Weak-lensing shear measurement with machine learning Teaching artificial neural networks about feature noise

Cosmic shear, that is weak gravitational lensing by the large-scale matter structure of the Universe, is a primary cosmological probe for several present and upcoming surveys investigating dark matter and dark energy, such as Euclid or WFIRST. The probe requires an extremely accurate measurement of the shapes of millions of galaxies based on imaging data. Crucially, the shear measurement must address and compensate for a range of interwoven nuisance effects related to the instrument optics and detector, noise in the images, unknown galaxy morphologies, colors, blending of sources, and selection effects. This paper explores the use of supervised machine learning as a tool to solve this inverse problem. We present a simple architecture that learns to regress shear point estimates and weights via shallow artificial neural networks. The networks are trained on simulations of the forward observing process, and take combinations of moments of the galaxy images as inputs. A challenging peculiarity of the shear measurement task, in terms of machine learning applications, is the combination of the noisiness of the input features and the requirements on the statistical accuracy of the inverse regression. To address this issue, the proposed training algorithm minimizes bias over multiple realizations of individual source galaxies, reducing the sensitivity to properties of the overall sample of source galaxies. Importantly, an observational selection function of these source galaxies can be straightforwardly taken into account via the weights. We first introduce key aspects of our approach using toy-model simulations, and then demonstrate its potential on images mimicking Euclid data. Finally, we analyze images from the GREAT3 challenge, obtaining competitively low multiplicative and additive shear biases despite the use of a simple training set. We conclude that the further development of suited machine learning approaches is of high interest to meet the stringent requirements on the shear measurement in current and future surveys. We make a demonstration implementation of our technique publicly available.

Machine-learning methods for weak lensing analysis of the ESA Euclid sky survey

Thibault Adrien Kuntzer

A clear picture has emerged from the last three decades of research: our Universe is expanding at an accelerated rate. The cause of this expansion remains elusive, but in essence acts as a repulsive force. This so-called dark energy represents about 69% of the energy content in the Universe. A further 26% of the energy is contained in dark matter, a form of matter that is invisible electromagnetically. Understanding the nature of these two major components of the Universe is at the top of the list of unsolved problems. To unveil answers, ambitious experiments are devised to survey an ever larger and deeper fraction of the sky. One such project is the European Space Agency (ESA) telescope Euclid, which will probe dark matter and infer desperately needed information about dark energy. Because light bundles follow null geodesics, their trajectories are affected by the mass distribution along the line of sight, which includes dark matter. This is gravitational lensing. In the vast majority of cases, deformations of the source objects are weak, and profiles are slightly sheared. The nature of the dark components can be fathomed by measuring the shear over a large fraction of the sky. The shear can be recovered by a statistical analysis of a large number of objects. In this thesis, we take on the development of the necessary tools to measure the shear. Shear measurement techniques have been developed and improved for more than two decades. Their performance, however, do not meet the unprecedented requirements imposed by future surveys. Requirements trickle down from the targeted determination of the cosmological parameters. We aim at preparing novel and innovative methods. These methods are tested against the Euclid requirements. Contributions can be classified into two major themes. A key step in the processing of weak gravitational lensing data is the correction of image deformations generated by the instrument itself. This point spread function (PSF) correction is the first theme. The second is the shear measurement itself, and in particular, producing accurate measurements. We explore machine-learning methods, and notably artificial neural networks. These methods are, for the most part, data-driven. Schemes must first be trained against a representative sample of data. Crafting optimal training sets and choosing the method parameters can be crucial for the performance. We dedicate an important fraction of this dissertation to describing simulations behind the datasets and motivating our parameter choices. We propose schemes to build a clean selection of stars and model the PSF to the Euclid requirements in the first part of this thesis. Shear measurements are notoriously biased because of their small size and their low intensity. We introduce an approach that produces unbiased estimates of shear. This is achieved by processing data from any shape measurement technique with artificial neural networks, and predicting corrected estimates of the shape of the galaxies, or directly the shear. We demonstrate that simple networks with simple trainings are sufficient to reach the Euclid requirements on shear measurements.

EPFL2018

Weak Gravitational Lensing by Large-Scale Structures

Marc Gentile

There is now very strong evidence that our Universe is undergoing an accelerated expansion period as if it were under the influence of a gravitationally repulsive “dark energy” component. Furthermore, most of the mass of the Universe seems to be in the form of non-luminous matter, the so-called “dark matter”. Together, these “dark” components, whose nature remains unknown today, represent around 96 % of the matter-energy budget of the Universe. Unraveling the true nature of the dark energy and dark matter has thus, obviously, become one of the primary goals of present-day cosmology. Weak gravitational lensing, or weak lensing for short, is the effect whereby light emitted by distant galaxies is slightly deflected by the tidal gravitational fields of intervening foreground structures. Because it only relies on the physics of gravity, weak lensing has the unique ability to probe the distribution of mass in a direct and unbiased way. This technique is at present routinely used to study the dark matter, typical applications being the mass reconstruction of galaxy clusters and the study of the properties of dark halos surrounding galaxies. Another and more recent application of weak lensing, on which we focus in this thesis, is the analysis of the cosmological lensing signal induced by large-scale structures, the so-called “cosmic shear”. This signal can be used to measure the growth of structures and the expansion history of the Universe, which makes it particularly relevant to the study of dark energy. Of all weak lensing effects, the cosmic shear is the most subtle and its detection requires the accurate analysis of the shapes of millions of distant, faint galaxies in the near infrared. So far, the main factor limiting cosmic shear measurement accuracy has been the relatively small sky areas covered. Next-generation of wide-field, multicolor surveys will, however, overcome this hurdle by covering a much larger portion of the sky with improved image quality. The resulting statistical errors will then become subdominant compared to systematic errors, the latter becoming instead the main source of uncertainty. In fact, uncovering key properties of dark energy will only be achievable if these systematics are well understood and reduced to the required level. The major sources of uncertainty resides in the shape measurement algorithm used, the convolution of the original image by the instrumental and possibly atmospheric point spread function (PSF), the pixelation effect caused by the integration of light falling on the detector pixels and the degradation caused by various sources of noise. Measuring the Cosmic shear thus entails solving the difficult inverse problem of recovering the shear signal from blurred, pixelated and noisy galaxy images while keeping errors within the limits demanded by future weak lensing surveys. Reaching this goal is not without challenges. In fact, the best available shear measurement methods would need a tenfold improvement in accuracy to match the requirements of a space mission like Euclid from ESA, scheduled at the end of this decade. Significant progress has nevertheless been made in the last few years, with substantial contributions from initiatives such as GREAT (GRavitational lEnsing Accuracy Testing) challenges. The main objective of these open competitions is to foster the development of new and more accurate shear measurement methods. We start this work with a quick overview of modern cosmology: its fundamental tenets, achievements and the challenges it faces today. We then review the theory of weak gravitational lensing and explains how it can make use of cosmic shear observations to place constraints on cosmology. The last part of this thesis focuses on the practical challenges associated with the accurate measurement of the cosmic shear. After a review of the subject we present the main contributions we have brought in this area: the development of the gfit shear measurement method, new algorithms for point spread function (PSF) interpolation and image denoising. The gfit method emerged as one of the top performers in the GREAT10 Galaxy Challenge. It essentially consists in fitting two-dimensional elliptical Sérsic light profiles to observed galaxy image in order to produce estimates for the shear power spectrum. PSF correction is automatic and an efficient shape-preserving denoising algorithm can be optionally applied prior to fitting the data. PSF interpolation is also an important issue in shear measurement because the PSF is only known at star positions while PSF correction has to be performed at any position on the sky. We have developed innovative PSF interpolation algorithms on the occasion of the GREAT10 Star Challenge, a competition dedicated to the PSF interpolation problem. Our participation was very successful since one of our interpolation method won the Star Challenge while the remaining four achieved the next highest scores of the competition. Finally we have participated in the development of a wavelet-based, shape-preserving denoising method particularly well suited to weak lensing analysis.

EPFL2013

Astrophysical applications of gravitationally lensed quasars

Alexander Eigenbrod

Gravitational lensing describes how light is deflected as it passes in the vicinity of a mass distribution. The amplitude of the deflection is proportional to the mass of the deflector, called "gravitational lens", and is generally weak, even for large masses. The faintness of this phenomenon explains why gravitational lensing remained essentially unobserved until the late 1970s (only gravitational lensing by the Sun has been observed during the solar eclipse of 1919). Before that time, gravitational lensing was considered merely as a theoretical curiosity. However, the situation dramatically changed with the discovery of the first extragalactic gravitational lens in 1979. Since then, together with the technological progress of astronomical instruments, gravitational lensing has turned from a curiosity into a powerful tool to address important astrophysical and cosmological questions. The present thesis focuses on applications related to gravitationally lensed quasars. Quasars are active galactic nuclei, where matter is heated up as it spirals down onto the central supermassive black hole. When a galaxy is located on the line of sight to a distant quasar, it acts as a gravitational lens and produces multiple images of this background source. The light of the quasar follows different paths for each of its images. Thus, variations of the intrinsic quasar luminosity are observed at different times in each image. The time delays between the images can be used to determine the Hubble constant H0, because they are inversely proportional to H0. This constant describes the current expansion rate of the Universe, and is one of the fundamental parameters of cosmological models. Many efforts have been spent over the years to determine H0, but its value is still poorly constrained. Gravitational lensing has the potential to noticeably decrease the uncertainty of H0. In practice, this requires regular and long-term monitoring of lensed quasars. We have run a series of numerical simulations to both optimize the available telescope time, and measure the time delays with an accuracy of a few percent. The results of these simulations are presented in the form of compact plots to be used to optimize the observational strategy of present and future monitoring programs. Once the time delays are measured, one can infer estimates of H0, provided several other observational constraints are available. A key element to accurately convert time delays into H0 is the redshift of the lensing galaxy. These redshift measurements are difficult because lensing galaxies are generally hidden in the glare of the much brighter quasar images. As a consequence, lens redshifts are often poorly constrained or even completely unknown. We have acquired spectroscopic data of sixteen lensing galaxies with the Very Large Telescope located in Chile. In combination with a powerful deconvolution algorithm, we determine the redshift of these sixteen lensing galaxies, which represents about 25% of all currently known quasar lensing galaxies. These results are useful for both H0 determinations and statistical studies of gravitational lenses, which can be used to provide new constraints on cosmological parameters. While the first part of this thesis focuses on the acquisition of observational constraints for the lens models, the main part consists in using the phenomenon of microlensing to determine the energy profile (or spatial structure) of quasar accretion disks. Microlensing is produced by the stars located in the lensing galaxy. These stars act as secondary lenses, and are called microlenses. Since the stars are moving in the galaxy, they induce flux and color variations in the images of the lensed quasar. These effects can be used as a natural telescope to probe the still mysterious inner structures of quasars with a spatial resolution about ten thousand times better than the capacities of current astronomical instruments, including the Very Large Telescope Interferometer. We present a three-year long spectrophotometric monitoring of the lensed quasar QSO 2237+0305, also known as the Einstein Cross, conducted at the Very Large Telescope. This monitoring reveals significant microlensing-induced variations in the spectra of the quasar images. In a subsequent analysis, we find that the source responsible for the optical and ultraviolet continuum has an energy profile well reproduced by a power-law R α λζ with ζ = 1.2 ± 0.3, where R is the size of the source emitting at wavelength λ. This agrees with the predictions of the standard thin accretion disk model and is, so far, the most accurate determination of a quasar energy profile. As a complement to our microlensing study, we have obtained high spectral and spatial resolution observations of the lensing galaxy of QSO 2237+0305. Our spectroscopic data are acquired with the SINFONI, FLAMES, and FORS2 spectrographs of the Very Large Telescope. We describe the reduction of these data, and provide the currently best and most complete determination of the kinematics of a gravitational lens. The comparison of our data with previously published dynamical models suggests that those may have overestimated the mass of the galaxy bulge. Thus, new and more sophisticated models are required. These models, combined with gravitational lensing, will provide two independent constraints on the mass distribution. This will allow to better determine the quantity and distribution of dark matter in this lensing galaxy, and especially in its extended halo.

EPFL2008