the sample (6/9) show $\sim 7$ Gyr old central ages, which reflects an active accretion history, and 33 per cent of the sample (3/9) have central ages older than 11 Gyr, which suggest no star formation since $z=2$. The BCGs show similar central stellar populations and stellar population gradients to early-type galaxies of similar mass (M$_{dyn}> 10^{11.3}$M$_{\odot}$) from the ATLAS$^{3D}$ survey (median [Z/H] $= 0.04\pm0.07$, $Δ$[Z/H] $= -0.19\pm0.1$). However, massive early-type galaxies from ATLAS$^{3D}$ have consistently old ages (median Age $=12.0\pm3.8$Gyr). We also analyse the close massive companion galaxies of two of the BCGs. These galaxies have similar stellar populations to their respective BCGs.

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The SAMI Galaxy Survey: Shocks and Outflows in a normal star-forming galaxy

We demonstrate the feasibility and potential of using large integral field spectroscopic surveys to investigate the prevalence of galactic-scale outflows in the local Universe. Using integral field data from SAMI and the Wide Field Spectrograph, we study the nature of an isolated disk galaxy, SDSS J090005.05+000446.7 (z = 0.05386). In the integral field datasets, the galaxy presents skewed line profiles changing with position in the galaxy. The skewed line profiles are caused by different kinematic components overlapping in the line-of-sight direction. We perform spectral decomposition to separate the line profiles in each spatial pixel as combinations of (1) a narrow kinematic component consistent with HII regions, (2) a broad kinematic component consistent with shock excitation, and (3) an intermediate component consistent with shock excitation and photoionisation mixing. The three kinematic components have distinctly different velocity fields, velocity dispersions, line ratios, and electron densities. We model the line ratios, velocity dispersions, and electron densities with our MAPPINGS IV shock and photoionisation models, and we reach remarkable agreement between the data and the models. The models demonstrate that the different emission line properties are caused by major galactic outflows that introduce shock excitation in addition to photoionisation by star-forming activities. Interstellar shocks embedded in the outflows shock-excite and compress the gas, causing the elevated line ratios, velocity dispersions, and electron densities observed in the broad kinematic component. We argue from energy considerations that, with the lack of a powerful active galactic nucleus, the outflows are likely to be driven by starburst activities. Our results set a benchmark of the type of analysis that can be achieved by the SAMI Galaxy Survey on large numbers of galaxies.

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IFU observations of luminous type II AGN - I. Evidence for ubiquitous winds

We present observations of 17 luminous (log(L[O III]/L_Sun) > 8.7) local (z < 0.11) type II AGN. Our aim is to investigate the prevalence and nature of AGN driven outflows in these galaxies by combining kinematic and ionization diagnostic information. We use non-parametric methods (e.g. W80, the width containing 80% of the line flux) to assess the line widths in the central regions of our targets. The maximum values of W80 in each galaxy are in the range 400 - 1600 km/s, with a mean of 790 +- 90 km/s. Such high velocities are strongly suggestive that these AGN are driving ionized outflows. Multi-Gaussian fitting is used to decompose the velocity structure in our galaxies. 14/17 of our targets require 3 separate kinematic components in the ionized gas in their central regions. The broadest components of these fits have FWHM = 530 - 2520 km/s, with a mean value of 920 +- 50 km/s. By simultaneously fitting both the Hβ/[O III] and Hα/[N II] complexes we construct ionization diagnostic diagrams for each component. 13/17 of our galaxies show a significant (> 95 %) correlation between the [N II]/Hα ratio and the velocity dispersion of the gas. Such a correlation is the natural consequence of a contribution to the ionization from shock excitation and we argue that this demonstrates that the outflows from these AGN are directly impacting the surrounding ISM within the galaxies.

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The WiggleZ Dark Energy Survey: Improved Distance Measurements to z = 1 with Reconstruction of the Baryonic Acoustic Feature

We present significant improvements in cosmic distance measurements from the WiggleZ Dark Energy Survey, achieved by applying the reconstruction of the baryonic acoustic feature technique. We show using both data and simulations that the reconstruction technique can often be effective despite patchiness of the survey, significant edge effects and shot-noise. We investigate three redshift bins in the redshift range 0.2<$z$<1, and in all three find improvement after reconstruction in the detection of the baryonic acoustic feature and its usage as a standard ruler. We measure model independent distance measures $D_{\mathrm V}(r_{\mathrm s}^\mathrm{fid}/r_{\mathrm s})$ of 1716 $\pm$ 83 Mpc, 2221 $\pm$ 101 Mpc, 2516 $\pm$ 86 Mpc (68% CL) at effective redshifts z = 0.44, 0.6, 0.73, respectively, where $D_{\mathrm V}$ is the volume-average-distance, and $r_{\mathrm s}$ is the sound horizon at the end of the baryon drag epoch. These significantly improved 4.8, 4.5 and 3.4 percent accuracy measurements are equivalent to those expected from surveys with up to 2.5 times the volume of WiggleZ. These measurements are fully consistent with cosmologies allowed by the analyses of the Planck Collaboration and the Sloan Digital Sky Survey.We provide the $D_{\mathrm V}(r_{\mathrm s}^\mathrm{fid}/r_{\mathrm s})$ posterior probability distributions and their covariances. When combining these measurements with temperature fluctuations measurements of Planck, the polarization of WMAP9, and the 6dF Galaxy Survey baryonic acoustic feature, we do not detect deviations from a flat LCDM model. Assuming this model we constrain the current expansion rate to $H_0$ = 67.15 $\pm$ 0.98 kms$^{-1}$Mpc$^{-1}$. Allowing the equation of state of dark energy to vary we obtain $w_\mathrm{DE}$ = -1.080 $\pm$ 0.135. When assuming a curved LCDM model we obtain a curvature value of $Ω_{\mathrm K}$ = -0.0043 $\pm$ 0.0047.

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Infrared-Faint Radio Sources are at high redshifts

Context: Infrared-Faint Radio Sources (IFRS) are characterised by relatively high radio flux densities and associated faint or even absent infrared and optical counterparts. The resulting extremely high radio-to-infrared flux density ratios up to several thousands were previously known only for High-redshift Radio Galaxies (HzRGs), suggesting a link between the two classes of object. Prior to this work, no redshift was known for any IFRS in the Australia Telescope Large Area Survey (ATLAS) fields which would help to put IFRS in the context of other classes of object, especially of HzRGs. Aims: This work aims at measuring the first redshifts of IFRS in the ATLAS fields. Further, we test the hypothesis that IFRS are similar to HzRGs, as higher-redshift or dust-obscured versions of these massive galaxies. Methods: A sample of IFRS was spectroscopically observed using the Focal Reducer and Low Dispersion Spectrograph 2 (FORS2) at the Very Large Telescope (VLT). The data were calibrated based on the Image Reduction and Analysis Facility (IRAF) and redshifts extracted. This information was then used to calculate rest-frame luminosities, and to perform the first spectral energy distribution modelling of IFRS based on redshifts. Results: We found redshifts of 1.84, 2.13, and 2.76, for three IFRS, confirming the suggested high-redshift character of this class of object. These redshifts as well as the resulting luminosities show IFRS to be similar to HzRGs. We found further evidence that fainter IFRS are at even higher redshifts. Conclusions: Considering the similarities between IFRS and HzRGs substantiated in this work, the detection of IFRS, which have a significantly higher sky density than HzRGs, increases the number of Active Galactic Nuclei in the early universe and adds to the problems of explaining the formation of supermassive black holes shortly after the Big Bang.

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The SAMI Pilot Survey: The Kinematic Morphology-Density Relation in Abell 85, Abell 168 and Abell 2399

We examine the kinematic morphology of early-type galaxies (ETGs) in three galaxy clusters Abell 85, 168 and 2399. Using data from the Sydney-AAO Multi-object Integral field spectrograph (SAMI) we measured spatially-resolved kinematics for 79 ETGs in these clusters. We calculate $λ_{R}$, a proxy for the projected specific stellar angular momentum, for each galaxy and classify the 79 ETGs in our samples as fast or slow rotators. We calculate the fraction of slow rotators in the ETG populations ($f_{SR}$) of the clusters to be $0.21\pm0.08$, $0.08\pm0.08$ and $0.12\pm0.06$ for Abell 85, 168 and 2399 respectively, with an overall fraction of $0.15\pm0.04$. These numbers are broadly consistent with the values found in the literature, confirming recent work asserting that the fraction of slow rotators in the ETG population is constant across many orders of magnitude in global environment. We examine the distribution of kinematic classes in each cluster as a function of environment using the projected density of galaxies: the kinematic morphology-density relation. We find that in Abell 85 $f_{SR}$ increases in higher density regions but in Abell 168 and Abell 2399 this trend is not seen. We examine the differences between the individual clusters to explain this. In addition, we find slow rotators on the outskirts of two of the clusters studied, Abell 85 and 2399. These galaxies reside in intermediate to low density regions and have clearly not formed at the centre of a cluster environment. We hypothesise that they formed at the centres of groups and are falling into the clusters for the first time.

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Angular Momenta, Dynamical Masses, and Mergers of Brightest Cluster Galaxies

Using the VIMOS Integral Field Unit (IFU) spectrograph on the Very Large Telescope (VLT), we have spatially mapped the kinematic properties of 10 nearby Brightest Cluster Galaxies (BCGs) and 4 BCG companion galaxies located within a redshift of $z=0.1$. In the hierarchical formation model, these massive galaxies $(10^{10.5} M_{\odot} < M_{dyn} < 10^{11.9} M_{\odot})$ are expected to undergo more mergers than lower mass galaxies, and simulations show that dry minor mergers can remove angular momentum. We test whether BCGs have low angular momenta by using the $λ_{Re}$ parameter developed by the SAURON and ATLAS\textsuperscript{3D} teams and combine our kinematics with Sloan Digital Sky Survey (SDSS) photometry to analyze the BCGs' merger status. We find that 30% (3/10) of the BCGs and 100% of the companion galaxies (4/4) are fast rotators as defined by the ATLAS\textsuperscript{3D} criteria. Our fastest rotating BCG has a $λ_{Re}=0.35\pm0.05$. We increase the number of BCGs analyzed from 1 in the combined SAURON and ATLAS\textsuperscript{3D} surveys to 11 BCGs total and find that above $M_{dyn}\sim11.5 M_{\odot}$, virtually all galaxies regardless of environment are slow rotators. To search for signs of recent merging, we analyze the photometry of each system and use the $G-M_{20}$ selection criteria to identify mergers. We find that $40\pm20$% of our BCGs are currently undergoing or have recently undergone a merger (within 0.2 Gyrs). Surprisingly, we find no correlation between galaxies with high angular momentum and morphological signatures of merging.

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The WiggleZ Dark Energy Survey: Star-formation in UV-luminous galaxies from their luminosity functions

We present the ultraviolet (UV) luminosity function of galaxies from the GALEX Medium Imaging Survey with measured spectroscopic redshifts from the first data release of the WiggleZ Dark Energy Survey. This sample selects galaxies with high star formation rates: at 0.6 < z < 0.9 the median star formation rate is at the upper 95th percentile of optically-selected (r<22.5) galaxies and the sample contains about 50 per cent of all NUV < 22.8, 0.6 < z < 0.9 starburst galaxies within the volume sampled. The most luminous galaxies in our sample (-21.0>M_NUV>-22.5) evolve very rapidly with a number density declining as (1+z)^{5\pm 1} from redshift z = 0.9 to z = 0.6. These starburst galaxies (M_NUV<-21 is approximately a star formation rate of 30 \msuny) contribute about 1 per cent of cosmic star formation over the redshift range z=0.6 to z=0.9. The star formation rate density of these very luminous galaxies evolves rapidly, as (1+z)^{4\pm 1}. Such a rapid evolution implies the majority of star formation in these large galaxies must have occurred before z = 0.9. We measure the UV luminosity function in 0.05 redshift intervals spanning 0.1<z<0.9, and provide analytic fits to the results. At all redshifts greater than z=0.55 we find that the bright end of the luminosity function is not well described by a pure Schechter function due to an excess of very luminous (M_NUV<-22) galaxies. These luminosity functions can be used to create a radial selection function for the WiggleZ survey or test models of galaxy formation and evolution. Here we test the AGN feedback model in Scannapieco et al. (2005), and find that this AGN feedback model requires AGN feedback efficiency to vary with one or more of the following: stellar mass, star formation rate and redshift.

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The WiggleZ Dark Energy Survey: constraining galaxy bias and cosmic growth with 3-point correlation functions

Higher-order statistics are a useful and complementary tool for measuring the clustering of galaxies, containing information on the non-gaussian evolution and morphology of large-scale structure in the Universe. In this work we present measurements of the three-point correlation function (3PCF) for 187,000 galaxies in the WiggleZ spectroscopic galaxy survey. We explore the WiggleZ 3PCF scale and shape dependence at three different epochs z=0.35, 0.55 and 0.68, the highest redshifts where these measurements have been made to date. Using N-body simulations to predict the clustering of dark matter, we constrain the linear and non-linear bias parameters of WiggleZ galaxies with respect to dark matter, and marginalise over them to obtain constraints on sigma_8(z), the variance of perturbations on a scale of 8 Mpc/h and its evolution with redshift. These measurements of sigma_8(z), which have 10-20% accuracies, are consistent with the predictions of the LCDM concordance cosmology and test this model in a new way.

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The WiggleZ Dark Energy Survey: measuring the cosmic growth rate with the two-point galaxy correlation function

The growth history of large-scale structure in the Universe is a powerful probe of the cosmological model, including the nature of dark energy. We study the growth rate of cosmic structure to redshift $z = 0.9$ using more than $162{,}000$ galaxy redshifts from the WiggleZ Dark Energy Survey. We divide the data into four redshift slices with effective redshifts $z = [0.2,0.4,0.6,0.76]$ and in each of the samples measure and model the 2-point galaxy correlation function in parallel and transverse directions to the line-of-sight. After simultaneously fitting for the galaxy bias factor we recover values for the cosmic growth rate which are consistent with our assumed $Λ$CDM input cosmological model, with an accuracy of around 20% in each redshift slice. We investigate the sensitivity of our results to the details of the assumed model and the range of physical scales fitted, making close comparison with a set of N-body simulations for calibration. Our measurements are consistent with an independent power-spectrum analysis of a similar dataset, demonstrating that the results are not driven by systematic errors. We determine the pairwise velocity dispersion of the sample in a non-parametric manner, showing that it systematically increases with decreasing redshift, and investigate the Alcock-Paczynski effects of changing the assumed fiducial model on the results. Our techniques should prove useful for current and future galaxy surveys mapping the growth rate of structure using the 2-dimensional correlation function.

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