Stellar orbits in cosmological galaxy simulations: the connection to formation history and line-of-sight kinematics
MMon. Not. R. Astron. Soc. , 1–21 (2013) Printed 24 September 2018 (MN L A TEX style file v2.2)
Stellar orbits in cosmological galaxy simulations: theconnection to formation history and line-of-sightkinematics
Bernhard R¨ottgers (cid:63) , Thorsten Naab & Ludwig Oser Max-Planck Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany Department of Astronomy and Astrophysics, Columbia University, New York, NY 10027, USA
Accepted ???. Received ??? in original form ???
ABSTRACT
We analyze orbits of stars and dark matter out to three effective radii for 42 galaxiesformed in cosmological zoom simulations. Box orbits always dominate at the centersand z -tubes become important at larger radii. We connect the orbital structure tothe formation histories and specific features (e.g. disk, counter-rotating core, minoraxis rotation) in two-dimensional kinematic maps. Globally, fast rotating galaxies withsignificant recent in situ star formation are dominated by z -tubes. Slow rotators withrecent mergers have significant box orbit and x -tube components. Rotation, quanti-fied by the λ R -parameter often originates from streaming motion of stars on z -tubesbut sometimes from figure rotation. The observed anti-correlation of h and V /σ inrotating galaxies can be connected to a dissipative formation history leading to high z -tube fractions. For galaxies with recent mergers in situ formed stars, accreted starsand dark matter particles populate similar orbits. Dark matter particles have isotropicvelocity dispersions. Accreted stars are typically radially biased ( β ≈ . − . Insitu stars become tangentially biased (as low as β ≈ − .
0) if dissipation was relevantduring the late assembly of the galaxy. We discuss the relevance of our analysis forintegral field surveys and for constraining galaxy formation models.
Key words: stellar dynamics—orbital structure—galaxies: elliptical and lenticular,cD—galaxy formation. (cid:63)
E-mail: [email protected] (cid:13) a r X i v : . [ a s t r o - ph . GA ] J a n B. R¨ottgers et al.
The observable properties of the stellar components of early-type galaxies (ETGs) result from the projected superpo-sition of the light of individual stars with given ages andmetallicities on particular orbits. Assuming that ETGs arein dynamical equilibrium the stars orbit in potentials whichare mostly generated by the stars themselves but also bydark matter (at larger radii) and in some cases by a ad-ditional gaseous components. Theoretically, a large numberof equilibrium configurations can be constructed (see e.g.Binney & Tremaine 2008) but only a subset of all possiblemodels seem to be realized in nature. Important informa-tion about the relevant formation and assembly processes ofETGs might therefore be stored in the orbital compositionand the observable projected stellar line-of-sight kinematics.Unlike for spiral galaxies, not all stars in present daymassive ETGs have formed in the galaxy itself. It is morelikely that the early formation ( z (cid:38)
2) is dominated by insitu star formation and the late assembly becomes domi-nated by stellar accretion (see e.g. Khochfar & Silk 2006;Guo & White 2008; Naab et al. 2009; Oser et al. 2010; Feld-mann et al. 2011; Lackner et al. 2012; Moster et al. 2013;Hilz et al. 2013). As dissipation is important during theearly phase the systems are very likely axisymmetric andit is expected that stars will mostly form and move on tubeorbits. Later on more and more stars (that have formed inother galaxies) are accreted in major and minor mergers andthe final assembly of massive ETGs might be governed bycollisionless dynamics alone. Mergers, however, can signif-icantly change the orbital composition (and dynamics) ofgalaxies and direct information about the early assemblyprocess might be hidden or lost (see e.g. Jesseit et al. 2005).But also long after the main epoch of star formation gascan have a significant and observationally testable impact onthe stellar morphology and kinematics. For example, it hasbeen demonstrated by Barnes & Hernquist (1996) that dur-ing galaxy mergers gas can be driven to the central regions ofthe merger remnants making the central potential more ax-isymmetric. Such a configuration results in a more axisym-metric stellar shape, disfavors the population of stars on boxorbits (which are the dominant orbit class for collisionlessmergers (e.g. Jesseit et al. 2005)), and supports the popu-lation of minor axis tube orbits (Barnes & Hernquist 1996;Naab et al. 2006). This change in orbital configuration hasa significant—and observable—impact on the line-of-sightkinematics of galaxies. Naab et al. (2006) showed that thepresence of gas and the resulting change in orbital configu-ration changes the asymmetry of line-of-sight velocity pro-files. Collisionless remnants show steep trailing (retrograde)wings (positive h ) (Naab & Burkert 2001) whereas gas richremnants have steep leading (prograde) wings (negative h )in much better agreement with observations (Naab et al.2006; Hoffman et al. 2009, 2010).Direct numerical cosmological simulations have becomea valuable tool to understand galaxy formation and are amajor driver for theoretical scientific progress in the field. Itis now possible to follow the evolution of individual galax-ies over a Hubble time at high resolution, starting to re-solve the internal stellar structure of galaxies (see e.g. Naabet al. 2007) and study the impact of feedback processes ongalaxy dynamics. For example, it has been demonstrated that simulations with identical initial conditions, but dif-ferent feedback models can yield galaxies with significantlydifferent morphological and kinematic properties (e.g. Pi-ontek & Steinmetz 2011; Scannapieco et al. 2012; Puch-wein & Springel 2013; Hirschmann et al. 2013; Aumer et al.2013). Any form of ‘feedback’ directly affects the distribu-tion and thermodynamic properties of the dissipative com-ponent (gas) in and around galaxies and thereby regulateswhen and where stars are formed—determining their initialorbits—and how much gas is funneled to the centers or ex-pelled from the galaxies at which stage of their evolution.For the same initial conditions, stronger feedback in generalleads to more in situ star formation, higher gas fractions,and less stellar accretion at late times (Hirschmann et al.2012; Lackner et al. 2012; Hirschmann et al. 2013). Thiswill also lead to a changes in the orbital composition at thepresent day.In this paper we provide the framework for a fast andself-consistent analysis of stellar orbits in high-resolutioncosmological zoom simulations similar to Jesseit et al.(2005). We focus on a set of cosmological simulations withweak stellar feedback and test for correlations with globaland detailed observable properties. The impact of feedbackon our results will be presented in a follow-up study. In alarger scale cosmological context, Bryan et al. (2012) havepresented a similar study on the orbital content of dark mat-ter halos of simulations with different feedback and radiativecooling models and indeed found the orbital content of thehalo to change strongly with different feedback models.In addition to the pure identification of the stellar or-bits we connect this information with observable propertiesshowing up in two-dimensional kinematic maps (see alsoNaab et al. (2013)). This information provides direct the-oretical input for the results from existing and upcomingintegral-field surveys like e.g. SAURON (Bacon et al. 2001),ATLAS (Cappellari et al. 2011), KMOS (Sharples et al.2006), VIRUS-P (Hill et al. 2008), CALIFA (S´anchez et al.2012), SAMI (Fogarty et al. 2012), SLUGGS (Arnold et al.2014), MASSIVE (Ma et al. 2014) or MANGA. Our resultswill help to understand how the assembly history of a galaxyinfluences its orbital content and the observable line-of-sightvelocity distributions (LOSVDs) which are extracted fromthe survey data.The paper is organized as follows: We briefly review thesimulations in Section 2 and present our analysis procedureincluding the reconstruction of the potential, the orbit classi-fication and the construction of LOSV maps in Section 3. InSection 4 we present results on the connection of orbit classeswith triaxiality, line-of-sight kinematics, LOSVD asymme-tries, and the two-phase assembly process. We summarizeand discuss our results in Section 5. In this paper we investigate the orbital structure of centralgalaxies of the cosmological hydrodynamic zoom simulationspresented in Oser et al. (2010). This sample of simulations(or parts of it) has been used to study cosmological size anddispersion evolution (Oser et al. 2012), the mass distribution(Lyskova et al. 2012) as well as the detailed two-dimensionalkinematic properties at small (Naab et al. 2013) and large c (cid:13) , 1–21 tellar orbits in cosmological simulations radii (Wu et al. 2014). The galaxies have present-day stellarmasses ranging from 6 . × M (cid:12) to 6 . × M (cid:12) .The simulations were performed using GADGET(Springel et al. 2001; Springel 2005) with cosmological pa-rameters based on the three year results of the WilkinsonMicrowave Anisotropy Probe (WMAP) (Spergel et al. 2007): σ = 0 .
77, Ω m = 0 .
26, Ω Λ = 0 . h = 0 .
72 and n s = 0 . ( ≈ ) particles in a cube with co-moving side length of 72 Mpc h − from redshift z (cid:39)
43 to z = 0 with a fixed gravitational smoothing length of 2 . h − and a mass of m p = 2 × M (cid:12) per particle (seeMoster et al. (2010)).All particles of the halos of interest within 2 × R at z = 0 were traced back to the beginning of the sim-ulation. A region enclosing all these particles at z (cid:39) dm = 0 .
216 and Ω b = 0 . .
89 kpc h − and 0 . h − , respectively. Theparticle masses were m ∗ , gas = 4 . × M (cid:12) for star and gasparticles and m dm = 2 . × M (cid:12) for dark matter parti-cles. Outside this region and beyond a ‘safety margin’ of1 Mpc h − the original dark matter particles were down-sampled depending on the distance with sufficient resolutionto represent long range forces.The simulations include the effect of a redshift-dependent uniform UV background, radiative cooling, starformation, and energy feedback from type-II supernovae us-ing the model of Springel & Hernquist (2003). As discussedin Oser et al. (2010, 2012) this sub-grid model favors theefficient conversion of gas into stars at high redshifts andsupports the formation of spheroidal systems. However, themassive galaxies forming with this particular sub-grid modelhave structural properties that agree reasonably well withobserved ellipticals (see also Naab et al. 2007; Johanssonet al. 2012; Lyskova et al. 2012; Naab et al. 2013; Wu et al.2014). An overview of some global galaxy properties is givenin Tab. 2 along with the global orbit fractions determinedlater in this work. At z = 0, we identify galaxies (including their dark mat-ter halos) with a friends-of-friends algorithm and determinetheir centers in configuration space (position and velocity)using a shrinking sphere technique (Power et al. 2003). Thecentral galaxies are then defined by all baryonic particleswithin R , i.e. 10% of the virial radius R vir ≡ R .The orbit classification scheme (see Section 3.3) requiresthe galaxies—or more precisely their potentials—to be ori-ented along their principal axes. Only a few degrees of mis-alignment can change the exact orbit fractions. We use themethod presented in Bailin & Steinmetz (2005) to computethe ‘reduced inertia tensor’ ˜I ,˜ I ij = (cid:88) Particles k m k r k,i r k,j r k , (1)where m k are the masses and (cid:126)r k are the positions of theindividual stellar particles within a given radius; in this work Figure 1.
The orientation of the eigenvectors of the reduced iner-tia tensor as a function of radius. The black circles on the projec-tions indicates the effective radius. Most galaxies like M0175 andM0163 show good internal alignment and the orientation of thereduced inertia tensor only changes at larger radii, where largesubstructures are (cf. M0163). Some very axisymmetric galax-ies like M0408 have radially fluctuating eigenvectors in the planeperpendicular to the symmetry axis. Only very few simulatedgalaxies show internal miss-alignment within R eff , like M0858. within the half mass radius of the stars. The eigenvectors ofthis tensor then give the orientation of the principal axes.An advantage of this method over the traditionalmoment-of-inertia tensor is that it weighs particles at dif-ferent distances from the center equally, whereas the nor-mal moment-of-inertia tensor, I ij = (cid:80) k m k ( δ ij r k − r k,i r k,j ),weighs masses m k with O ( r k ). We, however, would like todetermine the orientation of the potential, whose depth isproportional to the mass, and hence the reduced inertia ten-sor is more appropriate. For example massive substructuresat large radii would dominate the normal inertia tensor dueto the O ( r )-factor, whereas the potential would still bedominated by the galaxy at small radii.For most galaxies the orientation of the principal axesdefined via ˜I does not vary significantly within the effec-tive radius (see Fig. 1). Only a few galaxies show internaltwists or misaligned cores like M0858. Galaxies that are al-most axisymmetric like M0408 have the principal axis of thereduced inertia tensor perpendicular to the symmetry axisfluctuating with the radius up to which ˜I was determined.However, the potential is axisymmetric as well and thus itdoes not compromise the classification.Substructures, that are massive enough to signifi-cantly impact the potential (basically on-going/up-comingmergers) and the direction of the principal axis—like forM0163—, typically are located beyond R eff .We also compute the triaxiality parameter, T = 1 − ( b/a ) − ( c/a ) . (2) In this work we assume a constant light-to-mass ratio and weignore gas. Hence, the effective radius is simply the half-massradius of the stars.c (cid:13)000
The orientation of the eigenvectors of the reduced iner-tia tensor as a function of radius. The black circles on the projec-tions indicates the effective radius. Most galaxies like M0175 andM0163 show good internal alignment and the orientation of thereduced inertia tensor only changes at larger radii, where largesubstructures are (cf. M0163). Some very axisymmetric galax-ies like M0408 have radially fluctuating eigenvectors in the planeperpendicular to the symmetry axis. Only very few simulatedgalaxies show internal miss-alignment within R eff , like M0858. within the half mass radius of the stars. The eigenvectors ofthis tensor then give the orientation of the principal axes.An advantage of this method over the traditionalmoment-of-inertia tensor is that it weighs particles at dif-ferent distances from the center equally, whereas the nor-mal moment-of-inertia tensor, I ij = (cid:80) k m k ( δ ij r k − r k,i r k,j ),weighs masses m k with O ( r k ). We, however, would like todetermine the orientation of the potential, whose depth isproportional to the mass, and hence the reduced inertia ten-sor is more appropriate. For example massive substructuresat large radii would dominate the normal inertia tensor dueto the O ( r )-factor, whereas the potential would still bedominated by the galaxy at small radii.For most galaxies the orientation of the principal axesdefined via ˜I does not vary significantly within the effec-tive radius (see Fig. 1). Only a few galaxies show internaltwists or misaligned cores like M0858. Galaxies that are al-most axisymmetric like M0408 have the principal axis of thereduced inertia tensor perpendicular to the symmetry axisfluctuating with the radius up to which ˜I was determined.However, the potential is axisymmetric as well and thus itdoes not compromise the classification.Substructures, that are massive enough to signifi-cantly impact the potential (basically on-going/up-comingmergers) and the direction of the principal axis—like forM0163—, typically are located beyond R eff .We also compute the triaxiality parameter, T = 1 − ( b/a ) − ( c/a ) . (2) In this work we assume a constant light-to-mass ratio and weignore gas. Hence, the effective radius is simply the half-massradius of the stars.c (cid:13)000 , 1–21
B. R¨ottgers et al.
Here a is the major axis, b the intermediate axis and c theminor axis. The two axis ratios can be calculated from thesquare roots, ˜ a > ˜ b > ˜ c , of the eigenvalues of the reducedinertia tensor (Bailin & Steinmetz 2005): (cid:16) ca (cid:17) (cid:39) (cid:18) ˜ c ˜ a (cid:19) √ and (cid:18) ba (cid:19) (cid:39) (cid:18) ˜ b ˜ a (cid:19) √ . (3) To classify the orbits of the stellar particles we need to knowtheir trajectories—at high temporal resolution—in the po-tential of the galaxy. To speed up the orbital classificationwe freeze the system at redshift zero, use a self-consistentfield method (SCF, Hernquist & Ostriker 1992) to extractthe potential, and then integrate the individual orbits of theparticles we would like to classify (for a similar approach seeJesseit et al. 2005; Naab et al. 2006; Hoffman et al. 2009;Bryan et al. 2012).We have investigated two different basis functions forthe potential expansion. The first one (CB hereafter) waspresented in Clutton-Brock (1973). At zeroth order it is thedensity and potential of a Plummer sphere, ρ ( r ) = 3 M πa (cid:18) r a (cid:19) − / ,φ ( r ) = − GM √ r + a , where M is the total mass and a is the scale parameter.Another set of SCF basis functions (HO hereafter) was sug-gested by Hernquist & Ostriker (1992), for which the zerothorder density and potential are ρ ( r ) = M π ar r + a ) ,φ ( r ) = − GMr + a . This is the Hernquist density profile (Hernquist 1990) whichis a popular model for representing spheroidal galaxies (e.g.Hilz et al. 2013) and resembles a de Vaucouleur’s R / sur-face density profile (see however Naab & Trujillo 2006).For both basis functions the difference of the real (sim-ulated) potential and the zeroth order term is expanded in abi-orthogonal basis set built-up from the spherical harmon-ics and a radial basis set. The better the first order termsfollow the underlying model, the less terms in the basis setexpansion are needed to produce a good approximation tothe original potential. We have tested both basis set for vary-ing radial and angular expansion terms and in all cases wefind that the HO basis set results in a significantly betterrepresentation of the potential as it does not have a flat den-sity core inside the scale radius. In Fig. 2 we give an exampleof the potential reconstruction for galaxy M0163. The SCFpotential and the potential from the simulation agree verywell. In addition, substructures at larger radii are washedout which results in a smoother overall potential and makesthe orbit classification more stable. At the center, the HObasis set represents the potential much better than the CBbasis set (bottom panel of Fig. 2). Moreover the quality ofthe HO fit is less sensitive to the choice of the scale parame-ter a and the typical relative error of this basis set assuminga radial order n max = 18 and an angular order (cid:96) max = 7 is Figure 2.
Top panel:
Comparison of the potential extracted fromthe particle distribution (black dots) and the SCF potential witha HO basis function set ( n max = 18 , (cid:96) max = 7, green triangles)of galaxy M0163 for a set of randomly chosen stars. The fittedpotential agrees well at the center and substructures at large radiiare smoothed out. Bottom panel:
Comparison of the direct (black)and HO (green triangles) potential to a fit using the CB basisfunctions (red squares) using the same radial and angular order.At a fixed order the HO basis set fits the central potential muchbetter. less than 0 . In integrable systems bound orbits are confined on mani-folds of phase space that are topologically equivalent to tori.This allows one to describe them with angle-action variables( θ , J ) in which the equations of motion become0 = ˙ J i = − ∂ H ∂θ i (4)˙ θ i = − ∂ H ∂J i =: Ω i ( J ) , (5) c (cid:13) , 1–21 tellar orbits in cosmological simulations where H is the Hamiltonian. The Ω i are called fundamentalfrequencies and are conserved quantities. It can be shownthat real space trajectories x ( t ) are quasi-periodic, i.e. theycan be written in a Fourier series, x ( t ) = (cid:88) n ∈ N X n ( J ) e i n · θ ( t ) , (6)with constant amplitudes X n and linearly growing angles θ ( t ) = θ (0) + Ω · t . Such quasi-periodic orbits are also calledregular orbits.Galaxies do not have to be integrable systems. How-ever, orbit theory and in particular KAM theory (see e.g.Kolmogorov 1954, 1979; Moser 1973; Arnol’d 1989; Binney& Tremaine 2008; Arnol’d et al. 2007) tell us, that near-integrable systems (whose Hamiltonian differs only slightlyfrom an integrable Hamiltonian) still have ‘islands’ of reg-ular orbits next to their otherwise irregular/chaotic orbits.The smaller the deviation of the Hamiltonian from an inte-grable one, the larger these island are.It turns out that regular orbits can be classified intofour different main classes, depending on the ratios of the Ω i (see e.g. de Zeeuw 1985; Statler 1987; Binney & Tremaine2008): box orbits, minor-axis orbits (we call them z -tubesfor short) and inner and outer major-axis orbits ( x -tubesfor short, see Fig. 4). These classes have fundamentally dif-ferent physical properties. Box orbits have no mean angularmomentum and are typically centrophilic, whereas all tubeorbits are centrophobic and have a net angular momentumwhich is either aligned with the z -axis (for z -tubes) or withthe x -axis (for x -tubes). They also have different, often in-teresting geometries (e.g. the ‘boxlet’ in Fig. 4).Carpintero & Aguilar (1998) (CA98 hereafter) devel-oped a classification scheme, that almost entirely builds onthe detection of resonances (only inner and outer x -tubeshave to be distinguished morphologically). z -tubes, for in-stance, have a 1:1 resonance in the two dominant frequen-cies in the x - and the y -coordinate. CA98 have also written aprogram to automatically classify orbits by using the Fouriertransforms of the trajectories (in three dimensions), detect-ing the most prominent lines and then checking these linesfor resonances. Depending on the number of base frequen-cies that are needed to build up the detected lines (by theirlinear combinations) and the number and kind of resonancesthe orbits are classified (see Tab. 1).This scheme is capable of differentiating between z -tubes, x -tubes, non-resonant box orbits—so called‘ π -boxes’—and resonant box orbits (all resonance apart from1:1 resonances)—called ‘boxlets’—, as well as second orderresonances. These occur when a particle is oscillating res-onantly around a stable, already resonant orbit. We, how-ever, only make use of the differentiation between the mainorbit classes (boxes, z -tubes, x -tubes, irregulars) and non-classified orbits.The basic classification procedure works as follows: firstwe integrate the particles, starting from their coordinatesand velocities at z = 0 in the reconstructed SCF potential Base frequencies are very similar to the fundamental frequen-cies, but not necessarily the same. It might be that one of them istwice the corresponding fundamental frequency, for instance, andthe amplitude of uneven multiples of the fundamental frequencyare undetectable small. number of base frequencies < < number 0 low dim. 3-D π -box irregular1 (closed open π : m : n boxof and open π :1:1 tuberesonances 3 thin) open l : m : n boxorbits open l :1:1 tube Table 1.
Summary of the spectral orbit classification in threedimensions as defined in Carpintero & Aguilar (1998). Chaoticorbits have more than three base frequencies; regular orbits areclassified according to their resonance: tubes, boxlets ( π : m : n or l : m : n boxes) or (non-resonant) π -boxes. Depending on whethertheir trajectories fill a three dimensional volume (‘open’ orbits) ora lower dimensional one, they have three or less base frequencies,respectively. Figure 3.
An example for a ‘sticky’ orbit: A star particle ofgalaxy M0175 looks like a regular ‘fish orbit’ (a 2:3-resonance,left panel) if integrated for 50 orbital periods ( ∼ . ∼
30 Gyrs) the orbit shows itsirregular nature (right panel). For the classification in this paperall orbits are integrated for (cid:46)
50 orbital periods. with a Runge-Kutta integrator of 8th order with adaptivetime steps (capable of continuous on-the-fly output). We re-quire a relative accuracy in position and velocity of 10 − perstep, which leads to relative changes in the particles’ ener-gies of order 10 − . The CA98 code then actually classifiesan orbit three times using slightly different parts of the tra-jectory. If all three classifications differ the particle countsas ‘not classified’.The orbit classification for the almost 3 × star par-ticles in this work would have taken several months with theoriginal serial code. Therefore we have parallelized the loopover the particles with OpenMP and with that reduced thecomputation time to a couple of days. In addition, we addeda module to estimate the orbital period of each particle be-fore the final classification to ensure that it is integrated fora fixed number of orbital periods rather than a fixed globalintegration time. The orbital periods vary significantly withradius / binding energy for a typical galaxy: close to the cen-ters we find orbital periods less than 10 Myr and at 3 R eff they can be longer than 1 Gyr.The orbital period is usually defined as the inverse ofthe dominant frequency along the major axis. To first order,the particle should pass the y - z -plane twice for each period.To get an estimate for the orbital period of each particle wefirst integrate (with low accuracy) until the desired orbitalperiods sign changes (corresponding to ∼
40 periods) haveoccurred. We then terminate the integration and then re-integrate the orbit for the same time at high accuracy forthe orbit classification. c (cid:13)000
40 periods) haveoccurred. We then terminate the integration and then re-integrate the orbit for the same time at high accuracy forthe orbit classification. c (cid:13)000 , 1–21 B. R¨ottgers et al. irregular orbit(from M0175) π -box orbit(from M0175)boxlet(from M0190) z -tube(from M0175)inner x -tube(from M0125)outer x -tube(from M0175) Figure 4.
Selected examples of the most regular trajectories (for three projections along the principal axes, from left to right) of themain orbit classes for individual particles taken from different simulated galaxies complemented with one very chaotic/irregular orbit.All tube orbits are centrophobic, while box orbits and irregular orbits can go through the center. c (cid:13) , 1–21 tellar orbits in cosmological simulations Figure 5.
Orbit fractions as a function of radius for a boot-strapping ensemble of realizations of two representative galaxies,M0175 and M0858. Solid lines are the mean of 50 bootstrappedrealizations the errorbars indicate the standard deviations. Theuncertainties due to the coarse sampling of phase space are small.
To find an optimal integration time, the trajectory hasto be sufficiently long to detect peaks and their resonancesin the Fourier spectra. On the other hand, too long inte-gration time leads to inaccuracies and the sampling withthe FFT can become to coarse to detect low amplitude fre-quencies. A complication are so-called ‘sticky orbits’, irreg-ular orbits that come near to a resonantly trapped region inphase space, stick to it for some time and drift away slowly.These orbits look and behave very similarly to the resonantorbits nearby. Their actual irregular nature is not revealeduntil they have drifted away from the resonance (see Fig. 3),which in many cases requires integration for much more thanthe Hubble time. An appropriate integration time ensuresthat these orbits are classified as regular orbits. The clas-sification is most robust if we integrate for about 40 − In this section we present test of how well the potential issampled and how the sampling affects the orbit classifica-tion. For this we use the bootstrapping technique (see Heylet al. 1994; Naab & Burkert 2003). From the original en-semble of particles, we randomly draw the same number ofparticles with replacement. This is done separately for eachparticles species (gas, stars, and dark matter) to maintainthe mass of each component.We analyse 50 different realizations for two representa-tive galaxies without figure rotation (M0175 and M0858). InFig. 5 we show the mean orbit fractions and the variations(standard derivations) indicated by the error bars. The or-bit classification is very robust and hardly affected by thesampling of phase space. The variations are typically smallfor the stellar component and can increase slightly at largeradii ( r > R eff ; see Wu et al. 2014 for the effect of time av-eraging the potential to measurements at large radii). Mostimportantly, none of the conclusion in the paper are affectedby sampling issues. The small variations in orbit fractionsare caused by individual particles that change orbit familiesasymmetrically (see also Sec. 3.3) for different realizationsof the potential. Typically almost 90% of the particles in themain orbit families do not change classification.In Fig. 6 we investigate the evolution of orbit fractionsin time for the last five snapshots covering about 500 Myrs. Figure 6.
The time evolution of the orbit fractions as a functionof radius for the last five snapshots ( ∼ . r > R eff ). Again for both galaxies the orbit fractions are stable for themain part of the galaxies. At larger radii ( r > R eff ) thefluctuations with time become larger due to moving sub-structures (e.g. M0858).In summery, the orbit fractions presented in section 4are reliable and stable for a few dynamical times. Thereforenone of the conclusions in the paper are affected by samplingissues and time evolution of the modelled galaxies. Since we have fixed the potential using a time-independentSCF potential, the classification procedure does not accountfor the possibility of a rotating figure. Some of our galaxies,however, show clear signs of figure rotation. We find thatthe systems that rotate are rather prolate or have bar-likestructures that rotate.The rotation of the figure is also imprinted in the motionof the stars. Using the classification scheme without cautionwould lead to an incorrect orbit classification. Hence, weexcluded galaxies that show signs of figure rotation fromour orbit analysis. These are M0380, M0549, M0763, M0858,M1192 and M1306.A direct integration of rotating figure into the CA98classification scheme would be very demanding or even im-possible, because a) the measurement of figure rotationis quite error-prone, b) the amount of figure rotation canchange a lot over time due to external torques and c) figurerotation can be differential. The latter point means that theprincipal axis (of the reduced inertia tensor) change withradius and time. This not only complicates the methods ofclassification but a static potential is actually a premise oforbit theory. Hence, we restrict ourselves to galaxies withslowly varying/rotating potentials. In order to check the ro-bustness of the classification in slowly rotating potentials,we added small amounts of rigid rotation to the SCF po-tentials and found that the orbit composition within a feweffective radii does not change much for moderate patternspeeds. Therefore we trust the classification for all but theexcluded galaxies.
To connect the orbital structure of the galaxies to their line-of-sight kinematics we present two-dimensional maps of the c (cid:13)000
To connect the orbital structure of the galaxies to their line-of-sight kinematics we present two-dimensional maps of the c (cid:13)000 , 1–21 B. R¨ottgers et al.
LOS velocity, and dispersion as well as h (see below). Themaps are constructed in a similar way to observations andall details can be found in Naab et al. (2013). Here we justgive a short summary. In a first step the galaxies are orientedalong their principal axes and projected along the interme-diate axis, resulting in an edge-on view. We split each stellarparticle into 60 pseudo-particles with a Gaussian distribu-tion of standard deviation 0 . P ( v ) isfitted (van de Ven et al. 2006) with Gauss-Hermite functionsfollowing Gerhard (1993) and van der Marel & Franx (1993),using terms up to the fourth order: P ( v ) = γ √ πσ e − w (cid:16) h H ( w ) + h H ( w ) (cid:17) , (7)where w ≡ v − V σ (8)is the normalized deviation of the velocity from the meanvelocity V , and H and H are Gauss-Hermite polynomials. γ is a normalization parameter and also one of the fittingparameters ( γ, V , σ, h , h ). The amplitude h of the thirdorder term is connected to the skewness and h is a measureof the kurtosis of the velocity profile. Skewness and kurtosis,however, are more sensitive to statistical deviations at thefar ends of the wings (van der Marel & Franx 1993).We also calculate the λ R -parameter as introduced byEmsellem et al. (2007, 2011), a luminosity weighted measureof rotation: λ R = (cid:80) Ni =1 F i r i | V ,i | (cid:80) Ni =1 F i r i (cid:113) V ,i + σ i , (9)where F i is the flux (which here is the mass of the stars, for aconstant light-to-mass ratio) in bin i of the projected galaxy, r i is its projected radius, V ,i is the line-of-sight velocity and σ i is the line-of-sight velocity dispersion of bin i . We classify the orbits for stellar and dark matter particles upto 3 effective radii for all 42 galaxies (a summary is given inTab. 2). The particles populate all major orbit classes: boxorbits and boxlets (boxes), z -tubes (minor-axis loop orbits),inner and outer x -tubes (major-axis loop orbits), and irregu-lar orbits (see Fig. 4). In general, the dominant orbit familiesare boxes and z -tubes, sometimes x -tubes, with significantradial variation. A small fraction of the orbits, typically lessthan ∼ z -tubes, apart from thevery center ( r (cid:46) . R eff ). Such an orbit structure is verygeneric for galaxies of class A and B and it is very similar to gas-rich major mergers (see e.g. Naab et al. 2006; Hoffmanet al. 2010).A slowly rotating gas-rich merger remnant (M0664,class C) is shown in the upper right panel of Fig. 7. Thisgalaxy is triaxial, almost prolate ( T (cid:39) . − . z -tubes and x -tubes contributeequally. M0175, a massive galaxy assembled by minor merg-ers since z ≈ . (cid:46) R eff (cid:46) . z -tubes than the other classes, inparticular classes A and B. In slow rotators (classes C, E,and F) box orbits are more abundant. Also, x -tubes are rarein fast rotators. However, a high z -tube fraction is not theonly factor determining the amount of rotation as we willshow in section 4.2. A common feature for all galaxies ofthe radial orbit distributions is a very box orbit dominatedcenter (typically more than 60% are boxes). This can prob-ably be ascribed to the simulation model we use as we willdiscuss later.It has been shown that the orbital composition (orbitfractions) correlate with the three-dimensional shape (tri-axiality) of the system (Statler 1987; Jesseit et al. 2005).In Fig. 9 we show z -tube, x -tube, and box orbit fractionsas a function of triaxiality of the galaxies. As expected, z -tubes preferentially live in oblate ( T ≈
0) systems, wherethey can rotate around a well-defined minor axis, which ispoorly defined in a prolate ( T ≈
1) system. In a galaxy with T = 1 exactly there are no z -tubes at all. x -tubes are mostabundant in prolate systems with a well-defined major axis( x -axis) and the abundance of box orbits peaks roughly atthe most triaxial systems ( T ≈ .
5, see right panel of Fig. 9).The fact that all systems have at least 20% box orbits indi-cates that none of the systems is perfectly oblate.
In Fig. 10 we directly compare the orbital structure of thesix example galaxies to the two-dimensional (edge-on) line-of-sight velocity and velocity dispersion maps up to 1 . R eff . z -tubes are the only orbits with a definite sense of rotationaround the minor axis, and one expects a high line-of-sightvelocity (along the major-axis) at z -tube dominated radii.This can be seen for M0408 and M0163. c (cid:13) , 1–21 tellar orbits in cosmological simulations ID M ∗ R eff triax. T λ R in situ box z -tube x -tube Eff. prograde[10 M (cid:12) ] [kpc] frac. frac. frac. frac. z -tube frac.M0040 49.98 12.92 0.69 0.13 0.11 0.44 0.24 0.12 0.04M0053 69.45 13.03 0.51 0.093 0.19 0.29 0.40 0.17 0.02M0069 49.40 8.84 0.68 0.15 0.15 0.43 0.22 0.19 0.09M0089 52.34 10.43 0.45 0.074 0.084 0.44 0.27 0.11 0.03M0094 47.90 7.53 0.54 0.098 0.16 0.38 0.39 0.13 0.12M0125 43.35 9.07 0.85 0.078 0.12 0.26 0.17 0.48 0.02M0162 36.44 9.78 0.80 0.074 0.081 0.52 0.19 0.13 0.06M0163 35.20 10.39 0.63 0.31 0.098 0.49 0.25 0.10 0.12M0175 36.79 7.37 0.58 0.058 0.14 0.34 0.35 0.19 0.01M0190 31.48 6.98 0.77 0.083 0.093 0.51 0.18 0.17 0.01M0204 26.85 6.49 0.37 0.10 0.12 0.31 0.45 0.12 0.06M0209 19.96 3.81 0.41 0.14 0.17 0.46 0.36 0.06 0.09M0215 27.64 5.04 0.49 0.14 0.16 0.33 0.32 0.25 0.10M0224 24.84 5.95 0.26 0.16 0.14 0.24 0.54 0.10 0.11M0227 30.90 7.91 0.61 0.24 0.10 0.35 0.38 0.16 0.18M0259 19.83 4.53 0.06 0.40 0.15 0.28 0.58 0.02 0.30M0290 22.03 3.57 0.10 0.48 0.19 0.18 0.73 0.03 0.47M0300 18.65 4.58 0.37 0.19 0.12 0.42 0.40 0.05 0.17M0305 25.76 8.92 0.46 0.12 0.11 0.50 0.21 0.11 0.01M0329 21.33 4.32 0.49 0.071 0.16 0.44 0.29 0.16 0.03M0380 17.08 4.04 0.57 0.46 0.17 0.44 0.34 0.10 0.15M0408 17.71 3.60 0.07 0.37 0.20 0.23 0.67 0.02 0.34M0443 23.08 2.74 0.44 0.088 0.24 0.37 0.42 0.14 0.11M0501 16.31 4.29 0.55 0.075 0.16 0.47 0.23 0.15 0.05M0549 11.64 4.66 0.33 0.46 0.17 0.44 0.31 0.09 0.16M0616 13.04 4.07 0.72 0.077 0.16 0.47 0.19 0.21 0.02M0664 10.39 2.91 0.64 0.14 0.17 0.33 0.34 0.23 0.00M0721 13.35 2.32 0.14 0.40 0.38 0.29 0.60 0.02 0.24M0763 13.68 4.28 0.30 0.32 0.099 0.39 0.43 0.06 0.25M0858 14.26 2.69 0.31 0.52 0.32 0.50 0.35 0.03 0.18M0908 13.43 2.83 0.06 0.44 0.38 0.20 0.69 0.01 0.38M0948 9.23 4.75 0.69 0.088 0.12 0.31 0.20 0.35 0.03M0959 8.41 2.94 0.88 0.091 0.18 0.31 0.13 0.46 0.03M0977 6.32 3.26 0.47 0.35 0.37 0.47 0.26 0.11 0.16M1017 8.87 2.27 0.61 0.084 0.29 0.46 0.33 0.12 0.04M1061 7.20 3.13 0.64 0.066 0.21 0.54 0.16 0.17 0.02M1071 10.82 2.37 0.50 0.14 0.21 0.32 0.40 0.20 0.12M1091 10.46 2.00 0.54 0.040 0.25 0.57 0.25 0.09 0.02M1167 10.24 2.31 0.54 0.062 0.26 0.55 0.25 0.11 0.07M1192 6.05 2.64 0.69 0.50 0.20 0.54 0.18 0.16 0.11M1196 10.74 3.04 0.11 0.45 0.33 0.27 0.61 0.01 0.41M1306 9.04 1.84 0.13 0.59 0.28 0.39 0.50 0.03 0.31 Table 2.
Properties of simulated galaxies: M ∗ is the stellar mass of the galaxy, i.e. the stellar mass within 10% R , R eff is the halfmass radius of the galaxy’s stars (i.e. the effective radius assuming a constant mass-to-light ratio and ignoring gas), the triaxiality T ismeasured at R eff , λ R is the rotational parameter as defined in formula 9, the in situ fraction is the fraction of the stars that were formed in situ since z = 2 and the orbit class fractions were determined with the modified CA98 classifier within 3 R eff . The effective prograde z -tube fraction is defined as the difference between the prograde and the retrograde z -tube fraction. Uncertain orbit fractions for galaxieswith significant figure rotation are given in grey. However, not all particles on z -tube orbits have to ro-tate in the same direction and the net-rotation can cancelout, resulting in slow rotation like for M0664, M0190 andM0175, with a slightly higher velocity dispersion. To inves-tigate this effect, we separated the z -tubes into prograde(co-rotating) and retrograde (counter-rotating) orbits andplot the prograde z -tube fractions (green dashed lines inthe orbit fraction plots) in Fig. 10. Wherever they dominatethe z -tube population (M0408, and M0163), the galaxy isclearly rotating. Similar trends also hold for x -tubes, how-ever, M0190 is the only galaxy in the sample with noticeablemajor-axis rotation, which is why we concentrate on minoraxis rotation.We demonstrate the direct connection between the or- bital composition and the line-of-sight kinematics by per-forming a separate analysis for stars on different orbitclasses. In Fig. 11 we show the line-of-sight kinematics forM0408 for the full stellar population, and for the stars onbox orbits, z -tubes, and x -tubes respectively (from top leftto bottom right). For this galaxy the rotation originates fromthe dominant population (66.4 %) of z -tubes, whereas boxes(23.9 %) and x -tubes (1.9 %) show no (significant) rotation,typical for most fast rotators. Also the disk-like component,visible in the isodensity contours, is composed of stars on z -tubes. The box orbits contribute to the central dispersion,whereas the dispersion at R eff is almost entirely determinedby z -tubes.Slow rotators like M0175 (Fig. 12) have a non-rotating c (cid:13)000
Properties of simulated galaxies: M ∗ is the stellar mass of the galaxy, i.e. the stellar mass within 10% R , R eff is the halfmass radius of the galaxy’s stars (i.e. the effective radius assuming a constant mass-to-light ratio and ignoring gas), the triaxiality T ismeasured at R eff , λ R is the rotational parameter as defined in formula 9, the in situ fraction is the fraction of the stars that were formed in situ since z = 2 and the orbit class fractions were determined with the modified CA98 classifier within 3 R eff . The effective prograde z -tube fraction is defined as the difference between the prograde and the retrograde z -tube fraction. Uncertain orbit fractions for galaxieswith significant figure rotation are given in grey. However, not all particles on z -tube orbits have to ro-tate in the same direction and the net-rotation can cancelout, resulting in slow rotation like for M0664, M0190 andM0175, with a slightly higher velocity dispersion. To inves-tigate this effect, we separated the z -tubes into prograde(co-rotating) and retrograde (counter-rotating) orbits andplot the prograde z -tube fractions (green dashed lines inthe orbit fraction plots) in Fig. 10. Wherever they dominatethe z -tube population (M0408, and M0163), the galaxy isclearly rotating. Similar trends also hold for x -tubes, how-ever, M0190 is the only galaxy in the sample with noticeablemajor-axis rotation, which is why we concentrate on minoraxis rotation.We demonstrate the direct connection between the or- bital composition and the line-of-sight kinematics by per-forming a separate analysis for stars on different orbitclasses. In Fig. 11 we show the line-of-sight kinematics forM0408 for the full stellar population, and for the stars onbox orbits, z -tubes, and x -tubes respectively (from top leftto bottom right). For this galaxy the rotation originates fromthe dominant population (66.4 %) of z -tubes, whereas boxes(23.9 %) and x -tubes (1.9 %) show no (significant) rotation,typical for most fast rotators. Also the disk-like component,visible in the isodensity contours, is composed of stars on z -tubes. The box orbits contribute to the central dispersion,whereas the dispersion at R eff is almost entirely determinedby z -tubes.Slow rotators like M0175 (Fig. 12) have a non-rotating c (cid:13)000 , 1–21 B. R¨ottgers et al.
Figure 7.
Fraction of box (blue), x -tube (red), z -tube (green), irregular (light green) and not classified (black) orbits as a function ofradius for six galaxies with different formation histories (Naab et al. 2013). All simulated galaxies are dominated by box orbits at thecenter (which probably is an artifact of the simulation model we use). Galaxies of classes A and B besom z -tube dominated at ∼ . R eff , x -tubes can be found for classes C, D, E, and F. Typically less than 10 per cent of all orbits are irregular or not classified. Figure 8.
Fraction of z -tubes (left), x -tubes (middle), and box orbits (right) in the radial range of 0 . R eff to 1 . R eff (smaller radiiare dominated by box orbits—which probably is an artefact of the simulation model we use) for different assembly classes as defined inNaab et al. (2013). For the individual classes we also show the mean fractions with their standard deviation as error bars. Fast rotators(classes A,B, and D) have high z -tube fractions, slow rotators (C, E, and F) have significant x -tube and box orbit contributions. z -tube component (equally important co- and counter-rotating populations, see Fig. 14) with a relatively high line-of-sight velocity dispersion (peaking at about 280 km/s at ∼ . R eff with a drop in the center, see also Fig. 14). Alsothe z -tubes show a characteristic box shape, i.e. they arenot as flat as the one shown in Fig. 4, but rather ‘opened’ inthe edge-on projection (which is a typical behavior for tubesin non-axisymmetric potentials, see also Jesseit et al. 2005).Again, the nuclear dispersion is driven by the (very flat-tened) box orbit population. The system has a significant x -tube population (20.2%) contributing to the dispersionaround one R eff .We have one simulated galaxy (M0094) with a counter-rotating core. For which we show the line-of-sight kinemat-ics for the different orbit classes separated into prograde and retrograde z -tubes, boxes and x -tubes. In the global line-of-sight velocity map (upper left panel of Fig. 13) the counter-rotating core ( r (cid:46) . R eff (cid:39) . ∼ −
50 km/s and a pos-itive velocity at the opposite side. At larger radii the veloci-ties change sign. Again, the z -tubes alone carry a moderateamount of global rotation but the counter rotating core be-comes clearly visible (middle left panel of Fig. 13). It is not adistinct subsystem but generated by two extended counter-rotating z -tube components. The center is dominated byretrograde z -tubes—the counter rotating core—larger radii( r (cid:38) . R eff ) become dominated by prograde z -tubes (seeFig. 10). Overall, however, the system is dominated by boxorbits ( ∼
42% of the stars are on box orbits). The character- c (cid:13) , 1–21 tellar orbits in cosmological simulations Figure 9.
The total fraction of stars on z -tubes (left panel), x -tubes (middle panel), and box orbits (right panel) as a function of galaxystellar triaxiality T (both measured within R eff ). Oblate systems ( T = 0) are z -tube dominated, prolate systems ( T = 1) can support x -tubes, and triaxial systems ( T = 0 .
5) have the highest box orbit fraction as predicted by theory (Statler 1987) found for binary mergerremnants (Jesseit et al. 2005).
Figure 14.
Upper panel:
The z -tube fraction (within R eff ) of thesimulated galaxies versus the λ R -parameter. There is no corre-lation. Many low angular momentum galaxies have high z -tubefractions (dark grey shaded area) and high angular momentumsystems can have low z -tube fractions (light grey shaded area). Bottom panel:
The effective prograde z -tube fraction correlatesnicely with λ R for most of the galaxies. The galaxies below thelinear correlation (in the light-grey shaded triangle) are roughlythose, for which we find signs of significant figure rotation (un-filled circles). istics of this simulated counter-rotating core resembles theonly observed and modeled system with a counter-rotatingcore, NGC 4365 (van den Bosch et al. 2008). This system,however, is dominated by tube orbits and the core is moreclearly visible.In the upper panel of Fig. 14 the (global) z -tube frac-tion of the galaxies is plotted against their λ R -parameter.Surprisingly, there is almost no correlation. In particular,galaxies with low λ R can have z -tube fractions as high as0.5. As mentioned before, the global rotation of a galaxy canbe low if the angular momentum on prograde and retrograde z -tubes cancels out. This is the case for galaxies with low λ R in the dark grey region in Fig. 14, mostly slow rotatorsof classes C, D, E and F.A better measure for the amount of streaming motionis the ‘effective prograde z -tube fraction’, which we defineas the normalized difference of the fraction of prograde andretrograde z -tubes:( z -tubes) − ( z -tubes) . (10)Plotting this fraction against λ R (lower panel of Fig. 14)brings down the galaxies from the dark grey area onto a tightcorrelation with λ R for most galaxies. This indicates that formost simulated galaxies the z -tube orbit family (and theirseparation into prograde and retrograde orbits) determinesthe global rotation properties of the galaxies.Galaxies, which do not follow the correlation of λ R andthe effective prograde z -tube fraction (those in the light-greyarea in Fig. 14) are mostly of galaxy class A (fast-rotatorswith gas-rich minor mergers) and are also those, for whichwe found clear signs of figure rotation (indicated by open cir-cles in Fig. 14). Although the orbit classification for thosegalaxies is uncertain, we strongly suspect that the high λ R values have a significant contribution from figure rotation.The non-rotating galaxies for which we trust our classifica-tion, the effective prograde z -tube fraction correlates nicelywith the λ R -parameter. For most observed fast rotating galaxies the amplitude ofthe third-order component ( h ) of a Gauss-Hermite fit tothe line-of-sight velocity profile (Eq. 7) anti-correlates with c (cid:13)000
The effective prograde z -tube fraction correlatesnicely with λ R for most of the galaxies. The galaxies below thelinear correlation (in the light-grey shaded triangle) are roughlythose, for which we find signs of significant figure rotation (un-filled circles). istics of this simulated counter-rotating core resembles theonly observed and modeled system with a counter-rotatingcore, NGC 4365 (van den Bosch et al. 2008). This system,however, is dominated by tube orbits and the core is moreclearly visible.In the upper panel of Fig. 14 the (global) z -tube frac-tion of the galaxies is plotted against their λ R -parameter.Surprisingly, there is almost no correlation. In particular,galaxies with low λ R can have z -tube fractions as high as0.5. As mentioned before, the global rotation of a galaxy canbe low if the angular momentum on prograde and retrograde z -tubes cancels out. This is the case for galaxies with low λ R in the dark grey region in Fig. 14, mostly slow rotatorsof classes C, D, E and F.A better measure for the amount of streaming motionis the ‘effective prograde z -tube fraction’, which we defineas the normalized difference of the fraction of prograde andretrograde z -tubes:( z -tubes) − ( z -tubes) . (10)Plotting this fraction against λ R (lower panel of Fig. 14)brings down the galaxies from the dark grey area onto a tightcorrelation with λ R for most galaxies. This indicates that formost simulated galaxies the z -tube orbit family (and theirseparation into prograde and retrograde orbits) determinesthe global rotation properties of the galaxies.Galaxies, which do not follow the correlation of λ R andthe effective prograde z -tube fraction (those in the light-greyarea in Fig. 14) are mostly of galaxy class A (fast-rotatorswith gas-rich minor mergers) and are also those, for whichwe found clear signs of figure rotation (indicated by open cir-cles in Fig. 14). Although the orbit classification for thosegalaxies is uncertain, we strongly suspect that the high λ R values have a significant contribution from figure rotation.The non-rotating galaxies for which we trust our classifica-tion, the effective prograde z -tube fraction correlates nicelywith the λ R -parameter. For most observed fast rotating galaxies the amplitude ofthe third-order component ( h ) of a Gauss-Hermite fit tothe line-of-sight velocity profile (Eq. 7) anti-correlates with c (cid:13)000 , 1–21 B. R¨ottgers et al.
Figure 10.
Two-dimensional line-of-sight velocity and velocity dispersion maps with isodensity contours for the six prototypical galaxieswithin 1 . R eff . The λ R parameter and the isophotal ellipticity at R eff is given in the line-of-sight velocity panels. The black bar indicates1 kpc. For comparison we show the radial orbit fractions (Fig. 7) mirrored at r = 0. Galaxies with fastest rotation (M0408 and M0163),have the highest prograde z -tube factions with relatively few canceling retrograde z -tubes. If the latter is not the case, high z -tubefractions do not yield strong rotation (M0664 and M0175). M0094 has a counter-rotating core, where we see both: at the core theretrograde z -tubes (slightly) dominate and at larger radii the prograde z -tubes (clearly) dominate. c (cid:13) , 1–21 tellar orbits in cosmological simulations M0408 all particles boxes (23 . z -tubes (66 . x -tubes (1 . Figure 11.
The line-of-sight velocity and velocity dispersion maps with isodensity contours of all star particles of M0408 up to 1 . R eff (top left), for all stars on box orbits ( ∼ z -tubes ( ∼ x -tubes ( ∼ λ R values) and the flattening originates z -tubes. The high dispersion at the center is supported by box orbits. M0175 all particles boxes (36 . z -tubes (32 . x -tubes (20 . Figure 12.
The line-of-sight velocity and velocity dispersion maps of M0175 and its orbital components like for M0408 in Fig. 11. Theparticles on z -tubes (lower left panel) are distributed equally on prograde and retrograde orbits resulting in low net rotation ( λ R ∼ . x -tube population contributing to the dispersion at ∼ R eff . rotational support ( V /σ ; Bender et al. 1994; Halliday et al.2001; Pinkney et al. 2003; Krajnovi´c et al. 2013; for the V /σ data from the ATLAS sample see Krajnovi´c et al.2011, 2008). The velocity profile has a steep leading and along trailing wing. This holds for oblate systems resemblingtow-integral models (Dehnen & Gerhard 1994; Bender et al.1994) and/or can be indicative of an embedded disk com-ponent (van der Marel & Franx 1993; Bender et al. 1994;Fisher 1997; Naab & Burkert 2001; Krajnovi´c et al. 2013).In this section we use the cosmological galaxy formation simulations to explain the origin of the anti-correlation of h and V and its connection to the orbital structure.Naab et al. (2013) found that only fast rotating galaxieswith late gas-rich mergers or late dissipation (classes A andB in their classification) show a h - V /σ anti-correlation.These are also the galaxies with the highest λ R -parameterand, as we have shown here, those with a the highest effectiveprograde z -tube fraction.It has been shown with idealized experiments that gasdissipation (cooling gas flow to the center, triggered by c (cid:13)000
The line-of-sight velocity and velocity dispersion maps of M0175 and its orbital components like for M0408 in Fig. 11. Theparticles on z -tubes (lower left panel) are distributed equally on prograde and retrograde orbits resulting in low net rotation ( λ R ∼ . x -tube population contributing to the dispersion at ∼ R eff . rotational support ( V /σ ; Bender et al. 1994; Halliday et al.2001; Pinkney et al. 2003; Krajnovi´c et al. 2013; for the V /σ data from the ATLAS sample see Krajnovi´c et al.2011, 2008). The velocity profile has a steep leading and along trailing wing. This holds for oblate systems resemblingtow-integral models (Dehnen & Gerhard 1994; Bender et al.1994) and/or can be indicative of an embedded disk com-ponent (van der Marel & Franx 1993; Bender et al. 1994;Fisher 1997; Naab & Burkert 2001; Krajnovi´c et al. 2013).In this section we use the cosmological galaxy formation simulations to explain the origin of the anti-correlation of h and V and its connection to the orbital structure.Naab et al. (2013) found that only fast rotating galaxieswith late gas-rich mergers or late dissipation (classes A andB in their classification) show a h - V /σ anti-correlation.These are also the galaxies with the highest λ R -parameterand, as we have shown here, those with a the highest effectiveprograde z -tube fraction.It has been shown with idealized experiments that gasdissipation (cooling gas flow to the center, triggered by c (cid:13)000 , 1–21 B. R¨ottgers et al.
M0094 all particles boxes (41 . z -tubes (35 . x -tubes (14 . z -tubes (22 . z -tubes (12 . Figure 13.
The line-of-sight velocity and velocity dispersion maps of M0094 (galaxy class E) and its orbital components like for M0408in Fig. 11. The galaxy has a counter-rotating core visible in the line-of-sight velocity (upper left panel) which is generated by the z -tubepopulation (middle left panel) consisting of prograde and retrograde orbits (bottom panels). The overall kinematics of the system isdetermined by the dominant non-rotating box orbit population (upper right). This galaxy also has a sizable x -tube component (12.9 %). a merger event) can explain this behavior. In collisionlessmergers the stellar population of the remnant is dominatedby stars on box orbits and even if the remnant is rotatingthe LOSVD has steep trailing wing (positive h ) which ishardly observed (Naab & Burkert 2001). Gas inflow duringa merger, however, leads to centrally concentrated, axisym-metric potentials, suppressing the population of box orbits(Barnes & Hernquist 1996). With now more stars on z -tubes(which carry the angular momentum) the LOSVD gets asteep leading wing and the observed anti-correlation of h and V /σ can be recovered (Naab et al. 2006). This is sup-ported by the formation of new stars in a re-forming disk(Naab et al. 2006; Hoffman et al. 2009, 2010 and also seeBender et al. 1994).Here we present the same effect for two galaxies formedin a cosmological context. In the top panels of Fig. 15) weshow the two-dimensional maps of V , σ, V /σ , and h forM0277, a fast rotating galaxy that has experienced a lategas-poor (collisionless) major merger (typical for the classD galaxies in Naab et al. 2013). For this galaxy the LOS ve-locity and h are correlated. In the bottom panel of Fig. 15we show, as an example, the LOSVD at ∼ . R eff . It is dom-inated by non-rotating stars (73%) without net-rotation—mostly on box orbits. The stars on prograde z -tubes shiftthe peak towards positive velocities. The resulting distribu-tion is almost symmetric as not only the prograde z -tubes (not as dominant as the box orbits) broaden the distributiontowards positive values, but there are also some retrograde z -tubes, that do the same towards negative velocities. Hence,only a slightly positive value for h .For M0408 the situation is different. This galaxy is afast rotator with late gas-rich major merger and it shows aclear anti-correlation of the LOS velocity and h (top panelsFig. 16). A typical LOSVD is shown in the bottom panel ofFig. 16. At the same radius this galaxy is dominated byhigh angular momentum z -tube orbits which by themselvesalready generate a LOSVD with a steep leading wing. Thebroad trailing wing hosts stars on retrograde tubes. Stars onother orbits without angular momentum do not affect theshape of the LOSVD very much.If we restrict ourselves to galaxies without figure rota-tion, we can conclude that all orbits apart from z -tubes haveno intrinsic angular momentum (around the minor axis) andhence their LOS velocity profile is almost symmetric andpeaks around v = 0. The z -tube orbits can be approximatedas two peaks: one from retrograde and one from prograde z -tubes. For a rotating system (around the minor axis) thelatter peak has a larger amplitude. If the other orbits (cen-tering at v = 0) are subdominant (like in Fig. 16) the over-all distribution then peaks with the prograde z -tubes hasa trailing wing that is broadened by the retrograde z -tubesand other orbits. If the other orbits, however, are dominant c (cid:13) , 1–21 tellar orbits in cosmological simulations M0227Figure 15.
Characteristic line-of-sight velocity distribution forall stellar particles (bottom panel, black histogram) at the ma-jor axis around 0 . R eff (0 . R eff < x < . R eff and − . R eff 01. The LOSVD of stars on z -tube orbits (greenhistogram) peaks at v ≈ 200 km/s, but the total LOSVD is dom-inated by particles which are mostly on box orbits (red histogram)peaking at v ≈ 0. Such a profile is typical for fast rotating galax-ies formed in dissipationless mergers (Naab & Burkert 2001; Naabet al. 2006, 2013). (like in Fig. 15), the overall distribution peaks in-betweenthe prograde z -tubes and the other orbits and is rather sym-metric. All galaxies presented here consist of two populations ofstars. One has formed within the galaxy (the in situ compo-nent) and the second has formed in other galaxies and havebeen accreted in mergers (the accreted component). In gen-eral, in situ formation dominates at high redshift and theaccretion of stars becomes more important at low redshift,and more so for massive systems (Guo & White 2008; Oser M0408Figure 16. Same as Fig. 15 but for the fast rotating galaxyM0408 (Class B). Here the stellar orbits in the observed regionare dominated by tubes (green histogram) generating an overallLOSVD with a steep leading wing (black histogram and dashedline, h = − . et al. 2010; Lackner et al. 2012; Moster et al. 2013; Naab2013). The separate origin of these components might alsoresults in different orbit populations.In Fig. 17 we plot the orbit fractions of the in situ andaccreted component as well as for the dark matter parti-cles as a function of radius for four characteristic examples.Surprisingly, most galaxies show little difference in the or-bital composition of these components (M0163 and M0175).Possible small difference might be washed out, since for in-dividual particles the orbit classification is uncertain on theper-cent level (see Sec. 3.4). For M0664 and M0917, however,the orbit composition of the in situ component is clearly dis-tinct.The former has a tube biased in situ component and hasa recent gas-poor major merger, where the different dynami-cal history of the two merged galaxies is still imprinted in the c (cid:13)000 Same as Fig. 15 but for the fast rotating galaxyM0408 (Class B). Here the stellar orbits in the observed regionare dominated by tubes (green histogram) generating an overallLOSVD with a steep leading wing (black histogram and dashedline, h = − . et al. 2010; Lackner et al. 2012; Moster et al. 2013; Naab2013). The separate origin of these components might alsoresults in different orbit populations.In Fig. 17 we plot the orbit fractions of the in situ andaccreted component as well as for the dark matter parti-cles as a function of radius for four characteristic examples.Surprisingly, most galaxies show little difference in the or-bital composition of these components (M0163 and M0175).Possible small difference might be washed out, since for in-dividual particles the orbit classification is uncertain on theper-cent level (see Sec. 3.4). For M0664 and M0917, however,the orbit composition of the in situ component is clearly dis-tinct.The former has a tube biased in situ component and hasa recent gas-poor major merger, where the different dynami-cal history of the two merged galaxies is still imprinted in the c (cid:13)000 , 1–21 B. R¨ottgers et al. orbit structure. The latter, M0977, had a late gas-rich majormerger, in which new stars formed the dissipative compo-nent, and and thus it has a prominent late in situ formedcomponent that is populating mostly z -tubes (except for theinner radii, r (cid:46) . R eff ). The orbital structure of the darkmatter component, however, is always very similar to theaccreted component, independent of the different assemblyhistories of the galaxies. It is plausible to assume that fre-quent mergers, which are relevant for galaxy classes C, D,E, & F, mix the in situ and accreted stellar populations ef-ficiently and the dark matter particles behave in a similarway.In addition the orbit analysis might not be the bestdiagnostics. Although z -tubes are all centrophobic they cansignificantly differ in shape from circular to very eccentric. Agood measure for this behavior is provided by the anisotropy β (Binney & Tremaine 2008): β ≡ − (cid:104) v φ (cid:105) + (cid:104) v θ (cid:105) (cid:104) v r (cid:105) , (11)where v r , v φ , and v θ are the velocities in spherical coordi-nates. This parameter is zero for isotropic motion, positiveif the velocities are radial biased and negative if they aretangentially biased.We plot the corresponding radial anisotropy profiles ofM0163, M0175, M0664, and M0977 in the right panels ofFig. 17 and also separate the in situ component and accretedcomponent as well as the dark matter particles. For M0664and M0977 the orbital structure is reflected in the anisotropyprofiles: where in galaxy M0664 the in situ stars populatebox orbits more than the accreted stars do, there the motionof the in situ stars is also more radially biased than of theaccreted stars; similarly for M0408, where the in situ starsare more tangentially biased, they preferentially populate z -tubes. However, we also see different anisotropy profiles for in situ and accreted stars in galaxies which show no signif-icant difference in the orbit profiles, e.g. for M0175. Herethe accreted stars are moderately radially biased ( β ≈ . in situ stars—having almost identical orbitalstructure—are isotropic. But this is not true for all galax-ies. There are some that have alike β -profiles for in situ andaccreted stars (e.g. M0163).We also investigated the dark matter anisotropy pro-files (black lines in Fig. 17) and they turned out to be veryisotropic or sometimes mildly radially biased (cf. M0977)where they have a tendency to follow the accreted compo-nent. To see whether this is universal and to identify trendsin the anisotropies, we plotted the β -profiles of the differ-ent galaxy classes (except for those galaxies that show amassive near-by substructure that would compromise theresults) in Fig. 18. The dark matter particles are indeed al-ways isotropic to mildly radially biased, with no trend alongthe different galaxy classes. The profiles of the other com-ponents, however, have clear dependencies on the assemblyhistory of the galaxies.We find the in situ component to have smaller β thanthe accreted component in general and in agreement withWu et al. (2014), who grouped the galaxies among their insitu fractions and plotted the overall stellar anisotropy pro-files for all galaxies. This is not surprising, since in situ starsform from the dissipative gas component, that settles downonto a rotating disk conserving angular momentum. The ro- tating dynamical element is also imprinted in the in situ stars that then should preferentially populate z -tubes—theonly ones with intrinsic rotation. The accreted star compo-nent has fallen in from all directions and, hence, are expectedto be on more radially biased orbits.We furthermore find that fast-rotators with late gas-richmergers (classes A and B) have very tangentially anisotropic in situ components, especially beyond the effective radius.Accreted stars, however, are a bit radially biased and hencethe overall stellar anisotropy is slightly radially biased forclass A galaxies—those with late gas-rich minor mergers—anyway. Class B galaxies—those with late gas-rich majormergers—have similar anisotropies of the accreted stars, the in situ component, however, is even stronger tangentiallybiased than it is for class A galaxies. The importance of the in situ stars yields a tangentially biased stellar anisotropy.Interestingly, the in situ stars are always slightly ra-dially biased or isotropic at most for fast-rotators withlate gas-poor major mergers (class D). Slow-rotators withgas-rich major mergers (class C) have very similar stellaranisotropy profiles. The in situ star, however, are mildly tan-gentially biased at large radii in contrast to those galaxieswith gas-poor major mergers (classes D and E). We, hence,see that the gas fraction plays an about equally importantrole in determining the anisotropy of the in situ stars andwe consequently find the most radially biased motion of thestars in slow-rotators with gas-poor major/minor mergers(classes E and F). For those with major mergers (class E)even the in situ stars are no longer tangentially biased andthey are roughly isotropic for those with minor mergers.It seems as the anisotropy parameter β is better cor-related with the in situ fractions and the quantized natureof orbit classification can often not capture the different as-sembly histories of in situ and accreted stars. Moreover, β isbetter observable, and although the most prominent trendsare at large radii ( r (cid:38) R eff ), the differentiation between fast-rotators with gas-rich merger histories (classes A and B) andthe other galaxy classes is already strong at smaller radii(compare yellow lines for stellar β in Fig. 18).We see that the anisotropy indeed reveals more aboutthe assembly history of the galaxies than the orbit classesdo, but they also complement one another as the rotationof the galaxies is not directly reflected in the anisotropyprofiles. The dark matter particles have very similar orbitalstructures as the stellar component (see Fig. 17), but theyare very isotropic for all galaxies among our ensemble as itcan be seen from Fig. 18. The anisotropies we find are alsoconsistent with observational results: there is a relativelylarge variety of anisotropies (Thomas et al. 2007) but mostlymildly radially biased ones (de Lorenzi et al. 2008; Das et al.2011) the only strong exception is fast-rotating galaxies withlate gas-rich major mergers (class B) beyond the effectiveradius.We plot the global fraction of stars that formed in situ since z ≈ β in Fig. 19. In situ starsthat have formed earlier have undergone multiple mergerevents and, hence, the fingerprint of their dynamical historyin the anisotropy is probably washed out. We indeed seea weak correlation, though only for the inner parts ( r (cid:46) . R eff ) of the galaxies (Fig. 19). For the region 0 . R eff Figure 17. Left panels : The radial orbital structure of the in situ stars (solid lines) and the accreted stars (dashed lines) as well as darkmatter particles (dash-dotted lines) for four galaxies (M0163, M0175, M0664 , and M0977). For most galaxies with collisionless recentassembly histories (classes D, E, and F) there is almost no difference between the in situ and accreted component and the dark matterparticles. If there are mild variations (like for the box population in M0664) the accreted stars and dark matter are more alike. Thisis also true for M0977, but this galaxy has relevant late in situ star formation (and no late large mergers) forming a prominent z -tubepopulation dominating most of the galaxy. Right panels: The anisotropy parameter β as a function of radius for dark matter (black), allstars (yellow), as well as separated into the in situ (green) and accreted (blue) component. The dark matter is in general isotropic at allradii. M0163 is dominated by box orbits at all large radii and radially biased ( β ∼ . z -tubes at large radiibut here the in situ stars are more isotropic that the accreted stars which are also on z -tubes but clearly radially biased. For M0977 thiseffect is even stronger with a clearly tangentially biased in situ component.c (cid:13)000 The anisotropy parameter β as a function of radius for dark matter (black), allstars (yellow), as well as separated into the in situ (green) and accreted (blue) component. The dark matter is in general isotropic at allradii. M0163 is dominated by box orbits at all large radii and radially biased ( β ∼ . z -tubes at large radiibut here the in situ stars are more isotropic that the accreted stars which are also on z -tubes but clearly radially biased. For M0977 thiseffect is even stronger with a clearly tangentially biased in situ component.c (cid:13)000 , 1–21 B. R¨ottgers et al. Figure 18. The mean anisotropy parameter profile (line) for dark matter and stars as well for the in situ and accreted components onlyis plotted for the different galaxy classes. Three galaxies—M0069 (E), M0162 (E) and M0948 (F)—that have heavy nearby substructures(indicating an on-going/up-coming major merger) are excluded from these calculations. The pale bands around the mean indicate thestandard deviation among the galaxy classes. Figure 19. For the inner part of the galaxies ( r < . R eff , upperpanel) the anisotropy parameter β correlates with the in situ fraction. Furthermore, the galaxy classes from Naab et al. (2013)separate in the diagram. For larger radii, however, the correlationis nearly completely gone (see lower panel). region has decreased by a factor of almost two from thatwithin 0 . R eff , and hence they do not influence β as much.Moreover, we see that the galaxy classes defined byNaab et al. (2013) separate in the anisotropy– in situ frac-tion diagram. Fast-rotators with late gas-rich mergers or latedissipation (classes A and B) have rather high in situ frac-tion and are isotropic of slightly tangentially biased. Slow-rotators with late gas-rich major mergers (class C) still have high in situ fractions due to the shocking gas in the merg-ers, but are more radially biased, since they do not rotateas much. The remaining classes of fast-rotators with lategas-poor major mergers (class D) and slow-rotators withgas-poor mergers (classes E and F) are located in the upperleft corner in the diagram with small in situ fractions andare tangentially biased. We have presented an orbit analysis of star and dark mat-ter particles out to three effective radii for a sample of 42galaxies formed in cosmological zoom simulations of Oseret al. (2010). With an improved version of the Carpintero& Aguilar (1998) spectral classification scheme we classifiedorbits of stars and dark collisionless dark matter particles.For the stellar orbits we found that box orbits and z -tubesare most abundant among the simulated galaxies. The distri-bution of orbits with radius, however, can vary significantlyfrom galaxy to galaxy. A common feature is the relativelyhigh central ( r (cid:46) . R eff ) box orbit fraction, much higherthan what is found when triaxial Schwarzschild models areapplied to observed LOSV maps (c.f. NGC 4365, van denBosch et al. 2008 and NGC 3379 and NGC 821,Weijmanset al. 2009). It is likely that underestimating the influenceof dissipation of the assumed model (see the discussion inOser et al. 2010) and/or neglecting black hole impact playa significant role. Both (not included) effects will help tomake the central region more axisymmetric and thereforesuppress the population of box orbits.Galaxies with figure rotation (6 out of 42), which have c (cid:13) , 1–21 tellar orbits in cosmological simulations uncertain orbit fractions, were identified and we excludedthem from any interpretation that uses orbit analysis. Forthe remaining galaxies we show that LOS rotation, quanti-fied by the λ R -parameter, originates from streaming motionsof stars. We demonstrate that the value of λ R directly cor-relates with the ‘effective prograde z -tube fraction’ (i.e. thedifference of the fraction of prograde z -tubes and the frac-tion of retrograde z -tubes normalized by the total numberof z -tubes).We find the expected correlations of box orbit, z -tube,and x -tube fractions with galaxy triaxiality (e.g. Jesseitet al. 2005). z -tubes live in oblate systems, x -tubes in pro-late ones and box orbits are most abundant in very triaxialsystems ( T ≈ . z -tubes as expected from the investigation of thecorrelation of the effective prograde z -tube fraction and the λ R parameter. One galaxy has a counter-rotating core and,similar to NGC 4365, we are able to demonstrate that thecore is not a kinematically decoupled system, but originatesfrom a superposition of the smooth distributions of progradeand retrograde z -tubes (c.f. van den Bosch et al. 2008).Using the orbit classification, we also can also ex-plain the origin of the observed anti-correlation between h and V /σ . Many simulated fast rotators show and anti-correlation but correlated h and V /σ is also possible.The group of galaxies with enhanced dissipation, i.e. withmore ’late’ in situ star formation due to gas accretionor gas-rich mergers, shows a clear tendency for an anti-correlation (Naab et al. 2013). The increased relative frac-tion of prograde tube orbits creates a steep leading wingin the LOSVD. Physically, this originates from a suppres-sion of box orbits in more axisymmeric potentials. Rotatingsystems with little late dissipation do not show this anti-correlation. This conclusion is in agreement with studies ofisolated mergers (Naab et al. 2006; Hoffman et al. 2009,2010).Using the six galaxy classes with different formationhistories defined in Naab et al. (2013) we only see weaktrends of orbit fractions with the formation history apartfrom systems with late dissipation showing high z -tube frac-tions. Surprisingly, the distribution of orbits of the in situ formed stars, accreted stars, and dark matter particles arevery similar, with the exception of galaxies with a lot oflate dissipation. This result compares well with Bryan et al.(2012), who find similar distributions for stars and dark mat-ter particles at larger radii. Only two of our galaxies exhibita clear distinction between the orbit profiles of in situ formedand accreted stars. One system with a late gas-rich majormerger (M0977) has a higher fraction of z -tubes for the insitu formed stars than for the accreted stars. This is expectedas the in situ stars form from the dissipative gas componentwhich can settle onto an axisymmetric, oblate disk beforestar formation. This is ‘memorized’ in the kinematic fea-tures and preferentially populates stars on z -tubes.We found that the velocity anisotropy (measured bythe β parameter) depends more on the formation historythan orbit distribution. Galaxies with gas-rich mergers andgradual dissipation have can have mildly radially biased mo-tions of the stars ( β (cid:39) . 2) and tangentially biased motions of the stars (up to β (cid:39) − . r (cid:38) R eff ). Galaxies with dry mergers always have radiallybiased motions of stars (0 . (cid:46) β (cid:46) . insitu from the dissipative gas component tend to have tan-gentially biased motions, whereas accreted stars fall in onradially biased trajectories and hence preferentially end upon tangentially biased orbits. We find that in situ formedstars are mildly radially anisotropic ( β (cid:39) . 25) for gas-poormajor mergers remnants and otherwise isotropic to strongtangentially anisotropic ( β < − . 0) for fast-rotators withgas-rich mergers. The dark matter particles, however, arealways close to isotropic. Orbit families are less well corre-lated as for example tube orbits can become radially biasedwhen they become eccentric.It is plausible to assume that in situ stars and ac-creted stars can have different metallicities but the accretedgalaxies have lower mass (e.g. Villumsen 1982; Hilz et al.2013). Therefore it will be interesting to investigate a con-nection between metallicities and kinematic properties (or-bit families, anisotropy, etc.). Zoom-simulations reproducingthe observed evolution of the mass–metallicity relation (e.g.Hirschmann et al. 2013; Aumer et al. 2013) would be wellsuited for this. As our simulations do not follow metal evo-lution such an investigation is, however, beyond the scopeof this paper. However, orbit families do provide impor-tant information about the formation processes. Both AGNfeedback and stellar feedback can lead to a more or lessdissipative formation of galaxies (see e.g. Mo et al. 1998;Hirschmann et al. 2012; Dubois et al. 2013; ¨Ubler et al.2014). Enhanced dissipation results in more axisymmetricand oblate galaxies and with have higher z -tube fractions(the dissipative formation of disk galaxies is an extreme ex-ample, e.g. Aumer et al. 2013). For large radii Bryan et al.(2012) could indeed show that feedback rises the amount of z -tubes and reduced the amount of box orbits for star parti-cles as well as dark matter particles. However, the impact ofdissipation might be particularly important for galaxy cen-ters. Furthermore, feedback can change merger histories (ingeneral reduces the number of minor mergers) and increasesgas accretion and the amount of gas involved in mergers (e.g.Hirschmann et al. 2012; ¨Ubler et al. 2014). Therefore ‘feed-back physics’ might leave a clear fingerprint in the orbitalcomposition of massive galaxies. We thank Davor Krajnovi´c for his comments and suggestionsand thank the anonymous referee for valuable suggestions.Thorsten Naab acknowledges support by the DFG cluster ofexcellence ‘Origin and Structure of the Universe’. c (cid:13)000 0) for fast-rotators withgas-rich mergers. The dark matter particles, however, arealways close to isotropic. Orbit families are less well corre-lated as for example tube orbits can become radially biasedwhen they become eccentric.It is plausible to assume that in situ stars and ac-creted stars can have different metallicities but the accretedgalaxies have lower mass (e.g. Villumsen 1982; Hilz et al.2013). Therefore it will be interesting to investigate a con-nection between metallicities and kinematic properties (or-bit families, anisotropy, etc.). Zoom-simulations reproducingthe observed evolution of the mass–metallicity relation (e.g.Hirschmann et al. 2013; Aumer et al. 2013) would be wellsuited for this. As our simulations do not follow metal evo-lution such an investigation is, however, beyond the scopeof this paper. However, orbit families do provide impor-tant information about the formation processes. Both AGNfeedback and stellar feedback can lead to a more or lessdissipative formation of galaxies (see e.g. Mo et al. 1998;Hirschmann et al. 2012; Dubois et al. 2013; ¨Ubler et al.2014). Enhanced dissipation results in more axisymmetricand oblate galaxies and with have higher z -tube fractions(the dissipative formation of disk galaxies is an extreme ex-ample, e.g. Aumer et al. 2013). For large radii Bryan et al.(2012) could indeed show that feedback rises the amount of z -tubes and reduced the amount of box orbits for star parti-cles as well as dark matter particles. However, the impact ofdissipation might be particularly important for galaxy cen-ters. Furthermore, feedback can change merger histories (ingeneral reduces the number of minor mergers) and increasesgas accretion and the amount of gas involved in mergers (e.g.Hirschmann et al. 2012; ¨Ubler et al. 2014). Therefore ‘feed-back physics’ might leave a clear fingerprint in the orbitalcomposition of massive galaxies. We thank Davor Krajnovi´c for his comments and suggestionsand thank the anonymous referee for valuable suggestions.Thorsten Naab acknowledges support by the DFG cluster ofexcellence ‘Origin and Structure of the Universe’. c (cid:13)000 , 1–21 B. R¨ottgers et al. REFERENCES Arnold J. A., Romanowsky A. J., Brodie J. P., ForbesD. A., Strader J., Spitler L. R., Foster C., Blom C., KarthaS. 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