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Vol 437|29 September 2005|doi:10.1038/nature03970

LETTERS
Lost and found dark matter in elliptical galaxies
A. Dekel
1,2,3,4

, F. Stoehr2, G. A. Mamon2,3, T. J. Cox6, G. S. Novak5 & J. R. Primack

4

There is strong evidence that the mass of the Universe is dominated by dark matter, which exerts gravitational attraction but whose exact nature is unknown. In particular, all galaxies are believed to be embedded in massive haloes of dark matter1,2. This view has recently been challenged by the observation of surprisingly low random stellar velocities in the outskirts of ordinar y elliptical galaxies, which has been interpreted as indicating a lack of dark matter3,4. Here we show that the low velocities are in fact compatible with galaxy formation in dark-matter haloes. Using numerical simulations of disk-galaxy mergers5,6, we find that the stellar orbits in the outer regions of the resulting ellipticals are ver y elongated. These stars were torn by tidal forces from their original galaxies during the first close passage and put on outgoing trajectories. The elongated orbits, combined with the steeply falling density profile of the observed tracers, explain the observed low velocities even in the presence of large amounts of dark matter. Projection effects when viewing a triaxial elliptical can lead to even lower observed velocities along certain lines of sight. The common spiral galaxies are known to reside in extended darkmatter haloes. The rotational speeds of their gas disks do not decline outside the visible disk1, unlike the expectation from keplerian velocities at a radius r about a mass M, V 2 Ì GM/r (where G is Newton's constant). Thus, the dark-matter mass within r is growing roughly as M(r) / r and it dominates the gravitational potential beyond a certain radius. An extrapolation based on the typical halo density profile7 found in simulations of the standard LCDM cosmology predicts an outer `virial' radius R vir that is 50-100 times larger than the characteristic stellar radius, enclosing 10-20 times more dark matter than luminous matter. The conventional wisdom is that the potential wells created by the dark matter are crucial for seeding the formation of galaxies2,8,9. The standard hypothesis is that elliptical galaxies originate from mergers of disks10 and should therefore be embedded in similar darkmatter haloes. There is evidence for dark matter in giant ellipticals, from X-rays11 and gravitational lensing12. However, ordinary ellipticals lack obvious velocity tracers at the large projected radii r p where the dark matter is expected to be important. This is typically beyond R eff (ref. 13), the `effective' radius encompassing half the light, while measurements of the projected velocity dispersion j p of the stellar light are limited to r p , 2R eff. À The strong [O III ] emission line at 5,007 A from planetar y nebulae -- hot shells of gas expelled from dying stars of (1-3)M ( -- provides a unique tool for extracting j p(r p) beyond R eff. The j p of planetary nebulae in the normal ellipticals NGC 821, 3379 and 4494 (ref. 4) and in NGC 4697 (ref. 3) were found typically to drop by a factor .1.6 between r p Ì R eff and 3R eff. Kinematic modelling by the observers4 yielded low mass-to-light ratios, for example M =L . 7at 5R eff for NGC 3379, consistent with a "naked" stellar population. They interpreted this as "little if any dark matter in these galaxies' haloes". While noticing that increasing velocity anisotropies could in

principle produce declining j p, they ruled out such "pathological" or bit structure. Similar conclusions were obtained later from other ellipticals14. The apparent challenge to theory has already triggered radical explanations15. However, the earlier analysis4 might have missed alternative solutions because it was limited to specific density-profile shapes in stationary spherical systems, the halo planetar y nebulae were identified with the central stellar population, and their maximum-likelihood method may suffer from an incomplete orbit librar y or questionable convergence properties16. For given density profiles, a lower j p can result from more radial velocities. The dynamics implies a lower three-dimensional velocity dispersion j because the pressure needed for balancing gravity is provided by a radial j r that corresponds to a lower j. The projection introduces a further decrease in j p. This can be illustrated by toy models made purely of circular or radial orbits, with the same constant speed and random orientations. If the stellar-density profile is steep enough, j p is dominated by the tangential contribution near the equatorial plane perpendicular to the line of sight, which is high for circular orbits and low for radial orbits. The three-dimensional profiles of any component of a spherical gravitating system in equilibrium obey the Jeans equation17: V 2 ?r îÌÍa?r î? g?r î 2 2b?r îj2 ?r î r ?1î a manifestation of local hydrostatic balance between the inward pull of gravity (left) and the outward push of pressure (right). Here V 2 ?r îÌ GM ?r î=r is the squared circular velocity. The stellar density profile n(r) enters via a ; 2dln n=d ln r : Its velocity dispersion consists of radial and tangential components, j2 Ì j2 ? 2j2 ; we r v define g ; 2d ln j2 =d ln r : The velocit y anisotro py is b ; r 1 2 j2 =j2 ; with b Ì 21; 0; 1 for circular, isotropic and radial orbits r v respectively. The projection can be performed analytically when b, a and g are constant with r (power-law profiles, V 2 Ì V 2 ?r =Reff î2g î : 0 ?a ? gî 2 ?a ? g 2 1îb 2 r p 2g j2 ?r p îÌ A?a; gî ?2î V0 p Reff ?a ? gî 2 2b (see Methods for definition of A). We note that j p is a decreasing function of b and of a (for a ? g . 3 and b . 0). Local fits to the de-projection of the standard de Vaucouleurs18 surface-brightness profile of ellipticals give a . 3:13-3:37 at 2-3R eff (ref. 19). Our fits to j2 ?r p î in the observed ellipticals beyond R eff yield g . 0:8 ^ 0:2: p These give A?a; gî . 0:2 and j p drops by a factor of ,1.5 between b Ì 0 and 1. We learn that one could match the low j p at large radii either by a low V 0 or by a high b there, and that a high a helps. Ä In a more realistic model, we assume a Sersic stellar density Ä profile19 (equivalent to that of de Vaucouleurs for Sersic index m Ì 4), a standard dark-matter density profile7 with a typical concentration (,10) (ref. 20), and a virial stellar mass fraction of ,0.06. With b Ì 0 we recover the discrepancy, but m . 4 and b?r . Reff î . 0:5 (independent of its behaviour well inside R eff ) yield a

1 Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel. 2Institut d'Astrophysique, 98bis Boulevard Arago, Paris 75014, France. 3Observatoire de Paris, F-92195 Meudon, France. 4Department of Physics, 5UCO/Lick Observatories, University of California, Santa Cruz, California 95064, USA. 6Center for Astrophysics, Harvard University, 60 Garden Street, Cambridge, Massachusetts 02138, USA.

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,1j agreement with the observed j p. A good fit is obtained with either m . 4 and b . 0:75, or with m . 2:3 (for which a . 3:5 near 2.5R eff ) and b . 0:5: The required b is higher than the b # 0:2 predicted for dark matter in typical haloes13, so the planetary nebulae must not trace the dark-matter kinematics. Assuming that ellipticals form by mergers, and that major mergers of disks can reveal generic features of mergers in the LCDM cosmology, we appeal to a suite of simulations of such events5,6. Two spirals are put on a parabolic orbit, each consisting of stellar and gaseous disks and a bulge, all embedded in a LCDM halo, constructed to match a range of typical disk galaxies. The gravitational and hydrodynamical evolution is followed using an SPH code21, including gas cooling, star formation and supernova feedback (Methods). Figure 1 shows the stacked three-dimensional profiles of the merger remnants. The dark-matter density profile is slightly flatter than isothermal, r / r 22, similar to simulated LCDM haloes after they have responded to gas dissipation22. The robust stellar density falls off more steeply, r / r 23.2, as in ellipticals obeying the de Vaucouleurs profile near 2-3R eff, and with Reff . 0:015Rvir : For the "young" stars it is somewhat steeper: r / r 23.5. The total-to-stellar mass ratio rises from .2 at 3R eff to .14 at R vir, corresponding at 5R eff to M =L . 15 (compared to the earlier4 M =L . 7î: The threedimensional j profiles of the dark matter and stars have similar slopes (as in equation (2)), roughly j / r 20.2. Our main finding is the high b of the stellar halo velocities. While the dark-matter velocities are almost isotropic (b < 0.1), the typical stellar b grows from small values at r , R eff (sometimes negative, reflecting a small disk that is irrelevant beyond R eff ) to b < 0.5 at r . R eff. In one case b . 0.75, but in another it remains ,0.2. Given V(r) in the Jeans equation, the higher a is compensated by a higher b and a lower j.

The simulations demonstrate that the stellar halo originates from tidal processes during the first pericentre passage. Some of the halo stars are associated with the two cores and the tidal bridge between them; they pass near the centre at the coalesence before flying outward on radial orbits. Other halo stars first flow out in extended tidal tails and later fall back on radial orbits (Supplementar y Information). Indeed, we find that b is correlated with the strength of the tidal interaction; it is higher for more head-on collisions and when the spins are aligned with the orbit. The systems are `observed' from three orthogonal directions and stacked together, providing a robust average profile and the scatter about it. The data are scaled similarly (see Methods). Figure 2 shows the simulated surface-density profile and those of NGC 821 (ref. 23), NGC 3379 (ref. 24) and NGC 4697 (ref. 25), all fitted by S / r 22:3 in p 1-5R eff (as in the de Vaucouleurs profile at ,2R eff ). The simulated projected axial ratios near R eff range from 1:1 to 1:2, and the ellipticity is supported by an anisotropic, triaxial velocity dispersion rather than by rotation, similar to ellipticals (Supplementary Information). The distribution of global properties of the remnants, such as luminosity, radius and velocity dispersion, is consistent with the `fundamental plane' of ellipticals (Supplementar y Information). Thus, the merger remnants seem to resemble typical ellipticals near ,R eff in every relevant respect. The velocity dispersions in Fig. 2 illustrate our main point. While the dark-matter j p indeed lies above the outer observed points, the stellar j p, ,30% lower, provides a good fit everywhere in the range

Figure 1 | Three-dimensional profiles of the simulated merger remnants. Ten galaxies at two different times after the merger (typically 0.8 and 1.3 Gyr) are stacked. Shown are the profiles for the dark matter (blue) and the stars (red), divided into the "old" stars from the progenitors (dotted) and the "young" stars formed during the merger (dashed). The scaling is such that the curves for the stars ("all", solid red) are matched at R eff. The shaded areas mark 1j scatter. The panels refer to density r, mass M and circular velocity V, velocity dispersion j and anisotropy b, with subscript `eff ' referring to R eff.
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Figure 2 | Projected profiles: simulated galaxies versus observations. a, Surface density. b, Velocity dispersion. The merger remnants are viewed from three orthogonal directions and the 60 profiles are stacked such that the curves for "all" the stars match at R eff. Colours and line types are as in Fig. 1. The ,3-Gyr "young" stars may mimic the observed planetary nebulae. The 1j scatter is marked by a hashed area ("all"), a shaded area ("young") or a thick bar (dark matter). The galaxies are marked green (NGC 821), violet (NGC 3379), brown (NGC 4494) and blue (NGC 4697) with 1j errors; planetary nebulae (circles) and stars (crosses). The surface densities shown for three galaxies almost coincide with the simulated profile. Green lines refer to earlier models4 with (upper) and without (lower) dark matter.

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0.5-4R eff. The slope of the simulated j2 ?r p î in the range 0.5-6R eff is p g Ì 0.53 ^ 0.16 for "all" and g Ì 0.61 ^ 0.22 for the "young" stars, both consistent with the g Ì 0.59 ^ 0.13 observed for planetary nebulae. No adjustment of model parameters is involved -- simply stacking a sample of merger remnants. The j p of "young" stars is lower by ,9% at 3R eff (owing to their larger a). Stellar theory indicates that these objects, ,3 Gyr old, may represent the observed planetary nebulae. Emerging from 1.4-2.5M ( stars26, the nebulae are expected to be much more luminous than those of the older, less massive stars, which fall below the detection limits3,4 (Methods). However, the radial orbits are a generic result independent of the degree of gas dissipation during the merger: our mergers with initial gas-to-baryon ratio ranging from 0 to 70% show negligible differences in b beyond R eff. Dissipation results in a more centrally concentrated stellar distribution, associated with & 10% reduction in outer j p (Supplementary Information). We also find that the radial orbits and low j p emerge from major and minor mergers alike, independent of the progenitor mass ratio (Supplementary Information), and that the presence of a ,22% bulge does not make a significant difference. The tidal origin of the stellar halo explains this robustness to many merger characteristics. Furthermore, one simulation continued till 3.5 Gyr after the merger with no sign of evolution in b(r) and j p(r) beyond ,R eff (Supplementar y Information). The ^20% scatter in j p is partly due to the angular momentum of the merger orbit and the relative spin inclinations, but also due to the line of sight relative to the principal axes of the triaxial system (or rotation axis, A. Burkert, R. Kudritzki and R. Mendez, manuscript in preparation). When viewed `face-on', some of the remnants show j p values lower than observed, whereas other extreme `edge-on' cases show j p values almost as high as the dark matter (Supplementar y Information). The simulated line-of-sight velocity distribution is also consistent with the data beyond the second moment. The deviations from gaussian are small, with the fourth moment h 4 Ì 0.03 ^ 0.05 for the central stars (Supplementary Information). At r * Reff ; radial, prograde mergers produce negligible h 4 values, as in the planetary nebulae of NGC 3379 (ref. 4) (or small positive values as in NGC 5128; ref. 27), whereas more circular and retrograde mergers, or gasrich mergers, can produce negative h 4 as in NGC 4697 (ref. 3; Supplementary Information). We conclude that the planetary-nebulae data are consistent with the simple picture where normal ellipticals also reside in massive dark-matter haloes. The low j p is primarily due to the radial orbits of the halo stars, being tidally ejected from the inner regions during mergers independently of dissipation and mass ratio. This generic origin of the radial orbits indicates that the results based on our sample of simulations are representative of a broader range of merger types expected in the LCDM cosmology, and argues that the low observed planetar y-nebula velocities are a natural outcome of this standard model. This should be confirmed by cosmological simulations (such as low-resolution results28,29. The range of merger properties leads to a variety of b and j p profiles, and the triaxiality adds directional variations, allowing extreme j p values smaller and larger than the planetar y-nebula data. The possible association of the planetary nebulae with the younger stars, whose density profile is slightly steeper, may help reducing their j p a bit further. Other tracers, involving old stars, are expected to show a somewhat higher j p. This is especially true for globular clusters14 (G. Bergond, S. E. Zepf, A. J. Romanowsky, R. M. Sharples & K. L. Rhode, manuscript in preparation), given their flatter density profile30 and presumably lower anisotropy (due to tidal disruption in radial orbits). A somewhat higher j p may also be expected in elliptical-elliptical mergers, common especially in groups (as observed14), where the collision orbits may be circularized by two-body relaxation and dynamical friction. We recall4 that a nearly isotropic "naked" stellar system also

provides a fit to the j p(r p) data inside a few R eff, appealing to a low V 0 rather that a high b in equation (2). Our simulations provide another solution, which does include a standard dark-matter halo. The dark-matter model predicts that j p flattens toward ,10R eff (as in NGC 5128; ref. 27), where the "naked" model predicts a continuing decline beyond 3R eff and very low j p for other tracers as well. Whereas the "naked" model violates much of what we know about galaxy formation and cosmology, the dark-matter model, with the radial stellar orbits, seems to be a straightforward outcome of the selfconsistent picture of structure formation in the Universe.
METHODS
Equation 2 derivation. The coefficient in equation (2) is a weak function of a and g: A?a; gîÌ 1 GÍ?a ? g 2 1î=2 GÍ?a=2î ?a ? gî GÍ?a ? gî=2 GÍ?a 2 1î=2 ?3î

For instance, A?3:5; 1:0î . 0:18; while A?3:0; 0:4î . 0:26: Merger simulations. The simulations5,6 represent some of the major collisions that probably occurred during the hierarchical structure formation according to the LCDM cosmology. The evolution is followed using the entropy-conserving, gravitating, smoothed particle hydrodynamics (SPH) code GADGET21. Gas cooling, star formation and supernova feedback are treated using recipes that were calibrated to match observed star-formation rates. The progenitor disk galaxies mimic typical big spirals: one type (G) representing today's Sb galaxies and another type containing more gas as in Sbc-Sc galaxies and at high redshift. The sample consists of four G mergers, with darkmatter masses 1.2 ? 1012M ( (except one 5 ? 1011M (), and five Sbc merger plus one Sc merger with 8 ? 1011M ( haloes. The baryonic fraction is ,5% of the dark-matter halo mass in the G cases, and ,13% in the Sbc-Sc cases. The fraction of baryons in gas is ,20% in G, 52% in Sbc, and 70% in Sc. The particle mass is ,106M ( for gas and stars and & 107M ( for dark-matter. The smoothing length h is 100 and 400 pc respectively, with the force becoming newtonian at $2.3 h. Two identical galaxies are set on parabolic orbits and merge because of dynamical friction due to their massive haloes. Our sample consists of several different orbits and orientations, including prograde and retrograde configurations in which the galaxy spins are aligned or antialigned with the orbital angular momentum. The merger results in two succesive starbursts, one after the first close approach, and the other after the second, final coalescence (Supplementary Information). The starbursts occur 1-2 Gyr after the beginning of the simulation, and the remnant is `observed' ,1 Gyr later, The amount of stars formed during the merger is roughly proportional to the initial gas fraction, and is not very sensitive to the orbit or orientation. The instantaneous rate is 10-100 M ( yr21. The young stars formed during the merger constitute ,30% of the total stars; typically 20% in the G galaxies and 40% in Sbc galaxies. The remnant galaxies resemble normal elliptical galaxies, as demonstrated above (Supplementary Information). Scaling the data. The observed galaxies are presented together using the R eff of each surface-brightness profile4,24,25. We note that R eff for NGC 3379 (ref. 24, 25) is .50% larger than that quoted4. In Fig. 2, an open circle marks the last point had we used the smaller4 R eff, not making a qualitative difference. The amplitudes of S and j p are scaled by least-squares fits of the stellar data at r . 0.2R eff to the stacked simulated profile as a reference. Replacing this reference by a different function of a similar general shape yields similar results. Using only the stars at larger radii (up to r . R eff ), or using the planetary nebulae alone, yield j p adjusting factors that differ only by a few per cent. The R eff of NGCs 821, 3379, 4494 and 4697 match the mean simulation value after multiplication by 0.667, 1.57, 1.00 and 1.13, indicating that the simulated and observed galaxies are of comparable sizes. The j p were adjusted by factors 1.00, 1.19, 1.21 and 1.11 for best fit. Being comparable to the radius scaling factors indicates that the observed and simulated galaxies have a similar velocity structure. The mean and 1j sc atter in the simulated remnants are R eff Ì 4.05 ^ 1.04 kpc and j p (R eff ) Ì 154 ^ 33 km s21. Age of planetary nebulae. The [O III ] luminosity of a planetary nebula with mass ,2.5M ( is strongly increasing with the parent stellar mass (figures 10 and 14 in ref. 26), hence sharply decreasing with age. A limiting magnitude M 5007 then corresponds to a maximum stellar age t. For the complete sample of 328 planetar y nebulae in NGC 46973 it is M 5007 . 22:6; namely t M01 , 3Gyr (figures 18, 19, 26 in ref. 26). With only .100 planetary nebulae per galaxy4, the magnitude limit is brighter (by 20.8 magnitudes based on telescope gathering areas), so the stars are even younger. Based on theoretical planetary
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nebulae luminosity functions (figures 18, 26 in ref. 26), if the population is typically older than 1 Gyr, then t R03 , 2 Gyr. We therefore adopt t , 3 Gyr as a limit for most of the observed planetary nebulae in the four galaxies. This indicates an association with the "young" simulated stars, and that the mergers of gaseous disks are relevant to those ellipticals showing planetary nebulae. A caveat is the apparent relative invariance of the planetary-nebula luminosity function between galaxies, seemingly independent of signs for a recent major merger. When there are no such signs, the observed planetary nebulae may be the signature of recent minor mergers, which are expected to produce similar effects.
Received 27 January; accepted 22 June 2005.
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Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Acknowledgements We acknowledge discussions with M. Beasley, A. Burkert, K. Gebhardt, J. Navarro, A. Romanowsky and his group, and assistance from M. Covington. This research has been supported by the Israel Science Foundation and by NASA and NSF at UCSC. The simulations were run at NERSC. A.D. acknowledges a Miller Professorship at UC Berkeley, support from UCO/Lick Observatory, and a Blaise Pascal International Chair in Paris. Author Information Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests. Correspondence and requests for materials should be addressed to A.D. (dekel@phys.huji.ac.il).

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