Hot Stellar Systems Research Articles

The SAMI–Fornax Dwarfs Survey – II. The Stellar Mass Fundamental Plane and the dark matter fraction of dwarf galaxies

ABSTRACT We explore the kinematic scaling relations of 38 dwarf galaxies in the Fornax Cluster using observations from the SAMI integral field spectrograph. We focus on the Fundamental Plane (FP), defined by the physical properties of the objects (scale length, surface brightness, and velocity dispersion) and the Stellar Mass (Fundamental) Plane, where surface brightness is replaced by stellar mass, and investigate their dynamical-to-stellar-mass ratio. We confirm earlier results that the Fornax dEs are significantly offset above the FP defined by massive, hot stellar systems. For the Stellar Mass (Fundamental) Plane, which shows much lower scatter, we find that young and old dwarf galaxies lie at about the same distance from the plane, all with comparable scatter. We introduce the perpendicular deviation of dwarf galaxies from the Stellar Mass Plane defined by giant early-types as a robust estimate of their DM fraction, and find that the faintest dwarfs are systematically offset above the plane, implying that they have a higher dark matter fraction. This result is confirmed when estimating the dynamical mass of our dEs using a virial mass estimator, tracing the onset of dark matter domination in low mass stellar systems. We find that the position of our galaxies on the Stellar Mass FP agrees with the galaxies in the Local Group. This seems to imply that the processes determining the position of dwarf galaxies on the FP depend on the environment in the same way, whether the galaxy is situated in the Local Group or in the Fornax Cluster.

Multi-layered characterisation of hot stellar systems with confidence

Abstract Understanding the physical and evolutionary properties of Hot Stellar Systems (HSS) is a major challenge in astronomy. We studied the dataset on 13 456 HSS of Misgeld & Hilker (2011, MNRAS, 414, 3 699) that includes 12 763 candidate globular clusters using stellar mass ( $M_s$ ), effective radius ( $R_e$ ) and mass-to-luminosity ratio ( $M_s/L_\nu$ ), and found multi-layered homogeneous grouping among these stellar systems. Our methods elicited eight homogeneous ellipsoidal groups at the finest sub-group level. Some of these groups have high overlap and were merged through a multi-phased syncytial algorithm motivated from Almodóvar-Rivera & Maitra (2020, JMLR, 21, 1). Five groups were merged in the first phase, resulting in three complex-structured groups. Our algorithm determined further complex structure and permitted another merging phase, revealing two complex-structured groups at the highest level. A nonparametric bootstrap procedure was also used to estimate the confidence of each of our group assignments. These assignments generally had high confidence in classification, indicating great degree of certainty of the HSS assignments into our complex-structured groups. The physical and kinematic properties of the two groups were assessed in terms of $M_s$ , $R_e$ , surface density and $M_s/L_\nu$ . The first group consisted of older, smaller and less bright HSS while the second group consisted of brighter and younger HSS. Our analysis provides novel insight into the physical and evolutionary properties of HSS and also helps understand physical and evolutionary properties of candidate globular clusters. Further, the candidate globular clusters (GCs) are seen to have very high chance of really being GCs rather than dwarfs or dwarf ellipticals that are also indicated to be quite distinct from each other.

THE ACS FORNAX CLUSTER SURVEY. XII. DIFFUSE STAR CLUSTERS IN EARLY-TYPE GALAXIES

ABSTRACT Diffuse star clusters (DSCs) are old and dynamically hot stellar systems that have lower surface brightness and more extended morphology than globular clusters (GCs). Using the images from Hubble Space Telescope (HST)/ACS Fornax Cluster Survey, we find that 12 out of 43 early-type galaxies (ETGs) in the Fornax Cluster host significant numbers of DSCs. Together with literature data from the HST/ACS Virgo Cluster Survey, where 18 out of 100 ETGs were found to host DSCs, we systematically study the relationship of DSCs with GCs and their host galaxy environment. Two DSC hosts are post-merger galaxies, with most of the other hosts either having low mass or showing clear disk components. We find that while the number ratio of DSCs to GCs is nearly constant in massive galaxies, the DSC-to-GC ratio becomes systematically higher in lower-mass hosts. This suggests that DSCs may be more efficient at forming (or surviving) in low-density environments. DSC hosts are not special either in their position in the cluster or in the galactic color–magnitude diagram. Why some disk and low-mass galaxies host DSCs while others do not is still a puzzle, however. The mean ages of DSC hosts and nonhosts are similar at similar masses, implying that formation efficiency rather than survival is the reason behind different DSC number fractions in ETGs.

Cosmological simulations of dwarf galaxies with cosmic ray feedback

We perform zoom-in cosmological simulations of a suite of dwarf galaxies, examining the impact of cosmic rays (CRs) generated by supernovae, including the effect of diffusion. We first look at the effect of varying the uncertain CR parameters by repeatedly simulating a single galaxy. Then we fix the comic ray model and simulate five dwarf systems with virial masses range from 8 to 30 × 1010 M⊙. We find that including CR feedback (with diffusion) consistently leads to disc-dominated systems with relatively flat rotation curves and constant star formation rates. In contrast, our purely thermal feedback case results in a hot stellar system and bursty star formation. The CR simulations very well match the observed baryonic Tully–Fisher relation, but have a lower gas fraction than in real systems. We also find that the dark matter cores of the CR feedback galaxies are cuspy, while the purely thermal feedback case results in a substantial core.

The AIMSS Project – I. Bridging the star cluster–galaxy divide★†‡§¶

We describe the structural and kinematic properties of the first compact stellar systems discovered by the Archive of Intermediate Mass Stellar Systems project. These spectroscopically confirmed objects have sizes (∼6 < Re [pc] < 500) and masses (∼2 × 106 < M*/M⊙ < 6 × 109) spanning the range of massive globular clusters, ultracompact dwarfs (UCDs) and compact elliptical galaxies (cEs), completely filling the gap between star clusters and galaxies. Several objects are close analogues to the prototypical cE, M32. These objects, which are more massive than previously discovered UCDs of the same size, further call into question the existence of a tight mass–size trend for compact stellar systems, while simultaneously strengthening the case for a universal ‘zone of avoidance’ for dynamically hot stellar systems in the mass–size plane. Overall, we argue that there are two classes of compact stellar systems (1) massive star clusters and (2) a population closely related to galaxies. Our data provide indications for a further division of the galaxy-type UCD/cE population into two groups, one population that we associate with objects formed by the stripping of nucleated dwarf galaxies, and a second population that formed through the stripping of bulged galaxies or are lower mass analogues of classical ellipticals. We find compact stellar systems around galaxies in low- to high-density environments, demonstrating that the physical processes responsible for forming them do not only operate in the densest clusters.

P-277 Decitabine vs. best supportive care in elderly higher-risk MDS patients with or without monosomal karyotypes: EORTC-LG/GMDS-SG phase III trial 06011

A multivariate classification has been performed for a large sample of dynamically hot stellar systems comprising globular clusters to giant ellipticals, in quest of the formation theory of ultra compact dwarf galaxies (UCDs). For this K means cluster analysis is carried out together with the optimum criterion (Sugar et al., 2003) with respect to three parameters, logarithm of stellar mass, logarithm of effective radius and stellar mass to light ratio. The present data set has been taken from Misgeld and Hilker (2011). We found five groups MK1–MK5. These are predominated by giant ellipticals (gEs), faint dwarf ellipticals (dEs), globular clusters (GCs), massive compact objects (UCDs and nuclei of dE,Ns) and bright dwarf ellipticals respectively. Almost all UCDs are found either in MK3 or MK4. The fraction is roughly 50%–50% between MK3 and MK4. Comparable fraction of UCDs share properties either with normal GCs or with nuclei of dE,N. This adds a quantitative constraint to the long discussed hypothesis that UCDs may be formed either as massive globular clusters or have an origin similar to nuclei of dwarf galaxies. We finally find that for our clustering test in mass-size-stellar M/L ratios, ultra faint dwarf galaxies are attributed to globular cluster group (MK3) and not to the dwarf galaxy group (MK2). This highlights that there is no clear cut morphological distinction between extended star clusters and ultra faint dwarfs. These groups are highly consistent with the groups found in a previous classification for a smaller sample and completely different set of parameters.

Multivariate study of dynamically hot stellar systems: Clues to the origin of ultra compact and ultra faint dwarfs

A multivariate classification has been performed for a large sample of dynamically hot stellar systems comprising globular clusters to giant ellipticals, in quest of the formation theory of ultra compact dwarf galaxies (UCDs). For this K means cluster analysis is carried out together with the optimum criterion (Sugar et al., 2003) with respect to three parameters, logarithm of stellar mass, logarithm of effective radius and stellar mass to light ratio. The present data set has been taken from Misgeld and Hilker (2011). We found five groups MK1–MK5. These are predominated by giant ellipticals (gEs), faint dwarf ellipticals (dEs), globular clusters (GCs), massive compact objects (UCDs and nuclei of dE,Ns) and bright dwarf ellipticals respectively. Almost all UCDs are found either in MK3 or MK4. The fraction is roughly 50%–50% between MK3 and MK4. Comparable fraction of UCDs share properties either with normal GCs or with nuclei of dE,N. This adds a quantitative constraint to the long discussed hypothesis that UCDs may be formed either as massive globular clusters or have an origin similar to nuclei of dwarf galaxies. We finally find that for our clustering test in mass-size-stellar M/L ratios, ultra faint dwarf galaxies are attributed to globular cluster group (MK3) and not to the dwarf galaxy group (MK2). This highlights that there is no clear cut morphological distinction between extended star clusters and ultra faint dwarfs. These groups are highly consistent with the groups found in a previous classification for a smaller sample and completely different set of parameters.

Formation and evolution of dwarf early-type galaxies in the Virgo cluster

We place our sample of 18 Virgo dwarf early-type galaxies (dEs) on the V-K - velocity dispersion, Faber-Jackson, and Fundamental Plane (FP) scaling relations for massive early-type galaxies (Es). We use a generalized velocity dispersion, which includes rotation, to be able to compare the location of both rotationally and pressure supported dEs with those of early and late-type galaxies. We find that dEs seem to bend the Faber-Jackson relation of Es to lower velocity dispersions, being the link between Es and dwarf spheroidal galaxies (dSphs). Regarding the FP relation, we find that dEs are significantly offset with respect to massive hot stellar systems, and re-casting the FP into the so-called kappa-space suggests that this offset is related to dEs having a total mass-to-light ratio higher than Es but still significantly lower than dSph galaxies. Given a stellar mass-to-light ratio based on the measured line indices of dEs, the FP offset allows us to infer that the dark matter fraction within the half light radii of dEs is on average >~ 42% (uncertainties of 17% in the K band and 20% in the V band), fully consistent with an independent estimate in an earlier paper in this series. We also find that dEs in the size-luminosity relation in the near-infrared, like in the optical, are offset from early-type galaxies, but seem to be consistent with late-type galaxies. We thus conclude that the scaling relations show that dEs are different from Es, and that they further strengthen our previous findings that dEs are closer to and likely formed from late-type galaxies.

Analytical expressions for the deprojected Sérsic model

The Sérsic model is the de facto standard to describe the surface brightness distribution of hot stellar systems. An important inconvenience of this analytical model is that the corresponding luminosity density and associated properties cannot be expressed using elementary functions or even standard special functions. We present a set of compact and elegant analytical expressions for the luminosity density, cumulative luminosity, and potential for the Sérsic model in terms of the Fox H function for general values of the Sérsic index. Furthermore, we present explicit series expansions of these quantities and discuss the asymptotic behaviour. Our analysis completes earlier work and demonstrates the power of the underestimated Fox H function as a tool for analytical work.

Families of dynamically hot stellar systems over 10 orders of magnitude in mass

Dynamically hot stellar systems, whether star clusters or early-type galaxies, follow well-defined scaling relations over many orders of magnitudes in mass. These Fundamental Plane relations have been subject of several studies, which have been mostly confined to certain types of galaxies and/or star clusters so far. Here, we present a complete picture of hot stellar systems ranging from faint galaxies and star clusters of only a few hundred solar masses up to giant ellipticals (gEs) with 1012 M⊙, in particular including – for the first time – large samples of compact ellipticals (cEs), ultracompact dwarf galaxies (UCDs), dwarf ellipticals (dEs) of nearby galaxy clusters and Local Group ultrafaint dwarf spheroidals (dSphs). For all those stellar systems we show the effective radius luminosity, effective radius stellar mass and effective mass surface density stellar mass plane. Two clear families of hot stellar systems can be differentiated: the ‘galaxian’ family, ranging from gEs over ellipticals (Es) and dEs to dSphs, and the ‘star cluster’ family, comprising globular clusters (GCs), UCDs and nuclear star clusters (NCs). Interestingly, massive Es have a similar size–mass relation as cEs, UCDs and NCs, with a clear common boundary towards minimum sizes, which can be approximated by Reff≥ 2.24 × 10−6M4/5★ pc. No object of either family is located in the ‘zone of avoidance’ beyond this limit. Even the majority of early-type galaxies at high redshift obeys this relation. The sizes of dEs and dSphs (Reff∼ 1.0 kpc) as well as GCs (Reff∼ 3 pc) barely vary with mass over several orders of magnitude. We use the constant galaxy sizes to derive the distances of several local galaxy clusters. The size gap between star clusters and dwarf galaxies gets filled in by low mass, resolving star clusters and the faintest dSphs at the low mass end, and by GCs/UCDs, NCs and cEs in the mass range 106 < M★ < 109 M⊙. In the surface density–mass plane the sequences of star clusters and galaxies show the same slope, but are displaced with respect to each other by 103 in mass and 102 in surface density. Objects that fall in between both sequences include cEs, UCDs, NCs and ultrafaint dSphs. Both, galaxies and star clusters, do not exceed a surface density of Σeff= 3.17 × 1010M−3/5★ M⊙ pc−2, causing an orthogonal kink in the galaxy sequence for Es more massive than 1011 M⊙. The densest stellar systems (within their effective radius) are NCs.

Faint Dwarf Galaxies in Nearby Clusters

Besides giant elliptical galaxies, a number of low-mass stellar systems inhabit the cores of galaxy clusters, such as dwarf elliptical galaxies (dEs/dSphs), ultra-compact dwarf galaxies (UCDs), and globular clusters. The detailed morphological examination of faint dwarf galaxies has, until recently, been limited to the Local Group (LG) and the two very nearby galaxy clusters Virgo and Fornax. Here, we compare the structural parameters of a large number of dEs/dSphs in the more distant clusters Hydra I and Centaurus to other dynamically hot stellar systems.

On the mass—radius relation of hot stellar systems

Abstract Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber–Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultracompact dwarf galaxies, have a mass–radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass–radius relation at ∼106 M⊙ is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this ‘balanced’ evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass–radius relation of globular clusters, and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass–radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.

From star clusters to dwarf galaxies: the properties of dynamically hot stellar systems

Objects with radii of 10pc to 100pc and masses in the range from 10 6 M⊙ to 10 8 M⊙ have been discovered during the past decade. These so-called ultra compact dwarf galaxies (UCDs) constitute a transition between classical star clusters and elliptical galaxies in terms of radii, relaxation times and V -band mass-to-light ratios. Using new data, the increase of typical radii with mass for compact objects more massive than 10 6 M⊙ can be confirmed. There is a continuous transition to the typical, massindependent radii of globular clusters (GCs). It can be concluded from the different relations between mass and radius of GCs and UCDs that at least their evolution must have proceeded differently, while the continuous transition could indicate a common formation scenario. The strong increase of the characteristic radii also implies a strong increase of the median two-body relaxation time, trel, which becomes longer than a Hubble time, τH, in the mass interval between 10 6 M⊙ and 10 7 M⊙. This is also the mass interval where the highest stellar densities are reached. The mass-to-light ratios of UCDs are clearly higher than the ones of GCs, and the departure from mass-tolight ratios typical for GCs happens again at a mass of � 10 6 M⊙. Dwarf spheroidal galaxies turn out to be total outliers compared to all other dynamically hot stellar systems regarding their dynamical mass-to-light ratios. Stellar population models were consulted in order to compare the mass-to-light ratios of the UCDs with theoretical predictions for dynamically unevolved simple stellar populations (SSPs), which are probably a good approximation to the actual stellar populations in the UCDs. The SSP models also allow to account for the effects of metallicity on the mass-to-light ratio. It is found that the UCDs, if taken as a sample, have a tendency to higher mass-to-light ratios than it would be expected from the SSP models assuming that the initial stellar mass function in the UCDs is the same as in resolved stellar populations. This can be interpreted in several ways: As a failure of state-of-the-art stellar evolution and stellar population modelling, as a presence of dark matter in UCDs or as stellar populations which formed with initial stellar mass functions different to the canonical one for resolved populations. But it is noteworthy that evidence for dark matter emerges only in systems with trel ? τH.

Realistic triaxial density-potential-force profiles for stellar systems and dark matter haloes

Popular models for describing the luminosity-density profiles of dynamically hot stellar systems (e.g. Jaffe, Hernquist, Dehnen) were constructed to match the deprojected form of de Vaucouleurs' R 1/4 light-profile. However, we now know that elliptical galaxies and bulges display a mass-dependent range of structural profiles. To compensate this, the model in Terzic & Graham was designed to closely match the deprojected form of Sersic R 1/n light-profiles, including deprojected exponential light-profiles and galaxies with partially depleted cores. It is thus applicable for describing bulges in spiral galaxies, dwarf elliptical galaxies, both 'power-law' and 'core' elliptical galaxies, also dark matter haloes formed from A cold dark matter cosmological simulations. In this paper, we present a new family of triaxial density-potential-force triplets, which generalizes the spherical model reported in Terzic & Graham to three dimensions. If the (optional) power-law core is present, it is a five-parameter family, while in the absence of the core it reduces to three parameters. The isodensity contours in the new family are stratified on confocal ellipsoids and the potential and forces are expressed in terms of integrals which are easy to evaluate numerically. We provide the community with a suite of numerical routines for orbit integration, which feature: optimized computations of potential and forces for this family; the ability to run simulations on parallel platforms; and modular and easily editable design.

Formation of Early‐Type Galaxies from Cosmological Initial Conditions

We describe high resolution Smoothed Particle Hydrodynamics (SPH) simulations of three approximately $M_*$ field galaxies starting from \LCDM initial conditions. The simulations are made intentionally simple, and include photoionization, cooling of the intergalactic medium, and star formation but not feedback from AGN or supernovae. All of the galaxies undergo an initial burst of star formation at $z \approx 5$, accompanied by the formation of a bubble of heated gas. Two out of three galaxies show early-type properties at present whereas only one of them experienced a major merger. Heating from shocks and -PdV work dominates over cooling so that for most of the gas the temperature is an increasing function of time. By $z \approx 1$ a significant fraction of the final stellar mass is in place and the spectral energy distribution resembles those of observed massive red galaxies. The galaxies have grown from $z=1 \to 0$ on average by 25% in mass and in size by gas poor (dry) stellar mergers. By the present day, the simulated galaxies are old ($\approx 10 {\rm Gyrs}$), kinematically hot stellar systems surrounded by hot gaseous haloes. Stars dominate the mass of the galaxies up to $\approx 4$ effective radii ($\approx 10$ kpc). Kinematic and most photometric properties are in good agreement with those of observed elliptical galaxies. The galaxy with a major merger develops a counter-rotating core. Our simulations show that realistic intermediate mass giant elliptical galaxies with plausible formation histories can be formed from \LCDM initial conditions even without requiring recent major mergers or feedback from supernovae or AGN.

A Survey of Galaxy Kinematics toz∼1 in the TKRS/GOODS‐N Field. I. Rotation and Dispersion Properties

We present kinematic measurements of a large sample of galaxies from the Team Keck Redshift Survey in the GOODS-N field. We measure line-of-sight velocity dispersions from integrated emission for 1089 galaxies with median redshift 0.637 and spatially resolved kinematics for a subsample of 380 galaxies. This is the largest sample of galaxies to z ~ 1 with kinematics to date and allows us to measure kinematic properties without morphological preselection. Emission-line widths provide a dynamical measurement for the bulk of blue galaxies. To fit the spatially resolved kinematics, we construct models that fit both line-of-sight rotation amplitude and velocity dispersion. Integrated line width correlates well with a combination of the velocity gradient and dispersion and is a robust measure of galaxy kinematics. The spatial extents of emission and continuum are similar, and there is no evidence that line widths are affected by nuclear or clumpy emission. The measured rotation gradient depends strongly on slit position angle alignment with galaxy major axis, but integrated line width does not. Even for galaxies with well-aligned slits, some have kinematics dominated by dispersion (V/σ < 1) rather than rotation. These are probably objects with disordered velocity fields, not dynamically hot stellar systems. About 35% of the spatially resolved sample are dispersion dominated; galaxies that are both dispersion dominated and bright exist at high redshift but appear rare at low redshift. This kinematic morphology may probe galaxies' evolutionary state. It is linked to photometric morphology in HST ACS images: dispersion-dominated galaxies include a higher fraction of irregulars and chain galaxies, while rotation-dominated galaxies are mostly disks and irregulars. Only one-third of chain/hyphen galaxies are dominated by rotation; high-redshift elongated objects cannot be assumed to be inclined disks.

Density-potential pairs for spherical stellar systems with Sérsic light profiles and (optional) power-law cores

Popular models for describing the luminosity-density profiles of dynamically hot stellar systems (e.g. Jaffe, Hernquist, Dehnen) were constructed with the desire to match the deprojected form of an R1/4 light profile. Real galaxies, however, are now known to have a range of different light-profile shapes that scale with mass. Consequently, although highly useful, the above models have implicit limitations, and this is illustrated here through their application to a number of real galaxy density profiles. On the other hand, the analytical density profile given by Prugniel & Simien closely matches the deprojected form of Sérsic R1/n light profiles – including deprojected exponential light profiles. It is thus applicable for describing bulges in spiral galaxies, dwarf elliptical galaxies, and both ordinary and giant elliptical galaxies. Moreover, the observed Sérsic quantities define the parameters of the density model. Here we provide simple equations, in terms of elementary and special functions, for the gravitational potential and force associated with this density profile. Furthermore, to match galaxies with partially depleted cores, and better explore the supermassive black hole/galaxy connection, we have added a power-law core to this density profile and derived similar expressions for the potential and force of this hybrid profile. Expressions for the mass and velocity dispersion, assuming isotropy, are also given. These spherical models may also prove appropriate for describing the dark matter distribution in haloes formed from ΛCDM cosmological simulations.

The Observability of Abundance Ratio Effects in Dynamically Hot Stellar Systems

Using synthetic spectra, we construct a simple model of an elliptical galaxy with a velocity dispersion σ = 200 km s-1. Absorption feature indices are defined that are sensitive to the abundances of C, N, O, Na, Mg, Al, Si, S, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Ba, and Eu as a first step in determining the abundances of these elements in stellar populations such as elliptical galaxies for which integrated spectra are available. Using these indices and assuming a photon statistical error such that S/N = 100 around 5000 A, the feasibility of measuring individual elements in real galaxies is assessed. Of the elements studied, only S, K, Cu, Zn, and Eu appear to be difficult to determine. The rest appear to be measurable with high-quality data and models. The effects of abundance changes on Lick IDS indices, Rose indices, and BRVI colors are also tabulated.

Estimating Dark Matter Distributions

Thanks to instrumental advances, new, very large kinematic datasets for nearby dwarf spheroidal (dSph) galaxies are on the horizon. A key aim of these datasets is to help determine the distribution of dark matter in these galaxies. Past analyses have generally relied on specific dynamical models or highly restrictive dynamical assumptions. We describe a new, non-parametric analysis of the kinematics of nearby dSph galaxies designed to take full advantage of the future large datasets. The method takes as input the projected positions and radial velocities of stars known to be members of the galaxies, but does not use any parametric dynamical model, nor the assumption that the mass distribution follows that of the visible matter. The problem of estimating the radial mass distribution, M(r) (the mass interior to true radius r), is converted into a problem of estimating a regression function non-parametrically. From the Jeans Equation we show that the unknown regression function is subject to fundamental shape restrictions which we exploit in our analysis using statistical techniques borrowed from isotonic estimation and spline smoothing. Simulations indicate that M(r) can be estimated to within a factor of two or better with samples as small as 1000 stars over almost the entire radial range sampled by the kinematic data. The technique is applied to a sample of 181 stars in the Fornax dSph galaxy. We show that the galaxy contains a significant, extended dark halo some ten times more massive than its baryonic component. Though applied here to dSph kinematics, this approach can be used in the analysis of any kinematically hot stellar system in which the radial velocity field is discretely sampled.

Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?

We report high-quality near-IR spectroscopy of 12 ultraluminous infrared galaxy mergers (ULIRGs). Our new VLT and Keck data provide ~05 resolution, stellar and gas kinematics of these galaxies, most of which are compact systems in the last merger stages. We confirm that ULIRG mergers are in formation. Random motions dominate their stellar dynamics, but significant rotation is common. Gasdynamics and stellar dynamics are decoupled in most systems. ULIRGs fall on or near the fundamental plane of hot stellar systems, and especially on its less evolution-sensitive, reff-σ projection. The ULIRG velocity dispersion distribution, their location in the fundamental plane, and their distribution of vrot sin i/σ closely resemble those of intermediate-mass (~L*), elliptical galaxies with moderate rotation. As a group ULIRGs do not resemble giant ellipticals with large cores and little rotation. Our results are in good agreement with other recent studies indicating that disky ellipticals with compact cores or cusps can form through dissipative mergers of gas-rich disk galaxies while giant ellipticals with large cores have a different formation history.