Elsevier

New Astronomy

Volume 80, October 2020, 101405
New Astronomy

A robust determination of halo environment in the cosmic field

https://doi.org/10.1016/j.newast.2020.101405Get rights and content

Highlights

  • A robust cosmic web determination is introduced.

  • Contribution from nearby grid points considered.

  • 98% haloes holding the same large-scale environments with three resolutions.

  • 80% of haloes have eigenvalues within 10% of each other with three resolutions.

Abstract

A number of methods for studying the large-scale cosmic matter distribution exist in the literature. One particularly common method employed to define the cosmic web is to examine the density, velocity or potential field. Such methods are advantageous since a Hessian matrix can be constructed whose eigenvectors (and eigenvalues) indicate the principal directions (and strength) of local collapse or expansion. Technically this is achieved by diagonalizing the Hessian matrix using a fixed finite grid. The resultant large-scale structure quantification is thus inherently limited by the grid’s finite resolution. Here, we overcome the obstacle of finite grid resolution by introducing a new method to determine halo environment using an adaptive interpolation which is more robust to resolution than the typical “Nearest Grid Point” (NGP) method. Essentially instead of computing and diagonalizing the Hessian matrix once for the entire grid, we suggest doing so once for each halo or galaxy in question. We examine how the eigenvalues and eigenvector direction’s computed using our algorithm and the NGP method converge for different grid resolutions, finding that our new method is convergent faster. Namely changes of resolution have a much smaller effect than in the NGP method. We therefore suggest this method for future use by the community.

Introduction

The large-scale structure of the Universe is formed via gravitational instability from the initial seeding of perturbations in the otherwise homogenous density field. On large scales, the matter distribution of the Universe is not uniform, but exhibits a web-like structure, which can be well described by the linear theory and the Zel’dovich approximation(Zel’dovich, 1970). The multi-scale web-like structure, commonly referred to as “the cosmic web”(Bond et al., 1996), is well studied and has been been described as a cellular system (Joeveer and Einasto, 1978). Analyses of large galaxy surveys, such as the 2dF Galaxy Redshift Survey (Colless, 2003), the Sloan Digital Sky Survey (Tegmark, 2004) and the Two Micron All Sky Survey (2MASS) redshift survey (Huchra, 2005) have shown that the cosmic web can be decomposed classified into four categories, namely knots (sometimes referred to as clusters), filaments, walls (sometimes referred to as sheets) and voids. As these terms suggest, in general, knots are formed at the relatively denser regions which sit at the intersection of filaments and are fed by mass flowing along the spines filaments. Filaments are formed at the intersection of walls. Walls are formed abutting voids, which remain relatively under-dense. In general the classification of the cosmic web according to the above hierarchy (namely knots, filaments, sheets and voids) can be done by examining the rate of compression (or expansion) of cosmic material along the three orthonormal axes (Icke, van de Weygaert, 1991, Cautun, van de Weygaert, Jones, Frenk, 2014, Wang, Kang, 2018).

One of the original intentions of developing cosmic web classification methods is to understand whether, and if so how, the cosmic web influences the properties of galaxies and the evolution of galaxies within it. Clear evidence has been presented that properties of haloes/galaxies (such as shape, spin and satellite spatial distribution) correlate with their large scale environments (Aragon-Calvo, de, Jones, van der, 2007, Aragon-Calvo, Yang, 2014, Hahn, Carollo, Porciani, Dekel, 2007a, Hahn, Porciani, Carollo, Dekel, 2007b, Hahn, Teyssier, Carollo, 2010, Zhang, Yang, Faltenbacher, Springel, Lin, Wang, 2009, Zhang, Yang, Wang, Wang, Luo, Mo, van den Bosch, 2015, Wang, Kang, 2017, Wang, Kang, 2018, Metuki, Libeskind, Hoffman, Crain, Theuns, 2015, Libeskind, Hoffman, Knebe, Steinmetz, Gottlöber, Metuki, Yepes, 2012, Libeskind, Hoffman, Steinmetz, Gottlöber, Knebe, Hess, 2013, Libeskind, Knebe, Hoffman, Gottlöber, 2014, Pahwa, et al., 2016, Guo, Tempel, Libeskind, 2015, Tempel, Libeskind, 2013, Tempel, Guo, Kipper, Libeskind, 2015, Hirv, Pelt, Saar, Tago, Tamm, Tempel, Einasto, 2017). In order to understand how the large scale structure and the immediate environment of a halo/galaxy affects its formation and evolution, it is crucial to robustly identify and quantify this large scale environment (LSE) at the position of each halo or galaxy.

In the past two decades, a variety of methods have been devised to classify the cosmic environment based on local variations (density, gravitational potential and velocity) of the matter distribution. (Aragon-Calvo, de, Jones, van der, 2007, Hahn, Carollo, Porciani, Dekel, 2007a, Forero-Romero, Contreras, Padilla, 2014, Libeskind, Hoffman, Knebe, Steinmetz, Gottlöber, Metuki, Yepes, 2012, Cautun, van de Weygaert, Jones, Frenk, 2014). The reader is also referred to Libeskind (2018) for the comparison of 12 different methods. Here we focus on the computation of Hessian based methods that employ a fixed grid and assign haloes to the Nearest Grid Point (NGP). These methods are frequently used in the analysis of simulations or reconstructions (Libeskind et al., 2015) or wherever there is a continuous cosmic field. Hahn et al. (2007a) first proposed an dynamic classification scheme (often referred as T-web or P-web) of the cosmic web based on counting the positive number of the eigenvalues of the tidal tensor, i.e, the Hessian of gravitational potential. Studies argue that the value of the properly normalized threshold should be around unity (Forero-Romero et al., 2014) or zero (Hahn et al., 2007a). Similarly, Hoffman et al. (2012) and Libeskind et al. (2012) forwarded the V-web technique based on the signature of the velocity shear field. Instead of using the tidal or velocity shear field configuration, some works also define large scale environment based on the density field itself (Aragon-Calvo, de, Jones, van der, 2007, Cautun, van de Weygaert, Jones, Frenk, 2014, Zhang, Yang, Faltenbacher, Springel, Lin, Wang, 2009, Wang, Kang, 2017, Wang, Kang, 2018).

These Hessian-NGP-based methods have been used in numerous studies which are related to the correlation between haloes/galaxies and cosmic web. However there is still much room for improvement. Although some methods discretize cosmic fields using adaptive non-regular grids (i.e. a Delaunay tessellation Cautun et al., 2014), many still rely on regular grids, such as a “cloud-in-cell” algorithm. In those methods which employ a regular grid, the environment properties of a halo/galaxy is often replaced by the environment properties of the nearest grid point (MacNeice, 1995) without considering the contribution from other neighboring grid points. In other words, these methods discretize a given field and compute the cosmic web at each grid point. A given value/type for the cosmic web can then be assigned to a halo or galaxy which is in the same voxel (“volume pixel” or grid cell). Such methods may not be robust since a galaxy has an extended size and mass (i.e. is not simply a point) that will be affected by nearby grid points. In the standard NGP method, environment properties of a halo might change when the grid size changes, since they are related to the grid and not to the halo. This may be risky if one considers the time evolution of a halo since haloes move relative to the LSE and therefore occasionally they will cross the border of a grid cell. In order to avoid these issues, we introduce an improved algorithm for the computation of Hessian fields by considering the influence from nearby grid points. Our approach consists of three free parameters, the resolution Ngrid3, the smoothing length Rs and the threshold λth used to classify the cosmic web. In most works, they mainly focus on Rs (Aragon-Calvo, de, Jones, van der, 2007, Cautun, van de Weygaert, Jones, Frenk, 2014) and λth (Forero-Romero et al., 2014), while less discussed is Ngrid3.

Our paper is organized as follows. Section 2 presents the algorithm in detail of how our approach works. In Section 3, we introduce the test simulation we used. Our main results are presented in Section 4 by testing the stability of the six key parameters of large scale structure of haloes in our approach, and comparing with traditional one. Conclusions and discussion are presented in Section 5.

Section snippets

Web classification: algorithm

The algorithm presented in this paper is similar to that suggested by Hahn et al. (2007a) but uses the density field instead of the potential. We explain our algorithm in the context of cosmological simulations. We note that our algorithm is not limited to the Hessian of the density field, but could also be applied to any hessian method computed on a regular grid (i.e. such as the potential or the velocity field). I

The algorithm proceeds by computing the smoothed density field ρs(x) at each

Test simulation

The simulation data used in this work is Illustris-1 (Vogelsberger, 2014) with full physics and high mass resolution. The Illustris simulation suite consists of a set of cosmological hydrodynamical simulations carried out with the moving mesh code AREPO (Springel, 2010) with following cosmological parameters: Ωm=0.2726, ΩΛ=0.7274, Ωb=0.0456, σ8=0.809, ns=0.963 and H0=100hkms1 with h=0.704. These parameters are consistent with the latest Wilkinson Microwave Anisotropy Probe (WAMP)-9

Results: stability

In identifying the large-scale environment for each halo, our algorithm requires three free parameters: the resolution Ngrid3, the smoothing length Rs, and the threshold λth. As described in the introduction, a lot of work (Aragon-Calvo, de, Jones, van der, 2007, Cautun, van de Weygaert, Jones, Frenk, 2014, Forero-Romero, Contreras, Padilla, 2014) has focused on the effects of the smoothing length and threshold. In this work, we mainly discuss the dependence on the resolution from small to

Conclusion and discussion

Many studies have investigated the effect of environment on galaxy and halo formation. In cosmological simulations one of the common ways to define environment is via deformation of the matter field. This may be done by examining, for example, the tidal-shear field or the potential field. Such approaches rely on discretising the field, normally using a regular grid. However as particle number in cosmological simulations continues to grow, the computational resources required to analyse the

CRediT authorship contribution statement

Peng Wang: Conceptualization, Methodology, Software, Data curation, Writing - original draft. Xi Kang: Software, Supervision, Writing - review & editing. Noam I. Libeskind: Supervision, Writing - review & editing. Quan Guo: Writing - review & editing. Stefan Gottlöber: Writing - review & editing. Wei Wang: Visualization.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors acknowledge support from the joint Sino-German DFG research Project “The Cosmic Web and its impact on galaxy formation and alignment” (DFG-LI 2015/5-1). The work is supported by the NSFC (No.11825303, 11861131006, 11333008), the 973 program (No. 2015CB857003, No. 2013CB834900), and the NSF of Jiangsu Province (No. BK20140050). Q.G. acknowledges the sponsorship from Shanghai Pujiang Program 19PJ1410700. NIL acknowledges financial support of the Project IDEXLYON at the University of

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