Statistical uncertainties and systematic errors in weak lensing mass estimates of galaxy clusters

Upcoming and ongoing large area weak lensing surveys will also discover large samples of galaxy clusters. Accurate and precise masses of galaxy clusters are of major importance for cosmology, for example, in establishing well calibrated observational halo mass functions for comparison with cosmological predictions. We investigate the level of statistical uncertainties and sources of systematic errors expected for weak lensing mass estimates. Future surveys that will cover large areas on the sky, such as Euclid or LSST and to lesser extent DES, will provide the largest weak lensing cluster samples with the lowest level of statistical noise regarding ensembles of galaxy clusters. However, the expected low level of statistical uncertainties requires us to scrutinize various sources of systematic errors. In particular, we investigate the bias due to cluster member galaxies which are erroneously treated as background source galaxies due to wrongly assigned photometric redshifts. We find that this effect is significant when referring to stacks of galaxy clusters. Finally, we study the bias due to miscentring, i.e., the displacement between any observationally defined cluster centre and the true minimum of its gravitational potential. The impact of this bias might be significant with respect to the statistical uncertainties. However, complementary future missions such as eROSITA will allow us to define stringent priors on miscentring parameters which will mitigate this bias significantly.Comment: 14 pages, 7 figures; accepted for publication in MNRA

Weighing the dark : cosmological applications of gravitational lensing

According to Einstein's theory of general relativity the light of an object is deflected by a mass in its foreground. The deflections can be very weak or so strong that they are visible by eye yielding strangely distorted arcs or even multiple images of the same source. Measurements of strong or weak lensing let us infer the total mass of the light-deflecting object which is an important cosmological observable. In this thesis we employ gravitational lensing to measure key cosmological observables, such as dark matter and dark energy. Instead of observing the effects of gravitational lensing around single galaxies or galaxy clusters, the Universe itself can be used as a lens: light travelling to us through the cosmic large-scale structure is also weakly lensed by it. Measuring this effect at different cosmic times allows us to infer the evolution of structure in the cosmic web. Hence, we can study how that is affected by dark energy or massive neutrinos. A key result of this thesis is that we find a lower amplitude for the clustering of matter at fixed matter density than that inferred from the most recent measurements of the cosmic microwave background radiation by the Planck satellite

A direct measurement of tomographic lensing power spectra from CFHTLenS

We measure the weak gravitational lensing shear power spectra and their cross-power in two photometric redshift bins from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). The measurements are performed directly in multipole space in terms of adjustable band powers. For the extraction of the band powers from the data we have implemented and extended a quadratic estimator, a maximum likelihood method that allows us to readily take into account irregular survey geometries, masks, and varying sampling densities. We find the 68 per cent credible intervals in the $\sigma_8$-$\Omega_{\rm m}$-plane to be marginally consistent with results from $Planck$ for a simple five parameter $\Lambda$CDM model. For the projected parameter $S_8 \equiv \sigma_8(\Omega_{\rm m}/0.3)^{0.5}$ we obtain a best-fitting value of $S_8 = 0.768_{-0.039}^{+0.045}$. This constraint is consistent with results from other CFHTLenS studies as well as the Dark Energy Survey. Our most conservative model, including modifications to the power spectrum due to baryon feedback and marginalization over photometric redshift errors, yields an upper limit on the total mass of three degenerate massive neutrinos of $\Sigma m_\nu < 4.53 \, {\rm eV}$ at 95 per cent credibility, while a Bayesian model comparison does not favour any model extension beyond a simple five parameter $\Lambda$CDM model. Combining the shear likelihood with $Planck$ breaks the $\sigma_8$-$\Omega_{\rm m}$-degeneracy and yields $\sigma_8=0.818 \pm 0.013$ and $\Omega_{\rm m} = 0.300 \pm 0.011$ which is fully consistent with results from $Planck$ alone.Comment: 19 pages, 12 figures, 7 tables. Accepted for publication in MNRAS. Minor corrections and updates with respect to previous versio

When tension is just a fluctuation: How noisy data affect model comparison

Summary statistics of likelihood, such as Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in these model comparison statistics. For a realistic case of cosmological inference from large-scale structure, we show that the logarithm of the Bayes factor attains scatter of order unity, increasing significantly with stronger tension between the models under comparison. We develop an approximate procedure that quantifies the sampling distribution of the evidence at a small additional computational cost and apply it to real data to demonstrate the impact of the scatter, which acts to reduce the significance of any model discrepancies. Data compression is highlighted as a potential avenue to suppressing noise in the evidence to negligible levels, with a proof of concept demonstrated using Planck cosmic microwave background data

Quantifying Suspiciousness Within Correlated Data Sets

We propose a principled Bayesian method for quantifying tension between correlated datasets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness statistic, which is insensitive to priors. Our method uses global summary statistics, and as such it can be used as a diagnostic for internal consistency. We show how our approach can be combined with methods that use parameter space and data space to identify the existing internal discrepancies. As an example, we use it to test the internal consistency of the KiDS-450 data in 4 photometric redshift bins, and to recover controlled internal discrepancies in simulated KiDS data. We propose this as a diagnostic of internal consistency for present and future cosmological surveys, and as a tension metric for data sets that have non-negligible correlation, such as LSST and Euclid

Quantifying Suspiciousness Within Correlated Data Sets

We propose a principled Bayesian method for quantifying tension between correlated datasets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness statistic, which is insensitive to priors. Our method uses global summary statistics, and as such it can be used as a diagnostic for internal consistency. We show how our approach can be combined with methods that use parameter space and data space to identify the existing internal discrepancies. As an example, we use it to test the internal consistency of the KiDS-450 data in 4 photometric redshift bins, and to recover controlled internal discrepancies in simulated KiDS data. We propose this as a diagnostic of internal consistency for present and future cosmological surveys, and as a tension metric for data sets that have non-negligible correlation, such as LSST and Euclid.Comment: 7 pages, 4 figure

Infrared properties of Active OB stars in the Magellanic Clouds from the Spitzer SAGE Survey

We present a study of the infrared properties of 4922 spectroscopically confirmed massive stars in the Large and Small Magellanic Clouds, focusing on the active OB star population. Besides OB stars, our sample includes yellow and red supergiants, Wolf-Rayet stars, Luminous Blue Variables (LBVs) and supergiant B[e] stars. We detect a distinct Be star sequence, displaced to the red, and find a higher fraction of Oe and Be stars among O and early-B stars in the SMC, respectively, when compared to the LMC, and that the SMC Be stars occur at higher luminosities. We also find photometric variability among the active OB population and evidence for transitions of Be stars to B stars and vice versa. We furthermore confirm the presence of dust around all the supergiant B[e] stars in our sample, finding the shape of their spectral energy distributions (SEDs) to be very similar, in contrast to the variety of SED shapes among the spectrally variable LBVs.Comment: 5 pages, 1 figure, to appear in the proceedings of the IAUS 272 on "Active OB stars: structure, evolution, mass loss and critical limits" (Paris, July 19-23, 2010), Cambridge University Press. Editors C. Neiner, G. Wade, G. Meynet and G. Peter

A Bayesian quantification of consistency in correlated data sets

We present three tiers of Bayesian consistency tests for the general case of correlated data sets. Building on duplicates of the model parameters assigned to each data set, these tests range from Bayesian evidence ratios as a global summary statistic, to posterior distributions of model parameter differences, to consistency tests in the data domain derived from posterior predictive distributions. For each test, we motivate meaningful threshold criteria for the internal consistency of data sets. Without loss of generality we focus on mutually exclusive, correlated subsets of the same data set in this work. As an application, we revisit the consistency analysis of the two-point weak-lensing shear correlation functions measured from KiDS-450 data. We split this data set according to large versus small angular scales, tomographic redshift bin combinations, and estimator type. We do not find any evidence for significant internal tension in the KiDS-450 data, with significances below 3σ in all cases. Software and data used in this analysis can be found at http://kids.strw.leidenuniv.nl/sciencedata.php