Haloes gone MAD14: The Halo-Finder Comparison Project

A. Knebe et al. - A B S T R A C T We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends, spherical-overdensity and phase-space-based algorithms. We Airport code for Madrid, Spain E-mail: further introduce a robust (and publicly available) suite of test scenarios that allow halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo-finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo, and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Through a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 3040 particles. However, also here the phase-space finders excelled by resolving substructure down to 1020 particles. By comparing the halo finders using a highresolution cosmological volume, we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity and peak of the rotation curve). We further suggest to utilize the peak of the rotation curve, vmax, as a proxy for mass, given the arbitrariness in defining a proper halo edge. 1 I N T R O D U C T I O N While recent decades have seen great progress in the understanding and modelling of the large- and small-scale structure of the Universe by means of numerical simulations, there remains one very fundamental question that is yet to be answered: how to find a dark matter (DM) halo? The comparison of any cosmological simulation to observational data relies upon reproducibly identifying objects within the model. But how do we identify DM haloes or even galaxies in such simulations? Researchers in the field have developed a wide variety of techniques and codes to accomplish this task. But how does the performance of these various techniques and codes compare? While we still may argue about the proper definition of an object, the various approaches should nevertheless agree, once the same recipe for defining a (DM) halo is used. This introduction begins by establishing why it is important to have The Halo-Finder Comparison Project before continuing by laying out the groundwork for the comparison we have undertaken. It is therefore subdivided into a first subsection where we highlight the necessity for such a comparison and summarize the recent literature in this area. This section also includes a brief primer on halo finders and their history. The second part introduces the design of the test cases, illustrated with some analysis. The last part then raises the question how to cross-compare haloes? as well as what is actually a halo? and presents a possible answer the authors agreed upon. 1.1 The necessity for a comparison project Over the last 30 years, great progress has been made in the development of simulation codes that model the distribution of dissipationless DM while simultaneously following the (substantially more complex) physics of the baryonic component that accounts for the observable Universe. Nowadays, we have a great variety of highly reliable, cost-effective (and sometimes publicly available) codes designed for the simulation of cosmic structure formation (e.g. Couchman, Thomas & Pearce 1995; Gnedin 1995; Pen 1995; Kravtsov, Klypin & Khokhlov 1997; Bode, Ostriker & Xu 2000; Fryxell et al. 2000; Knebe, Green & Binney 2001; Springel, Yoshida & White 2001b; Teyssier 2002; Dubinski et al. 2004; OShea et al. 2004; Quilis 2004; Merz, Pen & Trac 2005; Springel 2005; Bagla & Khandai 2009; Doumler & Knebe 2010; Springel 2010). However, producing the (raw) simulation data is only the first step in the process; the model requires reduction before it can be compared to the observed Universe we inhabit. This necessitates access to analysis tools to map the data onto real objects; traditionally, this has been accomplished via the use of halo finders. Conventional halo finders search the (dark) matter density field within the simulations generated by the aforementioned codes to find locally overdense gravitationally bound systems, which are then tagged as (dark) matter haloes. Such tools have led to critical insights into our understanding of the origin and evolution of cosmic structure. To take advantage of sophisticated simulation codes and to optimize their predictive power, one obviously needs equally sophisticated halo finders! Therefore, this field has also seen great development in recent years (e.g. Gelb & Bertschinger 1994; Klypin & Holtzman 1997; Eisenstein & Hut 1998; Bullock et al. 2001; Springel et al. 2001a; Stadel 2001; Aubert et al. 2004; Gill et al. 2004; Neyrinck et al. 2005; Weller et al. 2005; Diemand et al. 2006; Kim & Park 2006; Gardner et al. 2007a,b; Shaw et al. 2007; Habib et al. 2009; Knollmann & Knebe 2009; Maciejewski et al. 2009; Ascasibar, in preparation; Behroozi, in preparation; Planelles & Quilis 2010; Rasera et al. 2010; Skory et al. 2010; Sutter & Ricker 2010; Falck et al., in preparation; see also Fig. 1, noting that for some halo finders no code paper exists yet). However, so far, comparison projects have tended to focus on the simulation codes themselves rather than the analysis tools. The increasing demand and supply for halo finders is schematically presented in Fig. 1 where we show the (cumulative) number of codes as a function of time, binned in 10-yr intervals since 1970. We can clearly see the increasing pace of development in the past decade, reflecting the necessity for sophisticated codes: in the last 10 years, the number of existing halo-finding codes has practically tripled. While for a long time the spherical-overdensity (SO) method first mentioned by Press & Schechter (1974) as well as the friend-offriends (FOF) algorithm introduced by Davis et al. (1985) remained the standard techniques, the situation changed in the 1990s when new methods were developed (Gelb 1992; Lacey & Cole 1994; van Kampen 1995; Pfitzner & Salmon 1996; Klypin & Holtzman 1997; Eisenstein & Hut 1998; Gottlober, Klypin & Kravtsov 1999). While the first generation of halo finders primarily focused on identifying isolated field haloes, the situation dramati (...truncated)