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 MNRA
Context. The control of systematic effects when measuring background galaxy shapes is one of the main challenges for cosmic shear analyses. Aims. Study the fundamental limitations on shear accuracy due to the measurement of the point spread function (PSF) from the finite number of stars that are available. We translate the accuracy required for cosmological parameter estimation to the minimum number of stars over which the PSF must be calibrated. Methods. We characterise the error made in the shear arising from errors on the PSF. We consider different PSF models, from a simple elliptical Gaussian to various shapelet parametrisations. First we 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 the elliptical Gaussian PSF. Results. 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. This means that these small scales should not be used to constrain cosmology unless the instrument and the observing strategy are optimised to make this variability extremely small. The minimum number of stars varies with the square of the star Signal-to-Noise Ratio, with the complexity of the PSF and with the pixel size. 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. Conclusions. 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. Due to the simplicity of our models these results should be interpreted as optimistic and therefore provide a measure of a systematic "floor' intrinsic to shape measurements.
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 other shape measurement methods. The best methods achieve sub‐per cent average biases. We find a strong dependence on accuracy as a function of signal‐to‐noise ratio, 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 be brought. This provides a foundation for a better understanding of the strengths and limitations of shape measurement methods.
Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear Testing Programmes and Gravitational lensing Accuracy Testing challenges, measuring galaxy shears is a non-trivial task: various methods introduce different systematic biases which have to be accounted for. We investigate how pixel noise on the image affects the bias on shear estimates from a maximum likelihood forward model-fitting approach using a sum of co-elliptical Sérsic profiles, in complement to the theoretical approach of an associated paper. We evaluate the bias using a simple but realistic galaxy model and find that the effects of noise alone can cause biases of the order of 1-10 per cent on measured shears, which is significant for current and future lensing surveys. We evaluate a simulation-based calibration method to create a bias model as a function of galaxy properties and observing conditions. This model is then used to correct the simulated measurements. We demonstrate that, for the simple case in which the correct range of galaxy models is used in the fit, the calibration method can reduce noise bias to the level required for estimating cosmic shear in upcoming lensing surveys.
We present and describe IM3SHAPE, a new publicly available galaxy shape measurement code for weak gravitational lensing shear. IM3SHAPE performs a maximum likelihood fit of a bulgeplus-disc galaxy model to noisy images, incorporating an applied point spread function. We detail challenges faced and choices made in its design and implementation, and then discuss various limitations that affect this and other maximum likelihood methods. We assess the bias arising from fitting an incorrect galaxy model using simple noise-free images and find that it should not be a concern for current cosmic shear surveys. We test IM3SHAPE on the GREAT08 Challenge image simulations, and meet the requirements for upcoming cosmic shear surveys in the case that the simulations are encompassed by the fitted model, using a simple correction for image noise bias. For the fiducial branch of GREAT08 we obtain a negligible additive shear bias and sub-two percent level multiplicative bias, which is suitable for analysis of current surveys. We fall short of the sub-percent level requirement for upcoming surveys, which we attribute to a combination of noise bias and the mis-match between our galaxy model and the model used in the GREAT08 simulations. We meet the requirements for current surveys across all branches of GREAT08, except those with small or high noise galaxies, which we would cut from our analysis. Using the GREAT08 metric we we obtain a score of Q=717 for the usable branches, relative to the goal of Q=1000 for future experiments. The code is freely available from https://bitbucket.org/joezuntz/im3shape.
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