The Fornax3D project: Assembly histories of lenticular galaxies from a combined dynamical and population orbital analysis
A. Poci, R. M. McDermid, M. Lyubenova, L. Zhu, G. van de ven, E. Iodice, L. Coccato, F. Pinna, E. M. Corsini, J. Falcón-Barroso, D. A. Gadotti, R. J. J. Grand, K. Fahrion, I. Martín-Navarro, M. Sarzi, S. Viaene, P. T. de Zeeuw
AAstronomy & Astrophysics manuscript no. f3dIv8 © ESO 2021February 9, 2021
The Fornax3D project: Assembly histories of lenticular galaxiesfrom a combined dynamical and population orbital analysis
A. Poci , , R. M. McDermid , , M. Lyubenova , L. Zhu , G. van de Ven , E. Iodice , , L. Coccato , F. Pinna ,E. M. Corsini , , J. Falcón-Barroso , , D. A. Gadotti , R. J. J. Grand , K. Fahrion , I. Martín-Navarro , , ,M. Sarzi , S. Viaene , P. T. de Zeeuw , Research Centre for Astronomy, Astrophysics, and Astrophotonics, Department of Physics and Astronomy, Macquarie University,NSW 2109, Australiae-mail: [email protected] ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia European Southern Observatory, Karl-Schwarzschild-Straße 2, D-85748 Garching bei München, Germany Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China Department of Astrophysics, University of Vienna, Türkenschanzstraße 17, 1180 Wien, Austria INAF - Astronomical Observatory of Capodimonte, Salita Moiariello 16, I-80131, Naples, Italy Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany Dipartimento di Fisica e Astronomia ‘G. Galilei’, Università di Padova, vicolo dell’Osservatorio 3, I-35122 Padova, Italy INAF - Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, I-35122 Padova, Italy Instituto de Astrofísica de Canarias, Calle Via Láctea s / n, 38200 La Laguna, Tenerife, Spain Depto. Astrofísica, Universidad de La Laguna, Calle Astrofísico Francisco Sánchez s / n, 38206 La Laguna, Tenerife, Spain Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, D-85748 Garching bei München, Germany Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DG, UK Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, 9000 Gent, Belgium Sterrewacht Leiden, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands Max-Planck-Institut für Extraterrestrische Physik, Gießenbachstraße 1, 85748 Garching bei München, GermanyReceived XXXXX; accepted XXXXX
ABSTRACT
In order to assess the impact of the environment on the formation and evolution of galaxies, accurate assembly histories of suchgalaxies are needed. However, these measurements are observationally di ffi cult owing to the diversity of formation paths that lead tothe same present-day state of a galaxy. In this work, we apply a powerful new technique in order to observationally derive accurateassembly histories through a self-consistent combined stellar dynamical and population galaxy model. We present this approach forthree edge-on lenticular galaxies from the Fornax3D project — FCC 153, FCC 170, and FCC 177 — in order to infer their massassembly histories individually and in the context of the Fornax cluster. The method was tested on mock data from simulations toquantify its reliability. We find that the galaxies studied here have all been able to form dynamically-cold (intrinsic vertical velocitydispersion σ z (cid:46)
50 km s − ) stellar disks after cluster infall. Moreover, the pre-existing (old) high angular momentum componentshave retained their angular momentum (orbital circularity λ z > .
8) through to the present day. Comparing the derived assemblyhistories with a comparable galaxy in a low-density environment — NGC 3115 — we find evidence for cluster-driven suppression ofstellar accretion and merging. We measured the intrinsic stellar age–velocity-dispersion relation and find that the shape of the relationis consistent with galaxies in the literature across redshift. There is tentative evidence for enhancement in the luminosity-weightedintrinsic vertical velocity dispersion due to the cluster environment. But importantly, there is an indication that metallicity may be akey driver of this relation. We finally speculate that the cluster environment is responsible for the S0 morphology of these galaxies viathe gradual external perturbations, or ‘harassment’, generated within the cluster.
Key words. galaxies: kinematics and dynamics – galaxies: stellar content – galaxies: structure – galaxies: elliptical and lenticular,cD – galaxies: evolution – galaxies: formation
1. Introduction
Galaxy formation and evolution is the culmination of compet-ing forces and processes over each galaxy’s lifetime. These pro-cesses can be internal to the galaxy, such as the energy generatedby the central super-massive black hole (SMBH) or the windsgenerated by star formation. They can also have external origins,such as the gravitational potential of other galaxies (Toomre &Toomre 1972) or cosmic gas filaments. Due to this ‘superposi-tion’ of evolutionary processes, it is di ffi cult to isolate the im- pact on the galaxy from only one of them, especially when manyare still occurring. The environment which a galaxy inhabits haslong been suspected of altering its evolutionary path (Gunn &Gott 1972; Dressler 1980; Postman & Geller 1984; Ryden et al.1993), but with conflicting results on the exact impact. Field en-vironments are relatively simple and provide a control samplefor comparison with higher-density environments such as groupsand clusters. This comparison is not straight forward, however,since cluster environments are a complex mixture of many, of- Article number, page 1 of 26 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. f3dIv8 ten dramatic, physical processes such as gravitational disruption(owing to the significantly deeper gravitational potential), hydro-dynamic e ff ects due to the hot intra-cluster medium (ICM), andthermodynamic e ff ects such as shocks due to the high relativevelocities that a galaxy can experience when it first encountersthe ICM during in-fall.A number of correlations have been observed between galac-tic observables and some metric for the local environment. His-torically, the projected density of galaxies or N -th nearest neigh-bour measurements of the local density have been found to cor-relate with visual morphology (e.g. Dressler 1980; Cappellariet al. 2011b; Oh et al. 2018; Gargiulo et al. 2019) and invoked toexplain morphological transformations (e.g. Bekki et al. 2002;Kau ff mann et al. 2004; Blanton et al. 2005; D’Onofrio et al.2015; Coccato et al. 2020). Yet morphology has also been ob-served to correlate with stellar mass at fixed local density (vander Wel 2008), and so the underlying cause is di ffi cult to dis-cern. This problem permeates through most observed correla-tions. Some works have shown that galaxies exhibit a lower netangular momentum for a higher local density (e.g. Cappellariet al. 2011a; Cortese et al. 2019; Graham et al. 2019; Cole et al.2020), while others find that there is no additional dependenceon the environment once the correlation between the angular mo-mentum and stellar mass is accounted for (Brough et al. 2017).Finally, the stellar population parameters also su ff er from con-flicting correlations. Some observations indicate reduced star-formation activity (e.g. Balogh et al. 2004; Poggianti et al. 2006;Allen et al. 2016; Owers et al. 2019), a higher stellar metallicity(e.g. Schaefer et al. 2019), older stellar ages (e.g. Thomas et al.2005; McDermid et al. 2015), and a lower gas content (e.g. Zabelet al. 2019) for higher local density, while others indicate thatstellar mass is the driver instead of environment (Alpaslan et al.2015; Goddard et al. 2017). Many of these correlations have alsobeen found in recent cosmological hydrodynamical simulations(e.g. Choi et al. 2018; Wang et al. 2018a,b). More broadly, it isnot straight forward to disentangle the e ff ects of mass and envi-ronment, and it is likely that both play a role (Peng et al. 2010;Smith et al. 2012; McDermid et al. 2015; Wang et al. 2020), andjoint analyses over all available parameters are needed such asthose applied by Christlein & Zabludo ff (2005) to global galaxyproperties. The morphology, mass, and other galactic propertiesare intricately connected through each galaxy’s unique assem-bly history. It is therefore clear that to uncover what impact theenvironment has, if any, the complete assembly history must beinvestigated directly as a function of the environment.The dynamical memory of galaxies plays an important rolein attempting to disentangle such assembly histories, assisted bythe (often long) dynamical times of galactic systems. As such,the stellar kinematics can provide insight into this history. Dy-namical models of stellar kinematics have been employed tomeasure constraints on galaxy formation for a variety of mor-phological types and environments, based on a number of dif-ferent principles. The Jeans equations have been readily appliedowing to their relative simplicity and computational e ffi ciency(e.g. Cappellari et al. 2013; Watkins et al. 2013; Zhu et al.2016a,b; Poci et al. 2017; Bellstedt et al. 2018; Nguyen et al.2019; Nitschai et al. 2020; Li et al. 2020, and Cappellari 2016for a review), though with specific assumptions about the in-trinsic velocity distributions of galaxies. Distribution-functionmodels (e.g. Cole & Binney 2017; Taranu et al. 2017; Pas-cale et al. 2018) can be quite general and computationally-e ffi cient, but usually use parametric expressions which maynot provide enough freedom. Finally, the Schwarzschild (1979)orbit-superposition method provides a general approach with- out the assumption of specific distribution functions or den-sity distributions, while also providing a wealth of informa-tion on the intrinsic properties of the model. Though it is farmore computationally-expensive, it has seen a growing diver-sity of applications (e.g. van der Marel et al. 1998; Cretton et al.1999; Verolme & de Zeeuw 2002; Gebhardt et al. 2003; Val-luri et al. 2004; Cappellari et al. 2006; Krajnovi´c et al. 2009,2015; Vasiliev 2013, 2019; Leung et al. 2018; Zhu et al. 2018a,b;Vasiliev & Valluri 2020). Through these models, a galaxy’smerger history can be traced through the potentially-complex ob-served kinematics, but only when confronted with a su ffi ciently-sophisticated dynamical model which can access the underlyingintrinsic properties (e.g. van den Bosch et al. 2008; Lyubenovaet al. 2013; Krajnovi´c et al. 2015). However, purely-dynamicalmodels can not produce a chronological assembly history, sincethey lack information about the ages of the stars and where theymight have originated.This work is part of the Fornax3D survey; an observationalprogramme to study the Fornax galaxy cluster with the Multi-Unit Spectroscopic Explorer (MUSE) at VLT. In total, the surveyobserved 31 members of the Fornax cluster with m B <
15 mag, ator interior to the Virial radius ( R vir ∼ . D ∼
20 Mpc, and with atotal halo mass of log ( M halo / M (cid:12) ) ∼ .
85 (Jordán et al. 2007).The application of the Schwarzschild models to Fornax3D datawas showcased in Sarzi et al. (2018), and a qualitative compari-son to the stellar populations was made in Martín-Navarro et al.(2019). In this work, we aim to measure complete chronologi-cal assembly histories of three edge-on S0 galaxies - FCC 153,FCC 170, and FCC 177 - by quantitatively combining these so-phisticated dynamical modelling techniques with the measuredstellar populations. They are discussed in conjunction with a pre-vious application of this method (Poci et al. 2019) to a massive[log ( M (cid:63) / M (cid:12) ) ∼
11] field S0, NGC 3115, to probe any poten-tial impact of the cluster environment.This work is organised as follows: the data and target selec-tion are briefly outlined in § 2, and the combined dynamical andpopulation modelling is detailed in § 3. Results for each galaxyare presented in § 4. The implications of these results in the con-text of the Fornax cluster and specific quantitative correlationsare investigated in § 5.
2. Data and targets
The photometric data for this work is taken from the FornaxDeep Survey (FDS; Iodice et al. 2016; Venhola et al. 2018),which acquired deep photometry of the Fornax cluster out to inthe u , g , r , and i bands using the Very Large Telescope (VLT)Survey Telescope (VST). We utilise the r -band photometry tomodel the surface brightness distribution of these galaxies. Wealso make use of the g − i colour to characterise the mass dis-tribution beyond the field-of-view (FOV) of the spectroscopy(see § 3.1). FDS data extend down to a surface brightness of µ r ∼
28 mag arcsec − in the r band.Distances to these galaxies were measured in Blakeslee et al.(2009) via surface-brightness fluctuations. We adopt those mea-surements here, given in Table 1. Article number, page 2 of 26. Poci et al.: F3D: Assembly Histories
The spectral data are taken from the Fornax3D project (Sarziet al. 2018). In this work, all data products are computed on thespectral range λ ∈ [4600 , ff ects. It is wide enough,however, to include many of the important absorption featuresfor the stellar population analyses. Moreover it encapsulates thebandwidth of the r filter of VST which is utilised in conjunc-tion with the spectroscopy to describe the luminosity density ofthe stellar kinematic tracer. To prepare the data products, thedata-cubes are spatially binned to a target signal-to-noise ratio( S / N ) of 100 using the Python implementation of the Voronoibinning technique (Cappellari & Copin 2003). This ensures thatthe kinematic and stellar-population measurements can achievemeasurement errors (cid:46)
5% (shown in Appendix B).Kinematics are extracted for each binned spectrum using the pPXF (Cappellari & Emsellem 2004; Cappellari 2017) Pythonpackage , which determines the line-of-sight velocity distribu-tion (LOSVD) through moments of the Gauss-Hermite series.We extract the first six moments of the LOSVD in each bin;mean velocity V , velocity dispersion σ , skewness h
3, kurtosis h
4, and higher-order deviations h h pPXF is run with theMILES empirical stellar library (Falcón-Barroso et al. 2011),and with an additive polynomial of degree 10 in order to ac-curately reproduce the line shapes. Naturally, spectra are dom-inated by the brightest components of the observed galaxiesthrough the LOS, and so the extracted kinematics are e ff ectivelyluminosity-weighted.Star formation histories (SFH) and their mean stellar pop-ulation properties are extracted by running pPXF with the E-MILES single stellar population (SSP) templates (Vazdekis et al.2016) using the ‘BaSTI’ isochrone models (Pietrinferni et al.2004). A multiplicative polynomial of degree 10 is included inorder to account for the continuum without a ff ecting the relativeline shapes. The SSP models are normalised such that we mea-sure luminosity-weighted stellar populations, in order to main-tain consistency with the stellar kinematics and subsequent dy-namical model (described in § 3.2). The stellar-population fitsuse a first-derivative linear regularisation with ∆ = .
0, whichprefers a smoother solution in the case of degeneracy betweenthe SSP models. We assume a fixed Kroupa (2002) galaxy ini-tial mass function (IMF). The canonical Salpeter (1955) IMF hasbeen shown to disagree with the mass-to-light ratios from stellardynamics (Lyubenova et al. 2016), while the low central veloc-ity dispersion of these galaxies (Iodice et al. 2019a) is consis-tent with an IMF which is relatively deficient of dwarf stars (e.g.Thomas et al. 2011; Cappellari et al. 2012; Wegner et al. 2012).In this work, we explore the projected distribution of mean stel-lar age ( t ) and metallicity (total metal abundance, [ Z / H ]). Rep-resentative spectral fits are presented in Fig. 1.The solutions from the stellar-population run of pPXF and thepredictions from E-MILES (Vazdekis et al. 2010) then enable thederivation of the R -band stellar mass-to-light ratio ( M (cid:63) / L R ) foreach spectrum, using the mass in stars and stellar remnants forthe assumed IMF. This is utilised for the dynamical modelling(§ 3.1). We generate Monte Carlo fits to the spectra by addingrandom noise within the variance spectra in the data-cubes. Eachspectrum is re-fit 100 times to generate a new distribution of SSPweights. Luminosity-weighted properties are re-derived for eachweight distribution. The ‘uncertainty’ in a given aperture is then Available at https: // pypi.org / project / vorbin / Available at https: // pypi.org / project / ppxf / F CC F CC F CC F CC F CC F CC Wavelength [A]Data Fit Residual
Fig. 1.
Fits ( red ) to spectra ( black ) from the centre and outer regions( top and bottom of each pair of spectra, respectively) for our galaxysample, as labelled on the right. Residuals are shown in green, o ff set forpresentation. The grey bands show regions which are masked during thefit. All spectra are normalised, but vertically o ff set for presentation. Itcan be seen that the outer spectra are more noisy, as expected, but thatin all cases the data are reproduced well by the fit. estimated from the variance of luminosity-weighted propertiesacross all Monte Carlo simulations in that aperture. These un-certainty maps (shown in Appendix B) are utilised to gauge thestability of our final results.Similar data products have already been measured for thesegalaxies as part of Fornax3D (Pinna et al. 2019a,b; Iodice et al.2019a). The motivation for re-extracting them in this work is toachieve higher S / N for higher-precision stellar population pa- Article number, page 3 of 26 & A proofs: manuscript no. f3dIv8 rameters (see, for instance, Asa’d & Goudfrooij 2020) and tominimise the impact of measuring σ los (cid:46) σ inst (for the line-of-sight velocity dispersion and instrumental velocity resolution σ los and σ inst , respectively; Cappellari 2017), albeit on largerspatial bins. Moreover, we fit the specific wavelength range,as discussed above. Finally, luminosity-weighted stellar popu-lations are required for the analyses in this work as describedabove, while previous measurements are mass-weighted (Pinnaet al. 2019a,b). The new kinematics from this work are consis-tent with previous measurements. The luminosity-weighted agesare systematically younger than the mass-weighted determina-tions while the metallicities are consistent, as expected (Serra &Trager 2007; McDermid et al. 2015). For this work, due to the nature of our dynamical and populationorbital analysis (§ 3), we selected a sub-sample of three galax-ies: FCC 153, FCC 170, and FCC 177. These galaxies are allapproximately edge-on, and have S0 morphology. They are suit-able targets for our analysis because they show no signs of dustor spiral arms. This is important because the dynamical modelassumes a steady-state gravitational potential while spiral armsare transient, and dust would impact the inferences of the stellarpopulations. Additionally, our methodology (§ 3) is most robustfor edge-on systems. Each galaxy has a central and outer point-ing from the Fornax3D survey, ensuring that the vast majorityof the stellar body is covered while retaining the high spatialresolution of MUSE. The FDS r -band images of the three galax-ies are shown in Fig. 2, with the MUSE outline shown in dashedbrown. As measured from the FDS data, FCC 153, FCC 170, andFCC 177 are at a projected distance of 1 . . . g − i colours of 0 . ± .
07, 1 . ± . . ± .
03, and r -band surface-brightness radial profileswhich extend down to 28 .
9, 29 .
2, and 29 . − , respec-tively, as derived from the FDS photometry (Iodice et al. 2019b).These galaxies are the focus of the spectral analyses pre-sented in Pinna et al. (2019a,b), where their SFH are discussedin the context of the Fornax cluster. Those works conclude thatFCC 170 matured more rapidly, having plausibly evolved in anearlier group environment in the initial stages of the Fornax clus-ter assembly. Conversely, FCC 153 and FCC 177 are seen toexhibit relatively smooth SFH in their thin disk regions. In thestudy on stellar accretion fractions in members of the Fornaxcluster, Spavone et al. (2020) find that it is di ffi cult to photomet-rically disentangle the various components of these three galax-ies, since they have indistinguishable surface brightness pro-files. They find that low accretion fractions ( (cid:46) (cid:38)
3. Stellar content of galaxies
We endeavour to consider the complete stellar information con-tent available through observations. The model we fit to thesedata was the self-consistent combination of Schwarzschild orbit-superposition dynamical models, using a triaxial implementa-tion (van de Ven et al. 2008; van den Bosch et al. 2008), andstellar-population measurements derived from full spectral fit-ting. We employed the method described in Poci et al. (2019) for this combination. We therefore refer to that work and referencestherein for details, but lay out the basic structure of the methodand the di ff erences with that work in this section.We also ensured that our data are tracing the galaxies them-selves, and not components of the cluster environment. The FDSdata show that FCC 170 is within the large-scale intra-clusterlight (ICL) detected towards the cluster centre (Iodice et al.2019a). This ICL component was measured to have total inte-grated magnitudes of 12 . ± . . ± . g - and r -band, respectively, over an area of ∼
432 arcmin (assuming auniform surface brightness distribution; Iodice et al. 2017). Atthe distance and direction from the cluster centre to FCC 170,the ICL has a r -band surface brightness of ∼ . − (Iodice et al. 2017). In contrast, the spectroscopic data from theFornax3D survey have a r -band target depth of 25 mag arcsec − in the faintest regions covered by the FOV. For our sample, theFOV extend to 4 .
90, 5 .
63, and 9 .
61 kpc along the major axis forFCC 153, FCC 170, and FCC 177, respectively, at our adopteddistances (see Table 1). In all three cases, therefore, we expectthe impact of the ICL on the measured properties to be negligi-ble, being at least ∼
100 times fainter than the faintest regions ofthe galaxies within our spectroscopic FOV.
One of the most crucial aspects of a dynamical model of stellarkinematics is the input mass model in which the observed tracerpopulation resides. This is often derived from the observed pho-tometry. We begin by fitting a multi-Gaussian Expansion (MGE;Monnet et al. 1992; Emsellem et al. 1994) to the r -band pho-tometry from FDS using a Python implementation (Cappel-lari 2002). This produces a projected surface-brightness model(MGE µ ), which serves as the luminous tracer of the gravitationalpotential of the galaxy. These models are shown in Appendix A.To reconstruct the mass, the surface brightness must be con-verted into surface mass density. While standard implementa-tions of Schwarzschild (and indeed dynamical) models assumea spatially-constant conversion from luminosity to mass, we ex-ploit the spatially-resolved map of stellar M (cid:63) / L R in order to ac-count for the prominent structures and variations in the stellarpopulations that are resolved by the high-quality spectroscopy.We make additional use of the deep FDS photometry to con-strain the stellar populations outside of the spectroscopic FOV toconstrain the dynamical model well beyond the measured kine-matics. We use the predictions from the E-MILES SSP modelsto derive a relation between g − i colours and M (cid:63) / L R , whichwe assume to be of the form log ( M (cid:63) / L R ) ∝ ( g − i ) as foundempirically (Tortora et al. 2011; Wilkins et al. 2013; McGaugh& Schombert 2014; Du & McGaugh 2020). The smaller spectro-scopic FOV, which is used where available, is thus augmented bythe larger photometric FOV to generate M (cid:63) / L R on the same ex-tent as the photometry. While the spectroscopic measurements of M (cid:63) / L R reach (cid:46) (cid:48)(cid:48) for the three galaxies, the depth of the FDSsurvey allows this coverage to be extended to ∼ (cid:48)(cid:48) providing adramatic improvement to the constraints of the mass model. Us-ing this large-scale combined (spectroscopic and photometric) M (cid:63) / L R map, MGE µ is then converted to a map of surface massdensity, to which a mass density MGE (MGE Σ ) is fit. The fits andresults for all MGE Σ are given in Appendix A. Figures A.1 to A.3show deviations of up to ±
30% compared to a spatially-constant M (cid:63) / L R (in projection). This approach takes into account not justthese deviations in the absolute scale, but also the structures of Available at https: // pypi.org / project / mgefit / Article number, page 4 of 26. Poci et al.: F3D: Assembly Histories
Fig. 2.
Full r -band images from FDS, overlaid with the MUSE FOV in dashed brown for FCC 153 ( left ), FCC 170 ( middle ), and FCC 177 ( right ). the stellar populations, producing a more accurate mass modeland subsequent dynamical model.The photometric measurements of M (cid:63) / L R are e ff ectively‘SSP-equivalent’, while the spectroscopic values are derivedfrom the full SFH. To mitigate any systematic o ff sets this maycause, the photometrically-derived values are re-scaled to matchthe spectroscopic values in the overlapping regions. We empha-sise that the rapidly-varying spatial structures in the stellar popu-lations — caused primarily by the thin edge-on disks — are cap-tured by the spectroscopy, while the photometry is utilised onlyin the region where variations are mild. Coupled with the intrin-sic symmetry of the MGE fitting, the photometric M (cid:63) / L R servesto extend the range of the MGE model and stabilise the shape ofthe gravitational potential in that region. It can be seen in Fig-ures A.1 to A.3 that there are no systematic o ff sets at the transi-tion from spectroscopically- to photometrically-derived M (cid:63) / L R ,and the level of noise in the colour region is no greater than thepixel-to-pixel scatter in images to which MGE is typically ap-plied. Overall, this procedure allows for the stellar populationsto be more robustly accounted for. The basic premise of the Schwarzschild method is to numeri-cally integrate a large number of permitted orbits within a modelfor the gravitational potential, then measure their kinematicsand compare to observations. For real observations, the gravi-tational potential is of course unknown and must be iterativelyfit for. To achieve this, we used a triaxial implementation of theSchwarzschild method that has been robustly developed and val-idated (van den Bosch et al. 2008; van de Ven et al. 2008; Zhuet al. 2018a,b, 2020; Jin et al. 2019). In this implementation, asingle model is described by seven parameters: ( a ) the three pa-rameters describing the intrinsic shape and viewing direction ofthe stellar mass distribution, q = C / A , p = B / A , and u = A (cid:48) / A ,where A , B , and C are the intrinsic major, intermediate, and mi-nor axes, respectively, and A (cid:48) is the projected major axis ( b ) themass of the central SMBH, M • ( c ) the parameters of the darkmatter (DM) profile, which is implemented as a spherical Navar-ro-Frenk-White (NFW) model (Navarro et al. 1996). These arethe concentration C DM and dark mass fraction at r , f DM ( d ) aglobal dynamical mass-to-light ratio, which we denote Υ . Thisparameter can shift the global depth of the potential in order tobetter match the observed kinematics, but does not change its shape nor therefore which orbital families can reside within it. Υ is included to account for any deviations in the absolute depthof the gravitational potential due to the assumption of the IMFwhen computing the M (cid:63) / L and / or systematics in the assumedDM halo model.We streamlined the search through this large parameter-space by making reasonable assumptions about some of theseparameters. The masses of the SMBH were fixed according tothe empirical M • − σ e relation of Kormendy & Ho (2013), usingthe σ e measurements for these galaxies reported in Iodice et al.(2019a). In addition, we estimated the sphere of influence r i ofeach SMBH, which is utilised by the model but is not a free pa-rameter, using the relation of van den Bosch et al. (2015). Thisis expected to have little impact on the model however — forthe galaxy with the largest central velocity dispersion, FCC 170, r i ≈ . (cid:48)(cid:48) , which is below the pixel scale of MUSE. In addi-tion, the stellar shape parameter u was fixed to u = (1 . − (cid:15) ) forsome small number (cid:15) to avoid numerical issues. This assumptionis reasonable since regular fast-rotator galaxies are found to beconsistent with oblate intrinsic shapes (Weijmans et al. 2014).We note that mild triaxiality is still permitted in these models,with the condition that the potential must be axisymmetric inprojection. The parameter-space is thus reduced to five dimen-sions; q , p , C DM , f DM , Υ .Each Schwarzschild model corresponds to a unique intrin-sic gravitational potential. The orbital families which can re-side within each gravitational potential are therefore also unique.Thus, each location in the hyper-parameter-space is accompa-nied by its own library of numerically-integrated orbits. Theseorbits are characterised by the integrals of motion which theyconserve, namely the binding energy E , angular momentum I ,and the third non-classical conserved integral I . Each library oforbits was generated by sampling these integrals in ( E , I , I ) = (30 , ,
10) steps (logarithmically for E and linearly for I and I ;see Cretton et al. 2000, for details of the integral sampling). Theregion around the best-fit model was re-computed with a higherorbit sampling of ( E , I , I ) = (60 , ,
15) to increase the resolu-tion of the resulting intrinsic properties. To avoid discreteness inthese libraries, each orbit was dithered by a factor of 5, creatinga cloud of orbits around each ( E , I , I ). Using a Non-NegativeLeast-Squares (NNLS; Lawson & Hanson 1995) fit, the modelselects the best sub-set of orbits from each library which repro-duces the observed kinematics in projection. It simultaneouslyfits a boundary constraint, which in this work is the projected lu- Article number, page 5 of 26 & A proofs: manuscript no. f3dIv8 ( R [arcsec])891011 l o g ( M [ M ]) FCC153FCC170FCC177
TotalStellarDM R max Fig. 3.
Enclosed-mass profiles of the total (dynamical) mass ( solid line ),stellar mass ( dashed line ), and DM ( dot-dashed line ) for the three galax-ies. The e ff ective radii are denoted by the small arrows, and the radialextent of each spectroscopic FOV is shown by the vertical dotted line.The lower radial bound of the figure is set to half the width of the point-spread function from the spectroscopic observations. minosity distribution, such that the weights assigned to the orbitsduring NNLS are luminosity weights. Thus, each unique gravita-tional potential has a corresponding unique set of best-fit orbits.By construction, Υ does not change the shape of the gravi-tational potential. In a gravitational potential with a fixed shapebut varying Υ , the families of orbits do not change. Rather, thevelocities of these orbits are simply scaled up or down to reflect adeeper or more shallow potential, respectively, and the NNLS fitis repeated for the scaled orbits. Therefore only four parametersrequire the computationally-expensive numerical integration ofan orbit library. The five free parameters were optimised usingan adaptive grid search, whose direction and step-size depend onthe existing set of evaluated models, with a large initial spread toavoid local minima. The search terminated once all surroundingmodels were worse fits to the data. The kinematic fits are shownin the top seven rows of Figures 7 to 9. The parameter-spacesearches and best-fit parameters are presented in Appendix B.To avoid artificial bias in the model due to systematic asym-metries in the data, the even (odd) kinematic moments werepoint-(anti)symmetrised to be consistent with the intrinsic modelsymmetry . These asymmetries present deviations of up to ∼ − in velocity and velocity dispersion with respect to thesymmetrised kinematics, which is of order the measurement un-certainties on the kinematics. The ‘raw’ un-symmetrised kine-matics and their Monte Carlo-derived errors are shown in Ap-pendix B.The Schwarzschild models allow us to investigate the dis-tribution of mass within these galaxies. Enclosed mass profilesare presented in Fig. 3, where the maximum extent of the spec-troscopy is marked by R max , while useful quantities are providedin Table 1. It can be seen that FCC 170 is baryon-dominatedwithin the spectroscopic FOV, while FCC 153 and FCC 177 tran-sition to DM-dominated at or below their e ff ective radii (givenin Table 1). We also define R enc , the spherical radius which en-closes 98% of the stellar mass (derived by integrating the stellarmass profile). This reduces the dependence of the mass profileon the lowest surface-brightness (most uncertain) regions. Theseradii are in good quantitative agreement with the maximum ex- using the plotbin package, available athttps: // pypi.org / project / plotbin / tent of the surface brightness profiles of Spavone et al. (2020).The corresponding stellar and DM masses within R enc are de-noted by M (cid:63) enc and M DMenc , respectively. These are given in Table 1.The amount of stellar mass outside of the spectroscopic FOV canbe estimated as log [ M (cid:63) ( R = R max ) / M (cid:63) ( R = R enc )]. This gives0 .
12, 0 .
09, and 0 .
07 dex, for FCC 153, FCC 170, and FCC 177,respectively. While the mass in this region ( R max < R < R enc ) isnot directly constrained by the kinematics, it is still constrainedby the mass model described in § 3.1. We explore these massdistributions further in the sections below. From the best-fit dynamical model, we used the phase-space ofcircularity (Zhu et al. 2018b), λ z , and cylindrical radius, R , inorder to conduct a dynamical decomposition. This radius repre-sents the time-averaged cylindrical radius of each orbit over itsorbital period. The circularity is a normalised measure of the in-trinsic orbital angular momentum, and we used it here to dividethe Schwarzschild model into orbits with varying degree of ro-tation ( | λ z | ∼
1) or pressure ( λ z ∼
0) support. In order to accountfor the structure in the kinematics and stellar-population mapssimultaneously, and motivated by tests conducted in Poci et al.(2019), we divided the phase-space into many ( ∼ ) ‘com-ponents’. This was achieved by imposing a log-linear grid onthe circularity phase-space. The radial axis was sampled loga-rithmically, but with a floor on the grid size. This preserves theorbital sampling from the Schwarzschild model but avoids gen-erating cells in the circularity phase-space which are below thespatial resolution of the data. The circularity axis was sampledlinearly. This phase-space and corresponding dynamical decom-positions are presented in Figures 4 to 6 for FCC 153, FCC 170,and FCC 177, respectively. This sampling in λ z − R was usedfor all three galaxies, however the final distribution of ‘compo-nents’ depends on the circularity distribution of each galaxy’sbest-fitting Schwarzschild model.A single component is composed of a unique subset of the or-bit library of its parent Schwarzschild model. The decompositionis an e ff ective way of simply bundling orbits of similar proper-ties — in this case, angular momentum and radius. Kinematics,masses, and mass densities are computed for each componentindividually, based on its specific subset of orbits and those or-bits’ relative contribution to the original dynamical model. Thus,each component has fixed projected kinematics and spatial dis-tributions. We now describe the extension beyond the standardSchwarzschild approach for the inclusion of the stellarpopulation measurements. In order to self-consistently combinethe kinematics and stellar populations, we exploited the factthat both the derivation of the SFH from full spectral fittingand the construction of the Schwarzschild model are basedon the same principle; they are weighted integrations overmany distinct populations, integrated through the line-of-sight(LOS). Specifically, the measured stellar populations areluminosity-weighted by construction as described in § 2.2, andthe orbital weights are constrained by the surface brightnesseven though their dynamical properties are computed in thetotal gravitational potential. Therefore, we assume that the The binding energy E , which is sampled logarithmically in theSchwarzschild models, is equivalent to the radius for a circular orbitArticle number, page 6 of 26. Poci et al.: F3D: Assembly Histories Galaxy
D R e M (cid:63) e M DMe R enc M (cid:63) enc M DMenc [Mpc] [log M (cid:12) ] [log M (cid:12) ] [log M (cid:12) ] [log M (cid:12) ](1) (2) (3) (4) (5) (6) (7) (8)FCC 153 20.8 19 . (cid:48)(cid:48) . (cid:48)(cid:48) .
00 kpc 16 .
72 kpcFCC 170 21.9 15 . (cid:48)(cid:48) . (cid:48)(cid:48) .
69 kpc 15 .
76 kpcFCC 177 20.0 35 . (cid:48)(cid:48) . (cid:48)(cid:48) .
48 kpc 12 .
93 kpc
Table 1.
Physical properties of the galaxy sample. (1) galaxy name (2) distance to the galaxy measured by Blakeslee et al. (2009) using surface-brightness fluctuations (3) r -band e ff ective radius taken from Iodice et al. (2019b) and converted into physical units at our adopted distances(3) − (4) stellar and DM masses enclosed within R e , respectively (5) radius which encloses 98% of the stellar mass (6) − (7) stellar and DM massesenclosed within R enc , respectively. Fig. 4.
Phase-space of circularity λ z as a function of cylindrical radius R for the best-fit model of FCC 153. The colour represents the orbitalweight from the Schwarzschild model, which has been normalised toan integral of unity. The dynamical decomposition is overlaid in black,where only those components which have non-zero contribution to theoriginal model are defined. The figure is shown on the radial extent ofthe spectroscopy for clarity, but the decomposition is conducted overthe full Schwarzschild model. The black dashed line is the half-massradius, derived from MGE Σ , shown for scale. The distribution indicatesthe prevalence of high-angular-momentum (cold disk-like) co-rotatingorbits in this galaxy, with very little contribution from hot ( λ z ∼
0) orcounter-rotating ( λ z <
0) orbits. distributions of stellar and dynamical populations are the same.The weight distributions from the dynamical models werethen used to derive the distributions of stellar populations thatreproduce their observed maps. The result is that each orbitwhich contributes to the dynamical model now has an associatedage and metallicity. Each dynamical component can thus beconsidered a mono-abundance population. By fitting age andmetallicity independently, we avoided the possibility of degen-eracies between them, as well as having to assume a specificage-metallicity relation. Instead, regularisation was utilised for
Fig. 5.
Same as Fig. 4, but for FCC 170. This galaxy has a large contri-bution from hot central orbits, with most of the cold orbits appearing atlarger radius. each stellar-population fit, and is analogous to what is routinelyused for spectral-fitting analyses such as in § 2.2. The specificimplementation is detailed in Poci et al. (2019). We testedthis approach using mock data from the Auriga simulations(Grand et al. 2016), presented in Appendix C, and find that themain results of this work are accurate to (cid:46)
10% (Fig. C.4). Analternative approach which uses a chemical-evolution modelto derive the age-metallicity relation is presented in Zhu et al.(2020).The subsequent integration through the LOS of the stellarorbits reproduces all measured kinematic and stellar-populationmaps. Fits to all maps are shown in Figures 7 to 9. We alsoconducted Monte Carlo simulations by re-fitting the stellar-population maps 100 times after randomly perturbing themwithin their measurement errors. These fits re-distribute the dy-namical components in the t − [ Z / H ] plane (without changingtheir kinematics), and so were used to estimate the uncertaintiesof our results. Using all available information – kinematics, ages, Article number, page 7 of 26 & A proofs: manuscript no. f3dIv8
Fig. 6.
Same as Fig. 4, but for FCC 177. Similarly to FCC 153, thisgalaxy is dominated by co-rotating cold orbits. metallicities, and density distributions – we can now investigatethe formation events that built up each galaxy.
4. Combined dynamical and stellar populations
The combination of dynamical and stellar populations is imper-ative to be able to decode the integrated assembly history intoits constituent events. We do this using the diagnostic power ofFigures 10 to 12 for FCC 153, FCC 170, and FCC 177, respec-tively. These figures show radial profiles of the intrinsic verticalstellar velocity dispersion σ z ( R ) and the projected surface bright-ness distributions for each galaxy as a function of both age andmetallicity. This combination of kinematic and population con-straints e ff ectively produces star-formation and accretion histo-ries simultaneously, resulting in genuine mass assembly histo-ries. The vertical velocity dispersion is a useful metric for dis-criminating between di ff erent dynamical structures, as well asbeing comparable to a variety of di ff erent observations (exploredbelow). However, for dissecting the model into di ff erent dynami-cal regimes, we used the intrinsic orbital circularity to determinedynamical temperature as this property is inherently connectedto the intrinsic orbital phase-space. Before exploring each galaxyindividually, we first qualitatively discuss how various featuresof these figures are interpreted.The presence of cold kinematics and flattened (‘disk’-like)mass distributions are interpreted as in situ star formation, es-pecially (though not necessarily) at high metallicity. Metal-richand metal-poor stars in this regime would indicate that the gaslikely originated from internal (recycling) and external (accre-tion) sources, respectively. This selection is in principle inde-pendent of age.Centralised spheroidal distributions which are dynamicallyhot are interpreted as the in situ core or ‘bulge’. There is nostrict selection on the stellar populations, since a large diversityhas been observed in this region, especially if a stellar bar is orwas present in the galaxy (Morelli et al. 2008, 2016; Coelho & Fig. 7.
Best-fitting Schwarzschild model for FCC 153. The data ( left ),fits ( middle ), and residuals ( right ) of, from top to bottom, the dynamicalmodel (surface brightness, velocity, velocity dispersion, and h − h ff erences (data - model), but are o ff set suchthat green is zero. The stellar-population maps share a common colour-bar between galaxies for comparison. We note that for FCC 153, sincethe observed metallicity map reaches 0 . . Gadotti 2011; Zhao 2012; Florido et al. 2015; Seidel et al. 2015;Corsini et al. 2018; Barsanti et al. 2021). Orbits at large radiuswith hot kinematics and with metallicities towards the metal-poor tail of the host galaxy’s distribution are interpreted as theresult of stellar accretion from many lower-mass systems. Suchaccretion is expected to be at least dynamically ‘warm’. This isbecause, although the impact of satellites may be preferentiallyalong a particular axis (Shao et al. 2019), accreted stars wouldnevertheless be on dynamically hotter orbits compared to the in
Article number, page 8 of 26. Poci et al.: F3D: Assembly Histories
Fig. 8.
Same as Fig. 7, but for FCC 170. situ cold disk. In the event of minor merging, the accreted sys-tems will, by definition, be lower mass than the host, and viathe mass-metallicity relation will thus have lower metallicitieson average. Since the age of the accreted stars depends criticallyon the SFH of the satellites, we make no selection on age for the‘accreted’ stars. It is possible that some orbits in this regime havean in situ origin, from either past major mergers or significant ex-ternal perturbations (since low-mass accretion events themselvesare not expected to perturb the existing disk significantly; Hop-kins et al. 2008). We nevertheless interpret this region as accre-tion under the assumption that it is dominated by ex situ material,subject to possible contamination by in situ material.In the remainder of this section, the results are discussedbriefly for each galaxy in the context of their individual assemblyhistories. We constrain the origin of dominant structures in eachgalaxy, which includes identifying the fraction of likely accretedmaterial. Since the condition described above for the selection ofaccreted material favours orbits at larger radii, the limited spec-troscopic FOV can bias these estimates. We instead estimate theaccretion fraction as f acc = M (cid:63) acc (cid:14) M (cid:63) enc , where the accreted stellar Fig. 9.
Same as Fig. 7, but for FCC 177. mass M (cid:63) acc is approximated for each galaxy below, and the to-tal enclosed stellar mass M (cid:63) enc is given in Table 1. This proposedaccreted fraction is discussed further in § 5. FCC 153 is suspected of being an ‘intermediate in-faller’ to theFornax cluster (4 < t in − fall < ∼ × M (cid:12) ) inrecent times ( < σ z ∼
50 km s − . The combination of late-time star-formation and persistent cold kinematics implies that the inte-grated assembly history of this galaxy (all mergers and interac-tions combined) has had a minimal impact, at least in the re- Article number, page 9 of 26 & A proofs: manuscript no. f3dIv8
Fig. 10.
Mass assembly history for FCC 153. The panels are ordered by increasing mean stellar age ( left to right ) and decreasing mean stellarmetallicity ( top to bottom ). The value given at the top and right of each column and row, respectively, denotes its upper bound (inclusive). Eachpanel is composed of a radial profile of the vertical stellar velocity dispersion σ z ( black / white curve ), the surface brightness distribution at thebest-fitting projection ( top-right ) with the outline of the MUSE mosaic shown in dashed brown, and the total stellar mass within the FOV for thatpanel. The σ z ( R ) profiles are coloured according to the stellar mass in that panel at that radius (sampled within the logarithmic radial bins). Thisindicates the spatial region in which each curve contributes most (white regions), and which regions may be impacted by numerical noise (blackregions). The grey shaded regions show the spread of velocity dispersion profiles for 100 Monte Carlo fits to the stellar-population maps. Thisgalaxy exhibits a dominant disk-like, metal-rich component that has steadily formed over the last ∼
10 Gyr. gion covered by the spectroscopy. There is a suggestion of stel-lar accretion through the old, kinematically-warm, metal-poorpopulation forming part of the stellar ‘halo’. We can use themodel to estimate the mass in accreted stars by quantitativelyisolating the orbits which meet the qualitative criteria discussedabove. Specifically, orbits are selected with [ Z / H ] ≤ − . | λ z | ≤ .
5, and mean guiding radius r ≥ ∼ (cid:48)(cid:48) ) to exclude any potential in situ ‘bulge’-likeorbits (see Fig. 4). This selection results in f acc ∼ M (cid:63) acc ∼ × M (cid:12) . This selec-tion has a luminosity-weighted average age and metallicity of t = . Z / H ] = − . f acc ,and its relatively late in-fall may explain that. This is supportedby the average age of the tentative accreted material, which im-plies that the main accretion events (those which dominate theluminosity-weighted average) occurred (cid:46) . FCC 170 is believed to be an ancient in-faller to the Fornaxcluster ( t in − fall > σ z (cid:46)
100 km s − . Applying thesame accretion criteria as for FCC 153, we estimate an accre-tion fraction of f acc ∼ M acc ∼ × M (cid:12) with aluminosity-weighted average age and metallicity of t = . Z / H ] = − . Article number, page 10 of 26. Poci et al.: F3D: Assembly Histories
Fig. 11.
Same as Fig. 10, but for FCC 170. This galaxy is dominated by an old central pressure-supported spheroidal component spanning ∼ FCC 177 is also believed to be an ancient in-faller (Iodice et al.2019a), as for FCC 170. It has the lowest stellar mass and high-est DM fraction of the three galaxies studied here (Table 1).It exhibits low velocity dispersion ( σ z <
100 km s − ) every-where and at all times, with the younger, metal-rich populationsreaching σ z (cid:46)
20 km s − (Fig. 12). We find evidence for a de-layed formation, with only a small fraction of old populations( t (cid:38)
12 Gyr) and without any clear spatial structures. At latertimes, FCC 177 appears to have sustained modest and roughly-constant star-formation for t (cid:46)
10 Gyr. This combination of pro-longed star-formation and cold kinematics is especially surpris-ing given its early in-fall, and poses problems for the expectationof group pre-processing and cluster quenching processes. Themass budget of FCC 177 is more complicated to disentangle, es-pecially due to the relatively di ff use mass at old ages. In fact,FCC 177 has formed the largest percentage of its stellar mass inrecent times, compared to the other two galaxies. Moreover, ourassembly history indicates that for lookback times greater 10 Gyrago, FCC 177 had just log ( M (cid:63) / M (cid:12) ) ∼
8, implying that the insitu component formed during that time would be lower metal-licity with respect to the other two galaxies during the same pe-riod. This caveat notwithstanding, applying the same criteria asfor the other galaxies, we estimate f acc ∼ M (cid:63) acc ∼ × M (cid:12) , with luminosity-weighted average age andmetallicity of t = . Z / H ] = − .
5. Mass assembly histories in context
In this section we review all the evidence a ff orded by this tech-nique in the context of the Fornax cluster in order to investigatethe dominant processes that built up the stellar mass in thesegalaxies. By analysing the trends in Figures 10 to 12, and ex-ploring them more quantitatively throughout this section, we canconstrain certain formation mechanisms.Interestingly, we see a diversity in the assembly historiesof the three galaxies studied here via the di ff erent distribu-tions of mass between Figures 10 to 12. Yet the persistence ofkinematically-cold orbits is common throughout all of the galax-ies for all stellar ages. The observation of such kinematics forold populations places constraints on both internal and exter-nal disruption processes. Owing to the archaeological nature ofthe methodology employed here, all stars are observed in theirpresent-day, not formation, configurations. It is clear, therefore,that in order for these orbits to remain kinematically-cold, thosestars need to not only form as such, but also experience little-to-no subsequent disruption until the epoch of observation. Thisimplies that neither internal instabilities nor the cluster poten-tial (or other members) can cause significant perturbations to thekinematics of the central regions of these galaxies (though thisis discussed further in §§ 5.1 and 5.2). For the same reason, weargue that these galaxies have likely not experienced any high-mass-ratio mergers, as they would have similarly disrupted theseold cold orbits (Hopkins et al. 2008). Article number, page 11 of 26 & A proofs: manuscript no. f3dIv8
Fig. 12.
Same as Fig. 10, but for FCC 177. This galaxy appears to have begun forming late. It is dominated by a young, thin disk, with contributionsfrom dynamically-warmer and slightly older stars.
There seems to be no lack of historic star-formation activityin these galaxies. This is perhaps most surprising for FCC 170which exhibits by far the oldest mean stellar age, and is pur-ported to reside in the central region of the cluster. We find ev-idence for the continued formation of stars in all three galax-ies down to relatively young ages, and at super-solar metallicity.These episodes occurred comfortably after each galaxy is sus-pected to have entered the cluster. Their metallicity is consistentwith self-enrichment, and thus in conjunction with their kine-matics, these stars very likely formed in-situ from recycled gas.The accretion of low-mass stellar systems is expected to de-posit material into the outer stellar ‘halo’ regions of galaxies. It isalso expected to contribute significantly to the present-day stellarmass of galaxies (Oser et al. 2010). We have estimated, however,low accretion fractions ( < f acc estimates in thiswork; contamination by in situ stars in the region we consider‘accreted’, and excluding some accreted material which residesat lower radius. We can not strictly exclude an in situ contribu-tion to these accretion fractions, but such contamination wouldimply an intrinsic accreted fraction even lower than estimatedhere. Without major mergers, any in situ stars that satisfy theproposed criteria for accretion are di ffi cult to explain, unless ex-ternal perturbations from the cluster have caused dramatic trans-formations. Moreover, Karademir et al. (2019) find that mergerswith smaller mass ratios deposit stars at larger radii. Once again,since we have argued against major (or even a significant amount of minor) mergers, it is plausible that at least the majority of ac-cretion for these galaxies resides at large radius. Davison et al.(2020) similarly find that for galaxies in the EAGLE simulation,most of the accreted mass is deposited beyond the half-mass ra-dius r / for host stellar masses within the range of our Fornaxgalaxies. We nevertheless caution that f acc is subject to these un-certainties, and highlight that the other main conclusions of thiswork do not depend on the measurements of accretion. While themass models are constrained over the full extent of the galaxiesusing the FDS photometry (§ 3.1), we can not exclude higheraccretion fractions being found at larger radii as inferred by, forinstance, Pulsoni et al. (2018) for the stellar mass range probedby our sample.A lack of accretion can be explained by the high relative mo-tions of member galaxies within a cluster, and reduced merginghas been seen previously for cluster members with respect tothe field (Berrier et al. 2008; Pipino et al. 2014). Specifically forthe Fornax cluster, its members and their globular cluster (GC)populations have been analysed previously (Jordán et al. 2015;Fahrion et al. 2020). Fahrion et al. (2020) finds that FCC 170has a significantly reduced number of GC for its stellar mass,and those that is has are notably metal-poor. While the numbersof GC for FCC 153 and FCC 177 are less unusual, since thehosts are themselves lower stellar mass, their GC are also moremetal-poor compared to the stellar body by ∼ Article number, page 12 of 26. Poci et al.: F3D: Assembly Histories merging for the three galaxies studied here. Low accretion frac-tions for these three galaxies were also inferred from the analysisof Pinna et al. (2019a). These galaxies appear to have been shuto ff from sources of external material by the cluster environment,which has likely stifled their growth. Their stellar mass assem-bly was able to continue through in situ star formation, but hasceased in the present day likely due to the exhaustion of internalgas in conjunction with the lack of replenishment. Here we quantitatively explore some of the correlations alludedto in the assembly histories. To this end, we investigate the verti-cal component of the intrinsic stellar velocity dispersion, σ z , asa function of formation time of the stars (converted to redshiftassuming the cosmology of Ade et al. 2016, as implemented in astropy ). This stellar age–velocity-dispersion relation (AVR)has been studied previously in the Local Group (Wielen 1977;Nordström et al. 2004; Rocha-Pinto et al. 2004; Seabroke &Gilmore 2007; Martig et al. 2014; Sharma et al. 2014; Beasleyet al. 2015; Hayden et al. 2017; Grieves et al. 2018; Bhattacharyaet al. 2019; Mackereth et al. 2019) and a number of cosmologicaland idealised simulations (Bird et al. 2013; Aumer et al. 2016;Grand et al. 2016; Kumamoto et al. 2017). The gas-phase AVRis also well-studied (e.g. Wisnioski et al. 2015). While the stel-lar AVR is derived through the properties of stars of di ff erentages within individual galaxies, in contrast, the gas-phase AVRis measured via the global properties of di ff erent galaxies ob-served directly at di ff erent redshifts. In all cases, σ z is seen todecrease towards the present day, but with competing explana-tions as to the physical driver of this relation. It is often thoughtto be the result of either internal instabilities whose cumulativee ff ects have disturbed older stars more (Saha et al. 2010; Aumeret al. 2016; Grand et al. 2016; Yu & Liu 2018) or that popula-tions of stars which formed at high redshift inherited higher ran-dom motion from their surroundings, which has been decreasingtowards the present day as conditions stabilise (Noguchi 1998;Bournaud et al. 2009; Bird et al. 2013; Leaman et al. 2017; Maet al. 2017). Since the AVR pertains to the conditions which leadto star-formation, the measurements of these properties are re-stricted to the disk plane, as this is where in situ star-formationis expected to occur.The stellar AVR measured in this work for the three Fornaxgalaxies are presented in Fig. 13, with comparisons to literaturemeasurements. We track the velocity dispersion as a functionof formation redshift, marginalised over metallicity and radius.That is, at fixed age, the metallicities are averaged according totheir luminosity-weighted contribution to the model, then simi-larly for radius. This maintains the appropriate weighting suchthat the final σ z measurements are also luminosity-weighted.For consistency with literature measurements, we measure theseproperties for the ‘disk’-like orbits of the models; that is, we con-sider only those orbits with | λ z | ≥ .
8. The resulting relations areshown by the large stars in Fig. 13. Additionally, the relationsfor all orbits (with no selection on circularity) are given by thedashed curves.All of these galaxies show the same general trend of decreas-ing σ z with decreasing stellar age. The trends we measure for thestellar σ z are flatter than those for direct gas measurements, asthe stars do not reach the coldest dynamical temperatures ob-served in gas in the present day. This is in agreement with pre-dictions from simulations (Pillepich et al. 2019). We also see thatthe field galaxy NGC 3115, despite being two times more mas-sive than our most massive Fornax object, exhibits comparable D I S K z [ k m s ] FCC153FCC170FCC177NGC3115 z HERACLES DYNAMOGHASPPHIBBSMASSIVOSIRISAMAZE-LSD SINS/zC-SINFKDSKMOS MW onMW off4 6 8 10 12 14Age of Orbits / Lookback Time [Gyr]
Fig. 13.
Stellar disk AVR as derived from our models. The colouredstars are the galaxies modelled in this work (and Poci et al. 2019, forNGC 3115). The symbol size is proportional to the fractional stellarmass in each age bin, for each galaxy independently. The horizon-tal error-bars denote the width of the age bin. The vertical error barsare computed as the weighted standard deviation within each age bin,for the best-fit model. The shaded regions show the spread in σ z for100 Monte Carlo fits to the stellar-population maps. The dashed curvesshow the stellar AVR of the four S0 galaxies when all orbits are in-cluded (no selection on orbital circularity). The box-whisker plots areliterature measurements of cold gas disks, from HERACLES (Leroyet al. 2009), DYNAMO (Green et al. 2014), GHASP (Epinat et al.2010), PHIBBS (Tacconi et al. 2013), MASSIV (Epinat et al. 2012),OSIRIS (Law et al. 2009), AMAZE-LSD (Gnerucci et al. 2011), SINS(Schreiber et al. 2009) and zC-SINF (Schreiber et al. 2014), KMOS (Wisnioski et al. 2015), and KDS (Turner et al. 2017). The black dotsand crosses are Milky-Way stellar measurements (Yu & Liu 2018) forstars on ( | z | <
270 pc) and o ff ( | z | >
270 pc) the plane, respectively.Galaxy disks become dynamically colder towards the present day. Thecluster S0 galaxies have a higher contribution from warmer orbits atmore recent times compared to the field galaxy (comparing the full anddisk-only σ z ). The Milky-Way, despite its higher stellar mass, is dynam-ically colder than the S0 galaxies studied here. vertical velocity dispersion. By comparing the disk AVR to thefull-orbit AVR, it can be seen that all three Fornax galaxies showa measurable contribution from non-disk-like orbits at all ages.Together, these observations imply that we are likely measuringthe impact of the cluster on the dynamics of its galaxies due toso-called ‘harassment’ (Moore et al. 1996); frequent though mi-nor gravitational interactions between galaxies in close proxim-ity. External perturbations have also been seen to cause heatingcoincident with the time of the interaction (Grand et al. 2016).Our results are also compared in Fig. 13 to data from theMilky-Way, both on ( | z | <
270 pc) and o ff ( | z | >
270 pc) thedisk plane (Yu & Liu 2018). For comparison, the physical pixelscale of the data used in this work is ∼
20 pc / pixel, but witha real physical resolution of ∼
70 pc due to the point-spreadfunction of the observations. So while our models are not sepa-rated based on height above the plane, they still probe the mostdynamically-cold physical scales, meaning that any di ff erencesbetween these results is not due to spatial resolution e ff ects. Allfour S0 galaxies exhibit a systematic increase of σ z with respectto the Milky-Way, which is expected since galaxies that can sup-port spiral arms should be dynamically colder. In this case, theo ff set is likely a combination of the di ff erent morphology and Article number, page 13 of 26 & A proofs: manuscript no. f3dIv8 environment, yet the general shape of the relation is preserveddespite these di ff erences.As discussed above, each galaxy retains a significant por-tion of mass with cold kinematics and disk-like morphology atthe oldest age. Specifically, these oldest age bins (as seen in thepresent day) exhibit σ z ∼
50 km s − on the disk plane at interme-diate radii and high metallicity. This is inconsistent with internalheating whose e ff ect should be maximal for the oldest stars. Forinstance, the simulations of Aumer et al. (2016) show that for theoldest stars, internal heating will increase σ z by ∼ −
20 km s − above the value at birth. For the old stars we measure in thepresent day which have σ z ∼
50 km s − , this would imply thatthey were born with σ z ∼ −
35 km s − at z = −
5, whichis significantly lower than the gas measurements at that epoch.Therefore, we conclude that the AVR for these galaxies is theresult of hotter dynamical temperatures at early times, while fur-ther minor heating is contributed by the cluster interactions.Closer inspection of Figures 10 to 12 indicates a 3D corre-lation between mean σ z , stellar age, and stellar metallicity, yetthe results of Fig. 13 marginalise over metallicity. We thereforecompute these relations without such marginalisation, to investi-gate the impact of age and metallicity independently. These arepresented in Fig. 14. In order to avoid numerical noise whichcould be introduced through the increasingly-complex selectioncriteria, we conduct this analysis on the full diversity of orbits(without selecting on circularity). The curves in Fig. 14 are con-structed by collecting individual rows and columns of Figures 10to 12. Each panel of those figures is integrated along the ra-dial profile, preserving the luminosity weighting at each point,to produce a single σ z measurement for that panel. Each rowin the assembly histories corresponds to a single curve of theAVR at fixed metallicity (left column of Fig. 14), while eachcolumn in the assembly histories corresponds to a single curveof the [ Z / H ] − σ z relation at fixed age (right column of Fig. 14).The Spearman rank correlation coe ffi cient r , which indicates thestrength and direction of a trend, is computed using the scipy implementation for all curves in a given panel. The correspond-ing p -value is also shown for each panel, which indicates theprobability that the two axes are uncorrelated.We observe a significant [ Z / H ] − σ z correlation at fixed age,such that the more metal-poor stars are dynamically hotter. Simi-lar correlations between the metallicity and vertical velocity dis-persion have been seen previously for the Milky-Way (for theiron abundance [ Fe / H ], and typically with non-trivial selectionfunctions; Meusinger et al. 1991; Ness et al. 2013; Minchevet al. 2014; Grieves et al. 2018; Arentsen et al. 2020) and forM 31 (Dorman et al. 2015) but those results are marginalisedover age. Similarly, all previous studies of the stellar AVR havebeen marginalised over metallicity — with the exception ofSharma et al. (2020), discussed below. Interestingly, Guiglionet al. (2015) see the inverse trend of σ z with [ Mg / Fe ] at fixed[ Fe / H ] for the Milky-Way. Fig. 14 shows that the AVR is a weakcorrelation once metallicity is accounted for, quantified by thecorrelation coe ffi cients in each case. At fixed age, the [ Z / H ] − σ z relation is significantly more correlated than the AVR at fixedmetallicity. We emphasise that the stellar AVR in Fig. 13 (eventhe dashed full-orbit curves) exhibits a correlation which is con-sistent with previous measurements when metallicity is not takeninto account. This means that the result in Fig. 14 can not be dueto any degeneracy between age and metallicity in our models.Furthermore, age and metallicity are fit independently in § 3.4,and the spatial coherence of the dynamical components (eachspatial bin is not independent) is exploited to reduce possibledegeneracies within each fit. At face value, this result implies F CC F CC F CC t [Gyr]050100150200 1.5 1.0 0.5 0.0 0.5[ Z / H ] [dex] N G C z [ k m s ] Fig. 14.
Correlations of σ z with stellar age at fixed metallicity ( left ), andstellar metallicity at fixed age ( right ) for, from top to bottom, the threegalaxies studied in this work, and the field S0 NGC 3115 (Poci et al.2019). The curves are coloured by their age / metallicity bin correspond-ing to those of Figures 10 to 12. The Spearman rank coe ffi cient r andthe associated p -value, computed for all curves collectively in a givenpanel, are inset. The shaded regions correspond to the variations derivedfrom 100 Monte Carlo fits to the stellar population maps. The stellarAVR at fixed metallicity exhibits lower significance than the [ Z / H ] − σ z at fixed age. that [ Z / H ] − σ z is the underlying physical correlation, while theimpact of age (or formation redshift) is of secondary importance.In this scenario, the stellar AVR would manifest through theage-metallicity relation and its scatter. Finally, while the resultsin Fig. 14 include the full diversity of orbits from our models,we confirmed, by removing the suspected accretion components(via the same selection identified in § 4) that neither the direc-tion nor the relative significance of these correlations change.This implies that the results of Fig. 14 are not merely driven bythe fact that accreted material is often dynamically hotter and Article number, page 14 of 26. Poci et al.: F3D: Assembly Histories relatively metal-poor, but rather that it is inherent to what weidentify as the in situ component.We posit that the [ Z / H ] − σ z relation is driven by the suc-cessive ‘generations’ of star formation, each becoming moreenriched and more dynamically-cold than those before (in theabsence of accretion which would result in the chemical anddynamical mixing of the populations). This could be the caseif, for instance, mass segregation of metals occurs vertically aswell as radially. Alternatively, this would be the result if higher-metallicity gas requires colder kinematics before star formationis possible, or if the cooling e ff ects of metals naturally producesmore dynamically-cold disks if the gas is more metal-rich. Choi& Nagamine (2009) show that metal cooling can significantly in-crease the star-formation e ffi ciency of the inter-stellar medium,though there is no direct link in that work to dynamics.Yet measurements of the gas-phase AVR show clear trendswith redshift, and the physical interpretation in that case explic-itly includes a redshift dependence. However this redshift de-pendence is via gas depletion through the cosmic specific SFR(such as in Whitaker et al. 2014); in that scenario, galaxies withlarger gas fractions experience larger inter-stellar medium turbu-lence, and higher σ z is imparted to the stars upon star formation(Leaman et al. 2017). So in much the same way as the scenarioproposed here for the stellar AVR, the gas-phase AVR is tied toepisodes of star formation, which happen to decline on averagewith redshift. This subtle di ff erence is especially important whenanalysing individual galaxies with individual assembly histories.There also remains significant scatter at fixed redshift within thegas-phase AVR that needs to be accounted for, which indicatesa potential additional dimension to this issue. Naturally, thesestar-formation episodes lead to enrichment of the gas over cos-mic time (Daigne et al. 2006; Kobayashi et al. 2007). Therefore,if metallicity is the underlying physical driver of the gas-phaseAVR, it would still manifest as an observed redshift dependencewithout intrinsically depending on redshift directly. But this isonly, at present, a circumstantial argument in lieu of an explicitexperiment for gas disks.In any case, a testable prediction of this hypothesis is thatat fixed present-day stellar mass (and without significant ex situcontributions or perturbations), galaxies with higher SFR (that is,faster chemical enrichment) should achieve dynamically-colderorbits at fixed age — or alternatively, the stellar AVR should havea steeper slope. This is because in such a scenario, the absolutecosmic time is not the driver of the AVR, but rather the timeit takes for a particular galaxy to achieve a particular degree ofenrichment. Since the stellar metallicity and σ z will depend onboth stellar mass and accretion history, it is imperative to controlfor those parameters to test this prediction. This is at present notpossible for the sample of galaxies for which our analysis hasbeen performed, but should be accessible to theoretical modelsand simulations. In fact, Just & Jahreiß (2010) explicitly inves-tigate the e ff ect of SFR on the stellar AVR, tailored to fit theMilky-Way, through a series of models. That work finds that forsimilar forms of the SFH, the model with a higher SFR has lowervertical velocity dispersion, despite peaking at earlier epochs.The outlier in this respect from Fig. 14 is NGC 3115. Wehave already established that accretion has played a minor rolein the stellar mass assembly of the three Fornax galaxies. Con-versely, Poci et al. (2019) conclude that NGC 3115 assembled ∼
68% of its present-day stellar mass from external sources. More-over, given the higher stellar mass of NGC 3115, these accretedsystems could be higher mass, and therefore more enriched onaverage, compared to lower-mass satellites accreted onto lower-mass hosts. Thus the age and metallicity trends would be sig- nificantly phase-mixed, as is seen by the reduced correlation co-e ffi cients. The persistence of an AVR, only at high metallicity,may be indicative of secular evolution following the last accre-tion event.A similar analysis has been performed for the Milky-Way us-ing a combination of many of the recent photometric and spec-troscopic surveys (Sharma et al. 2020). That work finds a strong[ Z / H ] − σ z relation at fixed age. Yet they also find a persistentstellar AVR at fixed metallicity, but only at young ages. The AVRthen flattens and correlates solely with metallicity at old ages.Yu & Liu (2018) see similar trends with two bins of metallic-ity. Sharma et al. (2020) interpret the [ Z / H ] − σ z correlation asa connection between σ z and the stellar birth radius. However,in the case of the Fornax galaxies, we see no clear (monotonic)radial gradients of metallicity in Figures 7 to 9. Comparisons tothat work are complicated, however, by the selection functionsof the Milky-Way data sets, and so these results may be tracingdi ff erent physical regimes. S0 formation All of our results indicate that the Fornax galaxies have under-gone mild transformations due to the cluster potential, primarilyin their outer regions. They have been able to retain their coldcentral kinematics, yet in a thicker configuration compared tothe field. We posit, thus, that their S0 morphology is a resultof these interactions. This is neither of the explanations typicallyinvoked to explain the transformations of galaxies into S0; merg-ers (Chilingarian et al. 2009; Querejeta et al. 2015; Tapia et al.2017; Poci et al. 2019) or the ‘fading’ of spiral galaxies (Lar-son et al. 1980; Bekki et al. 2002; D’Onofrio et al. 2015; Mishraet al. 2018; Rizzo et al. 2018). While cluster environments arecommon in the faded-spiral scenario, it is predicated on the sup-posed spiral progenitor first ceasing star-formation due to the en-vironment (for instance, Boselli & Gavazzi 2006; Book & Ben-son 2010; Peng et al. 2012; Mendel et al. 2013; Bekki 2014),allowing it to subsequently transform into an S0 galaxy. Yet wesee evidence for significant star formation activity well beyondthe suspected time of in-fall to the cluster for all three galax-ies. Gas was therefore readily available until relatively recently.The evidence for a lack of stellar accretion has been discussed,in agreement with other cluster studies, rendering this formationpath unlikely as well. This is also consistent with the deductionsof Comerón et al. (2019) and Pinna et al. (2019a) who find thataccretion does not play a major role in the formation of ‘thick’disks in local galaxies.An alternative scenario proposed by Diaz et al. (2018) statesthat at high redshift, gas-rich satellite accretion onto compact el-liptical galaxies leads to the formation of the disk componentof the resulting S0. Our models impose the constraint that ifthis scenario occurred for the three Fornax galaxies, such ac-cretion would have had to occur (cid:38)
12 Gyr ago for FCC 153and FCC 170, and (cid:38)
10 Gyr ago for FCC 177, since it mustprecede the formation of the dynamically-cold disk. However,this scenario supposes that the compact elliptical, which goeson to form the ‘bulge’ of the subsequent S0, is responsible forthe suppression of spiral arms in the disk. Conversely, our datasuggest that only FCC 170 has a significant contribution froma central pressure-supported structure. More broadly, a diversityof S0 properties is emerging (Fraser-McKelvie et al. 2018; Coc-cato et al. 2020; Deeley et al. 2020; Tous et al. 2020), and it isunlikely that a single formation path is responsible for this diver-sity.
Article number, page 15 of 26 & A proofs: manuscript no. f3dIv8
The photometric catalogue of Ferguson (1989), covering 40 sq.degrees, contains 35 S0-like galaxies (some of which have un-certain classification), with 20 being brighter than the magni-tude limit of the Fornax3D survey ( m B ≤
6. Conclusions
In this work we modelled three edge-on S0 galaxies in the For-nax cluster as part of the Fornax3D project. We applied so-phisticated dynamical and stellar-population techniques to self-consistently model the entire stellar information content. Thesemodels were used to infer how each galaxy formed, and allowedus to place strong constraints on some of the hypothesised pro-cesses that a ff ect galaxy formation and evolution, in particular inthe cluster environment. These findings are summarised here: • All three galaxies retain a strongly-rotating component thathas persisted for many dynamical times. These structures canbe composed of both young and old stars, implying that theyhave survived the galaxy’s entry into the cluster and subse-quent evolution therein (Figures 10 to 12). • There is evidence of continued star-formation in all threegalaxies, to varying degrees. Owing to the metallicity andkinematics, we suggest this star formation is almost exclu-sively in-situ through recycled gas, as there is no evidence ofgas accretion (Figures 10 to 12). • Our results are suggestive of a suppression of stellar accre-tion. We postulate that this is driven by the relative motionsof galaxies within the cluster (Figures 10 to 12), as proposedin previous works. • There is evidence against internal heating as the cause of thestellar age–velocity-dispersion relation, suggesting that olderstars were created with inherently-higher σ z , in agreementwith the results of Poci et al. (2019). There is tentative evi-dence that the relations for the cluster galaxies are elevatedwith respect to the field (Fig. 13), implying that harassmentmay be responsible for mild dynamical heating. • We find tentative observational evidence of a potential fun-damental stellar [ Z / H ] − σ z relation which we argue may con-tribute significantly to the observed age–velocity-dispersionrelation (Fig. 14).We endeavour in future work to incorporate more detailedstellar-population analyses, including variable IMF, while con-tinuing to apply this methodology to a variety of galaxies. De-riving these histories for other galaxies will enable a more thor- ough understanding of how galaxies piece together their mass,and which processes have dominant e ff ects in various regimes. Acknowledgements.
We thank Lorenzo Morelli, Thomas Spriggs, and AdrianBittner for discussions on this work. AP acknowledges financial support fromMacquarie University and the ESO Studentship Programme. RMM is the re-cipient of an Australian Research Council Future Fellowship (project num-ber FT150100333). LZ acknowledges the support from National Natural Sci-ence Foundation of China under grant No. Y945271001, and the National KeyR&D Program of China under grant No. 2018YFA0404501. GvdV acknowl-edges funding from the European Research Council (ERC) under the Euro-pean Union’s Horizon 2020 research and innovation programme under grantagreement no. 724857 (Consolidator Grant ArcheoDyn). EMC is supportedby MIUR grant PRIN 2017 20173ML3WW_001 and by Padua Universitygrants DOR1715817 /
17, DOR1885254 /
18, and DOR1935272 /
19. JF-B, IMN,and FP acknowledge support through the RAVET project by the grant PID2019-107427GB-C32 from The Spanish Ministry of Science and Innovation. Basedon observations collected at the European Southern Observatory under ESO pro-gramme 296.B-5054(A). This work makes use of the
SciGar compute clusterat ESO, and the
OzStar supercomputer at Swinbourne University. The workalso makes use of existing software packages for data analysis and presenta-tion, including A stro P y (Astropy Collaboration et al. 2013), C ython (Behnelet al. 2011), IP ython (Perez & Granger 2007), matplotlib (Hunter 2007), N um P y (Harris et al. 2020), the S ci P y ecosystem (Virtanen et al. 2020), and statsmod - els (Seabold & Perktold 2010). We finally thank the anonymous referee, whosefeedback greatly improved the depth and clarity of this work. References
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Article number, page 19 of 26 & A proofs: manuscript no. f3dIv8
Fig. A.1. the mass-density MGE for FCC 153.
Top:
Contours of theprojected mass density (black), the mass density MGE Σ (red), and thesurface brightness MGE µ (blue). Bottom:
The ratio between the massand surface-brightness models, showing the structural di ff erences. Thispanel is normalised by the average M (cid:63) / L such that values of 1 . M (cid:63) / L , andany deviations are percentages in stellar mass. The outline of the MUSEmosaic is shown in dashed brown. Σ σ q [M (cid:12) / pc ] [arcsec]68 , .
68 0 .
278 0.525244 , .
66 1 .
439 0.592532 , .
16 4 .
619 0.51940357 .
27 6 .
725 0.81297904 .
26 14 .
553 0.153444 , .
99 18 .
123 0.06621582 .
02 26 .
947 0.15240300 .
95 31 .
695 0.2901612 .
17 74 .
105 0.53099
Table A.1.
MGE Σ for FCC 153. The columns represent, from left toright, the projected mass surface density, the width (peak location), andaxis ratio, respectively. Appendix A: Mass density MGE
Here we present the fits to the scaled mass ‘images’ describedin § 3.1, in Figures A.1 to A.3, and the results themselves inTables A.1 to A.3, for FCC 153, FCC 170, and FCC 177, re-spectively. The MGE in this work have their major-axis o ff sets ψ fixed to zero, which generates axisymmetric (in projection)mass models. This section illustrates a number of key aspectsof this process. Firstly, it can be seen from the upper panels ofFigures A.1 to A.3 that the transition from spectroscopically-derived to photometric-derived M (cid:63) / L R is seamless, albeit withhigher noise in the photometry. Conversely, systematic over- andunder-estimations of M (cid:63) / L R from the photometry would presentas discontinuous shifts to larger and smaller radii, respectively,of a given contour at the transition between photometry andspectroscopy. Since there is no such discontinuity in these re-sults, it indicates that the photometrically-derived M (cid:63) / L R val-ues are quantitatively consistent with those derived from spec-troscopy. Secondly, the lower panels clearly highlight the shapedi ff erences between the luminosity and mass surface densities.This is a direct result of the resolved structures in stellar popula- Fig. A.2.
Same as Fig. A.1, but for FCC 170. Σ σ q [M (cid:12) / pc ] [arcsec]177 , .
31 0 .
358 0.7330444 , .
95 1 .
198 0.7488017 , .
47 2 .
819 0.756755 , .
28 6 .
776 0.76166127 .
74 12 .
580 0.999002 , .
11 23 .
103 0.102001 , .
45 29 .
559 0.18741170 .
86 38 .
541 0.3338018 .
98 68 .
965 0.710893 .
06 88 .
782 0.206641 .
81 88 .
782 0.99900
Table A.2.
Same as Table A.1, but for FCC 170.
Fig. A.3.
Same as Fig. A.1, but for FCC 177. tions, which are subsequently taken into account in the dynami-cal models by this approach.
Appendix B: Dynamical modelling
This section presents additional details of the Schwarzschildmodels and measured data products. The best-fit parameters ofthe Schwarzschild models are given in Table B.1, while theirparameter-space distributions are shown in Figures B.1 to B.3.The measured (un-symmetrised) kinematics and stellar popula-
Article number, page 20 of 26. Poci et al.: F3D: Assembly Histories Σ σ q [M (cid:12) / pc ] [arcsec]61 , .
78 0 .
231 0.795141 , .
36 1 .
497 0.80274915 .
55 3 .
190 0.72995315 .
87 9 .
467 0.4565413 .
62 20 .
762 0.99701363 .
99 22 .
622 0.07590463 .
00 25 .
577 0.17350174 .
70 29 .
337 0.356938 .
21 50 .
489 0.688177 .
51 64 .
291 0.23789
Table A.3.
Same as Table A.1, but for FCC 177. . . . . . p
051 01 5 C D M l o g [ f D M ( r )] . . q . . . . . . . p C DM log [ f DM ( r )]0.0 3.0 Fig. B.1.
Optimisation over the 5D parameter-space for FCC 153. Thegrey points indicate the exploration of the parameter-space with thesmaller orbit sampling, while the coloured points show the χ r of themodels with the high orbit sampling (see § 3.2). The best-fit parametersare indicated by the brown lines. tions are presented in Figures B.4 to B.6. It can be seen thatFCC 170 exhibits the highest degree of intrinsic triaxiality, withthe lowest p , though the triaxiality is small in all cases. The in-trinsic shapes recovered by our models are in good agreementwith, for instance, those of the oblate galaxies of Jin et al. (2019).Interestingly, the dynamical model of the field S0 NGC 3115(Poci et al. 2019) has larger intrinsic triaxiality than the threecluster S0 galaxies studied here, but this is likely a consequenceof its higher stellar mass, and the more violent assembly historyinferred for that galaxy. Appendix C: Validation on mock data
A crucial test to conduct for the modelling procedure used in thiswork is to determine the accuracy and precision with which itcan recover known properties. To this end, we conducted tests onmock data of realistic galaxies from the Auriga simulation suite(Grand et al. 2017). In Zhu et al. (2020), this Schwarzschild codeis used to fit the mock kinematic data of sub-halos from Auriga, . . . p
051 0 C D M . . . . . l o g [ f D M ( r )] . . q . . . . . . p C DM log [ f DM ( r )]0.0 3.0 Fig. B.2.
Same as Fig. B.1, but for FCC 170. . . . . . p . . .
51 0 . C D M l o g [ f D M ( r )] . . q . . . . . . . . p C DM log [ f DM ( r )]0.0 3.0 Fig. B.3.
Same as Fig. B.1, but for FCC 177. at various projected inclinations. Here we take the dynamicalmodels and apply the procedure described in §§ 3.3 and 3.4 inorder to fit stellar populations in exactly the manner that is ap-plied to the Fornax3D data. We then measure the diagnostics thatinform the main scientific conclusions of this work, and com-pare directly to the underlying intrinsic distributions from thesimulations. We conduct this analysis on Auriga halos 5 and 6,projected to an inclination of θ = Article number, page 21 of 26 & A proofs: manuscript no. f3dIv8
Galaxy log ( M • [M (cid:12) ]) ∗ q p u ∗ C DM log ( f DM ) Υ FCC 153 6 .
03 0 . . . .
00 4 .
00 0 . .
40 0 . . . .
50 2 .
70 0 . .
52 0 . . . .
00 5 .
00 0 . Table B.1.
Best-fit parameters for the Schwarzschild models. Columns marked with ∗ are fixed to the values given here. Fig. B.4.
Un-symmetrised kinematics extracted for FCC 153 ( left ), andassociated errors computed through Monte Carlo simulations ( right ).The outline of the MUSE mosaic is shown in dashed brown. case the outputs are less informative because the ‘errors’ on themock maps were generated artificially. The distributions of t − Z are presented in Fig. C.2. We note here that the ‘true’ distribu-tions are smoother due to the ∼ particles that are used togenerate them, in contrast to the ∼ dynamical componentswhich constitute the ‘model’ distributions. Kernel Density Es-timates (KDE) were computed from these data to compare themarginalised distributions. Owing to the di ff erence in the sizeof the data sets between the dynamical models and simulations,we derived the optimal bandwidth for the KDE of each data-setusing a data-driven approach which minimises the variance andalso takes into account each sample size (Silverman 1986). Thisexercise has shown that not only can the models fit the projectedmaps, but also that our implementation recovers the underlyingstellar-population distributions.The main results from this work are derived from the assem-bly histories in Figures 10 to 12, and the AVR in Fig. 13. Com-paring simulations to data in general can introduce inconsisten-cies in many ways, and so for clarity we describe the procedurefor testing the recovery of the assembly histories on simulations,and the steps taken to mitigate potential inconsistencies. Firstly,the Cartesian coordinates of the simulation data are binned to thesame spherical polar grid of the corresponding Schwarzschildmodel. The simulation kinematics, V x , V y , V z , are then convertedto cylindrical coordinates, in line with how the outputs fromthe Schwarzschild model are analysed. From here, the σ z mea-surements on the simulation data proceed in an identical fash-ion as for the Schwarzschild model. Moreover, the distributionsfrom the simulations are constructed using exactly the particlesthat lie within the mock FOV, by construction. Conversely, theSchwarzschild models (and indeed real observations) typicallyhave contributions from orbits which reside (on average) outsidethe FOV, which are not present in the simulation. This meansthat any measurement on these data would be probing di ff erentphysical regions between the two data sets. To remedy this in-consistency, the results from the Schwarzschild models do notinclude orbits with time-averaged radii outside the FOV. This isonly the case for the mock tests where strictly-consistent com-parisons are sought. Our main results in Figures 10 to 12 includethe full model.The recovery of the assembly histories is presented inFig. C.3. It can be seen that the radial profiles of σ z from the sim-ulations often extend to larger radii than the corresponding pro-files from the Schwarzschild model. This is due to the fact thateach particle in the simulation contributes to its profile, while forthe Schwarzschild model orbits are required to have spent sometime in a particular region before being included. A single parti-cle (or very few) in the simulations of a given t − [ Z / H ] compo-nent may give the impression of having a larger extent comparedto the Schwarzschild model, while actually contributing negligi-ble mass. Therefore we emphasise that it is the common radialregions for each pair of profiles, and the overall spatial distribu-tion of particles / orbits for each panel, that provides the best indi-cation of the model’s recovery as this is where the vast majorityof the mass resides. In this regime, there is clearly point-to-pointvariation between the intrinsic and recovered radial profiles of Article number, page 22 of 26. Poci et al.: F3D: Assembly Histories
Fig. B.5.
Same as Fig. B.4, but for FCC 170. velocity dispersion, which are noisy for some components. Theagreement is worse for decreasing mass, which is expected. Nev-ertheless, it can be seen that the general trends are accuratelyrecovered by the model, in particular the relative dynamics be-tween the di ff erent stellar populations. The absolute quantita-tive agreement between the model and simulations is also good,though in some cases there appears to be additional discretisatione ff ects in the model producing sharply-varying profiles in thelow-mass panels, which is likely due to the binning in circularityspace combined with the binning in the t − Z space. Reassuringly, Fig. B.6.
Same as Fig. B.4, but for FCC 177. the 2D distributions are also well-matched by the model. Somemass is re-distributed to di ff erent bins compared to the simu-lations, which are typically the compact spheroidal structures.Such ‘boundary’ e ff ects are inevitable when imposing discretebinning on the data, as those components with values close tothese boundaries may straddle one way or the other. The MonteCarlo simulations show similar behaviour, and in this way theshaded regions account for these boundary e ff ects. Finally, the Article number, page 23 of 26 & A proofs: manuscript no. f3dIv8
Fig. C.1.
Stellar-population Schwarzschild model fits to the mock data.Mean stellar age ( left ) and metallicity ( right ) are shown for Auriga halos5 ( top ) and 6 ( bottom ). From top to bottom, the rows represent the truemeans, models fits, and residuals. recovery of the AVR are shown in Fig. C.4. Once again, we seegood qualitative and quantitative agreement.We conclude that the model is su ffi ciently robust to be ableto draw strong inferences about real galaxies. With regards tothe main conclusions of this work, the relative behaviour ofthe chemo-dynamical populations is recovered well, where themodel stellar AVR for both Auriga halos are consistent to within ∼
10 km s − of their intrinsic values. We highlight that we be-lieve this is an upper limit on account of our real data hav-ing higher spatial resolution, the corresponding models hav-ing higher orbit sampling, and all galaxies studied here having θ >
80° (where more edge-on projections are more reliable; Zhuet al. 2020), which all work in favour of improving the reliabil-ity of this technique further. We are therefore confident that thismethod is able to recover not only projected average quantitieslike the 2D stellar-population maps of Fig. C.1, but also quantita-tively recover the underlying chemo-dynamic distributions, andthat our main conclusions are robust against systematic e ff ects. Fig. C.2.
Intrinsic t − Z distribution ( left ) and that retrieved from ourmodel ( right ) for halos 5 ( top ) and 6 ( bottom ). The 1D distributionsare also shown for each simulation, as kernel density estimates of theunderlying data. The intrinsic distributions are black dashed curves, andthe model distributions are the blue solid curves.Article number, page 24 of 26. Poci et al.: F3D: Assembly Histories Fig. C.3.
Similar to Fig. 10, showing the assembly history for halo 5 ( top ) and halo 6 ( bottom ). In addition to the σ z radial profile ( black / white line )and surface brightness distribution ( upper right ) from the Schwarzschild model, the shaded regions correspond to the variations derived from 100Monte Carlo fits to the stellar population maps. Each panel also contains the intrinsic σ z radial profile ( red line ) and surface brightness distribution( upper left ) from the simulations. Article number, page 25 of 26 & A proofs: manuscript no. f3dIv8
Fig. C.4.
Similar to Fig. 13, showing the recovered ( blue ) and intrinsic( redred