SEAGLE–II: Constraints on feedback models in galaxy formation from massive early-type strong lens galaxies
We use ten different galaxy formation scenarios from the EAGLE suite of CDM hydrodynamical simulations to assess the impact of feedback mechanisms in galaxy formation and compare these to observed strong gravitational lenses. To compare observations with simulations, we create strong lenses with M with the appropriate resolution and noise level, and model them with an elliptical power-law mass model to constrain their total mass density slope. We also obtain the mass-size relation of the simulated lens-galaxy sample. We find significant variation in the total mass density slope at the Einstein radius and in the projected stellar mass-size relation, mainly due to different implementations of stellar and AGN feedback. We find that for lens selected galaxies, models with either too weak or too strong stellar and/or AGN feedback fail to explain the distribution of observed mass-density slopes, with the counter-intuitive trend that increasing the feedback steepens the mass density slope around the Einstein radius ( 3-10 kpc). Models in which stellar feedback becomes inefficient at high gas densities, or weaker AGN feedback with a higher duty cycle, produce strong lenses with total mass density slopes close to isothermal (i.e. ) and slope distributions statistically agreeing with observed strong lens galaxies in SLACS and BELLS. Agreement is only slightly worse with the more heterogeneous SL2S lens galaxy sample. Observations of strong-lens selected galaxies thus appear to favor models with relatively weak feedback in massive galaxies.
keywords:gravitational lensing: strong – methods: numerical – galaxies: evolution – galaxy formation – galaxies: elliptical and lenticular, cD – galaxies: structure
Large-scale numerical simulations have established the Cold Dark Matter (CDM) paradigm as a viable framework for galaxy formation (e.g. davis1985; frenk1988). The CDM model predicts that galaxies form in dark matter halos having a Navarro-Frenk-White (NFW) density profile (navarro1996; navarro1997) and predict the abundance and distribution of substructures within these halos (e.g. gao2004; springel2010). The physics of galaxy formation, however, complicates the description of the matter distribution on small (several kpc) scales. Moreover, the central regions of CDM halos can also be strongly modified by baryonic matter and their associated physical processes.
Baryons settle into the centers of density concentrations due to dissipation, thereby modifying the inner DM slopes (e.g. Duffy2010; sonnenfeld2012; grilo2012; remus2013; cappellari2013a; Tortora14; Pontzen2014). Because a complete analytic theory of baryonic physics is lacking, hydrodynamic simulations that include many physical processes have emerged as the dominant tool to study the complex non-linear interactions taking place during galaxy formation (e.g. schaye2010; vogel2014; s15; Dubois2016; Hopkins2016). State-of-the art hydrodynamical simulations with improved stellar and AGN feedback, for example, can reproduce the cosmic star formation history of the Universe and the galaxy stellar mass function.
Hydrodynamic simulations are currently working only above certain mass and spatial resolutions, however, and physical processes on smaller scales are implemented via analytic prescriptions known as ‘sub-grid physics’. The impact of varying sub-grid physics prescriptions on large representative populations of stellar systems was first systematically explored in the ‘OverWhelmingly Large Simulations’ project (OWLS; schaye2010), a suite of over fifty large cosmological hydrodynamical simulations with varying sub-grid physics. Calibration of sub-grid prescriptions to reproduce a limited number of observables has been explored extensively (vogel2014; s15; c15; McCarthy2017), showing that their exact parameterizations are very important.
Strong gravitational lensing is one of the most robust and powerful techniques to measure the total mass and its distribution in galaxies on kpc scales (kochanek1991; koopmans2006), allowing their inner structure and evolution over cosmic time to be studied in detail (treu2006; treu2009; koopmans2006; koopmans2009; Dutton_Treu14), independently of the nature of the matter or its dynamical state. In particular, the mass density profile of massive lensing galaxies at can trace their formation and evolution mechanisms (e.g. barnabe2009; barnabe2011). The last two decades have seen major progress in observational studies of strong lensing thanks to surveys such as the Lenses Structure and Dynamics survey (LSD; treu2004), the Sloan Lens ACS Survey (SLACS; bolton2006; koopmans2006; bolton2008a; bolton2008b; koopmans2009; auger2010a; auger2010b; shu2015; Shu2017), the Strong Lensing Legacy Survey (SL2S; cabanac2007; ruff2011; gavazzi2012; sonnenfeld2013a; sonnenfeld2013b; sonnenfeld2015) and the BOSS Emission-Line Lens Survey (BELLS; Brownstein2012). Future surveys such as the Euclid (lau2011) and the Large Synoptic Survey Telescope (LSST; Ivezic2008), as well as the ongoing Kilo Degree Survey (KiDS; deJong15) and the Dark Energy Survey (DES; DES2005), are expected to increase the number of known strong lenses by several orders of magnitude (petrillo2017; Metcalf2018; Treu2018) and revolutionize strong lensing studies.
Although there have been simulation studies of strong lensing focusing on the mass-size relations, the total density slope and other observables (e.g. remus2017; Peirani2017; xu2017), the impacts of varying sub-grid physics (in particular baryonic feedback) on lensing statistics, their mass density slopes and stellar masses and sizes have not been studied comprehensively yet (peirani2018). Duffy2010 analyzed the impact of baryon physics on dark matter structure but only had low-resolution models at low redshift.
mukherjee2018 (hereafter M18), introduced the SEAGLE pipeline to systematically study galaxy formation via simulated strong lenses. SEAGLE aims to investigate and possibly disentangle galaxy formation and evolution mechanisms by comparing strong lens early-type galaxies (ETGs) from hydrodynamic simulations with those observed, analyzing them in a similar manner (although this is not always exactly possible).
As in M18, we make use of the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulations (s15; c15; McAlpine2016) – a suite of state-of-the-art hydrodynamical simulations – to create, model and analyze simulated strong lens-galaxies and compare them with observations. Throughout this study, we use ten selected galaxy formation scenarios (i.e. having different sub-grid physics prescriptions; s15; c15), the GLAMER ray-tracing package (metcalf2014; petkova2014), and the LENSED lens-modeling code (tessore15a). We preselect potential strong lenses based on their stellar masses and create projected mass maps for three different orientations. We calculate the half-mass radius from the simulated mass maps. We create mock lenses by ray tracing through the mass maps, placing an analytic sersic1968 source, at a higher redshift, having observationally motivated parameters. We ignore line-of-sight effects, which for massive ETGs is expected to be a good approximation (see e.g., koopmans2006). We use a single-orbit HST-ACS F814W noise level and PSF to mimic strong lenses found in SLACS and BELLS observations (auger2010a; Bolton2012).
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