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

A PCA-based automated finder for galaxy-scale strong lenses

We present an algorithm using Principal Component Analysis (PCA) to subtract galaxies from imaging data, and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is optimized to find full or partial Einstein rings. Starting from a pre-selection of potential massive galaxies, we first perform a PCA to build a set of basis vectors. The galaxy images are reconstructed using the PCA basis and subtracted from the data. We then filter the residual image with two different methods. The first uses a curvelet (curved wavelets) filter of the residual images to enhance any curved/ring feature. The resulting image is transformed in polar coordinates, centered on the lens galaxy center. In these coordinates, a ring is turned into a line, allowing us to detect very faint rings by taking advantage of the integrated signal-to-noise in the ring (a line in polar coordinates). The second way of analysing the PCA-subtracted images identifies structures in the residual images and assesses whether they are lensed images according to their orientation, multiplicity and elongation. We apply the two methods to a sample of simulated Einstein rings, as they would be observed with the ESA Euclid satellite in the VIS band. The polar coordinates transform allows us to reach a completeness of 90% and a purity of 86%, as soon as the signal-to-noise integrated in the ring is higher than 30, and almost independent of the size of the Einstein ring. Finally, we show with real data that our PCA-based galaxy subtraction scheme performs better than traditional subtraction based on model fitting to the data. Our algorithm can be developed and improved further using machine learning and dictionary learning methods, which would extend the capabilities of the method to more complex and diverse galaxy shapes

Only marginal alignment of disc galaxies

Testing theories of angular-momentum acquisition of rotationally supported disc galaxies is the key to understand the formation of this type of galaxies. The tidal-torque theory tries to explain this acquisition process in a cosmological framework and predicts positive autocorrelations of angular-momentum orientation and spiral-arm handedness on distances of 1Mpc/h. This disc alignment can also cause systematic effects in weak-lensing measurements. Previous observations claimed discovering such correlations but did not account for errors in redshift, ellipticity and morphological classifications. We explain how to rigorously propagate all important errors. Analysing disc galaxies in the SDSS database, we find that positive autocorrelations of spiral-arm handedness and angular-momentum orientations on distances of 1Mpc/h are plausible but not statistically significant. This result agrees with a simple hypothesis test in the Local Group, where we find no evidence for disc alignment. Moreover, we demonstrate that ellipticity estimates based on second moments are strongly biased by galactic bulges, thereby corrupting correlation estimates and overestimating the impact of disc alignment on weak-lensing studies. Finally, we discuss the potential of future sky surveys. We argue that photometric redshifts have too large errors, i.e., PanSTARRS and LSST cannot be used. We also discuss potentials and problems of front-edge classifications of galaxy discs in order to improve estimates of angular-momentum orientation.Comment: 20 pages, 15 figures; accepted by MNRA