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In simulation-based models of the galaxy-halo connection, theoretical predictions for galaxy clustering and lensing are typically made based on Monte Carlo realizations of a mock universe. In this paper, we use Subhalo Abundance Matching (SHAM) as a toy model to introduce an alternative to stochastic predictions based on mock population, demonstrating how to make simulation-based predictions for clustering and lensing that are both exact and differentiable with respect to the parameters of the model. Conventional implementations of SHAM are based on iterative algorithms such as Richardson-Lucy deconvolution; here we use the JAX library for automatic differentiation to train SHAMNet, a neural network that accurately approximates the stellar-to-halo mass relation (SMHM) defined by abundance matching. In our approach to making differentiable predictions for large scale structure, we map parameterized PDFs onto each simulated halo, and calculate gradients of summary statistics of the galaxy distribution by using autodiff to propagate the gradients of the SMHM through the statistical estimators used to measure one- and two-point functions. Our techniques are quite general, and we conclude with an overview of how they can be applied in tandem with more complex, higher-dimensional models, creating the capability to make differentiable predictions for the multi-wavelength universe of galaxies., 11 pages, 6 appendices, version accepted for publication by the Open Journal of Astrophysics

Using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first $k$-cut cosmic shear analysis constraining both $\Lambda$CDM and $f(R)$ Hu-Sawicki modified gravity. To generate the $f(R)$ cosmic shear theory vector, we use the matter power spectrum emulator trained on COLA (COmoving Lagrangian Acceleration) simulations. The $k$-cut method is used to significantly down-weight sensitivity to small scale ($k > 1 \ h {\rm Mpc }^{-1}$) modes in the matter power spectrum where the emulator is less accurate, while simultaneously ensuring our results are robust to baryonic feedback model uncertainty. We have also developed a test to ensure that the effects of poorly modeled small scales are nulled as intended. For $\Lambda$CDM we find $S_8 = \sigma_8 (\Omega_m / 0.3) ^ {0.5} = 0.789 ^{+0.039}_{-0.022}$, while the constraints on the $f(R)$ modified gravity parameters are prior dominated. In the future, the $k$-cut method could be used to constrain a large number of theories of gravity where computational limitations make it infeasible to model the matter power spectrum down to extremely small scales.

Testing a subset of viable cosmological models beyond general relativity, with implications for cosmic acceleration and the dark energy associated with it, is within the reach of Rubin Observatory Legacy Survey of Space and Time (LSST) and a part of its endeavor. Deviations from $\mathrm{GR}\text{\ensuremath{-}}w(z)\mathrm{CDM}$ models can manifest in the growth rate of structure and lensing, as well as in screening effects on nonlinear scales. We explore the constraining power of small-scale deviations predicted by the $f(R)$ Hu-Sawicki modified gravity candidate, by emulating this model with COLA (comoving Lagrangian acceleration) simulations. We present the experimental design, data generation, and interpolation schemes in cosmological parameters and across redshifts for the emulation of the boost in the power spectra due to modified gravity effects. Three preliminary applications of the emulator highlight the sensitivity to cosmological parameters, Fisher forecasting and Markov chain Monte Carlo inference for a fiducial cosmology. This emulator will play an important role for future cosmological analysis handling the formidable amount of data expected from Rubin Observatory LSST.

The problem of anomaly detection in astronomical surveys is becoming increasingly important as data sets grow in size. We present the results of an unsupervised anomaly detection method using a Wasserstein generative adversarial network (WGAN) on nearly one million optical galaxy images in the Hyper Suprime-Cam (HSC) survey. The WGAN learns to generate realistic HSC-like galaxies that follow the distribution of the data set; anomalous images are defined based on a poor reconstruction by the generator and outlying features learned by the discriminator. We find that the discriminator is more attuned to potentially interesting anomalies compared to the generator, and compared to a simpler autoencoder-based anomaly detection approach, so we use the discriminator-selected images to construct a high-anomaly sample of $\sim$13,000 objects. We propose a new approach to further characterize these anomalous images: we use a convolutional autoencoder to reduce the dimensionality of the residual differences between the real and WGAN-reconstructed images and perform UMAP clustering on these. We report detected anomalies of interest including galaxy mergers, tidal features, and extreme star-forming galaxies. A follow-up spectroscopic analysis of one of these anomalies is detailed in the Appendix; we find that it is an unusual system most likely to be a metal-poor dwarf galaxy with an extremely blue, higher-metallicity HII region. We have released a catalog with the WGAN anomaly scores; the code and catalog are available at https://github.com/kstoreyf/anomalies-GAN-HSC, and our interactive visualization tool for exploring the clustered data is at https://weirdgalaxi.es., Published in MNRAS

Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a long-standing challenge. This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems. Moreover, these sensors could be in motion and could become online or offline over time. The key leverage in addressing this scientific issue is the wealth of data accumulated from the sensors. As a solution to this problem, we propose a data-driven spatial field recovery technique founded on a structured grid-based deep-learning approach for arbitrary positioned sensors of any numbers. It should be noted that naive use of machine learning becomes prohibitively expensive for global field reconstruction and is furthermore not adaptable to an arbitrary number of sensors. In this work, we consider the use of Voronoi tessellation to obtain a structured-grid representation from sensor locations, enabling the computationally tractable use of convolutional neural networks. One of the central features of our method is its compatibility with deep learning-based super-resolution reconstruction techniques for structured sensor data that are established for image processing. The proposed reconstruction technique is demonstrated for unsteady wake flow, geophysical data and three-dimensional turbulence. The current framework is able to handle an arbitrary number of moving sensors and thereby overcomes a major limitation with existing reconstruction methods. Our technique opens a new pathway toward the practical use of neural networks for real-time global field estimation. Complex physical processes such as flow fields can be predicted using deep learning methods if good quality sensor data is available, but sparsely placed sensors and sensors that change their position present a problem. A new approach from Kai Fukami and colleagues based on Voronoi tessellation now allows to use data from an arbitrary number of moving sensors to reconstruct a global field.

Photometric redshift estimation algorithms are often based on representative data from observational campaigns. Data-driven methods of this type are subject to a number of potential deficiencies, such as sample bias and incompleteness. Motivated by these considerations, we propose using physically motivated synthetic spectral energy distributions in redshift estimation. In addition, the synthetic data would have to span a domain in colour-redshift space concordant with that of the targeted observational surveys. With a matched distribution and realistically modelled synthetic data in hand, a suitable regression algorithm can be appropriately trained; we use a mixture density network for this purpose. We also perform a zero-point re-calibration to reduce the systematic differences between noise-free synthetic data and the (unavoidably) noisy observational data sets. This new redshift estimation framework, SYTH-Z, demonstrates superior accuracy over a wide range of redshifts compared to baseline models trained on observational data alone. Approaches using realistic synthetic data sets can therefore greatly mitigate the reliance on expensive spectroscopic follow-up for the next generation of photometric surveys., Comment: 14 pages, 8 figures

We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (1) the shallow water equations, (2) a two-dimensional cylinder flow, (3) the wake of NACA0012 airfoil with a Gurney flap, and (4) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow {surrogate} model but also systematically quantifies the uncertainty therein to assist with model interpretability.

Large pristine samples of red clump stars are highly sought after given that they are standard candles and give precise distances even at large distances. However, it is difficult to cleanly select red clumps stars because they can have the same T$_{\mathrm{eff}}$ and log $g$ as red giant branch stars. Recently, it was shown that the asteroseismic parameters, $\rm{\Delta}$P and $\rm{\Delta\nu}$, which are used to accurately select red clump stars, can be derived from spectra using the change in the surface carbon to nitrogen ratio ([C/N]) caused by mixing during the red giant branch. This change in [C/N] can also impact the spectral energy distribution. In this study, we predict the $\rm{\Delta}$P, $\rm{\Delta\nu}$, T$_{\mathrm{eff}}$ and log $g$ using 2MASS, AllWISE, \gaia, and Pan-STARRS data in order to select a clean sample of red clump stars. We achieve a contamination rate of $\sim$20\%, equivalent to what is achieved when selecting from T$_{\mathrm{eff}}$ and log $g$ derived from low resolution spectra. Finally, we present two red clump samples. One sample has a contamination rate of $\sim$ 20\% and $\sim$ 405,000 red clump stars. The other has a contamination of $\sim$ 33\% and $\sim$ 2.6 million red clump stars which includes $\sim$ 75,000 stars at distances $>$ 10 kpc. For |b|>30 degrees we find $\sim$ 15,000 stars with contamination rate of $\sim$ 9\%. The scientific potential of this catalog for studying the structure and formation history of the Galaxy is vast given that it includes millions of precise distances to stars in the inner bulge and distant halo where astrometric distances are imprecise., Comment: 18 pages, 13 figures, 2 tables, submitted to MNRAS

Full author list: L. E. Bleem, S. Bocquet, B. Stalder, M. D. Gladders, P. A. R. Ade, S. W. Allen, A. J. Anderson, J. Annis, M. L. N. Ashby, J. E. Austermann, S. Avila, J. S. Avva, M. Bayliss, J. A. Beall, K. Bechtol, A. N. Bender, B. A. Benson, E. Bertin, F. Bianchini, C. Blake, M. Brodwin, D. Brooks, E. Buckley-Geer, D. L. Burke, J. E. Carlstrom, A. Carnero Rosell, M. Carrasco Kind, J. Carretero, C. L. Chang, H. C. Chiang, R. Citron, C. Corbett Moran, M. Costanzi, T. M. Crawford, A. T. Crites, L. N. da Costa, T. de Haan, J. De Vicente, S. Desai, H. T. Diehl, J. P. Dietrich, M. A. Dobbs, T. F. Eifler, W. Everett, B. Flaugher, B. Floyd, J. Frieman, J. Gallicchio, J. García-Bellido, E. M. George, D. W. Gerdes, A. Gilbert, D. Gruen, R. A. Gruendl, J. Gschwend, N. Gupta, G. Gutierrez, N. W. Halverson, N. Harrington, J. W. Henning, C. Heymans, G. P. Holder, D. L. Hollowood, W. L. Holzapfel, K. Honscheid, J. D. Hrubes, N. Huang, J. Hubmayr, K. D. Irwin, D. J. James, T. Jeltema, S. Joudaki, G. Khullar, M. Klein, L. Knox, N. Kuropatkin, A. T. Lee, D. Li, C. Lidman, A. Lowitz, N. MacCrann, G. Mahler, M. A. G. Maia, J. L. Marshall, M. McDonald, J. J. McMahon, P. Melchior, F. Menanteau, S. S. Meyer, R. Miquel, L. M. Mocanu, J. J. Mohr, J. Montgomery, A. Nadolski, T. Natoli, J. P. Nibarger, G. Noble, V. Novosad, S. Padin, A. Palmese, D. Parkinson, S. Patil, F. Paz-Chinchón, A. A. Plazas, C. Pryke, N. S. Ramachandra, C. L. Reichardt, J. D. Remolina González, A. K. Romer, A. Roodman, J. E. Ruhl, E. S. Rykoff, B. R. Saliwanchik, E. Sanchez, A. Saro, J. T. Sayre, K. K. Schaffer, T. Schrabback, S. Serrano, K. Sharon, C. Sievers, G. Smecher, M. Smith, M. Soares-Santos, A. A. Stark, K. T. Story, E. Suchyta, G. Tarle, C. Tucker, K. Vanderlinde, T. Veach, J. D. Vieira, G. Wang, J. Weller, N. Whitehorn, W. L. K. Wu, V. Yefremenko, and Y. Zhang, We describe the observations and resultant galaxy cluster catalog from the 2770 deg2 SPTpol Extended Cluster Survey (SPT-ECS). Clusters are identified via the Sunyaev-Zel'dovich (SZ) effect and confirmed with a combination of archival and targeted follow-up data, making particular use of data from the Dark Energy Survey (DES). With incomplete follow-up we have confirmed as clusters 244 of 266 candidates at a detection significance ξ ≥ 5 and an additional 204 systems at 4 < ξ < 5. The confirmed sample has a median mass of M500c ~ 4.4 ¿ 1014 M☉ h70 -1 and a median redshift of z = 0.49, and we have identified 44 strong gravitational lenses in the sample thus far. Radio data are used to characterize contamination to the SZ signal; the median contamination for confirmed clusters is predicted to be ∼1% of the SZ signal at the ξ > 4 threshold, and 10% of their measured SZ flux. We associate SZ-selected clusters, from both SPT-ECS and the SPT-SZ survey, with clusters from the DES redMaPPer sample, and we find an offset distribution between the SZ center and central galaxy in general agreement with previous work, though with a larger fraction of clusters with significant offsets. Adopting a fixed Planck-like cosmology, we measure the optical richness-SZ mass (l - M) relation and find it to be 28% shallower than that from a weak-lensing analysis of the DES data-a difference significant at the 4σ level-with the relations intersecting at λ = 60. The SPT-ECS cluster sample will be particularly useful for studying the evolution of massive clusters and, in combination with DES lensing observations and the SPT-SZ cluster sample, will be an important component of future cosmological analyses., This work was performed in the context of the South Pole Telescope scientific program. SPT is supported by the National Science Foundation through grant PLR-1248097. Partial support is also provided by the NSF Physics Frontier Center grant PHY-0114422 to the Kavli Institute of Cosmological Physics at the University of Chicago, the Kavli Foundation, and the Gordon and Betty Moore Foundation grant GBMF 947 to the University of Chicago. This work is also supported by the U.S. Department of Energy. PISCO observations are supported by NSF AST-1814719. Work at Argonne National Lab is supported by UChicago Argonne LLC, operator of Argonne National Laboratory (Argonne). Argonne, a U.S. Department of Energy Office of Science Laboratory, is operated under contract No. DE-AC02- 06CH11357. We also acknowledge support from the Argonne Center for Nanoscale Materials. M.G. and L.B. acknowledge partial support from HST-GO-15307.001. B.B. is supported by the Fermi Research Alliance LLC under contract No. De-AC02- 07CH11359 with the U.S. Department of Energy. The CU Boulder group acknowledges support from NSF AST-0956135. The McGill authors acknowledge funding from the Natural Sciences and Engineering Research Council of Canada, Canadian Institute for Advanced Research, and the Fonds de Recherche du Québec Nature et technologies. The UCLA authors acknowledge support from NSF AST-1716965 and CSSI-1835865. The Stanford/SLAC group acknowledges support from the U.S. Department of Energy under contract No. DE-AC02-76SF00515. A.S. is supported by the ERC-StG “ClustersXCosmo” grant agreement 716762 and by the FARE-MIUR grant “ClustersXEuclid” R165SBKTMA. C.H. acknowledges support from the Max Planck Society and the Alexander von Humboldt Foundation, in the framework of the Max Planck-Humboldt Research Award endowed by the Federal Ministry of Education and Research, in addition to support from the European Research Council under grant No. 647112. S.J. acknowledges support from the Beecroft Trust and ERC 693024. T.S. acknowledges support from the German Federal Ministry of Economics and Technology (BMWi) provided through DLR under projects 50 OR 1610 and 50 OR 1803, as well as support from the Deutsche Forschungsgemeinschaft, DFG, under project SCHR 1400/3-1. The Melbourne authors acknowledge support from the Australian Research Council’s Discovery Projects scheme (DP150103208). The 2dFLenS survey is based on data acquired through the Australian Astronomical Observatory, under program A/2014B/008. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at The Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at UrbanaChampaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University, and the OzDES Membership Consortium. Based in part on observations at Cerro Tololo InterAmerican Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The DES data management system is supported by the National Science Foundation under grant Nos. AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007- 2013), including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Brazilian Instituto Nacional de Ciência e Tecnologia (INCT) e-Universe (CNPq grant 465376/2014-2). This manuscript has been authored by Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation grant No. AST1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation

The Sunyaev-Zel'dolvich (SZ) effect is expected to be instrumental in measuring velocities of distant clusters in near future telescope surveys. We simplify the calculation of peculiar velocities of galaxy clusters using deep learning frameworks trained on numerical simulations to avoid the estimation of the optical depth. The image of distorted photon backgrounds are generated for idealized observations using one of the largest cosmological hydrodynamical simulations, the Magneticum simulations. The model is tested to be capable peculiar velocities from future kinetic SZ observations under different noise conditions. The deep learning algorithm displays robustness in estimating peculiar velocities from kinetic SZ effect by an improvement in accuracy of about 17% compared to the analytical approach., Comment: 10 pages, 12 figures, Submitted to MNRAS

We explore unsupervised machine learning for galaxy morphology analyses using a combination of feature extraction with a vector-quantised variational autoencoder (VQ-VAE) and hierarchical clustering (HC). We propose a new methodology that includes: (1) consideration of the clustering performance simultaneously when learning features from images; (2) allowing for various distance thresholds within the HC algorithm; (3) using the galaxy orientation to determine the number of clusters. This setup provides 27 clusters created with this unsupervised learning which we show are well separated based on galaxy shape and structure (e.g., S\'ersic index, concentration, asymmetry, Gini coefficient). These resulting clusters also correlate well with physical properties such as the colour-magnitude diagram, and span the range of scaling-relations such as mass vs. size amongst the different machine-defined clusters. When we merge these multiple clusters into two large preliminary clusters to provide a binary classification, an accuracy of $\sim87\%$ is reached using an imbalanced dataset, matching real galaxy distributions, which includes 22.7\% early-type galaxies and 77.3\% late-type galaxies. Comparing the given clusters with classic Hubble types (ellipticals, lenticulars, early spirals, late spirals, and irregulars), we show that there is an intrinsic vagueness in visual classification systems, in particular galaxies with transitional features such as lenticulars and early spirals. Based on this, the main result in this work is not how well our unsupervised method matches visual classifications and physical properties, but that the method provides an independent classification that may be more physically meaningful than any visually based ones., Comment: 22 pages, 18 figures. Accepted by MNRAS

The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web -- depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper we bring twelve of these methods together and apply them to the same data set in order to understand how they compare. In general these cosmic web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore one would not {\it a priori} expect agreement between different techniques however, many of these methods do converge on the identification of specific features. In this paper we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. $M_{\rm halo}\sim10^{13.5}h^{-1}M_{\odot}$) as being in filaments. Lastly, so that any future cosmic web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public., Comment: 24 pages, 8 figures, 2 tables. Submitted to MN. Comments Welcome

Mysterious dark matter constitutes about 85% of all mass in the Universe. Clustering of dark matter plays the dominant role in the formation of all observed structures on scales from a fraction to a few hundreds of Mega-parsecs. Galaxies play a role of lights illuminating these structures so they can be observed. The observations in the last several decades have unveiled opulent geometry of these structures currently known as the cosmic web. Haloes are the highest concentrations of dark matter and host luminous galaxies. Currently the most accurate modeling of dark matter haloes is achieved in cosmological N-body simulations. Identifying the haloes from the distribution of particles in N-body simulations is one of the problems attracting both considerable interest and efforts. We propose a novel framework for detecting potential dark matter haloes using the field unique for dark matter -- multistream field. The multistream field emerges at the nonlinear stage of the growth of perturbations because the dark matter is collisionless. Counting the number of velocity streams in gravitational collapses supplements our knowledge of spatial clustering. We assume that the virialized haloes have convex boundaries. Closed and convex regions of the multistream field are hence isolated by imposing a positivity condition on all three eigenvalues of the Hessian estimated on the smoothed multistream field. In a single-scale analysis of high multistream field resolution and low softening length, the halo substructures with local multistream maxima are isolated as individual halo sites., 16 pages, 15 figures. Accepted for publication in MNRAS. Portions of this work appeared as arXiv:1608.05469v1, which was divided during the refereeing process of the journal, and published separately

We report the results of the first study of the multi-stream environment of dark matter haloes in cosmological N-body simulations in the LCDM cosmology. The full dynamical state of dark matter can be described as a three-dimensional sub-manifold in six dimensional phase space - the dark matter sheet. In our study we use a Lagrangian sub-manifold x = x(q,t) (where x and q are co-moving Eulerian and Lagrangian coordinates respectively), which is dynamically equivalent to the dark matter sheet but is more convenient for numerical analysis. Our major results can be summarized as follows. At the resolution of the simulation i.e. without additional smoothing, the cosmic web represents a hierarchical structure: each halo is embedded in the filamentary framework of the web predominantly at the filament crossings, and each filament is embedded in the wall like fabric of the web at the wall crossings. Locally, each halo or sub-halo is a peak in the number of streams field. The number of streams in the neighbouring filaments is higher than in the neighbouring walls. The walls are regions where number of streams is equal to three or a few. Voids are uniquely defined by the local condition requiring to be a single-stream flow region. The shells of streams around haloes are quite thin and the closest void region is typically within one and a half FOF radius from the center of the halo., Comment: 12 pages, 25 figures. Matches version accepted by MNRAS

Topological connections in the single-streaming voids and multistreaming filaments and walls reveal a cosmic web structure different from traditional mass density fields. A single void structure not only percolates the multistream field in all the directions, but also occupies over 99 per cent of all the single-streaming regions. Sub-grid analyses on scales smaller than simulation resolution reveal tiny pockets of voids that are isolated by membranes of the structure. For the multistreaming excursion sets, the percolating structure is significantly thinner than the filaments in over-density excursion approach. Hessian eigenvalues of the multistream field are used as local geometrical indicators of dark matter structures. Single-streaming regions have most of the zero eigenvalues. Parameter-free conditions on the eigenvalues in the multistream region may be used to delineate primitive geometries with concavities corresponding to filaments, walls and haloes., 16 pages, 13 figures. Matches version accepted by MNRAS