Searcharxiv⌕ Search

arXiv subjects

U. Abbas

Publications and source records attributed to U. Abbas.

At least 37 records · Page 2Linked to original sources

The Short Term Stability of a Simulated Differential Astrometric Reference Frame in the Gaia era

We use methods of differential astrometry to construct a small field inertial reference frame stable at the micro-arcsecond level. Such a high level of astrometric precision can be expected with the end-of-mission standard errors to be achieved with the Gaia space satellite using global astrometry. We harness Gaia measurements of field angles and look at the influence of the number of reference stars and the star's magnitude as well as astrometric systematics on the total error budget with the help of Gaia-like simulations around the Ecliptic Pole in a differential astrometric scenario. We find that the systematic errors are modeled and reliably estimated to the $μ$as level even in fields with a modest number of 37 stars with G $<$13 mag over a 0.24 sq.degs. field of view for short time scales of the order of a day with high-cadence observations such as those around the North Ecliptic Pole during the EPSL scanning mode of Gaia for a perfect instrument. The inclusion of the geometric instrument model over such short time scales accounting for large-scale calibrations requires fainter stars down to G = 14 mag without diminishing the accuracy of the reference frame. We discuss several future perspectives of utilizing this methodology over different and longer timescales.

astro-ph.IM↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). The decline of cosmic star formation: quenching, mass, and environment connections

[Abridged] We use the final data of the VIMOS Public Extragalactic Redshift Survey (VIPERS) to investigate the effect of environment on the evolution of galaxies between $z=0.5$ and $z=0.9$. We characterise local environment in terms of the density contrast smoothed over a cylindrical kernel, the scale of which is defined by the distance to the $5^{th}$ nearest neighbour. We find that more massive galaxies tend to reside in higher-density environments over the full redshift range explored. Defining star-forming and passive galaxies through their (NUV$-r$) vs ($r-K$) colours, we then quantify the fraction of star-forming over passive galaxies, $f_{\rm ap}$, as a function of environment at fixed stellar mass. $f_{\rm ap}$ is higher in low-density regions for galaxies with masses ranging from $\log(\mathcal{M}/\mathcal{M}_\odot)=10.38$ (the lowest value explored) to at least $\log(\mathcal{M}/\mathcal{M}_\odot)\sim11.3$, although with decreasing significance going from lower to higher masses. This is the first time that environmental effects on high-mass galaxies are clearly detected at redshifts as high as $z\sim0.9$. We compared these results to VIPERS-like galaxy mock catalogues based on the galaxy formation model of De Lucia & Blaizot. The model correctly reproduces $f_{\rm ap}$ in low-density environments, but underpredicts it at high densities. The discrepancy is particularly strong for the lowest-mass bins. We find that this discrepancy is driven by an excess of low-mass passive satellite galaxies in the model. Looking at the accretion history of these model galaxies, i.e. the times when they become satellites, a better (yet not perfect) agreement with observations can be obtained in high density regions by assuming either that a not-negligible fraction of satellites is destroyed, or that their quenching time-scale is longer than $\sim 2$ Gyr.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structures at $0.5<z<1.2$ from redshift-space distortions in the clustering of the PDR-2 final sample

We present measurements of the growth rate of cosmological structure from the modelling of the anisotropic galaxy clustering measured in the final data release of the VIPERS survey. The analysis is carried out in configuration space and based on measurements of the first two even multipole moments of the anisotropic galaxy auto-correlation function, in two redshift bins spanning the range $0.5 < z < 1.2$. We provide robust and cosmology-independent corrections for the VIPERS angular selection function, allowing recovery of the underlying clustering amplitude at the percent level down to the Mpc scale. We discuss several improvements on the non-linear modelling of redshift-space distortions (RSD) and perform detailed tests of a variety of approaches against a set of realistic VIPERS-like mock realisations. This includes using novel fitting functions to describe the velocity divergence and density power spectra $P_{θθ}$ and $P_{δθ}$ that appear in RSD models. These tests show that we are able to measure the growth rate with negligible bias down to separations of $5h^{-1}Mpc$. Interestingly, the application to real data shows a weaker sensitivity to the details of non-linear RSD corrections compared to mock results. We obtain consistent values for the growth rate times the matter power spectrum normalisation parameter of $fσ_8=0.55\pm 0.12$ and $0.40\pm0.11$ at effective redshifts of $z = 0.6$ and $z=0.86$ respectively. These results are in agreement with standard cosmology predictions assuming Einstein gravity in a $Λ\rm{CDM}$ background.

astro-ph.CO↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS): PCA-based automatic cleaning and reconstruction of survey spectra

Identifying spurious reduction artefacts in galaxy spectra is a challenge for large surveys. We present an algorithm for identifying and repairing residual spurious features in sky-subtracted galaxy spectra with application to the VIPERS survey. The algorithm uses principal component analysis (PCA) applied to the galaxy spectra in the observed frame to identify sky line residuals imprinted at characteristic wavelengths. We further model the galaxy spectra in the rest-frame using PCA to estimate the most probable continuum in the corrupted spectral regions, which are then repaired. We apply the method to 90,000 spectra from the VIPERS survey and compare the results with a subset where careful editing was performed by hand. We find that the automatic technique does an extremely good job in reproducing the time-consuming manual cleaning and does it in a uniform and objective manner across a large data sample. The mask data products produced in this work are released together with the VIPERS second public data release (PDR-2).

astro-ph.IM↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS): Downsizing of the blue cloud and the influence of galaxy size on mass quenching over the last eight billion years

We use the full VIPERS redshift survey in combination with SDSS-DR7 to explore the relationships between star-formation history (using d4000), stellar mass and galaxy structure, and how these relationships have evolved since z~1. We trace the extents and evolutions of both the blue cloud and red sequence, by fitting double Gaussians to the d4000 distribution of galaxies in narrow stellar mass bins, for four redshift intervals over 0 10^11 M_sun, d4000<1.55) drops sharply by a factor five between z~0.8 and z~0.5. These galaxies are becoming quiescent at a rate that largely matches the increase in the numbers of massive passive galaxies seen over this period. We examine the size-mass relation of blue cloud galaxies, finding that its high-mass boundary runs along lines of constant M*/r_e or equivalently inferred velocity dispersion. Larger galaxies can continue to form stars to higher stellar masses than smaller galaxies. As blue cloud galaxies approach this high-mass limit, they start to be quenched, their d4000 values increasing to push them towards the green valley. In parallel, their structures change, showing higher Sersic indices and central stellar mass densities. For these galaxies, bulge growth is necessary for them to reach the high-mass limit of the blue cloud and be quenched by internal mechanisms. The blue cloud galaxies that are being quenched at z~0.8 lie along the same size-mass relation as present day quiescent galaxies, and seem the likely progenitors of today's S0s.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey: Measuring the growth rate of structure around cosmic voids

We identified voids in the completed VIMOS Public Extragalactic Redshift Survey (VIPERS), using an algorithm based on searching for empty spheres. We measured the cross-correlation between the centres of voids and the complete galaxy catalogue. The cross-correlation function exhibits a clear anisotropy in both VIPERS fields (W1 and W4), which is characteristic of linear redshift space distortions. By measuring the projected cross-correlation and then deprojecting it we are able to estimate the undistorted cross-correlation function. We propose that given a sufficiently well measured cross-correlation function one should be able to measure the linear growth rate of structure by applying a simple linear Gaussian streaming model for the redshift space distortions (RSD). Our study of voids in 306 mock galaxy catalogues mimicking the VIPERS fields would suggest that VIPERS is capable of measuring $β$ with an error of around $25\%$. Applying our method to the VIPERS data, we find a value for the redshift space distortion parameter, $β= 0.423^{+0.104}_{-0.108}$, which given the bias of the galaxy population we use gives a linear growth rate of $fσ_8 = 0.296^{+0.075}_{-0.078}$ at $z = 0.727$. These results are consistent with values observed in parallel VIPERS analysis using standard techniques.

astro-ph.CO↗

VIMOS Public Extragalactic Redshift Survey (VIPERS). The distinct build-up of dense and normal massive passive galaxies

We use the final data from the VIPERS redshift survey to extract an unparalleled sample of more than 2000 massive M > 10^11 M_sun passive galaxies (MPGs) at redshift 0.5 < z < 1.0, based on their NUVrK colours. This enables us to investigate how the population of these objects was built up over cosmic time. We find that the evolution of the number density depends on the galaxy mean surface stellar mass density, Sigma. In particular, dense (Sigma > 2000 M_sun pc^-2) MPGs show a constant comoving number density over this redshift range, whilst this increases by a factor ~ 4 for the least dense objects, defined as having Sigma < 1000 M_sun pc^-2. We estimate stellar ages for the MPG population both fitting the Spectral Energy Distribution (SED) and through the D4000_n index, obtaining results in good agreement. Our findings are consistent with passive ageing of the stellar content of dense MPGs. We show that at any redshift the less dense MPGs are younger than dense ones and that their stellar populations evolve at a slower rate than predicted by passive evolution. This points to a scenario in which the overall population of MPGs was built up over the cosmic time by continuous addition of less dense galaxies: on top of an initial population of dense objects that passively evolves, new, larger, and younger MPGs continuously join the population at later epochs. Finally, we demonstrate that the observed increase in the number density of MPGs is totally accounted for by the observed decrease in the number density of correspondingly massive star forming galaxies (i.e. all the non-passive M > 10^11 M_sun objects). Such systems observed at z ~ 1 in VIPERS, therefore, represent the most plausible progenitors of the subsequent emerging class of larger MPGs.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Full spectroscopic data and auxiliary information release (PDR-2)

We present the full public data release (PDR-2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS), performed at the ESO VLT. We release redshifts, spectra, CFHTLS magnitudes and ancillary information (as masks and weights) for a complete sample of 86,775 galaxies (plus 4,732 other objects, including stars and serendipitous galaxies); we also include their full photometrically-selected parent catalogue. The sample is magnitude limited to i_AB < 22.5, with an additional colour-colour pre-selection devised as to exclude galaxies at z<0.5. This practically doubles the effective sampling of the VIMOS spectrograph over the range 0.5 = 2 are shown to have a confidence level of 96% or larger and make up 88% of all measured galaxy redshifts (76,552 out of 86,775), constituting the VIPERS prime catalogue for statistical investigations. For this sample the rms redshift error, estimated using repeated measurements of about 3,000 galaxies, is found to be sigma_z = 0.00054(1+z). All data are available at http://vipers.inaf.it and on the ESO Archive.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS): Galaxy segregation inside filaments at $z \simeq 0.7$

We present the first quantitative detection of large-scale filamentary structure at $z \simeq 0.7$ in the large cosmological volume probed by the VIMOS Public Extragalactic Redshift Survey (VIPERS). We use simulations to show the capability of VIPERS to recover robust topological features in the galaxy distribution, in particular the filamentary network. We then investigate how galaxies with different stellar masses and stellar activities are distributed around the filaments and find a significant segregation, with the most massive or quiescent galaxies being closer to the filament axis than less massive or active galaxies. The signal persists even after down-weighting the contribution of peak regions. Our results suggest that massive and quiescent galaxies assemble their stellar mass through successive mergers during their migration along filaments towards the nodes of the cosmic web. On the other hand, low-mass star-forming galaxies prefer the outer edge of filaments, a vorticity rich region dominated by smooth accretion, as predicted by the recent spin alignment theory. This emphasizes the role of large scale cosmic flows in shaping galaxy properties.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Star formation history of passive galaxies

We trace the evolution and the star formation history of passive galaxies, using a subset of the VIMOS Public Extragalactic Redshift Survey (VIPERS). We extracted from the VIPERS survey a sample of passive galaxies in the redshift range 0.4<z<1.0 and stellar mass range 10<$log(M_{star}/M_{\odot})$<12. The sample was selected using an evolving cut in the rest-frame U-V color distribution and additional quality-ensuring cuts. We use the stacked spectra to measure the 4000$Å$ break (D4000) and the $Hδ$ Lick index ($Hδ_{A}$) with high precision. We compare the results with a grid of synthetic spectra to constrain the star formation epochs of these galaxies. We characterize the formation redshift-stellar mass relation for intermediate-redshift passive galaxies. We find that at $z\sim1$ stellar populations in low-mass passive galaxies are younger than in high-mass passive galaxies, similarly to what is observed at the present epoch. Over the full analyzed redshift and stellar mass range, the $D4000$ index increases with redshift, while $Hδ_{A}$ gets lower. This implies that the stellar populations are getting older with increasing stellar mass. Comparison to the spectra of passive galaxies in the SDSS survey shows that the shape of the relations of $D4000$, and $Hδ_{A}$ with stellar mass has not changed significantly with redshift. Assuming a single burst formation, this implies that high-mass passive galaxies formed their stars at $z_{form}\sim2$, while low-mass galaxies formed their main stellar population more recently, at $z_{form}\sim1$. The consistency of these results, obtained using two independent estimator of the formation redshift ($D4000$ and $Hδ_{A}$), further strengthens a scenario in which star formation proceeds from higher- to lower-mass systems as time passes, i.e. what has become known as the 'downsizing' picture.

astro-ph.GA↗

Gaia Data Release 1: Astrometry - one billion positions, two million proper motions and parallaxes

Gaia Data Release 1 (Gaia DR1) contains astrometric results for more than 1 billion stars brighter than magnitude 20.7 based on observations collected by the Gaia satellite during the first 14 months of its operational phase. We give a brief overview of the astrometric content of the data release and of the model assumptions, data processing, and validation of the results. For stars in common with the Hipparcos and Tycho-2 catalogues, complete astrometric single-star solutions are obtained by incorporating positional information from the earlier catalogues. For other stars only their positions are obtained by neglecting their proper motions and parallaxes. The results are validated by an analysis of the residuals, through special validation runs, and by comparison with external data. Results. For about two million of the brighter stars (down to magnitude ~11.5) we obtain positions, parallaxes, and proper motions to Hipparcos-type precision or better. For these stars, systematic errors depending e.g. on position and colour are at a level of 0.3 milliarcsecond (mas). For the remaining stars we obtain positions at epoch J2015.0 accurate to ~10 mas. Positions and proper motions are given in a reference frame that is aligned with the International Celestial Reference Frame (ICRF) to better than 0.1 mas at epoch J2015.0, and non-rotating with respect to ICRF to within 0.03 mas/yr. The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24 mas/yr. Based on less than a quarter of the nominal mission length and on very provisional and incomplete calibrations, the quality and completeness of the astrometric data in Gaia DR1 are far from what is expected for the final mission products. The results nevertheless represent a huge improvement in the available fundamental stellar data and practical definition of the optical reference frame.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Measuring nonlinear galaxy bias at z~0.8

We use the first release of the VImos Public Extragalactic Redshift Survey of galaxies (VIPERS) of ~50,000 objects to measure the biasing relation between galaxies and mass in the redshift range z=[0.5,1.1]. We estimate the 1-point distribution function [PDF] of VIPERS galaxies from counts in cells and, assuming a model for the mass PDF, we infer their mean bias relation. The reconstruction of the bias relation from PDFs is performed through a novel method that accounts for Poisson noise, redshift distortions, inhomogeneous sky coverage and other selection effects. With this procedure we constrain galaxy bias and its deviations from linearity down to scales as small as 4 Mpc/h and out to z=1.1. We detect small (~3%) but significant deviations from linear bias. The mean biasing function is close to linear in regions above the mean density. The mean slope of the biasing relation is a proxy to the linear bias parameter. It increases both with luminosity, in agreement with results of previous analyses, and with redshift. However, we detect a strong bias evolution only for z>0.9 in agreement with some, but not all, previous studies. We also detected a significant increase of the bias with the scale, from 4 to 8 Mpc/h, now seen for the first time out to z=1. The amplitude of nonlinearity depends on redshift, luminosity and on scales but no clear trend is detected. Thanks to the large cosmic volume probed by VIPERS we find that the mismatch between the previous estimates of bias at z~1 from zCOSMOS and VVDS-Deep galaxy samples is fully accounted for by cosmic variance. The results of our work confirm the importance of going beyond the over-simplistic linear bias hypothesis showing that non-linearities can be accurately measured through the applications of the appropriate statistical tools to existing datasets like VIPERS.

astro-ph.CO↗

Clustering-based redshift estimation: application to VIPERS/CFHTLS

We explore the accuracy of the clustering-based redshift estimation proposed by Ménard et al. (2013) when applied to VIPERS and CFHTLS real data. This method enables us to reconstruct redshift distributions from measurement of the angular clus- tering of objects using a set of secure spectroscopic redshifts. We use state of the art spectroscopic measurements with iAB < 22.5 from the VIMOS Public Extragalactic Redshift Survey (VIPERS) as reference population to infer the redshift distribution of galaxies from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) T0007 release. VIPERS provides a nearly representative sample to the flux limit iAB < 22.5 at redshift > 0.5 which allows us to test the accuracy of the clustering-based red- shift distributions. We show that this method enables us to reproduce the true mean color-redshift relation when both populations have the same magnitude limit. We also show that this technique allows the inference of redshift distributions for a population fainter than the one of reference and we give an estimate of the color-redshift mapping in this case. This last point is of great interest for future large redshift surveys which suffer from the need of a complete faint spectroscopic sample.

astro-ph.CO↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). The coevolution of galaxy morphology and colour to z~1

We explore the evolution of the statistical distribution of galaxy morphological properties and colours over the redshift range $0.5<z<1$, combining high-quality imaging data from the CFHT Legacy Survey with the large number of redshifts and extended photometry from the VIPERS survey. Galaxy structural parameters are measured by fitting Sérsic profiles to $i$-band images and then combined with absolute magnitudes, colours and redshifts, to trace the evolution in a multi-parameter space. We analyse, using a new method, the combination of colours and structural parameters of early- and late-type galaxies in luminosity--redshift space. We found that both the rest-frame colour distributions in the (U-B) vs. (B-V) plane and the Sérsic index distributions are well fitted by a sum of two Gaussians, with a remarkable consistency of red-spheroidal and blue-disky galaxy populations, over the explored redshift ($0.5<z<1$) and luminosity ($-1.5<B-B_*<1.0$) ranges. The combination of the UBV rest-frame colour and Sérsic index $n$ as a function of redshift and luminosity allows us to present the structure of early- and late-type galaxies and their evolution. We found that early type galaxies display only a slow change of their concentrations since $z\sim1$; it is already established by $z\sim1$ and depends much more strongly on their luminosities. In contrast, late-type galaxies get clearly more concentrated with cosmic time since $z\sim1$, with only little evolution in colour, which remains dependent mainly on their luminosity. This flipped luminosity (mass) and redshift dependence likely reflects different evolutionary tracks of early- and late-type galaxies before and after $z\sim1$. The combination of rest-frame colours and Sérsic index $n$ as a function of redshift and luminosity leads to a precise statistical description of the structure of galaxies and their evolution.

astro-ph.GA↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Environmental effects shaping the galaxy stellar mass function

We exploit the first public data release of VIPERS to investigate environmental effects in galaxy evolution between $z\sim0.5$ and $0.9$. The large number of spectroscopic redshifts over an area of about $10\,\mathrm{deg}^2$ provides a galaxy sample with high statistical power. The accurate redshift measurements, with $σ_z = 0.00047(1+z_\mathrm{spec})$, allow us to robustly isolate galaxies living in the lowest- and highest-density environments, as defined in terms of spatial 3D density contrast. We estimate the stellar mass function (SMF) of galaxies residing in these two environments, and constrain its high-mass end with unprecedented precision. We find that the galaxy SMF in the densest regions has a different shape than that measured at low densities, with an enhancement of massive galaxies and a hint of a flatter (less negative) slope at $z<0.8$. We normalise each SMF to the comoving volume occupied by the corresponding environment, and relate estimates from different redshift bins. We observe an evolution of the SMF of VIPERS galaxies in high densities, while the low-density one is nearly constant. We compare these results to semi-analytical models and find consistent environmental signatures. We discuss how the halo mass function and fraction of central/satellite galaxies depend on the environments considered, making intrinsic and environmental properties of galaxies physically coupled, and therefore difficult to disentangle. The evolution of our low-density regions is well described by the formalism introduced by Peng et al.~(2010), and is consistent with the idea that galaxies become progressively passive because of internal physical processes. The same formalism could also describe the evolution of the SMF in the high density regions, but only if a significant contribution from dry mergers is considered. [Abridged]

astro-ph.GA↗

A high-dimensional look at VIPERS galaxies

We investigate how galaxies in VIPERS (the VIMOS Public Extragalactic Redshift Survey) inhabit the cosmological density field by examining the correlations across the observable parameter space of galaxy properties and clustering strength. The high-dimensional analysis is made manageable by the use of group-finding and regression tools. We find that the major trends in galaxy properties can be explained by a single parameter related to stellar mass. After subtracting this trend, residual correlations remain between galaxy properties and the local environment pointing to complex formation dependencies. As a specific application of this work we build subsamples of galaxies with specific clustering properties for use in cosmological tests.

astro-ph.CO↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS): Reconstruction of the redshift-space galaxy density field

Aims. Using the VIMOS Public Extragalactic Redshift Survey (VIPERS) we aim to jointly estimate the key parameters that describe the galaxy density field and its spatial correlations in redshift space. Methods. We use the Bayesian formalism to jointly reconstruct the redshift-space galaxy density field, power spectrum, galaxy bias and galaxy luminosity function given the observations and survey selection function. The high-dimensional posterior distribution is explored using the Wiener filter within a Gibbs sampler. We validate the analysis using simulated catalogues and apply it to VIPERS data taking into consideration the inhomogeneous selection function. Results. We present joint constraints on the anisotropic power spectrum as well as the bias and number density of red and blue galaxy classes in luminosity and redshift bins as well as the measurement covariances of these quantities. We find that the inferred galaxy bias and number density parameters are strongly correlated although these are only weakly correlated with the galaxy power spectrum. The power spectrum and redshift-space distortion parameters are in agreement with previous VIPERS results with the value of the growth rate $fσ_8 = 0.38$ with 18% uncertainty at redshift 0.7.

astro-ph.CO↗

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Hierarchical scaling and biasing

We investigate the higher-order correlation properties of the VIMOS Public Extragalactic Redshift Survey (VIPERS) to test the hierarchical scaling hypothesis at z~1 and the dependence on galaxy luminosity, stellar mass, and redshift. We also aim to assess deviations from the linearity of galaxy bias independently from a previously performed analysis of our survey (Di Porto et al. 2014). We have measured the count probability distribution function in cells of radii 3 < R < 10 Mpc/h, deriving $σ_{8g}$, the volume-averaged two-,three-,and four-point correlation functions and the normalized skewness $S_{3g}$ and kurtosis $S_{4g}$ for volume-limited subsamples covering the ranges $-19.5 \le M_B(z=1.1)-5log(h) \le -21.0$, $9.0 < log(M*/M_{\odot} h^{-2}) \le 11.0$, $0.5 \le z < 1.1$. We have thus performed the first measurement of high-order correlations at z~1 in a spectroscopic redshift survey. Our main results are the following. 1) The hierarchical scaling holds throughout the whole range of scale and z. 2) We do not find a significant dependence of $S_{3g}$ on luminosity (below z=0.9 $S_{3g}$ decreases with luminosity but only at 1σ-level). 3) We do not detect a significant dependence of $S_{3g}$ and $S_{4g}$ on scale, except beyond z~0.9, where the dependence can be explained as a consequence of sample variance. 4) We do not detect an evolution of $S_{3g}$ and $S_{4g}$ with z. 5) The linear bias factor $b=σ_{8g}/σ_{8m}$ increases with z, in agreement with previous results. 6) We quantify deviations from the linear bias by means of the Taylor expansion parameter $b_2$. Our results are compatible with a null non-linear bias term, but taking into account other available data we argue that there is evidence for a small non-linear bias term.

astro-ph.CO↗