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In this paper we present results from the weak lensing shape measurement GRavitational lEnsing Accuracy Testing 2010 (GREAT10) Galaxy Challenge. This marks an order of magnitude step change in the level of scrutiny employed in weak lensing shape measurement analysis. We provide descriptions of each method tested and include 10 evaluation metrics over 24 simulation branches. GREAT10 was the first shape measurement challenge to include variable fields; both the shear field and the Point Spread Function (PSF) vary across the images in a realistic manner. The variable fields enable a variety of metrics that are inaccessible to constant shear simulations including a direct measure of the impact of shape measurement inaccuracies, and the impact of PSF size and ellipticity, on the shear power spectrum. To assess the impact of shape measurement bias for cosmic shear we present a general pseudo-Cl formalism, that propagates spatially varying systematics in cosmic shear through to power spectrum estimates. We also show how one-point estimators of bias can be extracted from variable shear simulations. The GREAT10 Galaxy Challenge received 95 submissions and saw a factor of 3 improvement in the accuracy achieved by shape measurement methods. The best methods achieve sub-percent average biases. We find a strong dependence in accuracy as a function of signal-to-noise, and indications of a weak dependence on galaxy type and size. Some requirements for the most ambitious cosmic shear experiments are met above a signal-to-noise ratio of 20. These results have the caveat that the simulated PSF was a ground-based PSF. Our results are a snapshot of the accuracy of current shape measurement methods and are a benchmark upon which improvement can continue. This provides a foundation for a better understanding of the strengths and limitations of shape measurement methods., Comment: Accepted to MNRAS

Cosmic shear has been identified as the method with the most potential to constrain dark energy. To capitalise on this potential it is necessary to measure galaxy shapes with great accuracy, which in turn requires a detailed model for the image blurring, the Point Spread Function (PSF). In general the PSF varies with wavelength and therefore the PSF integrated over an observing filter depends on the spectrum of the object. For a typical galaxy the spectrum varies across the galaxy image, thus the PSF depends on the position within the image. We estimate the bias on the shear due to such colour gradients by modelling galaxies using two co-centered, co-elliptical Sersic profiles, each with a different spectrum. We estimate the effect of ignoring colour gradients and find the shear bias from a single galaxy can be very large depending on the properties of the galaxy. We find that halving the filter width reduces the shear bias by a factor of about 5. We show that, to first order, tomographic cosmic shear two point statistics depend on the mean shear bias over the galaxy population at a given redshift. For a single broad filter, and averaging over a small galaxy catalogue, we find a mean shear bias which is subdominant to the predicted statistical errors for future cosmic shear surveys. However, the true mean shear bias may exceed the statistical errors, depending on how accurately the catalogue represents the observed distribution of galaxies in the cosmic shear survey. We then investigate the bias on the shear for two-filter imaging and find that the bias is reduced by at least an order of magnitude. Lastly, we find that it is possible to calibrate galaxies for which colour gradients were ignored using two-filter imaging of a fair sample of noisy galaxies, if the galaxy model is known. For a S/N of 25 the number of galaxies required in each tomographic redshift bin is of order 1e4., Comment: 13 pages of main text, 10 figures

Cosmic shear requires high precision measurement of galaxy shapes in the presence of the observational Point Spread Function (PSF) that smears out the image. The PSF must therefore be known for each galaxy to a high accuracy. However, for several reasons, the PSF is usually wavelength dependent, therefore the differences between the spectral energy distribution of the observed objects introduces further complexity. In this paper we investigate the effect of the wavelength-dependence of the PSF, focusing on instruments in which the PSF size is dominated by the diffraction-limit of the telescope and which use broad-band filters for shape measurement. We first calculate biases on cosmological parameter estimation from cosmic shear when the stellar PSF is used uncorrected. Using realistic galaxy and star spectral energy distributions and populations and a simple three-component circular PSF we find that the colour-dependence must be taken into account for the next generation of telescopes. We then consider two different methods for removing the effect (i) the use of stars of the same colour as the galaxies and (ii) estimation of the galaxy spectral energy distribution using multiple colours and using a telescope model for the PSF. We find that both of these methods correct the effect to levels below the tolerances required for per-cent level measurements of dark energy parameters. Comparison of the two methods favours the template-fitting method because its efficiency is less dependent on galaxy redshift than the broad-band colour method and takes full advantage of deeper photometry., Comment: 10 pages, 8 figures, version accepted for publication in MNRAS

Gravitational lensing shear has the potential to be the most powerful tool for constraining the nature of dark energy. However, accurate measurement of galaxy shear is crucial and has been shown to be non-trivial by the Shear TEsting Programme. Here we demonstrate a fundamental limit to the accuracy achievable by model-fitting techniques, if oversimplistic models are used. We show that even if galaxies have elliptical isophotes, model-fitting methods which assume elliptical isophotes can have significant biases if they use the wrong profile. We use noise-free simulations to show that on allowing sufficient flexibility in the profile the biases can be made negligible. This is no longer the case if elliptical isophote models are used to fit galaxies made up of a bulge plus a disk, if these two components have different ellipticities. The limiting accuracy is dependent on the galaxy shape but we find the most significant biases for simple spiral-like galaxies. The implications for a given cosmic shear survey will depend on the actual distribution of galaxy morphologies in the universe, taking into account the survey selection function and the point spread function. However our results suggest that the impact on cosmic shear results from current and near future surveys may be negligible. Meanwhile, these results should encourage the development of existing approaches which are less sensitive to morphology, as well as methods which use priors on galaxy shapes learnt from deep surveys., Comment: 10 pages, 8 figures

The control of systematic effects when measuring galaxy shapes is one of the main challenges for cosmic shear analyses. In this context, we study the fundamental limitations on shear accuracy due to the measurement of the Point Spread Function (PSF) from the finite number of stars. In order to do that, we translate the accuracy required for cosmological parameter estimation to the minimum number of stars over which the PSF must be calibrated. We first derive our results analytically in the case of infinitely small pixels (i.e. infinitely high resolution). Then image simulations are used to validate these results and investigate the effect of finite pixel size in the case of an elliptical gaussian PSF. Our results are expressed in terms of the minimum number of stars required to calibrate the PSF in order to ensure that systematic errors are smaller than statistical errors when estimating the cosmological parameters. On scales smaller than the area containing this minimum number of stars, there is not enough information to model the PSF. In the case of an elliptical gaussian PSF and in the absence of dithering, 2 pixels per PSF Full Width at Half Maximum (FWHM) implies a 20% increase of the minimum number of stars compared to the ideal case of infinitely small pixels; 0.9 pixels per PSF FWHM implies a factor 100 increase. In the case of a good resolution and a typical Signal-to-Noise Ratio distribution of stars, we find that current surveys need the PSF to be calibrated over a few stars, which may explain residual systematics on scales smaller than a few arcmins. Future all-sky cosmic shear surveys require the PSF to be calibrated over a region containing about 50 stars., Comment: 13 pages, 4 figures, accepted by A&A

Accurate measurements of the mass distribution in galaxy and cluster halos are essential to test the cold dark matter (CDM) paradigm. The cosmological model predicts a universal shape for the density profile in all halos, independent of halo mass. Its profile has a `cuspy' centre, with no evidence for the constant density core. In this paper we carry out a careful analysis of twelve galaxy clusters, using Chandra data to compute the mass distribution in each system under the assumption of hydrostatic equilibrium. Due to their low concentration, clusters provide ideal objects for studying the central cusps in dark matter halos. The majority of the systems are consistent with the CDM model, but 4 objects exhibit flat inner density profiles. We suggest that the flat inner profile found for these clusters is due to an underestimation of the mass in the cluster centre (rather than any problem with the CDM model), since these objects also have a centrally peaked gas mass fraction. We discuss possible causes for erroneously low mass measurements in the cores of some systems., Comment: 16 pages, 10 figures, 4 tables, accepted for publication in MNRAS

Conduction may play an important role in reducing cooling flows in galaxy clusters. We analyse a sample of sixteen objects using Chandra data and find that a balance between conduction and cooling can exist in the hotter clusters (T > 5 keV), provided the plasma conductivity is close to the unhindered Spitzer value. In the absence of any additional heat sources, a reduced mass inflow must develop in the cooler objects in the sample. We fit cooling flow models to deprojected data and compare the spectral mass deposition rates found to the values required to account for the excess luminosity, assuming Spitzer-rate heat transfer over the observed temperature gradients. The mass inflow rates found are lower than is necessary to maintain energy balance in at least five clusters. However, emission from cooling gas may be partially absorbed. We also compute the flux supplied by turbulent heat transport (Cho et al. 2003) and find conductivity profiles which follow a strikingly similar temperature dependence to the conductivity values required to prevent cooling. Finally, we show that the cluster radio luminosities vary by over five orders of magnitude in objects with X-ray luminosities differing by no more than a factor of a few. This suggests that there is unlikely to be a straightforward correlation between the mechanical power provided by the radio lobes and the rate of energy loss in cooling flow clusters., Comment: Submitted to MNRAS

On the basis of the universal gas fraction in clusters of galaxies, we estimate that the effective thermal conductivity required to balance radiative cooling in the cores, where the gas temperature is 3-10keV, is about one tenth of the Spitzer rate. This confirms that thermal conduction can be important for the energy balance provided that it is not highly suppressed by magnetic fields in the gas. We determine the global effective conductivity in a sample of 29 clusters using published X-ray data on the inferred cooling rates and show that most lie between one and one tenth of the Spitzer rate. More work on the profiles in cooling flow clusters is required to test the conduction hypothesis further. We examine the possibility that conduction operates during galaxy formation, and show that it provides a simple explanation for the upper-mass cutoff in galaxy masses., Comment: 4 pages, 3 figures, submitted to MNRAS

Chandra and XMM-Newton observations have confirmed the presence of large temperature gradients within the cores of many relaxed clusters of galaxies. Here we investigate whether thermal conduction operating over those gradients can supply sufficient heat to offset radiative cooling. Narayan & Medvedev (2001) and Gruzinov (2002) have noted, using published results on cluster temperatures, that conduction within a factor of a few of the Spitzer rate is sufficient to balance bremsstrahlung cooling. From a detailed study of the temperature and emission measure profiles of Abell 2199 and Abell 1835, we find that the heat flux required by conduction is consistent with or below the rate predicted by Spitzer in the outer regions of the core. Conduction may therefore explain the lack of observational evidence for large mass cooling rates inferred from arguments based simply on radiative cooling, provided that conductivity is suppressed by no more than a factor of three below the full Spitzer rate. To stem cooling in the cluster centre, however, would necessitate conductivity values at least a factor of two larger than the Spitzer values, which we consider implausible. This may provide an explanation for the observed star formation and optical nebulosities in cluster cores. The solution is likely to be time dependent. We briefly discuss the possible origin of the cooler gas and the implications for massive galaxies., Comment: 5 pages, 4 figures, accepted by MNRAS. Minor changes following referee's comments