Accreted or Not Accreted? The Fraction of Accreted Mass in Galaxies from Simulations and Observations
MMNRAS , 1–21 (2021) Preprint 1 February 2021 Compiled using MNRAS L A TEX style file v3.0
Accreted or Not Accreted? The Fraction of Accreted Mass inGalaxies from Simulations and Observations
Rhea-Silvia Remus (cid:63) and Duncan A. Forbes Universit¨ats-Sternwarte M¨unchen, Fakult¨at f¨ur Physik, LMU M¨unchen, Scheinerstr. 1, D-81679 M¨unchen, Germany Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn VIC 3122, Australia
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
In the two-phase scenario of galaxy formation, a galaxy’s stellar mass growth is firstdominated by in-situ star formation, and subsequently by accretion. We analyse the ra-dial distribution of the accreted stellar mass in ∼
500 galaxies from the hydrodynamicalcosmological simulation Magneticum. Generally, we find good agreement with othersimulations in that higher mass galaxies have larger accreted fractions, but we predicthigher accretion fractions for low-mass galaxies. Based on the radial distribution of theaccreted and in-situ components, we define 6 galaxy classes, from completely accretiondominated to completely in-situ dominated, and measure the transition radii betweenin-situ and accretion-dominated regions for galaxies that have such a transition. About70% of our galaxies have one transition radius. However, we also find about 10% of thegalaxies to be accretion dominated everywhere, and about 13% to have two transitionradii, with the centre and the outskirts both being accretion dominated. We show thatthese classes are strongly correlated with the galaxy merger histories, especially withthe mergers’ cold gas fractions. We find high total in-situ (low accretion) fractions tobe associated with smaller, lower mass galaxies, lower central dark matter fractions,and larger transition radii. Finally, we show that the dips in observed surface bright-ness profiles seen in many early-type galaxies do not correspond to the transitionfrom in-situ to accretion-dominated regions, and any inferred mass fractions are notindicative of the true accreted mass. Instead, these dips contain information about thegalaxies’ dry minor merger assembly history.
Key words: galaxies: structure – galaxies: evolution – galaxies: formation – methods:numerical – methods: observational
In the two-phase scenario of galaxy formation (e.g., Oseret al. 2010; Pillepich et al. 2014), galaxies undergo two mainphases of growth: first the in-situ, and subsequently the ex-situ (or accretion) growth phase. In the former phase, starsare formed within the primary galaxy. In the latter phase,mass growth occurs through accretion of satellite galaxies.A pioneering work in this area was presented by Oser et al.(2010), using a set of zoom simulations of massive galaxies,who found that the in-situ phase occurs between redshifts6 and 2, giving rise to a ‘galaxy core’ of size ∼ (cid:63) E-mail: [email protected] merger simulations of different mass ratios, demonstratingthat larger mass ratios for host and satellite galaxies aremore likely to lead to a deposition of the accreted stellarmass at larger radii, while small merger mass ratios usuallylead to full mixture of the accreted and in-situ formed stars(e.g., Hilz et al. 2012; Karademir et al. 2019). However, thepicture is not that clear, as the orbital configurations of themergers have been shown to influence the radius of mass de-position for satellite galaxies especially for mergers of largermass ratios, with circular orbits leading to mass depositionsat larger radii than radial merger orbits (e.g., Amorisco 2017;Karademir et al. 2019).This two-phase scenario has been further refined overthe last decade with increasingly sophisticated, full cosmo-logical simulations. Those focusing on predictions for the ac-creted stellar component of early-type galaxies include thedark matter particle tagging approach of Cooper et al. (2013,2015) and, more recently, hydrodynamical cosmological sim-ulations like Illustris (Pillepich et al. 2014; Rodriguez-Gomez © a r X i v : . [ a s t r o - ph . GA ] J a n R.-S. Remus and D. A. Forbes et al. 2016), EAGLE (Davison et al. 2020), and Illustris-TNG (Tacchella et al. 2019; Pulsoni et al. 2020).In particular, Cooper et al. (2013) modeled 1872 cen-tral galaxies in the mass range 10 . < log M ∗ < . . < log M < .
0) using a semi-analytic method totag dark matter particles, not including a full treatment ofgas physics in the simulation itself. Being mainly massivegalaxies, the sample is dominated by early-type galaxies.They found that accretion leads to a break, or change, in theslope of the stellar mass surface density profile at the radiuswhere the accreted material starts to dominate over thatformed in-situ. They fit S´ersic profiles to the in-situ and ac-creted stars separately in surface density space, finding thatthe resulting double S´ersic profiles provided a good overallfit. They showed that the fraction of accreted material ap-proaches 100% for the most massive early-type galaxies, withmore accretion dominated galaxies having shallower densityprofiles with little, or no, obvious transition in the overallprofile. This study was further expanded for the very highmass end (log M ∼
14) by Cooper et al. (2015). Theyfound double S´ersic profiles to be a good fit to the stellarmass surface density profiles, with the inner component hav-ing S´ersic indices of n ∼ n ∼ all galaxies reveal a clear ‘tran-sition’ radius for which the in-situ and accreted componentscontribute equally (i.e., 50:50), while Tacchella et al. (2019)reported for the new Illustris-TNG simulations that theirmost massive galaxies can be dominated by accreted starsat all radii. In addition, Tacchella et al. (2019) find muchhigher accreted mass fractions at a given stellar mass forthe new Illustris-TNG simulations than Rodriguez-Gomezet al. (2016) found for the old Illustris simulatios. Using theEAGLE simulation, Davison et al. (2020) found similar ex-situ fractions as a function of stellar mass as Tacchella et al.(2019). They also confirmed previous studies findings thatthe majority of accreted material is deposited in the outerregions, while for the most massive galaxies the accretedmass can dominate over in-situ material in the inner regions.However, the mass-size relations found for the galaxies fromthese two simulations are different, clearly showing that thedetails of galaxy formation still strongly differ between thedifferent simulations. More recently, these studies were also broadened tostudy the radial kinematic profiles of galaxies as possibletracers for the transition radii from in-situ to accretion dom-inated parts of galaxies (e.g., Schulze et al. (2020) usingthe Magneticum simulations and Pulsoni et al. (2020) usingthe Illustris-TNG simulations). Both studies find that theshape of the kinematic profile (i.e., v/σ ) does not, in gen-eral, trace the transition between in-situ and ex-situ domi-nated galaxy regions. Schulze et al. (2020) showed that thekinematic profiles only for a special subset of galaxies thatonly experienced very small mergers since z ∼ M ∗ > R e their surface brightness pro-files could be well represented by a single Serisc profile, butbeyond that an extra component was required. A transitionat similar radii have been reported in the globular clustersystems of massive ETGs (e.g., Forbes & Remus (2018)).D’Souza et al. (2014) fit 45,500 galaxies (avoiding edge-ondisks) in several stellar mass bins, finding good fits to adouble S´ersic. There have also been claims that the sur-face brightness profiles of elliptical galaxies are better repre-sented by three components (Huang et al. 2013), with radiiof < R e , ∼ . R e , and ∼ R e , all with S´ersic values of n ∼ R e to 8–10 R e , have been reported in the literature as key tran-sition radii. Very few studies have quantified the transitionradius between different galaxy components and the massassociated with each component. This has, however, been at-tempted by Spavone et al. (2017) and Spavone et al. (2020),using deep imaging of ETGs from the VEGAS survey. Fit-ting double S´ersic functions to the galaxy surface brightnessprofiles and deriving transition radii from this they inferredouter halo mass fractions, finding evidence for higher massfractions in the outer component for more massive galaxies.We note that several late-type galaxies have been stud-ied in order to measure their outer halo light, e.g., the deepimaging of Merritt et al. (2016) using the Dragonfly cam-era. This study revealed a large range in the fraction of halolight in late-type galaxies beyond 5 disk scale lengths from ∼
10% to < . MNRAS , 1–21 (2021) alaxy Accretion Fractions cially addressing the question in how far the transition radiifrom accreted to in-situ components can be inferred fromS´ersic fits to the radial surface density profiles. In Sec. 2we present the simulations and the details of our classifica-tion of in-situ and accreted. Results from the simulationsare presented in Sec. 3. This includes the classification ofthe radial density profiles into 6 classes (3.1), probing theirassembly history (3.2), a comparison with other simulations(3.3), and a study of the correlation of the in-situ/accretedfractions with various galaxy properties (3.4) and the tran-sition radii (3.5). Sec. 4 provides a comparison between the2D density profiles from simulations with observations andthe question of possible recovery of the accreted fractionsfrom the projected profiles. Finally we present our summaryand conclusions in Sec. 5. We use the Magneticum Pathfinder simulations (Dolag etal. 2021, in prep.), which are a set of cosmological hydro-dynamical SPH-simulations of several boxes with volumesranging from (2688 Mpc /h ) to (48 Mpc /h ) and differentresolutions, with the lowest having m Gas = 2 . × M (cid:12) /h and the currently highest having m Gas = 7 . × M (cid:12) /h .Each gas particle can spawn up to four stellar particles dur-ing its lifetime, and as such the average mass of a stel-lar particle is 1 / σ = 0 . h = 0 . Λ = 0 . M = 0 . B = 0 . n s = 0 . z = 2 (Re-mus et al. 2017; Schulze et al. 2018). As we are focusing on the internal properties of galaxiesin this work, we use the currently largest volume of Mag-neticum with the highest resolution level available. Thisbox has a size of (48 Mpc /h ) . It initially contains a to-tal of 2 × (dark matter and gas) particles. The massresolution for the dark matter, gas, and stellar particlesis m DM = 3 . × M (cid:12) /h , m Gas = 7 . × M (cid:12) /h , and m ∗ (cid:39) × M (cid:12) /h , respectively, with a softening of (cid:15) DM = (cid:15) Gas = 1 . /h for dark matter and gas particles, and (cid:15) ∗ = 0 . /h for stellar particles.We choose a lower stellar mass limit of M ∗ ≥ × M (cid:12) to ensure sufficient resolution for radial density profile fits,and additionally limit the sample to central galaxies toensure a proper treatment of the in-situ/ex-situ classifi-cation. The highest mass galaxies in this simulation are M ∗ ∼ M (cid:12) . With these restrictions, we select 511 galax-ies, which include 4 galaxies that are brightest cluster galax-ies (BCGs), and 43 galaxies which are brightest group galax-ies. We are interested in the accreted (ex-situ) and the in-situcomponents of the galaxies. Therefore, we have to trace allstars that are part of a galaxy at z=0 back to their formationredshift. If the star is born inside the main-branch progenitorof the galaxy, it is considered to be formed “in-situ”. If thestar was born outside the virial radius of the main-branchprogenitor of the galaxy, and only later in its life accretedonto that galaxy, then it is considered to be “accreted” inde-pendent of whether it was accreted smoothly or as part ofanother galaxy. If the star particle is born inside the virialradius of the main-branch progenitor but in the wake ofa gas-rich merger, we still consider the star to be formed“in-situ”, as otherwise all stars would be accreted since ulti-mately all gas has been accreted onto the galaxy. These starshave been handled differently in the literature, however, forthe sake of a clean classification with respect to the accretedfraction we use the classification described above. This givesus the smallest possible fraction of accreted stars, and thelargest possible fraction of in-situ formed stars.
The sample of 511 Magneticum galaxies includes all galaxytypes. However, in the second part of this study, we restrictour investigation to spheroidal (or early-type) galaxies. Theyare selected using the b -value b = log (cid:18) j ∗ kpc km / s (cid:19) −
23 log (cid:18) M ∗ M (cid:12) (cid:19) , which effectively gives a galaxies’ position in the M ∗ – j ∗ plane as discussed by Teklu et al. (2015). At z = 0, galax-ies with a b -value of b ≤ − .
73 are classified as spheroidals,while galaxies with b ≥ − .
35 are classified as disks (Tekluet al. 2017). Galaxies with b -values in between these limitshave intermediate properties, that is they include S0 galaxiesand disk galaxies with large bulges, but also a small numberof ongoing-merger and interacting galaxies. On this basis MNRAS000
35 are classified as disks (Tekluet al. 2017). Galaxies with b -values in between these limitshave intermediate properties, that is they include S0 galaxiesand disk galaxies with large bulges, but also a small numberof ongoing-merger and interacting galaxies. On this basis MNRAS000 , 1–21 (2021)
R.-S. Remus and D. A. Forbes
Figure 1.
Examples for three of the six different in-situ/accreted profile classes, from left to right: class A (extremely accretion dominated),class B (accretion dominated), and class C (classic). The vertical black dashed lines in the upper panels indicate the half mass radius.
Upper panels:
Radial stellar density profiles for all stars (black lines), in-situ formed stars (red lines) and accreted stars (blue lines).
Middle panels:
Relative mass fractions of the in-situ (red) and accreted (blue) subcomponents.
Bottom panels:
The assembly history ofthe stellar mass of the example galaxies. Dashed red lines show major mergers (mass ratios of 1:1 to 3:1), green lines show minor mergers(mass ratios of 3:1 to 10:1), and blue lines show mini mergers (mass ratios below 10:1). our sample includes 154 spheroidal, 105 disk, and 252 in-termediate galaxies. This is the same classification that hasbeen used by Teklu et al. (2017), Schulze et al. (2018), andSchulze et al. (2020).
We calculate the radial stellar mass density profiles for theMagneticum galaxies using equal particle bins with at least200 particles per bin, in spherical shells around the galaxycenter. For the in-situ and the accreted components, thesame radial bins are used as for the total profile to ensurea direct radial comparability of the two components. To ac-
MNRAS , 1–21 (2021) alaxy Accretion Fractions Figure 2.
Same as Fig. 1 but for the other three profile classes, from left to right: class D (double cross-over), class E (balanced), andclass F (in-situ dominated). commodate for the softening, we exclude the inner 1.4 kpc,but we do not use an outer radial limit.Inspecting the 3D radial stellar density profiles (in M (cid:12) / kpc ) of the Magneticum galaxies, we find six differentclasses based on their in-situ/accreted behaviour. Examplesfor each class are shown in Fig. 1 and Fig. 2, and Fig. 3, anddescribed in the following: • Class A:
Extremely accretion dominated profiles. Forthese galaxies, the accreted stellar component is always dom-inant, even in the inner regions (see left panels of Fig. 1 andupper left panels of Fig. 3). About 7% of all galaxies showthis kind of behaviour (see Tab. 1). Such galaxies have noclear transition radius between in-situ and accreted stellarmass. • Class B:
Accretion dominated profiles. For these galax-ies, the fraction of in-situ and accreted stars near the galaxycenter is equal, but for all larger radii the accreted fractiondominates (see middle panels of Fig. 1 and upper right pan-els of Fig. 3). This is a rare class, with only about 2% ofall Magneticum galaxies in this class (see Tab. 1). It couldalso be interpreted as an extreme case of class A, but wehere study it as a separate class. The transition radius forthese galaxies is very small, and is not a real transition inall cases as the in-situ component does not necessarily dom-inate in the center but are sometimes simply equal amountsof in-situ and accreted. • Class C:
Classic profiles. The inner regions of thesegalaxies are dominated by in-situ formed stars, while in the
MNRAS000
MNRAS000 , 1–21 (2021)
R.-S. Remus and D. A. Forbes
200 kpc 200 kpc200 kpc 200 kpc200 kpc 200 kpc100%0%25%50%75% 100%0%25%50%75%100%0%25%50%75% 100%0%25%50%75%100%0%25%50%75% 100%0%25%50%75%Intensity Origin Intensity OriginIntensity Origin Intensity OriginIntensity Origin Intensity Origin
Class BClass AClass C Class DClass E Class F
Figure 3.
Random 2D projected views of the example Magneticum galaxies for each of the six profile classes. For each galaxy, a box witha length of 200 kpc centred on the galaxy is shown, with the left plot showing the intensity map derived from all stars in the galaxy andthe right plot showing the origin of the stars colour coded according to the in-situ/accreted fraction (with blue colours showing 100%in-situ fractions and red colours showing 100% accreted fraction). From left to right, top to bottom, the shown galaxies are from class A(upper left), class B (upper right), class C (central left), class D (central right), class E (bottom left), and class F (bottom right). As canbe clearly seen, the amount of in-situ stars increases from the upper left class (A) to the lower right class (F). outskirts the accreted stellar component is dominant (seeright panels of Fig. 1 and central left panels of Fig. 3). Thisis by far the most common class of profiles, with 72% of allMagneticum galaxies showing this behaviour (see Tab. 1).This is also the behaviour found most commonly in previouswork for example by Cooper et al. (2010); Rodriguez-Gomezet al. (2016); Pulsoni et al. (2020). These galaxies have aclear transition radius from in-situ to accretion dominated. • Class D:
Double cross-over profiles. These galaxies havea large accreted fraction dominating in the inner and theouter regions, with their intermediate-radii regions domi-nated by in-situ formed stars (see left panels of Fig. 2 andcentral right panels of Fig. 3). 13% of all Magneticum galax-ies fall in this category (see Tab. 1), making this the secondmost common profile type. Given its nature, these profileshave two transition radii. • Class E:
Balanced profiles. A small fraction ( ≈ • Class F:
In-situ dominated profiles. Galaxies in this classhave radial density profiles that are always dominated byin-situ formed stars at all radii, even at their outskirts (seeright panels of Fig. 2 and bottom right panels of Fig. 3). Only2.7% of all Magneticum galaxies show this behaviour, withthe in-situ fraction always larger than the accreted fraction(Tab. 1). As for class A galaxies, there is no transition radiusfor these galaxies.Recently, a similar analysis of radial in-situ and accretedprofiles has been presented by Pulsoni et al. (2020) using theIllustris-TNG simulations. Differently to our six classes of 3Dmass density profiles, they reported four classes based on 2Dmass surface density profiles: Their class 1 (20% of the sam-ple) galaxies are in-situ dominated at all radii, equivalentto our class F galaxies, albeit our class F only covers 2.7%of the galaxies. Class 2 is their most common profile (57%),
MNRAS , 1–21 (2021) alaxy Accretion Fractions Class All Spheroidals DisksN % N % N %Class A 36 7.1 15 9.7 1 0.95Class B 9 1.8 6 3.9 1 0.95Class C 367 71.8 100 64.9 78 74.3Class D 66 12.9 24 15.6 18 17.1Class E 19 3.7 7 4.6 2 1.9Class F 14 2.7 2 1.3 5 4.8
Table 1.
Numbers and percentage for the six different profileclasses for all 511 galaxies from the Magneticum simulationused in this work, and for those galaxies that are classified asspheroidals (154 galaxies) or disks (105 galaxies). and is equivalent to our class C, albeit we have more galax-ies of class C (72%). This is also the kind of in-situ/accretedprofiles that have solely been reported for Illustris galaxies(Rodriguez-Gomez et al. 2016). Their class 3 (15%) is clos-est to our double cross-over profiles (class D), and with 13%of our galaxies being class D the numbers are very similarbetween the two simulations. Their class 4 galaxies are accre-tion dominated and their least common profile at 8%. In ourwork such profiles were divided into class A (extremely ac-cretion dominated) and B (accretion dominated), represent-ing a total of about 9% of galaxies, again in good agreementwith each others. We also classified ∼
4% of our galaxies tobe ‘balanced’ with similar in-situ and accreted components,a class that does not appear in the classifications by Pulsoniet al. (2020). Bearing in mind that the relative proportionsof each profile class will depend on the range of galaxy typesand masses in each simulation, the main differences are thatwe find more classic profiles (72% vs 57%) and fewer in-situdominated profiles (2.7% vs 20%), clearly highlighting theintrinsic differences between the simulations.
One of the first steps to understand the origin of the differ-ent profile classes is to test whether they correlate with thestellar mass of the galaxy. In the left panel of Fig. 4 we showthe normalised distribution of the different profile classes asa function of stellar mass. We find a clear trend that galaxiesof classes E and F, where the in-situ component is 50% orlarger, are always galaxies with relatively low stellar masses,while galaxies of classes A and B, which are everywhere ac-cretion dominated, usually reside at the high mass end. Thismass trend is expected, as more massive galaxies have gen-erally accreted more mass than low mass galaxies. Similartrends were seen by Pulsoni et al. (2020) in their study. In-terestingly, the two most common classes of galaxies, namelyclasses C and D, are most likely to be found in the middlemass range of our galaxy sample, with the galaxies havingstellar masses of 10 . < log( M ∗ ) <
11. This indicates that itis not the frequency of mergers, but the type of merger thatis crucial in establishing the differences.To understand this in more detail, we study the assem-bly history of all galaxies with respect to their main for-mation branch from z = 2 to z = 0. We distinguish threedifferent kind of mergers: • Major mergers with mass ratios of 1:1 to 3:1. • Minor mergers with mass ratios of 3:1 to 10:1. • Mini mergers with mass ratios below 10:1. For the mini mergers, there is no lower mass limit in general,however, due to the resolution limit of the simulation, thesmallest mergers that we can resolve here are on the order of100:1 in mass ratio. Below this limit, we do not call accretionevents mergers, even for those few cases where this wouldstill be resolvable, for the sake of completeness in numbers.Major mergers are known to have strong impacts on themain progenitor galaxy at all radii, however, this is not ingeneral the case for minor and mini mergers. While minormergers, especially in the mass range around 5:1, can stillstrongly influence the mass distribution of the progenitorgalaxies even at their centres (e.g., Hilz et al. 2013; Ka-rademir et al. 2019), mini mergers mostly contribute to theouter halos of galaxies and only play a role for the centralevolution of the host galaxy for radial infall orbits or head-oncollisions (Karademir et al. 2019). Since we focus on radialranges beyond the half-mass radius, all types of mergers canplay a role in establishing the different profile classes.Examples of the assembly history for the six classes aregiven in the lower panels of Fig. 1 and Fig. 2, with the historyalways belonging to the galaxy for which the radial densityprofiles are shown in the upper panels of the same figures,and the intensity maps are shown in the according panelsof Fig. 3. The redshifts of past merger events are marked asred/green/blue dashed lines for major/minor/mini mergers,respectively. These six examples show that all galaxies, butone, experience major mergers, with the galaxy that expe-riences no major merger being of class C. In the case of theexample galaxies from classes A and B (the accretion dom-inated profile classes), both show two major merger eventssince z = 2. Interestingly, the galaxy from class F, which isdominated by in-situ stars at all radii, experiences a majormerger at a redshift of about z = 1.More quantitatively, in the right panel of Fig. 4 we showfor each profile class histograms of the frequency of major(red dashed lines), minor (green dash-dotted lines), and minimergers (blue solid line) since redshift z = 2 ( ∼
10 Gyr inlook-back time). Furthermore, Fig. 5 shows the amount ofstellar mass relative to the present-day stellar mass that wasaccreted through the mergers of different mass ratios andthrough all mergers for each accretion class in the upperpanel, while the lower panel shows the fraction of gas rela-tive to the present-day stellar mass accreted through thesemergers for the different accretion classes.In general, about half of all Magneticum galaxies haveexperienced at least one major merger since z = 2. However,when considering individual profile classes, we find large dif-ferences. Most strikingly, major mergers generally play asignificant role in the formation of galaxies from accretionclasses A, B, D, and E, while they only play a minor rolein the evolution of galaxies from accretion classes C and F.This reflects what could already be seen from the examplecases, but more statistically we find the following accretionhistory patterns for our six accretion profile classes: • Class A:
The accretion history of this “overmerged”class of galaxies is not surprisingly completely dominatedby merger events, with a total of nearly 70% of the present-day stellar mass being accreted (see upper panel of Fig. 5).Surprisingly, these mergers are not necessarily dry. Espe-cially the major mergers contribute an average of 25% ofthe total stellar mass in gas, but the shear amount of ac-
MNRAS000
MNRAS000 , 1–21 (2021)
R.-S. Remus and D. A. Forbes
Figure 4.
Profile class dependence on stellar mass and merger frequency.
Left panel:
Histogram of the stellar mass distribution, colourcoded by profile class. Low mass galaxies are dominated by classes C, E and F, while classes A and B are common for high mass galaxies.
Right panels:
Histogram showing the frequency of major (red), minor (green), and mini (blue) mergers since z = 2 for each class. Majormergers are least common for galaxies of class C, where nearly 60% of the galaxies have had no major merger since z=2. creted stellar mass is enough to dominate the final galaxy atall radii. Additionally, most of these galaxies are rather mas-sive, and as such a larger amount of the gas will be presentas a hot gas halo and not participate in the star formationprocess. Galaxies of this profile class are rather common forthe spheroidals, but only one of these is found among thedisk galaxies . • Class B:
Galaxies from this accretion class have a similaraccretion history to galaxies of class A, with more than 60%of their stellar mass being accreted. The main difference hereis that the mergers were all gas poor, resulting in the lowestamount of gas accreted since z = 2 in the whole sample (seelower panel of Fig. 5). • Class C:
The “classic” profile shows a significantly differ-ent behaviour from all the others, namely 2/3 of the galaxiesin this class have never experienced a major merger since z = 2 (see right panel of Fig. 4). Even those class C galax-ies with major mergers only get about 10% of their massfrom this pathway, implying that the major mergers happenrather early for this class (see upper panel of Fig. 5). In gen-eral, galaxies of this class only accrete about 30% of theirstellar mass through mergers, which is the lowest fraction This is a very special case in which the accretion occurs along aplane along the galaxies disk-plane, similar to what was discussedfor mini mergers by Karademir et al. (2019) found for all classes. Furthermore, the mass accreted throughthe major and minor mergers is approximately equal, andthe relative contribution of the mini mergers is rather largefor galaxies of this group. This clearly shows the impor-tance of minor and mini mergers in the assembly history ofclass C galaxies. In addition, we find that the mergers thata galaxy of class C experiences, are usually rather dry, andcontribute only about 20% of the total stellar mass in gas(see lower panel of Fig. 5). This also explains the dominanceof the accreted material at large radii and the dominance ofthe in-situ components in the center, as the minor and minimerger, especially when dry, often do not reach the centralparts of the host galaxy at all but rather deposit their massat large radii (Purcell et al. 2007; Amorisco 2017; Karademiret al. 2019). • Class D:
Major mergers are important for half of thegalaxies in this profile class, but those mergers are relativelydry (gas-poor). The host galaxy, on the other hand, is rel-atively wet (gas-rich) at the time of merging, and throughthe merger the gas is moved outwards into a ring-like struc-ture, where the star formation occurs. Our simulation doesnot have the resolution to confirm this, but this may be onepossible way to form an (old) bulge inside a gas-rich galaxy.In addition, these galaxies are equally common for both disksand spheroidals (seen Tab. 1). • Class E:
The mass accretion history of galaxies from this
MNRAS , 1–21 (2021) alaxy Accretion Fractions Figure 5.
Mass fraction added via major, minor, mini merg-ers and all mergers together since z = 2 for the six dif-ferent profile classes. Classes A/B/C/D/E/F are given asred/orange/blue/cyan/yellow/green filled circles, respectively. Top panel:
Fraction of stellar mass accreted through mergersof different types.
Bottom panel:
Fraction of gas mass accretedthrough mergers of different types. Gas mass includes hot andcold gas. For the most massive galaxies a significant fraction ofthe gas is in a hot (and thus not star forming) phase. class is dominated by a single merger which is either a majormerger (60%) or a massive minor merger (see right panelsof Fig. 4). These mergers were gas-rich, causing a starburstafter accretion, which effectively leads to this special pro-file case where the in-situ and accreted radial fractions areidentical over a broad radial range. As known from classicalbinary merger simulations Hernquist & Barnes (e.g., 1991),these mergers usually result in a spheroidal galaxy as longas the merger is not in-plane or has a very high gas frac-tion (Springel & Hernquist 2005). This is reflected in thelow fraction of disk galaxies in this class (only 1.9%), whilefor the spheroidals they account for 4.6%, as seen in Tab. 1. • Class F:
Galaxies of class F show a similar behaviour togalaxies of class C, as only half of them experience a majormerger and only about 40% of their stellar mass is accreted(see right panel of Fig. 4 and upper panel of Fig. 5). Themajor difference is the amount of gas accreted through themerger events independent of the merger mass ratio: Wefind that all mergers deliver significantly more gas than for the galaxies of class C, with a total of about 80% of thestellar mass being accreted in gas mass (see lower panel ofFig. 5), which is the highest frequency found for the differentprofile classes. Since all these galaxies have stellar masseswell below 10 M (cid:12) , they do not host a large hot gas halo,and thus most of that gas is cold and contributes to starformation, resulting in an overall in-situ dominated radialdensity profile. This clearly shows that the origin of theseoverall-in-situ dominated profiles is gas-rich accretion, andas such it is surprising that two of these galaxies are actuallyspheroidals. Overall, there is broad agreement between simulations andmodels of different kinds that the fraction of accreted stars iscorrelated with the stellar (and halo) mass of galaxies. How-ever, the different simulations vary strongly in the actual(average) values found for the accreted (or ex-situ) fractionsat a given mass. This can clearly be seen in Fig. 6 for halomass (upper left panel) and for stellar mass (upper rightpanel). Here, we compile data from the literature for thefive large hydrodynamical simulations: • Magneticum from this study, shown as the blue solidline and shaded area in both panels. • Illustris-TNG, shown as the pink dash-dot-dot-dottedline and shaded area, from Pillepich et al. (2018) for thehalo mass comparison (left panel) and from Tacchella et al.(2019) for the stellar mass comparison (right panel). • EAGLE, shown as dash-dotted yellow line and shadedarea, from Davison et al. (2020), only for the stellar masscomparison (right panel). • Horizon-AGN, shown as green dashed lines, fromDubois et al. (2016), only for the stellar mass comparison(right panel) for the runs with (dark green) and without(light green) AGN. • Illustris, shown as black dotted line and gray shadedarea, from Rodriguez-Gomez et al. (2016), only for the stel-lar mass comparison (right panel).As can be seen immediately, Magneticum galaxies havelarger accreted fractions at the low mass end compared tothe other simulations, while at the high mass end the ac-creted fractions for all the simulations converge to around70-80% for galaxies of stellar masses above 3 × M (cid:12) (orhalo masses above 1 × M (cid:12) ).There are different reasons for these simulations to showsuch different behaviour, and it is up to now still unclearwhich ones are closest to reality. One commonly discussedreason for the different results with respect to the amountof accreted and in-situ components in galaxies is the stellarand/or AGN feedback, which is modeled slightly differentin each simulation. That both processes have strong effectson the resulting accretion fractions has been reported byprevious studies: Hirschmann et al. (2015) used a subsetof the galaxies presented by Oser et al. (2010) and simu-lated them with and without strong stellar feedback (seeopen black diamond and square in the upper right panel ofFig. 6, respectively). They found that, while the stellar massof the galaxies did not change much, the accreted fractiondropped significantly, on average from about 50% to 20%,when the stellar feedback was switched on. This is due to MNRAS , 1–21 (2021) R.-S. Remus and D. A. Forbes
Figure 6.
Ex-situ (accreted) fractions for Magneticum galaxies in comparison to other simulations.
Upper left panel:
Mean ex-situ fractionversus critical halo mass M for Magneticum (solid blue line), with the 1 σ scatter shown in light blue. For comparison, mean valuesare also shown for Illustris-TNG100 (Pillepich et al. (2018), dash-dot-dot-dotted pink line and shaded area), and the particle taggingmodels from Cooper et al. (2013) (dash-dotted lines). Lower left panel:
Same as upper panel but showing the individual values for theMagneticum galaxies, with the colours marking the different profile classes as indicated in the legend. The solid line (here black insteadof blue for better visibility) and blue shaded area mark the mean and 1 σ scatter for this distribution, as in the upper panel. Upperright panel:
Ex-situ fraction versus stellar mass M ∗ . The blue solid line and shaded area show the mean and the 1 σ scatter for theMagneticum galaxies, as in the left panel. For comparison, we include the relations for four other fully cosmological simulations: Illustris(Rodriguez-Gomez et al. (2016), dashed black line and gray shade), Eagle (Davison et al. (2020), yellow dash-dotted line and yellowshade), Illustris-TNG (Tacchella et al. (2019), pink dash-dot-dot-dotted line and shade), and Horizon-AGN (Dubois et al. (2016), greendashed lines, light green without AGN, dark green with AGN). Additionally, we include the mean values from two zoom-simulationsthat cover a range of stellar masses: the SPH-based GADGET from Oser et al. (2010) as x-circle symbols, and the AMR-based ENZOsimulations from Lackner et al. (2012) as +-circle symbols. The mean values in three mass bins from the semi-analytic modeling by Lee &Yi (2013) are shown as black half-circles. Finally, we also include the mean values for the zoom-simulations by Hirschmann et al. (2015)(square for non-feedback, diamond for the feedback-runs, joined by a vertical line). These data points were extracted from Rodriguez-Gomez et al. (2016). We include these simulations as they nicely demonstrate the impact of the stellar feedback on the simulations. Lower right panel:
Same as the upper right panel, but for the individual Magenticum galaxies with the colours marking the differentprofile classes as in the lower left panel. Again, the Magneticum mean is shown as solid black line and the blue shaded area marks the 1 σ scatter for this distribution, as in the upper panel. Magneticum galaxies tend to have higher accretion fractions at low masses comparedto other simulations. MNRAS , 1–21 (2021) alaxy Accretion Fractions the fact that the feedback from the stars heats up the gasinside the galaxies and thus suppresses star formation, es-pecially for the lower mass galaxies, leading to lower stellarmasses for the galaxies in general and thus smaller amountsof accreted stars. However, the merger events still lead tostarbursts and subsequent star formation, but this is thenin-situ star formation. An opposite effect was reported byDubois et al. (2016, see green dashed lines in Fig. 6) andDubois et al. (2013) for the AGN feedback. Here, the sim-ulation runs without AGN feedback (light green) result inlower accreted fractions than the simulation with AGN feed-back (dark green).As all five fully hydrodynamical simulations shown hereinclude both types of feedback, albeit in different implemen-tations, it is not possible to know which of the processes isthe main driver of the differences between the simulations.Note, for example, that the values found for Magneticum arevery similar to the average values found by Oser et al. (2010)in their zoom-simulations (x-circles), but the latter has noAGN feedback and the galaxies found in that simulation alsodiffer strongly from those in Magneticum in other parame-ters (see e.g., Remus et al. 2017). For Magneticum, we knowfrom Teklu et al. (2017) that our stellar feedback is slightlytoo weak for the low mass end and our AGN feedback isslightly too strong at the high mass end when looking atthe baryon convergence efficiency, which is most likely alsothe reason for the difference at the low mass end betweenMagneticum and EAGLE and Illustris-TNG.Another possible reason for the different accretion frac-tions found in the different simulations could be the useof AMR versus SPH codes. Those simulations, both fullycosmological and zoom-in, that were performed with AMRcodes (namely Horizon-AGN (Dubois et al. 2016) and thesimulations by Lackner et al. (2012)) show significantly loweraccreted fractions at all mass ranges than those simula-tions that were performed with SPH codes (namely Mag-neticum, EAGLE, and the simulations by Oser et al. (2010)and Hirschmann et al. (2014)), independent of the includedfeedback. This is especially interesting given that the stud-ies by Lackner et al. (2012) and Oser et al. (2010) both donot include the AGN feedback, but show the strongest differ-ences. It is well know that all codes have their shortcomings,and many improvements have been implemented in recentyears, but to understand how much influence the choice ofthe code has on the accreted fractions, however, would re-quire a detailed comparison study, which has not been doneso far.Note that, for the five large cosmological simulationsshown here, the definitions of in-situ and accreted largelyagree in that we only count those stars as accreted thatwere already born at infall, and count those stars that wereborn from gas that was accreted through a merger but onlyformed after the merger event from this gas as in-situ (seealso Rodriguez-Gomez et al. 2016; Tacchella et al. 2019).This means that, effectively, our accreted fractions are lowerlimits, and the values could only get higher for more elab-orate definitions of in-situ and accreted, but thus this def-inition is not responsible for the difference found betweenthese simulation samples.We also include the accreted fractions with mass ob-tained from two semi-analytic models (SAMs): Cooper et al.(2013) used a particle-tagging method on top of the SAM presented by Guo et al. (2011) based on the Millenium IIsimulation (Boylan-Kolchin et al. 2009), and the resultingaccretion fractions for different halo masses are shown asdash-dotted lines in the left panel of Fig. 6, split accord-ing to the morphology as disks (gray line) or spheroidals(black line). The results found for their sample of spheroidalgalaxies is close to the average values found for the Mag-neticum galaxies in this work, albeit our sample includesboth disks and spheroidals. When we separate our disks andspheroidals, we find a general trend for the disks to havelower accreted fractions than spheroidals of the same massin agreement with Cooper et al. (2013), but the trend ismuch less pronounced and the scatter is large. Lee & Yi(2013) use a SAM built on their own Gadget-2 based darkmatter only simulation, and provide accreted fractions for arange of stellar masses (see half-circles in the upper panelof Fig. 6). Their values lie in between the five different fullycosmological simulations, and are especially at the low-massend not in agreement with our Magneticum results.So far, we have discussed the mean values of the ac-creted fractions with stellar and halo mass for the Mag-neticum simulation in comparison to other simulations, nowwe want to take a closer look at the distribution of the in-dividual galaxies with regard to their accretion classes A–F.They are shown in the lower two panels of Fig. 6 in com-parison to the mean value lines shown in black. As can beseen immediately, there are strong differences between thegalaxies of the different accretion classes: The galaxies fromthe over-merged classes A and B all show high accretionfractions, well above 60%, with no real trend with mass vis-ible. On the other hand, the in-situ dominated galaxies ofclass F all have, as expected, low accretion fractions belowthe mean Magneticum values, and their spread in mass is toosmall to see any trend with mass for both stellar and halomass. Similarly, galaxies of the major merger class E alsoshow no trend in mass, and the overall accretion fractionsare around 50%. For the other two classes, C and D, we finda clear correlation of the accreted fraction with both stellarand halo mass, with a tendency for the galaxies of class Dto be slightly above the mean Magneticum accretion valuesper mass, and for class C to be slightly below on average.Interestingly, class C also includes the lowest accretion frac-tions at all mass bins, even lower than the galaxies of thein-situ dominated class F, clearly demonstrating that theaccretion fractions can be really low if most of the accretionis provided by dry minor and mini mergers in the outskirtsof a galaxy, while the centre is left undisturbed. Next we examine trends between the 3D half-mass radiusand dark matter fraction with total stellar mass and in-situfraction. It has been shown already by Remus et al. (2017)and Schulze et al. (2018) that the Magneticum galaxies suc-cessfully reproduce the observed stellar mass-size relations(e.g., GAMA, by Lange et al. 2015), but here we now takea closer look at the different profile classes in this relation(left panel of Fig. 7). The overmerged galaxies of classes Aand B show only small scatter close to the observed relationover the whole mass range, but due to the fact that they arethe by far most common class at high stellar masses, theyare also most common among the large galaxies. The classi-
MNRAS000
MNRAS000 , 1–21 (2021) R.-S. Remus and D. A. Forbes
Figure 7.
Left panel:
Stellar mass-size relation for the Magneticum galaxies, colour coded according to their profile class (see legend).The 3D half-mass radius is shown against total stellar mass. For comparison, the observed mass-size relation from the GAMA survey byLange et al. (2015) is shown for ETGs (dashed line) and LTGs (solid line). Note that the observations measure half-light radii instead ofhalf-mass radii.
Right panel:
In-situ fraction versus 3D half-mass radius for the Magneticum galaxies, colour coded as in the left panel.Only class C reveals a clear correlation between in-situ fraction and galaxy size. cal profile galaxies of class C, however, show a significantlydifferent behaviour from the galaxies of the other classes,in that they are the clearly dominant class for the smallgalaxies at all stellar mass ranges. Albeit the scatter is largefor this class and there are also very large galaxies amongthem, they clearly dominate the small size end especially atthe lower stellar mass end. This reflects our previous findingsthat these galaxies are dominated by compact star forma-tion in their centers and only little accretion mostly to theoutskirts, resulting in a rather compact central part and con-sequently a smaller half-mass radius. On the other hand, wesee a very different behaviour for those galaxies of classes D,E, and F, all of which have large sizes for their stellar masses,clearly dominating the region of the mass-size relation thatis usually occupied by disk galaxies. This is in good agree-ment with the fact that all of them have large amount ofcold gas accreted through their formation history since z=2,resulting in in-situ star formation in disks and thus largerhalf-mass radii (even if in case of class D galaxies the largecentral accreted component will prevent its classification asa disk given its massive bulge-like nature).As stellar mass M ∗ and 3D half-mass radius r / of agalaxy are correlated, it is not surprising that we also finda correlation between the in-situ fraction of a galaxy andits half-mass radius (right panel of Fig. 7). It can best beseen for the galaxies of accretion class C, as they cover thelargest range of both half-mass radii and in-situ fractions,with a clear tendency for smaller galaxies to have larger in-situ fractions and large galaxies to have small in-situ frac-tions. A similar behaviour is found for galaxies of classesD and E, albeit class E only covers such a small range ofin-situ fractions that no clear correlation between size andin-situ fraction can be inferred from these galaxies alone. Ingeneral, the in-situ fraction decreases with increasing half- mass radius, i.e., accretion leads to a growth in the scaledsize (e.g., Oser et al. 2012), which indicates that most of theaccreted stars are deposited at large radii (see also Amor-isco 2017; Lagos et al. 2018; Karademir et al. 2019; Davisonet al. 2020).For galaxies of the overmerged classes A and B we finda similarly large range of half-mass radii, but only a smallrange of in-situ fractions around 20%, and they reveal nocorrelation at all between size and in-situ fraction. This wellreflects the known fact that a major merger results in a muchmore compact galaxy than a series of minor mergers thatbring in the same total mass as the major merger but deposittheir masses at different radii (Naab et al. 2009; Hilz et al.2012). So while all galaxies of these two classes had plentyof mergers, we find the differences in the individual mergermass ratios mirrored in the size distribution. Galaxies of thein-situ dominated class F show the strongest deviation fromthe correlation between size and in-situ fraction: while allthe in-situ fractions are rather high, the sizes are generallylarger than those of the class C galaxies of similar in-situfraction, in agreement with our previous finding that class Fgalaxies are more similar to disks than the average class Cgalaxy.Finally, we investigate if the fraction of dark matterwithin the half-mass radius, f DM , is correlated with the in-situ fraction and stellar mass. As can be seen in Fig. 8, thereis a broad tendency for galaxies with smaller in-situ frac-tions to have larger central dark matter fractions, indicatingthat (massive) accretion events lead to larger fractions ofdark matter in the center by either enhancing the relativeamount of dark matter in the center or dispersing the bary-onic matter. This tendency can be seen for galaxies of allaccretion classes but those of class F, the in-situ dominatedclass. Galaxies of that class show much higher central dark MNRAS , 1–21 (2021) alaxy Accretion Fractions Figure 8.
Dark matter fraction within the half-mass radius trends.
Left panel:
Dark matter fraction f DM versus stellar mass M ∗ , withcolours as in the right panel. Observations for LTGs from the SPARCS survey (Tortora et al. 2019) are included as a lilac solid line andshaded area, and observations for ETGs from the SPIDER survey (Tortora et al. 2014) are included as an aqua solid line and shadedarea. Right panel:
Dark matter fraction f DM versus in-situ fraction f in − situ for the Magneticum galaxies, with colours indicating thedifferent accretion classes. matter fractions than galaxies of class C with similar in-situ fractions. This is in good agreement with our previousconclusion that class F galaxies closely resemble the typi-cal behaviour of disk galaxies, since observations show thatLTGs have, at the same stellar mass, larger central dark mat-ter fractions than ETGs (Tortora et al. 2019, but also e.g.,Courteau & Dutton (2015); Genzel et al. (2020), albeit theyuse velocity dispersions instead of stellar masses and differ-ent definitions of central radius). This can also be seen inthe left panel of Fig. 8 where we included the observationalresults for LTGs and ETGs from Tortora et al. (2019) andTortora et al. (2014), respectively. As can immediately beseen, most of the class D and F galaxies clearly resemble theproperties of the LTGs, while the clear observed correlationbetween f DM and M ∗ for ETGs is most strongly populatedby galaxies of the classical accretion profile class C, in goodagreement with the idea that dry merging lowers the centraldark matter fractions while wet merging and smooth gasaccretion lead to larger central dark matter fractions. How-ever, the details of the interactions between the baryons andthe dark matter in the centers of galaxies and the influenceof gas and feedback on this interaction are currently underdebate and are beyond the scope of this work. As discussed before, for most galaxies there exists a radiusat which the contribution from in-situ and accreted stars is50% each, that is at which the dominance of the two com-ponents switches. We call this radius the transition radius r trans . For our classic profile (class C), this is the radiuswhere the dominant stellar component switches from in-situin the center to accreted in the outskirts, and thus sepa- rates the inner, self-made part of the galaxy from the outer,dry-merger dominated part.Previous works by Cooper et al. (2013) and Rodriguez-Gomez et al. (2016) already reported this radius to besmaller for larger stellar masses and smaller in-situ frac-tions, and we can confirm these general trends for our class Cgalaxies as shown in Fig. 9. However, we do not find a tightcorrelation between the transition radius and stellar mass,and only a weak correlation is seen between transition radiusand in-situ fraction (see upper panels of Fig. 9), with a largescatter. Only when moving to normalised transition radius(i.e., the transition radius divided by the half-mass radius),the trends become more clear: we even see a clear positivecorrelation between normalised transition radius and in-situfraction, very similar to the correlation found by Rodriguez-Gomez et al. (2016) but slightly less steep (see lower panelsof Fig. 9). We also find a clear negative trend between thein-situ fractions and the stellar mass, with galaxies that haveaccreted a lot of material (i.e., high mass galaxies) tendingto have normalised transition radii of r trans /r / ≤
1. How-ever, this trend is more an upper limit for the in-situ frac-tions at a given mass, as we also find low-mass galaxies withnormalised transition radii r trans /r / ≤
1, but basically nohigh-mass galaxies with r trans /r / >
1. The trend foundfor the Magneticum galaxies is weaker than what has beenfound by Rodriguez-Gomez et al. (2016), and much weakerthan the trend reported for the Illustris-TNG galaxies byPulsoni et al. (2020). This reflects the result found alreadyin Fig. 6, namely that the galaxies in Magneticum have,on average, accreted more dry stellar mass through mergersthan galaxies in galaxies from Illustris or Illustris-TNG.So far, we only discussed those galaxies of profile class Cas most previous works only discussed this profile class with
MNRAS000
MNRAS000 , 1–21 (2021) R.-S. Remus and D. A. Forbes
Figure 9.
Transition radius trends for all profile classes as indicated in the label. Classes A and F have no transition radii and are thereforenot shown. Class D galaxies (cyan diamonds) have two transition radii, so the outer ones are shown as filled diamonds and the innerones are shown as open diamonds.
Upper left panel:
Stellar mass M ∗ versus 3D transition radius r trans in kpc. Upper right panel:
In-situfraction f in − situ versus transition radius r trans in kpc. Lower left panel:
Stellar mass M ∗ versus 3D transition radius r trans normalisedby 3D half-mass radius r / . Lower right panel:
In-situ fraction f in − situ versus normalised transition radius. The horizontal line in bothlower panels represents a normalised transition radius of 1 half-mass radius, i.e., r trans /r / = 1. Dashed black lines and shaded areasshow the results from the Illustris simulation (Rodriguez-Gomez et al. 2016), and the dash-dot-dot-dotted pink line and shaded areaare the results found for Illustris-TNG (Pulsoni et al. 2020). The horizontal dotted line marks where the transition radius equals thehalf-mass radius. no mention of other profile classes. For classes A and F, wecannot provide a transition radius as these galaxies are al-ways dominated by accreted or in-situ stars, respectively,but for the profile classes B, D, and E such transition radiiexist: Galaxies of class B usually have a very small transitionradius of only about 2 kpc, close to the limits of our spatialresolution (and hence may be somewhat smaller than indi-cated). We do not find any trend, positive or negative, withstellar mass, and only a weak positive correlation betweenin-situ fraction and normalised transition radius. This is not surprising as this class if very close to being overmerged likeclass A, and thus we do not expect the transition radius tohave any relevant meaning.In the case of class D, where the center and the out-skirts are dominated by accreted stars but the middle radialrange is dominated by in-situ stars, even two transition radiiexist. For the outer transition radii of class D (filled cyansymbols in Fig. 9) and class E we find the trend with in-situ fraction to be very similar, but generally steeper thanthe correlation seen for class C. This is even clearer for the MNRAS , 1–21 (2021) alaxy Accretion Fractions normalized transition radii again. For both classes we alsofind a tighter anti-correlation between normalised transitionradius and stellar mass, albeit the scatter is still large.The inner transition radii for class D galaxies (opencyan diamonds in Fig. 9) are usually comparably small andoften well below the half-mass radius. Generally, the innertransition radii of class D behave significantly different fromall other transition radii, as there is no trend at all for thestellar mass neither with the transition radius nor with thenormalised transition radius, and there is actually a negativetrend with in-situ fraction, clearly showing that the largerthe fraction of stars formed in-situ, the smaller the accretedcore in the centre, indicating that more stars are formed in-situ if the mass accreted onto the centre was small comparedto the gas disk of the progenitor galaxy.As these transition radii are very indicative of the ac-cretion history of the galaxies and may provide a methodto estimate the in-situ fraction of a galaxy, it would be veryinstructive to be able to measure this transition radius ob-servationally. Therefore, in the next section of this paper weaddress the question of whether it is possible to measure theradius of the transition from in-situ to accretion dominancefrom the observed surface brightness profiles of galaxies, assuggested by Cooper et al. (2013) and Rodriguez-Gomezet al. (2016). Motivated by previous simulation results from Cooper et al.(2013) and Rodriguez-Gomez et al. (2016), there have beenobservational attempts to measure the in-situ and accretedfractions of galaxies using a double S´ersic fit (S´ersic 1963)to the observed surface brightness profiles of galaxies. Thisassumes that the inner S´ersic fit describes the in-situ compo-nent of the galaxy, and the outer S´ersic fit describes the ac-creted component. In some cases, a third fit to the very out-skirts of a galaxy was carried out, under the assumption thatthe third component describes the stellar halo of the galaxyand not the galaxy itself (e.g., Spavone et al. 2017), but wewill not investigate this approach here. Instead, we investi-gate in this section from our simulated galaxies if the double-S´ersic approach really supplies a good measure for the in-situ and accreted components of galaxies. As the observa-tional work has so far focused mostly on early-type galaxies(ETGs), we restrict our sample to Magneticum ETGs only.
To compare the simulated mass density profiles with ob-served surface brightness profiles, we need to create 2D pro-jections of the simulated galaxies. As this projection is ratherarbitrary, we choose a random projection along with theface-on and edge-on projections to test for each galaxy inour sample. In all cases, we find that the profile class ofour galaxies does not change, and the in-situ to accretedrelations stay the same under all projections. Thus, for allgalaxies that have a transition radius ( r trans ) in 3D, we alsofind a radius in the 2D projections which indicates a transi-tion from in-situ to accretion dominance. To follow the observational approach, we fit the pro-jected surface density profiles with both single and doubleS´ersic fits. In most cases, a double S´ersic fit is a better fitto the projected surface density profiles, independent of theprojection. In those cases where a single S´ersic fit is suffi-cient, this is true for all tested projections. This is ratherpromising as this clearly indicates that, if a double S´ersic fitis needed to describe the observed surface brightness profile,then it is independent of the viewing angle and reflects theunderlying 3D density distribution. For the double S´ersicfits to the 2D surface density profiles, we define the crossingradius, R cross , as the radius where the inner and outer S´ersicprofiles cross each others.The upper row of Fig. 10 shows an example of a class Cprofile galaxy with its well defined transition radius in 3D(here r trans = 10 .
52 kpc, left panel). A transition is also seenbetween the in-situ and accretion dominated regions of thegalaxy in all three 2D projections (upper right panels), how-ever, the values of the transition radii in the 2D projectionsare all smaller than the 3D transition radius r trans . We findthat this is not simply a matter of unlucky projections butis rather a common feature of class C profiles (which makeup the majority of profiles). This disconnect between thetransition radii seen in 3D and the 2D profiles also occursin all other classes with well-defined transition radii, namelyclass B, D, and E.While the transition radii are already disconnected from3D to 2D, the matter is even worse if we use the double S´ersicfits to describe the underlying in-situ and accreted compo-nents: In a few cases like the one shown in the upper panelsof Fig. 10, the two S´ersic components are a good approxi-mation of the in-situ and accreted components, and the re-sulting crossing radius between the two S´ersic components, R cross , is a good approximation to the 2D transition radius.However, for most galaxies this is not the case. One exampleof a galaxy that demonstrates the issue nicely is shown inthe lower panels of Fig. 10: This galaxy is of class A, i.e., isaccretion dominated at all radii and has no transition radiusfrom in-situ to accretion dominated, neither in 3D (left lowerpanel) nor in projection (three panels on the lower right).However, the stellar 2D surface density profiles in this exam-ple, under all projections, clearly require a double S´ersic fit,thus providing a crossing radius R cross . The two resultingS´ersic components in this case do not describe the under-lying in-situ and accreted components. They instead markthe radius where accretion due to massive mergers transi-tions into accretion from small mergers and mini mergersthat never reach the centre of the galaxy.To further quantify this issue, the left panel of Fig. 11shows the differences between the crossing radii of the dou-ble S´ersic fits R cross for the random projection (with errorbars marking the values for the edge-on and face-on projec-tions), and the true 3D transition radius r trans between thein-situ and accreted components for all galaxies where sucha transition radius is well defined (classes B, C, D, and E).The plot is largely a scatter diagram with little, or no, cor-respondence between the two measured radii, independentof the profile class. This is also true for the projected 2Dtransition radii, but as the behaviour is nearly identical wedo not show this plot here.For galaxies of classes D and E, the 2D crossing radiiare much smaller than the real transition radii, while for MNRAS000
52 kpc, left panel). A transition is also seenbetween the in-situ and accretion dominated regions of thegalaxy in all three 2D projections (upper right panels), how-ever, the values of the transition radii in the 2D projectionsare all smaller than the 3D transition radius r trans . We findthat this is not simply a matter of unlucky projections butis rather a common feature of class C profiles (which makeup the majority of profiles). This disconnect between thetransition radii seen in 3D and the 2D profiles also occursin all other classes with well-defined transition radii, namelyclass B, D, and E.While the transition radii are already disconnected from3D to 2D, the matter is even worse if we use the double S´ersicfits to describe the underlying in-situ and accreted compo-nents: In a few cases like the one shown in the upper panelsof Fig. 10, the two S´ersic components are a good approxi-mation of the in-situ and accreted components, and the re-sulting crossing radius between the two S´ersic components, R cross , is a good approximation to the 2D transition radius.However, for most galaxies this is not the case. One exampleof a galaxy that demonstrates the issue nicely is shown inthe lower panels of Fig. 10: This galaxy is of class A, i.e., isaccretion dominated at all radii and has no transition radiusfrom in-situ to accretion dominated, neither in 3D (left lowerpanel) nor in projection (three panels on the lower right).However, the stellar 2D surface density profiles in this exam-ple, under all projections, clearly require a double S´ersic fit,thus providing a crossing radius R cross . The two resultingS´ersic components in this case do not describe the under-lying in-situ and accreted components. They instead markthe radius where accretion due to massive mergers transi-tions into accretion from small mergers and mini mergersthat never reach the centre of the galaxy.To further quantify this issue, the left panel of Fig. 11shows the differences between the crossing radii of the dou-ble S´ersic fits R cross for the random projection (with errorbars marking the values for the edge-on and face-on projec-tions), and the true 3D transition radius r trans between thein-situ and accreted components for all galaxies where sucha transition radius is well defined (classes B, C, D, and E).The plot is largely a scatter diagram with little, or no, cor-respondence between the two measured radii, independentof the profile class. This is also true for the projected 2Dtransition radii, but as the behaviour is nearly identical wedo not show this plot here.For galaxies of classes D and E, the 2D crossing radiiare much smaller than the real transition radii, while for MNRAS000 , 1–21 (2021) R.-S. Remus and D. A. Forbes
Figure 10.
Upper panels:
Example of a class C mass density profile in 3D and 2D projections.
Top left panel:
3D total stellar mass densityprofile (black curve) with the in-situ and accreted components in red and blue, respectively.
Top right panels:
Projected 2D stellar massdensity profiles from three different projections: The projected total stellar profile is shown as black curve, the in-situ and accretedcomponents are shown as solid red and blue lines, respectively. The dashed lines show the inner (red) and the outer (blue) fits from thedouble S´ersic fits, and the single S´ersic fits (green) to the total projected stellar density profiles. In the upper right of each panel welist the transition radius in 3D and the crossing radii in 2D, in units of kpc. In this example, the single S´ersic fit is never a good fit toany of the projections. The double S´ersic fits describe the total profile very well in all projections, and are also a good approximationto the in-situ and accreted profiles in all cases. However, the crossing radii R cross (i.e., the radius where the two S´ersic profiles cross)vary on the order of 1 kpc between the three projections, and are in all three cases only about half as large as the real 3D transitionradius r trans . Lower panels:
Same as upper panels but for a class A profile. Class A galaxies are extremely accretion dominated and haveno transition radius between in-situ and accreted components in their 3D or 2D stellar density profiles, as can be seen from the solidred and blue curves in all four panels. However, a single S´ersic fit is not a good fit to any of the projections and the double S´ersic fit isclearly needed in all three projections to describe the total total stellar profiles. Thus, we obtain crossing radii R cross from these doubleS´ersic components, that vary again between the three projections, but in no case are they representative of the true in-situ or accretedcomponents. galaxies of class B we find the opposite trend (with two ofthem having such large crossing radii R cross that they arewell above the plotted radius range). Galaxies of class Cshow both kind of behaviour, with R cross both lower andhigher than the true r trans . Independent of the profile class,we conclude that it is a lucky coincidence if the crossingradius R cross of the double S´ersic fits is a good approximationto the transition radius r trans . In summary, the transitionfrom an inner to an outer S´ersic fit to an observed surfacebrightness profile bears little, or no, connection to the truetransition between the in-situ and accreted components in agalaxy.We also measure the integrated mass within the outerS´ersic component and compare it to the true accreted massfraction. This is shown in the right panel of Fig. 11 for allgalaxies where a double S´ersic fit was a good fit, even thoseof profile classes A and E that are dominated by accretedor in-situ stars at all radii, respectively. This plot reveals alarge scatter with a very weak trend about the unity line,indicating that an outer (inner) S´ersic component fit to asurface brightness profile is a poor guide to the true accreted(in-situ) mass fraction.In summary, we find that fitting a double S´ersic pro- file to the 2D surface density profile of an ETG will not reveal the true radius for the transition from in-situ to ac-cretion dominated material. This suggests that the dips seenin observed surface brightness profiles can not, in general,be taken as a signature of a division between in-situ and ac-creted components of the galaxy. They may instead be moreindicative of a transition from stars being formed in-situplus stars accreted by major mergers, to the component ofstars mostly accreted through minor or mini mergers. Fur-thermore, the integrated mass associated with the inner andouter S´ersic functions provide a poor guide to the true in-situ and accreted mass fractions of a galaxy, respectively.We conclude that the (two) components visible in the (pro-jected) density profiles do not reflect the in-situ and accretedcomponents in general, but rather mark the transition fromthe inner part of the galaxy which can be dominated by in-situ stars but also be dominated by a massive merger event,and the outer part of the galaxy which is dominated by smallminor or mini mergers that get disrupted in the outskirts ofthe galaxy and never interact with its center . This is simi- Note that in the very inner parts of galaxies additional compo-MNRAS , 1–21 (2021) alaxy Accretion Fractions Figure 11.
Left panel:
Crossing radius R cross obtained from double S´ersic fits to the 2D projected mass density profiles (random projection)versus the 3D transition radius r trans between in-situ and accreted components, for all profile classes (colours as indicated in the rightpanel) with well defined transition radii. Right panel:
Fraction of integrated mass from the outer S´ersic function fit to the 2D mass densityprofiles versus the true accreted mass fraction. In both panels, the dashed line shows a 1:1 relation. Error bars indicate the maximumand minimum values obtained for edge-on and face-on projections. lar to the dynamical split of the ICL and the BCG in galaxyclusters, and might be a way to distinguish outer stellar ha-los of galaxies from the galaxies themselves instead.
Some of the deepest imaging of nearby ETGs available comesfrom the VEGAS survey (Capaccioli et al. 2015). The surveyprobes surface brightness profiles out to ∼ R e and down tosurface brightness levels of ∼
29 mag / arcsec in the g-band.The survey is still ongoing, however, results on the radialsurface brightness profiles have been published for severalmassive galaxies in group/cluster environments by Spavoneet al. (2017) and Spavone et al. (2020). Spavone et al. (2017)fit two or three S´ersic profiles to 6 ETGs, with the S´ersicparameters n constrained to a narrow range. More recently,Spavone et al. (2020) fit 19 ETGs in the Fornax cluster witheither two or three S´ersic components. Here we focus on thetwo component fit, for which n was a free parameter. Thetwo component fits have a single intermediate radius, andthe accreted mass fractions are calculated from the second(outer) component. These are referred to as the “relaxed”components following Cooper et al. (2015). Hence the ap-proach to provide unconstrained fits is more comparable toour approach, we focus on the study by Spavone et al. (2020)instead of Spavone et al. (2017).Another very deep imaging study has been carried outby Kluge et al. (2019), who fit double S´ersic profiles to ex-tremely low surface brightness profiles targeting especially nents can be visible in the (projected) density profiles, caused forexample by bars and bulges, but we cannot include these struc-tures in our analysis as the resolution of the Magneticum galaxiesis not high enough to resolve these inner structures of the galaxies. BCGs. Both single and double S´ersic fits were obtained, aswell as accreted fractions from the double S´ersic fits.We also compare to the double S´ersic fits of ∼ , z ∼ .
08 and stackedin mass bins by D’Souza et al. (2014). Taking mean valuesfrom their figure 13 for ETG-like galaxies, we note that theirdata covers a similar stellar mass range to our modelledgalaxies and that they find effective radii of the inner andouter components to be around 3 and 8 kpc, respectively.D’Souza et al. (2014) also provided such measurements fortheir stacked LTG sample, however, we will focuss on theirresults regarding the ETGs here.
In Fig. 12 we reproduce the top right panel of Fig. 6, showingthe ex-situ accretion fraction versus stellar mass. Again, thelines and shading show the results of various models, colorsas indicated in Fig. 6, with the blue solid line showing theaverage fraction of accreted mass for Magneticum galaxies.This time, we included in Fig. 12 observational data from theliterature. These observations do not directly measure thefraction of accreted mass but rather fit double S´ersic profilesto the surface brightness profiles of early-type galaxies, asdescribed in Sec. 4.2, inferring the mass fraction from theouter S´ersic component.While all simulations suggest a general trend of increas-ing accretion fraction for higher mass galaxies, there is noclear trend for the observational proxy (the outer componentmass) to vary with stellar mass for the Fornax galaxy sampleby Spavone et al. (2020) or the BCG sample by Kluge et al.(2019). Only the stacked sample provided by D’Souza et al.(2014) shows a decrease in accreted fraction with mass fortheir ETG sample. In fact, the different observations differstrongly from each others and do not show a clear picture
MNRAS000
MNRAS000 , 1–21 (2021) R.-S. Remus and D. A. Forbes
Figure 12.
Mass fraction of accreted stars versus stellar mass (sameas the upper right panel of Fig. 6) but with observations includedas black symbols: Data points from the VEGAS survey Spavoneet al. (2020) as open diamonds, with additional data points fromthe literature as presented by Spavone et al. (2020) as open trian-gles. Data points for BCGs from Kluge et al. (2019) are shown asfilled black diamonds. The values for the stacked SDSS galaxies byD’Souza et al. (2014) are shown as open squares, with the upperline the one obtained for the ETG-like galaxies where a doubleS´ersic fit is a good description, and the lower line for the LTG-likegalaxies where a third S´ersic fit is required. The blue solid lineand shaded region indicate the Magneticum average values fromthis work, and all other coloured lines and shaded areas indicateother cosmological simulations as described in Fig. 6. of the accreted fraction estimated through the outer S´ersicfit component being correlated with the total stellar massof a galaxy. This further supports our results from Sec. 4.1,that dips in the observed surface brightness profile do not,in general, correspond to the true transition from in-situto accreted dominated material. An alternative approach toestimating accretion fraction may come from star formationhistories (Boecker et al. 2020) or 2D chemo-dynamical anal-ysis (Poci et al. 2019), and needs to be investigated in futurestudies.
As a final test, we compare the S´ersic indices n from the sin-gle and double S´ersic fits to our projected simulated galaxieswith observations to ensure that the simulated and observedgalaxy samples really are comparable in their radial proper-ties. Fig. 13 shows the S´ersic indices n from single S´ersic fitsto the 2D projected mass density profiles of the Magneticumgalaxies, for all galaxies in the left panel and ETGs-only inthe right panel. We also include the observed relation forgalaxies using eq. 2.7 from Graham (2013) and simply as-suming M/L B = 10 for all galaxies as solid black line. Wefind a trend of increasing S´ersic index n for higher massgalaxies that matches the observed mean trend well, clearlyshowing that the overall mass distribution of the simulated galaxies is in good agreement with observations. Galaxiesof the different profile classes are well spread in S´ersic in-dex for a given stellar mass, with no clear trends apart fromthe fact that the largest S´ersic indices are clearly found inclass C galaxies. We also include the range of S´ersic indicesfrom the empirical model by Hopkins et al. (2009), whichcover a similar mass range than our simulated galaxies. Themodel predicts on average S´ersic indices that are, at a givenstellar mass, somewhat larger than the Magneticum and theobserved galaxies of Graham (2013), especially at the highmass end, but the scatter range is very similar, and the over-all trend of larger S´rsic indices with larger stellar mass is ingood agreement.When limiting our galaxy sample to ETGs-only (rightpanel of Fig. 13), we find the S´ersic indices to be slightlylarger on average. We additionally include the observationaldata for individual ETGs from Kormendy et al. (2009) andKluge et al. (2019), further showing that the simulations alsoprovide good descriptions of the stellar mass distributionsof ETGs especially. There is a slight tendency for galaxieswith stellar masses above log( M ∗ ) > . .For double S´ersic fits, we here focus only on ETGs asthe observational comparison samples only include ETGs.As shown in Fig. 14, we find the inner profiles of our sim-ulated ETGs to have S´ersic indices of n ∼ . n ∼ > M (cid:12) , is reasonable, with a slight tendency forthe obersved outer S´ersic indices to be larger than for thesimulated ETGs. Compared to the observations of BCGs byKluge et al. (2019), we find that the agreement with theirouter S´ersic indices is rather good, while their inner S´ersicare on average larger than those of our simulated galaxies.However, this could also be due to the fact that most ofthe Magneticum ETGs in the mass range comparable to thesample by Kluge et al. (2019) are not BCGs.Additionally, we also show in Fig. 14 the inner and outerS´ersic indices from the stacked observations by D’Souzaet al. (2014), using their double S´ersic fits (solid lines). Ascan clearly be seen they differ rather strongly from the sim-ulated galaxies, but also the other observations, with theirinner slopes generally smaller and their outer slopes muchlarger in comparison. We note that D’Souza et al. (2014)also fit triple S´ersic profiles to their highest mass galaxies.In this case, their outer S´ersic fits have n ∼ .
5, which ismuch closer to our simulation values and the other observa-tions, indicating that their inner slopes are actually really“inner” slopes which we do not fit in this work to avoid reso- For a more detailed comparison of the BCG properties froma larger Magneticum simulation volume with observations, seeRemus et al., in prep. MNRAS , 1–21 (2021) alaxy Accretion Fractions Figure 13.
S´ersic index n versus stellar mass for single S´ersic fits to the 2D projected mass density profiles of all Magneticum galaxies.The dashed black line show the results from simulations by Hopkins et al. (2009), with the shaded area marking the scatter inferred fromtheir simulations. The solid black line is the mean relation from observations by (Graham 2013) converted into stellar mass assuming M/L B = 10. Left panel:
All Magneticum galaxies are coloured according to their profile classes as indicated in the legend.
Right panel:
Only the ETGs from the Magneticum galaxy sample are shown. In addition, open black diamonds show observations of ETGs fromKormendy et al. (2009), and the solid black diamonds show BCGs from the observations by Kluge et al. (2019).
Figure 14.
S´ersic index n versus stellar mass for double S´ersic fits to the 2D projected mass density profiles of the Magneticum galaxies,with colours as indicated in the legend. Observations from the VEGAS survey (Spavone et al. 2020) are shown as open black diamonds,and BCGs from Kluge et al. (2019) as solid black diamonds. The black lines mark the values obtained by D’Souza et al. (2014) from fitsto over 45 ,
500 galaxies.
Left panel:
Inner S´ersic fits.
Right panel:
Outer S´ersic fits. lution issues. This clearly highlights the importance of cleardefinitions regarding the fitted regions of galaxies when per-forming comparisons.Overall, we find reasonable agreement between the S´er-sic indices n predicted by our simulated galaxies and theobserved S´ersic indices, especially of ETGs, for both single and double S´ersic fit indices, clearly showing that the simu-lated galaxies used in this work capture the observed matterdistributions. This clearly shows that our result, that doubleS´ersic fits do not describe the in-situ and accreted compo-nents of galaxies, is applicable to observations. We rathersuggest that the double S´ersic fit (excluding the central in- MNRAS000
Outer S´ersic fits. lution issues. This clearly highlights the importance of cleardefinitions regarding the fitted regions of galaxies when per-forming comparisons.Overall, we find reasonable agreement between the S´er-sic indices n predicted by our simulated galaxies and theobserved S´ersic indices, especially of ETGs, for both single and double S´ersic fit indices, clearly showing that the simu-lated galaxies used in this work capture the observed matterdistributions. This clearly shows that our result, that doubleS´ersic fits do not describe the in-situ and accreted compo-nents of galaxies, is applicable to observations. We rathersuggest that the double S´ersic fit (excluding the central in- MNRAS000 , 1–21 (2021) R.-S. Remus and D. A. Forbes ner bulge areas) describes the relaxed inner and the unre-laxed outer stellar (halo) components of galaxies and couldtherefore be used to distinguish the outer stellar halo froma galaxy.
Using the Magneticum simulation we have studied a sampleof 511 model galaxies in the log mass range 10 . < M ∗ < two transition radii at whichthe in-situ and accreted material are equal, with an accre-tion dominated core, an in-situ dominated shell around it,and an accretion dominated outskirt. This is actually thesecond most common class of galaxies in our sample.We show that these profile classes correlate with galaxymass, and that the type of mergers they undergo help toshape their profiles. We especially show that the amountof gas that is involved in these mergers is more importantin shaping these profiles than the actual merger, and thatthe most common class is to about 70% not dominated bymajor mergers but rather smaller merger events. Their outerregions are largely built up by dry minor and mini mergers,clearly showing the importance of minor and especially minimergers in shaping the outer stellar halos of galaxies.We find that galaxies with high in-situ fractions (low ac-cretion fractions) tend to be lower mass galaxies with smallerhalfmass radii, and we see a weak trend for high in-situ frac-tion galaxies to have lower central dark matter fractions,with the exception of the overall in-situ dominated galaxiesthat have clearly larger central dark matter fractions at agiven stellar mass than galaxies of the most common class,typical for what is found in disk galaxies. We measure theradius between the in-situ and accretion-dominated regionsfor those galaxies that reveal a clear transition, which arethe majority of our sample. This transition radius is found toweakly be inversely correlated with stellar mass, but stronglycorrelated with the in-situ fraction for our most commonclass of galaxies. However, galaxies of the other classes thathave one or even two transition radii, do not follow the samerelations.In order to compare our 3D profiles with observations,we projected the stellar mass density in different angles foreach galaxy to be able to directly compare with observed sur- face brightness profiles. We find that the transition radiusfrom in-situ to accretion dominated profiles seen in many 3Dprofiles also occurs in all projections, but always at differentradii in the 2D profiles, usually at smaller radii. None of ourgalaxies changes its in-situ-profile class during projections.We also find that, similar to observations, our projected stel-lar mass surface density profiles usually require a double S´er-sic fit to be described accurately, with S´ersic indices for bothcomponents similar to the range of observed S´ersic indices.However, we clearly see that these two S´ersic componentsusually do not describe the underlying in-situ and accretedcomponents, but are rather disjunct from those. Only invery few cases the crossing radius of the two S´ersic com-ponents coincides with the transition radius of the galaxy.Even worse, we also clearly see that most galaxies that aredominated by accreted stars at all radii, still require a dou-ble S´ersic fit to describe the stellar surface density profiles,thus having a crossing radius but no transition radius.In other words, we clearly conclude that the dip seen in2D profiles does not correspond to the true transition radiusbetween in-situ and accretion dominated regions. Similarly,any mass inferred from these double-S´ersci fits will not tracethe true in-situ or accreted mass of a galaxy. Thus, fits tothe dips seen in some observed surface brightness profilesof early-type galaxies are not a true measure of a galaxy’saccretion material. However, they do hold some informationabout the assembly history of that galaxy, as we find indi-cations that these dips are more likely an indication for thetransition from the inner (in-situ and massive merger dom-inated) core of a galaxy to its stellar halo, mostly accretedthrough minor and mini mergers, similar to the ICL compo-nent around BCGs. To confirm this, a more detailed studyincluding also the radial kinematics of a galaxy in addition toits density component is needed in the future, to disentan-gle the formation pathways of galaxies from observationaltracers. ACKNOWLEDGEMENTS
We thank Klaus Dolag and Felix Schulze for very use-ful discussions. We also thank Thomas Davison, En-rica Iodice, and Marilena Spavone for their helpful com-ments. We also acknowledge funding from the DAAD PPPGermany-Australia Exchange Program. The MagneticumPathfinder simulations were partially performed at theLeibniz-Rechenzentrum with CPU time assigned to theProject “pr86re”, supported by the DFG Cluster of Excel-lence “Origin and Structure of the Universe”. We are es-pecially grateful for the support by M. Petkova throughthe Computational Center for Particle and Astrophysics(C2PAP).
DATA AVAILABILITY
The data underlying this article will be shared on reasonablerequest to the corresponding author.
REFERENCES
Amorisco N. C., 2017, MNRAS, 464, 2882MNRAS , 1–21 (2021) alaxy Accretion Fractions Beck A. M., et al., 2016, MNRAS, 455, 2110Boecker A., Leaman R., van de Ven G., Norris M. A., MackerethJ. T., Crain R. A., 2020, MNRAS, 491, 823Boylan-Kolchin M., Springel V., White S. D. M., Jenkins A., Lem-son G., 2009, MNRAS, 398, 1150Capaccioli M., et al., 2015, A&A, 581, A10Cooper A. P., et al., 2010, MNRAS, 406, 744Cooper A. P., D’Souza R., Kauffmann G., Wang J., Boylan-Kolchin M., Guo Q., Frenk C. S., White S. D. M., 2013, MN-RAS, 434, 3348Cooper A. P., Gao L., Guo Q., Frenk C. S., Jenkins A., SpringelV., White S. D. M., 2015, MNRAS, 451, 2703Courteau S., Dutton A. A., 2015, ApJ, 801, L20D’Souza R., Kauffman G., Wang J., Vegetti S., 2014, MNRAS,443, 1433Davison T. A., Norris M. A., Pfeffer J. L., Davies J. J., CrainR. A., 2020, MNRAS, 497, 81Dolag K., Jubelgas M., Springel V., Borgani S., Rasia E., 2004,ApJ, 606, L97Dolag K., Vazza F., Brunetti G., Tormen G., 2005, MNRAS, 364,753Dolag K., Borgani S., Murante G., Springel V., 2009, MNRAS,399, 497Dolag K., Mevius E., Remus R.-S., 2017, Galaxies, 5, 35Donnert J., Dolag K., Brunetti G., Cassano R., 2013, MNRAS,429, 3564Dubois Y., Gavazzi R., Peirani S., Silk J., 2013, MNRAS, 433,3297Dubois Y., Peirani S., Pichon C., Devriendt J., Gavazzi R., WelkerC., Volonteri M., 2016, MNRAS, 463, 3948Duc P.-A., et al., 2015, MNRAS, 446, 120Fabjan D., Borgani S., Tornatore L., Saro A., Murante G., DolagK., 2010, MNRAS, 401, 1670Forbes D. A., Remus R.-S., 2018, MNRAS, 479, 4760Forbes D. A., Thomson R. C., 1992, MNRAS, 254, 723Genzel R., et al., 2020, arXiv e-prints, p. arXiv:2006.03046Graham A. W., 2013, Elliptical and Disk Galaxy Structure andModern Scaling Laws. p. 91, doi:10.1007/978-94-007-5609-0 2Guo Q., et al., 2011, MNRAS, 413, 101Hernquist L., Barnes J. E., 1991, Nature, 354, 210Hilz M., Naab T., Ostriker J. P., Thomas J., Burkert A., JesseitR., 2012, MNRAS, 425, 3119Hilz M., Naab T., Ostriker J. P., 2013, MNRAS, 429, 2924Hirschmann M., Dolag K., Saro A., Bachmann L., Borgani S.,Burkert A., 2014, MNRAS, 442, 2304Hirschmann M., Naab T., Ostriker J. P., Forbes D. A., Duc P.-A.,Dav´e R., Oser L., Karabal E., 2015, MNRAS, 449, 528Hopkins P. F., Hernquist L., Cox T. J., Keres D., Wuyts S., 2009,ApJ, 691, 1424Huang S., Ho L. C., Peng C. Y., Li Z.-Y., Barth A. J., 2013, ApJ,766, 47Karademir G. S., Remus R.-S., Burkert A., Dolag K., HoffmannT. L., Moster B. P., Steinwandel U. P., Zhang J., 2019, MN-RAS, 487, 318Kluge M., et al., 2019, arXiv e-prints, p. arXiv:1908.08544Komatsu E., et al., 2011, ApJS, 192, 18Kormendy J., Fisher D. B., Cornell M. E., Bender R., 2009, ApJS,182, 216Lackner C. N., Cen R., Ostriker J. P., Joung M. R., 2012, MN-RAS, 425, 641Lagos C. d. P., et al., 2018, MNRAS, 473, 4956Lange R., et al., 2015, MNRAS, 447, 2603Lee J., Yi S. K., 2013, ApJ, 766, 38Merritt A., van Dokkum P., Abraham R., Zhang J., 2016, ApJ,830, 62Naab T., Johansson P. H., Ostriker J. P., 2009, ApJ, 699, L178Oser L., Ostriker J. P., Naab T., Johansson P. H., Burkert A.,2010, ApJ, 725, 2312 Oser L., Naab T., Ostriker J. P., Johansson P. H., 2012, ApJ, 744,63Pillepich A., et al., 2014, MNRAS, 444, 237Pillepich A., et al., 2018, MNRAS, 475, 648Poci A., McDermid R. M., Zhu L., van de Ven G., 2019, MNRAS,487, 3776Pulsoni C., Gerhard O., Arnaboldi M., Pillepich A., Rodriguez-Gomez V., Nelson D., Hernquist L., Springel V., 2020, arXive-prints, p. arXiv:2009.01823Purcell C. W., Bullock J. S., Zentner A. R., 2007, ApJ, 666, 20Remus R.-S., Dolag K., Naab T., Burkert A., Hirschmann M.,Hoffmann T. L., Johansson P. H., 2017, MNRAS, 464, 3742Rodriguez-Gomez V., et al., 2016, MNRAS, 458, 2371Schulze F., Remus R.-S., Dolag K., Burkert A., Emsellem E., vande Ven G., 2018, MNRAS, 480, 4636Schulze F., Remus R.-S., Dolag K., Bellstedt S., Burkert A.,Forbes D. A., 2020, MNRAS, 493, 3778Schweizer F., Seitzer P., 1992, AJ, 104, 1039Seigar M. S., Graham A. W., Jerjen H., 2007, MNRAS, 378, 1575S´ersic J. L., 1963, Boletin de la Asociacion Argentina de Astrono-mia La Plata Argentina, 6, 41Spavone M., et al., 2017, A&A, 603, A38Spavone M., et al., 2020, A&A, 639, A14Springel V., Hernquist L., 2005, ApJ, 622, L9Springel V., White S. D. M., Tormen G., Kauffmann G., 2001,MNRAS, 328, 726Steinborn L. K., Dolag K., Hirschmann M., Prieto M. A., RemusR.-S., 2015, MNRAS, 448, 1504Steinborn L. K., Dolag K., Comerford J. M., Hirschmann M.,Remus R.-S., Teklu A. F., 2016, MNRAS, 458, 1013Tacchella S., et al., 2019, MNRAS, 487, 5416Tal T., van Dokkum P. G., 2011, ApJ, 731, 89Tal T., van Dokkum P. G., Nelan J., Bezanson R., 2009, AJ, 138,1417Teklu A. F., Remus R.-S., Dolag K., Beck A. M., Burkert A.,Schmidt A. S., Schulze F., Steinborn L. K., 2015, ApJ, 812,29Teklu A. F., Remus R.-S., Dolag K., Burkert A., 2017, MNRAS,472, 4769Teklu A. F., Remus R.-S., Dolag K., Arth A., Burkert A., ObrejaA., Schulze F., 2018, ApJ, 854, L28Tornatore L., Borgani S., Matteucci F., Recchi S., Tozzi P., 2004,MNRAS, 349, L19Tornatore L., Borgani S., Dolag K., Matteucci F., 2007, MNRAS,382, 1050Tortora C., La Barbera F., Napolitano N. R., Romanowsky A. J.,Ferreras I., de Carvalho R. R., 2014, MNRAS, 445, 115Tortora C., Posti L., Koopmans L. V. E., Napolitano N. R., 2019,MNRAS, 489, 5483Vogelsberger M., Marinacci F., Torrey P., Puchwein E., 2020, Na-ture Reviews Physics, 2, 42Wiersma R. P. C., Schaye J., Smith B. D., 2009, MNRAS, 393,99van de Sande J., et al., 2019, MNRAS, 484, 869This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS000