MNRAS 000, 1–23 (2015) Preprint 1 April 2021 Compiled using MNRAS LATEX style file v3.0

nIFTy Galaxy Cluster simulations IV: Quantifying theInfluence of Baryons on Halo Properties

Weiguang Cui,1,2? Chris Power,1,2 Alexander Knebe,3,4 Scott T. Kay,5 Fed-erico Sembolini,3,4 Pascal J. Elahi,6 Gustavo Yepes,3,4 Frazer Pearce,7 DanielCunnama,8 Alexander M. Beck,9 Claudio Dalla Vecchia,10,11 Romeel Davé,12,13,14Sean February,15 Shuiyao Huang,16 Alex Hobbs,17 Neal Katz,16 Ian G. McCarthy,18Giuseppe Murante,19 Valentin Perret,20 Ewald Puchwein,21 Justin I. Read,22Alexandro Saro,9,23 Romain Teyssier,23 and Robert J. Thacker241 ICRAR, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia2 ARC Centre of Excellence for All-Sky Astrophysics (CAASTRO)3 Departamento de Física Teórica, Módulo 8, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain4 Astro-UAM, UAM, Unidad Asociada CSIC6 Sydney Institute for Astronomy, University of Sydney, Sydney, NSW 2016, Australia7 School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, UK5 Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK8 Physics Department, University of the Western Cape, Cape Town 7535, South Africa9 University Observatory Munich, Scheinerstr. 1, D-81679 Munich, Germany10 Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain11 Departamento de Astrofísica, Universidad de La Laguna, Av. del Astrofísico Francisco Sánchez s/n, 38206 La Laguna, Tenerife,Spain12 Physics Department, University of Western Cape, Bellville, Cape Town 7535, South Africa13 South African Astronomical Observatory, PO Box 9, Observatory, Cape Town 7935, South Africa14 African Institute of Mathematical Sciences, Muizenberg, Cape Town 7945, South Africa15 Center for High Performance Computing, CSIR Campus, 15 Lower Hope Street, Rosebank, Cape Town 7701, South Africa16 Astronomy Department, University of Massachusetts, Amherst, MA 01003, USA17 Institute for Astronomy, Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 16, CH-8093, Zurich, Switzerland18 Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK19 INAF - Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34143 Trieste, Italy20 Centre for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Winterthurerstrasse190, 8057 Zurich, Switzerland21 Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK22 Department of Physics, University of Surrey, Guildford, GU2 7XH, Surrey, United Kingdom23 Excellence Cluster Universe, Boltzmannstr. 2, 85748 Garching, Germany24 Department of Astronomy and Physics, Saint Mary’s University, 923 Robie Street, Halifax, Nova Scotia, B3H 3C3, Canada

Accepted XXX. Received YYY; in original form ZZZ

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ABSTRACT

Building on the initial results of the nIFTy simulated galaxy cluster comparison,we compare and contrast the impact of baryonic physics with a single massive galaxycluster, run with 11 state-of-the-art codes, spanning adaptive mesh, moving mesh,classic and modern SPH approaches. For each code represented we have a dark matteronly (DM) and non-radiative (NR) version of the cluster, as well as a full physics(FP) version for a subset of the codes. We compare both radial mass and kinematicprofiles, as well as global measures of the cluster (e.g. concentration, spin, shape), inthe NR and FP runs with that in the DM runs. Our analysis reveals good consistency(

nIFTy IV: the influence of baryons 3

in Paper I; Paper II; Paper III, and focus on how the in-clusion of the baryonic component modifies the spatial andkinematic structure of the simulated cluster. We seek to un-derstand

• the scatter between simulation codes and different inputbaryon models; and• the effects of input baryon models on cluster properties,

as well as the extent to which they converge.

We consider the global properties of the cluster – concentra-tion, spin parameter, inner slope, masses, halo shapes, andvelocity anisotropy. The cluster mass is calculated withinthe radii containing overdensities of 200, 500 and 2500 timesthe critical density of the Universe at z=0 (i.e. R200, R500,R2500). Halo shapes, as measured for isodensity and isopo-tential surfaces, and velocity anisotropy are calculated atthese three radii. We also investigate the density, circularvelocity and velocity dispersion profiles.

The paper is organised as follows. In §2, we provide abrief summary of the main features of the astrophysical sim-ulation codes used in this study, while in §3, we recall thekey properties of the simulated galaxy cluster used in thecomparison. The main results are presented in §4 and §5, inwhich we investigate how the presence of a non-radiative andradiative physical baryonic influences the simulated cluster.Finally in §6, we discuss our results and state our conclu-sions.

2 THE SIMULATION CODES

Following the classification adopted in nIFTy Paper I; Pa-per II, the 11 simulation codes used in this study are di-vided into four groups based on their gas dynamic solvingtechniques:

• Grid-based: – Ramses (Teyssier 2002);• Moving-mesh: – Arepo (Springel 2010);• Modern SPH: – G2-Anarchy (Dalla Vecchia et al. in

prep.), G3-Sphs (Read & Hayfield 2012), G3-Magneticum(Hirschmann et al. 2014), G3-x (Beck et al. 2016), G3-Pesph (Huang et al. in prep.); and• Classic SPH: – G3-Music (Sembolini et al. 2013), G3-

Owls (Schaye et al. 2010), G2-x (Pike et al. 2014), Hydra(Couchman et al. 1995).

For each simulation code we have dark-matter-only (DM)runs and non-radiative (NR) runs, which include both gasand dark matter particles; for a subset of the codes, we havefull-physics (FP) runs, which include both stars, gas, anddark matter particles, and a range of baryonic physics, in-cluding gas heating and cooling, star formation, black holegrowth, and various sources of feedback.

Following on from the findings presented in Paper I, weseparate NR runs into two groups – those run with codesthat recover declining entropy profiles with decreasing ra-dius (classic SPH), which we refer to as “Classic SPH”, andthose run with codes that recover entropy cores at smallradii (mesh, moving mesh, and modern SPH), which we re-fer to as “non-Classic SPH”. Further, we separate FP runsinto runs with and without black hole growth and AGNfeedback (AGN and noAGN respectively). The AGN feed-back is believed to be essential for galaxy clusters, which can

solve the over-cooling problem, and provide better agree-ments with observational results (e.g. Puchwein et al. 2008;Fabjan et al. 2010; Planelles et al. 2014, 2015, and referencestherein). Although G3-Pesph does not directly include theAGN feedback, it uses the heuristic model (Rafieferantsoaet al. 2015) to quench star formation in massive galaxies,which can be viewed as mimicking AGN feedback. Thus, weinclude G3-Pesph in the AGN instead of noAGN subgroup.For reference, we list all simulation codes and implementedbaryonic physics models in Table 1. We summarise the keyfeatures of the codes that are relevant for this study in ap-pendix A. We refer the reader to nIFTy Paper I; Paper II;Paper III for a more detailed summary.

3 THE SIMULATED GALAXY CLUSTER

We use the same massive galaxy cluster simulated in Pa-per I; Paper II; Paper III with a virial mass of M200 '1.1× 1015h−1M� and virial radius of R200 ' 1.69 h−1 Mpcat z=0 1. This was selected from the MUSIC-2 sample(Sembolini et al. 2013, 2014; Biffi et al. 2014), a datasetof hydrodynamical simulations of galaxy clusters that werere-simulated from the parent MultiDark2 dark-matter-onlycosmological N -body simulation (Prada et al. 2012). Inthese simulations, cosmological parameters of ΩM = 0.27,Ωb = 0.0469, ΩΛ = 0.73, σ8 = 0.82, n = 0.95, and h = 0.7were assumed, in accordance with the WMAP7+BAO+SNIdataset presented in Komatsu et al. (2011).

The initial conditions of all the clusters of the MUSIC-2 dataset are publicly available3. Briefly, these were pro-duced using the zooming technique described in Klypinet al. (2001). All particles within a sphere with a radius of6 h−1 Mpc around the centre of the halo in the parent Mul-tiDark simulation at z=0 were found in a low-resolution ver-sion (2563 particles) of the parent, and mapped back to theparent’s initial conditions to identify the Lagrangian regionfrom which these particles originated. The initial conditionsof the original simulations were generated on a finer meshof size 40963. By doing so, the mass resolution of the re-simulated objects was improved by a factor of 8 with respectto the original simulations. In the high resolution region themass resolution for the dark matter only simulations corre-sponds to mDM = 1.09 × 109 h−1 M�, while for the runsincluding a baryonic component, mDM = 9.01×108 h−1 M�and mgas = 1.9 × 108 h−1 M�. In this paper, all the codesused the same aligned parameters (see the Table 4 in Pa-per I) to re-simulate the selected cluster.

In our analysis, the cluster is first identified withAMIGA’s-Halo-Finder (Gill et al. 2004; Knollmann &Knebe 2009, AHF) and then its centre is defined as the posi-tion of the minimum of the gravitational potential (see Cuiet al. 2015, for discussion about the agreement between dif-ferent centre definitions). All the cluster properties, such as,

1 R200 is the radius within which the enclosed mean matter over-density is 200 times the critical density of the Universe, whileM200 is the total mass within R200.2 www.cosmosim.org3 CLUSTER_00019 of the MUSIC-2 sample athttp://music.ft.uam.es

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4 Weiguang Cui et al.

Table 1. Brief summary of all the simulation codes participating in the nIFTy cluster comparison project.

Type Code name, Reference Baryonic models

DM NR FPgravity solver gas treatment noAGN AGN

Grid-based Ramses, Teyssier (2002) AMR Godunov schemewith Riemann solver

N Y

Moving-mesh Arepo, Springel (2010) TreePM Godunov schemeon moving mesh

Ya Yb

G2-Anarchy, Dalla Vecchia et al. in prep. TreePM SPH kernel: Wendland C2 N NG3-Sphs, Read & Hayfield (2012) TreePM Wendland C4 N N

Modern SPH G3-Magneticum, Hirschmann et al. (2014) TreePM Wendland C6 N YG3-x, Beck et al. (2016) TreePM Wendland C4 N YG3-Pesph, Huang et al. in prep. TreePM HOCTS B-spline Y N

G3-Music, Sembolini et al. (2013) TreePM Cubic spline Yc NClassic SPH G3-Owls, Schaye et al. (2010) TreePM Cubic spline N Y

G2-x, Pike et al. (2014) TreePM Cubic spline N YHydra, Couchman et al. (1995) AP3M Cubic spline N N

a This version is named Arepo-SH.b This version is named Arepo-IL.c Two versions (G3-Music and G2-Musicpi) are included in this model.

spherical overdensity mass, radial profiles, are recalculatedwith respect to the minimum of the potential.

4 RADIAL PROFILES

4.1 Mass Profiles

Visual Impression: We begin by inspecting the differ-ences in projected dark matter density between the DM andNR runs shown in Fig. 1, and between the DM and FP runs,shown in Fig. 2. Here we show two examples from simula-tion codes drawn from the “Classic SPH” and “non-ClassicSPH” subgroups – respectively, G3-Music and Arepo. Inpractice, we use only the high-resolution dark matter par-ticles within R200 and compute densities using a standardcubic spline SPH kernel with 128 neighbours at the posi-tion of each dark matter particle; these densities are thensmoothed to a 2D mesh (on x-y plane with a pixel size of5 h−1 kpc) using the same SPH kernel (Cui et al. 2014a,2015). To show the projected dark matter density differ-ence, these images are simply aligned with the cluster cen-tre without further adjustment. The density change is givenby δρ = ρNR,FP − ρDM ; in Fig. 1, blue (red) indicates anegative (positive) δρ, or depressed (enhanced) densities inthe NR and FP runs with respect to the DM run. Note thatdark matter particles have a slightly larger mass in DM runsthan in the NR and FP runs; we compensate for this by cor-recting the dark matter particle mass in NR and FP runs tobe the same as in the DM run.

Fig. 1 clearly shows that, at z=0, dark matter densitychanges are normally within 0.5 × 1015 h M� Mpc−2 overall the cluster, except within the central regions and at thepositions of satellites. In the centre, the dark matter den-sity is depressed relative to the DM runs in the non-classicSPH runs, as shown in the Arepo panels, while the major-ity of classic SPH codes showed enhanced central densities,

as shown in the G3-Music panels. The density variationsassociated with substructures are also evident, especially atz=0 associated with the large infalling substructure (to thebottom-left) on the outskirts of the cluster, indicating thatthe inclusion of gas can introduce an offset in the timing ofmergers between DM and NR runs. At redshift z=1, differ-ences in density are smaller than at z=0, and the enhanceddensity within the central regions is evident in both sub-groups of codes.

In Fig. 2, we show how the dark matter density changesbetween the DM and FP runs, and see similar trends as inFig. 1. Interestingly, the additional baryonic processes, mostlikely gas cooling, in the FP runs compared to the NR runsresult in obvious density contrasts within the central regionsand in substructures. It’s important to note at this point,and we shall make this clear in the remainder of the paper,that the split into the classic and non-classic SPH groupingsis not really appropriate for the FP runs; there are largecode to code variations within these subgroups, primarilydriven by the baryon physics implementations.

Total Enclosed Mass Profiles In Fig. 3 we show howthe enclosed total mass density profile varies between theNR and DM runs (left column) and FP and DM runs (rightcolumn) at z=0 (upper panels) and z=1 (lower panels). Weuse fixed size in logarithm for each radial bin. Within eachpanel, we show the radial profiles (upper section) and theresiduals with respect to the median profiles (lower section).Vertical lines denote R2500 and R500 measured in the fiducialG3-Music DM (black dotted lines) and corresponding NRand FP runs (red and blue dashed lines respectively). Alower cut of R = 20 h−1 kpc, roughly in accordance withthe convergence criterion presented in Power et al. (2003)has been applied. The data are separated according to theclassic and non-classic SPH classification (thin and thickcurves) in the case of the NR runs, and the AGN and noAGN

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nIFTy IV: the influence of baryons 5

500 h−1 kpcz = 0

Arepo G3-MUSIC

Arepo

z = 1

G3-MUSIC

−0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 0.5

ρNR − ρDM [1015hM⊙Mpc−2 ]

Figure 1. Projected dark matter density difference between DM and NR runs. We only show two simulation codes – Arepo and G3-Music for illustration here. The colour is coding for the projected density difference, from negative values (blue) to positive values (red).The white region indicates no difference between the two runs. The simulation code name is shown on the top centre. The lime greencross in each plot indicates the aligned cluster centre position. The results in the upper (lower) row are from redshift z=0 (z=1). Frominner to outer region, the three dotted circles represent R2500, R500 and R200 in the DM runs, respectively.

classification (thick and thin curves) in the case of the FPruns.

We have already seen evidence in Fig. 1 that the darkmatter density in the central regions of the cluster is de-pressed in the NR runs relative to the DM runs at z=0.This depression is evident in the total spherically averagedprofiles; the non-classic SPH codes show densities of ∼ 80% of their value in the DM run in the central regions of the

cluster, while the classic SPH codes show a greater varia-tion, ranging from a density of ∼ 80 % of the DM valuefor G3-Music to ∼ 120 % for Hydra. Similar behaviour asthe classic SPH code – G3-Music, has been reported in Cuiet al. (2012); see Fig. 4 in this paper for more details.

The density is enhanced in the NR runs relative to theDM runs at large radii, outside of R2500, in all of the codes.Interestingly, at z=1, this trend of an enhancement in den-

MNRAS 000, 1–23 (2015)

6 Weiguang Cui et al.

500 h−1 kpcz = 0

Arepo-IL G3-MUSIC

Arepo-IL

z = 1

G3-MUSIC

−0.5 −0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 0.5

ρFP − ρDM [1015hM⊙Mpc−2 ]

Figure 2. Projected dark matter density difference between DM and FP runs. Similarly to Fig. 1, we only show two sample simulationcodes – Arepo-IL and G3-Music here. Refer to Fig. 1 for the details.

sity continues to small radii, before plateauing and in somecases inverting, so that the density is depressed in the NRrun relative to the DM run; notably, the codes that invertand show density depressions relative to the DM run are allnon-classic SPH codes. At z=1, it is also noticeable that thevariation between codes is large at small radii; the changeis ∼ 20 − 50 % at 100 h−1 kpc. At z=0, the variation ismuch smaller, ∼ 20 % at 100 h−1 kpc, ∼ 30 % if we includethe outlier, Hydra. The mesh code Ramses shows largerincreases respected to its DM run between R2500 and R500than all the other codes at both z=0 and 1. It means that

this difference can be traced back to even high redshift. Thenon-classic SPH code G3-Pesph has the largest deviationwith respect to other non-classic SPH codes. It shows a sim-ilar behavior as the classic SPH code G2-x, which could becaused by a convergence issue (Read & Hayfield 2012).

To highlight the scatter between different codes, weshow residuals with respect to the median for each of thenon-classic SPH codes as individual curves in the lower pan-els, while we show residuals with respect to the median forthe grouped classic SPH codes as the median (black dashedcurves) and 1-σ variation (shaded region). This shaded re-

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nIFTy IV: the influence of baryons 7

0.8

1.0

1.2

1.4

1.6

1.8

M(<R

)/M

(<R

) DM

NRRamsesArepoG3-XG2-AnarchyG3-SPHSG3-Magneticum

G3-PESPHG3-OWLSG2-XG3-MUSICHydra

z = 0.00

FPRamsesArepo-ILG3-XG3-OWLSG2-X

G3-MagneticumArepo-SHG3-PESPHG2-MUSICpiG3-MUSIC

0.70.80.91.01.11.21.31.4

ratio

0.8

1.0

1.2

1.4

1.6

1.8

M(<R

)/M

(<R

) DM

z = 1.00

102 103

R [h−1kpc]

0.70.80.91.01.11.21.31.4

ratio

102 103

R [h−1kpc]

Figure 3. Differences in the cumulative mass profile between the NR/FP and DM runs. The left column shows the difference betweenthe mass profile in the NR and DM runs, while the right column shows the corresponding result for the FP and DM runs. The line style,colour and symbol for each code are indicated in the legend. Vertical dashed (red for the NR runs; blue for the FP runs) lines show R2500(inner) and R500 (outer) from the G3-Music runs, while vertical dotted black lines are from the DM run. We show the results at z=0(top panel) and z=1 (bottom panel). Under each plot, we show the residuals with respect to the median of the non-classic SPH densityprofiles (or the median profile of the AGN subgroup in the right column), which are also shown in thick lines in the upper panels. Thethin black dashed lines are the median profiles from classic SPH codes (or the median profiles from the noAGN subgroup in the rightcolumn) with 1-σ error shown by the shadow region. The classic SPH codes (also the noAGN codes in the right column) in the upperpanel are shown in thin lines.MNRAS 000, 1–23 (2015)

8 Weiguang Cui et al.

gion is only indicating the scatter between the classic SPHcodes. For example, its lower boundary does not mean thatthe classic SPH codes have the possibility of producingsuch low density. The disparity between the median val-ues of the classic and non-classic SPH codes can be seen atR ∼ R200, there is a good agreement be-tween all of the codes for both AGN and noAGN runs; forR200 >∼ R >∼ R2500, the differences become pronounced – upto ∼ 0− 20 % – again regardless of whether or not they areAGN or noAGN. It is worth to note that the Ramses stillhas the highest enhancement compared to the other codes asits NR run; while at R ∼ R >∼ 200 h−1 kpc (this valueis much smaller for the classic SPH codes and for the higherredshift). Similar results have been found in Rasia et al.(2004), Lin et al. (2006), and Cui et al. (2012).

The sensitivity of relative central densities to baryonicphysics – of the kind implemented in the FP runs – has beenreported previously (e.g. Duffy et al. 2010; Teyssier et al.2011; Martizzi et al. 2012; Cui et al. 2012, 2014b; Vellisciget al. 2014; Schaller et al. 2015a). What is particularly inter-esting about our results is how much variation is evident inruns that seek to implement broadly similar baryonic physicsprescriptions, especially at z=0. Such variation is consistentwith previous work; some studies report on enhancementsin relative central densities, consistent with the G2-x, G3-Magneticum and G3-Owls AGN runs (e.g. Duffy et al.2010; Cui et al. 2014b; Velliscig et al. 2014), while others re-port on relative central density depressions consistent withthe Ramses, Arepo-IL and G3-x AGN runs (e.g. Teyssieret al. 2011; Martizzi et al. 2012). Understanding this varia-tion is not straightforward – not only do the precise bary-onic physics implementations differ, but there are also dif-ferences in the underlying scheme to solve the equations ofgas dynamics, as the split between classic SPH codes, suchas G2-x and G3-Owls, and non-classic SPH codes, such asG3-Magneticum and G3-x highlights.

4.2 Kinematic Profiles

The previous results highlight that the inclusion of baryonshas a significant impact on the mass distribution within thesimulated cluster, especially within the central regions. Wenow investigate how this influences kinematic profiles.

Circular Velocity: In Fig. 4, we show how the circularvelocity profile within the cluster centre (R 6 60 h−1 kpc)varies between the NR and DM runs (left column) and FPand DM runs (right column) at z=0 (upper panels) and z=1(lower panels). We limit the profile within 60 h−1 kpc be-cause we are interesting in the core region of R2500, wherethe profile is dominated by the BCG in the FP sims. A fixedlinear radial bin size is applied here. Within each panel, inthe upper section we show the median profiles of the totalmatter (solid curves), gas (dashed curves), and, if present,stars (dotted curves), with the shaded regions and the hatch-ings between dot-dashed lines indicating the 1-σ variationwith respect to the median; in the lower section we showresiduals with respect to the corresponding total matter pro-files in the DM runs. Vertical lines denote a gravitationalsoftening length of 5 h−1 kpc, which was used in the DMand NR runs, and which is used as indicative of the soft-ening in the FP runs. NR runs are grouped into non-classicSPH (thick lines with red shadow region) and classic SPH(thin lines with magenta shadow region), while FP runs aregrouped into AGN (thick lines with red shadow region) andnoAGN (thin lines with magenta shadow region) runs.

The residuals are particularly instructive. For the NRruns, at z=0, there is a ∼ 1-5 % change in the total mattercircular velocity in the classic SPH runs compared to DMruns, ∼ 10-15 % lower for the non-classic SPH runs; thechange in circular velocity of the gas component between the

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nIFTy IV: the influence of baryons 9

Figure 4. The circular velocity profile at the centre of the simulated cluster from NR runs (left panel) and FP runs (right panel). Asindicated in the legends, the solid lines show the total circular velocity in the cluster centre; the dashed lines are the circular velocityfrom the gas component; the dotted lines are from the stellar component; the different coloured regions / hatchings and lines of differentwidth show the standard deviation and median profile between different simulation codes in each subgroup, as indicated in the legends.The lower subplot below each main panel shows the total circular velocity difference between the NR/FP and DM runs. From top tobottom, we show the results at z=0 and z=1. The vertical dotted lines show the softening length in the simulation.

MNRAS 000, 1–23 (2015)

10 Weiguang Cui et al.

Figure 5. Similarly to Fig. 4, but for the velocity dispersion profile at the centre of the simulated cluster. Refer to Fig. 4 for more detailsof the subplot distributions and to the legends for the line styles and coloured region / hatching meanings.

MNRAS 000, 1–23 (2015)

nIFTy IV: the influence of baryons 11

classic and non-classic SPH runs is significant, in excess of100 %. At z=1, the classic SPH total matter circular velocityprofile is ∼ 15 % higher than in the DM runs, whereas thenon-classic SPH total circular velocity changes by between∼ -10 to +10 % from the inner to outer radius; the circularvelocity profiles of the gas components are now much morein agreement with one another, differing by ∼ 10 % at most.

In the case of the FP runs, the impact of baryonicphysics on the total matter circular velocity profile is sub-stantial, with enhancements by factors of ∼ 1.5(3.5) at10 h−1 kpc and quickly decreasing to ∼ 0(40) % at ∼60 h−1 kpc, relative to the circular velocity profiles in theDM runs at z=0 for the AGN (noAGN) subgroup. The en-hancements are greatest for the noAGN runs, as we mightexpect – without the influence of the AGN, gas cooling canproceed relatively unhindered. There are significant differ-ences between the stellar circular velocity profiles in thenoAGN and AGN runs at both z=0 and z=1, by a fac-tor of ∼ 2− 3 over the radial range, whereas the differencesbetween the gas circular velocity profiles are comparativelysmall – there is good consistency between the AGN andnoAGN runs at z=0, although the noAGN profile is abouttens of per cent higher than the AGN profile at z=1.

Velocity dispersion profiles: As in Fig. 4, we show thetotal matter (solid line), gas (dashed line) and stellar (dot-ted line) velocity dispersion (σ) profiles from both NR andFP runs (left and right columns respectively) in Fig. 5. Inthe upper (lower) panels we show results from z=0 (1), andin the upper (lower) section we show the differences with re-spect to the velocity dispersion profile in the correspondingDM run. The data is also binning in the same fixed linearsize as in Fig. 4.

In the case of the NR runs, the total velocity dispersionprofiles in the classic SPH and non-classic SPH runs are invery good agreement at z=0 and reasonable agreement atz=1. At z=0, the difference with respect to the DM runs issmall, with the ratio of σ/σDM of order unity; at z=1, thedifference is slightly greater, showing an enhancement by afactor of ∼ 1.1 − 1.3 greater than in the DM run (greaterwithin ∼ 10 h−1 kpc). The gas velocity dispersion profilesare broadly similar in the classic and non-classic SPH runsat both redshifts.

Against the circular velocity profiles in the FP runs,here we see a less significant variation in the velocity dis-persion profiles with respect to the median, evident in Fig.5. At z=0, the median total matter and stellar velocity dis-persions have a broadly similar shape and amplitude, albeitwith the noAGN velocity dispersions being larger; the gasprofiles show a slightly larger discrepancy, although both areflat over most of the radial range, and here the AGN veloc-ity dispersion is larger, as we might expect in the presenceof feedback from the central AGN. Relative to the DM runsvelocity dispersion profiles, we see that the ratio with re-spect to both AGN and noAGN is flat and of order unityin the AGN runs and ∼ 1.1 in the noAGN runs. Both setsof runs show a decline within the central ∼ 10 h−1 kpc.At z=1, the total matter velocity dispersion in the AGNruns rises sharply in the inner regions before flattening offat R >∼ 30 h−1 kpc, whereas the noAGN case shows a steadyincrease with increasing radius. The difference with respect

to the DM run is shown in the lower section, and we seethat the ratio in both the AGN and noAGN runs is flat atR >∼ 20 h−1 kpc and corresponds to an enhancement by afactor of ∼ 1.2, but shows a smaller enhancement in theAGN run and a slightly larger enhancement in the noAGNrun at R

12 Weiguang Cui et al.

Ramses

Arepo

G3-X

G2-Anarchy

G3-SPHS

G3-Magneticum

G3-PESPH

G3-OWLS

G2-X

G3-MUSIC

Hydra

14.4 14.5 14.6 14.7 14.8 14.9 15.00.9

1.0

1.1

1.2

1.3

M/MDM

z = 0.00

NR

Ramses

Arepo-IL

G3-X

G3-OWLS

G2-X

G3-Magneticum

Arepo-SH

G3-PESPH

G2-MUSICpi

G3-MUSIC

14.4 14.5 14.6 14.7 14.8 14.9 15.0

FP

13.7 13.8 13.9 14.0 14.1 14.2 14.3 14.4

logMNR [h−1M⊙]

0.9

1.0

1.1

1.2

1.3

M/MDM

z = 1.00

Non-classic SPHClassic SPH

13.7 13.8 13.9 14.0 14.1 14.2 14.3 14.4

logMFP [h−1M⊙]

AGNnoAGN

Figure 6. Halo mass difference between the DM runs and the NR runs (left column) / the FP runs (right column). As indicated in thelegends in the top row, different coloured symbols indicate different simulation codes. In each panel, there are three groups of data witherror bars, which correspond to M2500,M500 and M200 from smaller to larger halo mass. The meaning of the error bars in both columnsis shown in the legends in the two lower panels: the brown thick one is for the non-classic SPH subgroup (AGN subgroup in the rightcolumn); while the black thin errorbar is for the classic SPH subgroup (noAGN subgroup in the right column). From top to bottompanel, we show the results at z=0 and 1, respectively.

sults are consistent with the findings of Cui et al. (2012) (seeFig. 2 for more details), and in particular, the insensitivityof M200 to simulation code and precise baryonic model is inbroad agreement with previous studies (cf. the work of Cuiet al. 2014b; Schaller et al. 2015a, who focused on clustermass scales).

5.2 Central Density Profile

Following Newman et al. (2013); Schaller et al. (2015b), wecharacterise the central total mass density profile by theaverage logarithmic slope over the radial range 0.003R200 to

0.03R200,

γ = − < d log ρtot(r)d log r >, (1)

here we used 25 equally spaced logarithmic bins to constructthe density profile. We have verified that the number of binshas little effect on the γ value as long as it is larger than 10.The results are shown in Fig. 7 and reveal some interestingtrends.

Firstly, the average slope in the NR runs increases fromγNR ' 0.7 at z=1 to γNR ' 0.8 at z=0, while the variation

MNRAS 000, 1–23 (2015)

nIFTy IV: the influence of baryons 13

0.6 0.8

γNR

0.5

1.0

1.5

γ/γDM

z = 0.00

Non-classic SPH

Classic SPH

0.6 0.8

γNR

z = 1.00

NR

1 2 3

γFP

2

4z = 0.00

1 2 3

γFP

z = 1.00

FP

AGN

noAGN

Figure 7. The inner slope changes for the NR runs (left panel) and the FP runs (right panel). The coloured symbols represent thedifferent simulation codes as in Fig. 6. The meaning of the errorbars are shown in the legends in both left and right panels.

in γNR with respect to the mean decreases by a factor of afew between z=1 and z=0.

Secondly, the ratio of the average slope in the NR runswith respect to the DM runs shows little variation withredshift – 〈γNR/γDM 〉 ' 1 for the non-classic SPH runs,〈γNR/γDM 〉 ' 0.9 for the classic SPH runs – whereas thevariation with respect to the mean shows a sharp decreasebetween z=1 and z=0, by a factor of several.

Thirdly, there is a large spread in slopes in the FP runs,ranging from γFP ' 1 to 3, at both z=0 and z=1; separatingruns into those with and without AGN and taking the aver-age reveals no difference at z=1 (〈γFP 〉 ' 2.2 for both AGNand noAGN runs), whereas there is a reasonably significantdifference at z=0 (〈γFP 〉 ' 1.5 for AGN runs, 〈γFP 〉 ' 2.2for noAGN runs) and in the sense we might expect (i.e.steeper slopes in the noAGN runs, indicating enhanced starformation and cold gas in the central galaxy). The medianvalue from the AGN runs is slightly higher than the resultfrom Schaller et al. (2015b).

Fourthly, there are dramatic enhancements in the aver-age slope in the FP runs with respect to the DM runs, with〈γFP /γDM 〉 ' 2 at z=0 and 〈γFP /γDM 〉 ' 3 − 4 at z=1,and as in the NR runs, the variation with respect to theseaverages shrinks by a factor of ∼ 2 − 3 between the AGNand noAGN runs at both redshifts.

5.3 Concentration

The results so far suggest that there should be a measurabledifference in the concentration parameter between the dif-ferent sets of runs. We investigate this by assuming that thespherically averaged dark matter density profile, ρ(r), canbe approximated by the Navarro et al. (1996, 1997) form,

ρ(r)ρcrit

= δc(r/rs)(1 + r/rs)2, (2)

here ρcrit is the critical density of the Universe, δc a charac-teristic density, and rs a characteristic radius that is directlyrelated to the concentration cNFW = R200/rs.

There is an extensive literature on the accuracy withwhich equation 2 describes density profiles in dark mat-ter only simulations, and while it represents a reasonable

approximation to the ensemble averaged density profile ofdark matter haloes in dynamical equilibrium, it cannot cap-ture the shape of the density profile in detail. The presenceof baryons complicates matters even further, as shown bySchaller et al. (2015a), but equation 2 provides a reasonabledescription of the dark matter density profile over the radialrange [0.05R200 −R200].

Following Schaller et al. (2015a), we fit both NFW pa-rameters (i.e. δc and rs) to the dark matter density profilewithin this radial range in the DM, NR, and FP runs, us-ing the curve_fit package from scipy (Jones et al. 2001) withequally spaced logarithmic bins. In Fig. 8, we show residu-als corresponding to these NFW fits using data drawn fromthe classic and non-classic SPH examples, G3-Music andArepo; solid, dashed, and dotted lines indicate DM, NR,and FP runs. Note that there are two versions of the FPruns for each code. Within the fitting radius range, whichis indicated by the thick lines, the dark matter componentmass profile agrees with the NFW profile to within ∼ 15 %(slightly worse at z=1) for all three baryonic models.

In Fig. 9, we show how the ratio of concentration inthe NR and FP runs (left and right panels) relative to theDM run varies with measured concentration. Within eachpanel, the left (right) section shows the z=0 (1) trend. Thebehaviour in both the NR and FP runs is similar. At z=0,the concentration is enhanced in both the classic and non-classic SPH runs, and in the AGN and noAGN runs, to asimilar extent, a factor of ∼ 1 − 1.2. At z=1, the enhance-ments are more pronounced in all of the NR and FP runs,a factor of ∼ 1.5, although the spread in values is largerin the FP runs. Interestingly, for the NR runs at z=0, wesee a clear separation in the median value and enhancementof the concentration, with the classic SPH runs showing ahigher concentration and enhancement, consistent with ourobservations in the previous section.

The concentration enhancements in the NR runs andthe noAGN FP runs are consistent with Duffy et al. (2010)and Fedeli (2012). The increased concentration found in theFP runs with AGN feedback is in agreement with Schalleret al. (2015a), but contradicting Duffy et al. (2010), whofound either no change or a decrement in concentration. We

MNRAS 000, 1–23 (2015)

14 Weiguang Cui et al.

0.8

0.9

1.0

1.1

1.2

ρ/ρfit

Arepo-IL

Arepo

z = 0

G2-MUSICpi

G3-MUSIC

z = 0

DM

NR

FP

10-1 100

R/rs

0.8

0.9

1.0

1.1

1.2

ρ/ρfit

Arepo-SH

z = 1

10-1 100

R/rs

G2-MUSICpi

z = 1

Figure 8. Mass profile ratio to the NFW fitting for the dark matter component as a function of radius, which is normalized to the fittedparameter rs. Similarly to Fig. 1, we only illustrate two example simulations at here. The simulation code names are shown in the topof each panel. Different color and style lines represent different baryonic models as indicated in the legend of the top-right panel. Thethick lines indicate the region used for the NFW fitting. Upper row shows the result at z=0, while the lower row is the result at z=1.

caution that our small number statistics may play a role inthe difference.

5.4 Spin Parameter

The spin parameter λ is commonly used to quantify thedegree to which the structure of a system is supported byangular momentum. Several definitions for spin have been

proposed, but we investigate the two most common defini-tions;

• λP , the dimensionless “classical” spin parameter (Peebles1969),

λP =J

√|E|

GM5/2, (3)

where J is the magnitude of the angular momentum of ma-

MNRAS 000, 1–23 (2015)

nIFTy IV: the influence of baryons 15

1.5 2.0 2.5

cNR

1.0

1.5

2.0

c/c D

M

z = 0.00

Non-classic SPH

Classic SPH

1.5 2.0 2.5

cNR

z = 1.00

NR

AGN

noAGN

1.5 2.0 2.5

cFP

1.0

1.5

2.0z = 0.00

1.5 2.0 2.5

cFP

z = 1.00

FP

Figure 9. Concentration changes with respect to the DM runs. The left column shows the results from NR runs, while the right columnis from the FP runs. The two subplots in each column show the results at both z=0 and z=1, which is indicated in the top left of eachpanel. The coloured symbols represent the different simulation codes, as indicated on Fig. 6. Again, the NR runs are separated intonon-classic and classic SPH subgroups, while the FP runs are separated into AGN and noAGN subgroups, as indicated by the errorbarsin the legends.

0.022 0.024 0.0260.7

0.8

0.9

1.0

1.1

1.2

λB/λB,DM

z = 0.00

0.034 0.036 0.038

z = 1.00

NR

0.016 0.018 0.020

λNR

0.7

0.8

0.9

1.0

1.1

1.2

λP/λP,DM

0.024 0.026 0.028 0.030

λNR

Non-classic SPH

Classic SPH

0.022 0.024 0.026

z = 0.00

0.034 0.036 0.038

z = 1.00

FP

0.016 0.018 0.020

λFP

0.024 0.026 0.028 0.030

λFP

AGN

noAGN

Figure 10. Spin parameter changes with respect to the DM runs. The left column shows the results from NR runs, while the rightcolumn is for the FP runs. The two different methods (indicated as λB (Bullock et al. 2001), λP (Peebles 1969), in the y-label) are shownin each row. There are two subplots for each panel, which show the results at the two redshifts as indicated in the uppermost panels.The coloured symbols represent the different simulation codes, as indicated on Fig. 6. Again, we separate the NR runs into non-classicSPH and classic SPH subgroups, the FP runs into AGN and noAGN subgroups, as indicated by the errorbars in the legends.

terial within the virial radius, M is the virial mass, and Eis the total energy of the system; and

• λB , the modified spin parameter of Bullock et al. (2001),which avoids the expensive calculation of the total energy E

of a halo,

λB =J√

2MVR, (4)

here V =√GM/R is the circular velocity at the virial ra-

dius R, and M and J have the same meaning as in the

MNRAS 000, 1–23 (2015)

16 Weiguang Cui et al.

“classical” spin parameter λP . Both spin parameters are cal-culated including all material with r 6 R200.

The spin parameters measured in the NR and FP runsare shown in the left and right panels respectively of Fig. 10;coloured symbols are as in Fig. 6. FP runs are grouped intoAGN (brown thick errorbars) and noAGN models (blackthin errorbars); NR runs are separated into non-classic(brown thick errorbars) and classic SPH (black thin error-bars) runs.

There are a couple of points worthy of note in this Fig-ure. Firstly, there is a systematic drop between z=1 and z=0in the ratio of λB and λP with respect to their DM counter-parts in both the NR and FP runs and in all of the groupings(classic vs non-classic SPH, AGN vs noAGN). Secondly, themeasured spins are broadly similar in the NR runs, indepen-dent of either redshift or classic vs non-classic SPH group-ing, but there is a much larger spread in values in the FPruns, and the result is sensitive to whether or not AGN isincluded.

Interestingly, Bryan et al. (2013) found that the z=0spin distribution of dark matter haloes extracted from runsincluding baryonic physics, both with and without AGNfeedback, is not significantly different from that of dark mat-ter only haloes. They reported that their baryon runs exhibitslightly lower median spin values at z=2 than in their dark-matter-only runs, in apparent contradiction to our results.However, their median halo mass isM200 = 2×1012 h−1M�,which is about 3 orders lower than our cluster, and these sys-tems will have significantly different merging histories thanour cluster. Merging history is likely to influence the angu-lar momentum content of the system, especially that of thegaseous component, with angular momentum cancellationoccurring in response to collisions and shocks of gas frommultiple infall directions.

5.5 Shape of Isodensity and Isopotential Shells

Having considered the spin parameter, we now move on tothe shape of the cluster’s isodensity and isopotential sur-faces. We adopt the common method of diagonalization ofthe inertia tensor and characterization with ellipsoids of ei-ther the interpolated density field (e.g. Jing & Suto 2002)or the underlying gravitational potential (e.g. Springel et al.2004; Hayashi et al. 2007; Warnick et al. 2008). FollowingBett et al. (2007); Warnick et al. (2008), the inertia tensor(see Warnick et al. 2008; Vera-Ciro et al. 2011, for morediscussions of the choice of inertia tensor) is defined as:

Iαβ =N∑i=1

mi(r2i δαβ − xi,αxi,β), (5)

where ri is the position vector of the ith particle, α and βare tensor indices (α, β = 1, 2, 3), xi,α are components ofthe position vector of ith particle, and δαβ is the Kroneckerdelta. We estimate the shape of isodensity and isopoten-tial shells at three radii: R2500, R500 and R200, selecting allparticles (including dark matter, star and gas components)within these shells as described in Appendix B. Eigenvaluescan be computed by noting that

I = M5

[b2 + c2 0 0

0 a2 + c2 00 0 a2 + b2

](6)

These axes then describe a hypothetical uniform ellipsoidwhose axes a > b > c are those of the halo itself. Thus, wecan have b/a =

√(Ia + Ic − Ib)/(Ib + Ic − Ia) and c/a =√

(Ia + Ib − Ic)/(Ib + Ic − Ia). For completeness, we alsouse a direct linear least squares fitting method to fit el-lipsoids to the 3D isodensity surfaces to verify our results,which we describe in Appendix C.

In Fig. 11, we show how the axis ratios, b/a and c/a,change between the DM runs and the corresponding NR andFP runs (left and right columns) within thin isodensity andisopotential shells (upper and lower panels) at R2500, R500and R200 (left, middle, and right panels within each column)as a function of b/a and c/a in the NR and FP runs; therelevant redshift is shown in the leftmost panel of each row.

Broadly similar trends are evident in both the NR andFP runs at both redshifts. At z=0, the isopotential shellsbecome slightly rounder at all radii, by a factor of∼ 1.1−1.2.The outermost isodensity shell becomes slightly rounder bya similar factor; the inner shells become more oblate, withnegligible change in c/a, but b/a drops by a factor of ∼ 0.8.At z=1, the trend is such that the inner isodensity shellsbecome slightly rounder by a factor of ∼ 1.1 in both the NRand FP runs, whereas the outermost shell can be either moreoblate (NR) or prolate (FP). The isopotential shells changein such a way that c/a is enhanced whereas b/a is reduced,resulting in negligible net change in the overall shape of thehalo.

The effect of including baryonic physics on the shapes ofdark matter haloes has been studied previously with hydro-dynamic simulations in (Kazantzidis et al. 2004; Knebe et al.2010; Bryan et al. 2013; Tenneti et al. 2014; Butsky et al.2015; Velliscig et al. 2015, etc.). Kazantzidis et al. (2004)found that halos formed in simulations with gas cooling aresignificantly more spherical than corresponding halos formedin adiabatic simulations. Knebe et al. (2010) found that theinclusion of gas physics has no affect on the (DM) shapesof subhaloes, but an influence on their suite of host haloes,which drives the DM halo to become more spherical espe-cially at the central regions (see also Debattista et al. 2008;Tissera et al. 2010; Abadi et al. 2010; Bryan et al. 2013;Tenneti et al. 2014; Butsky et al. 2015; Tenneti et al. 2015,etc.). Our results from the isopotential shell are in agreementwith these literatures. However, at the most inner isodensityshell – R2500, there is a decrease of b/a (slightly smaller de-crease for c/a). However, the increases for both b/a and c/aat R2500 are very clear from the isopotential shell. This ispossibly caused by the substructures in the isodensity shell,which has less effect with the isopotential shell method. Us-ing hydro-dynamical simulations with different versions ofbaryon models, Velliscig et al. (2015) showed these differentbaryon models have less effect on the halo shape. This agreeswith our findings from Fig. 11, which shows a broadly agree-ment between different simulation codes as well as betweenthe NR and FP runs.

5.6 Velocity Anisotropy

We finish our analysis by looking at the velocity anisotropy

β = 1− σ2tan

2σ2r, (7)

MNRAS 000, 1–23 (2015)

nIFTy IV: the influence of baryons 17

0.4 0.6 0.8

0.8

1.0

1.2

1.4

1.6

c/a

c/aDM

b/a

b/aDM

z = 0.00 R2500

0.4 0.6 0.8

R500

NR Density shell

0.4 0.6 0.8

R200

0.4 0.6 0.8

0.8

1.0

1.2

1.4

1.6

c/a

c/aDM

b/a

b/aDM

z = 1.00

0.4 0.6 0.8 0.4 0.6 0.8

0.4 0.6 0.8

R2500

0.4 0.6 0.8

R500

FP Density shell

0.4 0.6 0.8

R200

0.4 0.6 0.8 0.4 0.6 0.8 0.4 0.6 0.8

0.4 0.6 0.8

0.9

1.0

1.1

1.2

c/a

c/aDM

b/a

b/aDM

z = 0.00

0.4 0.6 0.8

NR Potential shell

0.4 0.6 0.8

0.4 0.6 0.8

0.9

1.0

1.1

1.2

c/a

c/aDM

b/a

b/aDM

z = 1.00

0.4 0.6 0.8

ca NR

ba NR

0.4 0.6 0.8

0.4 0.6 0.8 0.4 0.6 0.8

FP Potential shell

0.4 0.6 0.8

0.4 0.6 0.8 0.4 0.6 0.8

ca FP

ba FP

0.4 0.6 0.8

Figure 11. The halo shape (axis ratios: caand b

a) changes between the DM runs and NR runs (left column) / FP runs (right column)

from both the isodensity shells (top two panels) and the isopotential shells (lower two panels). These results are calculated through theinertia method. We refer to Fig. 6 for the meanings of the coloured symbols. Inside each panel, we show the results at three shells atR2500, R500 and R200 from left to right within each subplot, and at redshifts of z=0 and z=1 in the top and bottom subplots. Again,the errorbars from the FP runs are grouped into AGN (brown thick errorbars) and noAGN (black thin errorbars); while the errorbarfrom the NR runs are grouped into non-classic SPH (brown thick errorbars) and classic SPH (black thin errorbars) methods.

where σtan and σr are the tangential and radial velocity dis-persions. We compute these components of the velocity dis-persion using the particles selected in the isopotential shellsat the three radii, and show the results in Fig. 12, reveal-ing how β varies between NR and FP runs (left and rightcolumns) at z=0 and 1 (upper and lower rows within eachcolumn) at R2500, R500 and R200 (left, middle, and right pan-els within each column).

Again, we see very similar values and changes of the βparameter between the NR and FP runs at fixed radius andredshift. At redshift z=1, we have larger β values atR200 andR2500 than at R500; while at z=0 the β value is much largerat R500 than at the other two radii. The incrementation ofβ at R200 is ∼ 10 % at both redshifts; at R500, there is aslightly small increase of β (∼ 5 %) at z=0, while there arelarge disagreements between the subgroups at z=1; at theinnermost radius R2500, there are about 10 % increase of β atz=0, but about 10 % decrease of β at z=1 compared to their

DM runs. Similar to the halo shape changes, we do not finda clear separation between these subgroups, except the onesat R500 and z=1. There are also broad agreements betweenthe results from the isodensity and from the isopotentialshells.

Lau et al. (2010) investigated two hydro-dynamical sim-ulations: one with no-radiative gas; the other including gascooling, star formation and feedback. By comparing the two,they found that the dark matter velocity anisotropy profileis almost unaffected by the addition of cooling, star forma-tion and feedback and insensitive to redshift between z=0and 1. This is in very good agreement with what we find inFig. 12 – there are very similar values and changes of the βparameter between the NR and FP runs.

MNRAS 000, 1–23 (2015)

18 Weiguang Cui et al.

0.5

1.0

1.5

β/βDM

z = 0.00

R2500 R500

NR Potential Shell

R200

0.2 0.4 0.6

0.5

1.0

1.5

β/β

DM

z = 1.00

0.2 0.4 0.6

βNR

0.2 0.4 0.6

0.5

1.0

1.5R2500 R500

FP Potential Shell

R200

0.2 0.4 0.6

0.5

1.0

1.5

0.2 0.4 0.6

βFP

0.2 0.4 0.6

Figure 12. The halo velocity anisotropy, β. The difference between the DM runs and NR runs (left column) / FP runs (right column).This figure is very similar to Fig. 11 in subplot distribution, symbols and errorbars. We refer to Fig. 11 for more details.

6 DISCUSSION AND CONCLUSIONS

We have investigated the performance of 11 modern astro-physical simulation codes – Hydra, Arepo, Ramses and 8versions of Gadget with different SPH implementations –and with different baryonic models – by carrying out cosmo-logical zoom simulations of a single massive galaxy cluster.By comparing different simulation codes and different runsranging from dark matter only to full physics runs, whichincorporate cooling, star formation, black hole growth, andvarious forms of feedback, we set out to

(i) quantify the scatter between codes and different baryonmodels.(ii) understand the impact of baryons on cluster properties,and the extent to which these properties converge.

For clarity, and motivated by the results of Paper I, wegrouped codes according to whether or not they are “Clas-sic SPH”, which produce declining entropy profiles with de-creasing radius in non-radiative runs, or “non-Classic SPH”,which include the mesh, moving mesh, and modern SPHcodes, which recover entropy cores at small radii. We alsogrouped full physics runs according to whether or not theyinclude black hole growth and AGN feedback as “AGN” and“noAGN” runs respectively. Our key findings can be sum-marised as follows:

Code Scatter: In Paper I, we already saw that code-to-code scatter between codes for the aligned dark-matter-only runs is within 5 % for the total mass profile. If we ignorethis difference, the non-radiative gas boosts this scatter upto ∼ 30 % at z=0, with the largest difference evident inthe central regions, and up to ∼ 50 % at z=1. However, bygrouping codes into classic and non-classic SPH, the scatterfor the total mass profile within a grouping is reduced to ∼20 %; this means that the disagreement is driven by the ap-proach to solving the equations of gas dynamics. The scatter

for the total density profile is reduced to 6 5 % between allcodes at R > R2500, and even smaller at larger radius.The scatter in the total mass profile between different

codes in the FP runs, when compared to the NR runs, islarger – over 100 per cent at z=0, greater at z=1, within thecentral regions. Grouping the runs into those that includeAGN feedback and those that do not, the scatter in thecentral regions is still substantial, which implies that thecomplexities of sub-grid physics can produce very differentresults, even when similar baryonic physics prescriptions areadopted. This is especially true for the codes with AGNfeedback. The scatter between different runs reduces to 6 10per cent at R ≈ R2500, and smaller at larger radii.For most of the global cluster properties investigated in

this paper, we find the scatter between different codes anddifferent baryonic physics models is within ∼ 20 %, in agree-ment with Paper I; Paper II; Paper III.

Impact of Baryons: Using the DM runs as our refer-ence, we find that the change in total mass profile in the FPruns is more marked than in the NR runs, especially withinthe central regions. Already within R500 we see ∼ 10 %variations with respect to the median in the FP runs, whichgrows to ∼ 20 % variations at R2500. In contrast, the varia-tions with respect to the median are markedly smaller in theNR runs,

nIFTy IV: the influence of baryons 19

at both redshifts between the NR and FP runs,and with theconclusions of Paper II. Because of the large scatter of thetotal mass profile in the central regions, the total inner den-sity slope γ and the concentration CNFW , shows the largestscatter, with a clear separation between the different sub-groups at z=0.By choosing the three characteristic radii – R2500, R500

and R200, we investigate how the cluster properties changeat different radii. The halo mass changes have a clear radiusdependence at both redshifts, the inner radius shows thelargest increase for both the NR and FP runs compared tothe DM runs. There is almost no mass change for M200 atboth redshifts. The halo shape changes are dependent on thechoice of the shells; isodensity shells change from inner toouter radii, but are weakly dependent on redshift, whereasisopotential shell changes are systematic with radius andredshift.

It’s interesting to note that the clear separation we seebetween classic and non-classic SPH runs in the mass pro-files in the NR runs is not reproduced in the FP runs. Howmuch of this difference is driven by the hydrodynamical tech-nique? In the AGN runs (right upper panel of Fig. 3), theclassic SPH codes G2-x and G3-Owls tend to have muchhigher density at the cluster centre than the non-classic SPHcodes G3-x, Arepo and Ramses, while the non-classic SPHcodes G3-Pesph, which uses a heuristic model to quenchstar formation, produces a much lower density profile thanthe other codes from the noAGN group. In addition, thegas profile difference between these simulation codes in theNR runs is about 100 % at the cluster centre, as was shownin Paper I. This seems to suggest that the hydrodynamictechnique can be as important as baryonic physics in set-ting the mass profile in the FP runs. However, we note alsothat the total mass profile in the non-classic SPH code –Arepo-SH – that does not include AGN feedback is veryclose to the classic SPH codes without AGN feedback, andthe non-classic SPH code G3-Magneticum has a highercentral density than codes that do not include AGN feed-back, despite having AGN feedback included. This suggeststhat the hydrodynamic scheme may be important, but thedetails of the baryonic physics prescription is more impor-tant in shaping the mass profile.

There are two FP runs of G3-Music in this study, theoriginal one runs with Gadget-3 code and the Springel &Hernquist (2002) baryon model; while the other one – G2-Musicpi run with Gadget code and the Piontek & Stein-metz (2011) baryon model. Through this study, we find thatthere is almost no difference between the two simulations,which can be understood as there are no differences betweenthe two simulation codes and between the two versions ofbaryon models for this simulated galaxy cluster.

Although we have shown the scatter between differentsimulation codes / techniques and between different bary-onic models, a detailed comparison of the algorithms as wellas of the numerical implementation methods of baryonicmodels is in great needs, because these details are essentialfor explaining the scatter we show in this paper. To achievethis goal, we are planning to first perform a convergencetest in a following study, and then extend this comparisonproject to an extensive examination on these parameters inthe baryon models.

Although this work is based on the analysis of only onesimulated galaxy cluster, we argue that our results are ro-bust, because most of them are mainly shown by the differ-ences, in which most systematic errors should be canceled.However, it will be worth to increase the statistics by sim-ulating more clusters in further comparisons: for example,relaxed and un-relaxed clusters may give different answersdue to their different dynamical state. We are including moreMUSIC clusters to our comparison project and will presentthe results in future papers.

ACKNOWLEDGEMENTS

The authors would like to thank Joop Schaye and StefanoBorgani for their kind helps and suggestions. The authorswould like to acknowledge the support of the InternationalCentre for Radio Astronomy Research (ICRAR) node atthe University of Western Australia (UWA) for the hostingof the “Perth Simulated Cluster Comparison" workshop inMarch 2015, the results of which has led to this work; the fi-nancial support of the UWA Research Collaboration Award(RCA) 2014 and 2015 schemes; the financial support of theAustralian Research Council (ARC) Centre of Excellencefor All Sky Astrophysics (CAASTRO) CE110001020; andARC Discovery Projects DP130100117 and DP140100198.We would also like to thank the Instituto de Fisica Teorica(IFT-UAM/CSIC in Madrid) for its support, via the Centrode Excelencia Severo Ochoa Program under Grant No.SEV-2012-0249, during the three week workshop “nIFTyCosmology" in 2014, where the foundation for much of thiswork was established.

WC acknowledges support from UWA RCAs PG12105017and PG12105026, and from the Survey Simulation Pipeline(SSimPL; http://www.ssimpl.org/).CP is supported by an ARC Future FellowshipFT130100041 and ARC Discovery Projects DP130100117and DP140100198.AK is supported by the Ministerio de Economía y Com-petitividad (MINECO) in Spain through grant AYA2012-31101 as well as the Consolider-Ingenio 2010 Programme ofthe Spanish Ministerio de Ciencia e Innovación (MICINN)under grant MultiDark CSD2009-00064. He also acknowl-edges support from ARC Discovery Projects DP130100117and DP140100198. He further thanks Dylan Mondegreen forsomething to dream on.PJE is supported by the SSimPL programme and the Syd-ney Institute for Astronomy (SIfA), and Australian ResearchCouncil (ARC) grants DP130100117 and DP140100198.GY and FS acknowledge support from MINECO (Spain)through the grant AYA 2012-31101. GY thanks also the RedEspañola de Supercomputacion for granting the computingtime in the Marenostrum Supercomputer at BSC, where allthe MUSIC simulations have been performed.

GM acknowledges supports from the PRIN-MIUR 2012Grant "The Evolution of Cosmic Baryons" funded by theItalian Minister of University and Research, from the PRIN-INAF 2012 Grant "Multi-scale Simulations of Cosmic Struc-tures" funded by the Consorzio per la Fisica di Trieste.AMB is supported by the DFG Cluster of Excellence "Uni-

MNRAS 000, 1–23 (2015)

20 Weiguang Cui et al.

verse" and by the DFG Research Unit 1254 "Magnetisationof interstellar and intergalactic media".CDV acknowledges support from the Spanish Ministry ofEconomy and Competitiveness (MINECO) through grantsAYA2013-46886 and AYA2014-58308. CDV also acknowl-edges financial support from MINECO under the 2011Severo Ochoa Program MINECO SEV-2011-0187.EP acknowledges support by the Kavli foundation and theERC grant "The Emergence of Structure during the epochof Reionization".RJT acknowledges support via a Discovery Grant fromNSERC and the Canada Research Chairs program. Simu-lations were run on the CFI-NSRIT funded Saint Mary’sComputational Astrophysics Laboratory.

The authors contributed to this paper in the followingways: WC, CP, & AK formed the core team that organizedand analyzed the data, made the plots and wrote thepaper. CP, WC, LO, AK, MK, FRP & GY organized thenIFTy workshop at which this program was completed.GY supplied the initial conditions. PJE assisted withthe analysis. All the other authors, as listed in Section 2performed the simulations using their codes. All authorsread and comment on the paper.

The simulation used for this paper has been run on Marenos-trum supercomputer and is publicly available at the MUSICwebsite.The Arepo simulations were performed with resourcesawarded through STFCs DiRAC initiative.G3-Sphs sumulations were carried out using resources pro-vided by the Pawsey Supercomputing Centre with fundingfrom the Australian Government and the Government ofWestern Australia.G3-Pesph simulations were carried out using resources atthe Center for High Performance Computing in Cape Town,South Africa.G2-Anarchy simulations were performed on the TeideHigh-Performance Computing facilities provided by the In-stituto Tecnológico y de Energías Renovables (ITER, SA).This research has made use of NASA’s Astrophysics DataSystem (ADS) and the arXiv preprint server.All the figures in this paper are plotted using the pythonmatplotlib package (Hunter 2007).

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APPENDIX A: SIMULATION CODES

RAMSES (Perret, Teyssier)Ramses is based on adaptive mesh refinement (AMR) tech-nique, with a tree-based data structure allowing recursivegrid refinements on a cell-by-cell basis. The hydrodynami-cal solver is based on a second-order Godunov method withthe HLLC Riemann solver. For the baryon physics, Ramsesmodifies Haardt & Madau (1996) for the gas cooling andheating with metal cooling function of Sutherland & Do-pita (1993). The UV background and a self-shielding recipeis based on Aubert & Teyssier (2010). The star formationfollows Rasera & Teyssier (2006) with density threshold ofn∗ = 0.1Hcm−3. The formation of super massive black hole(SMBH) uses the sink particle technique (Teyssier et al.2011). The SMBH accretion rate can have a boost factorcompared to the Bondi accretion rate (Booth & Schaye2009). It can not exceed the instantaneous Eddington limit,however. The AGN feedback used is a simple thermal en-ergy dump with 0.1c2 of specific energy, multiplied by theinstantaneous SMBH accretion rate.

AREPO (Puchwein)

MNRAS 000, 1–23 (2015)

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22 Weiguang Cui et al.

Arepo employs a TreePM gravity solver and the hydrody-namic equations are solved with a finite-volume Godunovscheme on an unstructured moving Voronoi mesh (Springel2010). Detailed descriptions of the galaxy formation mod-els implemented in Arepo-IL can be found in Vogelsbergeret al. (2013, 2014). The other FP version (Arepo-SH) ofArepo has the same baryon model as G3-Music.

G2-ANARCHY (Dalla Vecchia)G2-Anarchy is an implementation of Gadget-2 (Springel2005) employing the pressure-entropy SPH formulation de-rived by Hopkins (2013). G2-Anarchy uses a purely numer-ical switch for entropy diffusion similar to the one of Price(2008), but without requiring any diffusion limiter. The ker-nel adopted is the C2 function of Wendland (1995) with 100neighbors, with the purpose of avoiding particle pairing (assuggested by Dehnen & Aly 2012). A FP version of this codeis not available yet.

G3-X (Murante, Borgani, Beck)Based on Gadget-3, an updated version of Gadget, G3-x(Beck et al. 2016) employs a Wendland C4 kernel with 200neighbours (cf. Dehnen & Aly 2012), artificial conductivityto promote fluid mixing following Price (2008) and Tricco &Price (2013), but with an additional limiter for gravitation-ally induced pressure gradients. In the FP run of G3-x, gascooling is computed for an optically thin gas and takes intoaccount the contribution of metals (Wiersma et al. 2009a),with a uniform UV background (Haardt & Madau 2001).Star formation and chemical evolution are implemented asin Tornatore et al. (2007). Supernova feedback is thereforemodeled as kinetic and the prescription of Springel & Hern-quist (2003) is followed. AGN feedback follows the modeldescribed in Steinborn et al. (2015). It sums up both theAGN mechanical and radiative power, which is a functionof the SMBH mass and the accretion rate (Churazov et al.2005) and gives the resulting energy to the surrounding gas,in form of purely thermal energy.

G3-SPHS (Power, Read, Hobbs)G3-Sphs is a modification of the standard Gadget-3 code,developed to overcome the inability of classic SPH to re-solve instabilities. G3-Sphs uses as an alternative either theHOCT kernel with 442 neighbours or the Wendland C4 ker-nel with 200 neighbours, based on a higher order dissipationswitch detector. A FP version of this code is under develop-ment.

G3-MAGNETICUM (Saro)G3-Magneticum is an advanced version of Gadget-3. Inthe non-radiative version, a higher order kernel based on thebias-corrected, sixth-order Wendland kernel (Dehnen & Aly2012) with 200 neighbors is included. It also includes a lowviscosity scheme to track turbulence (Dolag et al. 2005; Becket al. 2016) and isotropic thermal conduction with 1/20thSpitzer rate (Dolag et al. 2004). For its FP runs, the simula-tion allows for radiative cooling according to Wiersma et al.(2009a) with metal line cooling from the CLOUDY pho-toionization code (Ferland et al. 1998), and heating from auniform time-dependent ultraviolet background (Haardt &Madau 2001). The star formation model is improved fromSpringel & Hernquist (2003), and it also includes chemical

evolution model according to Tornatore et al. (2007). Thestellar feedback triggers galactic winds with a velocity of350 km/s. The detailed SMBH growth and AGN feedbackmodel is presented in Hirschmann et al. (2014); Dolag et al.(2015).

G3-PESPH (February, Davé, Katz, Huang)G3-Pesph is an implementation of Gadget-3 withpressure-entropy SPH (Hopkins 2013) which features specialgalactic wind models. The SPH kernel is an HOCTS (n=5)B-spline with 128 neighbors. For the FP run, the radiativecooling in this simulation code is described in Katz et al.(1996), with metal lines cooling (Wiersma et al. 2009a) anda uniform ionizing UV background (Haardt & Madau 2001).The star formation in this code is based on Springel & Hern-quist (2003). In addition, the heuristic model of Rafiefer-antsoa et al. (2015), tuned to reproduce the exponentialtruncation of the stellar mass function, is used to quench starformation in massive galaxies. It uses a highly constrainedheuristic model for galactic outflows, described in detail inDavé et al. (2013), which utilises outflows scalings expectedfor momentum-driven winds in sizable galaxies, and energy-driven scalings in dwarf galaxies. It does not include AGNfeedback in this process.

G3-MUSIC (Yepes)The original MUSIC runs (G3-Music) were done with theGadget-3 code, based on the entropy-conserving formula-tion of SPH (Springel & Hernquist 2002). Gadget-3 em-ploys a spline kernel (Monaghan & Lattanzio 1985) andparametrize artificial viscosity following the model describedby Monaghan (1997). G3-Music uses the basic Springel &Hernquist (2003) model without SMBH growth and AGNfeedback for its FP runs. In addition, an alternative versionof MUSIC performed using the radiative feedbacks describedin Pionte