## Final Report Summary - WEBMAP (Mapping the Dark Web of the Cosmos)

Introduction

The general aim of this project was to find new measures to characterise the dark matter distribution of the very largest structures in the Universe, clusters of galaxies and the elusive web-like shape of the large-scale structure itself. This characterisation is most important since it probes the mechanisms of cosmic structure formation, which still faces many open questions such as: What is the underlying model of gravity, driving the creation of structure? Is Einstein's general relativity sufficient or does it need modification? What are the microscopic properties of dark matter? What is the impact of baryonic feedback?

The way to address these questions theoretically is by numerical simulations of structure formation. Different models are implemented in such simulations to probe the aforementioned questions on gravity, dark matter and baryonic physics. A cosmological interpretation is subsequently achieved by comparing the outcomes to real observations. Unfortunately, most current characterisations of real dark matter structure make significant over-simplifications in their description of the observations. They characterise complex structure by single numbers, such as mass, or a few numbers via a simple density profile. Such descriptions are generally not able to capture the subtle differences between models of structure formation. The aim of WEBMAP was hence to overcome these shortcomings and develop a characterisation measure which uses the full morphological information provided by observed maps of structure in the sky.

Implementation

WEBMAP addresses this research aim by implementing three main branches of research. a) The development of a theoretical framework to describe the morphology of dark matter maps. b) The development of numerical algorithms, which optimally map the distribution of dark matter in the sky. c) The application of these concepts to recent observations.

a) The morphology of dark matter maps

Within WEBMAP we developed a unique, interdisciplinary framework to characterise the 2D morphology of dark matter maps. The main idea is based on computer vision, a branch of digital image processing and computer science, which extracts information from image data in an automated fashion. As a first step we analyse a suite of numerical simulations which implements different models of structure formation, for example different models of gravity. We then extract surface mass density maps of the most prominent structures in these simulations and treat them as a digital image. A commonly used computer vision algorithm then extracts up to 3000 unique image descriptors from the data. Such image descriptors encode properties of the image such as pixel statistics, information on texture, complexity and homogeneity or the number of objects in the image which are clearly distinct from the background. We apply this to all images of a given structure formation model and group the data in the different models into classes. This forms a well-defined and controlled training set which we can then use to classify dark matter maps of unknown origin. For these, we again calculate the 3000 descriptors describing the image and then compare how similar they are to the different classes of our training set. This ultimately tells us to which class of structure formation a given model is most similar to and, most importantly, it does so by using the full morphological information in the image.

b) Optimal mass mapping algorithms

The question remains how these mass maps will be derived from observational data. While this is a trivial task in a numerical simulations, real dark matter distributions cannot be observed directly. This is why WEBMAP also developed an optimal tool to derive the distribution of dark matter in the sky from real observational data. Such a technique is commonly referred to as mass mapping. It is mainly based on a phenomenon known as gravitational lensing, which is the effect that light rays coming from distant galaxies are bent by the mass of intervening structure. This alters the apparent shape of these background galaxies and can directly be related to the underlying dark matter distribution that causes the distortion. Our newly developed algorithm implements a number of unique features to increase the quality of these maps to a level which enables us to use them for morphological characterisation. The first of these features is that the algorithm follows a so-called free-form approach, which means that no initial assumptions on the underlying distribution of dark matter is made. Secondly, the approach optimally adapts to the real distribution of input data from different sources, such as constraints from weak and strong gravitational lensing, X-ray surface brightness and temperature maps, or the Sunyaev-Zeldovich effect. This optimal adaption is reached by a mesh-free organisation of the reconstruction domain with the help of radial basis functions. This versatile tool is available in an efficient implementation, tested to deliver robust results and ready for the application to real data.

c) Application to real observational data

WEBMAP also applied the developed numerical methods to real observational data. We have two unique data sets in hand to map the distribution of structure and analyse their morphology. The first one is the Cluster Lensing and Supernova Survey with Hubble (CLASH), which uses the Hubble Space Telescope to image 25 clusters of galaxies, the largest gravitationally bound objects in the observable Universe. In a first study we used our mass mapping techniques to combine multiple constraints from gravitational lensing and produce multi-resolution mass maps of these clusters. We compared the results to numerical simulations in different models of structure formation including the standard LCDM model of cosmology. In general, we find good agreement between reality and this simplest model. Furthermore, we also used the same mass maps to study very distant lensed supernovae which, among other findings, led to the discovery of the first multiply-imaged supernova in the field of a massive galaxy cluster.

The second data set is the Kilo Degree Survey (KiDS), which, in contrast to CLASH, does not focus on single objects but delivers a wide-field galaxy survey covering a significant fraction of the sky. The KiDS survey is still on-going and in its data-acquisition phase. The WEBMAP project has made significant contributions to the KiDS main data product which is a catalogue of millions of galaxies that includes, among other properties, their position, redshift and measured shape. Such a catalogue can be used for gravtitational lensing applications, including our mass mapping effort. First cosmological results from the first observed 450 square degrees of the KiDS survey have been published recently. Within WEBMAP we also delivered the important aspect of shear calibration to the KiDS calibration. This is the careful and thorough calibration of the shape measurement process with the help of image simulations of galaxies. While the data set is growing, the next step will be to apply our mass mapping algorithm to the KiDS data and derive the morphological descriptors from the data which will then be compared to results from simulations.

The WEBMAP project with the research areas we just described resulted in 19 peer-reviewed publications, two press releases and one featured article in a broad audience magazine. Our newly developed approach to characterise dark matter structure based on computer vision can be used to distinguish any model of structure formation that has an effect on the 2D morphology of its contained structure. Our newly developed mass mapping technique has been successfully applied to CLASH data of real galaxy clusters, indicating that the standard LCDM model of cosmology is sufficient to describe the data. This has been confirmed by our thorough comparison to numerical simulations. The delivery of the CLASH mass maps has led to development in different areas besides our main cosmological results. The study of lensed supernovae in cluster fields has been boosted by our detailed view on the mass distribution in clusters and our most precise mass estimates of these objects has led to a new calibration of the mass scale in the Planck SZ catalogue. The KiDS survey is still on-going but first cosmological results have been published which show some intriguing discrepancies to the results of e.g. the Planck satellite.

The general aim of this project was to find new measures to characterise the dark matter distribution of the very largest structures in the Universe, clusters of galaxies and the elusive web-like shape of the large-scale structure itself. This characterisation is most important since it probes the mechanisms of cosmic structure formation, which still faces many open questions such as: What is the underlying model of gravity, driving the creation of structure? Is Einstein's general relativity sufficient or does it need modification? What are the microscopic properties of dark matter? What is the impact of baryonic feedback?

The way to address these questions theoretically is by numerical simulations of structure formation. Different models are implemented in such simulations to probe the aforementioned questions on gravity, dark matter and baryonic physics. A cosmological interpretation is subsequently achieved by comparing the outcomes to real observations. Unfortunately, most current characterisations of real dark matter structure make significant over-simplifications in their description of the observations. They characterise complex structure by single numbers, such as mass, or a few numbers via a simple density profile. Such descriptions are generally not able to capture the subtle differences between models of structure formation. The aim of WEBMAP was hence to overcome these shortcomings and develop a characterisation measure which uses the full morphological information provided by observed maps of structure in the sky.

Implementation

WEBMAP addresses this research aim by implementing three main branches of research. a) The development of a theoretical framework to describe the morphology of dark matter maps. b) The development of numerical algorithms, which optimally map the distribution of dark matter in the sky. c) The application of these concepts to recent observations.

a) The morphology of dark matter maps

Within WEBMAP we developed a unique, interdisciplinary framework to characterise the 2D morphology of dark matter maps. The main idea is based on computer vision, a branch of digital image processing and computer science, which extracts information from image data in an automated fashion. As a first step we analyse a suite of numerical simulations which implements different models of structure formation, for example different models of gravity. We then extract surface mass density maps of the most prominent structures in these simulations and treat them as a digital image. A commonly used computer vision algorithm then extracts up to 3000 unique image descriptors from the data. Such image descriptors encode properties of the image such as pixel statistics, information on texture, complexity and homogeneity or the number of objects in the image which are clearly distinct from the background. We apply this to all images of a given structure formation model and group the data in the different models into classes. This forms a well-defined and controlled training set which we can then use to classify dark matter maps of unknown origin. For these, we again calculate the 3000 descriptors describing the image and then compare how similar they are to the different classes of our training set. This ultimately tells us to which class of structure formation a given model is most similar to and, most importantly, it does so by using the full morphological information in the image.

b) Optimal mass mapping algorithms

The question remains how these mass maps will be derived from observational data. While this is a trivial task in a numerical simulations, real dark matter distributions cannot be observed directly. This is why WEBMAP also developed an optimal tool to derive the distribution of dark matter in the sky from real observational data. Such a technique is commonly referred to as mass mapping. It is mainly based on a phenomenon known as gravitational lensing, which is the effect that light rays coming from distant galaxies are bent by the mass of intervening structure. This alters the apparent shape of these background galaxies and can directly be related to the underlying dark matter distribution that causes the distortion. Our newly developed algorithm implements a number of unique features to increase the quality of these maps to a level which enables us to use them for morphological characterisation. The first of these features is that the algorithm follows a so-called free-form approach, which means that no initial assumptions on the underlying distribution of dark matter is made. Secondly, the approach optimally adapts to the real distribution of input data from different sources, such as constraints from weak and strong gravitational lensing, X-ray surface brightness and temperature maps, or the Sunyaev-Zeldovich effect. This optimal adaption is reached by a mesh-free organisation of the reconstruction domain with the help of radial basis functions. This versatile tool is available in an efficient implementation, tested to deliver robust results and ready for the application to real data.

c) Application to real observational data

WEBMAP also applied the developed numerical methods to real observational data. We have two unique data sets in hand to map the distribution of structure and analyse their morphology. The first one is the Cluster Lensing and Supernova Survey with Hubble (CLASH), which uses the Hubble Space Telescope to image 25 clusters of galaxies, the largest gravitationally bound objects in the observable Universe. In a first study we used our mass mapping techniques to combine multiple constraints from gravitational lensing and produce multi-resolution mass maps of these clusters. We compared the results to numerical simulations in different models of structure formation including the standard LCDM model of cosmology. In general, we find good agreement between reality and this simplest model. Furthermore, we also used the same mass maps to study very distant lensed supernovae which, among other findings, led to the discovery of the first multiply-imaged supernova in the field of a massive galaxy cluster.

The second data set is the Kilo Degree Survey (KiDS), which, in contrast to CLASH, does not focus on single objects but delivers a wide-field galaxy survey covering a significant fraction of the sky. The KiDS survey is still on-going and in its data-acquisition phase. The WEBMAP project has made significant contributions to the KiDS main data product which is a catalogue of millions of galaxies that includes, among other properties, their position, redshift and measured shape. Such a catalogue can be used for gravtitational lensing applications, including our mass mapping effort. First cosmological results from the first observed 450 square degrees of the KiDS survey have been published recently. Within WEBMAP we also delivered the important aspect of shear calibration to the KiDS calibration. This is the careful and thorough calibration of the shape measurement process with the help of image simulations of galaxies. While the data set is growing, the next step will be to apply our mass mapping algorithm to the KiDS data and derive the morphological descriptors from the data which will then be compared to results from simulations.

The WEBMAP project with the research areas we just described resulted in 19 peer-reviewed publications, two press releases and one featured article in a broad audience magazine. Our newly developed approach to characterise dark matter structure based on computer vision can be used to distinguish any model of structure formation that has an effect on the 2D morphology of its contained structure. Our newly developed mass mapping technique has been successfully applied to CLASH data of real galaxy clusters, indicating that the standard LCDM model of cosmology is sufficient to describe the data. This has been confirmed by our thorough comparison to numerical simulations. The delivery of the CLASH mass maps has led to development in different areas besides our main cosmological results. The study of lensed supernovae in cluster fields has been boosted by our detailed view on the mass distribution in clusters and our most precise mass estimates of these objects has led to a new calibration of the mass scale in the Planck SZ catalogue. The KiDS survey is still on-going but first cosmological results have been published which show some intriguing discrepancies to the results of e.g. the Planck satellite.