Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.Comment: 18 pages, 19 figures, 2 tables, submitted to A

Weak gravitational lensing with DEIMOS

We introduce a novel method for weak-lensing measurements, which is based on a mathematically exact deconvolution of the moments of the apparent brightness distribution of galaxies from the telescope's PSF. No assumptions on the shape of the galaxy or the PSF are made. The (de)convolution equations are exact for unweighted moments only, while in practice a compact weight function needs to be applied to the noisy images to ensure that the moment measurement yields significant results. We employ a Gaussian weight function, whose centroid and ellipticity are iteratively adjusted to match the corresponding quantities of the source. The change of the moments caused by the application of the weight function can then be corrected by considering higher-order weighted moments of the same source. Because of the form of the deconvolution equations, even an incomplete weighting correction leads to an excellent shear estimation if galaxies and PSF are measured with a weight function of identical size. We demonstrate the accuracy and capabilities of this new method in the context of weak gravitational lensing measurements with a set of specialized tests and show its competitive performance on the GREAT08 challenge data. A complete C++ implementation of the method can be requested from the authors.Comment: 7 pages, 3 figures, fixed typo in Eq. 1

Deconvolution with Shapelets

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.Comment: 9 pages, 9 figures, submitted to A&

Limitations for shapelet-based weak-lensing measurements

We seek to understand the impact on shape estimators obtained from circular and elliptical shapelet models under two realistic conditions: (a) only a limited number of shapelet modes is available for the model, and (b) the intrinsic galactic shapes are not restricted to shapelet models. We create a set of simplistic simulations, in which the galactic shapes follow a Sersic profile. By varying the Sersic index and applied shear, we quantify the amount of bias on shear estimates which arises from insufficient modeling. Additional complications due to PSF convolution, pixelation and pixel noise are also discussed. Steep and highly elliptical galaxy shapes cannot be accurately modeled within the circular shapelet basis system and are biased towards shallower and less elongated shapes. This problem can be cured partially by allowing elliptical basis functions, but for steep profiles elliptical shapelet models still depend critically on accurate ellipticity priors. As a result, shear estimates are typically biased low. Independently of the particular form of the estimator, the bias depends on the true intrinsic galaxy morphology, but also on the size and shape of the PSF. As long as the issues discussed here are not solved, the shapelet method cannot provide weak-lensing measurements with an accuracy demanded by upcoming missions and surveys, unless one can provide an accurate and reliable calibration, specific for the dataset under investigation.Comment: 8 pages, 5 figures, submitted to A&

Star formation efficiency in galaxy interactions and mergers: a statistical study

We investigate the enhancement of star formation efficiency in galaxy interactions and mergers, by numerical simulations of several hundred galaxy collisions. All morphological types along the Hubble sequence are considered in the initial conditions of the two colliding galaxies, with varying bulge-to-disk ratios and gas mass fractions. Different types of orbits are simulated, direct and retrograde, according to the initial relative energy and impact parameter, and the resulting star formation history is compared to that occuring in the two galaxies when they are isolated. Our principal results are: (1) retrograde encounters have a larger star formation efficiency (SFE) than direct encounters; (2) the amount of gas available in the galaxy is not the main parameter governing the SFE in the burst phase; (3) there is an anticorrelation between the amplitude of the star forming burst and the tidal forces exerted per unit of time, which is due to the large amount of gas dragged outside the galaxy by tidal tails in strong interactions; (4) globally, the Kennicutt-Schmidt law is retrieved statistically for isolated galaxies, interacting pairs and mergers; (5) the enhanced star formation is essentially occurring in nuclear starbursts, triggered by inward gas flows driven by non-axisymmetries in the galaxy disks. Direct encounters develop more pronounced asymmetries than retrograde ones. Based on these statistical results, we derive general laws for the enhancement of star formation in galaxy interactions and mergers, as a function of the main parameters of the encounter.Comment: 22 pages, 37 figures, 4 tables. Accepted on Astronomy & Astrophysic

L'étude des phénomènes de marée gravimétrique

Cet article présente une description des phénomènes de marée terrestre et des méthodes de mesure. Les résultats des profils mondiaux de marée gravimétrique sont corrigés des effets indirects liés aux marées océaniques. Une corrélation entre marées gravimétriques, flux de chaleur et tectonique globale est proposé

Calibration biases in measurements of weak lensing

As recently shown by Viola et al., the common (KSB) method for measuring weak gravitational shear creates a non-linear relation between the measured and the true shear of objects. We investigate here what effect such a non-linear calibration relation may have on cosmological parameter estimates from weak lensing if a simpler, linear calibration relation is assumed. We show that the non-linear relation introduces a bias in the shear-correlation amplitude and thus a bias in the cosmological parameters Omega_matter and sigma_8. Its direction and magnitude depends on whether the point-spread function is narrow or wide compared to the galaxy images from which the shear is measured. Substantial over- or underestimates of the cosmological parameters are equally possible, depending also on the variant of the KSB method. Our results show that for trustable cosmological-parameter estimates from measurements of weak lensing, one must verify that the method employed is free from ellipticity-dependent biases or monitor that the calibration relation inferred from simulations is applicable to the survey at hand.Comment: 5 pages, 3 figures, submitted to A&

First measurement of gravitational lensing by cosmic voids in SDSS

We report the first measurement of the diminutive lensing signal arising from matter underdensities associated with cosmic voids. While undetectable individually, by stacking the weak gravitational shear estimates around 901 voids detected in SDSS DR7 by Sutter et al. (2012a), we find substantial evidence for a depression of the lensing signal compared to the cosmic mean. This depression is most pronounced at the void radius, in agreement with analytical models of void matter profiles. Even with the largest void sample and imaging survey available today, we cannot put useful constraints on the radial dark-matter void profile. We invite independent investigations of our findings by releasing data and analysis code to the public at https://github.com/pmelchior/void-lensingComment: 6 pages, 5 figures, as accepted by MNRA

Biases in, and corrections to, KSB shear measurements

We analyse the KSB method to estimate gravitational shear from surface-brightness moments of small and noisy galaxy images. We identify three potentially problematic assumptions. These are: (1) While gravitational shear must be estimated from averaged galaxy images, KSB derives a shear estimate from each individual image and then takes the average. Since the two operations do not commute, KSB gives biased results. (2) KSB implicitly assumes that galaxy ellipticities are small, while weak gravitational lensing assures only that the change in ellipticity due to the shear is small. (3) KSB does not invert the convolution with the point-spread function, but gives an approximate PSF correction which - even for a circular PSF - holds only in the limit of circular sources. The effects of assumptions (2) and (3) partially counter-act in a way dependent on the width of the weight function and of the PSF. We quantitatively demonstrate the biases due to all assumptions, extend the KSB approach consistently to third order in the shear and ellipticity and show that this extension lowers the biases substantially. The issue of proper PSF deconvolution will be addressed in a forthcoming paper.Comment: 12 pages, 10 figures, MNRAS submitte