The Origin of the Milky Way's Halo Age Distribution
Daniela Carollo, Patricia B. Tissera, Timothy C. Beers, Dmitrii Gudin, Brad K. Gibson, Ken C. Freeman, Antonela Monachesi
TThe Origin of the Milky Way’s Halo Age Distribution
Daniela Carollo
Center of Exellence for All Sky Astrophysics (CAASTRO) - AustraliaINAF, Astrophysical Observatory of Turin, Torino, Italy [email protected]
Patricia B. Tissera
Departamento de Ciencias Fisicas, Universidad Andres Bello, Av. Republica 220, Santiago, ChileMillennium Institute of Astrophysics, Av. Republica 220, Santiago, Chile
Timothy C. Beers, Dmitrii Gudin
Department of Physics and JINA Center for the Evolution of the Elements, University of Notre Dame,Notre Dame, IN 46556 USA
Brad K. Gibson
E. A Milne Centre for Astrophysics, University of Hull, Hull, HU6 7RX, United Kingdom
Ken C. Freeman
ANU - Research School of Astronomy and Astrophysics, Weston - ACT, Australia
Antonela Monachesi
Instituto de Investigaci´on Multidisciplinario de Ciencia y Tecnolog´ıa, Universidad de La Serena, Ra´ulBitr´an 1305, La Serena, Chile.Departamento de F´ısica y Astronom´ıa, Universidad de La Serena, Avda. Juan Cisternas 1200, La Serena,Chile
ABSTRACT
We present an analysis of the radial age gradients for the stellar halos of five Milky Waymass-sized systems simulated as part of the Aquarius Project. The halos show a diversity of agetrends, reflecting their di ff erent assembly histories. Four of the simulated halos possess clearnegative age gradients, ranging from approximately − −
19 Myr / kpc , shallower than thosedetermined by recent observational studies of the Milky Way’s stellar halo. However, whenrestricting the analysis to the accreted component alone, all of the stellar halos exhibit a steepernegative age gradient with values ranging from − −
32 Myr / kpc, closer to those observedin the Galaxy. Two of the accretion-dominated simulated halos show a large concentration ofold stars in the center, in agreement with the Ancient Chronographic Sphere reported obser-vationally. The stellar halo that best reproduces the current observed characteristics of the age a r X i v : . [ a s t r o - ph . GA ] M a y ∼ . M (cid:12) , and a minimal in situ contribution. Subject headings:
Galaxy: structure – stars: Population II – stars: stellar dynamics – Galaxy:simulations – Galaxy: stellar content
1. Introduction
The stellar halos of galaxies play a particularly crucial role in understanding the early formation ofgalaxies due to the dynamical and chemical fingerprints they carry; fingerprints which shed light on a givengalaxy’s assembly history and the chemical history of its accreted satellite galaxies. In the Milky Way(MW), the advent of massive photometric and spectroscopic surveys has revolutionized the understandingof our own stellar halo. With respect to the di ff use halo, Carollo et al. (2007, 2010), and Beers et al.(2012) demonstrated that it comprises at least two stellar components with di ff erent kinematics, dynamics,and chemical composition (the inner and outer halos). These findings have now been supported by a largenumber of authors (de Jong et al. 2010; Deason et al. 2011; An et al. 2013; Nissen & Schuster 2010;Kafle et al. 2013; Hattori et al. 2013; An et al. 2015; Das, Williams & Binney 2016), and most recentlyby Helmi et al. (2016) using Gaia data. The MW’s stellar halo is also populated by numerous stellarstreams and overdensities, the product of past mergers of satellite galaxies (Helmi 2008; Bell et al. 2008),suggesting a complex superposition of stellar populations.Another crucial parameter that can provide a comprehensive picture of the MW assembly process is theage distribution of the halo system. Recently, Santucci et al. (2015) determined the age of the underlyingstellar populations in the MW’s halo out to ∼
25 kpc from the Galactic center by employing a small sample( ∼ ∼ ∼
60 kpc, using a much larger sample ( ∼ − ± − was derived, and numerous knownand unknown structures and overdensities were identified. The existence and claimed value of a negativeage gradient was confirmed by Das, Williams & Binney (2016) in an investigation based on a sample ofspectroscopically-identified BHB stars from SDSS-DR8.In cosmological simulations of MW-mass galaxies, it is possible to follow the evolution of the satellitegalaxies which merge as part of a system’s assembly (Brook, et al. 2004; Bullock & Johnston 2005; Cooperet al. 2010; Few et al. 2012, 2014; Gomez et al. 2012; Tissera et al. 2014; Cooper et al. 2015). In thisscenario, stellar halos are predicted to form primarily through the accretion of satellite galaxies, each withdi ff erent stellar masses, gas fractions, and stellar population distributions (e.g., Tissera et al. 2014; Cooperet al. 2015). An important contribution from in situ stars within the inner ∼
15 kpc has been also identified 3 –in hydrodynamical simulations, which have a range of possible origins (e.g., Zolotov et al. 2009; Font etal. 2011; House et al. 2011; Brook, et al. 2012; Tissera et al. 2013; Cooper et al. 2015; Pillepich et al.2015; Monachesi et al. 2016b).Recent simulations of MW-mass galaxies provide information on the age distribution of stars formedboth in situ and in accreted satellites, however, most such studies do not include a discussion of the overallage gradients (e.g., Brook, et al. 2012; Tissera et al. 2013; Pillepich et al. 2015). This was in part drivenby the lack of any strong empirical constraints with which to compare. One early exception is the semi-cosmological, sticky-particle work of Bekki & Chiba (2001), who found an age gradient of −
30 Myr kpc − over the galactocentric radial range of 20-50 kpc in one low-resolution simulation (see also Samland et al.2004).In this paper, we focus on the age structure of the stellar halo system in a set of five simulated MW mass-sized halos from the Aquarius Project. Understanding the age structure of the stellar halos can contribute toreveal their origin and evolution. These stellar halos have been considered extensively in previous papers,including their chemical abundance patterns, density and metallicity profiles, and assembly histories (Tisseraet al. 2012, 2013, 2014, 2016). Here, the age gradients and the relative contributions of the in situ andaccreted components, as a function of the galactocentric radius, are explored. The aim of this analysis is toexamine to what extent the simulated Aquarius halos are able to reproduce the age trends found in the MW’shalo, and to investigate the connection between the age profiles and halo assembly. For these purposes, weselect a subset of the level-5 runs from Scannapieco et al. (2009), specifically Aq-A, Aq-B, Aq-C, Aq-D,and Aq-G. Although none of the five realizations underwent a recent major merger, this simulated set ofgalaxies produce an excess of stars, and consequently, more massive stellar halos than the MW. Such issuesa ff ect other simulations as well (e.g., Font et al. (2011); Pillepich et al. (2015)), and should be addressedin future work, given that the MW is an L ∗ spiral galaxy with perhaps the least massive stellar halo for itsgiven total mass (Harmsen et al. 2017). A more e ffi cient supernova feedback can contribute to decreasethe stellar mass fraction, and form more extended disk structures (e.g. Aumer & White 2013; Pedrosa &Tissera 2015). We note, however, that the measured mass of the MW stellar halo may be underestimated bycurrent observational methods (Sanderson et al. (2017)). The analysis presented in this paper apply a newobservational constraint; the MW stellar age distribution, a critical piece of information for the confrontationof models and observations, and contribute to understanding the origin of the MW’s stellar halo. This paperis organized as follows: Section 2 provides a short description of the simulations, while Section 3 describesthe analysis of the age distributions and associated age maps. The summary and conclusions are reported inSection 4.
2. The Simulated Aquarius Galaxies
We analyzed a subset of five MW-mass galaxies from the Aquarius Project run with a version of
GADGET-3 , an optimized version of
GADGET-2 (Springel 2005), which was modified to include super-nova feedback and chemical evolution by Scannapieco et al. (2005) and Scannapieco et al. (2006). Thiscode allows the description of a multiphase medium and the triggering of mass-loaded galactic outflowswithout introducing mass-dependent scaling parameters. The chemical model describes the enrichmentby Type II (SNII) and Type Ia (SNIa) supernovae according to the nucleosynthesis yields of Woosley &Weaver (1995) and Thielemann et al. (1993), respectively. These simulations are explained in detail 4 –by Scannapieco et al. (2009), and have been used throughout our ongoing series of papers (Scannapiecoet al. 2009, 2010; Tissera et al. 2012, 2013, 2014, 2018); here, we only provide their main character-istics. The initial conditions are consistent with a Λ -CDM cosmology having the following parameters: Ω m = . , Ω Λ = . , Ω b = . , σ = . , n s = H = h km s − Mpc − , with h = .
73. The darkmatter particle mass was 10 M (cid:12) h − and the initial gas particle mass 2 × M (cid:12) h − . The correspondinggravitational softenings ranged from 0.5 − h − . The halos were selected not to have had a major mergersince z < (cid:15) = J z / J z , max ( E ) for each star, where J z is the angularmomentum component perpendicular to the disk plane and J z , max ( E ) is the maximum J z over all particles ofgiven total energy, E. A star on a prograde circular orbit in the disk plane has (cid:15) =
1; stars with (cid:15) > .
65 areconsidered a part of the disk components. Particles which do not satisfy this requirement are taken to be partof the spheroidal components. Motivated by observations of the MW spheroid that exhibit di ff erences instellar kinematics and chemical abundances as one moves outwards (Carollo et al. 2007, 2010; Zoccali et al.2008), we separate our spheroids into two stellar populations according to their binding energy. The centralspheroid (bulge) is defined by stars more bound than those with the minimum energy (E cen ) at r ≥ opt (r opt is defined as the radius that encloses ∼
80% of the stellar mass identified by the SUBFIND algorithm(Springel et al. 2001). Stars more weakly bound than E cen are taken as part of the stellar halo. In this paper,and to confront with observations, the stellar halos are not separated into inner and outer components, asdone in previous works but are taken as an ensemble system. These criteria are chosen so that the definitionof the stellar halos adapts to the overall size of each individual galaxy, and is the same definition used inthe aforementioned series of Aquarius Project stellar-halo papers. For the analysis that follows, we haveremoved satellite galaxies identified by the SUBFIND as individual systems, but disrupted satellites and / orany residual stellar streams remain.Tissera et al. (2013) and Tissera et al. (2014) analyzed the spatial distributions, chemical abundances,and formation histories of the stellar populations of the Aquarius halos and found evidence that they aremainly built by stars formed in satellite galaxies, and later accreted onto the main halo. However, andas in agreement with previous numerical results, an important contribution of in situ stars are detected inthe central regions (recall, § > . M (cid:12) ) exhibit steeper metallicity gradients (see also Cooper et al.2010). They also reported that low-metallicity stars are mainly contributed by low-mass satellites, and aremore frequent in the outskirts of halos. The central regions of such systems (within ∼
10 kpc, including thebulge) have been analyzed in detail by Tissera et al. (2018), where a significant contribution of old stars wasfound. Moreover, one of the simulated halos (Aq-C-5) showed a good match with the spatial, kinematic, andmetallicity properties observed in the MW (Zoccali & Valenti 2016). The analysis of the assembly historyof the central regions shows that this halo did not accrete satellite galaxies more massive than ∼ M (cid:12) during its assembly. This characteristic is also relevant in the analysis of the age gradients in our simulatedhalos. 5 –
3. Analysis of the Age Distributions
For the five simulated halos, we identify those stars that formed in situ or in accreted satellite galaxiesby adopting the following criteria: in situ stars were assumed to form within the virial radius, while accretedstars were assumed to form in separate galaxies prior to accretion (i.e., before entering the virial radius ofthe progenitor galaxy). Tissera et al. (2013) defined three di ff erent sub-populations of in situ stars: 1) thoseborn from gas accreted in the first stages of assembly, 2) disk-heated stars formed in the disk structure ofthe main progenitor galaxy, then heated kinematically, and 3) those formed from gas carried in by gas-richsatellite galaxies (endo-debris). As described in previous works, disk-heated and endo-debris stars exhibitdistinct chemical properties that can help to link observations to the galaxy-formation models (Brook, et al.2012; Tissera et al. 2013). Nevertheless, in this paper, for the sake of clarity and simplicity, all stars borninside the virial radius are grouped and analyzed as in situ stars, as they dominate the inner region of thestellar halos, while the outer regions are mainly populated by accreted stars .For illustration purposes, Figure 1 shows the smoothed stellar age-map distribution projected onto (x,z)plane (z is the direction of rotation of the galaxy) for three of the analyzed halos . The maps have been builtby removing the contribution of the bulge according to the criteria given in Section 2. The upper panelsrepresent the entire population of stars assigned to the halos, while the lower panels show the maps for theaccreted stellar population only; both maps extend to a radius of 100 kpc. As can be seen, the halos exhibitclumpy age structure at large distances from the center, reflecting the mixture of stars with di ff erent ages.The presence of younger structures and their increasing number with galactocentric distance are globallyconsistent with the observational results of the MW reported in Carollo et al. (2016). By comparing the agedistributions of the entire stellar halo population (upper panels) with those of the accreted stars only (lowerpanels), di ff erent features emerge: when the in situ stars are removed from the age map, an age distributionqualitatively more similar to that observed in the MW’s halo is visible, consisting of younger structures atlarge distances from the galactic center and a concentration of older stars in the central region.Examination of the panels in Figure 1 reveals that the accreted central region of Aq-C and Aq-A isdominated by old stellar populations (dark blue area), in agreement with the Ancient Chronographic Sphere(ACS) observed in the MW by Santucci et al. (2015) and Carollo et al. (2016). We note that the in situ components also contribute with old stars as shown in Tissera et al. (2018). Apart from this commonfeature, each halo has its own peculiarities. In the case of Aq-C, when the entire stellar-halo population isconsidered, the central region of the galaxy exhibits a disk-shaped feature, due to the contribution of younger,disk-heated stars. In fact, the mass fraction of halo stars which originated in the disk is ∼ ff erent age distribution, withslightly younger accreted stars, compared to the other two halos.To quantify the age variations, we estimate the age profiles for each stellar component as a functionof galactocentric radius. The age profiles are derived by taking the median values in concentric shells of2 kpc radial extension. Figure 2 shows the age trends for the in situ (left panel), accreted (middle panel), We checked that, if endo-debris stars were considered part of the accreted subsample, the age distributions would not changesignificantly. The stellar age-maps are mass-weighted and smoothed using a spline kernel consistently with the hydrodynamical code usedto perform the simulations. in situ sub-populations possess, on average, flat age gradients, and in some cases (Aq-A, Aq-C, Aq-D) a significantcontribution of younger stars in the very central regions (10-20 kpc). Such contributions are caused by gasbrought in by gas-rich satellite galaxies that enter the virial radius (these stars are classified as the endo-debris population and included in the in situ component) or by disk-heated stars. Each age profile reflectsits particular history of assembly.The accreted stellar population exhibits a steeper age gradient in most of the analyzed halos, as canbe seen from the linear regressions applied to the age profiles of these components (Fig. 2, middle panels).In fact, the inspection of Fig. 2 reveals that the accreted components are younger than the in situ stellarpopulations for Aq-B and Aq-G by 1 − in situ one only in the outer halo region (r >
25 kpc), by less than 1 Gyr. The accreted populationin Aq-B exhibits a quadratic-shape age gradient, but it does not appear statistically significant, while modelAq-C shows a significant linear age gradient in the range from ∼ −
11 to ∼ −
12 Gyr (not labeled in thepanel).In the right column of Fig. 2, the total age profiles for the entire stellar halo are shown together with thelinear regression fits (solid black and red lines, respectively). Negative age gradients are found for Aq-A,Aq-B, and Aq-C, with values of − ± − , − ± − , and − ± − (not labeled in the panels), respectively, while Aq-D and Aq-G show very weak age gradients. The gradientsderived for the entire stellar halos of the Aquarius set are shallower than those determined in observationalstudies of the MW’s stellar halo : −
25 Myr kpc − (Carollo et al. 2016) and −
30 Myr kpc − (Das, Williams& Binney 2016). It is worth noting that observations of halo stars, both within the MW and in external galaxies, are opti-mized to reduce disk-component contamination. In particular, observations carried out in external galaxiesare generally performed along the major axis of disk rotation (Monachesi et al. 2016a; Harmsen et al.2017). To better match the observational conditions, we re-calculate the age profiles and fractions by ex-cluding all stars within 5 kpc of the mid-plane. By doing this, the influence of stars which might still belongto an extended vertical disk is minimized (Harmsen et al. 2017). The age profiles for these sub-samples(hereafter referred to as the fiducial stellar halos) are represented in Figure 2 with dot-dashed lines. As canbe seen from the figure, most of the discarded stars belong to the in situ stellar populations (larger discrep-ancies in the in situ age profiles with respect to the original sample). The recalculated age profiles are, inmost cases, steeper than those derived by adopting the entire halo sample and are labeled in the panels.The age gradients for the fiducial stellar halo populations ( in situ and accreted stars combined) are, − ± − , − ± − , − ± − , + ± − , and − ± − , for Aq-A, Aq-B, Aq-C, Aq-D, and Aq-G, respectively. These slopes are shaped significantly bythe particular assembly history of each halo.The global age trend in a given halo is a ff ected not only by the median age of the in situ and accretedstars, but also by their relative contribution as a function of the radius. Figure 3 shows the stellar mass frac- Note that in the MW’s stellar halo, spherically averaged profiles cannot be estimated. Errors on the age gradients are 1-2 Myr kpc − . in situ (red), accreted (green), and the total (black) stellar populationsin the simulated halos. The stellar mass fraction is calculated within the virial radius for both the entire(solid line) and the fiducial (dot-dashed line) stellar halos. It is also important to mention that Aquariusstellar halos have a contribution of stars younger than 10 Gyr representing ∼ −
8% of the total stellarhalo mass, except for Aq-B (29%) which has experienced a more recent massive accretion. These stars aremostly associated to the in situ component and to the accretion of more massive satellites. Such youngerstellar population is not represented in current observations that make use of BHB stars to derive the agestructure of the halo system. Nevertheless, in the Aquarius simulations the presence of stars younger than10 Gyr do not strongly a ff ect the overall trends of the age gradients, except in the central regions.As can be seen in Figure 3, the stellar mass fraction of the in situ population is dominant out to ∼
20 kpcfor all the halos except Aq-B. Beyond ∼
20 kpc, the accreted component dominates over the in situ one atall galactocentric distances, within the virial radius, and for all the simulated halos. This is consistent withthe findings of previous works (e.g. Tissera et al. 2014; Cooper et al. 2015). The negative age trends aredetermined principally by the accreted stars, assembled as the satellite galaxies fall into the potential well ofthe main galaxies and then are disrupted. Di ff erent mechanisms take place during the assembly of the stellarhaloes and the mass of the accreted satellite galaxies as well as their time of accretion play a major role. Inlower-mass satellites, the star formation is truncated earlier due to the gas exhaustion, gas outflows drivenby Supernova, tidal stripping and / or reionization. Such quenching likely occurs before these clumps mergedwith the main galaxy, thus these satellites possess mainly very old stars. On the contrary, more-massivesatellites experience a more prolonged star formation activity due to their e ffi ciency in retaining gas in thedeeper potential wells. These massive satellites have both young and old populations (Tissera et al. 2014).A combination accretion time and mass of the satellites will set the age profile. A negative age profilecould arise when low mass satellites are accreted very early on. These will contribute mostly to the innerregions with their old stars (Tissera et al. 2018). Intermediate and high-mass satellites accreted later-on willhave younger stellar populations (since they continued forming stars for longer periods) and their stars willpopulate both the inner and outer regions. The presence of a larger fraction of oldest early-on accreted starsin the center of the galaxy (small radii) will set the negative age gradient, but the strenght of such profilesdepends on the particular assembly history of each galaxy. The slope is also a ff ected by the generally flatage profile of the in situ stars and their dominance in the inner-halo region. The in situ component comprisesa combination of well-mixed stellar populations primarily located in the inner region of the stellar haloes.Disk-heated stars populate the inner regions of haloes increasing the fraction of younger stellar populationsand contribute to flatten the age profile. In some cases, like in Aq-D, a flat age gradient can be generated bythe opposite age dependance of the in situ and accreted stellar populations.The Aquarius stellar halos have greater masses than expected from observations (Harmsen et al. 2017).Since the stellar-halo profiles are consistent with an Einasto profile, most of the mass is concentrated in thecentral regions (Tissera et al. 2014). Part of the mass excess could be due to ine ffi cient regulation of the star-formation activity or an overproduction of disk-heated stars. In the inner halo, the fraction of disk-heatedstars can di ff er from one halo to another, as reported in Table 1 of Tissera et al. (2013) (in percentages:31 (Aq-A), 3 (Aq-B), 24 (Aq-C), 26 (Aq-D), and 35 (Aq-G)). These stars could also originate througha misclassification of thick-disk stars or by the presence of endo-debris stars that contribute significantly(from 20% to 40%), as given in Table 1 of Tissera et al. (2013). The contribution of endo-debris stars canbe diminished by improving the e ffi ciency of the SN feedback. If the in situ contributions were removed, ordiminished significantly, then the stellar mass of these halos would be more in agreement with current MW 8 –observations, and the stellar age profiles of some of them would likely be closer to the reported values ( seeMonachesi et al. 2018 for similar conclusions using the Auriga simulations.)In order to close the interpretation of the age profiles, we make use of the analysis presented in Tissera etal. (2014), where the mass contributions of satellites with di ff erent dynamical masses is investigated. FromFig. 6 in that paper, it is clear that Aq-A and Aq-C formed their stellar halos with important contributionsfrom less-massive satellites, while the remaining halos accreted stars from satellites more massive than10 . M (cid:12) . This is particularly relevant for the properties of the central regions. Indeed, Aq-A and Aq-Cshow central age distributions which resemble the ACS observed in the MW. Hence, the analysis of thesesimulations suggests that the MW should have formed its central regions by the accretion of less-massivesatellites ( < ∼ . M (cid:12) ) and did not have a significant major-merger contribution. This is consistent withprevious works where other methods and models have been adopted (Deason et al. 2017; D’Souza & Bell2017; Monachesi et al. 2018).
4. Summary and Conclusions
In this paper, we focused on an analysis of the age gradients in the stellar halos of a subset of MW-mass galaxies drawn from the Aquarius Project. We found that these stellar halos exhibit a diversity ofage profiles, reflecting their di ff erent histories of formation and assembly. Our results suggest that negativeage gradients are determined principally by the accreted component, and that the in situ stars a ff ect theslopes in the inner regions, depending upon their relative importance. The flatter age profile of the in-situcomponent is caused by the presence of di ff erent well-mixed stellar populations, including the contributionof disk heated stars and those formed by the gas transported inward by more massive satellites. The negativeage gradient set by the accreted stellar component reflects the inside out assembly of the halo with thecontribution of the latest merger events to the outkirts. The characteristics of the accreted satellites suchas mass, gas fraction, and their accretion time contribute to modulate the slope, making it less negative ifthey are able to reach the inner regions carrying younger stars and gas to fuel star formation activity. Ingeneral, the in situ component flattens the gradients of the global profiles. The two halos that show thesteepest age gradients are those which formed primarily from the contributions of small- and intermediate-mass satellite galaxies. Halos assembled with significant contributions from more-massive satellites tendto have shallower age gradients, because these systems carried in younger stars and gas to feed new starformation activity. Our analysis shows that similar slopes of the age gradient reported in the MW’s halo canbe reproduced by considering only the contribution of the accreted stars. This suggests that the simulatedgalaxies might be producing an excess of in situ stars, and that the subgrid physics should be improved toreduce such an overproduction of stars. The strong negative age gradient observed in the MW’s halo is foundin the simulated halos with important contributions from less-massive satellites, suggesting that the MW’shalo assembled from satellites with total dynamical mass lower than 10 . M (cid:12) and a minimal contributionfrom in situ stars.PBT acknowledges partial support from Fondecyt Regular 1150334 (CONICYT) and UNAB Project The dynamical masses (dark matter and baryons) of the satellites galaxies are estimated before they enter the virial radius ofthe progenitor using the SUBFIND algorithm / / JINA Center for the Evolution of the Elements (JINA-CEE), awarded by the US NationalScience Foundation. BKG acknowledges the support of STFC through the University of Hull ConsolidatedGrant ST / R000840 /
1, and access to viper , the University of Hull High Performance Computing Facility.
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This preprint was prepared with the AAS L A TEX macros v5.2.
12 –Fig. 1.— Projected smoothed stellar-age maps onto the x-z plane, where z is the direction of rotation of thecentral galaxy, in the Aq-A-5 (left panel), Aq-C (middle panel) and Aq-D (right panel) simulations. Theupper panels show the age maps estimated by considering the total stellar halo populations, while the lowerpanels show the corresponding maps for the accreted stars only. The age-maps extend to 100 kpc. 13 –Fig. 2.— The median age profiles for the in situ (left panels), the accreted (middle panels), and the total(right panels) stellar populations in the five selected Aquarius halos (from top to botton: Aq-A, Aq-B, Aq-C,Aq-D and Aq-G). The linear regressions applied to the median age profiles are shown in all plots (red lines).The continuous lines represent the halo samples where the spherical averages have been implemented, whilethe dot-dashed lines denote the fiducial stellar halo , where stellar particles within | z | < in situin situ