Mon. Not. R. Astron. Soc. 000, 000–000 (2016) Printed July 16, 2018 (MN LATEX style file v2.2) Characterising Strong Lensing Galaxy Clusters using the Millennium-XXL and MOKA simulations Carlo Giocoli1?, Mario Bonamigo1, Marceau Limousin1, Massimo Meneghetti2;3, Lauro Moscardini4;2;3, Raul E. Angulo5, Giulia Despali1;6, Eric Jullo1 1 Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France 2 INAF - Osservatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy 3 INFN - Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy 4 Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Università di Bologna, viale Berti Pichat, 6/2, 40127 Bologna, Italy 5 Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan 1, Planta-2, 44001 Teruel, Spain 6 Max Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85740 Garching, Germany July 16, 2018 ABSTRACT In this paper we investigate the strong lensing statistics in galaxy clusters. We extract dark matter haloes from the Millennium-XXL simulation, compute their Einstein ra- dius distribution, and find a very good agreement with Monte Carlo predictions pro- duced with the MOKA code. The distribution of the Einstein radii is well described by a log-normal distribution, with a considerable fraction of the largest systems boosted by different projection effects. We discuss the importance of substructures and triax- iality in shaping the size of the critical lines for cluster size haloes. We then model and interpret the different deviations, accounting for the presence of a Bright Cen- tral Galaxy (BCG) and two different stellar mass density profiles. We present scaling relations between weak lensing quantities and the size of the Einstein radii. Finally we discuss how sensible is the distribution of the Einstein radii on the cosmological parameters ΩM − σ8 finding that cosmologies with higher ΩM and σ8 possess a large sample of strong lensing clusters. The Einstein radius distribution may help distinguish Planck13 and WMAP7 cosmology at 3σ. Key words: Gravitational lensing: strong lensing – galaxy clusters; Numerical meth- ods: simulations; Galaxies: clusters 1 INTRODUCTION particular, optical and near-infrared data provided by, for in- arXiv:1604.03109v2 [astro-ph.CO] 9 Jul 2016 stance, the Subaru and the Hubble Space telescopes (HST) Spectroscopic galaxy redshift surveys and numerical N-body are allowing to indirectly infer the total projected matter simulations have revealed a large-scale distribution of mat- density distribution in clusters through its effect of gravi- ter in the Universe featuring a complex network of intercon- tationally bending the light of background galaxies (Jullo nected filamentary galaxy associations (Tormen et al. 2004; et al. 2007; Merten et al. 2015; Limousin et al. 2015). Gravi- Springel et al. 2005; The Dark Energy Survey Collaboration tational lensing, as predicted by the Einstein’s General Rela- 2005; Sousbie et al. 2008, 2011; Guzzo et al. 2014; Percival tivity, deflects light rays once they get close to a deep poten- et al. 2014; Le Fèvre et al. 2015; Codis et al. 2015). Vertices, tial well (Einstein 1918; Landau & Lifshitz 1971). Light-rays i.e. interconnections among the filaments, correspond to the from distant galaxies travelling in the space-time of our Uni- very dense compact nodes within this cosmic web where one verse can be weakly or strongly bent when they approach a can find massive galaxy clusters (Tormen 1998; Bryan & galaxy cluster (Bartelmann & Schneider 2001; Bartelmann Norman 1998; Shaw et al. 2006; Borgani & Kravtsov 2011; 2010). The weak lensing regime happens when the light-rays Bellagamba et al. 2011). travel far from the centre of the cluster. In this case, the The mass density distribution in clusters can be inferred shapes of background galaxies are only slightly altered and, using different wavelength observations (Meneghetti et al. for a good determination of the signal, it is usually neces- 2010b; Donnarumma et al. 2011; Donahue et al. 2016). In sary to average over a large sample of background systems (Hoekstra et al. 2012, 2013; Giocoli et al. 2014; Radovich et al. 2015; Formicola et al. 2016). The strong lensing regime ? E-mail: [email protected] c 2016 RAS 2 Giocoli C. et al. 2016 takes place when the light-rays transit close to the centre shape. Furthermore, a visual inspection has revealed that of the cluster, and the mass density becomes critical: the approximately 20 percent of SLCs are boosted by various lensing event in this case is non-linear and images of back- projection effects. ground galaxies may be multiplied and/or appear stretched Given the significance of SLCs, characterising this pe- and elongated. Depending on the quality of the data and culiar class of object is crucial and this has been the focus of on their availability, weak and strong lensing data can be many studies (for example: Hennawi et al. 2007; Meneghetti used separately or jointly for a better reconstruction of the et al. 2010a; Redlich et al. 2012; Waizmann et al. 2012). projected mass from the very central region to the outskirts This is also the motivation of the present work, where we of the cluster. In the following, we will concentrate on the aim at characterising which clusters do generate strong lens- strong lensing regime and on the objects that originate it, ing features. Our approach is twofold: (i) first we will use the which we will refer to as Strong Lensing Clusters (SLCs). large sample of cluster statistics afforded by the Millennium SLCs may constitute a peculiar class of objects. While -XXL simulation (Angulo et al. 2012) – exploiting its large their existence is a natural consequence of General Relativ- size (3 Gpc/h box side), that allows to follows the formation ity, “giant arcs” – extremely distorted images of background of many massive haloes; (ii) second we will complement the galaxies – hosted in clusters have been discovered only 30 statistics with a cosmological study based on clusters mod- years ago in the core of Abell 370, independently by Lynds elled using the MOKA code (Giocoli et al. 2012a). & Petrosian (1986) and Soucail et al. (1987). This obser- We want to spend few words about the fact that the vation was recognised by Paczynski (1987) as the result of Einstein radius of lenses is not a direct observable quantity. strong gravitational lensing, a hypothesis later confirmed by The Einstein radius, defined by the location of the tangential the measurement of the redshift of the arc (Soucail et al. critical lines (more will be discussed about this in the first 1988a,b). section) is a byproduct of the mass reconstruction pipeline Since then, SLCs have led to many important advances by mean of parametric algorithms that typically assume that in cosmology: (i) being a direct and precise probe of the two- mass traces the light (Jullo et al. 2007; Zitrin et al. 2011) or dimensional projected mass density, Strong Lensing (SL) has adaptively reconstruct the mass density distribution using provided accurate mass maps, constraining structure forma- non-parametric approaches (Merten 2014). tion properties and evolution scenarios (for example: Broad- The paper is organised as follows: in Section 2 we hurst et al. 2000; Sand et al. 2002; Saha & Williams 2006; present the numerical simulations and the pseudo-analytical Bradač et al. 2006; Zitrin et al. 2009a; Zitrin & Broadhurst methods we adopt as bases for our analyses; in Section 3 we 2009b; Newman et al. 2011; Verdugo et al. 2011; Sharon discuss the scaling relations between the size of the Einstein et al. 2014); (ii) producing a natural gravitational amplifi- radius and weak lensing-derived quantities; in Section 4 we cation, SL has allowed to push the frontier of our telescopes present how the Einstein radius distribution depends on the (for example: Richard et al. 2006; Coe et al. 2013; Atek matter content of the universe and on the initial normali- et al. 2014; Zitrin et al. 2014); (iii) providing a method sation of the power spectrum. Finally in Section 5 we sum- to probe the dark energy equation of state, since images marise and discuss our results. position depends on the underling cosmology (for example: Soucail et al. 2004; Jullo et al. 2010). SLCs are now well established as a promising class of 2 METHODS objects that cannot be ignored in cosmology, and their fu- ture is extremely promising, since future facilities are ex- In this paper we aim at studying the strong lensing prop- pected to detect thousands of SLCs (Laureijs et al. 2011; erties of galaxy clusters – through the size of their Einstein Boldrin et al. 2012, 2016; Serjeant 2014), and the exquisite radius – extracted from a very large cosmological box. How- resolution of the James Webb Space Telescope (JWST) will ever, the limitation of possessing the simulation only for one deliver unique multi-colour data sets for some of them. cosmological model in addition to the fact that the run has The growing importance of SLCs has been recently il- been performed only using collisionless dark matter parti- lustrated by the CLASH program (Postman et al. 2012) cles forced us to complement the analyses using a pseudo- which has been awarded of 500 HST orbits to observe 25 analytic approach to simulate convergence maps of triaxial massive SLCs. More recently, the Hubble Deep Fields Ini- clusters. This latter method allows us, in a more flexible way, tiative has unanimously recommended a “Frontier Field” to investigate which properties of clusters mainly contribute program of six deep fields concentrated on SL clusters in shaping the Einstein radius, to quantify the contribution (together with six deep “blank fields”) in order to ad- of the stellar component and to understand how the Ein- vance our knowledge of the early epochs of galaxy forma- stein radius distribution of clusters may depend on specific tion and to eventually offer a glimpse of JWST’s universe cosmological parameters.