The Galaxy Cluster Concentration-Mass Scaling Relation
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Mon. Not. R. Astron. Soc. 000, 000{000 (0000) Printed 23 November 2015 (MN LATEX style file v2.2) The Galaxy Cluster Concentration-Mass Scaling Relation A. M. Groener,1? D. M. Goldberg,1 M. Sereno,2 3 1Department of Physics, Drexel University Philadelphia, PA 19104 2Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Universit`adi Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italia 3INAF, Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italia ABSTRACT Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, concentration (cvir) and mass (Mvir). We have collected the largest known sample of measurements from the literature which make use of one or more of the following reconstruction techniques: Weak gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion (LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is highly variable depending upon the re- construction technique used. We also find concentrations derived from dark matter 14 only simulations (at approximately Mvir ∼ 10 M ) to be inconsistent with the WL and WL+SL relations at the 1σ level, even after the projection of triaxial halos is taken into account. However, to fully determine consistency between simulations and obser- vations, a volume-limited sample of clusters is required, as selection effects become increasingly more important in answering this. Interestingly, we also find evidence for a steeper WL+SL relation as compared to WL alone, a result which could perhaps be caused by the varying shape of cluster isodensities, though most likely reflects differences in selection effects caused by these two techniques. Lastly, we compare concentration and mass measurements of individual clusters made using more than one technique, highlighting the magnitude of the potential bias which could exist in such observational samples. Key words: galaxies: clusters: general { cosmology: dark matter { gravitational lensing: strong { gravitational lensing: weak 1 INTRODUCTION The radial density profiles of clusters, well-modeled by the universal NFW profile (Navarro et al. 1997), appears to Galaxy clusters have long been used as probes of cosmology. be a prevailing outcome of simulations regardless of cosmol- arXiv:1510.01961v2 [astro-ph.CO] 20 Nov 2015 Cluster observables, like X-ray luminosity, L , optical rich- X ogy (Navarro et al. 1997; Craig 1997; Kravtsov et al. 1997; ness, and line-of-sight galaxy dispersion, σ , are closely tied v Bullock et al. 2001). to the formation and evolution of large scale structures, and δ ρ scale with redshift and the mass of the host halo (Sereno ρ(r) = c cr (1) 2 & Ettori 2015). Scaling relations of clusters also provide a r 1 + r way of testing cosmology (Vikhlinin et al. 2009; Rozo et al. rs rs 2010; Mantz et al. 2010, 2014), though are imperfect prox- 3H(z)2 ies for mass, due to the 2-Dimensional view they provide ρcr = (2) for us. Large cosmological simulations provide a detailed 3- 8πG dimensional view of the hierarchical process of structure for- However, the details of the relationship between the two mation, one that is unattainable by even the most accurate model parameters, halo mass, M, and concentration, c, is reconstruction techniques available. sensitive to small changes in initial parameters (Macci`oet al. 2008; Correa et al. 2015b). The physical interpretation of a halo's concentration (defined as the ratio of the virial ra- ? −2 [email protected] dius, Rvir, to the radius at which ρ / r ; called the scale c 0000 RAS 2 Groener, Goldberg, & Sereno radius, rs), is that it is a measure of the `compactness' of the concentration, this feature disappears (see Meneghetti & Ra- halo, and determines the physical scale on which the density sia 2013). profile rises steeply. The connection between the observed concentration, The first indication of the connection between halo con- c2D, and the intrinsic concentration, c3D, is further compli- centration and mass (hereafter, the c-M relation) was discov- cated, since it has been shown that relaxed cluster isodensi- ered through simulations of structure formation by Navarro ties are not constant on all scales (Frenk et al. 1988; Cole & et al. (1997), and later confirmed by Bullock et al. (2001), Lacey 1996; Dubinski & Carlberg 1991; Warren et al. 1992; who found a strong correlation between an increasing scale Jing & Suto 2002; Hayashi et al. 2007; Groener & Gold- berg 2014). Indeed, in a previous study by Groener & Gold- density, ρs = δcρcr, for decreasing mass, Mvir. The expla- nation for this anti-correlation between concentration and berg (2014), it has been shown that a halo's concentration mass is that low-mass halos tend to collapse and form re- is an ill-defined 2-dimensional quantity, without first speci- laxed structures earlier than their larger counterparts, which fying the scale on which the measurement was made. Using are still accreting massive structures until much later. A con- the MultiDark MDR1 Cosmological Simulation, Groener & sequence of early collapse is that halos will have collapsed Goldberg (2014) found a systematic shift of about ∼ 18% during a period of higher density, leading to a larger cen- in the mean value of the projected concentration, c2D, be- tral density (and hence larger concentration) as compared tween weak and strong lensing scales, for low-mass cluster 13 −1 to halos which formed later. halos (2:5 − 2:6 × 10 h M ) observed with their major axes aligned with the line-of-sight direction. Though this Many studies (most recently, e.g., Correa et al. 2015a) difference is notably smaller than the intrinsic scatter of the focus on the physical motivation for the existence of this concentration parameter (c3D) for a given halo mass, the relationship, and suggest that the mass accretion history origin of this systematic effect is solely due to the changing (MAH) of halos is the key to understanding the connection shape of cluster isodensities as a function of radius. between cluster observables and the environment in which For many objects, not only do observed concentrations they formed (Bullock et al. 2001; Wechsler et al. 2002; Zhao seem to differ substantially from those obtained in cosmolog- et al. 2003). These studies have found that while the mass ical simulations, but concentrations can also vary depend- accretion rate onto the halo is slow, the concentration tends ing on which method is used. Since different reconstruction to scale with the virial radius, c / rvir (caused by a constant methods probe varying scales within the halo, it is not un- scale radius), while the concentration remains relatively con- reasonable to suspect that there exist systematic differences stant for epochs of high mass accretion. The MAH itself in the observed c-M relation caused by shape. depends upon the physical properties of the initial density peak (Dalal et al. 2008), which is a function of cosmology, In this paper, we focus on three main objectives. redshift, and mass (Diemer & Kravtsov 2015). Longstanding tension has existed between cluster con- (i) We present the current state of the observational centrations derived from simulations and observational mea- concentration-mass relation for galaxy clusters by aggregat- surements. Concentrations have been found to differ the ing all known measurements from the literature. The raw most for gravitational lensing techniques (Comerford & data are reported in Table A-1, and have been made pub- Natarajan 2007; Broadhurst et al. 2008; Oguri et al. 2009; licly available (see Appendix A). We also provide an addi- Umetsu et al. 2011a). This over-concentration in favor of tional table (available only online), where data have been observational measurements can be partially explained by normalized over differences in assumed cosmology, overden- the orientation of triaxial structure along our line-of-sight sity convention, and uncertainty type found in the original (Oguri et al. 2005; Sereno & Umetsu 2011), which has the studies. effect of enhancing the lensing properties (Hennawi et al. (ii) We model the observed concentration-mass relation 2007). Neglecting halo triaxiality (Corless et al. 2009) and for each method, and compare these to one another, high- substructure (Meneghetti et al. 2010; Giocoli et al. 2012) lighting potential differences which exist, caused by the pro- also each have significant effects on halo parameters. For its jection of structure along the line-of-sight, the varying shape effect on WL and X-ray mass estimates, see Sereno & Ettori of cluster isodensities, and the selection of clusters from the (2014). cosmic population. (iii) Using the largest cluster sample to date, we deter- Discrepancies in how measurements of the intrinsic con- mine if the observed c-M relation is consistent with the- centration are made using simulations also exist, along with ory, when taking halo triaxiality and elongation of structure studies who disagree on the inner slope of the density profile along the line-of-sight into account. (Moore et al. 1999; Ghigna et al. 2000; Navarro et al. 2004). However, the most puzzling and potentially interesting dis- In section 2, we summarize many of the most common parity between simulations is the existence of the upturn mass reconstruction techniques which are used throughout feature in the c-M relation (see for example, Fig. 12 of Prada the cluster community, and include a discussion regarding et al. 2012) at high redshift (Prada et al. 2012; Dutton & physical scales probed within the cluster using these meth- Macci`o2014; Klypin et al. 2014; Diemer & Kravtsov 2015), ods. In section 3, we discuss the procedure for collecting our which some argue is an artifact caused by the selection of sample from the literature, and normalizing over conven- halos which are dynamically unrelaxed (Ludlow et al.