Visualizing the Life and Anatomy of Dark Matter

Transcription

1 Visualizing the Life and Anatomy of Dark Matter Subhashis Hazarika Tzu-Hsuan Wei Rajaditya Mukherjee Alexandru Barbur ABSTRACT In this paper we provide a visualization based answer to understanding the evolution and structure of dark matter halos by addressing the tasks assigned in 2015 IEEE Scienti c Visualization Contest. The data released this year is a Cosmological Simulation dataset generated from the Dark Sky Simulation experiments. Out of the assigned tasks we are addressing the following: data integration and browsing, halo identi cation and visualization and diving deep into halo substructure. Index Terms: [Scienti c Visualization][Dark Matter Halo][Particle Data] 1 INTRODUCTION The Cosmological simulation dataset provided for the contest is generated from the Dark Sky Simulation which is an ongoing series of cosmological N-body simulations designed for modeling the evolution of the large scale Universe. The provided data were mainly of three types: raw data describing the particle position, potential and velocity at individual time-steps, a halo catalog which is a database of the gravitationally bound particles, called halos and nally a merger tree database that links individual halo catalogs. In this work we have shown how the dark matter halos evolve over time along with variations of their mass and size. We also visualize the evolution of a single halo with information extracted from the merger tree data-structure. We convert the particle data to a regular grid scalar eld to help apply some out-of-box visualization techniques like isosurface and volume rendering. We have also extracted the particles comprising a halo and have created visualizations which help understanding the sub-structures of a halo. 2 DATA INTEGRATION AND BROWSING In this task we provide the user with different ways of exploring and browsing through the data. We provide a multivariate exploration framework as well as a real-time interface to select and visualize different halo trees. 2.1 Multivariate Data Browsing The Halo data provided is a multivariate data with over 50 attributes per halo. Visualization of multivariate data is a very common problem and the use of parallel coordinate plot (PCP) is one of the most common ways of visualizing and exploring relationships in multivariate data. We decided to provide a web-based framework for exploring the multivariate halo data using the popular d3.js platform equipped with the interactive PCP library[3]. Fig. 4 shows an interactive web-page with the multivariate halo data, users can brush the axis to select the halos of interest as shown in Fig. 5. There is also a tabular form of the data at the bottom of the web-page, on moving the cursor over a table entry it highlights the corresponding line in hazarika.3@osu.edu wei.225@osu.edu mukherjee.62@osu.edu barbur.1@osu.edu IEEE Scientific Visualization Conference (SciVis) October, Chicago, Il, USA /15/$ IEEE the PCP. The user can select and upload any one of the halo-list les that he/she wants to explore. This will help the user discover relationships between different halo attributes which otherwise might not have been apparent. 2.2 Tree-Based Data Browsing We also provide an exploration tool to assist users to visualize the halos based on the tree structures provided from the merger trees database. The merger tree database describes the evolution of the halos in different time-steps. Through the tree-based browsing, users can trace how halos move, merge or split. Three browsing modes are provided to users to visualize the halo tree, which are single tree browsing, forest browsing and block-wise browsing as shown in the Fig. 6. For the single tree and forest browsing modes, they allow the user to focus on a speci c tree or a forest which contains multiple trees and visualize the trajectory of halos. The block-wise browsing mode provides the user with the option to select a region in space where he wants to see the halo transitions and visualize all trees located in that region block. In the current version, we split data space into multiple non-overlap region blocks and assign a tree to the speci c region block based on its root. The supplementary video provides additional illustration. By visualizing trees in a speci c region, the user can explore the relation or the interaction between trees which reside closely. To display the halo trees, we connected halos by lines based on the halo ID and the ID of descendant halo information which are extracted from the merger tree dataset. Loading the merger trees and pre-processing is done when the program starts up. Through connecting halos by lines as shown in Fig. 6, the user is able to observe the behavior of a small set of halos as they interact with each other. We also provide a transfer function window to allow users to color the halos based on different attributes such as snapshot ID, mass, momentum, spin etc as shown in Fig. 7. By means of transfer function users can differentiate different value ranges by assigning different color and opacity. Furthermore, a lter function is provided as well to lter displayed halos by attributes which is showninfig.8.the lter function can work with transfer function together to explore the correlation between different attributes. In Fig. 8, for example, we assigned color and opacity based on the spin attribute and lter out some halos based on its velocity. By using the transfer function and lter function together, the user can focus on speci c value ranges of different variables and differentiate different value ranges of a selected attribute by transfer function. 3 HALO IDENTIFICATION AND VISUALIZATION We used a 3D spherical glyph based visualization to show the evolution of different halos across time. Fig. 2 shows the nal state of all the halos. To visualize the accrual of virial mass and radius of the halos alongside their evolution we have mapped the mass to the color and the radius to the size of the spherical glyphs. We also combine the particle s potential with the glyphs as shown in Fig. 3. We get this from the volume rendering of the particle data after converting it to regular grid scalar eld form as explained in Section 4.2. The supplementary video shows an animation of how the halos evolve over time along with their mass and size. Halos essentially are groups of gravitationally bound dark matter particles and they evolve over time by merging and splitting apart 101

2 from the other halos. Tracking the evolution time of speci c halos especially halos with interesting features becomes possible by parsing the merger tree database. Fig. 9 and Fig. 10 shows a visualization of the tree for the halo with the highest mass using 3D spherical glyphs. The color is mapped to mass and the radius to the size of the sphere. Through the interactive visual browsing framework users can also select speci c trees that he wants to visualize as shown in Fig. 7. To further visualize the life of halos, we also provide the animation mode to display the movement of halos over time based on the halo ID and the ID of descendant halo extracted from the merger tree. By animating the movement trajectory of halos, we can assist the user to easily and quickly exploring interactions between multiple halos. The transfer function and lter function can also work in the animation mode interactively which can satisfy the user s need while exploring the relations between different variables. More elaborations can be seen in the supplementary video. 4 DIVING DEEP INTO HALO SUBSTRUCTURE In order to understand the structure of halos we tried to visualize the dark matter particles that comprise each halo. 4.1 Extracting Particles from Halo Halos are collection of gravitationally bound dark matter particles, so the particles that de ne a halo are all con ned within the sellipsoid centered at the halo center. The major and minor axes information were used to de ne the ellipsoid for all the halos and this helped us identify the dark matter particles for the halos. Fig. 11 shows the dark matter particles comprised within the halo with the largest mass using 3D spherical glyphs and colored by the potential of the particles. Slicing through these collection of particles will allow the user to further analyze the particle structure of the halo. This can be see in the video provide with the submission. We went ahead and extracted the particles for all the halos that were part of the tree that correspond to the halo with largest mass. This allowed us to create an animation showing how the dark matters interacted over time to form the nal large halo. The animation is part of the supplementary video. 4.2 Convert the Particle Data to Regular Grid Scalar Field We have converted the particle data to a regular grid density eld so that we can apply out-of-box visualizations like isosurface and volume rendering. While there are several visualization approaches for particle data such as [1], we will use a more simpli ed approach for this dataset which follows the method outlined in [2]. There are three basic steps for this process which are 1. We nd the appropriate grid resolution (denoted by cpud) suitable for the grid by the following formula[2] cn 1 3 cpud = Length Major Axis (1) Δ Major Axis where c is a constant, n is the number of particles in the data set and Δ Major Axis is the length of the longest axis of the bounding box around the particle data. In our work, we used c = We insert the particles in the newly formulated grid-cells using its actual position in the space. We directly calculate the grid to which the particle belongs to by the grid resolution and length computed in the previous step and insert it in a 4D vector (Essentially think of this as a list along each cell of the 3D grid.) 3. Finally, we use an inverse-distance weighted interpolation at each grid point to get the scalar values. It involves iterating over each grid cell, nding the number of points which are in the radius of in uence of the cell and computing the scalar values at each point. In this step, there are two major factors which in uence the nal result. The rst one is the radius of in uence. It is the area around a grid cells near which we consider all the particles as shown in Fig. 1 [2]. Any particle outside this area is considered as not contributing to the value at that grid cell. The second parameter is the maximum number of particles that in uence the value at a particular grid cell (call this number K). If a grid cell has more than K particles in its radius of in uence, then we will only count the K nearest particles and ignore the result. Proper value of K helps to speed up the computation for large particle dataset. After we get the particles that in uence the particular grid, we simply do a weighted interpolation where the weight is equal to the inverse of their distance. This ensures that particles nearest to the grid point contribute more to the scalar values than the particles far away from it. Figure 1: Radius of In uence:for K=5 different scenarios of particle selection.top left shows that exactly 5 particles are within the radius which gets selected. Top right shows that only 3 particles are within the radius that gets selected. Bottom left shows that there are 8 particles within the radius but only the closest 5 gets picked. Bottom right shows that none of the particles are selected. We created a 128x128x128 resolution grid for the particle data and used it to extract isosurface using potential of the dark matter particles as the scalar value, as shown in Fig. 12. We can also use this converted data to perform volume rendering as shown in Fig. 13, we created such grid for all the time-steps and created an animation of how the particle density changes across time. 4.3 Particle Rendering We also created a WebGL based real-time rendering of over 2 million dark matter particles as shown in Fig. 14. The particles are color mapped to their potential values. The purpose of this visualization is to provide a way for the user to explore the structure of just the raw dark matter particle data without any halo information. This real-time rendering allows the user to zoom in and out for the dark matter particles. The dark matter particles are rendered as textures of a lens- are which gives it a nice visual appeal as can be seen in Fig IMPLEMENTATION The parallel coordinates was implemented using d3.js platform and the PCP library from [3]. The 3D spherical glyphs were rendered using Paraview after the particle and halo data were pre-processed with python and C++ programs to vtk le format. The particle rendering was done using the WebGL platform along with THREE.js library. 102

3 The tree-based browsing interface was created with SFGUI [12] and SFML [13]. SFGUI is a C++ GUI library for SFML which is a cross-platform software development library. We used SFML to create the application window, OpenGL rendering context, and to process keyboard and mouse input in our work. 6 CONCLUSION In this work we have provided visualizations that help understand how the dark matter halos form over time and how some of their attributes like mass, radius etc changes accordingly. The user interface part allows user to explore more of these features and understand different relations among them. The biggest challenge that we faced was the lack of proper domain knowledge on what could be a more useful feature to visualize for the given dataset. However we feel that users with proper knowledge about the eld can make use of our tools to explore more about the dark matter structures. ACKNOWLEDGEMENTS We would like to thank Dr. Han-Wei Shen for motivating us to participate in the contest. We would also like to thank the event organizer for providing such an interesting data to the visualization community. REFERENCES [1] C.S.Co, K.I.Joy. Isosurface Generation for Large-Scale Scattered Data Visualization. Proceedings of Vision, Modelling and Visualization, pages , Nov [2] P.A.Navratil, J.L.Johnson, V.Bromm. Visualization of Cosmological Particle-Based Datasets. IEEE Transactions On Visualization and Computer Graphics, VOL. 13, NO. 6, November/December 2007 [3] syntagmatic/parallel-coordinates [4] simple and fast graphical user interface [5] simple and fast multimedia library Figure 3: 3D glyphs of halos as in Fig 2, overlayed with the potential values of the dark matter particles obtained after converting particle data to regular grid scalar eld. The orange color corresponds to the potential of the particles in that region of space. Figure 4: PCP of the halo data, colored based on radius of halo, green being the smallest and purple for biggest radius. Figure 2: 3D spherical glyphs representing halos in the last timestep. Size of the sphere is mapped to the radius of halo and mass to the color. Figure 5: PCP of the halo data with brushing and selection 103

4 Figure 6: An example of connecting halos by lines based on the halo ID and ID of the descendant halo. In the red box, the users can select three browsing modes: single-tree browsing, forest browsing and block-wise browsing. Figure 8: Filter function interface. The user can select attributes in the red box to focus on speci c value ranges of different variables. In this example, we lter out the lower velocity and focus on the velocity larger than km/s. The lter function can also work with transfer function. In this example, the color and opacity are assigned based on the spin attribute which is the same as the Fig. 7. Figure 7: Transfer function interface. The user can select attribute in the red box and assign the opacity and color based on its value in the blue box. In this example, red represents small spin value and white represents large spin value. Figure 9: A glyph based visualization of the tree corresponding to the halo with the highest mass. This shows all the halos that interacted over time to form the root halo i.e, the biggest halo. This actually is a visualization of the merger tree for the biggest halo. The color of the glyphs are mapped to their mass and size to their radius. 104

5 Figure 10: A big picture of where the Fig 9 above is positioned with respect to the other halos. Figure 12: Isosurface extracted from the potential scalar eld of the particle data after converting it to regular grid form. Figure 11: Dark matter particles comprising the halo with highest mass at the last time step. These were extracted by using the ellipsoidal equation of each halo. They are colored as per their potential(phi). Figure 13: Volume rendering for the dark matter particle density eld. 105

6 Figure 14: Real-time particle rendering of 2 million dark matter particles in web browser. Figure 15: A zoomed in version of the particle renderer. 106