Adebusola Alabi Thesis

Mass distribution in early-type galaxies

Adebusola Bamidele Alabi

Presented in fulﬁllment of the requirements of the degree of Doctor of Philosophy

2017

Faculty of Science, Engineering and Technology Swinburne University of Technology

i Abstract

This thesis uses the largest, homogeneously compiled globular cluster kinematics data in nearby early-type galaxies to study galaxy formation and evolution by addressing the following questions:

• What is to be learnt from the globular cluster kinematics proﬁles of early-type galaxies with respect to galaxy formation and evolution?

• What is the nature of mass distribution in early-type galaxies at large radii, i.e. ﬁve eﬀective radii and beyond?

• When and how did the haloes of early-type galaxies assemble?

Globular clusters are the luminous, gravitationally bound collection of stars that are found abundantly in early-type galaxies. The data used in this thesis have been obtained over the last decade as part of the SLUGGS survey, using the Keck telescope and the DEIMOS spectrograph. SLUGGS survey is the SAGES Legacy Unifying Globulars and GalaxieS survey. The galaxies studied are diverse in that their stellar masses span 10 12 10 − 10 M , they reside in cluster, group and field environments and have either been morphologically classified as ellipticals or lenticular galaxies. This thesis pays particular 11 attention to the nature of large radii mass distribution in ≤ 10 M early-type galaxies, hitherto, not adequately studied in the literature. In Chapter 2, I study the globular cluster kinematics of NGC 4473, a double-sigma galaxy, with complex stellar kinematics features. The globular cluster system shows a double-sigma feature, similar to, but more radially extended when compared to results previously reported in the literature for the stars. This is direct evidence for the co-evolution of this galaxy’s stellar and globular cluster systems. I also identify other statistically significant kinematic components in the globular cluster system, which hint at the complex evolutionary history of NGC 4473 through a gas-rich major merger event. In Chapter 3, I study the mass distribution within and beyond five effective radii in 23 early-type galaxies, using the tracer mass estimator from Watkins et al. I account for the effects of rotation and kinematic substructures in the globular cluster systems as well as that of galaxy flattening and inclination on my mass estimates. The mean scatter between my mass estimates and previous results from the literature is less than 0.2 dex. The early-type galaxies studied show a large spread in dark matter fractions within five effective radii, ranging from 0.3 to 0.9, with the lowest dark matter fractions solely due ii

11 to some ∼10 M galaxies. This observed dark matter fraction trend is independent of assumptions made for the orbital anisotropy of the globular clusters, the stellar mass-to- light ratios or the shape of the gravitational potential. In Chapter 4, I expand the galaxy sample from chapter 3 to 32, and obtain the dark matter fractions and the average dark matter densities within five effective radii, using newly measured galaxy sizes and stellar mass estimates from Spitzer data. I compare the dark matter fractions with expectations from state-of-the-art cosmological hydrodynamical simulations as well as simple galaxy models based on galaxy scaling relations. The wide range of measured dark matter fractions persist, and it is difficult to explain with any single cosmological simulation. From the average dark matter densities, I inferred the halo assembly epochs and find that early-type galaxies have haloes that assembled at redshifts, z ∼ 2 − 4. While lenticulars and elliptical galaxies have haloes with similar structural properties and assembly epochs, there are hints that there may be differences in their late-phase, i.e. z ≤ 2, mass assembly channels as shown by trends in their large radii mass distributions. iii iv Acknowledgements First, I want to appreciate my supervisor, Duncan Forbes, for his excellent mentorship and awesome support all through this Ph.D. project.

Special thanks goes to all members of Duncan’s group here at Swinburne, and the SLUGGS survey collaboration, in general. I am going to miss the weekly meetings! Joachim, thanks for the conversations, they were truly helpful. Aaron, words are not enough to thank you for your invaluable guidance.

To Themiya, Manisha, George and Angela, thanks for the moments, the trips and literally dragging me out of my hole.

To friends and family, who had to endure my absence, thanks for your understanding and unﬂinching support. To mum, of course, you deserve a special thanks for making this dream come true.

My special gratitude goes to all the kind folks at Tuorla Observatory and University of Turku, Finland, especially, Laura Portinari and Harry Lehto. To Ricardo Sali- nas, thanks for pointing me in the right direction, for the kind words in those early days and for the encouragement all along, I am eternally grateful.

I gratefully acknowledge the ﬁnancial support I have enjoyed through the Swinburne Uni- versity Postgraduate Research Award (SUPRA) over the entirety of this Ph.D. project.

Lastly, to all the corporate entities and kind taxpayers that have contributed, over the years in various scholarships, to my education, I say thanks. v vi Declaration

The work presented in this thesis has been carried out in the Centre for Astrophysics & Supercomputing at Swinburne University of Technology between November 2013 and March 2017. This thesis contains no material that has been accepted for the award of any other degree or diploma. To the best of my knowledge, this thesis contains no material previously published or written by another author, except where due reference is made in the text of the thesis. Figures 1.1, 1.2 and 5.1 were produced solely for this thesis. The content of the chapters listed below has appeared in refereed journals. I acknowledge the contributions of co-authors on the publications.

• Chapter 2 has been published as Alabi, Adebusola B.; Foster, Caroline; Forbes, Duncan A.; Romanowsky, Aaron J.; Pastorello, Nicola; Brodie, Jean P.; Spitler, Lee R.; Strader, Jay; Usher, Christopher The SLUGGS survey: globular cluster kinematics in a “double sigma” galaxy - NGC 4473, 2015, Monthly Notices of the Royal Astronomical Society, 452, 2208

• Chapter 3 has been published as Alabi, Adebusola B.; Forbes, Duncan A.; Ro- manowsky, Aaron J.; Brodie, Jean P.; Strader, Jay; Janz, Joachim; Pota, Vincenzo; Pastorello, Nicola; Usher, Christopher; Spitler, Lee R.; Foster, Caroline; Jennings, Zachary G.; Villaume, Alexa; Kartha, Sreeja, The SLUGGS survey: the mass distribution in early-type galaxies within ﬁve eﬀective radii and beyond, 2016, Monthly Notices of the Royal Astronomical Society, 463, 3838

• Chapter 4 has been accepted for publication by the Monthly Notices of the Royal As- tronomical Society as Alabi, Adebusola B.; Forbes, Duncan A.; Romanowsky, Aaron J.; Brodie, Jean P.; Strader, Jay; Janz, Joachim; Usher, Christopher; Spitler, Lee R.; Bellstedt, Sabine; Ferr-Mateu, Anna, The SLUGGS Survey: Dark matter fractions at large radii and assembly epochs of early-type galaxies from globular cluster kinematics, 2017, arXiv:1701.05904

I warrant that I have obtained, where necessary, permission from the copyright owners to use any third part copyright material reproduced in the thesis, or to use any of my own published work in which the copyright is held by another party. Oxford University Press grants back to authors the non-exclusive right of republication, subject only to giving appropriate credit to the journal in which the article was published. This non-exclusive right of republication gives authors the right to approve or deny reproduction of all or vii part of the article and to post the ﬁnal published version online. No written permission is required to have the papers reproduced in the thesis with the original journal format1.

Alabi Adebusola Melbourne, Victoria, Australia March 2017

1For more information, see http://www.oxfordjournals.org/our journals/mnras/rights permissions ras.html viii

Dedicated to mum, your labour has not been in vain Swinburne Research

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Contents

Abstract i

Acknowledgements iii

Declaration v

1 Introduction 1 1.1 Dark sectors of the universe ...... 2 1.1.1 Spirals vs early-type galaxies ...... 2 1.1.2 How do early-type galaxies form? ...... 3 1.1.3 Dearth of easy-to-use mass tracers in early-type galaxies ...... 4 1.1.4 Brief explanation of degeneracies in dynamical mass modelling . . . 4 1.2 Globular clusters ...... 6 1.2.1 Globular cluster kinematics as probes of galaxy formation ...... 6 1.2.2 Globular clusters as probes of galaxy mass ...... 7 1.3 Multi-object spectroscopy ...... 7 1.4 State of the data: GC kinematics data and systematic mass modelling of ETGs ...... 9 1.4.1 Testing expectations from ΛCDM cosmological simulations . . . . . 11 1.4.2 Mass distribution and halo assembly epochs ...... 11 1.5 Thesis outline ...... 12

2 Globular cluster kinematics of a double-sigma galaxy - NGC 4473 15

3 Mass distribution in early-type galaxies within ﬁve eﬀective radii and beyond 29

4 Dark matter fractions at large radii and assembly epochs of early-type galaxies 53

5 Conclusion 71 5.1 Principal ﬁndings and future directions ...... 71

Bibliography 81

Publications 82

xix

1 Introduction

now, we know in part —Pauline text adapted

Understanding the universe, the most complex and vast thing there is, is no trivial task. Yet, despite the enormity of this challenging endeavour, it has always captured the imagination and attention of both casual observers and professional scientists through- out history. History is awash with myths and stories invented to describe these unknown worlds, since they are beyond what could be perceived physically. The modern scientist, armed with more sophisticated tools, can now see further and probe deeper into these unknown realms. But with this added advantage comes the perpetual obligation to rec- oncile new data with physically motivated models which explain how the universe should be. This often results in the need to get better data, or to apply modiﬁcations to well- established paradigms or in some revolutionary cases, totally abandon the old paradigms and adopt more radical ones. A good example of this scientiﬁc process at work can be found in the several updates that have been progressively applied to our understanding of the nature and constitution of matter in the universe. The initial seeds of these changes are to be found in the results obtained in the early 20th century by Zwicky (1933, 1937) - Coma cluster, Smith (1936) - Virgo cluster, Babcock (1939) - M31 and Oort (1940) - NGC 3115 and NGC 4494, where they found that luminous baryons in the various systems studied were inadequate to account for the total masses measured. It was not until the 1970s, however, that overwhelming evidence for this mass discrepancy, or dark matter as it was aptly labelled, became ubiquitous. Rotation curves of nearly all gas-rich spiral galaxies studied during this era (Rubin & Ford, 1970; Roberts & Rots, 1973; Ostriker & Peebles, 1973; Einasto et al., 1974; Roberts & Whitehurst, 1975; Bosma, 1978; Rubin et al., 1978) did not show the

1 2 Chapter 1. Introduction expected Keplarian decline at large radii. This deluge of new data thus led to a widespread adoption of the dark matter paradigm. It should also be noted that the observed mass discrepancy can alternatively be understood as a gravity discrepancy problem, as espoused more recently in some theories which seek to modify Newtonian dynamics on galactic scales (Milgrom, 1983a,b; Verlinde, 2016). However the fundamental physical theory(s) on which such gravity modiﬁcations are built, the kind of cosmology that they imply as well as their actual meaning in terms of galaxy formation and evolution are still unclear. This thesis assumes that the mass discrepancy in galaxies is due to dark matter.

1.1 Dark sectors of the universe

Even though what exactly makes up dark matter is still unknown, we now know that dark matter is cosmologically important, non-baryonic, dynamically cold and dissipationless. It accounts for almost 25 per cent of the total cosmic energy density (almost a factor of ﬁve more abundant than the luminous baryons), and it is needed, amongst other things, to understand the large-scale distribution of structures in the universe, the cosmic microwave background and the initial dark matter clusterings from which led to galaxy formation. This cold dark matter (CDM) co-exists with an even more mysterious and dominant component of the universe (almost a factor of 3 more abundant than CDM), the dark or vacuum energy, in the standard ΛCDM cosmology. It is against this background of ill-understood components of the universe that one must try to understand how galaxies formed and have since assembled their masses. The picture gets even more complicated when one considers the role of baryonic processes in the hierarchical build-up of galaxies.

1.1.1 Spirals vs early-type galaxies

Our understanding of galaxy formation and mass assembly has beneﬁted immensely from studies of the relative distribution of the various mass components in galaxies, e.g. dark matter and baryons (stars, gas, dust). We now expect that baryons should dominate galaxy mass distribution in the central parts while dark matter should become more dominant in the galaxy outskirts. This is relatively easy to show in spiral galaxies due to their copious supply of HI gas at large radii which act as tracers of the galaxy potential. The same cannot be said about early-type galaxies (ETGs) which are mostly poor in cold gas. It is therefore not surprising that the early results which established the dark matter paradigm were almost exclusively from studies of spiral galaxies. More recently, systematic studies of mass distribution within spiral galaxies have shown that the dark matter fraction within the 1.1. Dark sectors of the universe 3 central part, decreases as galaxy stellar mass increases (e.g. de Blok et al., 2008; Martinsson et al., 2013; Courteau & Dutton, 2015). For early-type galaxies, dark matter fraction 1 11 within the central part reaches a minimum at galaxy stellar mass ∼10 M , increasing with both increasing and decreasing stellar mass (Gerhard et al., 2001; Cappellari et al., 2006; Tortora et al., 2009; Napolitano et al., 2010; Auger et al., 2010; Dutton et al., 2011; Thomas et al., 2011, etc). However, it is unclear if this same trend extends to large radii in early-type galaxies.

1.1.2 How do early-type galaxies form?

Early-type galaxies (galaxies morphologically classified as ellipticals or lenticulars), some of which are the most massive galaxies known (e.g. Collins et al., 2009), contain more than half of the total stellar mass in the universe (e.g. Bell et al., 2003). When compared to ETGs at higher redshifts, e.g. z∼2, the sizes of massive ETGs are seen to have increased by a factor of ∼ 5 and in mass, by a factor of ∼2 (e.g. van Dokkum et al., 2008; Naab et al., 2009), through repeated mergers (dry or wet and/or major or minor) and gas accretion (clumpy or smooth) (e.g. Genel et al., 2010). This is in agreement with the hierarchical structure formation paradigm (e.g. Peebles, 1982), where small structures form at earlier epochs and later merge into larger ones, and it is adequately captured in the well known two-phase galaxy formation model (e.g. Oser et al., 2010). It should be noted that the stellar mass fraction that formed ex-situ in present day ETGs could range from 10 to 80 per cent (Rodriguez-Gomez et al., 2016), implying a variety of formation mechanisms which may correlate with total mass, morphology or environment. For example, it is reasonable to expect that galaxies in sparse environments have experienced fewer mergers during their evolution. It is also reasonable to expect ETGs harbouring large scale discs that are dominated by old stars not to have experienced any recent gas-rich major mergers. Therefore, on one hand, this chaotic formation paradigm easily accounts for the observed diversity in the shape, structure, size and mass constitution of z∼0 ETGs, yet on the other hand, z∼0 ETGs follow galaxy scaling relations (e.g. the Faber-Jackson relation - Faber & Jackson 1976, the Kormendy relation - Kormendy 1977, the Fundamental plane - Djorgovski & Davis 1987, etc.) with such a fidelity that apparently belies the complexity in their evolution. Recent classification of ETGs from ATLAS3D based on their central kinematics (Cap- pellari et al., 2013), rather than how they appear, provide additional clues on how they

1 The fiducial radius adopted in studies of the central mass distribution in spiral galaxies is 2.2Rd, with Rd being the disk scale length. In early-type galaxies, the fiducial radius used to study central mass distribution is the effective radius, Re. The effective radius contains half of the galaxy’s light. 4 Chapter 1. Introduction formed. Primarily, a galaxy’s kinematics depends on how well it accretes cold gas and then converts them into stars as well as the preponderance of minor mergers in its evolutionary history. Fast rotators, similar to spiral galaxies, are discy and flattened. Their progenitors are most likely quenched or faded high redshift discy galaxies. Slow rotators, however, have their later evolution history dominated by multiple minor mergers.

1.1.3 Dearth of easy-to-use mass tracers in early-type galaxies

Results from stellar kinematics of ETGs, usually limited to the inner 1 Re, show that the central parts are baryon-dominated, just like Spiral galaxies. Yet to properly attend to the question of the nature of mass distribution in ETGs, one needs to probe out to at least ∼5Re, where dark matter is expected to dominate the mass profiles. This is very expensive to do with stellar kinematics, even on a 10-m telescope, given that galaxy starlight is very faint in these outer regions and also bearing in mind that one has to contend with several degeneracies, e.g. mass-anisotropy degeneracy, stellar mass-dark matter degeneracy, mass inclination-flattening degeneracy, stellar initial mass function- adiabatic contraction degeneracy (see next section for more details). Strong gravitational lensing is also available to probe mass distribution within the Einstein radius (usually comparable to the inner 1Re) but its application is limited to the most-massive ETGs (e.g. Auger et al., 2010). Weak gravitational lensing (e.g. Hoekstra et al., 2013), galaxy satellites (e.g. Wojtak & Mamon, 2013), hot X-ray gas (e.g. Buote et al., 2007) and discrete mass tracers e.g. globular clusters (GCs) and planetary nebulae (PNe) are alternate candidates for probing mass distribution at large radii in ETGs. While these mass tracers have radial ranges over which they are more efficient, they also have limitations which make all of them apart 10 12 from the discrete tracers, inapplicable to study 10 − 10 M ETGs systematically. For example, weak lensing is more relevant for galaxy groups and clusters, galaxy satellites are limited by number statistics and X-ray haloes are mostly observed in the most-massive ETGs that often reside in dense environments.

1.1.4 Brief explanation of degeneracies in dynamical mass modelling

Degeneracies in dynamical mass modelling are a huge source of uncertainties when deter- mining the mass distribution in galaxies. Here, I describe them in more details.

• Mass-anisotropy degeneracy: The observed mass tracer kinematics is usually consistent with a wide range of total mass and orbital distributions (Binney & Ma- mon, 1982; Merriﬁeld & Kent, 1990; Gerhard et al., 1998;Lokas & Mamon, 2003; 1.1. Dark sectors of the universe 5

Napolitano et al., 2014; Pota et al., 2015, etc). For example, a radially declining velocity dispersion profile might be due to less mass at larger radii or a tracer velocity distribution dominated by radial orbits. Likewise, a flat or rising velocity dispersion profile might be indicative of more mass at larger radii or a tracer velocity distribution that is tangentially biased. This, therefore, means that mass determinations may not be unique unless the orbital distribution is well constrained.

• Stellar mass-dark matter degeneracy: Even when the total mass has been determined as accurately as possible, it is not immediately obvious how one should account for the portion of the measured total mass that is of stellar nature. This is because a reasonable but uncertain stellar mass-to-light conversion ratio has to be adopted to convert stellar light into mass. For example, if one assumes that the stars are at least 9 Gyrs old, the stellar mass-to-light ratio can vary from 0.6 to 1.2 (R¨ock et al., 2016), accounting for a factor of 2 diﬀerence in the inferred stellar mass estimate.

• Stellar initial mass function-adiabatic contraction degeneracy: The stellar systems of massive elliptical galaxies are dominated by low mass stars (e.g. van Dokkum & Conroy, 2010; Treu et al., 2010; Dutton et al., 2012) i.e. they are consistent with bottom heavy stellar initial mass function (IMF) e.g. Salpeter IMF. An IMF lighter than this, e.g Kroupa or Chabrier IMFs, implies less stellar mass at the same luminosity, thus more dark matter content may be inferred, similar to the eﬀect of adiabatic halo contraction (Blumenthal et al., 1986; Gnedin et al., 2004; Napoli- tano et al., 2010; Dutton et al., 2013) during smooth dissipative baryonic processes which drags dark matter towards the galaxy centres.

• Mass inclination-flattening degeneracy: This is similar in effect to the mass- anisotropy degeneracy. For edge-on, intrinsically flattened galaxies, if one assumes that they are spherical, then their masses would be over-estimated. On the contrary, for face-on, intrinsically flattened galaxies, their total masses would be underestimated if sphericity is assumed (Bacon, 1985; Bender et al., 1994). It is important to bear this degeneracy in mind since most dynamical modelling techniques operate under the assumption of sphericity. 6 Chapter 1. Introduction

1.2 Globular clusters

The use of GCs as mass probes boomed with the dawn of this century. This is mostly due to the advent of large telescopes and stable multi-object spectrographs e.g. the GEM- INI telescopes and GMOS, the Keck telescopes and DEIMOS, etc. GCs are luminous, compact, stable, self-gravitating stellar systems that are found in a wide range of galaxy morphologies (ETGs are usually very rich in GCs) and mass (Brodie & Strader, 2006). They are formed during periods of intense star formation in their host (or progenitor) galaxies (Strader et al., 2005). They are found in large numbers out to large radii from the centers of their host galaxies, hence they are ideal probes of their host galaxy’s gravitational potential even where the galaxy starlight is faint. It is interesting to note that the number of globular clusters in a galaxy scales directly and tightly with the virial mass of the galaxy (Blakeslee et al., 1997; Spitler & Forbes, 2009; Hudson et al., 2014; Harris et al., 2015; Forbes et al., 2016). From their ages (generally, age ≥ 10 Gyrs), we know that they have survived the formation and assembly history of the host galaxy, thus, they contain fossil records of the early universe and can also be used to probe galaxy formation.

1.2.1 Globular cluster kinematics as probes of galaxy formation

If the assumption that GCs witnessed the formation and assembly of their host galaxies is true, then one could expect that features seen in the galaxy kinematics should be observable in the GC kinematics as well. These features (Krajnovićet al., 2011) include counter-rotation components, misalignment between stellar kinematics axis and photometric axis, the so called double-sigma feature, kinematically decoupled cores, etc. What makes GCs even more powerful as tools in understanding galaxy kinematics is that they probe far out into the galaxy outskirts, where dynamical timescales are longer and relics of galaxy assembly could still be present. This is important since the often spectacular photometry markers (e.g. shells, plumes, streams, extended tidal tails, etc.) of galaxy assembly are too faint in the galaxy outskirts. We test this hypothesis in Chapter 2 by studying the globular cluster kinematics of NGC 4473, a galaxy with two bumps2 in its stellar kinematics velocity dispersion profile (this is the definitive signature of a double- sigma galaxy).

Kinematic studies restricted to the inner 1 Re (eﬀective radius) often do not give a complete picture of the complexities in galaxies. Even though half of the galaxy light is contained in this region, one needs to probe out to 5 Re to reach ∼ 50 per cent of the

2These bumps must be oﬀset along the major axis and symmetrically located around the galaxy center, they are believed to be the result of two superimposed, counter-rotating disk-like structures 1.3.Multi-objectspectroscopy 7 totalangularmomentum(Coccatoetal.,2009).Kinematicpatternsobservedwithin1 Re oftenchangeatlargerradii,indicatingadiﬀerentassemblychanneland/orepoch,from materialswithdecoupledangularmomentum.Forexample,centrallyfast-rotatorshave beenobservedtorotatemorerapidlyorevenrotatewithrapidlydecliningamplitudes inthegalaxyoutskirts(Arnoldetal.,2014).Studyingkinematicsouttolargeradiiin ETGsalsogivesustheimportantopportunitytounderstandmassdistributioninthe dark-matterdominatedrealmsinETGs.

1.2.2 Globularclustersasprobesofgalaxymass

InoneofthepioneeringworkswhichusedGCkinematicsdatatodeterminethemassof anETGoutsidethelocalgroup,theauthors,Huchra& Brodie(1987),remarkedthat ...thisapproachisexceedinglydiﬃcult. Itshouldbenotedthatittookalmost40yearsof braveeﬀorts,inseveralsmallsteps,toincreasethenumberofGCswithradialvelocity measurementsfrom17to70intheGalaxy(seeSlipher1917;Stromberg1925;Edmondson 1935;Mayall1946;Kinman1959).Remarkably,astheMW GCradialvelocitycatalog grewbyafactorof4,theuncertaintiesontheindividualvelocitiesreducedbyafactor ofalmost8to ∼20kms −1. Forcomparison,theaverageuncertaintyoftheGCradial velocitiesusedinHuchra& Brodie(1987)is ∼50kms −1. Morerecently( ∼100years afterSlipher 3 introducedhisGCradialvelocitycatalogtotheastronomycommunity), similarprogresshasbeenmadewithextragalacticGCsystems(e.g.Forbesetal.,2017). PreciselymeasuredGCradialvelocities(averageuncertaintyonmeasuredradialvelocities ∼13kms −1)arenowavailableinalargenumberofETGs,withstellarmassrangingfrom 10 10 −10 12 M .

1.3 Multi-objectspectroscopy

Theworkpresentedinthisthesiswouldnotbepossiblewithouttherelativelyrecentde- velopmentof6 −10m-classtelescopesandspectrographswithmultiplexingabilities.With asingleexposure,itisnowpossibletoobtainspectroscopicdataformultiplesourcesthat areclusteredwithintheﬁeld-of-viewofthedetectorintheplaneofthesky.Forexample, withina2-hrintegrationonKeck/DEIMOS 4instrument,wecanobtainspectrawithrea- sonablygoodsignaltonoiseratiofrom ∼100GCcandidatesdowntoamagnitudeof23 .5 inthe i-band.WiththesetupusedinHuchra&Brodie(1987),eachtargetrequiredupto

3Slipher(1917)reporteduncertaintiesof200 −300kms 1,whileMayall(1946)reporteduncertainties of ∼20kms 1,respectively 4DEepImagingMulti-ObjectSpectrograph 8 Chapter 1. Introduction

Figure 1.1 DEIMOS masks footprint for NGC 4473. Footprint of the four DEIMOS masks observed in NGC 4473 overlaid on a 27 × 20 arcmin (120 × 90 kpc) cutout from combined g, r, i-band Subaru/Suprime-Cam images. The red marks are the slits, positioned on globular cluster candidates, as shown in the inset image. The North and east directions are shown by the compass in the ﬁgure. Varying the position angles of the masks ensures that we have a good azimuthal coverage of the galaxy’s globular cluster system. 1.4. State of the data: GC kinematics data and systematic mass modelling of ETGs 9

0.5 − 4 hrs integration to obtain decent-enough spectrum, under similar seeing conditions. In the SLUGGS (SAGES Legacy Unifying Globulars and GalaxieS, Brodie et al. 2014) survey5, we further optimise the process by placing slits on GC candidates, initially iden- tiﬁed from wide-ﬁeld imaging usually from the Subaru/Suprime-Cam instrument. Figure 1.1 shows the DEIMOS masks footprint with slits targeting GC candidates in NGC 4473.

1.4 State of the data: GC kinematics data and systematic mass modelling of ETGs

11.5 11.0 10.5 It is now common for typical ≥ 10 , ∼10 and ≤ 10 M - stellar mass ETGs to have radial velocity sample sizes of ∼300, ∼70 and ∼30, respectively, usually extending −1 out to a large radii of ∼13 Re, with an average uncertainty of ∼13 km s on the radial velocities. Figure 1.2 shows the galactocentric distribution of all the GCs with radial velocity measurements in the SLUGGS survey. However, due to the relatively poor sample size of the low and intermediate stellar mass (≤ L∗) ETGs and the demands of the traditional mass modelling techniques for ETGs, these galaxies have seldom been probed to large radii. For example, Chanaméet al. (2008) showed that at least a sample of 100 GCs would be needed to reliably constrain the mass profiles of ETGs with the Schwarzschild’s orbit modelling technique. A similar limitation that has made the dynamical study of the less massive galaxies difficult is the requirement for the kinematic data to be binned, e.g. Jeans dynamical modelling, which, due to the paucity of the dataset as noted above, makes them unfit to be studied this way. While the most massive ETGs show that dark matter dominates the mass profiles at 11 large radii, results from some of the few intermediate stellar mass galaxies (M∗∼10 M ) probed out to large radii show some inconsistencies with expectations from ΛCDM cosmology, often reporting a dearth of dark matter in the galaxy outskirts (Romanowsky et al., 2003; Napolitano et al., 2009; Deason et al., 2012). It should be noted that these early studies used PNe as mass tracers. PNe could preferentially be on radial orbits (Dekel et al., 2005; Brodie & Strader, 2006), hence, these results need to be properly interpreted in view of the mass-anisotropy degeneracies. The picture is even worse for low-stellar mass ETGs, since they have hardly been probed out to large radii. It is interesting to note that even for the more massive galaxies, different mass modelling methods and assumptions often produce contradictory results with the same dataset, making the results difficult to interpret, e.g. the mass distribution studies of NGC 3379 by Romanowsky et al. (2003)

5http://sluggs.swin.edu.au 10 Chapter 1. Introduction

11.8 3

2 11.4 ) ¯ kpc 1 ) /σ / M 0 11.0 ∗ sys

1 log( M ( V − 2 10.6

3 10.2 0 5 10 15 20 25 30 R/Re

Figure 1.2 Radial velocities of globular clusters from the SLUGGS survey. Radial velocities of the ∼4000 globular clusters from the SLUGGS survey sample of 25 early-type galaxies obtained with multi-object spectroscopy on the Keck II telescope with the DEIMOS instrument, normalised by their respective galaxy central velocity dispersion. Vsys is the systemic velocity of the respective host galaxies. The circles are the individual GCs and they have been coloured according to the stellar mass of their host galaxies, as shown in the colour bar. On average, globular cluster radial velocities are available out to 13 Re for SLUGGS survey galaxies. 1.4. State of the data: GC kinematics data and systematic mass modelling of ETGs 11 and de Lorenzi et al. (2009). Based on the foregoing, there is therefore the need to adopt a mass estimation method suitable for use in galaxies where the GC kinematics data could be as small as 20 in order to probe the mass distribution in ETGs systematically. The method obviously has to do away with the need to bin the data. Furthermore, it should be ﬂexible enough to accom- modate corrections, where necessary, due to the orbital anisotropy of the tracers, the mass support of the galaxy due to rotation, inclination and ﬂattening of the galaxy. Moreover, the opportunity cost of systematically probing mass distribution across two orders of magnitude in stellar mass out to large radii should only be the loss of sophistication in method and not in accuracy or reliability. I address these concerns in Chapters 3 and 4, adopting the tracer mass estimator of Watkins et al. (2010) and applying relevant corrections as explained in those chapters.

1.4.1 Testing expectations from ΛCDM cosmological simulations

Galaxy simulations have steadily become more realistic, with reasonably accurate im- plementations of feedback and naturally producing galaxies of diﬀerent morphologies in approximately the right proportions that is observed (e.g. Vogelsberger et al., 2014; Schaye et al., 2015; Remus et al., 2017). Though there still remains a plethora of issues to be resolved, mostly due to resolution limitations and the complex interplay between baryons and dark matter during galaxy formation and evolution, we can however, now, compare mass distribution at large radii with expectations from these state-of-the-art cosmological simulations based on ΛCDM cosmology. This avoids the well known tension at smaller radial scales (< 10 kpc), i.e. the cusp-core problem, and provides another alternative to see if our understanding of the universe as encapsulated in the ΛCDM paradigm is adequate.

1.4.2 Mass distribution and halo assembly epochs

If the mass distribution is parametrised in terms of the dark matter density, then some extra insight on the formation and assembly history of ETGs can be gained. This is because the initial dark matter density is set by the density of the universe when the haloes assembled (Gunn & Gott, 1972). Haloes which assembled when the universe was younger would have higher dark matter densities, and vice versa. These densities may have been altered during galaxy formation and evolution through processes such as adiabatic halo contraction (e.g. Blumenthal et al., 1986), halo expansion (e.g. El-Zant et al., 2001), gravitational halo heating (e.g. Johansson et al., 2009), feedbacks (e.g. Croton et al., 2006; Macci`oet al., 2012), especially within the core radius of the dark matter halo. The 12 Chapter 1. Introduction assembly epochs of the haloes can then be compared with the average stellar age to see if there is a decoupling or co-evolution of the DM haloes and the baryonic components. I use this approach to study the assembly epochs of ETGs in Chapter 4.

1.5 Thesis outline

This thesis aims to use globular cluster kinematics data to understand galaxy formation and evolution, first, by probing galaxy kinematics out to large radii and second, by systematically obtaining mass distribution out to large radii in a large sample of early-type galaxies. In Chapter 2, I study the GC kinematics of NGC 4473, a so-called double-sigma galaxy, using data obtained from HST, Subaru and Keck telescopes. Using GC kinematics data which extends out to 9 Re, I investigate the radial extent of the double-sigma feature. I compare the globular cluster kinematics with earlier results obtained from stellar kinematics in the most central parts (Cappellari & McDermid, 2005) and even more extended stellar kinematics (Foster et al., 2013). I also compare my results with predictions from idealised galaxy mergers. Finally, I investigate if the GC system share a common history with the galaxy stars. In Chapter 3, I study mass distribution in a sample of 23 ETGs using data obtained from Keck/DEIMOS instrument. The galaxies span a wide range of stellar masses, environments and morphologies. I investigate if the tracer mass estimation method is applica- ble for use with GC kinematics data. I further show the nature of corrections that must be applied if the mass estimates are to be reliable. I compare my mass estimates with results from the literature, obtained using different mass tracers and modelling techniques. I then investigate the nature of mass distribution in the galaxy outer parts, parametrised as dark matter fraction, which I then compare with a simple galaxy model based on galaxy scaling 11.0 relations. Lastly, I try to understand why a few ∼10 M ETGs systematically deviate from ΛCDM predictions. In Chapter 4, I expand the sample of ETGs studied in chapter 3 to 32, supplementing Keck/DEIMOS GC kinematics data with data from the literature. Here, I use homogeneously measured galaxy sizes, stellar masses and Sérsic indices from Forbes et al. (2016) and re-derive the dark matter fractions for the new galaxy sample. I compare the dark matter fractions to expectations from state-of-the-art cosmological hydrodynamical simulations, with and without feedback. I also use the mass distributions to investigate the halo structural parameters and infer the epoch of halo assembly. Lastly, I compare the halo assembly epoch with the average stellar age to better understand how ETGs formed. 1.5. Thesis outline 13

In Chapter 5, I summarise the results obtained in this PhD thesis and suggest future directions to be explored.

2 Globular cluster kinematics of a double-sigma galaxy - NGC 4473

but one galaxy diﬀers from the other galaxy in splendour —Pauline text adapted

15 MNRAS 452, 2208–2219 (2015) doi:10.1093/mnras/stv1426

The SLUGGS survey: globular cluster kinematics in a ‘double sigma’ galaxy – NGC 4473

Adebusola B. Alabi,1‹ Caroline Foster,2 Duncan A. Forbes,1‹ Aaron J. Romanowsky,3,4‹ Nicola Pastorello,1 Jean P. Brodie,3 Lee R. Spitler,2,5 Jay Strader6 and Christopher Usher1 1Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn, VIC 3122, Australia 2Australian Astronomical Observatory, PO Box 915, North Ryde, NSW 1670, Australia 3University of California Observatories, 1156 High Street, Santa Cruz, CA 95064, USA 4Department of Physics and Astronomy, San Jose´ State University, San Jose, CA 95192, USA 5Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia 6Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA

Accepted 2015 June 24. Received 2015 June 23; in original form 2015 March 4

ABSTRACT NGC 4473 is a so-called double sigma (2σ ) galaxy, i.e. a galaxy with rare, double peaks in its 2D stellar velocity dispersion. Here, we present the globular cluster (GC) kinematics in NGC 4473 out to ∼10Re (effective radii) using data from combined Hubble Space Telescope/Advanced Camera for Surveys and Subaru/Suprime-Cam imaging and Keck/Deep Imaging Multi-Object Spectrograph. We find that the 2σ nature of NGC 4473 persists up to 3Re, though it becomes misaligned to the photometric major axis. We also observe a significant offset between the stellar and GC rotation amplitudes. This offset can be understood as a co-addition of counter- rotating stars producing little net stellar rotation. We identify a sharp radial transition in the GC kinematics at ∼4Re suggesting a well defined kinematically distinct halo. In the inner region (<4Re), the blue GCs rotate along the photometric major axis, but in an opposite direction to the galaxy stars and red GCs. In the outer region (>4Re), the red GCs rotate in an opposite direction compared to the inner region red GCs, along the photometric major axis, while the blue GCs rotate along an axis intermediate between the major and minor photometric axes. We also find a kinematically distinct population of very red GCs in the inner region with elevated rotation amplitude and velocity dispersion. The multiple kinematic components in NGC 4473 highlight the complex formation and evolutionary history of this 2σ galaxy, as well as a distinct transition between the inner and outer components. Key words: galaxies: evolution – galaxies: kinematics and dynamics – galaxies: star clusters: general.

More recently, the probed radii have been extended into the halo 1 INTRODUCTION region, where some of these features have been shown to persist, Kinematically distinct components (KDCs) in early-type galaxies while in others, changes are seen at large radii (Arnold et al. 2014; (ETGs) provide clues about their formation and evolution. The Raskutti, Greene & Murphy 2014; Foster et al. 2015). Stellar light KDCs can be viewed as fossils of the accretion and merger pro- is, however, faint in the halo region, hence the need for bright kine- cesses that built up present-day galaxies in the hierarchical for- matic tracers like planetary nebulae and globular clusters (GCs). mation framework. Early studies of the kinematics of ETGs were Galaxies, apart from forming GCs ‘in situ’, are expected to have limited to the central regions, where rotation, sometimes along acquired some GCs formed ‘ex situ’ through galaxy mergers in a misaligned or twisted rotation axis, and KDCs were observed the two-phase galaxy formation model (e.g. Oser et al. 2010). Al- (Davies et al. 2001; Emsellem et al. 2004; Krajnovicetal.´ 2011). most all ETGs, studied with deep enough photometry, have been shown to have at least a bimodal GC colour distribution (e.g. Ostrov, Geisler & Forte 1993; Zepf & Ashman 1993). This colour E-mail: [email protected] (ABA); [email protected] (DAF); bimodality usually points at an underlying bimodality in metallicity [email protected] (AJR) (Usher et al. 2012), which has been linked with the hierarchical

C 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Globular cluster kinematics in NGC 4473 2209

merging history of the host galaxies (Tonini 2013). It is possible, by et al. (2013) were able to identify a KDH, they could only probe observing correlations in position–velocity parameter space of GCs the inner edge of this region. GCs are better suited to probe this (Romanowsky et al. 2012; Blom et al. 2014;Fosteretal.2014), to KDH properly. We therefore study the radial profile of the GC unearth relics of the assembly history of the host galaxy. This is system kinematics, with particular interest in any sharp kinematic because in the galaxy outskirts, dynamical time-scales are longer transition(s). These transitions can be used to understand the nature – on the order of ∼1 Gyr (Coccato, Arnaboldi & Gerhard 2013), of the last major merger the galaxy experienced, as proposed by hence a ‘memory’ of the infalling galaxies’ orbital properties is ex- Hoffman et al. (2010). We also investigate the radial extent of the 2σ pected to be retained (Johnston, Hernquist & Bolte 1996; Helmi & velocity dispersion feature, using GCs. We study the kinematics of White 1999). GCs therefore contain fossil records of the chemical the blue and red GC subpopulations separately: differences in their and dynamical processes that shaped the structure of present-day kinematics, besides providing additional evidence for GC colour galaxies. Similarities between the kinematics (amplitude of rotation bimodality, also provide clues about the progenitor galaxies (Bekki velocity, velocity dispersion, direction of rotation, etc.) of stars and et al. 2005). GCs in galaxies (Foster et al. 2011;Potaetal.2013) can be used to This paper is structured as follows. In Section 2, we present the further constrain their likely assembly history. photometric and spectroscopic data used in this study. In Section 3, Double sigma (2σ ) galaxies (Krajnovicetal.´ 2011) are examples we focus on the photometric analysis, produce 2D mean velocity of multispin galaxies (Rubin 1994), easily identified by observing and velocity dispersion maps, as well as statistically determine the their stellar two-dimensional (2D) velocity dispersion maps. These significance of the 2σ feature. We also produce one-dimensional maps uniquely show a pair of symmetric, off-centre, significant (1D) kinematic radial and colour profiles. Section 3 ends with a bumps (2σ peaks) aligned along the photometric major axis (Bois discussion of the line-of-sight velocity distributions (LOSVDs) of et al. 2011; Krajnovicetal.´ 2011;Fosteretal.2013). This feature has the GC system. In Section 4, we briefly summarize models from been linked to the presence of a pair of extended, counter-rotating the literature which form 2σ galaxies. In Section 5, we discuss disc-like stellar structures at the centre of the galaxy. 2σ galaxies are our results, relating them to model predictions from the literature. rare – ∼4 per cent in the ATLAS3D survey (Krajnovicetal.´ 2011) Finally, in Section 6, we briefly summarize the paper. – probably because the conditions required to produce them are uncommon, as shown in idealized binary merger simulations (e.g. Jesseit et al. 2007;Boisetal.2011). They were formed in these 2 OBSERVATIONS AND DATA REDUCTION simulations only when the merging spiral progenitors have similar masses (mass ratio 1:1 to 3:1) and are coplanar (Crocker et al. 2009). NGC 4473 was observed with Suprime-Cam on the Subaru tele- It should be noted that an alternative channel for forming galaxies scope on the night of 2010 November 4. The total exposure times with counter-rotating stellar components is accretion of cold gas were 688, 270 and 450 s with average seeing of 0.65, 0.65 and along cosmological filaments (Rix et al. 1992; Thakar & Ryden 0.67 arcsec in the g, r and i bands, respectively. The raw images were 1996; Algorry et al. 2014). Generally, the 2σ galaxies from the reduced using the SDFRED2 reduction pipeline (Ouchi et al. 2004). 3D ATLAS survey are flattened (ellipticity, >0.4), viewed at high To detect GCs, a model of the galaxy light using the IRAF/ELLIPSE task ◦ inclination (i>70 ) and have low to intermediate luminosities. was first subtracted from the reduced images and the IRAF/DAOFIND NGC 4473 is the most massive known 2σ galaxy (Krajnovicetal.´ task was then used to find bright and compact objects. At a distance 2011), though it can be described as an L∗ galaxy. It has an absolute of 15.2 Mpc, GCs in NGC 4473 are unresolved and appear as point magnitude of MK =−23.8 and is photometrically undisturbed. It is a sources. The objects detected from different bands were matched flattened ( = 0.43) elliptical galaxy at a distance of 15.2 Mpc in the and aperture photometry was carried out with the IRAF/PHOT task Virgo Cluster, with effective radius Re of 27 arcsec and photometric to remove extended sources using the method described in Spitler position angle of 92◦.2 (Brodie et al. 2014, and references therein). et al. (2008). Finally, we corrected our photometry for reddening −1 It has a galaxy recession velocity (Vsys) of 2260 km s .ASersic´ using the dust extinction maps from Schlegel, Finkbeiner & Davis function fit to its surface brightness shows that NGC 4473 is a (1998). We used a (g − r)versus(r − i) colour–colour plot to ‘cuspy’ galaxy with excess central light (Kormendy et al. 2009; identify GC candidates. We supplement our photometric catalogue Dullo & Graham 2013), suggesting a dissipative merger origin. It with g-andz-band photometry from the Hubble Space Telescope has fast rotation in its inner region (<1Re) and harbours a pair of (HST) Advanced Camera for Surveys (ACS) for NGC 4473 (see counter-rotating stellar discs (Cappellari et al. 2007; Krajnovicetal.´ Spitler et al. 2006; Strader et al. 2006, for details of the photometric 2011). Foster et al. (2013) studied the stellar kinematics out to ∼3Re reduction). We used the colour transformation equation from Usher and observed counter-rotation which extends beyond ∼60 arcsec et al. (2012) to convert the HST z-band photometry into the i band. along the photometric major axis. They used the Stellar Kinematics Our final photometric catalogue consists of 1097 GC candidates. with Multiple Slits (SKiMS) method (Norris et al. 2008;Proctor We used the Deep Imaging Multi-Object Spectrograph et al. 2009) which extends the stellar kinematics to relatively large (DEIMOS) on the Keck II telescope to obtain spectra for objects radii. They also identified multiple stellar kinematic components in that are probable GCs from our photometric catalogue. The spec- the galaxy outskirts, rotating along both the photometric major and troscopic observations were taken on the nights of 2011 March 30, minor axes. They concluded therefore that NGC 4473 is triaxial, 2012 February 19 and 2012 February 20. Seeing was between 0.7 with a kinematically distinct halo (KDH). and 0.95 arcsec and four DEIMOS masks were observed during the Here, we study the kinematics of the GC system of NGC 4473 campaign. We used the usual SLUGGS set-up described in Pota using photometric and spectroscopic data from the SAGES Legacy et al. (2013) and integrated for 2 h per mask, though one of the Unifying Globulars and Galaxies (SLUGGS)1 survey (Brodie et al. masks was observed for 2.75 h. We reduced our raw spectra using 2014) out to large galactocentric radii (i.e. ∼10Re). While Foster the DEEP SPEC2D pipeline (Cooper et al. 2012)inIDL. We determined the heliocentric radial velocities by cross-correlating each spectrum with 13 stellar templates, obtained with the same DEIMOS instru- 1 http://sluggs.swin.edu.au/ mental set-up, using the IRAF/RV.FXCOR task. For each object, the

MNRAS 452, 2208–2219 (2015) 2210 A. B. Alabi et al.

Table 1. Spectroscopically conﬁrmed GCs, stars and galaxies. Column (1): object identiﬁer, written as galaxy name and object type (GC, stars and galaxies). Columns (2) and (3): object position (RA and Dec., respectively) in degrees (J2000.0). Columns (4) and (5): measured heliocentric radial velocities and uncertainties, respectively. Columns (6)–(11): Subaru gri photometry and corresponding uncertainties. The photometry has been corrected for Galactic extinction. The full version of this table is available in the online version.

ID RA Dec. V Vggrrii (◦)(◦)(kms−1)(kms−1) (mag) (mag) (mag) (mag) (mag) (mag) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

NGC 4473_GC1 187.45086 13.42309 2112 14 22.492 0.016 21.905 0.016 21.640 0.017 NGC 4473_GC2 187.45636 13.42486 2390 12 22.024 0.013 21.387 0.013 21.102 0.014 NGC 4473_GC3 187.46807 13.42744 2524 20 21.715 0.009 20.953 0.009 20.569 0.008 NGC 4473_GC4 187.46594 13.42724 2327 12 23.364 0.022 22.679 0.022 22.309 0.024 NGC 4473_GC5 187.46444 13.43094 2279 12 22.251 0.011 22.682 0.012 21.442 0.013 ...... NGC 4473_star1 187.47899 13.52667 −206 12 22.992 0.011 22.391 0.011 22.196 0.011 NGC 4473_star2 187.38470 13.53626 −148 23 22.609 0.009 22.095 0.010 21.915 0.010 ...... NGC 4473_gal1 187.42701 13.48026 z = 0.3 – 23.067 0.011 22.464 0.011 22.284 0.012 NGC 4473_gal2 187.52558 13.36814 – – 22.595 0.010 22.107 0.010 21.863 0.010 ...... radial velocity is the average of the measured radial velocities from FXCOR. The uncertainty of each radial velocity is estimated by adding in quadrature the error output from FXCOR to the standard deviation among the templates, which is an estimate of the systematics. The peaks of the calcium triplet (CaT) lines (at 8498, 8542 and 8662 Å) and the Hα (6563 Å) line were used to identify GCs associated with NGC 4473 based on their radial velocities. For secure GC confirmation, we require at least two clearly visible CaT lines (usually 8542 and 8662 Å) and the Hα when probed, as well as GC- status consensus by at least two members of the team. Four spectroscopic GCs had repeated measurements from different masks, all in good agreement and consistent within the uncertainties associated with our observations. The final measurements used for these objects (and recorded in our final spectroscopic object catalogue) are the weighted average of the individual measurements. These repeated observations show that the errors in our radial velocity measurements are ≤15 km s−1. Our final spectroscopic catalogue (see Table 1) contains 105 unique GCs with redshift-corrected radial velocities, alongside Galactic stars and background galaxies. Figure 1. GC radial velocity distribution as a function of galactocentric radius. The solid line and dashed curves show the recession velocity of In Fig. 1 we show the radial velocity distribution of GCs as NGC 4473 and the 3σ envelope of GC velocities, respectively. Blue circles a function of galactocentric radius. We have used the FRIENDLESS and red stars are spectroscopically confirmed blue and red GCs, respectively. algorithm of Merrett et al. (2003) to identify possible outliers from our spectroscopic GC catalogue. We implemented the algorithm to ω ≈− identify objects with radial velocities outside the 3σ envelope of (using the integrated magnitude of -Cen, Mi 11.0 mag from their 20 nearest neighbours. The algorithm returned no outliers. We Pota et al. 2013, and distance modulus from Villegas et al. 2010) note here the apparent asymmetry in the velocity distribution in the to isolate likely ultracompact dwarf (UCD) candidates from our inner 2 arcmin, especially in the red GCs. This can be viewed as sample, since they may have different chemodynamical properties a signature of rotation, an issue we explore in details later in this (see Strader et al. 2011). While this cut excludes the two brightest paper. GCs in our sample (with i-band magnitudes of 19.8 and 19.85), we however chose to retain them after cross-matching them with the published catalogue of GCs in NGC 4473 from Jordan et al. (2009), where they have sizes consistent with being GCs. 3ANALYSIS Using the Gaussian Mixture Modelling (GMM) code by Muratov & Gnedin (2010), we determine that the GC colour distribution of 3.1 Photometric analysis NGC 4473 is best described by a bimodal, heteroscedastic distri- The final colour–magnitude diagram (CMD) of all unique GC can- bution at a 99.99 per cent significance level. This is shown in the didates from the combined HST and Subaru data, brighter than histogram in the bottom panel of Fig. 2, where the modes are clearly i < 23.5 mag – 1 mag fainter than the GC turnover magnitude, well separated. The (g − i) peaks for the Gaussian modes are 0.78 MTOM, i =−8.4 mag, from Villegas et al. (2010)–isshowninthe and 1.06 with dispersions of 0.08 and 0.09, respectively. We group upper panel of Fig. 2. We use an upper magnitude cut of i ≥ 19.9 mag our GC candidates into blue and red GC subpopulations, using a

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Gaussian kernels that vary linearly with radius to recover the global kinematics. We produce mean velocity and velocity dispersion 2D maps for combined Spectrographic Areal Unit for Research on Op- tical Nebulae (SAURON; Emsellem et al. 2004) and SKiMS data (Foster et al. 2013) for comparison. Even though the data sets have different spatial extents and sampling, the maps agree well. In the left-hand panel of Fig. 3, where we have combined SAURON and SKiMS data, NGC 4473 shows an axisymmetric, disc-like structure that extends to the edges of the SAURON map. The dumb-bell feature in the velocity dispersion map (right-hand panel of Fig. 3) is typical of 2σ galaxies and the peaks are separated by ∼3Re.The kinematic position angle (PAkin), defined as the angle between the direction of maximum rotation and north, is aligned with the photometric major axis (92◦.2). There is significant minor axis rotation beyond 50 arcsec as well as counter-rotation along the photometric major axis (as reported by Foster et al. 2013). Note that rotation along an axis, e.g. major axis, implies that the velocity signature would be seen around the perpendicular axis, i.e. the minor axis. Figure 2. GC (g − i) colour distribution. Top panel: CMD of GC candidates In Fig. 4, the red GCs dominate the rotation of the GC system in ∼ from HST and Subaru photometric catalogues. Black, open and filled circles the inner 7Re region, resulting in 2D maps akin to that of the are HST and Subaru GC candidates, respectively. The vertical line (in both galaxy stars, with counter-rotation evident along the photometric panels) shows the fiducial colour cut (g − i) = 0.93 mag used to separate blue major axis (bottom left-hand panel of Fig. 4). The mean velocity and red GCs in our spectroscopically confirmed sample. Mean photometric map of the blue GCs (middle left-hand panel) shows a non-regular uncertainties are shown on the right as error bars. Bottom panel: black rotation pattern, especially in the outer region, with rotation along histogram is the distribution of GC colour from combined HST and Subaru an axis intermediate to the photometric major and minor axes. The photometric catalogues, while the red histogram is the colour distribution of velocity dispersion maps for the blue and red GCs are similar, with spectroscopically confirmed GCs. Gaussian fits from GMM are overplotted the red GCs having higher velocity dispersion within the inner ∼7R on the histogram. The GC colour distribution is bimodal at a 99.99 per cent e region. However, we see a 2σ -like feature in the velocity disper- significance level. sion map when all the GCs are combined together (top right-hand panel). These elevated, offset bumps in the 2D velocity disper- fiducial colour split of (g − i) = 0.93 mag, and find that the fractions sion map are however not aligned along the photometric major of blue and red GCs in our photometric sample are 0.58 and 0.42, axis. respectively.

3.2 Mean velocity and velocity dispersion 2D maps 3.3 Significance of the extended 2σ feature We use the method of Coccato et al. (2009) and Pota et al. (2013) To determine how far out the 2σ feature extends in the galaxy stars to construct mean radial velocity and velocity dispersion 2D maps and GCs, we assume that our measured velocities (and their asso- for the spectroscopic GC sample. We construct an equally spaced ciated errors), at all positions on the sky, are drawn from the same n × m = 100 × 100 grid in position space and at every grid point, we distribution (see Walker et al. 2006). We then create mock cata- use the N-nearest GCs to compute the interpolated mean velocity, logues (Nsim = 1000), using the same sky positions as in our real v¯(i,j), and velocity dispersion, σ (i, j) (see equations 1 and 2), catalogue, but with velocities (and errors) drawn randomly, with- weighting the measured radial velocities, Vk(α, δ), by the inverse out replacement, from the measured values. This non-parametric square of their separations from the grid point, wk. The optimal approach ensures that each mock catalogue has the same velocity number of the nearest neighbours, N = 10, used was determined as distribution as the measured data, but destroys any correlation be- the square-root of the GC sample size, as suggested by Pinkney et al. tween position and velocities. We use the method in Section 3.2 to (1996). We however varied this by 20 per cent to test the robustness then make velocity dispersion maps for each mock catalogue, and of our maps (i.e. N = 8, 12) and found no significant difference in note the maximum velocity dispersion, σ mock, per mock catalogue. the map features. It should be noted that the maps we show here The significance of the 2σ feature at every grid point p(i, j)isthen are mostly illustrative, hence we only quote qualitative trends from quantified as the ratio N(σ real(i, j) >σmock)/Nsim. From Fig. 5,the them: 2σ feature is significant in both galaxy stars and GCs with p > 0.95. σ N V α, δ /w 2 The symmetrical form of the 2 feature is observed in the GCs as k=1 k( ) k ◦ v¯(i,j) = , (1) well, within ∼3Re, though it appears inclined at ∼30 to the photo- N /w2 k=1 1 k metric major axis. This misalignment needs to be studied in more detail to understand its true nature. However, from the mean veloc- 1/2 N 2 2 Vk(α, δ) /wk itymapsinFig.4, a large velocity difference is evident between σ i,j = k=1 − v i,j 2 − v i,j 2 . ( ) N ¯( ) ¯( ) (2) the blue and red GCs in the spatial region corresponding to the 2σ 1/w2 k=1 k feature. Also, these velocity offset regions are misaligned, with the In equations (1) and (2), (i, j)and(α, δ) are grid and sky coordi- blue GCs rotating along an axis intermediate to the photometric nates, respectively, v¯(i,j) is obtained as in equation (1) but using major and minor axis, coincident with the axis of the misaligned 2σ the estimated uncertainties and w = (α − i)2 + (δ − j)2. The 2D feature. We therefore conclude that the blue GCs drive the observed maps shown in Figs 3 and 4 have additionally been smoothed with misalignment in the 2σ feature.

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Figure 3. 2D smoothed mean velocity (left-hand panel) and velocity dispersion (right-hand panel) maps for galaxy stars in NGC 4473, using data from SAURON (Emsellem et al. 2004) and SKiMS (Foster et al. 2013). In the left-hand panel, rapid disc-like rotation and counter-rotation beyond the footprint of the SAURON data (i.e. ≤1Re) can be seen along the photometric major axis. In the right-hand panel, the 2σ feature is prominent along the major axis. Stellar isophotes at 1 and 2Re have been overplotted in both panels.

Figure 4. 2D smoothed mean velocity (left-hand panels) and velocity dispersion (right-hand panels) maps for GCs in NGC 4473. In the top, middle and bottom panels, we show all the GCs, the blue GCs and red GCs, respectively, using the method described in Section 3.2. The ellipses are 2 and 7Re stellar isophotes and the circles correspond to observed GC positions. In the top right-hand panel, there are signs of the 2σ feature in the velocity dispersion map for all GCs out to ∼3Re, although misaligned to the photometric major axis. In the middle left-hand panel, the blue GCs rotate intermediate between the photometric major and minor axes in the galaxy outskirts, while in the bottom panel, the red GCs counter-rotate along the photometric major axis, similar to the galaxy stars as showninFig.3.

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We therefore consider two cases: (i) where we fix qkin = qphot and (ii) qkin = 1. Both cases result in similar GC kinematics, hence we adopt profiles where qkin = qphot, as done by Foster et al. (2013). We fit kinematic parameters by minimizing the function in equation (5) in rolling bins of fixed bin size (N = 20), starting with the innermost GCs. This choice of bin size ensures that Vrot is not artificially inflated,2 especially when rotation is small. To obtain the 68 per cent confidence interval on our kinematic parameters, we randomly sample 1000 times (with replacement) from each bin and minimize the function in equation (5). The bin is continuously updated by deleting the innermost object and adding the next further out GC until we get to the outer radial boundary. In Fig. 6, we show radial profiles of the kinematic parameters for SAURON, SKiMS, blue and red GCs data for NGC 4473. The kinematic parameters for SAURON and SKiMS data were obtained using the method described in Foster et al. (2011). We fit for Vrot and PA kin together, and σ separately, keeping qkin = qphot for consistency. We have applied an offset of 20 km s−1 to the SAURON velocity dispersion as discussed in Arnold et al. (2014) and Foster et al. −1 (2015). We constrained Vrot and σ to vary between 0 and 300 km s while PAkin was allowed to vary freely in order to probe all possible kinematic components. The model we fit may not be sensitive to the radially superimposed components identified in the stellar kinematics study of Foster et al. (2013), since it fits a single component function at every radius. To unravel the likely degeneracy in the kinematics, we therefore study kinematics in the blue and red GCs, separately. Figure 5. Contours of the 2σ velocity dispersion feature in galaxy stars (top panel) and GCs (bottom panel). Contour levels are taken from the fraction of While contamination from the overlapping tails of the blue and red mock catalogues with a maximum velocity dispersion less than the estimate GC distributions could introduce some uncertainty in our fit, we ex- from the observed velocity dispersion. Blue and red GCs are overplotted in pect our fit to be robust enough to show dominant kinematic trends. the bottom panel as blue circles and red stars, respectively. The ellipse in As a further test of the robustness of our fit, we obtain kinematic the top panel is the 2Re stellar isophote. In the bottom panel, we show the 2 profiles for the GC subpopulations, adopting only GCs with clas- and 7Re stellar isophotes. The 2σ feature is significant in the GCs, along an sification probability greater than 0.68. We recover profiles similar ∼ ◦ ∼ axis inclined at 30 to the photometric major axis, out to 3Re. to those obtained when we applied a straight colour cut, confirming that our fitting is indeed robust against the overlap. We also tested 3.4 Kinematic 1D radial profiles the robustness of our fit against the choice of N, the number of GCs = To understand the 1D kinematic radial profiles of the GC system, per bin. We varied N by 20 per cent (i.e. N 16, 24) and found that we fit an inclined disc model to our discrete GC data (Foster et al. our kinematic profiles are similar in all cases. 2011). We evaluate the circularized galactocentric radius, R,using As seen in Fig. 6, the blue and red GCs show similar rotation amplitude profiles at all radii. However, there is a large and significant Y 2 offset between their rotation amplitudes compared to that of the R = q X2 + , phot q (3) galaxy stars. This is strange and contrary to results from previous phot studies (e.g. Pota et al. 2013) of other GC systems where the stellar where qphot is the ratio of the minor to major photometric axis rotation profile usually matches with that of the red GCs, though a (qphot = 1 − ), and X and Y are the projected Cartesian coordinates similar discrepancy was observed in NGC 4494 (Foster et al. 2011). of individual GCs on the sky, relative to the galaxy photometric We tentatively associate this offset with the counter-rotating stellar axes. The model we fit is discs believed to be responsible for the 2σ feature – an issue we V address later in Section 5. Here we investigate further by modelling V = V ± rot , mod,i sys (4) the kinematics for all the GCs (i.e. combined blue and red GCs) in − 2 + tan(PAi PAkin) 1 q the region where we have very good azimuthal sampling and Vrot is kin ≤ significantly high ( 4Re), and show the result in Fig. 7. Vrot for all as in Foster et al. (2011), Blom et al. (2012) and Pota et al. (2013), GCs is significantly reduced, and comparable to that of the galaxy where we minimize the function stars, giving credence to our earlier hypothesis. V − V 2 The velocity dispersion profiles for both GC subpopulations are 2 ( i mod,i) 2 2 χ ∝ + ln(σ + (Vi ) ) (5) σ 2 + V 2 similar in the inner ∼4Re region. We see signs of decline in the i ( ( i ) ) velocity dispersion of the red GCs while the blue GCs maintain to obtain the best-fitting amplitude of rotation Vrot, velocity dis- a flat profile. In the region of overlap (see Fig. 7), the velocity persion σ and PAkin. In equations (4) and (5), Vsys is the recession dispersion profiles of the red GCs and galaxy stars are similar. velocity of the galaxy, while Vi, Vi and PAi are the radial velocities, uncertainties in measured radial velocities and position angle 2 The amplitude of velocity rotation is artificially inflated when V /σ ≤ for the ith GC, respectively. We do not fit for qkin, the flattening rot 20 due to rotation, since it is not easily constrained with sparse data. 0.55 N (Strader et al. 2011).

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Figure 6. Kinematic radial profiles for blue and red GCs and stars in NGC 4473. Top, middle and bottom panels show the rotation velocity (Vrot), velocity dispersion (σ ) and kinematic position angle (PAkin) from the kinematic fit, respectively. We show 68 per cent confidence interval contours in all panels. Blue (solid), red (dashed), green and black contours are for blue GCs, red GCs, SKiMS and SAURON data, respectively. Note the offset in rotation amplitude between galaxy stars and GCs in the top panel. In the middle panel, the blue GCs have a flat velocity dispersion profile. In the bottom panel, the dashed and dot–dashed lines are the photometric major and minor axes, respectively. The galaxy stars have major and minor axis rotation while the red GCs at <4Re rotate in the same sense as the galaxy stars. There is significant counter-rotation along the major axis between the inner blue and red GCs up to ∼4Re. Beyond this, the red GCs begin to wrap around the north direction, rotating along the major axis, but in opposite direction to the galaxy stars. The blue GCs can be seento rotate predominantly along the minor axis in the outer regions.

Both GC subpopulations, however, differ in their PAkin profiles. In the inner 4Re, the blue and red GCs counter-rotate along the photometric major axis, with the red GCs rotating in the same sense as the inner galaxy stars. The red GCs in the outer region (>4Re) also rotate along the photometric major axis but counter-rotate with respect to the inner red GCs. In the outer region, the blue GCs show rotation along the minor axis, with multiple components. Hence, we a see counter-rotation along the photometric major axis as well as a minor axis rotation in the GC kinematics, similar to the result of Foster et al. (2013) for the stellar component. In the study of GC kinematics, it is possible to overestimate the rotation amplitude (Sharples et al. 1998; Romanowsky et al. 2009; Strader et al. 2011; Zhang et al. 2015), and we therefore perform statistical tests to ascertain that our rotation profile is real. We quantify possible bias using GCs in the inner (≤4Re) radial bin by generat- ing artificial discrete velocities at the GC position angles using our kinematic model. In the model, we fix σ and PAkin to the best-fitting values for this region and vary Vrot over the range of possible values −1 (from 0 to 300 km s ). Vrot retrieved from the artificial data set reveals that our kinematic fitting only suffers from bias at extreme Figure 7. Same as in Fig. 6, but for stars and all GCs in the inner ≤4Re, with the purple lines now showing profiles for all the GCs, binned together rotation amplitudes, i.e. we tend to overestimate Vrot at low intrin- −1 in this region, regardless of their colour. We show the 1σ uncertainties sic rotation amplitudes (e.g. at 30 km s , we overestimate Vrot by − for SAURON, SKiMS and all GCs. In the bottom panel, we do not show 30 km s 1) and underestimate at very high rotation amplitudes (e.g. −1 −1 the uncertainties for clarity. The rotation amplitude, when the GCs are not at 270 km s , we underestimate Vrot by 20 km s ). At the best- separated by colour, is now significantly reduced with respect to that of the fitting values for the blue GCs, the bias in Vrot is negligible, while blue and red GCs, and now comparable to that of the stars. for the red GCs, it is ∼10 km s−1.

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Figure 8. Rotation dominance, Vrot/σ (top panel) and Vrms (bottom panel) profiles for blue GCs and red GCs. Colour scheme is the same as in Fig. 6. Below the dashed horizontal line, Vrot would be artificially inflated for our bin size choice (see Section 3.4 for details). The Vrot/σ profiles suggest that V both blue and red GCs have high rotation. The rms profile for the red GCs Figure 9. GC kinematics as a function of (g − i) colour in the inner <4Re declines more rapidly than that of the blue GCs, which stays relatively flat (black-dashed contours) and outer >4Re (green-solid contours) regions. at all radii. Dashed and dot–dashed lines are the same as Fig. 6 and contours show the 68 per cent confidence interval. The black vertical line is the colour cut, (g − i) = 0.93 mag used in our analysis. GCs in the inner bin show counter- We also created artificial data sets by randomly shuffling the rotation along the photometric major axis while the outer bin is dominated position angles of the GCs in the inner radial bin, and then fit by minor axis rotation. The inner region has a population of very red GCs, for kinematic parameters. We constructed 1000 such data sets. The i.e. (g − i) > 1.05 mag with high velocity dispersion that are rotating along random shuffling serves to destroy any intrinsic correlation between the major axis. GC position angle that could be driving the rotation amplitude. From the fit, we determined the probabilities that the GC rotation is non- = zero for the blue and red GC in the inner radial bin are 95 and for the kinematic parameters while fixing qkin qphot.Weshow 89 per cent, respectively. the results in Fig. 9 and note the similar Vrot profiles for GCs with − < We show the rotation dominance parameter (V /σ ) in the top (g i) 1.05 mag. For GC colours redder than this in the inner rot < σ panel of Fig. 8. This parameter quantifies how ‘discy’ a system radial bin (i.e. 4Re), Vrot and are significantly higher than the average for the entire GC system and PA is aligned along the is, such that when Vrot/σ > 1, the system is described as rotation kin dominated. Though the blue and red GCs show high rotation within photometric major axis. Again, the inner blue and red GCs counter- rotate along the photometric major axis. In the outer region, for the the inner ∼4Re, the GC system is overall not rotation dominated. The blue GCs, the dominant rotation mode is along the minor axis. Vrot/σ profile has a negative gradient, at least within the inner ∼4Re and we note the spike in the profile for the blue GCs at ∼6Re.This may be a substructure signature. We also show the Vrms profile for blue and red GCs in Fig. 8 3.6 Line-of-sight velocity distribution obtained using To better understand the variations of GC kinematics with radius N and colour, as well as the sharp transition at ∼4R , we construct 2 1 2 2 e V = (Vi − V ) − (Vi ) , (6) rms N sys LOSVDs for our spectroscopic GC data set. We consider three sam- i=1 ∼ ples: all GCs in a single bin, GCs within 4Re in a single bin and and evaluating the uncertainty on our estimated Vrms using the rela- GCs beyond ∼4Re from the galaxy centre in a single bin. We make tion from Danese, de Zotti & di Tullio (1980). The Vrms is equivalent LOSVDs for the blue and red GC subpopulations using the bins to the velocity dispersion in the absence of projected rotation and defined above and present the results in Fig. 10. The LOSVDs it is a measure of the total specific kinetic energy of the galaxy. have been smoothed with optimal bandwidth Gaussian kernels Overall, the profile for red GCs declines with radius, unlike the (Silverman 1986) and normalized for easy comparison. blue GCs which have a flat radial profile, with two bumps at ∼3 From the top panel, all our three samples have LOSVDs that and ∼6Re. Since the blue and red GCs independently trace the same are approximately Gaussian with peaks consistent with the galaxy galaxy potential, differences in their Vrms profiles are linked to their recession velocity. This can be interpreted as overall dynamic equi- different orbital anisotropies and spatial distributions. librium. The middle panel, however, shows that the red GCs in the inner radial bin have an asymmetric LOSVD with a significantly redshifted velocity peak and an excess of low-velocity GCs. The 3.5 Kinematics as a function of GC colour LOSVD is such that the prograde wing has a steeper gradient than The sharp twist in PAkin for both blue and red GCs at ∼4Re (Sec- the retrograde wing. In the outer bin, the LOSVD has a flattened tion 3.4) suggests that this could be a radial boundary between the shape, which might be due to tangentially biased orbits. This sug- inner and outer GC subpopulations. We therefore use this fiducial gests that the inner red GCs are dynamically different from those in radial limit to define inner and outer GC subsamples and study the outer radial bin. In the bottom panel, the ‘peaked’ shape of the their kinematics as a function of colour. For both cases, we use the LOSVDs suggests that the blue GCs, especially in the outer bin, are model and method in Section 3.4, binning by GC colour and fitting likely to be on radially biased orbits.

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tral rotators. The extent of the KDC depends on the initial orbits and mass ratio of the merging pair. Progenitors on antiparallel orbits produce counter-rotating cores usually within 1Re while those on parallel orbits produce more extended decoupled features. The KDC is usually illusory (van den Bosch et al. 2008), in the sense that it is formed by the superposition of a pair of counter-rotating stellar systems. The inclination of the merger remnant is important in observing the 2σ feature, especially for 1:1 mergers. Though the idealized binary mergers of Bois et al. (2011) produced 2σ-like remnants, the simulations were not cosmological. They did not include effects from disc regrowth through cold accretion flows, bulge growth through minor mergers or late major mergers. These could produce remnants that would be intermediate between fast and slow rotators. Recently, Naab et al. (2014) used cosmological simulations to track the assembly history of present-day galaxies from z ∼ 2 within the ‘two-phase’ galaxy formation model. The only galaxy, out of 44 in the simulations (∼2 per cent), with a clear 2σ velocity dispersion feature (their M0209 in class E) is a slow rotator that experienced a late (z<1) gas-poor major merger, and very little in situ star formation (since z ∼ 2). It is therefore dominated by old (∼10 Gyr) stars. We suspect that the shortfall in the reported number of remnant galaxies with a clear 2σ feature could be due to multiple late mergers which could conspire to wash away the 2σ feature. The two simulations described above do not consider GCs. There is a dearth of simulation studies for GC kinematics in ETGs compared to stellar kinematics. Bekki et al. (2005) studied the kinematics of GCs in disspationless major mergers of Milky Way-like galaxies using numerical simulations; no new GCs were formed in these simulations. Even though the GCs in the progenitor spirals were not given any initial rotation, they were predicted to have significant rotation at large radii in binary major merger remnants. This was interpreted as conversion of orbital angular momentum to intrinsic angular momentum. Also, the blue GCs were predicted to have a higher central velocity dispersion than the red GCs with the rotational dominance parameter (Vm/σ ) for GCs interior to 6Re greater than that of the galaxy stars within 2Re. Vm is the maximum rotation velocity, so we take the ratio Vm/σ as an upper limit to our Vrot/σ . The velocity dispersion is expected to decrease with radius in binary mergers, unlike in multiple mergers, where it is expected to have a more flattened profile. Figure 10. LOSVD for GCs in radial bins, and by GC subpopulation. Pan- We therefore compare our results with these model predictions, els from top to bottom show all the GCs, red GCs and blue GCs, respectively. in an attempt to unravel the unique assembly history of NGC 4473. Different colours correspond to different radial bins. The middle panel reveals a kinematic difference between the inner and outer bin red GCs. In the bottom panel, the blue GCs have ‘peaked’, symmetrical LOSVDs suggesting 5 DISCUSSION radially biased orbits. It has been shown from stellar kinematics within 1Re that NGC 4473 has two embedded, counter-rotating stellar discs, with mass ratio 3:1 4 MODEL PREDICTIONS FOR 2σ GALAXIES (Cappellari & McDermid 2005;Cappellarietal.2007). Counter- Before discussing our results, we first briefly summarize models rotation beyond 60 arcsec along the photometric major axis, as well which produce 2σ galaxies. Bois et al. (2011) used idealized nu- as multiple kinematic components up to 3Re, have also been re- merical simulations to study the mergers of Sb–Sc galaxy pairs ported from the SLUGGS survey (Foster et al. 2013, 2015; Arnold with dissipation over a range of initial conditions. In the simula- et al. 2014). Koleva et al. (2011) showed that NGC 4473 has a tions, and in agreement with Crocker et al. (2009), 2σ galaxies are younger and more metal-rich stellar population in the central parts produced when the merging progenitor pair have opposite spin and compared to the average for the galaxy. This agrees with the results are coplanar. Tsatsi et al. (2015) recently showed that major merg- of Kuntschner et al. (2006, 2010) and Pastorello et al. (2014), who ers of spiral galaxies on prograde orbits could also produce galaxies found an extended, metallicity-enhanced region along the photo- with 2σ features, although in their simulations, the remnant galaxy metric major axis. These studies, along with the central extralight showed a centrally elevated velocity dispersion – a feature not nor- from Kormendy et al. (2009) and Dullo & Graham (2013), suggest mally associated with 2σ galaxies. In all cases, galaxies with 2σ that a gas-rich event can be linked to the complex features we see features are flattened (>0.4) but could be either fast or slow cen- in the kinematics of NGC 4473.

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Our results show that the GC system kinematics of NGC 4473 et al. 2011) and the radial extent of the counter-rotating region with is equally as complex as that of the galaxy stars, suggesting co- coherent GC kinematics we observe here argues against a minor evolution between the GCs and galaxy stars. Within the GC system, merger origin. While counter-rotating stellar components can be the blue and red GCs independently show distinct and complex formed from gas accreted on retrograde orbits, this channel is un- kinematics suggesting different formation processes and/or epochs. likely to be responsible for the large-scale counter-rotation observed This again reinforces the conclusion that GC colour bimodality is in the GCs, unless the accretion event was early (Algorry et al. 2014; real (Brodie et al. 2012; Usher et al. 2012) reflecting some more Danovich et al. 2015; Lagos et al. 2015). Explaining the sharp radial fundamental, underlying galaxy property, i.e. metallicity, as well kinematic transition and counter-rotation of the blue and red GCs as the complex formation and assembly history of galaxies (Tonini in a 2σ galaxy in terms of minor mergers is difficult. We therefore 2013). The velocity dispersion and the PAkin profiles of the red GCs link the large-scale stellar and GC counter-rotation to the gas-rich trace those of the galaxy stars in the region of overlap, unlike the major merger event that formed the 2σ feature. blue GCs (see Figs 4 and 6). Similar features are seen in some other The classic gas-rich major merger scenario for GC formation galaxies (e.g. Schuberth et al. 2010; Coccato et al. 2013;Potaetal. (Ashman & Zepf 1992) suggests that the merger remnant, apart from 2013), where the red GCs and galaxy stars are believed to share a acquiring GCs from the progenitor spirals, can also form metal-rich common formation history. stars and GCs (Bournaud, Duc & Emsellem 2008;Kruijssenetal. Both GC subpopulations however show a large offset between 2011). The group of dynamically ‘hot’, very red GCs in the inner 4Re their rotation amplitudes and that of the galaxy stars. This is odd, radial region (see Fig. 9) could have been formed in such a merger as studies of GC system kinematics usually find a match between event. Their rotation direction suggests that they are kinematically the rotation profiles of stars and the red GCs (e.g. Coccato et al. coupled to the galaxy stars. They could be the GC counterpart of the 2013;Potaetal.2013). Here, contrary to the norm, we find that younger stars reported in Koleva et al. (2011). Measuring their age, the rotation profiles only match when all the GCs, i.e. the blue and metallicity and α abundance could reveal a younger GC population red GC subpopulations, are used together in our analysis. Having that matches the ∼6 Gyr age measured by Koleva et al. (2011)in shown that our Vrot profiles are not biased, we suggest that this offset the galaxy core. is due to the presence of the two counter-rotating, flattened stellar The central velocity dispersion of the blue GCs is lower than structures at the galaxy centre. When galaxy starlight from the ra- that of the red GCs, contrary to the prediction of the major merger dially overlapping stellar components is integrated along the line of simulation of Bekki et al. (2005) (see middle panel of Fig. 6). We do sight, as in the case of the stellar kinematics from SAURON and not see signs of increasing rotation amplitude or rotation dominance SKiMS, the net effect is to lower the recovered rotation amplitude, with radius, for both blue and red GC subpopulations as predicted. since the components are counter-rotating. When we combined all However, our rotation profiles agree with the prediction of fast the GCs, i.e. without separating them into blue and red GC sub- rotation at large radii from Bekki et al. (2005), with comparable populations (see Fig. 7), we observe that the rotation amplitude is Vrot/σ for blue and red GCs at all radii. It should, however, be noted significantly reduced, comparable to what is obtained for the galaxy that the predictions from Bekki et al. (2005) are for a dry major stars. Here, separating the GCs into subpopulations by colour also merger, where no new stars are formed. It has been shown from separates them into counter-rotating components and reveals the simulations (e.g. Barnes & Hernquist 1996; Jesseit et al. 2007; true rotation amplitude. We therefore predict that similar offsets Hoffman et al. 2010) that the presence of gas significantly alters would be obtained between the rotation profiles of galaxy stars and the kinematics of merger remnants, especially in the central parts, discrete tracers for all 2σ galaxies, depending on the luminosity alongside the formation of new GCs. contributions from the cospatial stellar components. In the inner region, where PAkin is aligned with the photometric We have also found counter-rotation in the GCs, with a sharp tran- major axis (see Figs 6 and 9), the kinematic misalignment is negli- ◦ sition in both blue and red GCs, at ∼4Re. This adds to the kinematic gible, i.e. ∼ 0 . However, in the outer region, where the blue GCs complexity of the GC system. In the inner ∼4Re,blueandredGCs dominate, the average PAkin is intermediate between the photometric counter-rotate along the photometric major axis, while beyond this, major and minor axes, implying a non-zero kinematic misalignment. the blue and red GCs show a sharp ∼180◦ kinematic twist, with the This suggests that the GC system of NGC 4473 is triaxial, closely blue GCs rotating intermediate to the major and minor axes in the following the galaxy (see also Foster et al. 2013). Orbital structures GC system outskirts. This transition radius and counter-rotation, from the merging progenitors are predicted to be preserved in the unambiguously show that the galaxy mass assembly occurred in galaxy outer regions, where the effect of dissipation is negligible. phases from materials that had decoupled angular momenta. This is In the galaxy outskirts, the ‘peaked’ shape of the LOSVD of the in agreement with the ‘two-phase’ galaxy formation paradigm and blue GCs suggests that they are preferentially on radial orbits. This predictions from Crocker et al. (2009) and Bois et al. (2011). We agrees with the predicted multiple minor merger or accretion origin find further evidence for distinct kinematics on either side of this for the blue GCs (Cotˆ e,´ Marzke & West 1998;Hilkeretal.1999; transition radius from the colour profiles of kinematic parameters Dekel et al. 2005; Bekki et al. 2008). Incidentally, the same argu- and the LOSVD (see Figs 9 and 10). We note that this strong inter- ment can be made entirely from the Vrms profiles (see Fig. 8), where nal transition is however not seen in photometry, underscoring the the flat profile for the blue GCs indicates a multiple minor merger importance of kinematics in obtaining a complete picture of galaxy origin (Bekki et al. 2005;Potaetal.2013). This, therefore, suggests assembly. that the outer envelope of the galaxy was assembled through minor Gas-rich major mergers have been shown to produce sharp radial mergers. kinematic transitions, similar to what we have observed, between 1and5R (Hoffman et al. 2010). Kormendy et al. (2009) sug- e 6 CONCLUSIONS gested that the counter-rotating component in NGC 4473 might have formed in a late gas accretion or gas-rich minor merger event, Here we present mean velocity and velocity dispersion 2D maps due to the small region (∼0.8Re) associated with the extralight. from GCs and stars in NGC 4473 to reveal complex kinematic However, gas-rich minor mergers do not form 2σ galaxies (Bois features which extend up to 10Re. We show that the double sigma

MNRAS 452, 2208–2219 (2015) 2218 A. B. Alabi et al. feature of the stellar velocity dispersion map extends to the GC Bois M. et al., 2011, MNRAS, 416, 1654 system, reaching out to 3Re, but is misaligned with respect to the Bournaud F., Duc P.-A., Emsellem E., 2008, MNRAS, 389, L8 photometric major axis. Brodie J. P., Usher C., Conroy C., Strader J., Arnold J. A., Forbes D. A., By fitting an inclined disc model to our GC data, we find that Romanowsky A. J., 2012, ApJ, 759, L33 the blue and red GCs have different kinematics, with a sharp tran- Brodie J. P. et al., 2014, ApJ, 796, 52 Cappellari M., McDermid R. M., 2005, Classical Quantum Gravity, 22, 347 sition in the kinematics at ∼4Re in both GC subpopulations. In the < Cappellari M. et al., 2007, MNRAS, 379, 418 inner ( 4Re) region, the blue and red GCs counter-rotate along the Coccato L. et al., 2009, MNRAS, 394, 1249 > photometric major axis while in the outer ( 4Re) region, the blue Coccato L., Arnaboldi M., Gerhard O., 2013, MNRAS, 436, 1322 GCs rotate intermediate to the photometric major and minor axes. Cooper M. C., Newman J. A., Davis M., Finkbeiner D. P., Gerke B. F., 2012, The red GCs in the outer region rotate along the major axis, but in spec2d: DEEP2 DEIMOS Spectral Pipeline. Astrophysics Source Code opposite sense compared to the inner red GCs. The large-scale GC Library, record ascl:1203.003 counter-rotation, sharp kinematic transition, both as a function of Cotˆ e´ P., Marzke R. O., West M. J., 1998, ApJ, 501, 554 galactocentric radius and GC colour, and the discovery of a group Crocker A. F., Jeong H., Komugi S., Combes F., Bureau M., Young L. M., of centrally located, kinematically hot, very red GCs provide addi- Yi S., 2009, MNRAS, 393, 1255 tional evidence that NGC 4473 could have been formed in a gas-rich Danese L., de Zotti G., di Tullio G., 1980, A&A, 82, 322 Danovich M., Dekel A., Hahn O., Ceverino D., Primack J., 2015, MNRAS, major merger event. In the future, stellar population analysis of this 449, 2087 hot GC subsample would help to determine the merger history of Davies R. L. et al., 2001, ApJ, 548, L33 the galaxy. We find that the outer region is dominated by GCs on Dekel A., Stoehr F., Mamon G. A., Cox T. J., Novak G. S., Primack J. R., radial orbits with a flat Vrms profile – which suggests that multiple 2005, Nature, 437, 707 minor mergers may have contributed to the build up of the outer Dullo B. T., Graham A. W., 2013, ApJ, 768, 36 regions of NGC 4473. Emsellem E. et al., 2004, MNRAS, 352, 721 We conclude that the GCs in NGC 4473 share a common assem- Foster C. et al., 2011, MNRAS, 415, 3393 bly history with the stars, based on the similarities in their radially Foster C., Arnold J. A., Forbes D. A., Pastorello N., Romanowsky A. J., decoupled, complex kinematics. Our results differ significantly, in Spitler L. R., Strader J., Brodie J. P., 2013, MNRAS, 435, 3587 some aspects, from the predictions of GC kinematics in simulated Foster C. et al., 2014, MNRAS, 442, 3544 Foster C. et al., 2015, MNRAS, submitted mergers of spiral galaxies. We attribute this to the assumptions Helmi A., White S. D. M., 1999, MNRAS, 307, 495 made in the simulations. A detailed simulation of GC kinematics in Hilker M., Infante L., Vieira G., Kissler-Patig M., Richtler T., 1999, A&AS, galaxies formed via gas-rich mergers with dissipation is needed to 134, 75 better understand rare but interesting galaxies like NGC 4473. Hoffman L., Cox T. 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MNRAS 452, 2208–2219 (2015) Globular cluster kinematics in NGC 4473 2219

Schuberth Y., Richtler T., Hilker M., Dirsch B., Bassino L. P., Romanowsky SUPPORTING INFORMATION A. J., Infante L., 2010, A&A, 513, A52 Sharples R. M., Zepf S. E., Bridges T. J., Hanes D. A., Carter D., Ashman Additional Supporting Information may be found in the online ver- K. M., Geisler D., 1998, AJ, 115, 2337 sion of this article: Silverman B. W., 1986, Monographs on Statistics and Applied Probability. Chapman and Hall, London Table 1. Spectroscopically conﬁrmed globular clusters, stars Spitler L. R., Larsen S. S., Strader J., Brodie J. P., Forbes D. A., Beasley M. and galaxies. (http://mnras.oxfordjournals.org/lookup/suppl/ A., 2006, AJ, 132, 1593 doi:10.1093/mnras/stv1426/-/DC1). Spitler L. R., Forbes D. A., Strader J., Brodie J. P., Gallagher J. S., 2008, MNRAS, 385, 361 Please note: Oxford University Press are not responsible for the Strader J., Brodie J. P., Spitler L., Beasley M. A., 2006, AJ, 132, 2333 content or functionality of any supporting materials supplied by Strader J. et al., 2011, ApJS, 197, 33 the authors. Any queries (other than missing material) should be Thakar A. R., Ryden B. S., 1996, ApJ, 461, 55 directed to the corresponding author for the article. Tonini C., 2013, ApJ, 762, 39 Tsatsi A., Maccio` A. V., van de Ven G., Moster B. P., 2015, ApJ, 802, L3 Usher C. et al., 2012, MNRAS, 426, 1475 van den Bosch R. C. E., van de Ven G., Verolme E. K., Cappellari M., de Zeeuw P. T., 2008, MNRAS, 385, 647 Villegas D. et al., 2010, ApJ, 717, 603 Walker M. G., Mateo M., Olszewski E. W., Pal J. K., Sen B., Woodroofe M., 2006, ApJ, 642, L41 Zepf S. E., Ashman K. M., 1993, MNRAS, 264, 611 Zhang H.-X. et al., 2015, ApJ, 802, 30 This paper has been typeset from a TEX/LATEX ﬁle prepared by the author.

MNRAS 452, 2208–2219 (2015)

3 Mass distribution in early-type galaxies within ﬁve eﬀective radii and beyond

We still see through a glass, darkly —Pauline text adapted

29 MNRAS 460, 3838–3860 (2016) doi:10.1093/mnras/stw1213 Advance Access publication 2016 May 20

The SLUGGS survey: the mass distribution in early-type galaxies within ﬁve effective radii and beyond

Adebusola B. Alabi,1‹ Duncan A. Forbes,1 Aaron J. Romanowsky,2,3 Jean P. Brodie,3 Jay Strader,4 Joachim Janz,1 Vincenzo Pota,5 Nicola Pastorello,1 Christopher Usher,1,6 Lee R. Spitler,7,8 Caroline Foster,7 Zachary G. Jennings,3 Alexa Villaume3 and Sreeja Kartha1 1Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn, VIC 3122, Australia 2Department of Physics and Astronomy, San Jose´ State University, San Jose, CA 95192, USA 3University of California Observatories, 1156 High Street, Santa Cruz, CA 95064, USA 4Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA 5INAF – Observatorio Astronomico di Capodimonte, Salita Moiariello, 16, I-80131 Napoli, Italy 6Astrophysics Research Institute, Liverpool John Moores University, Liverpool L3 5RF, UK 7Australian Astronomical Observatory, PO Box 915, North Ryde, NSW 1670, Australia 8Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia

Accepted 2016 May 18. Received 2016 May 18; in original form 2016 January 18

ABSTRACT We study mass distributions within and beyond 5 effective radii (Re) in 23 early-type galaxies from the SAGES Legacy Unifying Globulars and Galaxies Survey, using their globular cluster (GC) kinematic data. The data are obtained with Keck/DEep Imaging Multi-Object Spectrograph, and consist of line-of-sight velocities for ∼3500 GCs, measured with a high −1 precision of ∼15 km s per GC and extending out to ∼13 Re. We obtain the mass distribution in each galaxy using the tracer mass estimator of Watkins et al. and account for kinematic substructures, rotation of the GC systems and galaxy flattening in our mass estimates. The observed scatter between our mass estimates and results from the literature is less than 0.2 dex. The dark matter fraction within 5 Re (fDM) increases from ∼0.6 to ∼0.8 for low- and high- 11 mass galaxies, respectively, with some intermediate-mass galaxies (M∗∼10 M)havinglow fDM ∼ 0.3, which appears at odds with predictions from simple galaxy models. We show that these results are independent of the adopted orbital anisotropy, stellar mass-to-light (M/L)ra- 11 tio, and the assumed slope of the gravitational potential. However, the low fDM in the ∼10 M galaxies agrees with the cosmological simulations of Wu et al. where the pristine dark matter distribution has been modified by baryons during the galaxy assembly process. We find hints 11 that these M∗∼10 M galaxies with low fDM have very diffuse dark matter haloes, implying that they assembled late. Beyond 5 Re,theM/L gradients are steeper in the more massive galaxies and shallower in both low and intermediate mass galaxies. Key words: globular clusters: general – galaxies: evolution – galaxies: kinematics and dynamics.

and evolution models. For example, at the same stellar mass, early- 1 INTRODUCTION type galaxies (ETGs) are thought to have a higher DM concentration One of the fundamental properties of galaxies is their total mass compared to spiral galaxies. This is because the central portions of (baryonic + dark matter). The total mass proﬁles of giant galaxies the haloes in ETGs are already in place at a higher redshift compared are dominated by baryons in the central parts, with the dark matter to spiral galaxies for the same galaxy mass (e.g. Thomas et al. 2009). (DM) component becoming more dominant at large radii, eventually For late-type galaxies, it is relatively easy to determine the total dominating the total mass budget. Studying the distribution of these mass distribution out to large radii using the motions of the read- mass components provides a viable way of testing galaxy formation ily available H I gas as a tracer of the galaxy potential. However, this exercise is more difﬁcult for (individual) ETGs. This is because ETGs are generally poor in cold gas, their stellar motions are E-mail: [email protected] predominantly random by nature and at large galactocentric radii,

C 2016 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Mass distribution in ETGs at large radii 3839

they are optically faint. These properties combine to make studies tracers). A tracer population with number density n(r) ∝ r−γ re- of the mass distribution in ETGs challenging. Yet, to properly un- sides in a power-law gravitational potential of the form (r) ∝ r−α. derstand the DM content in ETGs, one needs to probe out to at least The total mass density, ρ, is directly related to the gravitational five effective radii (Re), where DM is expected to begin dominating potential via Poisson’s equation and hence it has the power-law the enclosed mass (Romanowsky et al. 2003; Napolitano et al. 2005; form ρ(r) ∝ r−α−2. Also, the TMEs assume that the tracer popula- Cappellarietal.2015). tion is spherically symmetric and that galaxies are in steady-state Various mass tracers such as planetary nebulae (PNe; e.g. Mor- equilibrium, i.e. virialized. ganti et al. 2013), globular clusters (GCs; e.g. Pota et al. 2015)and This paper uses the GC kinematic data from the SLUGGS1 diffuse X-ray gas (e.g. Su et al. 2014) have been used to explore (SAGES Legacy Unifying Globulars and Galaxies Survey; Brodie the mass distribution in ETGs out to large radii. For PNe- and GC- et al. 2014) and TMEs to study in a homogeneous way the mass based studies, their orbital distributions are usually not known, and distribution within and beyond 5 Re in ETGs. The galaxies we study are notoriously difficult to determine due to the mass–anisotropy cover a stellar mass range of 1.9 × 1010–4.0 × 1011 M and include degeneracy (Binney & Mamon 1982). The discrete kinematic data galaxies from cluster, group and field environments. We therefore are often binned and smoothed in order to determine the mass extend the range of galaxies with mass profiles beyond 5 Re into the profile, leading to loss of vital information. Since binning is im- low stellar mass galaxy regime. The science questions we seek to practicable for sparse samples, only galaxies with relatively rich answer are straightforward – Are TMEs appropriate mass estimators systems of bright tracers, i.e. massive ETGs, are usually studied. using GCs as the tracers? How is mass distributed between baryons This limitation also extends to X-ray-based studies, where X-ray and DM in the outer haloes of ETGs, especially in intermediate and haloes are observed mostly around massive galaxies that usually low stellar mass ETGs? Are ETGs always DM dominated in their reside in dense environments. Hence most ETGs with radially ex- outer parts? If they are not always DM dominated, as some results tended mass modelling results in the literature are the more massive from the literature seem to suggest, then why? Are the measured ones, with the low and intermediate mass ETGs usually overlooked. mass and DM content estimates consistent with predictions from Furthermore, ETGs tend to be studied one at a time, with different CDM models? methods and assumptions. This makes it problematic to compare In Section 2 we describe the observations, data reduction and the results in a systematic way. data preparation. Section 3 starts by introducing in detail the TMEs, Apart from the observational difficulties, results at large galac- defines the mass estimator parameters and quantifies the sensitivity 11 tocentric radii in some intermediate mass ETGs (M∗ ∼ 10 M) of the mass estimators to these parameters. In this section, we also have suggested inconsistencies with the predictions from CDM quantify the effects of galaxy flattening, rotation and kinematic cosmology (e.g. Romanowsky et al. 2003; Napolitano et al. 2009; substructures on our mass estimates. We study the deviation of + Deason et al. 2012, hereafter D 12). While results from the well- ETGs from isotropy. We obtain the DM fractions within 5 Re and studied massive ETGs agree with the prediction that in the outer beyond, and compare with expectations from a simple galaxy model, halo, DM dominates the galaxy mass budget, the same is less clear composed of DM and stars only. In Section 4, we discuss how in intermediate mass ETGs, as different mass modelling techniques predictions and observations compare. We complete this section by using the same tracers seem to produce contradictory results (see studying correlations between the DM fraction and various galaxy Romanowsky et al. 2003; Napolitano et al. 2009; D+12; Morganti properties. In Section 5, we summarize our results. et al. 2013, for the peculiar case of NGC 4494). The situation is even worse for low stellar mass ETGs, since they have hardly been studied out to large radii. It is therefore imperative to probe the DM 2 OBSERVATIONS, DATA REDUCTION AND halo in these galaxies systematically. DATA PRUNING The traditional methods of mass modelling are difficult to apply 2.1 Observations and data reduction to GC kinematic data for sub-L∗ ETGs. It is therefore desirable to have mass estimators that use the projected kinematic information The GC kinematic data used in this work were obtained through directly without the need for binning – an approach that lends itself spectroscopic observations, mostly as part of the SLUGGS sur- to relatively sparse tracer populations. Examples include the virial vey, with the DEIMOS (DEep Imaging Multi-Object Spectrograph; mass estimator (VME) from Limber & Mathews (1960) and the pro- Faber et al. 2003) instrument on the 10 m Keck-II telescope. For jected mass estimator (PME) from Bahcall & Tremaine (1981), later NGC 3115, NGC 4486 and NGC 4649, we have supplemented our modified by Heisler, Tremaine & Bahcall (1985). These assume that catalogue with data from some external sources (see Arnold et al. the tracers (e.g. GCs, PNe, satellite galaxies) have a number den- 2011; Strader et al. 2011;Potaetal.2015, respectively, for details sity distribution – n(r), that directly follows the total mass density of these externally sourced kinematic data and the re-calibration of the galaxy – ρ(r), i.e. n(r) ∝ ρ(r). This is not usually true since of their uncertainties to match with those of DEIMOS). Spectro- the total mass density is dominated by the DM component, espe- scopic data collection with DEIMOS began in 2006 and we have cially at large radii. The VME and PME are in principle similar now obtained ∼3500 GC radial velocities in 25 carefully chosen to earlier attempts at estimating mass in a spherically symmetric, ETGs (Brodie et al. 2014). Here, we only consider 23 galaxies from self-gravitating system where the tracers orbit a central point mass the SLUGGS survey with 20 or more spectroscopically confirmed (e.g. Zwicky 1937; Schwarzschild 1954). GCs. Readers interested in a detailed explanation of our DEIMOS A more recent class of mass estimators, the tracer mass estimators data reduction method are encouraged to check Pota et al. (2013) (TMEs), however, allows for the more general case where the trac- though we give a brief description here. ers and total mass densities, while both assumed to be scale-free, We design masks with 1 arcsec wide slits targeting GC candidates have different distributions. They were first introduced by Evans and integrate per mask for an average of 2 h. We set up DEIMOS et al. (2003) and later modified by Watkins, Evans & An (2010, hereafter W+10), and (An & Evans 2011, see also Watkins et al. 2013 for an axisymmetric Jeans modelling of discrete kinematic 1 http://sluggs.swin.edu.au

MNRAS 460, 3838–3860 (2016) 3840 A. B. Alabi et al.

Figure 1. Line-of-sight velocities of the ∼3500 GCs in our sample of 23 galaxies normalized by their respective galaxy central velocity dispersion (σ kpc from Table 2) versus galactocentric radius (in effective radius). The left-hand panel shows the low-mass galaxies (NGC 7457, NGC 3377 and NGC 4564), the middle panel shows intermediate mass galaxies (NGC 3608, NGC 4473, NGC 4278, NGC 821, NGC 3115, NGC 5866, NGC 1023, NGC 4494, NGC 4697, NGC 4697, NGC 1400, NGC 4526, NGC 2768 and NGC 3607), while the right-hand panel shows the high-mass galaxies (NGC 720, NGC 5846, NGC 4374, NGC 4365, NGC 4486, NGC 4649 and NGC 1407). GCs belonging to kinematic substructures have been excluded from this 2D histogram. The black dots are the individual GCs, while the colour bar shows the density of the points. On average, the GC line-of-sight velocities extend out to 13 Re per galaxy. This figure is available in colour in the online version. with the 1200 lines mm−1 centred on 7800 Å. This ensures we have mixed can sometimes be isolated in position–velocity phase space, a wavelength resolution of ∼1.5 Å and cover the CaT absorption even when the coherent structures are no longer evident in photo- lines in the near-infrared (8498, 8542, 8662 Å) and often the H α metric studies. For the immediate task of mass modelling, it is im- line at 6563 Å. We reduce our raw spectra using the IDL SPEC2D data portant to isolate tracers that show correlations in position–velocity reduction pipeline (Cooper et al. 2012) and obtain radial velocities phase space, i.e. kinematic substructures, in order to avoid spurious by measuring the Doppler shifts of the CaT absorption lines using mass estimates. FXCOR task in IRAF. We cross-correlate our science spectra with For each galaxy, we use the Dressler–Schectman (DS) test spectral templates of 13 carefully chosen Galactic stars, obtained (Dressler & Shectman 1988; Ashman & Bird 1993; Pinkney et al. with the same instrument and setup. The final radial velocity for each 1996;Mendeletal.2008; Einasto et al. 2012) to detect substructures object is the average from the cross-correlation. The uncertainties in position–velocity phase space and to quantify the significance of on our radial velocities are obtained by adding in quadrature the the substructures. For each GC, we compute the local average√ veloc- V¯ σ N = N uncertainty outputs from FXCOR to the standard deviation among ity ( local) and velocity dispersion ( local) using the nn GC the templates, typically ∼3kms−1. Finally, our science spectra are nearest neighbours (as advised by Pinkney et al. 1996). We then redshift corrected. compare the local and global kinematics and sum over all the GCs To classify an object as a GC, we ensure that the CaT features to obtain , the DS statistic, for the GC system using in the rest-frame spectra are seen at the expected rest wavelength N + and the radial velocity is consistent with the host galaxy’s systemic = nn 1 σ σ 2 velocity (through a 3 clipping implemented via the friendless al- i global gorithm of Merrett et al. (2003)). For secure classification as a GC, / × V¯ − V¯ 2 + σ − σ 2 1 2 . we require that at least the 8542 and 8662 Å CaT lines are ob- [( local,i global) ( local,i global) ] (1) served, as well as the H α line (when the H α wavelength region is probed). In addition, we obtain a consensus from at least two For a Gaussian-like Vlos distribution, is approximately of the or- members of the SLUGGS team on the status of our GC candidates. der of NGC and the larger its value, the more likely it is that the GC Objects with contentious status, but radial velocities consistent with system has substructures. However, a non-Gaussian Vlos distribution the host galaxy’s systemic velocity, are classified as marginal GCs. can also produce a significantly different from NGC even when We do not use such objects in this work. Fig. 1 shows the com- there are no real substructures. Therefore, to properly identify sub- posite galactocentric distribution of our homogeneous sample of structures and statistically quantify their significance, we perform a Monte Carlo experiment (repeated 5000 times) where we randomly ∼3500 GC line-of-sight velocities (Vlos) with well-understood errors used in this work. On average, our GC data extends to 10, shuffle the Vlos of the GCs while keeping their positions fixed. This breaks any correlation between position and Vlos while keeping the 13 and 15 Re in the low (log(M∗/ M) < 10.8), intermediate same velocity distribution and tests against the null hypothesis that (10.8 ≤ log(M∗/ M) ≤ 11.3) and high (log(M∗/ M) > 11.3) stellar mass galaxies in our sample, respectively. there is no correlation between position and Vlos. The significance (p-value) is the number of times from the Monte Carlo experiment is greater than that from the observed data divided by the 2.2 Kinematic substructures in GC systems total number of simulations, such that smaller p-values correspond A fundamental assumption of mass modelling methods is that the to stronger substructure signatures. For GC systems with statisti- system of tracers is in dynamical equilibrium. However, if galax- cally significant substructures, i.e. p-val < 0.05, we identify and ies assembled their mass hierarchically via mergers and accretion isolate the GCs with correlated kinematics and re-perform the DS events, a lumpy ‘outer’ halo is expected, especially in position– test on the ‘cleaned’ data set iteratively until p-val > 0.05. The velocity phase space (Bullock & Johnston 2005; Helmi 2008; total numbers of GCs removed per GC system are summarized in Cooper et al. 2013). The fossils of the accreted galaxies or satel- Table 1.Table2 contains the p-values for all the galaxies. We show lite galaxies undergoing disruption that have not been totally phase the identified kinematic substructures from the DS test in Fig. 2.

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Table 1. Summary of the spectroscopic observations for our galaxy sample. where rin is the deprojected radius of the innermost GC and 1/2 α + π ( 2 1) Galaxy Masks Exp. time NGC Nsub Rmax Iα,β = [α + 3 − β(α + 2)] (4) α + 5 (NGC) (h) (Re) 4 ( 2 2 )

720 5 10.6 69 – 19.05 with (x) being the gamma function. Equations (3) (i) and (ii) 821 7 11.2 69 – 8.70 are from Evans et al. (2003)andW+10;An&Evans(2011), 1023 4 8.8 115 21 16.15 respectively. λ ≡ 1 in the TME of Evans et al. (2003)andλ ≡ α in 1400 4 9.0 69 – 20.62 those of W+10 and An & Evans (2011). Our kinematic data consist 1407 10 22.0 372 – 14.14 of N line-of-sight velocity (Vlos, i) measurements at circularized 2768 5 13.9 107 – 11.36 galactocentric radii (Ri)deﬁnedas 3115 5 14.0 150 12 18.35 3377 4 8.3 122 – 14.34 Y 2 R = qX2 + , 3608 5 9.9 36 – 9.75 q (5) 4278 4 8.8 270 – 14.87 4365 6 9.0 251 – 12.90 where q is the ratio of the galaxy photometric minor to major axis 4374 3 5.5 41 – 9.22 (q = 1 − ), with X and Y as the projected Cartesian coordinates 4473 4 2.8 106 – 17.35 of individual GCs on the sky. Equation (5) is from Romanowsky 4486 5 5.0 702 60 30.52 et al. (2012), and it ensures that Ri is in a consistent format with the 4494 5 4.6 107 10 8.52 circularized effective radii (Cappellari et al. 2013b)wehaveused 4526 4 8.0 107 25 12.06 for our analysis. 4564 3 4.5 27 – 8.33 + 4649 4 8.0 431 21 24.25 The TME of W 10 has been shown to outperform that of Evans + 4697 1 2.0 20 – 4.66 et al. (see W 10), and that of An et al. is just a special case of 5846 6 9.1 191 – 13.68 W+10 where γ ≡ 3. We therefore use the more general TME of 7457 4 7.5 40 6 6.26 W+10 for further analyses and hereafter refer to it as TME. 3607 5 9.9 36 – 20.72 5866 1 2.0 20 – 5.75 3.2 Deﬁning α, β and γ

Notes. The last two galaxies, NGC 3607 and NGC 5866, are bonus galaxies, 3.2.1 The power-law slope of the gravitational potential – α in the sense that they were not originally included in the SLUGGS survey but we have obtained and analysed their data using the standard SLUGGS pro- In the TME formalism, the gravitational potential is described math- cedure. NGC is the number of spectroscopically confirmed GCs per galaxy ematically by a power-law function. This is assumed to be valid in and Nsub is the number of GCs identified as belonging to kinematic sub- the region probed and the slope is allowed to vary over −1 ≤ α ≤ structures in Section 2.2. Rmax shows the radial extent probed per galaxy in 1 such that units of the effective radius, Re. v2 a α 0 (α = 0) r ∝ α r We ensure that our final samples are free of substructures as ( ) ⎧ a (6) v2 log (α = 0). identified by the DS test. We further compare mass estimates with ⎨⎪ 0 r and without the identified substructures in Section 3.5 to ascertain α = 0 corresponds to an isothermal potential with a flat circular the effect of substructures on our mass estimation. However, we ⎩⎪ velocity curve (CVC) and α = 1 corresponds to a Keplerian potential defer a detailed discussion of these substructures, within the context around a point mass, characterized by a declining CVC. v is the of hierarchical galaxy mass assembly, to a future paper. 0 circular velocity at scale radius a. The power-law slope of the gravitational potential is a priori 3ANALYSIS unknown and in the following we use different assumptions based on observations and/or theory to constrain our choice of α.The 3.1 TMEs simplest clue about α is to be found from recent studies (e.g. Auger et al. 2010; Thomas et al. 2011; Cappellari et al. 2015)where The TMEs are generally expressed as the total mass density of ETGs was found to be nearly isothermal ρ ∝ −2 C N with a small intrinsic scatter, i.e. (r) r . These studies therefore M (

Table 2. General properties of our galaxies. Column description: (1) galaxy name; (2) total extinction-corrected K-band magnitude, obtained using the absolute K-band magnitude from 2MASS (Jarrett et al. 2000), dust extinction correction from Schlegel, Finkbeiner & Davis (1998) and the correction to the 2MASS photometry due to sky oversubtraction from Scott, Graham & Schombert (2013); (3)–(8) are from Brodie et al. (2014) and include (3) distance; (4) systemic velocity; (5) effective (half-light) radius; (6) central stellar velocity dispersion within 1 kpc; (7) ellipticity and (8) environmental density of neighbouring galaxies; (9) total logarithmic stellar mass, obtained from the absolute K-band magnitude, assuming M/LK = 1 (here and elsewhere in the paper, stellar M/L / ∼ ratio is quoted in units of M L, K); typical uncertainties on our stellar masses are 0.15 dex.; (10) statistical significance of having kinematic substructures in GC system [see Section 2.2 for derivation of column (10)]; (11) the power-law slope of the gravitational potential; (12) the power-law slope of the deprojected GC density profile [see Section 3.2 for derivation of columns (11) and (12)]; (13) normalizing factor to correct for effect of galaxy flattening on dynamical mass estimate and (14) rotation dominance parameter for the GC system, after removing kinematic substructures where relevant [see Section 3.4 for columns (13) and (14)].

Galaxy MK Dist. Vsys Re σ kpc ρenv log(M∗/ M) p-val αγcorr Vrot/σ (NGC) (mag) (Mpc) (km s−1) (arcsec) (km s−1)(Mpc−3) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) − . +0.24 720 25.09 26.9 1745 35 227 0.49 0.25 11.35 0.051 0.058 2.66 0.92 0 42−0.17 − . +0.20 821 24.14 23.4 1718 40 193 0.35 0.08 10.97 0.411 0.234 2.90 0.98 0 40−0.18 − < . +0.21 1023 24.16 11.1 602 48 183 0.63 0.57 10.98 0.009 0.230 2.89 0.85 0 65−0.18 − . +0.20 1400 24.53 26.8 558 28 236 0.13 0.07 11.12 0.288 0.163 2.80 1.01 0 22−0.15 − − . +0.08 1407 25.72 26.8 1779 63 252 0.07 0.42 11.60 0.106 0.056 2.60 1.01 0 04−0.07 − . +0.15 2768 24.91 21.8 1353 63 206 0.57 0.31 11.28 0.364 0.092 2.70 0.88 0 50−0.15 − . +0.15 3115 24.15 9.4 663 35 248 0.66 0.08 10.97 0.043 0.232 2.89 0.83 0 94−0.16 − . +0.14 3377 22.83 10.9 690 36 135 0.33 0.49 10.44 0.419 0.477 3.23 0.98 0 23−0.10 − . +0.26 3608 23.78 22.3 1226 30 179 0.20 0.56 10.82 0.953 0.301 2.99 1.01 0 21−0.18 − . +0.08 4278 23.93 15.6 620 32 228 0.09 1.25 10.88 0.73 0.273 2.95 1.01 0 13−0.07 − − . +0.10 4365 25.43 23.1 1243 53 253 0.24 2.93 11.48 0.195 0.003 2.57 1.00 0 15−0.08 − . +0.25 4374 25.36 18.5 1017 53 284 0.05 3.99 11.46 0.472 0.009 2.59 1.01 0 45−0.24 − . +0.15 4473 23.90 15.2 2260 27 189 0.43 2.17 10.87 0.537 0.279 2.96 0.95 0 23−0.11 − < − . +0.06 4486 25.55 16.7 1284 81 307 0.16 4.17 11.53 0.001 0.027 2.54 1.01 0 14−0.05 − . +0.15 4494 24.27 16.6 1342 49 157 0.14 1.04 11.02 0.018 0.210 2.86 1.01 0 51−0.14 − < . +0.23 4526 24.81 16.4 617 45 233 0.76 2.45 11.23 0.001 0.111 2.73 0.77 0 61−0.24 − . +0.51 4564 23.17 15.9 1155 20 153 0.53 4.09 10.58 0.054 0.414 3.14 0.90 1 80−0.33 − < − . +0.07 4649 25.61 16.5 1110 66 308 0.16 3.49 11.56 0.001 0.037 2.53 1.01 0 34−0.08 − . +0.83 4697 24.29 12.5 1252 62 180 0.32 0.60 11.03 0.394 0.206 2.86 0.98 2 37−0.86 − . +0.09 5846 25.22 24.2 1712 59 231 0.08 0.84 11.40 0.553 0.034 2.62 1.01 0 08−0.07 − . +0.53 7457 22.42 12.9 844 36 74 0.47 0.13 10.28 0.014 0.552 3.33 0.93 1 90−0.42 − . +0.22 3607 24.96 22.2 942 39 229 0.13 0.34 11.29 0.227 0.084 2.69 1.01 0 18−0.15 − . +1.06 5866 24.15 14.9 755 36 163 0.58 0.24 10.97 0.978 0.232 2.89 0.88 0 16−0.36

2012). We use the logarithmic slopes of their CVCs as analysed with the results for the Galaxy potential in Yencho et al. (2006)and by Wu et al. (2014, hereafter Wu+14), in 42 of these simulated W+10.Table2 contains a summary of α adopted for the galaxies ETGs. The simulated ETGs have stellar masses over the range in this study, given their stellar mass. 2.7 × 1010–4.7 × 1011 M, comparable to the stellar mass range in this study. The logarithmic slope is evaluated at 5 R .Wefindan e β empirical relation between α and the logarithm of the stellar mass 3.2.2 The orbital anisotropy parameter – by fitting a linear function to the data (see Fig. 3). The best-fitting The Binney anisotropy parameter, β, (Binney & Tremaine 1987) linear function to the data is describes the orbital distribution of the GCs. It can be a major source of uncertainty in mass modelling of ETGs as it is poorly α = (−0.46 ± 0.06) × log(M∗/ M) + (5.29 ± 0.68) (8) constrained. It is defined (assuming spherical symmetry) as ± with an rms scatter of 0.13 0.01. Using equation (7) and the σ 2 radially extended CVC data (out to 20 kpc) for ETGs published in β = 1 − θ , (9) σ 2 Trujillo-Gomez et al. (2011), we confirm that the relation obtained r above is consistent with observations in the region of overlap. Our where σ θ and σ r are the tangential and radial velocity dispersions, best-fitting function is similar to those reported in Tortora et al. respectively. The TMEs are based on the assumption of constant (2014) determined at much more central radii of 0.5 and 1 Re.When anisotropy with radius. We do not fit for β, but rather we derive mass constrained this way, α reflects the shallower (steeper) total mass estimates assuming β = 0, 0.5, −0.5, corresponding to isotropic, density profiles for more (less) massive ETGs. With equation (8), strong radial and mild tangential anisotropies, respectively. Our α ∼ 0.4 for an arbitrary galaxy with MW-like stellar mass, consistent choice of ±0.5 is predicated on results from mass modelling where

MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3843

Figure 2. GC bubble diagrams from the DS substructure test. The circles represent the GCs and have been scaled to show the differences between local and global kinematics, such that bigger circles show higher probability of kinematic substructures. Galaxy ID and statistical significance of the identified substructures are shown on each plot (the smaller the p-value, the higher the significance of the substructure). North is up and east is left in all the plots.

MNRAS 460, 3838–3860 (2016) 3844 A. B. Alabi et al.

Figure 3. The power-law slope of the gravitational potential, α versus galaxy stellar mass. The blue circles are from the simulated ETGs in Wu+14, Figure 4. The power-law slope of the deprojected GC density profile, γ while the brown stars are from the observational data published in Trujillo- versus galaxy stellar mass. Data points are from Kissler-Patig (1997), Okon´ Gomez et al. (2011). The solid line is the best fit to the predictions from & Harris (2002), Puzia et al. (2004), Bassino, Richtler & Dirsch (2006), Wu+14. Sikkema et al. (2006), Rhode et al. (2007), Faifer et al. (2011)andD+12, as summarized in the plot legend. The solid line is a linear fit to all of the data. typical anisotropies are usually defined such that −0.5 ≤ β ≤ 0.5 (Gerhard et al. 2001; Cappellari et al. 2007). We show in Section 3.3 3.3 Sensitivity of pressure-supported mass estimates to α, β the sensitivity of our mass estimates to this parameter. and γ We investigate the effects of the adopted values of α, β and γ on the pressure-supported mass estimates, Mp, from equation (2), using NGC 1407 as a test case. Di Cintio et al. (2012) showed that 3.2.3 The power-law slope of the deprojected GC density while the variations in Mp due to uncertainties in γ and β can be profile – γ generalized, that due to changes in α is a complicated function (see their equation 19) that varies from galaxy to galaxy, depending on We follow Harris (1976) and derive the deprojected GC density −γ the radial distribution of the tracers. Fig. 5 shows M within 5 R distribution n(r) ∼ r given the projected density profiles of pho- p e − γ − for NGC 1407. For our sensitivity tests, we extend the range of β tometric GCs in the plane of the sky, i.e. N(R) ∼ R ( 1). It is well out to ±1 to study mass–anisotropy dependences at more extreme known that the slope of the GC surface density profile varies with values. The left-hand panel shows M when γ ≡ 3, −0.1 ≤ α ≤ 0.5 the galaxy luminosity (e.g. Harris 1986; Kissler-Patig 1997;Dirsch, p and −1.0 ≤ β ≤ 1.0. In the middle panel, α ≡ 0, 2 ≤ γ ≤ 4and Schuberth & Richtler 2005; Bekki & Forbes 2006). We therefore −1.0 ≤ β ≤ 1.0. The two plots reveal that mass estimates are least make a compilation of measured slopes of the GC density profiles sensitive to β and most sensitive to the assumed potential slope, (which we de-project) from wide-field photometric studies in the lit- α. For example, a 0.5 change in γ when β = 0andα = 0 alters erature (Kissler-Patig 1997;Okon´ & Harris 2002; Puzia et al. 2004; the mass estimate by ∼20 per cent, while a change of 0.1 in α at Bassino et al. 2006; Sikkema et al. 2006; Rhode et al. 2007;Faifer β = 0andγ = 3 changes the mass by ∼30 per cent. Ignorance of et al. 2011; D+12) and the corresponding stellar mass of the host the nature of β becomes an increasingly important issue only when galaxy (using distance from Tonry et al. 2001; Blakeslee et al. 2009; the orbital distribution of the tracers is strongly radial, i.e. β ≥ 0.5. Brodie et al. 2014, the absolute K-band magnitude from 2MASS, the We have also performed this test on all the other galaxies in the correction from Scott et al. 2013 and assuming a stellar M/L = 1). K sample and confirm that in all cases M is most sensitive to α and Fig. 4 shows the deprojected power-law slopes as a function of p least sensitive to β. galaxy stellar mass. The best-fitting linear function to the data is For galaxies with nearly isothermal gravitational potentials, ra-

γ = (−0.63 ± 0.17) × log(M∗/ M) + (9.81 ± 1.94) (10) dially biased orbital distributions increasingly lead to lower total mass estimates. However, in strongly Keplerian potentials, radially with an rms scatter of 0.29 ± 0.04 in the data around the best-fitting biased orbital distributions would lead to higher mass estimates. line. With this linear relation we estimate the deprojected slope of This implies that when α + γ<3, the total mass obtained under the GC density profile of a galaxy given its stellar mass. This is the assumption of tangential anisotropy is greater than that obtained a useful tool when the photometric data are not readily available. assuming radial anisotropy. In the same way, when α + γ>3, the Table 2 contains a summary of γ for all the galaxies in this study. total mass obtained under the assumption of tangential anisotropy The power-law slope of the deprojected GC density profile is is less than that obtained assuming radial anisotropy. This is the thus constrained to 2 ≤ γ ≤ 4, with more massive ETGs having classic situation from dynamical modelling studies with stars and shallower profiles and lower mass ETGs showing steeper profiles. PN in the far outer haloes e.g. (Dekel et al. 2005). When α + γ For a galaxy with MW-like stellar mass, we find γ = 3.3, similar to ∼ 3, the mass estimates are insensitive to β, similar to the result that of the Galaxy, ∼3.5 (Harris 1976; W+10). reported in Wolf et al. (2010) for pressure supported galaxies. Also,

MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3845

Figure 5. Sensitivity of pressure-supported mass estimate for NGC 1407 within 5 effective radii to parameters α, β and γ . Left-hand panel: mass estimate when γ ≡ 3, with −0.1 ≤ α ≤ 0.5 and −1.0 ≤ β ≤ 1.0. A 0.1 change in α at β = 0andγ = 3 corresponds to a change in the mass estimate of ∼30 per cent. Middle panel: mass estimate when α ≡ 0, with 2.0 ≤ γ ≤ 4.0 and −1.0 ≤ β ≤ 1.0. A change of 0.5 in γ at β = 0andα = 0 changes the mass estimate by ∼20 per cent. Mass estimates signiﬁcantly diverge for β = 0.5, with strongly radial orbital distributions producing extremely divergent mass estimates. Note that when α + γ = 3, mass estimates are very insensitive to β. The asterisks show the pressure-supported mass estimates for NGC 1407 when β is −0.5, 0, 0.5, respectively. Right-hand panel: at the shallow limit of the power-law slope of the mass tracers (i.e. γ = 2) and isothermal gravitational potential (i.e. α ∼ 0), strongly radial orbits produce degenerate mass estimates. This ﬁgure is available in colour in the online version.

when β → 1(seeright-hand panel), particularly for galaxies with an isothermal gravitational potential, i.e. more massive ellipticals, the mass estimates become degenerate (see also Wolf et al. 2010). The typical α and γ pairs adopted for the low-, intermediate- and high-mass galaxies in our sample are (0.4, 3.4), (0.2, 2.9) and (0, 2.6), respectively.

3.4 Quantifying the effects of galaxy flattening and GC rotation on mass estimates The TMEs are built on the assumption that galaxies are spherically symmetric and pressure supported. However, these assumptions are not always valid and mass estimates thus need to properly account for other realities. Edge-on and face-on galaxies, under the sphericity assumption, would have their masses overestimated or underestimated, respectively (see Bacon 1985; Bender, Saglia & Gerhard 1994; Magorrian & Ballantyne 2001), closely mimicking the mass– anisotropy degeneracy. A flattening-based mass correction of some Figure 6. Bar chart showing effect of galaxy flattening on the total dynam- sort is therefore necessary. Galaxies in our sample have been delib- ical mass within 5 Re. For our galaxy sample, we are largely affected by erately chosen with a bias towards edge-on inclinations to reduce mass overestimation, with an average mass overestimation due to galaxy confusion in mass estimates from projection effects, hence we are flattening of ∼5 per cent. affected more by overestimation. We apply the normalizing factor from Bacon 1985 to correct for the effect of galaxy flattening on The average difference in total mass estimates due to galaxy flat- ∼ our dynamical mass estimates (their equation 9), assuming that GC tening is 5 per cent. This reflects the bias of our galaxy sample systems have the same ellipticity as the galaxy stars. We multiply in favour of edge-on galaxies. We note that the severity of the overestimation is highest for NGC 4526 (with = 0.76, where our mass estimate Mp (obtained under the assumption of sphericity, ∼ i.e. q ∼ 1), from equation (2), by a factor corr to normalize to mass the total mass would have been overestimated by 20 per cent). when q = 1 − .Weuse We list the correction factors so obtained for each galaxy in Table 2 and report dynamical mass estimates corrected for galaxy flattening −3 e in Table 3. corr(q ,q) = e Similarly, dynamical masses obtained under the assumption of (sin−1e−eq)(1−q2) − 2q2(sin−1e−e/q)(q2−q2) non-rotating tracers would be largely underestimated for galaxies × , (11) where the tracer population has kinematics dominated by rotation. (1−q2)(sin−1e−eq) Flattened (discy) ETGs have been shown to be mostly fast central where e = (1 − q)1/2 and e = (1 − q)1/2. rotators (Krajnovicetal.´ 2011), with some of them observed to Fig. 6 shows the effects of galaxy flattening on the total mass esti- remain fast rotators even at large radii (e.g. Arnold et al. 2014). This mates within 5 Re after applying the correction from equation (11). result has been confirmed in studies that probed the kinematics of

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Table 3. Summary of mass estimates and DM fractions assuming different anisotropy. The results shown here have been obtained using the TME of W+10 (see Section 3.1 for details) and assuming stellar M/LK = 1. Mp is the pressure-supported mass and it has been corrected for the effect of galaxy ﬂattening. Mrot is the rotationally supported mass. Mtot is the total dynamical mass after correcting for galaxy ﬂattening, rotation in the GC system and the presence of kinematic substructures (for galaxies with p < 0.05). fDM is the DM fraction. We list masses enclosed within spheres of radius 5 Re and Rmax, the maximum galactocentric radius where we have GC kinematic data.

Galaxy β Mrot(<5 Re) Mp(<5Re) Mtot(<5 Re) fDM(<5 Re) Rmax Mrot(

720 0 2.0 ± 0.4 3.4 ± 0.8 3.6 ± 0.7 0.46 ± 0.16 19.05 7.6 ± 1.4 11.9 ± 2.4 12.7 ± 2.2 0.83 ± 0.05 0.5 3.3 ± 0.7 3.5 ± 0.7 0.43 ± 0.19 7.6 ± 1.4 11.3 ± 2.2 12.1 ± 2.1 0.82 ± 0.05 − 0.5 3.5 ± 0.8 3.7 ± 0.7 0.47 ± 0.16 7.6 ± 1.4 12.1 ± 2.4 12.9 ± 2.2 0.83 ± 0.05 821 0 1.9 ± 0.4 4.0 ± 0.8 4.2 ± 0.8 0.81 ± 0.06 8.70 3.4 ± 0.7 5.6 ± 1.0 6.0 ± 1.0 0.85 ± 0.04 0.5 4.2 ± 0.8 4.4 ± 0.8 0.81 ± 0.06 3.4 ± 0.7 5.8 ± 1.1 6.2 ± 1.1 0.86 ± 0.04 − 0.5 4.0 ± 0.8 4.2 ± 0.8 0.8 ± 0.06 3.4 ± 0.8 5.5 ± 1.0 5.9 ± 1.0 0.85 ± 0.04 1023 0 2.4 ± 0.4 1.4 ± 0.3 1.6 ± 0.2 0.48 ± 0.13 16.15 7.7 ± 1.4 3.2 ± 0.6 4.0 ± 0.5 0.76 ± 0.05 0.5 1.5 ± 0.3 1.7 ± 0.2 0.49 ± 0.12 7.7 ± 1.4 3.3 ± 0.6 4.1 ± 0.5 0.77 ± 0.05 −0.5 1.4 ± 0.3 1.6 ± 0.2 0.47 ± 0.12 7.7 ± 1.4 3.1 ± 0.6 3.9 ± 0.5 0.76 ± 0.05 1400 0 0.4 ± 0.1 2.3 ± 0.5 2.3 ± 0.5 0.5 ± 0.19 20.62 1.6 ± 0.6 7.2 ± 1.3 7.4 ± 1.3 0.82 ± 0.04 0.5 2.3 ± 0.5 2.4 ± 0.5 0.5 ± 0.18 1.6 ± 0.6 7.2 ± 1.3 7.4 ± 1.3 0.82 ± 0.05 −0.5 2.3 ± 0.5 2.3 ± 0.6 0.49 ± 0.23 1.6 ± 0.6 7.2 ± 1.3 7.3 ± 1.3 0.82 ± 0.05 1407 0 0.1 ± 0.0 11.5 ± 1.1 11.5 ± 1.1 0.71 ± 0.06 14.14 0.2 ± 0.1 36.6 ± 2.7 36.6 ± 2.6 0.9 ± 0.02 0.5 10.2 ± 1.0 10.2 ± 1.0 0.67 ± 0.07 0.2 ± 0.1 32.3 ± 2.4 32.3 ± 2.3 0.88 ± 0.02 −0.5 12.2 ± 1.2 12.2 ± 1.2 0.72 ± 0.06 0.2 ± 0.1 38.7 ± 2.8 38.7 ± 2.9 0.9 ± 0.02 2768 0 4.5 ± 0.4 6.7 ± 1.1 7.1 ± 1.0 0.77 ± 0.07 11.36 10.3 ± 0.9 13.1 ± 2.1 14.1 ± 1.8 0.87 ± 0.04 0.5 6.5 ± 1.1 6.9 ± 0.9 0.76 ± 0.07 10.3 ± 0.9 12.7 ± 2.0 13.7 ± 1.8 0.87 ± 0.04 −0.5 6.8 ± 1.1 7.2 ± 1.0 0.77 ± 0.07 10.3 ± 0.8 13.3 ± 2.1 14.3 ± 1.8 0.87 ± 0.04 3115 0 3.2 ± 0.6 1.7 ± 0.3 2.0 ± 0.3 0.57 ± 0.08 18.35 11.8 ± 2.3 4.5 ± 0.7 5.7 ± 0.6 0.83 ± 0.02 0.5 1.8 ± 0.3 2.1 ± 0.3 0.58 ± 0.07 11.8 ± 2.3 4.6 ± 0.7 5.8 ± 0.6 0.84 ± 0.02 −0.5 1.7 ± 0.3 2.0 ± 0.3 0.56 ± 0.09 11.8 ± 2.2 4.4 ± 0.6 5.6 ± 0.6 0.83 ± 0.02 3377 0 0.1 ± 0.1 0.6 ± 0.1 0.6 ± 0.1 0.58 ± 0.08 14.34 0.3 ± 0.2 1.2 ± 0.2 1.3 ± 0.2 0.79 ± 0.04 0.5 0.7 ± 0.1 0.7 ± 0.1 0.63 ± 0.07 0.3 ± 0.1 1.4 ± 0.2 1.5 ± 0.2 0.81 ± 0.03 −0.5 0.6 ± 0.1 0.6 ± 0.1 0.55 ± 0.1 0.3 ± 0.1 1.2 ± 0.2 1.2 ± 0.2 0.77 ± 0.04 3608 0 0.3 ± 0.2 3.3 ± 1.1 3.4 ± 1.1 0.82 ± 0.18 9.75 0.7 ± 0.4 4.3 ± 1.2 4.4 ± 1.2 0.85 ± 0.08 0.5 3.6 ± 1.1 3.6 ± 1.2 0.83 ± 0.26 0.7 ± 0.4 4.6 ± 1.3 4.7 ± 1.3 0.86 ± 0.07 −0.5 3.2 ± 1.0 3.3 ± 1.1 0.82 ± 0.6 0.7 ± 0.4 4.2 ± 1.2 4.3 ± 1.1 0.85 ± 0.06 4278 0 0.2 ± 0.1 2.8 ± 0.3 2.8 ± 0.4 0.75 ± 0.06 14.87 0.5 ± 0.2 6.5 ± 0.6 6.5 ± 0.6 0.88 ± 0.02 0.5 2.9 ± 0.4 3.0 ± 0.4 0.76 ± 0.06 0.5 ± 0.2 6.9 ± 0.6 6.9 ± 0.6 0.89 ± 0.02 −0.5 2.7 ± 0.3 2.7 ± 0.3 0.74 ± 0.06 0.5 ± 0.2 6.3 ± 0.5 6.4 ± 0.6 0.88 ± 0.03 4365 0 1.0 ± 0.2 12.0 ± 1.3 12.1 ± 1.3 0.78 ± 0.05 12.90 2.6 ± 0.5 29.5 ± 2.6 29.8 ± 2.7 0.9 ± 0.02 0.5 11.0 ± 1.2 11.1 ± 1.2 0.76 ± 0.05 2.6 ± 0.5 27.0 ± 2.4 27.3 ± 2.5 0.89 ± 0.02 −0.5 12.5 ± 1.3 12.6 ± 1.4 0.79 ± 0.05 2.6 ± 0.5 30.8 ± 2.8 31.1 ± 2.8 0.91 ± 0.02

4374 0 8.8 ± 2.0 13.2 ± 3.4 14.1 ± 3.3 0.82 ± 0.06 9.22 16.2 ± 3.7 21.0 ± 4.8 22.6 ± 4.8 0.88 ± 0.04 0.5 12.2 ± 3.1 13.1 ± 3.1 0.81 ± 0.07 16.2 ± 3.9 19.4 ± 4.5 21.0 ± 4.5 0.87 ± 0.04 −0.5 13.7 ± 3.5 14.6 ± 3.7 0.83 ± 0.07 16.2 ± 3.6 21.8 ± 5.0 23.4 ± 5.1 0.88 ± 0.04

4473 0 0.2 ± 0.1 1.4 ± 0.3 1.4 ± 0.3 0.52 ± 0.12 17.35 0.8 ± 0.4 3.6 ± 0.5 3.6 ± 0.5 0.8 ± 0.04 0.5 1.5 ± 0.3 1.5 ± 0.3 0.55 ± 0.12 0.8 ± 0.4 3.8 ± 0.6 3.9 ± 0.5 0.81 ± 0.04 −0.5 1.4 ± 0.3 1.4 ± 0.3 0.51 ± 0.12 0.8 ± 0.4 3.5 ± 0.5 3.5 ± 0.5 0.79 ± 0.04 4486 0 1.6 ± 0.2 24.0 ± 1.7 24.2 ± 1.8 0.88 ± 0.01 30.52 9.8 ± 1.1 146.0 ± 8.2 147.0 ± 8.1 0.98 ± 0.0 0.5 21.6 ± 1.6 21.8 ± 1.6 0.86 ± 0.01 9.8 ± 1.1 131.0 ± 7.4 132.0 ± 7.2 0.97 ± 0.0 −0.5 25.2 ± 1.8 25.4 ± 1.9 0.88 ± 0.01 9.8 ± 1.1 153.0 ± 8.6 154.0 ± 8.6 0.98 ± 0.0 4494 0 1.2 ± 0.1 1.4 ± 0.2 1.5 ± 0.2 0.39 ± 0.12 8.52 2.0 ± 0.3 1.9 ± 0.3 2.1 ± 0.3 0.53 ± 0.09 0.5 1.4 ± 0.2 1.6 ± 0.2 0.41 ± 0.12 2.0 ± 0.2 2.0 ± 0.3 2.2 ± 0.3 0.54 ± 0.08 −0.5 1.4 ± 0.2 1.5 ± 0.2 0.38 ± 0.13 2.0 ± 0.2 1.9 ± 0.3 2.1 ± 0.3 0.52 ± 0.09 4526 0 2.9 ± 0.6 3.1 ± 0.8 3.4 ± 0.6 0.56 ± 0.14 12.06 7.0 ± 1.5 6.5 ± 1.3 7.2 ± 1.1 0.77 ± 0.06 0.5 3.1 ± 0.8 3.4 ± 0.6 0.55 ± 0.14 7.0 ± 1.4 6.4 ± 1.3 7.1 ± 1.0 0.77 ± 0.06 −0.5 3.2 ± 0.8 3.5 ± 0.6 0.56 ± 0.13 7.0 ± 1.4 6.6 ± 1.4 7.3 ± 1.1 0.77 ± 0.06 4564 0 2.4 ± 0.4 0.8 ± 0.3 1.0 ± 0.2 0.65 ± 0.17 8.33 4.0 ± 0.7 0.9 ± 0.3 1.3 ± 0.3 0.72 ± 0.1 0.5 0.9 ± 0.3 1.1 ± 0.3 0.68 ± 0.13 4.0 ± 0.6 1.0 ± 0.3 1.4 ± 0.3 0.74 ± 0.08 −0.5 0.7 ± 0.2 1.0 ± 0.2 0.64 ± 0.16 4.0 ± 0.6 0.9 ± 0.3 1.3 ± 0.3 0.71 ± 0.09

MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3847

Table 3 – continued

Galaxy β Mrot(<5 Re) Mp(<5 Re) Mtot(<5 Re) fDM(<5 Re) Rmax Mrot(

4649 0 3.8 ± 0.3 10.9 ± 0.9 11.3 ± 0.9 0.72 ± 0.05 24.25 18.6 ± 1.6 53.8 ± 3.8 55.7 ± 3.7 0.94 ± 0.01 0.5 9.8 ± 0.8 10.2 ± 0.8 0.69 ± 0.06 18.6 ± 1.6 48.2 ± 3.4 50.1 ± 3.4 0.93 ± 0.01 −0.5 11.5 ± 0.9 11.9 ± 1.0 0.74 ± 0.05 18.6 ± 1.6 56.6 ± 4.0 58.5 ± 4.1 0.94 ± 0.01 4697 0 20.3 ± 3.4 7.0 ± 2.4 9.1 ± 2.4 0.9 ± 0.04 4.66 – – – – 0.5 7.2 ± 2.4 9.3 ± 2.4 0.9 ± 0.05 – – – – −0.5 6.9 ± 2.3 9.0 ± 2.3 0.9 ± 0.04 – – – – 5846 0 0.3 ± 0.1 12.4 ± 1.6 12.4 ± 1.7 0.83 ± 0.05 13.68 0.8 ± 0.2 32.6 ± 3.5 32.7 ± 3.5 0.93 ± 0.02 0.5 11.6 ± 1.5 11.6 ± 1.5 0.81 ± 0.05 0.8 ± 0.2 30.6 ± 3.3 30.7 ± 3.2 0.92 ± 0.02 −0.5 12.8 ± 1.7 12.8 ± 1.7 0.83 ± 0.04 0.8 ± 0.2 33.6 ± 3.6 33.7 ± 3.5 0.93 ± 0.02 7457 0 1.9 ± 0.2 0.9 ± 0.3 1.1 ± 0.2 0.84 ± 0.05 6.26 2.4 ± 0.3 1.0 ± 0.3 1.2 ± 0.2 0.85 ± 0.05 0.5 1.1 ± 0.3 1.3 ± 0.3 0.86 ± 0.05 2.4 ± 0.3 1.1 ± 0.3 1.3 ± 0.3 0.87 ± 0.05 −0.5 0.9 ± 0.2 1.0 ± 0.2 0.83 ± 0.06 2.4 ± 0.3 0.9 ± 0.2 1.1 ± 0.2 0.84 ± 0.05 3607 0 0.3 ± 0.1 2.5 ± 0.7 2.5 ± 0.7 0.3 ± 0.45 20.72 1.3 ± 0.6 10.0 ± 2.4 10.1 ± 2.4 0.81 ± 0.1 0.5 2.4 ± 0.6 2.4 ± 0.6 0.28 ± 0.6 1.3 ± 0.6 9.6 ± 2.3 9.7 ± 2.4 0.8 ± 0.09 −0.5 2.5 ± 0.7 2.5 ± 0.7 0.31 ± 0.32 1.3 ± 0.6 10.1 ± 2.4 10.2 ± 2.4 0.81 ± 0.07 5866 0 0.1 ± 0.3 1.2 ± 0.6 1.3 ± 0.5 0.33 ± 0.45 5.75 – – – – 0.5 1.3 ± 0.6 1.3 ± 0.5 0.35 ± 0.54 – – – – −0.5 1.2 ± 0.6 1.2 ± 0.5 0.31 ± 0.61 – – – –

ETGs beyond 5 Re (e.g. Coccato et al. 2009;Potaetal.2013) with dynamical tracers often showing significant rotation in the outer haloes. Therefore, there is a non-negligible mass contribution from rotation, especially in the flattened ETGs, that needs to be accounted for. We obtain the best-fitting rotation amplitude (Vrot), velocity dispersion (σ ) and kinematic position angle (PA kin), respectively, for each galaxy by fitting

Vrot Vmod,i = Vsys ± (12) PA −PA 2 1 + tan( i kin) qkin to our GC data while we minimize

V − V 2 2 ( i mod,i) 2 2 χ ∝ + ln(σ + ( Vi ) ) . (13) σ 2 + V 2 i ( ( i ) ) These equations are commonly used in studies of GC kinematics (e.g. Bergond et al. 2006;Potaetal.2013). In equations (12) and Figure 7. Bar chart showing effect of rotation in the tracer population on (13), V , V and PA are the measured radial velocities, uncertain- the total dynamical mass within 5 Re. For our galaxy sample, the average i i i ∼ ties on the measured radial velocities and position angles of the GCs, mass underestimation is 6 per cent. respectively. Vsys is the galaxy recession velocity and we fix qkin to the photometric axial ratio q. The uncertainties on the kinematic imum underestimation of ∼20 per cent in NGC 4526 and NGC parameters are obtained through Monte Carlo simulations. 4564. We summarize the significance of rotation by quantifying Vrot/σ for each GC system. We note that while few ETGs have GC systems that are rotation dominated with Vrot/σ > 1, most of them 3.5 Quantifying the effect of kinematic substructures on mass show significant rotation (Vrot/σ ≥ 0.4). We therefore quantify the estimates rotationally supported mass, M , enclosed within projected radius rot For the galaxies with statistically significant kinematic substruc- R using out tures, identified in Section 2.2, we obtain new mass estimates us- R V 2 ing the cleaned catalogues and compare them with the mass es- M = out rot . (14) rot G timates from the original catalogues, within 5 Re and under different isotropy assumptions. Fig. 8 shows the fractional change in Fig. 7 shows the contribution from rotation to the total mass the mass estimate due to the kinematic substructure ( M/Mtot)sub within 5 Re. For galaxies in our sample, the average contribu- for isotropic, radial and tangential velocity distributions. Remov- tion from rotation to the total mass is ∼6 per cent, with the max- ing kinematic substructures lead to reduction in mass estimates and

MNRAS 460, 3838–3860 (2016) 3848 A. B. Alabi et al.

Figure 8. Effect of kinematic substructures on mass estimates within 5 Re Figure 9. Deviation of mass estimate for radial or tangential anisotropy for galaxies with statistically significant kinematic substructures. The bar compared to the isotropic mass estimate. The circles are the mass estimates chart shows the fractional mass overestimation due to kinematic substruc- when orbital anisotropy is radially biased (β = 0.5), while the stars are mass tures. It also shows how the mass estimate changes depending on the as- estimates when tangential anisotropy (β =−0.5) is assumed. The total mass sumption made for the orbital anisotropy parameter, β. For our galaxy estimates within 5 Re in most of the galaxies are insensitive to anisotropy, sample, kinematic substructures lead to ∼14–19 per cent overestimation in with the average variation of the mass estimates being ≤5 per cent. total mass, depending on β. ings of Bacon (1985). In what follows, we adopt the mass estimates for our galaxy sample, the average overestimation varies from ∼14 obtained under isotropy conditions, bearing in mind the potential to 19 per cent, depending on velocity anisotropy. This agrees with deviations for each galaxy. the study of Yencho et al. (2006) where the effect of substructure on mass estimate of galaxies was found to be ∼20 per cent. The greatest fractional mass overestimation is found in NGC 4526 3.7 Comparison of mass estimates with results from the (∼30 per cent). For the galaxies with identified kinematic substruc- literature tures, the total mass estimates in Table 3 are from the cleaned In Table 4, we compare mass estimates for our galaxies to the lit- catalogues, i.e. corrected for substructures. erature. We show the comparison in Fig. 10. The literature sample include studies with PNe, GCs and X-rays as the mass tracers and a 3.6 Total mass estimates variety of generally more sophisticated mass modelling techniques. For example, 9 galaxies from our sample were studied homoge- Table 3 contains a summary of the mass contribution from rotation, neously by D+12 using PNe and/or GC kinematic data out to 5 Re. Mrot and pressure support, Mp (corrected for galaxy flattening) for They did not account for galaxy flattening, rotation of the tracers all the galaxies studied in this paper. Mp is calculated with Vrot and kinematic substructures in their mass estimates, even though subtracted from Vlos, i as prescribed in Evans et al. (2003). We they modelled the velocity anisotropy. The comparisons are done at account for the effects of galaxy flattening and rotation in our total the same galactocentric radii (not always at 5 Re) as reported in the dynamical mass estimate, Mtot(Eridanus A group, which may be wrong as the ing β ≡−0.5, 0, 0.5. The uncertainty on the total mass varies with ripples in the X-ray maps (Su et al. 2014) seem to suggest. Mass the total number of GCs, NGC, such that when NGC ≥ 100 and after estimates obtained by studying the phase-space distribution func- accounting for individual Vlos error via Monte Carlo simulations, tion of tracers (D+12) tend to be systematically lower than those the typical uncertainty is ∼0.12 dex. For galaxies with NGC ∼ 70 from other methods. This is most likely related to the modelling and ≤40, typical uncertainties on total mass are ∼0.20 and ∼0.25 assumptions made in the study e.g. they restricted α>0. For mass dex, respectively. estimates obtained from GC kinematics, the two galaxies with the We show how the total mass estimates, assuming mildly tangen- greatest offsets from our results are NGC 4486 (Murphy et al. 2011) tial and strong radial anisotropies, deviate from that obtained under and NGC 4649 (Shen & Gebhardt 2010). The mass overestimation isotropy condition in Fig. 9. Mass estimates are largely insensitive for NGC 4486 has been attributed in the literature to the problematic to our choice of β: only NGC 3377, NGC 7457 and NGC 1407 data used in the study (see Strader et al. 2011; Zhu et al. 2014). For show deviations larger than 10 per cent, in agreement with the find- NGC 4649, there is a wide spread in the mass estimates obtained

MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3849

Table 4. Mass estimates from the literature obtained using different mass the results are from Cappellari et al. (2015, hereafter C+15), where tracers and modelling techniques, and comparison with results from this we obtain the total mass by integrating their total mass density work, obtained assuming β = 0 and allowing the slope of the gravitational profiles. We have also added results from the extended stellar kine- potential to vary with galaxy stellar mass. Mlit. and MTME are the total matics of Weijmans et al. (2009) and Forestell & Gebhardt (2010) masses from the literature and this work, respectively, within projected for NGC 821 and the cold-gas study of den Heijer et al. (2015)for radial distance R. NGC 4278. The agreement between our mass estimates and literature mass measurements from stellar kinematics is similar to that in Galaxy RMlit. MTME Tracer (NGC) (kpc) (1011 M)(1011 M) the right-hand panel of Fig. 10, though with some individual discrepancies. For example, we find the largest deviation in NGC 821, 720 20 5.1 ± 0.4 2.8 ± 0.6 X-raya where our mass estimate differs from that of C+15 by a factor of 4, b 821 22 2.3 ± 0.6 4.3 ± 0.1 PNe while being more consistent with the results from Weijmans et al. ± ± c 1023 10 1.7 0.6 1.6 0.3 PNe (2009) and Forestell & Gebhardt (2010). Also, the mass estimate 1407 68 30.6 ± 3.9 20.9 ± 1.7 GCd for NGC 4494 from C+15 is a factor of ∼2 higher than what we 29 9.4 ± 1.3 8.2 ± 0.9 GCb 25 21.6 ± 6.9 7.1 ± 0.7 X-raye have found. 100 100.0 30.5 ± 2.2 X-rayf From Fig. 10, mass estimates from PNe appear to be systemati- 2768 14 3.2 ± 1.5 3.7 ± 0.6 PNec cally lower compared to those from GCs and X-ray data, especially 3115 7 1.1 ± 0.5 2.1 ± 0.3 PNec for the more massive galaxies. Our masses also appear to be sys- 3377 10 0.7 ± 0.2 0.6 ± 0.1 PNeb tematically lower than literature values obtained using GCs. If we 4365 15 3.9 ± 0.6 6.2 ± 0.6 X-rayg assume that all the mass measurements (stars, GCs, PN and X-rays) 4374 32 11.5 ± 1.2 17.7 ± 3.9 PNes have comparable errors, then the observed 1σ scatter about the one- b 30 15.9 ± 1.9 17.1 ± 3.8 PNe to-one relation between the literature values and our mass estimates ± ± i 29 19.2 1.8 16.5 3.7 PNe is 0.3 dex. If we exclude the X-ray data, the scatter is reduced to 4486 46 33.3 ± 3.3 35.4 ± 2.3 GCb ± ± j 0.2 dex. These rms scatters are however upper limits since we only 135 85.2 10.1 97.2 5.4 GC α 180 149.6 ± 20.0 130.6 ± 7.2 GCi consider total mass estimates obtained assuming isotropy, varying / = 180 191.0 ± 21.0 130.6 ± 7.2 GCk with stellar mass and stellar M LK 1 for the comparison. On a 47 57.0 ± 11.0 36.3 ± 2.3 GCl galaxy by galaxy basis, the scatter can be reduced significantly by 120 125.0 ± 7.0 86.7 ± 4.9 X-raye considering specific combinations of these parameters. Our mass 4494 20 1.6 ± 0.3 1.4 ± 0.2 PNem estimates therefore compare well with results from more sophisti- 20 1.2 ± 0.2 1.4 ± 0.2 PNeb cated modelling techniques, and from different mass tracers over a 19 2.1 ± 0.1 1.3 ± 0.2 PNen wide radial range that extends out to 180 kpc. 4564 7 0.4 ± 0.1 1.0 ± 0.2 PNeb 4649 46 8.7 ± 1.3 19.1 ± 1.3 PNeb 25 16.3 ± 4.3 10.5 ± 0.8 X-raye o 45 34 18.6 ± 1.3 GC 3.8 DM fraction 45 22 18.6 ± 1.3 GCp 4697 17 1.4 ± 0.2 8.9 ± 2.2 PNeb The DM fraction is a useful parameter in understanding the mass 15 1.9 ± 0.3 8.3 ± 2.2 PNeq distribution as a function of radius in galaxies. We define the DM ± ± r 5846 56 17.0 3.0 19.8 2.1 PNe,GC fraction, fDM,as 45 16.0 ± 3.3 16.2 ± 1.8 GCh ± ± b 45 11.2 2.7 16.2 1.8 PNe fDM(

from GC (Shen & Gebhardt 2010), X-ray (Das et al. 2010)andPN (D+12) data. The GC data used in Shen & Gebhardt (2010) come 3.9 Total mass and DM fraction beyond 5 R in part from the catalogue of Lee et al. (2008), in which Pota et al. e (2015) identiﬁed some extreme velocity objects. This, combined We extend our mass estimation method to GC kinematic data beyond with the kinematic substructures we have identiﬁed in this galaxy, 5 Re and obtain the total mass and DM fraction enclosed within could be the source of the differences in the mass estimates for the maximum probed radius (Rmax ). We summarize our results in NGC 4649. Another interesting case is NGC 4494, where results Table 3, where we have assumed stellar M/LK = 1. NGC 4697 and using essentially the same data set but different methods give mass NGC 5866 have been excluded from this analysis due to the limited estimates that vary by a factor of ∼2. radial extent of their GC kinematic data. Lastly, we compare our mass estimates to results from the ex- To properly understand how the total mass changes with galac- tended stellar kinematics in the right-hand panel of Fig. 10.Mostof tocentric radius, we use the method of Napolitano et al. (2005)

MNRAS 460, 3838–3860 (2016) 3850 A. B. Alabi et al.

Figure 10. Comparison of mass estimates for galaxies in our sample with results from the literature obtained using different mass tracers and modelling techniques. Left-hand panel: galaxies are identified as shown in the plot legend, with brown, blue and black symbols highlighting the mass tracers used. The hatch marks differentiate galaxies according to the modelling technique employed. DF indicates the phase-space distribution function technique used in D+12, JM is the traditional Jeans mass modelling technique, e.g. Pota et al. (2015), M2M is the made-to-measure mass model, e.g. DeLorenzi et al. (2008), SOM is the Schwarzschild orbit-based modelling technique used in Murphy et al. (2011) while KIN is the asymmetric drift method employed by Cortesi et al. (2013) to extract circular velocities from PNe kinematics, respectively. Right-hand panel: comparison of mass estimates with results from the literature based on extended stellar kinematics. Most of the data points are from the extended stellar kinematics study of Cappellari et al. (2015) which we supplement with results from Weijmans et al. (2009) and Forestell & Gebhardt (2010) for NGC 821. We also include the mass estimate for NGC 4278 from the cold-gas study of den Heijer et al. (2015), assuming their result was measured at 15 kpc (the arrow shows how the mass estimates compare towards 28 kpc). Combining all the data (i.e. PNe, GCs and stars, without the X-ray data) and assuming comparable errors, we observe a 1σ scatter of 0.2 dex between our mass estimates and literature values. This figure is available in colour in the online version. to obtain the mass-to-light (M/L) gradient between 5 Re and the maximum radius. We use R M M ∇ϒ ≡ e DM − DM , (17) R M∗ M∗ out in where ∇ϒ is the M/L gradient, MDM and M∗ are the enclosed DM and stellar mass, respectively. Fig. 11 shows ∇ϒ versus the total stellar mass of our galaxies. For comparison, we have added data points from Napolitano et al. (2005), where a similar analysis was done using data extending out to ∼4 Re (they compiled results from the literature from dynamical studies based on discrete tracers and extended integrated stellar light). The systematic offset between the trend in our data and that of Napolitano et al. (2005) is because we probe radial regions that are more DM dominated (see their Fig. 3). We note that similar results are obtained when α = 0 or an outer radius beyond 5 Re is used. The gradient is shallow for galaxies with stellar mass below ∼ 11.2 10 M, however beyond this transition stellar mass, a sharp Figure 11. M/L gradient (between 5 Re and the maximum radial limit) upturn in the gradient is observed, with the more luminous galaxies versus total stellar mass. The circles are the results from this work, while the showing a wide variety of gradients. This dichotomy is the direct stars are from Napolitano et al. (2005). Note that Napolitano et al. (2005) effect of the difference in the relative radial distribution of stellar obtained their gradients over the range 0.1–4 Re, while the gradients in this mass and DM in ETGs. The transition stellar mass coincides with work have been obtained between 5 Re and larger radii. The systematic offset between the trend in our data and that of Napolitano et al. (2005) the upturn in the galaxy M∗–Re relation, such that in the lower mass is because we probe radial regions that are more DM dominated (see their galaxies, where R varies slowly with M∗, the scale radius of the e Fig. 3). The low and intermediate stellar mass galaxies have shallow total DM halo also varies slowly with M∗, hence the flat gradients. For M mass gradients and the more massive galaxies show much steeper gradients. the more massive galaxies, as Re increases rapidly with ∗,weare NGC 4697 and NGC 5866 are not shown in this plot due to the limited radial able to probe more DM. extent of their GC kinematic data.

that our mass estimates are consistent with previous studies in the 4 DISCUSSION literature, with an observed rms scatter (upper limit) of 0.2 dex. In the previous section, we homogeneously obtained total mass We also used the DM fraction, fDM, to describe the relative radial estimates and DM fraction within 5 Re and beyond, and showed distribution of the stellar and DM in our sample.

MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3851

4.1 DM fractions and galaxy models low and high stellar mass galaxies are seen to be DM dominated within 5 R , consistent with the model predictions. However, our f To properly understand these results within the CDM framework, e DM measurements reveal discrepancies between predicted and mea- we compare the f within 5 R with predictions from a simple DM e sured f for galaxies in the intermediate stellar mass bin galaxy model where we assume that the DM content follows an DM (∼1011 M). To ascertain if this trend is driven by our stellar NFW profile (Navarro, Frenk & White 1996), with the stellar con- M/L = 1 assumption, we repeat the entire analyses, adopting tent described by a Sersic´ (1968) mass profile. Starting with the K the stellar masses obtained earlier with alternative M/LK assump- galaxy stellar mass, we use the R –M∗ relation from Lange et al. e tions. This is an important exercise, bearing in mind the uncertain (2015) to obtain model galaxy sizes over our stellar mass range. contribution from the stellar mass to the total mass estimate. The Next, the non-linear M∗–halo mass relation for ETGs from Dutton trend in the measured f within 5 R persists for a variety of stellar et al. (2010) gives the galaxy halo mass, M , for a given total DM e 200 M/L assumptions. We note again for clarity that while the results we stellar mass. The halo is then completely parametrized by obtaining show in Fig. 12 were obtained under the additional assumption of the halo concentration parameter, c , using the M –c relation 200 200 200 isotropy, the trends are the same regardless of orbital anisotropies. from Dutton & Maccio(` 2014) based on the Planck cosmology. We For some of our galaxies, especially in the intermediate stellar mass note that at a fixed halo mass, Planck cosmology yields higher halo bin, the Salpeter IMF (Salpeter 1955) gives stellar mass greater concentration than the WMAP5 cosmology, but only slightly alters than the total dynamical mass estimate. The tension between pre- the f . We then obtain the scale radius, r , of the galaxy halo using DM s dictions and measurements is however reduced when a Kroupa IMF M = 4π ρ r 3/3andr ≡ r /c . Armed with the r , 200 vir cri 200 s 200 200 s (Kroupa et al. 1993) is assumed. This is not surprising as a Kroupa c for any given R –M∗ pair plus a universal baryon fraction of 200 e IMF implies ∼40 per cent less stellar mass compared to a Salpeter 0.17 (Spergel et al. 2007), we then produce the cumulative NFW IMF. The low- and high-stellar mass galaxies are however consistent DM-only radial profiles out to large radii. Likewise, for each R –M∗ e with both Salpeter and Kroupa IMF. pair, we use the R –n relation from Graham (2013) and describe the e We have also checked to see if the corrections we applied for cumulative stellar mass radial profile as defined in Terzic´ & Graham galaxy flattening and inclinations alter our results. We performed (2005). our entire analysis assuming that all our galaxies are spherical and Our total stellar masses have been obtained assuming a global observed edge-on, i.e. q = 1andi = 90 deg. This implies that stellar M/L ratio of M/L = 1. This assumption does not reflect K in Table 3 and in equations (5) and (15), q = 1andcorr= 1, differences in the stellar population parameters (e.g. age, metallicity, respectively. A two-sided KS test of M and f thus obtained stellar initial mass function) of ETGs, especially in their central tot DM with our earlier results shows that they are identical, i.e. one cannot regions. However, we note that our SLUGGS galaxies are generally rule out that they are drawn from the same distribution. dominated by very old (8–14 Gyr) stellar populations and have The galaxy model above is simplistic and does not explicitly a small range in mean metallicity (McDermid et al. 2015). The account for processes which may alter the distribution of DM during M/L is largely insensitive to metallicity variations (Forbes et al. K galaxy assembly. In Fig. 13, we therefore compare the observed 2008; Conroy & van Dokkum 2012). For example, fig. 10 from f within 5 R with results from the simulation of W+14, where Forbes et al. (2008) shows that the stellar M/L can vary by ∼0.15 DM e K both the observed and simulated galaxies covered a comparable dex within the metallicity range of our sample (−0.2 ≤ [Fe/H] ≤ stellar mass range. In their simulations, they allowed the DM density 0.1), which is comparable to the uncertainties on our stellar mass distribution to be modified during galaxy assembly via processes estimates. A similar uncertainty is associated with the observed age like adiabatic halo contraction and halo expansion, such that the variation, i.e. 8–14 Gyr, of our sample. inner DM density is different from the NFW DM density we adopted To test how adopting a stellar M/L = 1 (corresponding to a K in our simple galaxy model. The W+14 simulations however did not Kroupa IMF; Kroupa, Tout & Gilmore 1993) may affect our fDM, 3D account for AGN and/or supernovae feedback processes, therefore, we also obtain f using stellar masses from the ATLAS survey. DM their haloes host galaxies with efficient star formation histories We first use their (M/L ) , obtained from stellar population syn- r Salp and stellar masses a factor of 2–3 above the expectations from a thesis models which assumed a Salpeter IMF (table 1, column 5 in typical galaxy M∗–halo mass relation. At any given halo mass, their Cappellarietal.2013b) and the galaxy luminosity in the SDSS r simulations yield significantly lower f than our vanilla model band (table 1, column 15 in Cappellari et al. 2013a) to estimate in- DM predicts, but in better agreement with our measurements for the dividual stellar masses for the galaxies we have in common. For the 3D intermediate mass galaxies with lowered fDM. While it is obvious four galaxies in our sample that are not in the ATLAS survey, we use that processes which maximize the stellar mass would result in the best-fitting function to the K-band magnitude and stellar mass lower f , it is however not clear from the simulation if the low data of their 260 galaxies to infer the stellar masses. We also use DM f is exclusively driven by the baryon–DM interaction or by the their best fit (M/L ) (table 1, column 4 in Cappellari et al. 2013b), DM r stars feedback processes. obtained from dynamical modelling as total mass minus DM mass, to obtain the stellar mass. This method avoids the potential issue of a non-universal stellar M/LK for our sample when deriving the 4.2 Total mass and DM fraction, with α ≡ 0 stellar masses, since recent results suggest that stellar M/L system- In our total mass estimation, we used α derived from the slopes atically varies with galaxy mass (e.g. Cappellari et al. 2012; Conroy of the circular velocity profiles in the simulation of Wu+14 (see & van Dokkum 2012; Pastorello et al. 2014; Spiniello et al. 2014). Section 3.2). This allowed α to vary freely between the extremes On average, these stellar masses are consistent with those listed in of Keplerian and logarithmic potentials depending on the galaxy Table 2 within ∼0.3 dex. stellar mass. For the most massive galaxies, α ∼ 0(seeTable2). In Fig. 12, we compare the predicted f for our galaxy sample DM However, it is plausible that the low and intermediate stellar mass with the measured f within 5 R . The average f for our sam- DM e DM ETGs reside in isothermal gravitational potential, such that they are ple is 0.6 ± 0.2, varying from 0.3 in NGC 3607 to 0.9 in NGC better described by α ≡ 0. For example, C+15 found α = 0.27 ± 4486. fDM is predicted to increase with galaxy stellar mass while 0.23, on 1–4 Re scales for galaxies with a wide range of stellar mass.

MNRAS 460, 3838–3860 (2016) 3852 A. B. Alabi et al.

Figure 12. Measured DM fraction, fDM, versus the total mass, Mtot, within 5 effective radii (Re). Top panels: in all the top panels, the solid lines show the predicted DM fractions within 5 Re assuming Planck cosmology. The dashed lines show the same but assuming WMAP5 cosmology (see text for details). 11 The marker colour shows the stellar mass of the galaxies. Minimum fDM is observed at stellar mass ∼10 M. In the left-hand panel, we assume a stellar 3D M/LK = 1, while in the middle and right-hand panels, we use stellar M/L ratios from the ATLAS survey based on a Salpeter IMF and best-fitting stellar M/L ratios from dynamical modelling (total dynamical mass minus DM mass), respectively (Cappellari et al. 2013a,b). Regardless of the adopted stellar M/L ratios, galaxies in the intermediate stellar mass bin have fDM significantly different from what is predicted. Also, low- and high-stellar mass galaxies have higher measured DM fractions than intermediate stellar mass galaxies. Bottom panels: these panels show residuals between predictions (with Planck cosmology) and observations, calculated as (observed-predicted)/predicted. This figure is available in colour in the online version.

Also, Thomas et al. (2009) showed that ETGs in the Coma cluster 4.3 Tension between observations and predictions are better described by logarithmic DM haloes rather than NFW The results in Figs 12 and 14 show that the mismatch between ob- DM haloes. This would mean that in our earlier analysis, the total servations and predictions of fDM is systematic. Intermediate stellar mass and fDM especially for these galaxies would be underestimated, 11 mass galaxies with M∗ ∼ 10 M (NGC 4494, NGC 3607 and depending on how much their α parameter deviates from 0. Since NGC 5866) show the greatest deviation from the predicted f , our mass estimator is most sensitive to the α parameter on a galaxy DM all with low f within 5 R . It is helpful to note that this stellar by galaxy basis, it is imperative that we check if the earlier trend DM e mass range coincides with the sharp upturn in the galaxy R –M∗ we found in the distribution f with stellar mass is robust to the e DM relation (e.g. Hyde & Bernardi 2009; Lange et al. 2015) and galaxy value of α. peak star formation efﬁciency (e.g. Shankar et al. 2006; Conroy & We therefore re-perform our mass estimation assuming a loga- Wechsler 2009; Sparre et al. 2015) beyond which halo quenching rithmic gravitational potential, i.e. α ≡ 0, for our sample, and show prevents massive galaxies from accretion of cold gas (e.g. White & the result in Fig. 14. The earlier-observed trends in f persist, and DM Rees 1978; Dutton & Maccio` 2014). From our simple galaxy model they are therefore independent of the assumed slope of the gravita- (see Section 3.8), it is also the stellar mass beyond which R /r ,the tional potential, α, as well as the adopted stellar M/L and the orbital e s ratio of the galaxy size to the scale radius of the DM halo, starts anisotropy of the tracers. NGC 3607 has the least f within 5 R DM e to fall sharply. While the low f of these galaxies can be directly in our sample regardless of the adopted stellar M/L ratio. The total DM linked to a more efﬁcient star formation history, it is interesting mass for NGC 7457 and NGC 4494 are also increased by ∼45 and to explore why they show more scatter in their f compared to 35 per cent, respectively. We summarize these mass estimates and DM CDM predictions. Dutton et al. (2011) showed that intermediate f in Tables A2 and A4. DM mass galaxies are consistent with Salpeter IMF only when their

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Galaxies with marginally low fDM within 5 Re e.g. NGC 720, NGC 4526 and NGC 1023, they can be seen to rapidly increase their fDM between 5 Re and their respective Rmax, showing that they are DM dominated. Our study also includes the two most dominant members of the Leo II group (NGC 3607 and NGC 3608) with intriguing fDM measurements. The most luminous member of the group, NGC 3607 (MK =−24.96) has fDM ∼ 0.3 within 5 Re. NGC 3607 has the lowest fDM within 5 Re in our sample even when the DM content is maximized with a logarithmic potential, regardless of the adopted stellar M/LK. However, beyond 5 Re,thefDM in NGC 3607 increases steeply up to ∼0.8, again showing that the outer halo is dominated by DM. The next most luminous member of the group with MK =−23.78, NGC 3608, however, has a higher fDM of ∼0.8 within 5 Re. Within 5 Re, NGC 3607 has an average DM density of −3 log ρDM∼6.2M kpc , the lowest in our sample, unlike NGC −3 3608 with a denser DM halo with log ρDM∼7.2M kpc .This suggests that both galaxies have DM haloes that are structurally different, with implications for their assembly time, such that the Figure 13. DM fraction within 5 Re versus circular velocity (at 5 Re) galaxy with the denser DM halo assembled earlier (Navarro et al. and galaxy size. Left-hand panel: DM fraction within 5 Re versus circular 1996; Bullock et al. 2001; Thomas et al. 2009). As a group, the velocity. Data from our sample, D+12 and from the simulations of Wu+14 intermediate stellar mass galaxies with low f in our galaxy sample σ DM are shown as indicated in the plot legend. The best linear ﬁt and intrinsic 1 also have the lowest average DM densities. This mirrors the results scatter to our data are shown by the line and the shaded band, respectively. from Romanowsky et al. (2003) and Napolitano et al. (2005, 2009) Right-hand panel: same as in left-hand panel, but now showing DM fraction where some discy, fast rotating, intermediate stellar mass galaxies versus galaxy size. Our study, as well as that of D+12 ﬁnds a wider range of DM fraction than in the simulations of Wu+14. The simulations yield showed more diffuse DM haloes than expected. A more detailed DM fractions more consistent with the low measurements we have for some investigation of the structural parameters of the DM haloes (with of our intermediate mass galaxies. The dashed lines in both panels are from adiabatic halo contraction) is however beyond the scope of this the simple galaxy model with a pristine NFW DM density distribution as paper. discussed in the text.

4.4 Correlations between DM fraction and galaxy properties Vc(Re)/σ ≥ 1.6. In the top middle panel of Fig. 12, the intermediate mass galaxies that are consistent with a Salpeter IMF are NGC In this section, we look for trends in fDM as a function of other 3608, NGC 821, NGC 4697, NGC 2768 and NGC 4278. We find galaxy properties. Fig. 15 shows how the measured fDM within 5 Re that these galaxies have Vc(5Re)/σ ≥ 1.3. NGC 3607, which has varies with galaxy ellipticity, central velocity dispersion, galaxy the lowest Vc(5Re)/σ ∼ 0.9, has a negative fDM when a Salpeter size and galaxy rotation dominance parameter, and we also high- IMF is assumed. A simple experiment in which we vary the stellar light the environment and morphology of the galaxies (see Table 2). M/LK ratio (a proxy for the IMF) reveals that the maximum stellar The rotational dominance parameters are from Arnold et al. (2011). M/LK that gives positive fDM for all the galaxies in our sample is Table 5 shows the Spearman rank correlation coefficient and sta- ∼1.4. This is shallower than the Salpeter IMF, but steeper than a tistical significance of the correlation between the fDM and galaxy Kroupa/Chabrier IMF (at a fixed age and metallicity). properties. The correlations are generally weak, mainly due to the One of the intermediate mass galaxies studied here, NGC 4494, huge scatter introduced by the intermediate stellar mass galaxies has been notoriously difficult to model in the literature, with re- identified and discussed in Section 4.3. There is a visible trend in sults ranging from a low DM content (Romanowsky et al. 2003; fDM with . Here, we find that fDM within 5 Re decreases with . Napolitano et al. 2009; D+12) to a high DM content (Morganti However, there are notable outliers to this trend. The trends with et al. 2013). Here, using GC kinematic data that extend far out Re, σ and V/σ are weak. While the slow rotators in our sample into the halo, we find that NGC 4494 is DM poor, i.e. fDM ≤ 0.5 generally have high fDM, there is no clear pattern in the fast rotators. at Rmax ∼ 9 Re regardless of the adopted stellar M/LK and the GC The S0 galaxies, however, show a decreasing fDM with σ and Re. orbital anisotropy when α, the slope of the gravitational potential, is We do not see any strong trend as a function of environment or assumed to be 0.2. Our Rmax for NGC 4494 is close to the scale ra- morphology. In Fig. 16,weshowhow∇ϒ varies with galaxy prop- dius of the NFW DM halo, where the mass distribution is expected erties. The correlations are now stronger and statistically significant 13 to be DM dominated, such that in a typical 10 M halo, fDM ∼ (see Table 5). The gradients are shallower for flattened galaxies, 0.9 at the scale radius. However, when α ≡ 0 in equation (6), we with the more spherical galaxies showing a great variety of ∇ϒ. obtain fDM ∼ 0.3–0.6 within 5 Re and fDM ∼ 0.5–0.7 within Rmax , Larger and more massive galaxies have steeper ∇ϒ. There is no for varying stellar M/LK. This is similar to the result from Morganti clear trend with galaxy environment. However, when the different et al. (2013), obtained also by assuming a logarithmic DM halo. A galaxy morphologies are highlighted, the S0 galaxies are seen to more detailed dynamical mass modelling of NGC 4494 that com- have shallow ∇ϒ regardless of galaxy ellipticity, size, total mass bines the existing literature data and the GC data we have studied or rotational dominance parameter (the same trend is also evident here would be desirable. Such a study should explore a wide suite from the result in Napolitano et al. 2005). The net effect for massive of gravitational potentials, galaxy shapes and orbital distributions S0 galaxies is to reduce their Re/rs compared to similar stellar mass while incorporating stellar population models. ellipticals, hence their flattened gradients, i.e. lower ∇ϒ.

MNRAS 460, 3838–3860 (2016) 3854 A. B. Alabi et al.

Figure 14. Same as in Fig. 12, but assuming a logarithmic potential for our sample, i.e. α ≡ 0 in equation (6). The intermediate stellar mass galaxies still have the lowest fDM in our sample, same as in Fig. 12. This ﬁgure is available in colour in the online version.

Table 5. Spearman correlation test and statistical signiﬁcance of the correlation between the fDM and ∇ϒ and galaxy properties.

Parameters coeff p-val Parameters coeff p-val

fDM − − 0.22 0.32 ∇ϒ − −0.37 0.09 fDM − σ 0.18 0.44 ∇ϒ − σ 0.76 0.001 fDM − Re 0.32 0.16 ∇ϒ − Re 0.75 0.001 fDM − V/σ − 0.44 0.04 ∇ϒ − V/σ −0.63 0.001

5 CONCLUSIONS We have employed a TME to homogeneously obtain mass estimates of 23 ETGs out to 5 Re and beyond, using their GC kinematic data. The galaxies we have studied cover a wide range of total galaxy stellar mass and include galaxies from the ﬁeld, group and cluster environments. The GC kinematic data have been obtained using the Keck/DEIMOS multi-object spectrograph as part of the SLUGGS survey. We accounted for kinematic substructures, galaxy ﬂattening

Figure 15. DM fraction within 5 Re versus galaxy parameters. Top panels and rotation in the GC system in our mass estimates. We have are colour-coded according to galaxy environment as shown in panel (a) and done an extensive comparison of our mass estimates with results the bottom panels according to galaxy morphology as shown in panel (e). from the literature obtained using various mass tracers and more (Panels a, e) galaxy ellipticity – , (panels b, f) central velocity dispersion, sophisticated modelling techniques. (panel c, g) effective radius and (panels d, h) rotation dominance param- From the mass profiles, we have obtained the DM fraction en- eter. There is no clear trend either as a function of galaxy morphology or closed within 5 Re and compared our results with predictions from a environment and the trends with galaxy properties are generally weak. simple galaxy model (NFW profile for DM plus Sersic´ mass profile for the stars). We have also studied the effect of varying the stellar

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mological simulations of Wu+14 where the pristine DM density distribution has been modified via baryon–DM interactions during galaxy assembly. The widely reported dearth of DM in the outer halo of NGC 4494 is alleviated by assuming a logarithmic gravitational potential. (v) Using total mass estimates within 5 Re and larger radii (usually comparable to the scale radii of the DM haloes), low and intermediate stellar mass galaxies in our sample have shallow M/L gradients, with the more massive galaxies generally having steeper gradients. This reflects the relative difference in the radial scale of baryons and DM in ETGs. However, lenticular galaxies, regardless of galaxy stellar mass, ellipticity, size and rotational dominance parameter, have shallow gradients. (vi) We find hints that intermediate stellar mass galaxies with low DM fractions have halo structural parameters that are not typical, i.e. they possess very diffuse DM haloes and they assembled late. This result is interesting and calls for a systematic study of the structural parameters of the haloes of ETGs. Figure 16. M/L gradient, ∇ϒ, versus galaxy parameters. Colour coding is same as in Fig. 15. (Panels a, e) ∇ϒ versus galaxy ellipticity – , (panels b, ACKNOWLEDGEMENTS f) ∇ϒ versus central velocity dispersion, (panels c, g) ∇ϒ versus effective radius and (panels d, h) ∇ϒ versus rotation dominance parameter. Galaxies We wish to thank the anonymous referee for the useful feedback. ∼ σ with 0, large and larger Re have steeper gradients. An interesting The data presented herein were obtained at the W.M. Keck Ob- ∇ϒ trend is seen in panel h where the S0 galaxies have shallow regardless servatory, which is operated as a scientific partnership among the of galaxy ellipticity, size or mass. California Institute of Technology, the University of California and M/L ratio (consistent with either a Salpeter or a Kroupa-like IMF the National Aeronautics and Space Administration. The Observa- or one that varies with galaxy stellar mass) on our results. Since our tory was made possible by the generous financial support of the GC data extend well beyond 5 R , we have quantified the gradient W.M. Keck Foundation. The authors wish to recognize and ac- e knowledge the very significant cultural role and reverence that the of the DM fraction between 5 Re and the maximum probed radius. Lastly, we studied trends in the DM fraction as a function of galaxy summit of Mauna Kea has always had within the indigenous Hawai- properties. ian community. The analysis pipeline used to reduce the DEIMOS The salient results are as follows. data was developed at UC Berkeley with support from NSF grant AST-0071048. JPB acknowledges support from NSF grant AST- (i) Mass estimates obtained using GC kinematic data and the 1211995. DAF and JJ thank the ARC for financial support via DP TME are consistent with those obtained from more sophisticated 130100388. 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MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3857

Wu X., Gerhard O., Naab T., Oser L., Martinez-Valpuesta I., Hilz M., Chu- Table A2 – continued. razov E., Lyskova N., 2014, MNRAS, 438, 2701 (Wu+14) Yencho B. M., Johnston K. V., Bullock J. S., Rhode K. L., 2006, ApJ, 643, Galaxy β Mtot(<5 Re) fDM(<5 Re) Mtot(

MNRAS 460, 3838–3860 (2016) 3858 A. B. Alabi et al.

Table A3. Mass estimates (Mtot) and DM fractions (fDM) within 5 Re and Rmax assuming different anisotropy, obtained with stellar M/L corresponding to a Salpeter IMF from Cappellari et al. (2013a,b) (see Section 3.8 for details). Columns 3–6 show Mtot and fDM obtained by allowing α to vary while in columns 7–10, α ≡ 0, Rmax can be found in Table 3.

Galaxy β Mtot(<5 Re) fDM(<5 Re) Mtot(

720 0 3.6 ± 0.7 0.28 ± 0.41 13.5 ± 2.3 0.78 ± 0.11 3.6 ± 0.7 0.28 ± 0.41 13.5 ± 2.4 0.78 ± 0.11 0.5 3.4 ± 0.7 0.23 ± 0.43 12.7 ± 2.2 0.77 ± 0.12 3.4 ± 0.7 0.23 ± 0.42 12.7 ± 2.1 0.77 ± 0.11 −0.5 3.8 ± 0.7 0.3 ± 0.39 13.9 ± 2.4 0.79 ± 0.11 3.8 ± 0.8 0.3 ± 0.4 13.9 ± 2.4 0.79 ± 0.1 821 0 4.3 ± 0.8 0.77 ± 0.06 6.1 ± 1.0 0.83 ± 0.04 4.5 ± 0.8 0.78 ± 0.06 7.1 ± 1.2 0.85 ± 0.03 0.5 4.4 ± 0.8 0.78 ± 0.06 6.3 ± 1.1 0.83 ± 0.04 4.4 ± 0.8 0.78 ± 0.06 7.0 ± 1.2 0.85 ± 0.04 −0.5 4.2 ± 0.8 0.77 ± 0.05 6.0 ± 1.0 0.83 ± 0.04 4.6 ± 0.8 0.79 ± 0.05 7.1 ± 1.2 0.85 ± 0.04 1023 0 1.7 ± 0.2 0.29 ± 0.15 4.2 ± 0.5 0.7 ± 0.05 1.8 ± 0.3 0.34 ± 0.14 5.2 ± 0.7 0.75 ± 0.05 0.5 1.7 ± 0.3 0.31 ± 0.15 4.3 ± 0.6 0.7 ± 0.05 1.7 ± 0.3 0.33 ± 0.14 5.1 ± 0.7 0.75 ± 0.05 −0.5 1.7 ± 0.2 0.29 ± 0.15 4.2 ± 0.5 0.69 ± 0.06 1.8 ± 0.3 0.34 ± 0.13 5.3 ± 0.7 0.75 ± 0.05 1400 0 2.4 ± 0.6 0.36 ± 0.41 7.7 ± 1.4 0.78 ± 0.11 2.4 ± 0.5 0.37 ± 0.42 8.7 ± 1.5 0.81 ± 0.1 0.5 2.3 ± 0.6 0.36 ± 0.42 7.7 ± 1.3 0.78 ± 0.11 2.3 ± 0.5 0.34 ± 0.38 8.4 ± 1.5 0.8 ± 0.1 −0.5 2.4 ± 0.6 0.36 ± 0.43 7.8 ± 1.4 0.78 ± 0.11 2.4 ± 0.6 0.38 ± 0.41 8.9 ± 1.6 0.81 ± 0.09 1407 0 11.6 ± 1.1 0.58 ± 0.21 38.2 ± 2.9 0.86 ± 0.07 11.5 ± 1.1 0.58 ± 0.22 35.4 ± 2.5 0.84 ± 0.06 0.5 10.0 ± 1.0 0.51 ± 0.25 32.8 ± 2.3 0.83 ± 0.07 10.3 ± 1.0 0.53 ± 0.24 31.8 ± 2.4 0.83 ± 0.08 −0.5 12.4 ± 1.3 0.61 ± 0.2 41.0 ± 3.1 0.87 ± 0.06 12.0 ± 1.2 0.59 ± 0.22 37.2 ± 2.7 0.85 ± 0.06 2768 0 7.4 ± 1.0 0.72 ± 0.06 15.0 ± 2.0 0.85 ± 0.03 7.6 ± 1.1 0.73 ± 0.06 16.0 ± 2.1 0.86 ± 0.03 0.5 7.1 ± 0.9 0.71 ± 0.06 14.5 ± 1.8 0.84 ± 0.03 7.2 ± 0.9 0.72 ± 0.06 15.2 ± 2.1 0.85 ± 0.03 −0.5 7.5 ± 1.0 0.73 ± 0.05 15.3 ± 2.0 0.85 ± 0.03 7.8 ± 1.1 0.74 ± 0.06 16.4 ± 2.1 0.86 ± 0.03 3115 0 2.0 ± 0.3 0.47 ± 0.26 5.8 ± 0.6 0.8 ± 0.09 2.0 ± 0.3 0.47 ± 0.26 6.5 ± 0.7 0.82 ± 0.08 0.5 2.1 ± 0.3 0.48 ± 0.25 5.9 ± 0.6 0.81 ± 0.08 2.0 ± 0.3 0.46 ± 0.25 6.4 ± 0.7 0.82 ± 0.08 −0.5 2.0 ± 0.3 0.46 ± 0.26 5.7 ± 0.6 0.8 ± 0.09 2.0 ± 0.3 0.47 ± 0.26 6.6 ± 0.7 0.83 ± 0.08 3377 0 0.6 ± 0.1 0.37 ± 0.14 1.3 ± 0.2 0.69 ± 0.06 0.8 ± 0.1 0.49 ± 0.12 2.0 ± 0.3 0.79 ± 0.04 0.5 0.7 ± 0.1 0.43 ± 0.12 1.5 ± 0.2 0.72 ± 0.05 0.8 ± 0.1 0.5 ± 0.11 2.0 ± 0.3 0.79 ± 0.04 −0.5 0.6 ± 0.1 0.34 ± 0.16 1.3 ± 0.2 0.67 ± 0.06 0.7 ± 0.1 0.49 ± 0.11 1.9 ± 0.3 0.79 ± 0.04 3608 0 3.3 ± 1.0 0.66 ± 0.24 4.6 ± 1.2 0.74 ± 0.11 3.3 ± 1.1 0.66 ± 0.93 5.1 ± 1.3 0.76 ± 0.11 0.5 3.4 ± 1.1 0.67 ± 0.42 4.7 ± 1.3 0.74 ± 0.1 3.2 ± 1.0 0.66 ± 0.45 5.0 ± 1.4 0.76 ± 0.12 −0.5 3.2 ± 1.0 0.66 ± 0.26 4.5 ± 1.3 0.74 ± 0.12 3.3 ± 1.1 0.67 ± 0.23 5.1 ± 1.4 0.77 ± 0.18 4278 0 2.8 ± 0.3 0.59 ± 0.08 6.8 ± 0.6 0.82 ± 0.03 2.8 ± 0.3 0.6 ± 0.07 7.7 ± 0.7 0.84 ± 0.02 0.5 2.8 ± 0.3 0.6 ± 0.07 7.0 ± 0.6 0.82 ± 0.03 2.8 ± 0.3 0.59 ± 0.07 7.5 ± 0.7 0.84 ± 0.02 −0.5 2.7 ± 0.3 0.59 ± 0.08 6.7 ± 0.6 0.82 ± 0.03 2.9 ± 0.4 0.61 ± 0.07 7.8 ± 0.7 0.84 ± 0.02 4365 0 12.3 ± 1.3 0.69 ± 0.05 31.8 ± 2.9 0.87 ± 0.02 12.0 ± 1.2 0.68 ± 0.06 29.6 ± 2.6 0.86 ± 0.02 0.5 11.0 ± 1.2 0.65 ± 0.06 28.3 ± 2.6 0.85 ± 0.02 11.0 ± 1.2 0.65 ± 0.06 27.1 ± 2.4 0.84 ± 0.02 −0.5 13.0 ± 1.4 0.7 ± 0.05 33.6 ± 3.0 0.87 ± 0.02 12.5 ± 1.4 0.69 ± 0.05 30.9 ± 2.7 0.86 ± 0.02 4374 0 14.2 ± 3.5 0.75 ± 0.12 23.7 ± 5.0 0.84 ± 0.05 14.0 ± 3.3 0.74 ± 0.09 22.7 ± 4.9 0.83 ± 0.05 0.5 12.9 ± 3.1 0.72 ± 0.09 21.5 ± 4.7 0.82 ± 0.05 13.0 ± 3.2 0.72 ± 0.12 20.9 ± 4.4 0.81 ± 0.06 −0.5 14.9 ± 3.6 0.76 ± 0.08 24.8 ± 5.5 0.84 ± 0.05 14.6 ± 3.5 0.75 ± 0.1 23.5 ± 4.8 0.83 ± 0.05 4473 0 1.4 ± 0.3 0.37 ± 0.17 3.8 ± 0.5 0.74 ± 0.05 1.5 ± 0.3 0.39 ± 0.16 4.5 ± 0.6 0.78 ± 0.04 0.5 1.5 ± 0.3 0.39 ± 0.15 3.9 ± 0.6 0.75 ± 0.05 1.5 ± 0.3 0.39 ± 0.16 4.5 ± 0.6 0.78 ± 0.04 −0.5 1.4 ± 0.3 0.35 ± 0.19 3.7 ± 0.5 0.73 ± 0.05 1.5 ± 0.3 0.4 ± 0.16 4.5 ± 0.6 0.78 ± 0.04 4486 0 23.9 ± 1.7 0.8 ± 0.03 166.0 ± 9.0 0.97 ± 0.0 23.8 ± 1.7 0.79 ± 0.03 139.0 ± 7.8 0.96 ± 0.01 0.5 20.6 ± 1.5 0.76 ± 0.04 143.0 ± 8.3 0.96 ± 0.01 21.4 ± 1.5 0.77 ± 0.03 125.0 ± 7.0 0.96 ± 0.01 −0.5 25.6 ± 1.8 0.81 ± 0.03 178.0 ± 10.0 0.97 ± 0.0 24.9 ± 1.8 0.8 ± 0.03 146.0 ± 8.3 0.96 ± 0.0 4494 0 1.5 ± 0.2 0.29 ± 0.14 2.2 ± 0.3 0.46 ± 0.11 1.7 ± 0.3 0.36 ± 0.15 2.5 ± 0.4 0.53 ± 0.09 0.5 1.6 ± 0.2 0.31 ± 0.14 2.2 ± 0.3 0.47 ± 0.11 1.7 ± 0.2 0.34 ± 0.14 2.4 ± 0.3 0.52 ± 0.1 −0.5 1.5 ± 0.2 0.29 ± 0.15 2.2 ± 0.3 0.45 ± 0.11 1.7 ± 0.3 0.36 ± 0.14 2.5 ± 0.4 0.53 ± 0.09 4526 0 3.5 ± 0.6 0.53 ± 0.11 7.4 ± 1.1 0.76 ± 0.05 3.6 ± 0.7 0.54 ± 0.11 8.0 ± 1.2 0.77 ± 0.05 0.5 3.5 ± 0.6 0.52 ± 0.11 7.3 ± 1.1 0.75 ± 0.05 3.5 ± 0.6 0.52 ± 0.12 7.7 ± 1.2 0.76 ± 0.05 −0.5 3.5 ± 0.6 0.53 ± 0.11 7.5 ± 1.1 0.76 ± 0.05 3.7 ± 0.6 0.55 ± 0.11 8.1 ± 1.2 0.78 ± 0.05 4564 0 1.1 ± 0.2 0.56 ± 0.16 1.3 ± 0.3 0.64 ± 0.1 1.3 ± 0.3 0.65 ± 0.13 1.7 ± 0.4 0.72 ± 0.09 0.5 1.1 ± 0.3 0.59 ± 0.14 1.4 ± 0.3 0.66 ± 0.11 1.3 ± 0.3 0.65 ± 0.12 1.8 ± 0.4 0.73 ± 0.09 −0.5 1.0 ± 0.2 0.55 ± 0.15 1.3 ± 0.3 0.63 ± 0.1 1.3 ± 0.3 0.65 ± 0.13 1.7 ± 0.4 0.72 ± 0.08 4649 0 11.5 ± 0.9 0.57 ± 0.07 63.1 ± 4.4 0.91 ± 0.01 11.1 ± 0.9 0.56 ± 0.07 52.1 ± 3.5 0.89 ± 0.01 0.5 9.9 ± 0.8 0.5 ± 0.08 54.4 ± 3.7 0.9 ± 0.01 10.0 ± 0.8 0.51 ± 0.08 47.1 ± 3.2 0.88 ± 0.02 −0.5 12.3 ± 1.0 0.6 ± 0.06 67.5 ± 4.7 0.92 ± 0.01 11.6 ± 0.9 0.57 ± 0.07 54.6 ± 3.7 0.9 ± 0.01 4697 0 9.1 ± 2.4 0.86 ± 0.07 – – 9.3 ± 2.4 0.86 ± 0.05 – – 0.5 9.2 ± 2.4 0.86 ± 0.06 – – 9.1 ± 2.3 0.86 ± 0.06 – – −0.5 9.1 ± 2.3 0.86 ± 0.05 – – 9.4 ± 2.6 0.86 ± 0.06 – – 5846 0 12.4 ± 1.6 0.77 ± 0.04 34.0 ± 3.6 0.91 ± 0.02 12.4 ± 1.7 0.77 ± 0.04 33.6 ± 3.6 0.91 ± 0.02 0.5 11.5 ± 1.5 0.75 ± 0.05 31.4 ± 3.3 0.9 ± 0.02 11.6 ± 1.5 0.76 ± 0.05 31.2 ± 3.3 0.9 ± 0.02 −0.5 12.9 ± 1.7 0.78 ± 0.04 35.3 ± 3.8 0.91 ± 0.01 12.9 ± 1.7 0.78 ± 0.04 34.7 ± 3.7 0.91 ± 0.02

MNRAS 460, 3838–3860 (2016) Mass distribution in ETGs at large radii 3859

Table A3 – continued.

Galaxy β Mtot(<5 Re) fDM(<5 Re) Mtot(

7457 0 1.1 ± 0.2 0.87 ± 0.04 1.2 ± 0.2 0.88 ± 0.04 1.7 ± 0.4 0.92 ± 0.03 1.9 ± 0.4 0.92 ± 0.02 0.5 1.3 ± 0.3 0.89 ± 0.04 1.3 ± 0.3 0.89 ± 0.03 1.8 ± 0.4 0.92 ± 0.03 1.9 ± 0.4 0.92 ± 0.02 −0.5 1.0 ± 0.2 0.86 ± 0.04 1.1 ± 0.2 0.87 ± 0.04 1.6 ± 0.4 0.91 ± 0.03 1.8 ± 0.4 0.92 ± 0.03 3607 0 2.6 ± 0.7 0.01 ± 0.45 10.9 ± 2.6 0.74 ± 0.1 2.6 ± 0.7 0.01 ± 0.45 11.0 ± 2.7 0.74 ± 0.09 0.5 2.4 ± 0.6 −0.0 ± 0.45 10.3 ± 2.4 0.72 ± 0.09 2.4 ± 0.6 −0.0 ± 0.45 10.3 ± 2.5 0.72 ± 0.09 −0.5 2.6 ± 0.7 0.04 ± 0.41 11.2 ± 2.7 0.75 ± 0.09 2.7 ± 0.7 0.04 ± 0.45 11.4 ± 2.7 0.75 ± 0.08 5866 0 1.3 ± 0.5 0.33 ± 0.45 – – 1.6 ± 0.6 0.46 ± 0.45 – – 0.5 1.3 ± 0.5 0.36 ± 0.45 – – 1.6 ± 0.6 0.46 ± 0.45 – – −0.5 1.2 ± 0.5 0.32 ± 0.45 – – 1.6 ± 0.6 0.46 ± 0.45 – –

Table A4. Mass estimates (Mtot) and DM fractions (fDM) within 5 Re and Rmax assuming different anisotropy, obtained using the best-ﬁtting stellar M/L ratios from the dynamical modelling of Cappellari et al. (2013a,b), i.e. total dynamical mass minus DM mass (see Section 3.8 for details). Columns 3–6 show Mtot and fDM obtained by allowing α to vary, while in columns 7–10, α ≡ 0, Rmax can be found in Table 3.

Galaxy β Mtot(<5 Re) fDM(<5 Re) Mtot(

720 0 3.5 ± 0.7 0.46 ± 0.13 11.5 ± 2.0 0.81 ± 0.04 3.6 ± 0.7 0.46 ± 0.14 13.2 ± 2.3 0.84 ± 0.04 0.5 3.4 ± 0.7 0.44 ± 0.15 11.1 ± 1.8 0.8 ± 0.04 3.3 ± 0.7 0.42 ± 0.15 12.3 ± 2.2 0.82 ± 0.04 −0.5 3.6 ± 0.7 0.47 ± 0.14 11.7 ± 2.0 0.81 ± 0.04 3.7 ± 0.7 0.48 ± 0.14 13.7 ± 2.3 0.84 ± 0.04 821 0 4.1 ± 0.8 0.78 ± 0.06 5.7 ± 0.9 0.83 ± 0.04 4.4 ± 0.8 0.8 ± 0.05 7.0 ± 1.2 0.86 ± 0.03 0.5 4.3 ± 0.8 0.79 ± 0.06 5.9 ± 1.0 0.84 ± 0.04 4.3 ± 0.8 0.79 ± 0.05 6.8 ± 1.1 0.86 ± 0.03 −0.5 4.0 ± 0.8 0.78 ± 0.06 5.6 ± 0.9 0.83 ± 0.04 4.5 ± 0.8 0.8 ± 0.05 7.1 ± 1.2 0.86 ± 0.03 1023 0 1.6 ± 0.2 0.63 ± 0.08 3.5 ± 0.4 0.81 ± 0.03 1.9 ± 0.3 0.68 ± 0.07 5.4 ± 0.7 0.88 ± 0.02 0.5 1.7 ± 0.3 0.65 ± 0.08 3.7 ± 0.5 0.82 ± 0.03 1.8 ± 0.3 0.68 ± 0.07 5.4 ± 0.7 0.88 ± 0.02 −0.5 1.5 ± 0.2 0.61 ± 0.08 3.4 ± 0.4 0.81 ± 0.03 1.9 ± 0.3 0.68 ± 0.07 5.4 ± 0.7 0.88 ± 0.02 1400 0 2.3 ± 0.5 0.46 ± 0.18 6.9 ± 1.2 0.8 ± 0.05 2.4 ± 0.5 0.47 ± 0.16 8.6 ± 1.5 0.84 ± 0.04 0.5 2.3 ± 0.5 0.46 ± 0.37 6.9 ± 1.2 0.8 ± 0.05 2.2 ± 0.5 0.45 ± 0.17 8.2 ± 1.4 0.83 ± 0.04 −0.5 2.3 ± 0.5 0.46 ± 0.18 6.8 ± 1.3 0.8 ± 0.05 2.4 ± 0.6 0.48 ± 0.18 8.7 ± 1.6 0.84 ± 0.04 1407 0 10.8 ± 1.1 0.61 ± 0.06 33.9 ± 2.5 0.86 ± 0.02 10.8 ± 1.0 0.61 ± 0.06 33.3 ± 2.4 0.86 ± 0.02 0.5 9.2 ± 0.9 0.55 ± 0.06 28.9 ± 2.2 0.84 ± 0.02 9.3 ± 0.9 0.55 ± 0.07 28.7 ± 2.1 0.84 ± 0.02 −0.5 11.6 ± 1.1 0.64 ± 0.05 36.4 ± 2.8 0.87 ± 0.01 11.5 ± 1.2 0.64 ± 0.05 35.6 ± 2.6 0.87 ± 0.02 2768 0 6.8 ± 0.9 0.57 ± 0.09 13.9 ± 1.8 0.77 ± 0.04 6.9 ± 1.0 0.58 ± 0.09 14.6 ± 1.8 0.78 ± 0.04 0.5 6.2 ± 0.8 0.52 ± 0.1 12.6 ± 1.7 0.74 ± 0.05 6.2 ± 0.8 0.53 ± 0.1 13.1 ± 1.7 0.75 ± 0.05 −0.5 7.1 ± 1.0 0.58 ± 0.08 14.5 ± 1.9 0.77 ± 0.04 7.3 ± 1.0 0.6 ± 0.08 15.3 ± 2.0 0.79 ± 0.04 3115 0 2.0 ± 0.3 0.57 ± 0.08 5.4 ± 0.6 0.83 ± 0.02 2.0 ± 0.3 0.57 ± 0.08 6.5 ± 0.7 0.86 ± 0.02 0.5 2.1 ± 0.3 0.59 ± 0.07 5.6 ± 0.6 0.83 ± 0.02 2.0 ± 0.3 0.56 ± 0.08 6.4 ± 0.7 0.85 ± 0.02 −0.5 2.0 ± 0.3 0.56 ± 0.08 5.3 ± 0.6 0.82 ± 0.02 2.0 ± 0.3 0.57 ± 0.08 6.6 ± 0.7 0.86 ± 0.02 3377 0 0.6 ± 0.1 0.57 ± 0.1 1.2 ± 0.2 0.78 ± 0.04 0.8 ± 0.1 0.68 ± 0.07 2.0 ± 0.3 0.87 ± 0.03 0.5 0.7 ± 0.1 0.62 ± 0.09 1.4 ± 0.2 0.81 ± 0.04 0.8 ± 0.1 0.69 ± 0.07 2.1 ± 0.3 0.87 ± 0.02 −0.5 0.5 ± 0.1 0.54 ± 0.1 1.2 ± 0.2 0.76 ± 0.05 0.8 ± 0.1 0.67 ± 0.07 2.0 ± 0.3 0.86 ± 0.03 3608 0 3.3 ± 1.1 0.78 ± 0.25 4.3 ± 1.2 0.81 ± 0.37 3.3 ± 1.1 0.78 ± 2.63 5.1 ± 1.4 0.85 ± 0.18 0.5 3.5 ± 1.0 0.79 ± 0.14 4.5 ± 1.3 0.82 ± 0.22 3.3 ± 1.0 0.78 ± 0.13 5.1 ± 1.4 0.84 ± 0.08 −0.5 3.2 ± 1.1 0.77 ± 0.25 4.1 ± 1.1 0.81 ± 0.09 3.4 ± 1.1 0.78 ± 0.31 5.2 ± 1.4 0.85 ± 0.82 4278 0 2.7 ± 0.3 0.68 ± 0.06 6.3 ± 0.5 0.85 ± 0.02 2.8 ± 0.3 0.69 ± 0.06 7.7 ± 0.7 0.88 ± 0.02 0.5 2.9 ± 0.3 0.69 ± 0.06 6.6 ± 0.6 0.86 ± 0.02 2.8 ± 0.4 0.69 ± 0.06 7.5 ± 0.7 0.87 ± 0.02 −0.5 2.6 ± 0.3 0.67 ± 0.06 6.1 ± 0.6 0.85 ± 0.02 2.9 ± 0.3 0.7 ± 0.05 7.8 ± 0.7 0.88 ± 0.02 4365 0 11.6 ± 1.2 0.78 ± 0.04 27.4 ± 2.5 0.9 ± 0.02 11.8 ± 1.2 0.78 ± 0.04 29.1 ± 2.6 0.9 ± 0.02 0.5 10.7 ± 1.1 0.76 ± 0.04 25.3 ± 2.3 0.89 ± 0.02 10.6 ± 1.1 0.76 ± 0.04 26.2 ± 2.3 0.89 ± 0.02 −0.5 12.0 ± 1.2 0.79 ± 0.04 28.5 ± 2.5 0.9 ± 0.01 12.4 ± 1.3 0.79 ± 0.04 30.5 ± 2.8 0.91 ± 0.01 4374 0 13.4 ± 3.2 0.78 ± 0.07 21.1 ± 4.5 0.85 ± 0.05 13.5 ± 3.3 0.78 ± 0.09 21.7 ± 4.8 0.85 ± 0.05 0.5 12.2 ± 2.9 0.76 ± 0.08 19.3 ± 4.2 0.83 ± 0.05 12.1 ± 2.9 0.75 ± 0.09 19.6 ± 4.2 0.84 ± 0.05 −0.5 14.0 ± 3.2 0.79 ± 0.13 22.1 ± 4.7 0.85 ± 0.04 14.2 ± 3.4 0.79 ± 0.07 22.8 ± 5.0 0.86 ± 0.05 4473 0 1.4 ± 0.3 0.6 ± 0.11 3.4 ± 0.5 0.82 ± 0.03 1.5 ± 0.3 0.63 ± 0.19 4.6 ± 0.6 0.87 ± 0.02 0.5 1.5 ± 0.3 0.64 ± 0.09 3.7 ± 0.5 0.84 ± 0.03 1.5 ± 0.3 0.63 ± 0.11 4.6 ± 0.6 0.87 ± 0.03 −0.5 1.4 ± 0.3 0.59 ± 0.12 3.3 ± 0.5 0.81 ± 0.04 1.5 ± 0.3 0.63 ± 0.11 4.6 ± 0.6 0.87 ± 0.03 4486 0 22.4 ± 1.6 0.81 ± 0.03 136.0 ± 7.6 0.96 ± 0.0 22.4 ± 1.7 0.81 ± 0.03 131.0 ± 7.4 0.96 ± 0.0 0.5 19.1 ± 1.3 0.78 ± 0.04 116.0 ± 6.8 0.96 ± 0.01 19.4 ± 1.4 0.78 ± 0.03 113.0 ± 6.5 0.96 ± 0.01 −0.5 24.1 ± 1.7 0.83 ± 0.03 146.0 ± 8.3 0.97 ± 0.0 23.9 ± 1.7 0.83 ± 0.03 140.0 ± 8.0 0.97 ± 0.0

MNRAS 460, 3838–3860 (2016) 3860 A. B. Alabi et al.

Table A4 – continued.

Galaxy β Mtot(<5 Re) fDM(<5 Re) Mtot(

4494 0 1.5 ± 0.2 0.51 ± 0.11 2.0 ± 0.3 0.61 ± 0.07 1.7 ± 0.2 0.59 ± 0.08 2.5 ± 0.4 0.7 ± 0.06 0.5 1.5 ± 0.2 0.54 ± 0.1 2.1 ± 0.3 0.63 ± 0.07 1.7 ± 0.2 0.58 ± 0.08 2.5 ± 0.4 0.7 ± 0.06 −0.5 1.4 ± 0.2 0.5 ± 0.11 1.9 ± 0.3 0.6 ± 0.08 1.7 ± 0.2 0.59 ± 0.08 2.6 ± 0.4 0.7 ± 0.06 4526 0 3.3 ± 0.6 0.53 ± 0.11 6.8 ± 1.0 0.75 ± 0.05 3.5 ± 0.6 0.55 ± 0.11 7.7 ± 1.1 0.78 ± 0.04 0.5 3.3 ± 0.6 0.53 ± 0.12 6.7 ± 1.0 0.75 ± 0.05 3.3 ± 0.6 0.53 ± 0.11 7.3 ± 1.1 0.77 ± 0.05 −0.5 3.4 ± 0.6 0.54 ± 0.12 6.9 ± 1.0 0.75 ± 0.05 3.6 ± 0.6 0.57 ± 0.11 7.9 ± 1.2 0.79 ± 0.05 4564 0 1.0 ± 0.2 0.65 ± 0.11 1.3 ± 0.3 0.71 ± 0.08 1.3 ± 0.3 0.74 ± 0.09 1.8 ± 0.4 0.8 ± 0.07 0.5 1.1 ± 0.3 0.68 ± 0.12 1.4 ± 0.3 0.73 ± 0.07 1.4 ± 0.3 0.75 ± 0.09 1.8 ± 0.4 0.8 ± 0.06 −0.5 0.9 ± 0.2 0.63 ± 0.11 1.2 ± 0.2 0.7 ± 0.08 1.3 ± 0.3 0.74 ± 0.11 1.8 ± 0.4 0.79 ± 0.07 4649 0 10.6 ± 0.8 0.63 ± 0.05 50.9 ± 3.5 0.91 ± 0.01 10.5 ± 0.8 0.62 ± 0.06 49.6 ± 3.2 0.91 ± 0.01 0.5 9.2 ± 0.7 0.57 ± 0.07 44.2 ± 2.9 0.9 ± 0.01 9.2 ± 0.7 0.57 ± 0.07 43.4 ± 2.9 0.9 ± 0.01 −0.5 11.3 ± 0.9 0.65 ± 0.06 54.2 ± 3.7 0.92 ± 0.01 11.2 ± 0.9 0.65 ± 0.06 52.8 ± 3.5 0.92 ± 0.01 4697 0 8.9 ± 2.3 0.88 ± 0.26 – – 9.3 ± 2.3 0.89 ± 0.04 – – 0.5 9.1 ± 2.2 0.89 ± 0.04 – – 9.0 ± 2.2 0.89 ± 0.08 – – −0.5 8.8 ± 2.3 0.88 ± 0.05 – – 9.4 ± 2.4 0.89 ± 0.05 – – 5846 0 11.8 ± 1.5 0.76 ± 0.05 30.7 ± 3.3 0.9 ± 0.02 11.7 ± 1.6 0.76 ± 0.05 31.6 ± 3.4 0.9 ± 0.02 0.5 10.7 ± 1.4 0.74 ± 0.05 28.0 ± 3.1 0.89 ± 0.02 10.5 ± 1.3 0.74 ± 0.05 28.4 ± 3.1 0.89 ± 0.02 −0.5 12.3 ± 1.7 0.77 ± 0.04 32.1 ± 3.4 0.9 ± 0.02 12.3 ± 1.6 0.77 ± 0.04 33.3 ± 3.5 0.91 ± 0.02 7457 0 1.0 ± 0.2 0.92 ± 0.03 1.1 ± 0.2 0.92 ± 0.02 1.8 ± 0.4 0.95 ± 0.02 2.0 ± 0.4 0.95 ± 0.01 0.5 1.2 ± 0.3 0.93 ± 0.02 1.3 ± 0.3 0.93 ± 0.02 1.9 ± 0.4 0.95 ± 0.01 2.1 ± 0.5 0.96 ± 0.01 −0.5 1.0 ± 0.2 0.91 ± 0.03 1.0 ± 0.2 0.91 ± 0.02 1.7 ± 0.4 0.95 ± 0.02 1.9 ± 0.4 0.95 ± 0.02 3607 0 2.4 ± 0.7 0.21 ± 0.45 9.3 ± 2.2 0.78 ± 0.08 2.5 ± 0.7 0.27 ± 0.45 10.8 ± 2.6 0.81 ± 0.08 0.5 2.3 ± 0.6 0.19 ± 0.45 9.0 ± 2.2 0.77 ± 0.1 2.4 ± 0.6 0.21 ± 0.45 10.1 ± 2.4 0.79 ± 0.07 −0.5 2.4 ± 0.6 0.23 ± 0.36 9.4 ± 2.2 0.78 ± 0.07 2.6 ± 0.7 0.3 ± 0.28 11.2 ± 2.8 0.81 ± 0.07 5866 0 1.2 ± 0.5 0.24 ± 0.45 – – 1.5 ± 0.6 0.41 ± 0.45 – – 0.5 1.2 ± 0.5 0.27 ± 0.45 – – 1.5 ± 0.6 0.4 ± 0.45 – – −0.5 1.2 ± 0.5 0.22 ± 0.45 – – 1.6 ± 0.6 0.42 ± 0.45 – –

This paper has been typeset from a TEX/LATEX ﬁle prepared by the author.

MNRAS 460, 3838–3860 (2016) 4 Dark matter fractions at large radii and assembly epochs of early-type galaxies

we still know in part... —Pauline text adapted

53 MNRAS 468, 3949–3964 (2017) doi:10.1093/mnras/stx678 Advance Access publication 2017 April 1

The SLUGGS survey: dark matter fractions at large radii and assembly epochs of early-type galaxies from globular cluster kinematics

Adebusola B. Alabi,1‹ Duncan A. Forbes,1‹ Aaron J. Romanowsky,2,3 Jean P. Brodie,3 Jay Strader,4 Joachim Janz,1 Christopher Usher,5 Lee R. Spitler,6,7,8 Sabine Bellstedt1 and Anna Ferre-Mateu´ 1 1Centre for Astrophysics and Supercomputing, Swinburne University, Hawthorn VIC 3122, Australia 2Department of Physics and Astronomy, San Jose´ State University, San Jose, CA 95192, USA 3University of California Observatories, 1156 High Street, Santa Cruz, CA 95064, USA 4Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA 5Astrophysics Research Institute, Liverpool John Moores University, Liverpool L3 5RF, UK 6Australian Astronomical Observatory, PO Box 915, North Ryde, NSW 1670, Australia 7Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia 8Research Centre for Astronomy, Astrophysics and Astrophotonics, Macquarie University, North Ryde, NSW 2109, Australia

Accepted 2017 March 15. Received 2017 March 10; in original form 2017 January 18

ABSTRACT We use globular cluster kinematics data, primarily from the SAGES Legacy Unifying Globulars and GalaxieS (SLUGGS) survey, to measure the dark matter fraction (fDM) and the average dark matter density (ρDM) within the inner 5 effective radii (Re) for 32 nearby early-type galaxies (ETGs) with stellar mass log (M∗/M) ranging from 10.1 to 11.8. We compare our results with a simple galaxy model based on scaling relations as well as with cosmological hydrodynamical simulations where the dark matter profile has been modified through various physical processes. We find a high fDM (≥0.6) within 5 Re in most of our sample, which we interpret as a signature of a late mass assembly history that is largely devoid of gas-rich major mergers. However, around log (M∗/M) ∼ 11, there is a wide range of fDM which may be challenging to explain with any single cosmological model. We find tentative evidence that lenticulars (S0s), unlike ellipticals, have mass distributions that are similar to spiral galaxies, with decreasing fDM within 5 Re as galaxy luminosity increases. However, we do not find any difference between the ρDM of S0s and ellipticals in our sample, despite the differences in their stellar populations. We have also used ρDM to infer the epoch of halo assembly (z ∼ 2– 4). By comparing the age of their central stars with the inferred epoch of halo formation, we are able to gain more insight into their mass assembly histories. Our results suggest a fundamental difference in the dominant late-phase mass assembly channel between lenticulars and elliptical galaxies. Key words: galaxies: evolution – galaxies: haloes – dark matter – cosmology: observations.

back processes due to active galactic nuclei (AGNs) or supernovae 1 INTRODUCTION (SNe), etc.). These baryonic processes may also alter the DM dis- The natural expectation within the hierarchical structure forma- tribution, especially in the most central parts, through adiabatic tion paradigm and cold dark matter (CDM) cosmology (e.g. halo contraction (e.g. Blumenthal et al. 1986) or halo expansion Peebles 1982) is that dark matter (DM) haloes and their resident through gravitational heating from infalling gas clumps (e.g. Jo- galaxies grow in tandem. The growth channels include mergers hansson, Naab & Ostriker 2009) or outﬂows linked to feedback (major/minor, with/without gas) and gas accretion (smooth or events (e.g. Maccioetal.` 2012). The implication is that the relative clumpy, e.g. Genel et al. 2010; Rodriguez-Gomez et al. 2016), distributions of DM and baryons in present-day galaxies contain with galaxy assembly showing more complexities due to the bary- clues about when (epoch of formation) and how (nature of the mass onic processes involved (e.g. gas dissipation, star formation, feed- assembly) they formed and how they have evolved. Both halo and galaxy growth have been divided into two phases in the literature (e.g. Zhao et al. 2003;Oseretal.2010; Klypin E-mail: [email protected] (ABA); [email protected] (DAF) et al. 2016). At early times, when the Universe was denser, DM

C 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 3950 A. B. Alabi et al. haloes grew rapidly via frequent mergers and accretion. In paral- is still unclear. Cosmological hydrodynamical simulations of ETGs lel, gas-rich, dissipative events were very common, and the stellar where baryons have modified the present-day DM profiles have also cores of present-day galaxies were formed. Galaxies then grew pre- started to report predictions for fDM at 5 Re (e.g. Wu et al. 2014). dominantly by rapidly forming stars in situ, such that the DM frac- More recently, simulations with realistic implementation of AGN tion (fDM) at the centres of young galaxies is relatively low and the and SN feedback recipes (e.g. Vogelsberger et al. 2014; Schaye galaxies themselves are very compact (e.g. van Dokkum et al. 2008; et al. 2015; Remus et al. 2017), covering the stellar mass range of Naab, Johansson & Ostriker 2009; Napolitano, Romanowsky & Tor- ETGs in this work, that is, 1010–1012 M, have been released. The tora 2010; Remus et al. 2017). DM haloes experienced an increase time is therefore ripe to systematically compare results from obser- in both core size and extent (core size and halo extent are usually vations with theoretical predictions, and thereby unravel the nature parametrized by the scale radius (rs) and virial radius (r200), respec- of mass distributions in ETGs within a cosmological context. tively). Thus, the halo concentration (c200 ≡ r200/rs) is kept fairly Unfortunately, the halo concentration is difficult to directly con- constant during this phase (Klypin et al. 2016). The halo concen- strain in ETGs (e.g. Napolitano et al. 2005, 2009; Samurovic´ 2014), tration is directly linked to the density of the universe at the epoch due in part to the limited radial extent of kinematics data and the −1 when the halo formed (c200 ∝ (1 + zform) e.g. Bullock et al. 2001; degeneracy between the halo virial mass and concentration. How- Wechsler et al. 2002) and is well described by the c200–M200 scaling ever, it is possible to infer the epoch of halo assembly from the 3 relation (e.g. Dutton et al. 2010), where M200 is the virial mass. average dark density within the scale radius (ρDM∝(1 + zform) , At later times (z ≤ 2), in the two-phase paradigm, when gas-rich where ρDM and zform are the average DM density and the epoch events become fewer, mass growth (be it baryonic or dark matter) of halo assembly, respectively). Thomas et al. (2009) inferred zform occurs predominantly in the galaxy outskirts. The progenitors of for several ETGs in the Coma cluster using ρDM obtained from present-day massive early-type galaxies (ETGs) increase rapidly in stellar kinematics within the inner 2 Re and found that their haloes mass and size through a multitude of minor mergers and/or dry must have assembled at zform ≈ 2–3. major mergers, thereby increasing significantly their fraction of In this work, we expand our sample of ETGs with homoge- stars formed ex situ (e.g. Naab et al. 2009; Pillepich et al. 2014; neously measured fDM at 5 Re in Alabi et al. (2016)from23to32, Rodriguez-Gomez et al. 2016; Remus et al. 2017). This is con- using GC kinematics data mostly obtained as part of the SLUGGS1 sistent with the low angular momentum content (e.g. Emsellem survey (Brodie et al. 2014). SLUGGS stands for SAGES Legacy et al. 2011;Arnoldetal.2014; Moody et al. 2014; Raskutti, Greene Unifying Globulars and GalaxieS. This brings the number of ∼L∗ & Murphy 2014;Fosteretal.2016), old central stars (e.g. Ter- ETGs with total mass measurements within 5 Re up to 16. We also levich & Forbes 2002; McDermid et al. 2015) and high fDM at large adopt the recently published galaxy sizes, Sersic´ indices and stel- radii (e.g. Deason et al. 2012; Alabi et al. 2016) usually reported lar mass measurements from Forbes et al. (2016) for our galaxy in studies of massive ETGs. The DM haloes also get bigger in size sample. With this larger sample, homogeneously measured galaxy while the core sizes may grow or shrink depending on whether vio- parameters and the suite of cosmological simulations that are now lent relaxation, adiabatic halo contraction or halo expansion events available, we investigate the cosmological origins of the measured occur (e.g. Johansson et al. 2009;Governatoetal.2010; Klypin fDM at large radii in ETGs. We also address the curious cases of et al. 2016). Therefore, the observed DM density within the scale ETGs with low DM fractions in more detail. We study the struc- radius should reflect the epoch of halo assembly as well as im- tural properties of the DM haloes within the inner 5 Re using their prints of how baryonic processes have altered the distribution of average DM densities, and infer their halo assembly epochs. Lastly, DM within the halo during galaxy evolution. we use the halo formation epoch, the age of the central stars and DM fractions at large radii, e.g. 5 effective radii (Re), are becom- the DM fraction to probe the nature of mass assembly in ETGs. We ing increasingly available, especially in ∼L∗ ETGs, that is, ETGs pay special attention to the morphology, environment and angular 11 with stellar mass (M∗) ∼10 M (e.g. Deason et al. 2012;Alabi momentum in this exercise. et al. 2016). This is due to the use of dynamical mass tracers, such The paper structure is as follows. In Section 2, we describe the as planetary nebulae (PNe) or globular clusters (GCs), which probe new data we introduce in this work. In Section 3, we obtain the dy- further out into the galaxy halo where the light from galaxy stars is namical mass estimates and fDM (for the newly introduced galaxies) faint. At a fiducial 5 Re, which is always interior to the halo rs (it is and ρDM (for the combined sample) and compare with cosmologi- expected on average that, 5 Re ∼ 0.4rs), DM should dominate the cal hydrodynamical simulations. We also obtain DM halo properties mass profiles in ETGs. While most ETGs studied show a high DM and compare them with results from the literature. In Section 4, we fractionwithin5Re (on average, fDM ≥ 0.6), in agreement with the- discuss the diverse nature of fDM in ETGs and the nature of their oretical predictions and an increasing trend with total galaxy stellar mass assembly. We summarize our results in Section 5. 11 mass, some ETGs with M∗∼10 M have been found to have sur- prisingly low DM content within 5 Re (e.g. Romanowsky et al. 2003; Napolitano et al. 2005; Deason et al. 2012; Alabi et al. 2016). 2DATA Several reasons have been given in the literature for this intriguing tension between observations and simulations including the stellar 2.1 New SLUGGS survey GC kinematics data initial mass function (IMF), the orbital anisotropy of the mass trac- Here, we introduce new Keck/DEIMOS GC kinematics data for ers, modification of the DM profile during mass assembly (net effect NGC 2974, NGC 4474, NGC 4459 and NGC 4697. These ETGs of adiabatic halo contraction and inner DM halo expansion), the na- have log (M∗/M) ∼ 10–11. NGC 4697 was already studied in ture of the DM halo profile, that is, logarithmic or Navarro-Frenk- Alabi et al. (2016, hereafter Alabi+16), but the total number of White (NFW) or even a failure of the CDM cosmology (e.g. Dekel GCs (NGC) with radial velocities was 20. Here, we use an improved et al. 2005; Napolitano et al. 2005, 2010, 2011; Thomas et al. 2009; data set for NGC 4697, with NGC = 90 and radial extent out to 4 Re. Morganti et al. 2013). In Alabi et al. (2016), we suggested that these galaxies with low DM fractions could have different halo structures, that is, diffuse DM haloes. However, the exact origin of this anomaly 1 http://sluggs.swin.edu.au

MNRAS 468, 3949–3964 (2017) DM fractions and assembly epochs of ETGs 3951

The remaining newly introduced lower mass ETGs have relatively a Kroupa/Chabrier stellar IMF, it does not account for variations > sparse data√ sets but always with NGC 20. This limit is set due in stellar age or metallicity. The implication of this assumption to the 1/ NGC nature of the uncertainty on total mass estimate becomes critical in ETGs whose stellar population is dominated by such that below NGC = 20, the uncertainty increases rapidly beyond younger stars, since stellar M/LK for ETGs is known to be age- 0.5 dex. We have therefore adopted NGC = 20 as a sample size limit dependent. For example, at a mean stellar age of ∼6 Gyr, assuming for our analysis. This is consistent with recent results from Toloba solar metallicity and Padova isochrones, Rock¨ et al. (2016) recently et al. (2016) and was pointed out earlier in Strader et al. (2011). reported a stellar M/LK ∼ 0.6. This corresponds to an ∼0.2 dex decrease in stellar mass and an ∼0.1 increase in fDM, which may change our earlier conclusions, especially in galaxies with low f . 2.2 GC kinematics data from the literature DM One way of addressing this concern would be to apply an age- We also include six ETGs (NGC 1316, NGC 1399, NGC 4472, weighted correction to our previous M/LK = 1 assumption. Forbes NGC 4594/M104, NGC 4636 and NGC 5128) from the literature, et al. (2016) applied this correction to their stellar mass estimates with rich GC kinematics data sets (NGC > 170) obtained from (they assumed a Kroupa IMF) from the 3.6 μm Spitzer data. We various telescopes/instruments. For NGC 1316, we use the GC note that there is a one-to-one correspondence with the 2MASS kinematics catalogue published in Richtler et al. (2014), obtained K-band stellar mass estimates if they are also corrected for stellar from VLT/FORS2. The data for NGC 1399 and NGC 4636 are age variations. from Schuberth et al. (2010) and Schuberth et al. (2012), respec- We use the homogeneously measured effective radii and total tively, also obtained from VLT/FORS2. The data for NGC 4472 are stellar mass estimates for the 27 galaxies we have in common with from Keck/LRIS (Cotˆ eetal.´ 2003). The data for NGC 4594 are Forbes et al. (2016). For the remaining galaxies, we obtain their stel- from Keck/DEIMOS but with a different setup that did not use the lar mass estimates from 2MASS absolute K-band magnitudes, cor- CaT features as we have done in the SLUGGS survey (Alves-Brito recting for sky oversubtraction (Scott, Graham & Schombert 2013) et al. 2011). Finally, we also considered NGC 5128 (Centaurus and stellar age variation (Rock¨ et al. 2016). Their effective radii are A), using the GC kinematics catalogue compiled in Woodley et al. obtained from the literature studies that used 3.6 μm Spitzer imag- (2010). The GC kinematics data for NGC 5128 have been obtained ing data and a similar effective radius measurement procedure as over two decades from an array of telescopes and instruments such in Forbes et al. (2016). Our ﬁnal sample of 32 galaxies now spans as CTIO/SIT, Magellan/LDSS-2, VLT/VIMOSand CTIO/HYDRA. alog(M∗/M) range of 10.1–11.8, with the typical uncertainty Unlike Keck/DEIMOS data obtained with the SLUGGS setup, on M∗ and Re being ∼0.1 dex and ∼0.15 dex, respectively. Table 1 where the average uncertainty on the kinematics data is ∼15 km s−1, contains a summary of the salient properties of the galaxies used in these externally sourced data have an average uncertainty of this work. ∼50 km s−1. Higher uncertainty in the kinematics data tends to wash out subtle but important details in the velocity distributions, e.g. kinematics substructures and higher velocity moments (see for 3 METHOD AND RESULTS example, Amorisco & Evans 2012), needed to accurately determine galaxy dynamical mass. Also, larger uncertainties on the velocities 3.1 Total mass estimates and DM fractions within 5 Re tend to bias mass estimates, especially in galaxies with low-velocity We use the tracer mass estimator (TME) of Watkins, Evans & dispersions. This bias typically scales with Vi/σ ,whereVi and σ are the uncertainties on individual velocity measurements and the An (2010) to obtain the total mass estimates and subsequently the central velocity dispersion of the galaxies, respectively. DM fractions for our galaxy sample, following the implementation described in Alabi+16. We give a brief summary of the implementation below and encourage interested readers to see Alabi+16 for 2.3 Size and stellar mass measurements more details. Systematic deviation of galaxies from the size–stellar mass scaling The TME assumes that the discrete dynamical tracers follow a relation could create artiﬁcial tension between our DM fraction mea- power-law density distribution when de-projected and a power-law surements and expectations from cosmological simulations. Here, description for the gravitational potential. The pressure-supported < we revisit and update (where necessary) the size and stellar mass mass within a sphere with projected radius R, Mp( R), is then measurements used in Alabi+16, as described below. 2 α Mp(

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Table 1. General properties of our galaxies. Columns: (1) galaxy name: † = bonus galaxies, ‡ = SLUGGS galaxies not studied in Alabi+16; (2) distance; (3) systemic velocity; (4) central stellar velocity dispersion within 1 kpc; (5) ellipticity; (6) galaxy environment: F=field, G=group, C=cluster; (7) galaxy morphology, mostly sourced from Brodie et al. (2014), otherwise from Makarov et al. (2014), although NGC 4594 (Sombrero galaxy) is classified as an Sa, we include it in our ETG sample; (8) average luminosity-weighted age of central (1 Re) stellar population, mostly from McDermid et al. (2015) unless otherwise noted and listed below; (9) number of GCs with kinematics data; (10) effective (half-light) radius; (11) stellar mass; (12) Sersic´ n index; (10)–(12) are mostly from Forbes et al. (2016) unless otherwise noted and listed below (also see text for more details); (13) the power-law slope of the gravitational potential; (14) the power-law slope of the de–projected GC density profile; (15) normalizing factor to correct for effect of galaxy flattening on dynamical mass estimate and (16) rotation dominance parameter for the GC system [details on the derivation of columns (13)–(16) can be found in Alabi+16]. Galaxies below the horizontal line are not part of the SLUGGS survey, we have obtained their GC kinematics data from the literature.

Galaxy Dist. Vsys σ kpc Env. Morph. Age NGC Re log (M∗) n αγCorr Vrot/σ (NGC) (Mpc) ( km s−1)(kms−1) (Gyr) (kpc) (M) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

b . +0.24 720 26.9 1745 227 0.49 F E 7.8 69 3.80 11.27 3.8 0.106 2.71 0.92 0 42−0.17 . +0.20 821 23.4 1718 193 0.35 F E 11.0 69 4.90 11.00 6.0 0.230 2.88 0.98 0 40−0.18 . +0.21 1023 11.1 602 183 0.63 G S0 12.3 115 2.58 10.99 4.2 0.235 2.89 0.85 0 65−0.18 c . +0.20 1400 26.8 558 236 0.13 G E/S0 13.8 69 3.33 11.08 5.0 0.193 2.83 1.01 0 22−0.15 c − . +0.08 1407 26.8 1779 252 0.07 G E 12.0 372 12.14 11.60 4.9 0.046 2.50 1.01 0 04−0.07 . +0.15 2768 21.8 1353 206 0.57 G E/S0 12.3 107 6.37 11.21 3.8 0.133 2.75 0.88 0 50−0.15 . +0.12 2974† 20.9 1887 231 0.36 F S0 9.3 26 3.06 10.93 4.3 0.262 2.92 0.97 0 31−0.17 d . +0.15 3115 9.4 663 248 0.66 F S0 9.0 150 1.66 10.93 4.7 0.262 2.92 0.83 0 94−0.16 . +0.14 3377 10.9 690 135 0.33 G E 7.0 122 2.40 10.50 5.9 0.460 3.20 0.98 0 23−0.10 . +0.22 3607‡ 22.2 942 229 0.13 G S0 10.3 36 5.19 11.39 5.3 0.051 2.63 1.01 0 18−0.15 . +0.26 3608 22.3 1226 179 0.20 G E 9.9 36 4.64 11.03 5.3 0.216 2.86 1.01 0 21−0.18 . +0.08 4278 15.6 620 228 0.09 G E 11.8 270 2.14 10.95 6.2 0.253 2.91 1.01 0 13−0.07 − . +0.10 4365 23.1 1243 253 0.24 G E 13.4 251 8.71 11.51 4.9 0.005 2.56 1.00 0 15−0.08 − . +0.25 4374 18.5 1017 284 0.05 C E 14.9 41 12.45 11.51 8.0 0.005 2.56 1.01 0 45−0.24 . +0.13 4459† 16.0 1192 170 0.21 C S0 7.0 36 3.75 10.98 5.4 0.239 2.89 1.01 0 20−0.18 . +0.15 4473 15.2 2260 189 0.43 C E 13.1 106 2.23 10.96 5.0 0.248 2.91 0.95 0 23−0.11 . +1.55 4474† 15.5 1611 88 0.42 C E/S0 10.8 23 1.50 10.23 2.8 0.584 3.37 0.95 2 04−1.89 − . +0.06 4486 16.7 1284 307 0.16 C E 17.7 702 7.01 11.62 5.1 0.055 2.49 1.01 0 14−0.05 . +0.15 4494 16.6 1342 157 0.14 G E 8.0 107 4.23 11.02 4.5 0.221 2.87 1.01 0 51−0.14 . +0.23 4526 16.4 617 233 0.76 C S0 11.0 107 2.58 11.26 3.6 0.110 2.72 0.77 0 61−0.24 . +0.51 4564 15.9 1155 153 0.53 C E 11.8 27 1.14 10.58 3.2 0.423 3.14 0.90 1 80−0.33 − . +0.07 4649 16.5 1110 308 0.16 C E/S0 17.7 431 6.34 11.60 4.6 0.046 2.50 1.01 0 34−0.08 . +0.51 4697† 12.5 1252 180 0.32 G E 11.3 90 5.81 11.15 5.3 0.161 2.79 0.98 0 72−1.31 . +0.09 5846 24.2 1712 231 0.08 G E/S0 17.7 190 10.54 11.46 5.2 0.018 2.59 1.01 0 08−0.07 . +1.06 5866‡ 14.9 755 163 0.58 G S0 5.9 20 1.69 10.83 2.8 0.308 2.99 0.88 0 16−0.36 . +0.53 7457 12.9 844 74 0.47 F S0 3.8 40 2.13 10.13 2.6 0.63 3.43 0.93 1 90−0.42 e h n n − . +0.10 1316 20.8 1760 225 0.28 C S0 4.7 175 8.57 11.55 5.0 0.023 2.53 1.00 0 60−0.11 f i o o . +0.05 1399 21.2 1425 335 0.01 C E 11.0 514 15.83 11.50 11.1 0.002 2.57 1.00 0 09−0.05 j p p − . +0.07 4472 16.7 981 288 0.19 C E 17.7 263 15.74 11.78 6.0 0.126 2.39 1.00 0 19−0.08 g m . +0.08 4594 9.77 1024 231 0.46 G Sa 12.5 232 3.41 11.41 3.2 0.041 2.62 1.00 0 13−0.10 k p p . +0.08 4636 14.3 930 198 0.23 C E 13.4 386 12.71 11.17 5.7 0.153 2.77 1.00 0 35−0.08 a −− l n n . +0.07 5128 3.8 547 107 0.11 G E/S0 549 2.21 10.94 3.5 0.258 2.92 1.00 0 17−0.07 References: a. Harris, Rejkuba & Harris (2010), b. Rembold, Pastoriza & Bruzual (2005), c. Spolaor et al. (2008), d. Norris, Sharples & Kuntschner (2006), e. Koleva et al. (2011), f. Trager et al. (2000), g.Sanchez-Bl´ azquez´ et al. (2006), h. Richtler et al. (2014), i. Schuberth et al. (2010), j.Cotˆ eetal.(´ 2003), k. Schuberth et al. (2012), l. Woodley et al. (2010), m. Alves-Brito et al. (2011), n. Sani et al. (2011), o.Lasker,¨ Ferrarese & van de Ven (2014), p. Kormendy et al. (2009).

respectively. The most massive galaxies in our sample have α ∼ 0, sight velocity, Vlos, before evaluating equation (1). Vrot is obtained that is, they are nearly isothermal, and the less massive ones are by fitting an inclined-disc model to the GC kinematics data. Our more Keplerian. Also, γ defined this way is such that 2 ≤ γ ≤ total mass estimate, Mtot, is then evaluated as the sum of the rota- 4, with the most massive galaxies well described by shallow GC tionally supported mass, Mrot, and the pressure-supported mass, Mp. density profiles. The contribution from rotation to the total mass is usually small, Since the TME assumes that the GC system is pressure-supported, ∼6 per cent. We evaluate Mtot assuming that the orbital anisotropy we first subtract the contribution of rotation, Vrot, from the line-of- of the GC system is either strongly radial, mildly tangential or

MNRAS 468, 3949–3964 (2017) DM fractions and assembly epochs of ETGs 3953

isotropic, i.e. β =±0.5, 0, respectively. Since our mass estimates (2008) where they obtained a DM fraction of 0.55 within 5 Re 11 are largely insensitive to the choice of β (deviating by ≤10 per cent), and a Mtot(< 5Re) = 2.7 × 10 M for their maximal disc model, we adopt Mtot obtained when β = 0, that is, the velocity distribution compared to our values (for the isotropic orbit case) of 0.08 ± 11 is isotropic. As a further test, we have also obtained Mtot assuming 0.45 and Mtot(< 5Re) = 0.8 ± 0.4 × 10 M. The stellar mass a more extreme velocity anisotropy of β =−1. This is motivated and galaxy size used in the two studies are comparable. If we as- by recent results from dynamical studies and cosmological simu- sume α = 0 (i.e. the isothermal case as suggested by their flat lations where such anisotropies were reported (e.g. Rottgers,¨ Naab rotation curve), we would derive a somewhat higher DM fraction &Oser2014;Potaetal.2015; Zhang et al. 2015). Even with such of 0.15. The main limitation on our DM fraction measurement for extreme anisotropies, the maximum deviation in total mass is less NGC 2974 is likely the limited sample size of 26 GCs; this results than 20 per cent, never producing a shift in DM fraction greater in a relatively large error. Despite different data sets and modelling than 0.1 (see Appendix A1 for more details). Note that we have also assumptions in both studies, our low DM fraction is consistent applied small corrections to Mp to account for galaxy flattening and within ∼1σ of the Weijmans et al. value. Therefore, these intrigu- projection effects (on average, ∼5 per cent) and non-equilibrium ing results of very low DM fractions would need confirmation by conditions (∼20 per cent when kinematics substructures are identi- future studies to rule out that it is not the poor number statistics fiedintheGCsystem). that is driving these results, although we also find fDM ∼ 0.8 in 11 For the newly introduced galaxies and at the lower M∗ end, the NGC 3608 with M∗∼10 M and similarly sparse GC kinematics average fractional uncertainty on Mtot is 0.4 dex. At the high M∗ data. end of our sample, there is no significant difference between the To properly understand our observed fDM, we compare our results fractional uncertainties on Mtot for galaxies with externally sourced with expectations from simple galaxy models and the cosmological kinematics data, compared to galaxies with Keck/DEIMOS data. hydrodynamical simulations reported in Wu et al. (2014, hereafter We are unable to identify any kinematics substructures that may be Wu+14) and in Remus et al. (2017, hereafter Remus+17). The in the GC systems of these newly introduced galaxies. This is due simple galaxy model, labelled SGM1, (details of which are pre- to the large uncertainties on the individual radial velocities. Since sented in Alabi+16) does not account directly for processes that our kinematics data extend well beyond 5 Re for most galaxies are believed to alter the distribution of baryons and non-baryons in our sample, we also obtain Mtot enclosed within the maximum in present-day ETGs during their evolution. It takes as input the radial extent, Rmax, of our data. We obtain the DM fraction, fDM,as Re–M∗, M∗–M200 and M200–c200 scaling relations from the litera- 1 − M∗( < R)/Mtot( < R) where we assume that all of the baryonic ture, adopts the Planck cosmology and predicts the fDM and the Mtot mass within R in our galaxies is stellar in nature. We describe the within 5 Re for a given M∗. On the other hand, the mass distribution total stellar mass within 5 Re with de-projected Sersic´ profiles, using is explicitly modified in the cosmological simulation of Wu+14 the Sersic´ indices from Table 1.Table2 contains a summary of the via dissipative and/or non-dissipative processes during galaxy as- total masses and DM fractions enclosed within 5 Re and Rmax. sembly. However, they did not include feedback models from AGN For the galaxies originally studied in Alabi+16, we compare and/or SN winds in their simulations. The immediate effect of this results in Fig. 1 to see how the newly adopted sizes and stellar is that their galaxies contain more baryons relative to DM when masses affect both parameters of interest. We remark that while compared to conventional M∗–M200 scaling relations for ETGs. If these new galaxy parameters result in changes to the total mass and we allow for a factor of 2–3 excess stellar mass at any defined DM fraction estimates within 5 Re on a galaxy by galaxy basis, M200 in our SGM1 model, we adequately predict the fDM reported their overall distributions, which we will present shortly, for our in Wu+14, as shown in Fig. 2. The predicted fDM from our SGM1 galaxy sample remain unchanged. In particular, at the high M∗ end, is then reduced by ∼0.1 at all galaxy stellar mass. The cosmologi- galaxies are now more massive within the 5 Re aperture and a few cal simulation of Remus+17 is an improvement on Wu+14 in that ∼L∗ galaxies also have slightly lowered DM fractions compared to they have included a feedback model that accounts for AGN and SN Alabi+16. winds effects. However, at low M∗, their galaxies are larger than the Fig. 2 shows the fDM versus M∗ for our galaxy sample, assuming expectations from conventional Re–M∗ scaling relations for ETGs β = 0 and a Kroupa IMF. For most galaxies in our combined (e.g. Lange et al. 2015). This probably indicates AGN feedback that sample, the DM content already dominates the mass budget at 5 is too strong in their lower stellar mass regime. Lastly, we construct Re with the DM domination increasing as we probe beyond 5 Re a variant of our SGM1 where we use the galaxy sizes, stellar masses into the outer haloes. There is a wide diversity in the measured fDM and Sersic´ indices listed in Table 1 and compare the predicted DM within 5 Re, ranging from 0.1to0.9, generally increasing with galaxy fractions with what we have measured within 5 Re. We show the stellar mass, with some log(M∗/M) ∼ 11 galaxies having very comparison in Fig. 3 as a function of galaxy stellar mass. We also low fDM,thatis,≤0.4, less than what a simple galaxy model (SGM) show this simple galaxy model (labelled SGM2) in Fig. 2 where predicts. This trend persists for a variety of stellar M/L assumptions, we have used a double-power law fit to the galaxy sizes and stellar assumed slope of the gravitational potential and orbital anisotropies. masses in Table 1, and show that it is consistent (within 1σ ) with The large spread in fDM is driven exclusively by log(M∗/M) ∼ 11 the dark matter fractions predicted by SGM1. This galaxy model ETGs. The updated list of galaxies with fDM within 5 Re lower than captures the shape of our measured dark matter fractions better than the prediction from our SGM now consist of NGC 720, NGC 2974, SGM1. NGC 3607, NGC 4494, NGC 4526 and NGC 5866. A complete inventory of our galaxy sample shows that 2 out of 5 field galaxies, 3 out of 15 group galaxies and 1 out of 12 cluster galaxies have 3.2 Average DM density low DM fractions. This is the same as 2 out of 16 ellipticals, 4 We obtain the average enclosed DM density, ρ , within a sphere out of 10 lenticulars and none of the 6 galaxies with ambiguous DM with radius R, as in Thomas et al. (2009)using morphological classification having low DM fractions. The results we have obtained for NGC 2974 may appear to M (

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Table 2. Summary of mass estimates and DM fractions assuming different anisotropy. The results shown here have been obtained using the TME and a stellar M/L that accounts for stellar age variation. Mp is the pressure-supported mass and has been corrected for the effect of galaxy ﬂattening. Mrot is the rotationally supported mass. Mtot is the total mass after correcting for galaxy ﬂattening, rotation in the GC system and the presence of kinematics substructures. fDM is the DM fraction. We list masses enclosed within spheres of radius 5 Re and Rmax, the maximum galactocentric radius where we have GC kinematics data. Note that the kinematics data for NGC 4374, NGC 4472, NGC 4636 and NGC 4697 do not extend out to 5 Re.

Galaxy β Mrot( < 5Re) Mp( < 5Re) Mtot( < 5Re) fDM( < 5Re) Rmax Mrot( < Rmax) Mp( < Rmax) Mtot( < Rmax) fDM( < Rmax) 10 11 11 10 11 11 (NGC) (10 M)(10M)(10M)(Re)(10M)(10M)(10M) 720 0 1.7 ± 0.3 2.4 ± 0.6 2.6 ± 0.5 0.36 ± 0.20 22.91 7.6 ± 1.6 11.4 ± 2.2 12.2 ± 2.0 0.85 ± 0.04 0.5 2.4 ± 0.6 2.6 ± 0.5 0.34 ± 0.21 11.1 ± 2.2 11.9 ± 2.0 0.84 ± 0.04 −0.5 2.5 ± 0.6 2.6 ± 0.6 0.37 ± 0.18 11.6 ± 2.3 12.4 ± 2.2 0.85 ± 0.04 821 0 2.1 ± 0.4 4.3 ± 0.8 4.5 ± 0.8 0.81 ± 0.05 8.06 3.4 ± 0.6 5.6 ± 1.0 5.9 ± 1.0 0.85 ± 0.04 0.5 4.4 ± 0.8 4.6 ± 0.9 0.82 ± 0.05 5.8 ± 1.0 6.1 ± 1.0 0.85 ± 0.04 −0.5 4.2 ± 0.8 4.4 ± 0.8 0.81 ± 0.05 5.5 ± 1.0 5.8 ± 1.0 0.85 ± 0.04 1023 0 2.4 ± 0.4 1.4 ± 0.3 1.6 ± 0.2 0.47 ± 0.12 16.15 7.7 ± 1.4 3.2 ± 0.6 3.9 ± 0.5 0.76 ± 0.05 0.5 1.5 ± 0.3 1.7 ± 0.2 0.49 ± 0.12 3.3 ± 0.6 4.1 ± 0.5 0.76 ± 0.05 −0.5 1.4 ± 0.3 1.6 ± 0.2 0.46 ± 0.13 3.1 ± 0.5 3.9 ± 0.5 0.75 ± 0.05 1400 0 0.3 ± 0.1 2.2 ± 0.5 2.2 ± 0.6 0.54 ± 0.21 22.55 1.6 ± 0.6 7.1 ± 1.3 7.2 ± 1.3 0.84 ± 0.04 0.5 2.2 ± 0.6 2.3 ± 0.6 0.54 ± 0.2 7.2 ± 1.3 7.4 ± 1.3 0.84 ± 0.04 −0.5 2.2 ± 0.5 2.2 ± 0.5 0.53 ± 0.17 7.0 ± 1.3 7.1 ± 1.2 0.83 ± 0.04 1407 0 0.1 ± 0.1 18.6 ± 1.5 18.6 ± 1.5 0.82 ± 0.04 9.54 0.2 ± 0.1 36.4 ± 2.7 36.4 ± 2.7 0.90 ± 0.02 0.5 16.5 ± 1.4 16.5 ± 1.4 0.79 ± 0.04 32.2 ± 2.4 32.2 ± 2.4 0.88 ± 0.02 −0.5 19.7 ± 1.6 19.7 ± 1.7 0.83 ± 0.03 38.5 ± 2.8 38.5 ± 2.7 0.90 ± 0.02 2768 0 4.3 ± 0.4 6.3 ± 1.1 6.8 ± 0.9 0.78 ± 0.05 11.36 9.8 ± 0.9 12.0 ± 1.9 13.0 ± 1.7 0.88 ± 0.02 0.5 6.3 ± 1.0 6.7 ± 0.9 0.78 ± 0.05 11.9 ± 1.9 12.9 ± 1.7 0.88 ± 0.03 −0.5 6.4 ± 1.1 6.8 ± 0.9 0.79 ± 0.05 12.1 ± 1.9 13.1 ± 1.7 0.88 ± 0.02 2974 0 0.5 ± 0.1 0.8 ± 0.4 0.8 ± 0.4 0.08 ± 0.45 10.69 1.0 ± 0.3 4.9 ± 1.5 5.0 ± 1.5 0.84 ± 0.09 0.5 0.8 ± 0.4 0.9 ± 0.4 0.12 ± 0.44 5.1 ± 1.6 5.2 ± 1.6 0.84 ± 0.11 −0.5 0.8 ± 0.4 0.8 ± 0.4 0.06 ± 0.48 4.8 ± 1.5 4.9 ± 1.4 0.83 ± 0.09 3115 0 3.4 ± 0.6 1.7 ± 0.3 2.1 ± 0.3 0.64 ± 0.08 17.6 11.8 ± 2.1 4.4 ± 0.6 5.6 ± 0.6 0.85 ± 0.03 0.5 1.8 ± 0.4 2.2 ± 0.3 0.65 ± 0.08 4.6 ± 0.7 5.8 ± 0.6 0.86 ± 0.03 −0.5 1.7 ± 0.3 2.0 ± 0.3 0.63 ± 0.09 4.3 ± 0.6 5.5 ± 0.6 0.85 ± 0.03 3377 0 0.1 ± 0.1 0.7 ± 0.1 0.7 ± 0.1 0.62 ± 0.09 11.37 0.3 ± 0.1 1.3 ± 0.2 1.3 ± 0.2 0.77 ± 0.05 0.5 0.8 ± 0.1 0.8 ± 0.1 0.66 ± 0.09 1.4 ± 0.2 1.5 ± 0.2 0.80 ± 0.04 −0.5 0.6 ± 0.1 0.7 ± 0.1 0.60 ± 0.10 1.2 ± 0.2 1.2 ± 0.2 0.76 ± 0.05 3607 0 0.4 ± 0.1 2.4 ± 0.7 2.5 ± 0.7 0.16 ± 0.44 16.76 1.3 ± 0.5 10.2 ± 2.4 10.3 ± 2.4 0.77 ± 0.09 0.5 2.3 ± 0.6 2.4 ± 0.6 0.11 ± 0.38 9.6 ± 2.3 9.7 ± 2.2 0.75 ± 0.08 −0.5 2.5 ± 0.7 2.6 ± 0.6 0.18 ± 0.38 10.4 ± 2.5 10.5 ± 2.6 0.77 ± 0.24 3608 0 0.5 ± 0.2 3.9 ± 1.1 4.0 ± 1.2 0.77 ± 0.19 6.82 0.7 ± 0.3 4.4 ± 1.2 4.5 ± 1.2 0.78 ± 0.12 0.5 4.1 ± 1.2 4.1 ± 1.2 0.78 ± 0.11 4.5 ± 1.2 4.6 ± 1.2 0.79 ± 0.1 −0.5 3.9 ± 1.1 3.9 ± 1.1 0.77 ± 0.2 4.3 ± 1.2 4.4 ± 1.2 0.78 ± 0.12 4278 0 0.1 ± 0.1 2.6 ± 0.3 2.7 ± 0.4 0.72 ± 0.07 16.81 0.5 ± 0.2 6.5 ± 0.6 6.6 ± 0.6 0.87 ± 0.02 0.5 2.8 ± 0.4 2.8 ± 0.4 0.73 ± 0.06 6.8 ± 0.6 6.9 ± 0.6 0.88 ± 0.02 −0.5 2.6 ± 0.3 2.6 ± 0.3 0.72 ± 0.07 6.3 ± 0.6 6.4 ± 0.5 0.87 ± 0.02 4365 0 1.5 ± 0.2 16.5 ± 1.6 16.6 ± 1.6 0.83 ± 0.03 8.79 2.6 ± 0.3 29.7 ± 2.6 30.0 ± 2.6 0.90 ± 0.02 0.5 15.1 ± 1.4 15.2 ± 1.5 0.82 ± 0.04 27.1 ± 2.4 27.4 ± 2.4 0.89 ± 0.02 −0.5 17.3 ± 1.6 17.4 ± 1.6 0.84 ± 0.03 31.0 ± 2.8 31.3 ± 2.7 0.90 ± 0.02 4374 0 16.1 ± 1.4 20.9 ± 4.8 22.5 ± 4.9 0.89 ± 0.04 3.51 −−−− 0.5 19.1 ± 4.4 20.7 ± 4.4 0.88 ± 0.04 −−−− −0.5 21.8 ± 5.0 23.4 ± 5.3 0.90 ± 0.04 −−−− 4459 0 0.2 ± 0.1 2.1 ± 0.6 2.2 ± 0.6 0.62 ± 0.32 7.27 0.3 ± 0.1 2.6 ± 0.7 2.7 ± 0.7 0.68 ± 0.14 0.5 2.2 ± 0.6 2.2 ± 0.6 0.64 ± 0.17 2.7 ± 0.7 2.8 ± 0.7 0.69 ± 0.13 −0.5 2.1 ± 0.6 2.1 ± 0.6 0.62 ± 0.39 2.6 ± 0.7 2.6 ± 0.7 0.67 ± 0.13 4473 0 0.2 ± 0.1 1.6 ± 0.3 1.6 ± 0.3 0.51 ± 0.15 15.51 0.8 ± 0.4 3.6 ± 0.5 3.7 ± 0.5 0.76 ± 0.05 0.5 1.7 ± 0.3 1.7 ± 0.3 0.53 ± 0.12 3.7 ± 0.6 3.8 ± 0.5 0.77 ± 0.05 −0.5 1.5 ± 0.3 1.6 ± 0.3 0.50 ± 0.14 3.5 ± 0.5 3.6 ± 0.5 0.75 ± 0.05 4474 0 1.2 ± 1.2 0.4 ± 0.2 0.6 ± 0.2 0.71 ± 0.42 17.18 4.2 ± 4.6 0.9 ± 0.3 1.3 ± 0.6 0.87 ± 0.38 0.5 0.5 ± 0.2 0.6 ± 0.3 0.75 ± 0.41 1.0 ± 0.4 1.4 ± 0.6 0.88 ± 0.44 −0.5 0.4 ± 0.2 0.5 ± 0.2 0.70 ± 0.45 0.8 ± 0.3 1.2 ± 0.6 0.86 ± 0.44 4486 0 1.7 ± 0.2 25.5 ± 1.8 25.7 ± 1.9 0.86 ± 0.03 28.55 9.8 ± 1.0 148.0 ± 8.4 149.0 ± 8.4 0.97 ± 0.01 0.5 22.5 ± 1.6 22.7 ± 1.6 0.84 ± 0.03 130.0 ± 7.3 131.0 ± 7.6 0.97 ± 0.01 −0.5 27.1 ± 1.9 27.3 ± 1.9 0.87 ± 0.03 157.0 ± 8.8 158.0 ± 9.2 0.97 ± 0.01 4494 0 1.3 ± 0.1 1.4 ± 0.2 1.5 ± 0.2 0.4 ± 0.14 7.95 2.0 ± 0.2 1.9 ± 0.3 2.1 ± 0.3 0.53 ± 0.11 0.5 1.4 ± 0.2 1.6 ± 0.2 0.41 ± 0.13 1.9 ± 0.3 2.2 ± 0.3 0.54 ± 0.10 −0.5 1.4 ± 0.2 1.5 ± 0.2 0.39 ± 0.14 1.9 ± 0.3 2.1 ± 0.3 0.52 ± 0.10 4526 0 2.1 ± 0.6 2.7 ± 0.8 2.9 ± 0.6 0.43 ± 0.18 16.75 7.0 ± 2.1 6.5 ± 1.3 7.2 ± 1.1 0.75 ± 0.05 0.5 2.6 ± 0.8 2.8 ± 0.6 0.41 ± 0.20 6.4 ± 1.3 7.1 ± 1.0 0.74 ± 0.06 −0.5 2.7 ± 0.8 2.9 ± 0.6 0.43 ± 0.19 6.6 ± 1.4 7.3 ± 1.1 0.75 ± 0.06

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Table 2 – continued

Galaxy β Mrot( < 5Re) Mp( < 5Re) Mtot( < 5Re) fDM( < 5Re) Rmax Mrot( < Rmax) Mp( < Rmax) Mtot( < Rmax) fDM( < Rmax) 10 11 11 10 11 11 (NGC) (10 M)(10M)(10M)(Re)(10M)(10M)(10M) 4564 0 1.8 ± 0.4 0.7 ± 0.2 0.9 ± 0.2 0.59 ± 0.22 11.25 4.0 ± 0.9 0.9 ± 0.3 1.3 ± 0.3 0.71 ± 0.09 0.5 0.8 ± 0.3 0.9 ± 0.3 0.62 ± 0.15 1.0 ± 0.3 1.4 ± 0.3 0.73 ± 0.09 −0.5 0.6 ± 0.2 0.8 ± 0.2 0.57 ± 0.2 0.9 ± 0.3 1.3 ± 0.3 0.70 ± 0.08 4649 0 4.6 ± 0.3 12.9 ± 1.0 13.4 ± 1.0 0.74 ± 0.05 20.2 18.6 ± 1.3 53.9 ± 3.8 55.8 ± 3.8 0.93 ± 0.01 0.5 11.4 ± 0.9 11.9 ± 0.9 0.71 ± 0.05 47.8 ± 3.3 49.7 ± 3.4 0.92 ± 0.01 −0.5 13.7 ± 1.1 14.2 ± 1.1 0.75 ± 0.05 57.0 ± 4.0 58.9 ± 3.9 0.93 ± 0.01 4697 0 3.1 ± 0.2 3.6 ± 0.6 3.9 ± 0.6 0.7 ± 0.07 4.0 −−−− 0.5 3.6 ± 0.6 3.9 ± 0.6 0.7 ± 0.07 −−−− −0.5 3.5 ± 0.6 3.9 ± 0.5 0.7 ± 0.07 −−−− 5846 0 0.4 ± 0.1 18.4 ± 1.9 18.4 ± 1.9 0.87 ± 0.03 8.99 0.8 ± 0.2 32.5 ± 3.3 32.6 ± 3.3 0.92 ± 0.02 0.5 17.0 ± 1.8 17.0 ± 1.8 0.86 ± 0.03 30.1 ± 3.0 30.2 ± 3.1 0.91 ± 0.02 −0.5 19.0 ± 2.0 19.0 ± 2.0 0.87 ± 0.03 33.7 ± 3.4 33.8 ± 3.4 0.92 ± 0.02 5866 0 0.1 ± 0.1 1.0 ± 0.5 1.0 ± 0.4 0.34 ± 0.45 8.85 0.1 ± 0.6 1.2 ± 0.5 1.2 ± 0.4 0.44 ± 0.39 0.5 1.0 ± 0.5 1.0 ± 0.4 0.38 ± 0.45 1.3 ± 0.5 1.3 ± 0.5 0.48 ± 0.42 −0.5 0.9 ± 0.5 0.9 ± 0.4 0.32 ± 0.44 1.1 ± 0.5 1.2 ± 0.4 0.42 ± 0.38 7457 0 1.8 ± 0.2 0.9 ± 0.3 1.1 ± 0.2 0.88 ± 0.04 6.61 2.4 ± 0.3 0.9 ± 0.3 1.2 ± 0.2 0.89 ± 0.04 0.5 1.1 ± 0.3 1.2 ± 0.3 0.90 ± 0.04 1.1 ± 0.3 1.3 ± 0.3 0.90 ± 0.03 −0.5 0.8 ± 0.2 1.0 ± 0.2 0.87 ± 0.04 0.8 ± 0.2 1.1 ± 0.2 0.88 ± 0.04 1316 0 12.0 ± 0.4 14.6 ± 2.1 15.8 ± 2.0 0.81 ± 0.04 9.45 22.6 ± 0.8 29.3 ± 3.6 31.6 ± 3.4 0.89 ± 0.02 0.5 13.2 ± 1.9 14.4 ± 1.9 0.79 ± 0.05 26.4 ± 3.2 28.7 ± 3.4 0.88 ± 0.02 −0.5 15.4 ± 2.2 16.6 ± 2.1 0.82 ± 0.04 30.8 ± 3.7 33.1 ± 3.6 0.90 ± 0.02 1399 0 0.2 ± 0.1 40.8 ± 2.7 40.8 ± 2.6 0.94 ± 0.01 6.06 0.2 ± 0.1 49.4 ± 3.2 49.4 ± 3.1 0.95 ± 0.01 0.5 37.4 ± 2.5 37.4 ± 2.4 0.94 ± 0.01 45.3 ± 2.9 45.3 ± 3.0 0.95 ± 0.01 −0.5 42.5 ± 2.8 42.5 ± 2.9 0.94 ± 0.01 51.5 ± 3.3 51.5 ± 3.4 0.95 ± 0.01 4472 0 0.2 ± 0.1 29.6 ± 2.8 29.6 ± 2.8 0.85 ± 0.04 3.12 −−−− 0.5 24.6 ± 2.3 24.6 ± 2.4 0.82 ± 0.04 −−−− −0.5 32.2 ± 3.1 32.2 ± 3.0 0.86 ± 0.03 −−−− 4594 0 0.3 ± 0.1 5.6 ± 0.6 5.7 ± 0.6 0.58 ± 0.08 10.0 0.6 ± 0.3 9.9 ± 0.9 9.9 ± 0.9 0.75 ± 0.05 0.5 5.3 ± 0.5 5.3 ± 0.6 0.56 ± 0.09 9.3 ± 0.9 9.4 ± 0.9 0.73 ± 0.05 −0.5 5.8 ± 0.6 5.8 ± 0.6 0.59 ± 0.08 10.2 ± 1.0 10.3 ± 1.0 0.75 ± 0.05 4636 0 1.0 ± 0.1 9.5 ± 0.7 9.6 ± 0.7 0.88 ± 0.02 3.48 −−−− 0.5 9.5 ± 0.7 9.6 ± 0.7 0.88 ± 0.03 −−−− −0.5 9.5 ± 0.7 9.6 ± 0.7 0.88 ± 0.02 −−−− 5128 0 0.1 ± 0.1 1.7 ± 0.2 1.7 ± 0.2 0.53 ± 0.09 21.73 0.6 ± 0.3 7.4 ± 0.5 7.5 ± 0.5 0.88 ± 0.02 0.5 1.7 ± 0.2 1.7 ± 0.2 0.54 ± 0.09 7.6 ± 0.5 7.7 ± 0.5 0.89 ± 0.02 −0.5 1.6 ± 0.2 1.6 ± 0.1 0.52 ± 0.09 7.3 ± 0.5 7.4 ± 0.5 0.88 ± 0.02

Figure 1. Comparison of total mass estimates (left-hand panel) and DM fractions (right-hand panel) obtained using different galaxy sizes and stellar masses (see text for details). Note that we have excluded NGC 4697 from these plots due to the additional change to its kinematics data.

MNRAS 468, 3949–3964 (2017) 3956 A. B. Alabi et al.

Figure 2. Measured dark matter fraction, fDM, within 5 effective radii (Re) versus the total stellar mass, M∗ assuming β = 0, i.e. isotropic velocity distribution. The solid black line (SGM1) shows the predicted dark matter fraction within 5 Re assuming Planck cosmology and Kroupa IMF for a simple galaxy model based on scaling relations for early-type galaxies. The dot-dashed black lines are the 1σ scatter in the predicted dark matter fractions from the adopted Re − M∗ relation. We also show results from the cosmological hydrodynamical simulations reported in Wu et al. (2014) and Remus et al. (2017) for comparison. The dashed green line (SGM2) is the predicted dark matter fraction from a simple galaxy model using a ﬁt to galaxy sizes and stellar masses in Table 1. The orange-coloured circles and the lower left representative errorbar are for our galaxy sample. Galaxies with log (M∗/M) ∼ 11 have a larger spread in their measured fDM, with a few of them having fDM lower than predicted by any cosmological model. At any stellar mass, central dominant galaxies (marked with crosses) mostly have higher fDM.

where MDM is the enclosed DM mass, evaluated as Mtot( < R) − M∗( < R). Again we have followed the approach used in Alabi+16, where we assume that all the baryonic matter within our 5 Re aperture is in the stellar component. Fig. 4 shows the log ρDM within 5 Re for our galaxy sample. We also show similar data from Thomas et al. (2009), Weg- ner et al. (2012) and Corsini et al. (2017), but obtained within 2 Re for several ETGs in the Coma cluster, the nearby Abell 262 cluster and low-density environments, respectively. The offset between these literature results and our measurements is due to the difference between the apertures used. The general trend, regardless of the adopted aperture, is for ρDM to decrease with M∗, with an enhanced scatter around log(M∗/M)∼11. A wide range of average DM densities is possible at any stellar mass, in agreement with theory, where galaxies are expected to have diverse mass assembly histories at any stellar mass. We do not see any difference between the mean average densities for the lenticulars Figure 3. Residuals between observed and predicted DM fractions, assum- or ellipticals in our galaxy sample, neither do we see any sig- ing a Planck cosmology and using galaxy sizes, stellar masses and Sersic´ niﬁcant trend with galaxy environment. The increasing trend ear- indices from Table 1 in the simple galaxy model, that is, SGM2. lier observed in fDM as a function of mass is now reversed when ρDM is compared with M∗. This is due to the steep increase of Re with M∗, such that in the more massive galaxies, our ﬁdu- cial radius now encloses more DM within a much more increased

MNRAS 468, 3949–3964 (2017) DM fractions and assembly epochs of ETGs 3957

Figure 4. Average DM density within 5 Re, ρDM, versus the stellar mass for our galaxy sample. Results from Thomas et al. (2009) for ETGs in the Coma cluster, Wegner et al. (2012) for eight galaxies in the nearby, but poor Abell 262 cluster and Corsini et al. (2017) for two galaxies in low-density environments within 2 Re are also shown. The offset from our data is due to differences in the apertures used. Galaxies with sub-5 Re kinematics data are marked with downward-pointing arrows. The solid and dashed lines are the predicted average dark matter densities within 5 Re from our simple galaxy models, that is, SGM1 and SGM2, respectively. We have also included results from the cosmological simulations of Wu+14 and Remus+17. Average DM density within 5 Re (as well as within any other aperture) decreases mildly with total stellar mass, with a larger scatter around log(M∗/M)∼11.

volume, hence the lowered density. The increased offset at the low (i) For mock galaxies with M∗ identical to our galaxy sample, stellar mass end between our measurements and the predictions obtain galaxy sizes using the Re–M∗ relation from Lange et al. from Remus+17 is due to the relatively large galaxies produced in (2015). their simulations. (ii) Use the Re–n relation from Graham (2013) to obtain Sersic´ indices (Sersic´ 1968) for each mock galaxy. (iii) Calculate the total M∗ enclosed within 5 R with the de– 3.3 Inferring DM halo properties from dynamical e projected Sersic´ mass profile (Terzic´ & Graham 2005). measurements (iv) Calculate M200 for each mock galaxy using the M∗–M200 Next, we turn to one of the main questions we wish to address in this relation for ETGs from Dutton et al. (2010), which assumes a Planck work, that is, given dynamical mass measurements at some fiducial cosmology. Note that r200 follows directly from M200. radii (in our case, 5 Re), which are smaller than the typical scale (v) Calculate the total DM mass, MDM enclosed within 5 Re, from radii in DM haloes, can we reliably infer the structural properties the cumulative NFW DM only profile. of these haloes, that is, M200 (virial mass), c200 (halo concentration) (vi) Calculate the ratio of M200 to Mtot within 5 Re for each mock and zform (the halo assembly epoch)? galaxy. DM haloes can generally be described by Navarro–Frenk–White (vii) Assume that for any M∗, given the ratio of M200 to Mtot (NFW) profiles (Navarro, Frenk & White 1996) where the average within 5Re obtained from our mock galaxies, we can extrapolate enclosed DM density, ρDM, can be expressed as our measured Mtot within 5 Re to obtain the corresponding M200. 200 ln(1 + cx) − cx/(cx + 1) ρ (

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Table 3. Summary of inferred halo parameters. Columns: (1) galaxy name; Table 4. Comparison of halo properties with literature results. Columns: (1) (2) average DM density within 5 Re; (3) halo mass; (4) halo concentration; galaxy name; (2) halo mass; (3) halo concentration; (4) corrected halo mass (5) halo assembly epoch (we have set the halo assembly epoch of galaxies from the literature; (5) corrected halo concentration from the literature; (6) with invalid zform to 0.1; these are all galaxies with very low DM fractions); virial overdensity, halo mass and concentration (where necessary, we have (6) redshift corresponding to the mean luminosity-weighted stellar age from obtained corresponding halo mass and concentration at virial overdensity of Table 1. For galaxies with mean stellar ages comparable to or older than the 200). age of the universe, we have set their corresponding zstars to a lower limit of 10. Galaxy logM200 c200 logM200 c200 Notes (NGC) (M)(M) x,logMx, cx Galaxy log M200 log ρDM c200 zform zstars (NGC) (M)(Mpc−3) This work Literature 720 12.83 3.0 12.77 14.15 101.6, 12.82, 18.50a 720 12.83 ± 0.38 −2.48 ± 0.65 3.0 ± 2.0 0.6 ± 0.8 1.0 821 12.99 6.4 17.52 1.73 101, 17.68, 2.45b 821 12.99 ± 0.29 −2.23 ± 0.22 6.4 ± 1.5 2.3 ± 0.6 2.4 821 14.31 1.77 101, 14.46, 2.50c 1023 12.56 ± 0.28 −2.07 ± 0.37 6.2 ± 2.2 2.3 ± 0.9 4.1 1400 12.71 5.4 11.92 3.98 101, 12.02, 5.38d 1400 12.71 ± 0.36 −2.21 ± 0.49 5.4 ± 2.6 1.9 ± 1.1 >10 1407 13.82 2.3 13.23 7.77 101, 13.3, 10.30e 1407 13.82 ± 0.40 −2.79 ± 0.11 2.3 ± 0.3 0.5 ± 0.3 3.5 13.78 6.85 101, 13.85, 9.10f 2768 13.22 ± 0.33 −2.41 ± 0.18 4.7 ± 0.9 1.6 ± 0.5 4.1 12.99 5.63 101, 13.07, 7.53d 2974 12.25 ± 0.55 −3.34 ± 6.34 0.01 ± 6.6 0.1 1.4 13.57 12.11 200, 13.57, 12.11g 3115 12.65 ± 0.25 −1.26 ± 0.23 17.9 ± 3.7 6.9 ± 1.4 1.3 13.34 18.59 200, 13.34, 18.60h 3377 12.19 ± 0.20 −2.22 ± 0.27 5.7 ± 1.6 2.0 ± 0.7 0.8 12.96 13.68 101.7, 13.02, 17.88a 3607 12.85 ± 0.45 −3.27 ± 1.98 0.2 ± 2.0 0.1 1.9 2768 13.22 4.7 11.69 4.72 101, 11.78, 6.35d 3608 12.95 ± 0.38 −2.23 ± 0.39 6.2 ± 2.5 2.2 ± 1.0 1.7 3115 12.65 17.9 12.08 13.79 101, 12.14, 18.07d 4278 12.76 ± 0.26 −1.43 ± 0.20 15.7 ± 2.9 6.1 ± 1.1 3.2 3377 12.19 5.7 11.28 5.25 101, 11.36, 7.03d 4365 13.73 ± 0.39 −2.40 ± 0.12 4.4 ± 0.5 1.4 ± 0.3 10.0 4278 12.76 15.7 11.71 13.23 101, 11.77, 17.35d 4374 13.86 ± 0.43 −2.24 ± 0.25 5.6 ± 1.4 2.0 ± 0.7 10.0 4365 13.73 4.4 12.53 11.01 101, 12.59, 14.48d 4459 12.67 ± 0.37 −2.31 ± 0.47 5.1 ± 2.5 1.7 ± 1.0 0.8 4374 13.86 5.6 13.14 10.97 178, 13.15, 11.50i 4473 12.55 ± 0.29 −1.84 ± 0.40 8.5 ± 3.2 3.2 ± 1.3 7.5 13.32 5.59 100, 13.4, 7.50j 4474 12.13 ± 0.46 −1.65 ± 0.63 11.6 ± 7.2 4.5 ± 2.5 2.2 4486 13.97 7.8 13.93 6.98 101, 14.0, 9.27k 4486 13.97 ± 0.40 −1.91 ± 0.09 7.8 ± 0.7 2.9 ± 0.3 >10 12.61 12.78 101, 12.67, 16.77d 4494 12.53 ± 0.28 −2.82 ± 0.45 1.9 ± 1.1 0.1 1.0 14.67 3.21 101, 14.78, 4.38l 4526 12.87 ± 0.38 −1.87 ± 0.54 7.2 ± 3.5 2.7 ± 1.4 2.4 13.90 3.88 101, 14.0, 5.25m 4564 12.27 ± 0.29 −1.19 ± 0.44 18.6 ± 7.3 7.2 ± 2.7 3.2 13.95 3.83 101, 14.05, 5.19n 4649 13.68 ± 0.40 −2.13 ± 0.11 5.7 ± 0.6 2.0 ± 0.3 >10 4494 12.53 1.9 11.97 6.23 101, 12.05, 8.30c 4697 12.96 ± 0.32 −2.29 ± 0.23 5.4 ± 1.3 1.9 ± 0.6 2.6 12.02 4.32 101, 12.11, 5.82d 5846 13.75 ± 0.38 −2.58 ± 0.13 3.5 ± 0.5 0.9 ± 0.3 >10 4649 13.68 5.7 13.49 15.94 101.5, 13.54, 20.80a 5866 12.31 ± 0.46 −1.89 ± 1.26 6.9 ± 6.3 2.6 ± 2.0 0.6 13.47 5.94 not statedo 7457 12.43 ± 0.24 −1.73 ± 0.24 11.4 ± 2.7 4.4 ± 1.1 0.3 4697 12.96 5.4 12.66 4.53 101, 12.75, 6.10c p 1316 13.73 ± 0.41 −2.41 ± 0.17 4.1 ± 0.7 1.3 ± 0.4 0.4 5846 13.75 3.5 13.16 6.00 101, 13.24, 8.00 d 1399 14.11 ± 0.38 −2.73 ± 0.07 2.9 ± 0.2 0.5 ± 0.2 2.4 12.76 11.40 101, 12.82, 14.99 q 4472 14.11 ± 0.42 −2.30 ± 0.12 4.5 ± 0.5 1.4 ± 0.3 >10 13.10 8.90 200, 13.1, 8.90 w 4594 12.75 ± 0.14 −1.70 ± 0.21 15.3 ± 3.4 5.9 ± 1.3 4.6 1316 13.73 4.1 13.37 6.10 not stated r 4636 13.36 ± 0.30 −2.63 ± 0.09 3.7 ± 0.4 1.0 ± 0.2 >10 1399 14.11 2.9 13.31 13.57 101, 13.26, 11.00 s 5128 12.56 ± 0.24 −1.81 ± 0.24 8.9 ± 2.0 3.4 ± 0.8 – 12.89 10.20 101, 12.95, 13.44 4472 14.11 4.5 13.45 9.93 101.4, 13.51, 13.07a 13.94 – 200, eqn.16t 4636 13.36 3.7 13.13 7.37 101, 13.07, 5.90u 12.99 20.09 200, 12.99, 20.10v order of magnitude increase in ρDM corresponds to a factor of ∼3 a b c increase in c200. References: Buote et al. (2007), Forestell & Gebhardt (2010), Napolitano The final step in estimating the epoch of halo assembly is to trans- et al. (2009), dSamurovic(´ 2014), ePota et al. (2015), fRomanowsky et al. g h i j form our inferred halo concentrations into halo assembly epochs. (2009), Su et al. (2014), Zhang et al. (2007), Zhu et al. (2014), Napolitano k l m Tools that efficiently do this transformation are now readily avail- et al. (2011), Oldham & Auger (2016), McLaughlin (1999), Strader et al. (2011), nMurphy, Gebhardt & Adams (2011), oShen & Gebhardt able. For each estimated c , we use the COMMAH package from 200 (2010), pNapolitano et al. (2014), qZhu et al. (2016), rRichtler et al. (2014), Correa et al. (2015), which is based on NFW DM profiles, to obtain sSchuberth et al. (2010), tSamurovic(´ 2016), uCotˆ eetal.(´ 2003), vSchuberth the corresponding halo formation redshift, zform, given the halo con- et al. (2012), wJohnson et al. (2009). centration, c200, while adopting the Planck cosmology. This NFW parametrization matches well with our earlier preference to describe the COMMAH package and for these, we fix their halo formation epoch our DM haloes with NFW profiles, rather than with cored logarith- at zform ∼ 0.1. These are all galaxies with low fDM within 5 Re. mic DM haloes or other alternate parametrizations and thus enables us to calibrate our DM densities directly into halo assembly epochs. 3.4 Comparison of halo properties with literature studies In the COMMAH package, zform is the epoch when the virial mass of any progenitor halo is equivalent to the mass within its present-day Some of the galaxies in our sample have published c200 and M200 scale radius. Table 3 contains a summary of the inferred halo prop- results in the literature from various studies. These studies are based erties for our galaxy sample. From Table 3,lowρDM corresponds on data from extended PNe and/or GC kinematics (sometimes sup- to more recently formed haloes and vice versa. Galaxies with c200 plemented with stellar kinematics data) and X-ray studies, with ≤ 2 (NGC 4494, NGC 2974 and NGC 3607) have invalid zform from different modelling techniques. We compile these results in Table 4

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and where a virial overdensity other than 200 has been used in the ∼0.2 dex scatter in the M∗–M200 and an ∼0.11 dex scatter in the literature, we rescale the results using the conversion relations from M200–c200 scaling relations, with the scatter in the Re–M∗ being Hu & Kravtsov (2003). Note that while our M200 and literature M200 the most critical. Deviations of individual galaxies from the Re–M∗ are generally consistent, our c200 values are generally lower than scaling relation produce an asymmetrical bias towards lowered fDM literature results and by construction, are more consistent with ex- (see Fig. 3, where we measure higher fDM than predicted for most of pectations from the M200–c200 relations. The implication of adopting our galaxies), resulting in the wide range of plausible DM fractions. the c200 reported in the literature for our galaxy sample is that on However, these deviations do not explain why the galaxies with average, their haloes are already in place at zform ∼ 5, whereas we low DM fractions preferentially have log(M∗/M)∼11. SGM2, find a mean zform ∼ 3. This is due to the extra constraint from the the simple galaxy model we constructed based on a fit to the sizes stellar mass–halo mass relation that we have placed on M200.Asim- and stellar masses in Table 1, could potentially help shed more light ilar approach was used in Auger et al. (2013) where the M200–c200 on this since it captures better the general trend in our measured fDM. relation was used as a conditional prior on c200. This eased the ten- However, to properly address this issue, one would need to study sion between theoretical expectations and results often reported in more galaxies with log(M∗/M) ≤ 10.5toruleoutanyartificial the literature (e.g. Napolitano et al. 2011; Samurovic´ 2014, 2016). bias from our sample selection. The low fDM ETGs, all with log(M∗/M)∼11, have very low average DM densities within 5 R , and from our preceding anal- 4 DISCUSSION e ysis, they have unrealistic halo assembly epochs, appearing to be Present-day galaxies are expected to have experienced different incompatible with the Planck cosmology. However, they are normal merger (major and/or minor) and gas accretion (smooth and/or ETGs in that they have Re and M∗ that are compatible with the Re– clumpy) histories of DM and baryons. It is also expected that signa- M∗ galaxy scaling relation. It is remarkable that log(M∗/M)∼11 tures of these varied assembly histories should be reflected in their corresponds to the sharp upturn in the Re–M∗ scaling relation and mass distributions and halo structural properties. In this work, we the knee in the M∗–M200 scaling relation. At this stellar mass (also at have obtained DM fractions and average DM densities within the all redshifts), galaxies are most efficient at converting baryons into inner 5 Re for our sample of ETGs. We interpret the diversity we stars e.g. Rodriguez-Gomez et al. (2016), such that a low DM frac- observe in these parameters as a reflection of their different mass tion should then be a natural expectation. Above log(M∗/M)∼11, assembly histories. We also use these homogeneously obtained mass galaxy haloes are too massive for gas to cool and form stars while measurements to infer the assembly epochs of their haloes as well below this mass they are not massive enough to hold on to their as their structural parameters. gas. This makes log(M∗/M)∼11 ETGs interesting as one should be able to observe the effects of extended star formation history on galaxy evolution through their mass distributions. 4.1 Origin of the diverse DM fractions within 5 Re in ETGs From our SGM1, we find that haloes of log(M∗/M)∼11 ETGs From our results above, it appears that galaxies with fDM ∼ 0.7, have significantly lower rs/Re (ratio of DM halo scale radius to in particular, the central dominant types, are well described by the galaxy size) compared to ETGs at other stellar masses (see Ap- simulation from Remus+17, while those with fDM ∼ 0.5 appear pendix A2). A simple experiment with a mock log(M∗/M)∼11 to be better described by Wu+14. A few galaxies have inferred galaxy, where we increase rs by a factor of 3 to reflect a more diffuse fDM well below the results from both cosmological simulations. DM halo, sufficiently reduces the fDM by a factor of 2, that is, from Again, we note that in the simulations of Wu+14 and Remus+17, ∼0.6 to ∼0.3. This implies that any mechanism that can produce the DM distributions have been modified from the standard NFW- normal galaxies in diffuse DM haloes should be able to explain the like profiles through baryon–DM interactions. Also, Remus+17 low DM fractions we have observed in these galaxies. The physical included feedback from AGN and SN. processes to achieve this include halo expansion through dynami- During the late phase of the mass assembly (i.e. z ≤ 2) in these cal friction from infalling stellar clumps (Johansson et al. 2009)or simulations, growth is dominated by dry mergers (major/minor) and feedback-induced DM outflows (Governato et al. 2010). The mod- happens predominantly in the outer haloes. Due to this mostly non- ified DM profile would then be non-NFW and as such our analysis dissipative growth in size and mass, our fiducial 5 Re now encloses here which assumes an NFW-like profile would be inadequate. more DM relative to stars compared to their high-redshift progen- The low DM fractions could also be due to the preferential tidal itors. At any given stellar mass, ETGs with higher DM fractions stripping of DM haloes relative to their stars (e.g. Smith et al. 2016) have experienced a late phase mass assembly that is increasingly from gravitational interactions with their neighbours. If this were to dominated by dry mergers. However, the present-day mass distribu- be the case, then one would expect to find signatures of depletion tion, parametrized by the fDM, also depends on the extent to which in the GC population, especially in the galaxy outskirts, since they the inner DM halo has been modified by baryonic processes during are more radially extended than the starlight. However, we find the mass build-up of the galaxies, as well as the initial conditions evidence to the contrary from their GC subpopulations (e.g. Forbes set by the density of the universe during the initial halo collapse. We et al. 2016), where for example, the low DM fraction galaxy NGC explore this in more details below and note that none of the cosmo- 4494 still retains a high fraction of blue GCs relative to its entire logical simulations (nor any that we are aware of in the literature) GC system in the galaxy outskirts (the blue GCs usually dominate produce galaxies with fDM within 5 Re as low as we have measured the GC system in galaxy outer haloes). in some of our ETGs. Alternatively, their low DM fractions could mean that their DM While the simple galaxy model (SGM1) clearly captures the mean haloes are poorly described by NFW DM profiles. This suggests DM fraction at any stellar mass, its use in properly understanding the need for an alternate halo description, e.g. using logarithmic the origin of the diversity in our measured fDM is hampered by the DM haloes (Thomas et al. 2009;Morgantietal.2013; Alabi+16). large scatter around the mean fDM. This scatter is from the combined Interestingly, logarithmic DM haloes are characterized by shallow uncertainties from the input scaling relations (i.e. Re–M∗, M∗–M200 central DM densities with a maximal stellar contribution (e.g. Gen- and M200–c200). There is an ∼0.25 dex scatter in the Re–M∗,an tile et al. 2004; Napolitano et al. 2011), reinforcing our earlier

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Figure 5. DM fraction versus total stellar mass, highlighting different galaxy environments in the left-hand panel, galaxy morphologies in the middle panel and galaxy central kinematics in the right-hand panel (SR = slow rotators; FR = fast rotators). Centrally dominant galaxies have been marked with black crosses and they mostly have high DM fractions. As a function of morphology, DM fraction appears to increase with galaxy stellar mass in ellipticals while lenticulars show a noisy, somewhat decreasing trend with mass and a lower median fDM compared to elliptical galaxies. The decreasing trend with stellar mass in lenticulars from the middle panel is not seen in the fast rotators in the right-hand panel. inference. The presence of self-interacting DM in haloes can also ellipticals. Disc-dominated galaxies would then have a global mass lower the central DM densities (e.g. Rocha et al. 2013; Di Cintio distribution where the DM fraction decreases with stellar mass, at et al. 2017) by making the core radius larger, but it would be chal- least within 1 Re (e.g. Courteau & Dutton 2015), and out to large lenging to separate its effects from those purely driven by feedback radii. This agrees with results from Cappellari et al. (2015)where outflows, especially in log(M∗/M)∼11 galaxies. they found that central fast-rotators and discy lenticular galaxies have similar mass distributions out to 4 Re. A larger and more complete sample of ETGs probed to large radii would be needed to 4.2 DM fractions and correlation with galaxy properties confirm if indeed this dichotomy is real or not, as well as predictions We revisit the issue of correlation between the DM fractions within of the large-scale mass distributions from cosmological simulations 5 Re for our enlarged sample and some of their galaxy properties. that produce S0s and ellipticals. We briefly summarize the interesting trends below and show the trends in Fig. 5. The Spearman rank correlations between the DM 4.3 When did the haloes of ETGs form? fractions and galaxy properties are all statistically insignificant and generally weak, mainly due to the large scatter due to the ∼1011 M We summarize the inferred halo assembly epochs for our galaxy galaxies. sample in Fig. 6, showing how they vary with galaxy total stellar First, trends as a function of environment are generally weak. mass and size. Lower mass galaxies are associated with haloes that The only stand-out trend we find as a function of galaxy environ- assembled earlier; zform ∼ 4, while the more massive galaxies have ment is that central dominant ETGs mostly have high DM fractions haloes that assembled later, at zform ∼ 2. Likewise, more compact with low DM fraction ETGs preferentially residing in less-dense galaxies are associated with haloes that assembled earlier, and vice environments. Second, we find that S0s are observed to have lower versa. These results are consistent with hierarchical growth of struc- median DM fractions compared to ellipticals, and probably show tures such that smaller objects virialize early in gas-rich events, with a hint of an opposite trend in their DM fractions with stellar mass today’s massive galaxies undergoing a more extended halo build- compared to ellipticals. This is similar to results reported for spirals up. The Spearman rank correlation between zform and stellar mass in the literature (Persic, Salucci & Ashman 1993; Dutton et al. 2011; is ∼− 0.5 and only marginally significant; however, if we remove Courteau & Dutton 2015), where the most massive spirals have the the galaxies with very low DM fractions, that is, NGC 2974, NGC lowest central DM fractions. This trend was also tentatively identi- 3607 and NGC 4494, the correlation becomes statistically signifi- fied in the S0s studied in Tortora et al. (2009), although, due to their cant, that is, p-val <0.005. The correlation between zform and size, spherical modelling technique, they claimed that the trend may not on the other hand, is stronger (∼− 0.7) and statistically significant be real. Interestingly, this trend is lost when our sample is classified (p-val <0.005) regardless of whether we exclude the three galaxies according to their central kinematics, that is, fast or slow rotators with low DM fractions or not. 3D (using results from the ATLAS ; Cappellari et al. 2013). In Fig. 7, we compare zform with that of the central stellar pop- If this dichotomy in the large-scale mass distribution between S0s ulations (obtained from the luminosity-weighted ages within their and ellipticals is real, it implies that S0s are akin to spirals, more than central 1 Re; McDermid et al. 2015) for our galaxies. We adopt the

MNRAS 468, 3949–3964 (2017) DM fractions and assembly epochs of ETGs 3961

cosmological parameters of a flat universe from the Planck Collab- −1 −1 oration XVI (2014), that is, H0 = 67.8 km s Mpc , M = 0.307 and use the ASTROPY.COSMOLOGY package to convert the ages to formation epochs. This exercise enables us to infer the nature of the late mass assembly in our sample of ETGs, that is, dissipational or non– dissipational, assuming that late gas-rich merger events are always accompanied by central star formation. For some of our galaxies, the stellar age from the literature is comparable to, or more than, the age of the universe (∼13.8 Gyr). In such cases, we adopt a fixed upper limit of ≥13.3 Gyr (zstars ≥ 10). Due to the strong correlation of zform with stellar mass, we make our comparisons after binning our galaxies by their stellar masses. Bearing in mind our modest sample size, we consider two stellar mass bins, that is, log(M∗/M) ≤ 11 and log(M∗/M) > 11 and make the comparison with respect to galaxy morphology, environment and central kinematics. From Fig. 7, massive ellipticals have haloes that assembled late, that is, zform < 2, compared to massive lenticulars, whose haloes assembled earlier (zform ∼ 4). The halo assembly epoch of low-mass ellipticals is not significantly different Figure 6. Halo assembly epoch as a function of total stellar mass (left-hand from that of lenticulars, in that their haloes also assembled early panel) and galaxy size (right-hand panel). The three galaxies with unrealistic (z ∼ 3). The late halo assembly in the field for the most mas- halo assembly epochs are shown at z ∼ 0.1. Lower mass and/or smaller form form sive galaxies is mainly driven by the galaxies with very low DM galaxies reside in haloes that assembled earlier than their more massive and larger counterparts, in agreement with the hierarchical structure growth. fractions. This is in line with results from semi-analytic models However, at any stellar mass or galaxy size, there exists a large spread in (e.g. De Lucia & Blaizot 2007) of galaxy formation where galax- the inferred halo formation epoch. Also note the correlation between the ies in low-density environments are expected to be associated with average DM density from Fig. 4 and the halo assembly epoch, such that haloes that assembled later than those in cluster environments (see galaxies with high DM densities assemble their haloes early. also Corsini et al. 2017, where they arrived at a similar conclusion based on their low-density environment dynamical study). How- ever, we only find this agreement in our most massive field galaxies, that is, log(M∗/M) > 11. If on the other hand, we disregard the stellar mass binning, halo assembly epoch then has no correlation with galaxy environment (see Appendix A3 for a version of Fig. 7 but without stellar mass binning). Haloes associated with more massive slow or fast rotating galaxies also have late assembly epochs compared to their low-mass counterparts. There is however a strong trend in the central stellar age as a function of galaxy morphology, environment and central kinematics in both stellar mass bins, where the central stars are usually in place at earlier times relative to the halo in bulge-dominated systems. The only exception to this is in low-mass, slow rotators that form their central stars relatively late, that is, zform ∼ 2. Our results therefore suggests a dichotomy between the late mass evolution of the bulge-dominated ellipticals and the discy lenticulars. This dichotomy, together with our earlier results, where at any stellar mass, more massive and centrally dominant ETGs have Figure 7. Summary plot showing the mean halo assembly epoch for our higher DM fractions and lower average DM densities within 5 Re, M / ≤ galaxy sample, in low (log( ∗ M) 11, circles and solid lines) and high form a consistent picture when considered in the context of the M / > (log( ∗ M) 11, diamonds and dash–dotted lines) stellar mass bins. two-phase galaxy formation paradigm for massive ETGs (e.g. Naab Filled symbols correspond to halo assembly epochs while open symbols et al. 2009;Oseretal.2010; Forbes et al. 2016). Dry mergers, after show the mean formation epoch that corresponds the luminosity-weighted ages of the central stars in our sample. Panel a shows the mean assembly the early dissipational phase, increase the inner DM fractions in epoch according to galaxy morphology (E=elliptical, S0=lenticular). Note massive ETGs since they do not bring a significant amount baryons that we have excluded all galaxies with ambiguous morphological classifica- to the galaxy centres but rather lead to a net outward transfer of an- tion from this analysis. Panel b shows mean assembly epoch as a function of gular momentum via dynamical friction. They also reduce the inner galaxy environment (F=field, G=group, C=cluster) and panel c shows the average DM densities since they make the galaxies larger. These mean assembly epoch as a function of central galaxy kinematics (FR=fast findings therefore rule out wet-major merger or gas-rich accretion central rotator, SR=slow central rotator). The error bars are the standard events as the predominant channel for the late mass build-up of deviations about the mean. While there are large spreads about the mean, massive ETGs. massive ellipticals have haloes that assemble relatively late compared to lenticulars or low-mass ellipticals. We also find that massive ellipticals in the field have haloes that assemble very late in agreement with predictions 5 CONCLUSIONS from the semi-analytic galaxy formation models of De Lucia & Blaizot (2007). We have measured the DM fraction and average DM density within 5 Re in a sample of 32 ETGs using their GC kinematics. We compared

MNRAS 468, 3949–3964 (2017) 3962 A. B. Alabi et al. our DM fractions with predictions from cosmological simulations. Arnold J. A. et al., 2014, ApJ, 791, 80 We also used our measured dynamical parameters to infer the epochs Astropy Collaboration, 2013, A&A, 558, A33 of assembly of our ETG haloes, assuming DM haloes are well Auger M. W., Budzynski J. M., Belokurov V., Koposov S. E., McCarthy I. described by NFW profiles. We briefly summarize our results here. G., 2013, MNRAS, 436, 503 Binney J., Tremaine S., 1987, Galactic Dynamics. Princeton Univ. Press, (i) ETGs have a wide range of DM fractions within 5 Re, ranging Princeton, NJ from 0.1 to 0.9, typically increasing with galaxy stellar mass, and Blumenthal G. R., Faber S. M., Flores R., Primack J. R., 1986, ApJ, 301, 27 largely independent of the galaxy’s environment. We find that a high Brodie J. P. et al., 2014, ApJ, 796, 52 DM fraction is consistent with a late (z ≤ 2) mass assembly that is Bryan S. E., Kay S. T., Duffy A. R., Schaye J., Dalla Vecchia C., Booth C. dominated by dissipationless mergers. M., 2013, MNRAS, 429, 3316 Bullock J. S., Kolatt T. S., Sigad Y.,Somerville R. S., Kravtsov A. V.,Klypin (ii) We find that ETGs with low DM fractions within 5 Re are M / ∼ A. A., Primack J. R., Dekel A., 2001, MNRAS, 321, 559 typically those with log( ∗ M) 11 and diffuse DM haloes. We Buote D. A., Gastaldello F., Humphrey P. J., Zappacosta L., Bullock J. S., associate their low DM fractions with a mass assembly likely dom- Brighenti F., Mathews W. G., 2007, ApJ, 664, 123 inated by halo expansion. Cappellari M. et al., 2011, MNRAS, 413, 813 (iii) By comparing our results with predictions from a suite of Cappellari M. et al., 2013, MNRAS, 432, 1709 cosmological simulations, we are able to show that modifications Cappellari M. et al., 2015, ApJ, 804, L21 of the mass distribution due to physical processes during mass Correa C. A., Wyithe J. S. B., Schaye J., Duffy A. 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(v) S0s and ellipticals reside in DM haloes with similar struc- Volume I: Explanations and references. Volume II: Data for galaxies tural properties and assembly epochs. However, we find hints that between 0h and 12h. Volume III: Data for galaxies between 12h and 24h. there may be a dichotomy in their mass distributions at large radii, Springer-Verlag, New York with S0s showing signs of a decreasing DM fraction with increas- Deason A. J., Belokurov V., Evans N. W., McCarthy I. G., 2012, ApJ, 748, ing galaxy stellar mass, unlike ellipticals. We attribute this to a 2 Dekel A., Stoehr F., Mamon G. A., Cox T. J., Novak G. S., Primack J. R., fundamental difference in their dominant late-phase mass assembly 2005, Nature, 437, 707 channel. Di Cintio A., Tremmel M., Governato F., Pontzen A., Zavala J., Basti- das Fry A., Brooks A., Vogelsberger M., 2017, MNRAS, preprint (arXiv:1701.04410) ACKNOWLEDGEMENTS Dutton A. A., Conroy C., van den Bosch F. C., Prada F., More S., 2010, We wish to thank Rhea Remus and Alan Duffy for interesting con- MNRAS, 407, 2 Dutton A. A. et al., 2011, MNRAS, 416, 322 versations and their assistance with simulation results and software Emsellem E. et al., 2011, MNRAS, 414, 888 packages. We thank the anonymous referee for comments and sug- Forbes D. A., Romanowsky A. J., Pastorello N., Foster C., Brodie J. P., gestions that have been helpful. Strader J., Usher C., Pota V., 2016, MNRAS, 457, 1242 The data presented herein were obtained at the W. M. Keck Forestell A. D., Gebhardt K., 2010, ApJ, 716, 370 Observatory, which is operated as a scientific partnership among Foster C. et al., 2016, MNRAS, 457, 147 the California Institute of Technology, the University of California Genel S., Bouche´ N., Naab T., Sternberg A., Genzel R., 2010, ApJ, and the National Aeronautics and Space Administration. The Ob- 719, 229 servatory was made possible by the generous financial support of Gentile G., Salucci P., Klein U., Vergani D., Kalberla P., 2004, MNRAS, the W. M. Keck Foundation. We also wish to recognize and ac- 351, 903 knowledge the very significant cultural role and reverence that the Governato F. et al., 2010, Nature, 463, 203 Graham A. W., 2013, Elliptical and Disk Galaxy Structure and Modern summit of Maunakea has always had within the indigenous Hawai- Scaling Laws. Springer-Verlag, Berlin, p. 91 ian community. The analysis pipeline used to reduce the DEIMOS data Harris G. L. H., Rejkuba M., Harris W. E., 2010, PASA, 27, 457 was developed at UC Berkeley with support from NSF grant AST- Hu W., Kravtsov A. V., 2003, ApJ, 584, 702 0071048. JB acknowledges support from NSF grant AST-1616598. Johansson P. H., Naab T., Ostriker J. P., 2009, ApJ, 697, L38 AJR was supported by NSF grant AST-1616710. 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P., Gomez´ M., Dirsch B., 2014, A&A, 569, A41 We investigate if the results we have obtained assuming mild Rocha M., Peter A. H. G., Bullock J. S., Kaplinghat M., Garrison-Kimmel velocity anisotropies are robust against extreme anisotropies, by S., Onorbe˜ J., Moustakas L. A., 2013, MNRAS, 430, 81 adopting a more extreme velocity anisotropy, that is, β =−1.0. Rock¨ B., Vazdekis A., Ricciardelli E., Peletier R. F., Knapen J. H., Falcon-´ This is motivated by results from some dynamical studies (e.g. Barroso J., 2016, A&A, 589, A73 Pota et al. 2015; Zhang et al. 2015) and cosmological simulations Rodriguez-Gomez V. et al., 2016, MNRAS, 458, 2371 (e.g. Rottgers¨ et al. 2014) where such anisotropies were obtained. Romanowsky A. J., Douglas N. G., Arnaboldi M., Kuijken K., Merrifield There are also indications from cosmological simulations (Bryan M. R., Napolitano N. R., Capaccioli M., Freeman K. C., 2003, Science, et al. 2013;Rottgers¨ et al. 2014;Wuetal.2014) that the stellar ve- 301, 1696 Romanowsky A. J., Strader J., Spitler L. R., Johnson R., Brodie J. P., Forbes locity anisotropy out to 5 Re correlates with the fraction of stars that D. A., Ponman T., 2009, AJ, 137, 4956 formed in situ. The nature of the reported correlation is such that in Rottgers¨ B., Naab T., Oser L., 2014, MNRAS, 445, 1065 galaxies with low in situ stellar fractions, that is, galaxies where the Samurovic´ S., 2014, A&A, 570, A132 late mass assembly is dominated by dry mergers, mostly the slow Samurovic´ S., 2016, Ap&SS, 361, 199 rotators, the anisotropy is mildly radial (β>0.2–0.4). Galaxies Sanchez-Bl´ azquez´ P., Gorgas J., Cardiel N., Gonzalez´ J. J., 2006, A&A, with high in situ stellar fractions, on the other hand, show strongly 457, 809 tangential up to isotropic anisotropies, that is, −1.0 ≤ β<0.2. This Sani E., Marconi A., Hunt L. K., Risaliti G., 2011, MNRAS, 413, 1479 anisotropy range is similar to what we now explore; however, GCs Schaye J. et al., 2015, MNRAS, 446, 521 may not have the same velocity anisotropy as stars. From the few Schuberth Y., Richtler T., Hilker M., Dirsch B., Bassino L. P., Romanowsky massive galaxies with published GC anisotropy profiles, it is diffi- A. J., Infante L., 2010, A&A, 513, A52 Schuberth Y., Richtler T., Hilker M., Salinas R., Dirsch B., Larsen S. S., cult to pick out a clear pattern (e.g. Pota et al. 2013; Zhu et al. 2016); 2012, A&A, 544, A115 see also Pota et al. 2015; Zhang et al. 2015, where GCs are reported Scott N., Graham A. W., Schombert J., 2013, ApJ, 768, 76 to be have strongly tangential anisotropies at large radii. More so, Sersic´ J. L., 1968, Atlas de galaxias australes. Observatorio Astronomico, in the lower M∗ galaxies, GC kinematics data are mostly too sparse Cordoba to extract any anisotropy information; although from the PNe data Shen J., Gebhardt K., 2010, ApJ, 711, 484 associated with these galaxies, the trend is one where the PNe are Smith R., Choi H., Lee J., Rhee J., Sanchez-Janssen R., Yi S. K., 2016, ApJ, isotropic near the galaxy centre and radially biased around 5 Re. 833, 109 Again, PNe and GCs may not have similar anisotropies. Spolaor M., Forbes D. A., Proctor R. N., Hau G. K. T., Brough S., 2008, The top panel in Fig. A1 shows the fractional changes in Mtot as MNRAS, 385, 675 a function of M∗ while the bottom panel shows the corresponding Strader J. et al., 2011, ApJS, 197, 33 Su Y., Gu L., White R. E., III, Irwin J., 2014, ApJ, 786, 152 changes in fDM versus M∗, for different anisotropy assumptions. Taylor M. B., 2005, in Shopbell P., Britton M., Ebert R., eds, ASP Conf. Note that assuming a more strongly tangential anisotropy results in Ser. Vol. 347, Astronomical Data Analysis Software and Systems XIV. an increase in Mtot and fDM only in the most mass-massive galaxies Astron. Soc. Pac., San Francisco, p. 29 and the opposite effects in the lower M∗ galaxies in our sample. Terlevich A. I., Forbes D. A., 2002, MNRAS, 330, 547 If we assume a correlation between β and M∗ that maximizes Mtot Terzic´ B., Graham A. W., 2005, MNRAS, 362, 197 within 5 Re, the fractional change in Mtot is <0.2 dex, and this

MNRAS 468, 3949–3964 (2017) 3964 A. B. Alabi et al.

Figure A3. Summary plot showing the mean halo assembly epoch for our galaxy sample (black circles) without binning by stellar mass. The plot also shows the mean formation epoch that corresponds the luminosity-weighted ages of the central stars in our sample (red diamonds). Panel a shows the mean assembly epoch according to galaxy morphology (E=elliptical, S0=lenticular), with the dashed lines joining the mean epochs when galaxies with ambiguous classifications are added to either morphologies. Panel b shows mean assembly epoch as a function of galaxy environment (F=field, G=group, C=cluster) and panel c shows the mean assembly epoch as a function of central galaxy kinematics (FR=fast central rotator, SR=slow central rotator). Comparing the panels with those in Fig. 7 highlights the need to account for the strong dependence of halo assembly epoch with galaxy stellar mass. The trend we earlier observed in the field, where haloes of massive galaxies assemble at later epochs is not obvious.

results in a <0.1 change in fDM. Around log(M∗/M) ∼ 11, where we measure our the lowest fDM, we now observe the least change in Figure A1. Top panel: fractional change in total mass within 5 Re for differ- Mtot. While it is interesting to understand the nature and systematics ent velocity anisotropy assumptions. Bottom panel: corresponding change of GC velocity anisotropy, our analysis suggest that its effect on in DM fraction within 5 Re for different velocity anisotropy assumptions. the total mass estimates and DM fractions within large radii is minimal.

A2 Variation of rs/Re with stellar mass This plot is in reference to how stellar mass varies with the ratio of the scale radius of the DM halo and galaxy size from our SGM1. The minimum in rs/Re observed at log(M∗/M) ∼ 11 implies that at this stellar mass, galaxies with may already be structurally different.

A3 Halo assembly epoch as a function of galaxy properties, without binning by stellar mass Here, we show a version of Fig. 7, without binning our galaxies by stellar mass. We have also included galaxies with ambiguous morphological classiﬁcation. Note that the late halo assembly epoch for galaxies in the ﬁeld is not obvious without the correction we have applied to account for the strong dependence of zform on galaxy

Figure A2. Top panel: variation of rs/Re with stellar mass in our simple stellar mass. galaxy model (SGM1). The ratio of the scale radius of the DM halo to galaxy M / ∼ size reaches a minimum around log( ∗ M) 11. This paper has been typeset from a TEX/LATEX ﬁle prepared by the author.

MNRAS 468, 3949–3964 (2017)

5 Conclusion

reaching forward to what lies ahead —Pauline text adapted

The work presented in this thesis made use of globular cluster kinematics data obtained as part of the SLUGGS survey over the last decade, using the Keck telescope and the DEIMOS instrument. The main aim is to use globular clusters to constrain mass distribution out to large radii in early-type galaxies as well as provide invaluable clues about galaxy formation and evolution. I summarise the key results and provide possible future research directions below.

5.1 Principal ﬁndings and future directions

I have shown how complex kinematics features, like the double-sigma feature, only previously identified in stellar kinematics, are also present in a globular cluster system, i.e. NGC 4473. These kinematics signatures provide clues that aid our understanding of galaxy formation and evolution. While NGC 4473 is the only known double-sigma galaxy in the SLUGGS survey galaxy sample, more have been identified in the literature (Krajnović et al., 2011) and a systematic study of their globular cluster systems is therefore desirable. The case of NGC 4473 clearly shows a co-evolution of the galaxy’s stellar and globular cluster systems. In Chapter 2, I also identified a group of red globular clusters that are kinematically hot and spatially correlated providing more evidence that the galaxy likely formed during a gas-rich major merger event. Follow-up stellar population study of this substructure is highly desirable to further constrain the galaxy’s merger history and the progenitors from which it formed. Along the same line, the systematic exploration of globular cluster kinematics within the SLUGGS survey now needs to be extended to the entire

71 72 Chapter 5. Conclusion sample, since we have successfully completed our data collection. Only thirteen galaxies (twelve in Pota et al. 2013 and NGC 4473 in Alabi et al. 2015) have so far been studied out of a total of 27 galaxies. The total masses I have homogeneously measured at large radii in 32 early-type galaxies show unambiguously that there is a discrepancy between the luminous mass and that inferred from the motions of their globular clusters. These galaxies span two orders of magnitude in luminosity, reside in different environments and have different morphologies. One important question that remains yet unanswered is what is the nature of this mass discrepancy? Is it due to dark matter (this is the approach I explored in the preceding chapters), or is it due to some modifications to the laws of gravity when acceleration is less than 10−10 m s−2? It is already well known that ΛCDM is very difficult to falsify. Moreso, results from cosmological simulations based on the ΛCDM paradigm have begun to show that this mass discrepancy is a natural expectation, since they now observe the same (Ludlow et al., 2016; Navarro et al., 2016). Yet one cannot ignore the efficiency with which the MONDian approach predicts, reasonably well, mass estimates similar to that which I have measured (more expensively), given only the stellar mass. Figure 5.1 compares my mass discrepancies, expressed as log (Mtot/M∗), with the binned late-type galaxy data from 2 Lelli et al. (2017). I have estimated gbar as GM∗(< R)/R where G is the gravitational constant and 5Re ≤ R ≤ 20Re. From the comparison, it appears that mass estimates at large radii in early-type galaxies may not be enough to discriminate between these two models as claimed in the literature (see also Janz et al. 2016). Going forward, accurate measurement of the dynamical friction time-scales in our ETGs sample and comparison with expectations from MOND and ΛCDM could help shed some light on the nature of the mass discrepancy. It has already been shown from dwarf galaxy observations (e.g. Lotz et al., 2001; Sánchez-Salcedo et al., 2006) and simulations (e.g. Nipoti et al., 2008) that the dynamical friction time-scale within MOND framework 9 is too short in ∼10 M galaxies, and may be incompatible with the size of their globular cluster systems. This idea neatly ties in with the need for a systematic study of the orbital anisotropy profiles of globular cluster systems around early-type galaxies. In dynamical friction studies, and more importantly, in mass modelling of early-type galaxies, assumptions are often made about the nature of the globular cluster orbits which may or may not be consistent with the data. Some anecdotal studies have already reported the lack of globular clusters on radial orbits in some ETGs, especially near the galaxy centers, but the pic- 5.1. Principal findings and future directions 73

1.4 11.8 MOND : Lelli +2017 Alabi +2017 : 5R e 11.5 Alabi +2017 : R 1.0 max )

11.2 ) ¯ bar /M 0.6 / M 10.9 ∗ tot

10.6 log( M

log( M 0.2

10.3

-0.2 10.0 -12.0 -11.0 -10.0 -9.0 2 log(gbar/m s− )

Figure 5.1 Comparison of mass estimates and discrepancies with binned data for late-type galaxies from Lelli et al. (2017). The circles and squares are from the mass estimates at 5 Re and Rmax (the maximum radial position where globular cluster kinematics extends out to, on average, 13 Re for our galaxy sample) from Table 2 in Chapter 4. They have been color-coded according to the stellar mass of their respective galaxies. The dashed lines are the standard deviation of the binned data from Lelli et al. My dynamical mass measurements compares well with MONDian expectations for late-type galaxies. At any baryonic acceleration, gbar, low and high stellar mass early-type galaxies show more mass discrepancies. 74 Chapter 5. Conclusion ture is not clear if this extends to all early-type galaxies (e.g. Pota et al., 2013; Zhang et al., 2015; Zhu et al., 2016). The preferential destruction of globular clusters on radial orbits would be understandable if they were accreted on highly elongated orbits, which plunges them to the deepest part of the galaxy’s gravitational potential well, where they could be disrupted (e.g. Baumgardt & Makino, 2003). There is therefore an urgent need to properly understand the orbital behaviour of globular clusters. The precise velocity measurements we have made in the SLUGGS survey then becomes very helpful, as large uncertainties in velocity measurements could make determination of velocity anisotropies uncertain (Amorisco & Evans, 2012). Such an exercise, if extended to planetary nebulae, 11 which have been found around ≤ 10 M early-type galaxies in even more abundant numbers relative to globular clusters (e.g. Douglas et al., 2007), could also alleviate the poor number statistics problem we have experienced in our mass determination in Chapters 3 and 4 of this thesis. One could then properly combine planetary nebulae with globular clusters and determine more robustly the galaxy masses and dark matter content of these galaxies.

Assuming that the mass discrepancy is due to dark matter, there are also other chal- lenges that would need to be addressed. For example, what is the nature of the dark matter? Is it self-interacting, or is it a mixture of cold and self-interacting dark matter? In a universe where the non-baryons are mostly self-interacting, structure formation would happen later compared to a cold dark matter universe. Since the dark matter densities in 3 virialised structures follow a hρDMi ∝ (1 + zform) , galaxy haloes in such a universe would have significantly lower average dark matter densities and dark matter fractions. This is important since cosmological simulations based on self-interacting dark matter have now begun to produce constraint on dark matter fractions at large radii comparable to the low dark matter fractions, i.e. fDM ≤ 0.4, we measured in some of our galaxies (Di Cintio et al., 2017), but for a narrow stellar mass range. More simulations covering a wider stellar mass range and galaxies of different morphologies are therefore needed, as well as predictions that could be tested and used to discriminate between the different flavours of dark matter. For example, the observable effects of self-interacting dark matter and feedback outflows on galaxy mass distribution are very similar and it is not yet clear how one should differentiate between both processes. Similarly, ΛCDM cosmological simulations needs to be improved as well, since they still do not produce the wide span of dark matter fractions we have reported in this thesis. Such improvements may include how baryonic processes are represented in their simulations.

One other key result from Chapters 3 and 4 is the large spread of the dark matter 5.1. Principal ﬁndings and future directions 75

11 fractions, i.e. 0.2 ≤ fDM ≤ 0.9 within 5 Re, due mostly to the ∼10 M stellar mass galaxies. While we identified a lot of factors that could be responsible for this result, it 10.5 is not clear what exactly the main driver is. Amongst other things, more ≤ 10 M galaxies would need to be studied to effectively rule out that the scatter is not correlated to deviations of our galaxy sizes from the adopted galaxy size - stellar mass scaling relation. In addendum and for clarification, I note that the simple galaxy model (SGM2) in Figure 3 of Chapter 4 was obtained using the galaxy parameters reported in Table 1. SGM2 in Figure 2, however, is from a fit to those values, hence the continuous distribution that spans the entire stellar mass range.

The total mass estimates summarised in Table 2 of Chapter 4 can be written as Mtot = 2 2 Kσ R/G + VrotR/G with K = f(α, γ, β), where K has a complicated analytical form and R being either 5 Re or Rmax, respectively. The total mass can then be written as 2 Mtot ∼ Kσ Re/G, since the average contribution from rotation to the total mass within

5 Re for galaxies in the SLUGGS sample is ∼ 6 per cent. This gives the possibility of retrieving K, the virial factor. K, obtained this way, is 2.15, comparable to 2.08 reported in Dutton et al. (2011). A more precise determination of K is possible if better constraints on α, β and γ are available. For example, γ could be improved through a modern, systematic photometric study of early-type galaxies (Jennings et al. in prep.) It is well known that at the same stellar mass, dark matter haloes of elliptical galaxies assembled earlier than those of spiral galaxies (De Lucia & Blaizot, 2007; Thomas et al., 2009; Wojtak & Mamon, 2013; Corsini et al., 2017). However, it is not obvious how the assembly epoch of lenticular galaxies compare. The analyses done in Chapter 4 are initial steps in addressing this important issue with the important result that the average dark matter densities and assembly epochs of lenticular and elliptical galaxies are not statistically different. It therefore appears that ellipticals and lenticulars reside in dark matter haloes with similar structural properties and assembly epochs but they differ in their stellar assembly history. In Chapter 4, we identified that some of the haloes of ETGs assembled relatively recently. In Chapter 3, we actually identified GCs that could be kinematic substructures in some of our ETG sample. In Chapter 2, we had already showed that clues about ETG assembly could still be retrieved from the GC kinematics, even out to large radii. Putting all of this together, there is a good opportunity therefore to perform extragalactic archae- ology with our precisely measured SLUGGS GC kinematics data. This would provide more constraints on galaxy assembly models.

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In addition to my three lead-author papers published in this thesis as Chapters 2, 3 & 4, I also participated in the following publications during the course of my PhD project:

• Pastorello, Nicola; Forbes, Duncan A.; Usher, Christopher; Brodie, Jean P.; Ro- manowsky, Aaron J.; Strader, Jay; Spitler, Lee R.; Alabi, Adebusola B.; Foster, Caroline; Jennings, Zachary G.; Kartha, Sreeja S.; Pota, Vincenzo, The SLUGGS survey: combining stellar and globular cluster metallicities in the outer regions of early-type galaxies, 2015, MNRAS, 451, 2625

• Cortesi, Arianna; Chies-Santos, Ana L.; Pota, Vincenzo; Foster, Caroline; Coccato, Lodovico; Mendes de Oliveira, Claudia; Forbes, Duncan A.; Merriﬁeld, Michael M.; Bamford, Steven P.; Romanowsky, Aaron J.; Brodie, Jean P.; Kartha, Sreeja S.; Alabi, Adebusola B.; Proctor, Robert N.; Almeida, Andres, The SLUGGS survey: chromodynamical modelling of the lenticular galaxy NGC 1023, 2015, MNRAS, 456, 2611

• Kartha, Sreeja S.; Forbes, Duncan A.; Alabi, Adebusola B.; Brodie, Jean P.; Ro- manowsky, Aaron J.; Strader, Jay; Spitler, Lee R.; Jennings, Zachary G.; Roediger, Joel C., The SLUGGS survey*: exploring the globular cluster systems of the Leo II group and their global relationships, 2016, MNRAS, 458, 105

• Forbes, Duncan A.; Alabi, Adebusola; Romanowsky, Aaron J.; Brodie, Jean P.; Strader, Jay; Usher, Christopher; Pota, Vincenzo, The SLUGGS survey: globular clusters and the dark matter content of early- type galaxies, 2016, MNRAS, 458, 44L

• Pastorello, Nicola; Forbes, Duncan A.; Poci, Adriano; Romanowsky, Aaron J.; Mc- Dermid, Richard; Alabi, Adebusola B.; Brodie, Jean P.; Cappellari, Michele; Pota, Vincenzo; Foster, Caroline, The SLUGGS Survey: A New Mask Design to Re- construct the Stellar Populations and Kinematics of Both Inner and Outer Galaxy Regions, 2016, PASA, 33, 35

• Janz, Joachim; Cappellari, Michele; Romanowsky, Aaron J.; Ciotti, Luca; Alabi, Adebusola; Forbes, Duncan A., The mass discrepancy acceleration relation in early- type galaxies: extended mass proﬁles and the phantom menace to MOND, 2016, MNRAS, 461, 2367 Bibliography 83

• Forbes, Duncan A.; Alabi, Adebusola; Romanowsky, Aaron J.; Kim, Dong-Woo; Brodie, Jean P.; Fabbiano, Giuseppina, The SLUGGS survey: revisiting the correlation between Xray luminosity and total mass of massive earlytype galaxies, 2017, MNRAS, 464, L26

• Bellstedt, Sabine; Forbes, Duncan A.; Foster, Caroline; Romanowsky, Aaron J.; Brodie, Jean P.; Pastorello, Nicola; Alabi, Adebusola; Villaume, Alexa, The SLUGGS survey: Using extended stellar kinematics to disentangle the formation histories of low mass S0 galaxies, 2017, accepted for publication in MNRAS, arXiv:1702.05099

• Forbes, Duncan A.; Alabi, Adebusola; Brodie, Jean P.; Romanowsky, Aaron J.; Strader, Jay; Foster, Caroline; Usher, Christopher; Spitler, Lee; Bellstedt, Sabine; Pastorello, Nicola; Villaume, Alexa; Wasserman, Asher; Pota, Vincenzo, The SLUGGS Survey: A Catalog of Over 4000 Globular Cluster Radial Velocities in 27 Nearby Early-type Galaxies, 2017, AJ, 114, 153

• Christopher Usher, Nicola Pastorello, Sabine Bellstedt, Adebusola Alabi, Pier- luigi Cerulo, Leonie Chevalier, Amelia Fraser-McKelvie, Samantha Penny, Caroline Foster, Richard M. McDermid, Ricardo P. Schiavon, Alexa Villaume The WAGGS project - I. The WiFeS Atlas of Galactic Globular cluster Spectra, 2017, accepted for publication in MNRAS, arxiv:1703.07397