arXiv subjects

Tim de Zeeuw

Publications and source records attributed to Tim de Zeeuw.

At least 19 recordsLinked to original sources

arXiv2024

Improving constraints on the extended mass distribution in the Galactic Center with stellar orbits

Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*.

astro-ph.GA↗

arXiv2023

The GRAVITY+ Project: Towards All-sky, Faint-Science, High-Contrast Near-Infrared Interferometry at the VLTI

The GRAVITY instrument has been revolutionary for near-infrared interferometry by pushing sensitivity and precision to previously unknown limits. With the upgrade of GRAVITY and the Very Large Telescope Interferometer (VLTI) in GRAVITY+, these limits will be pushed even further, with vastly improved sky coverage, as well as faint-science and high-contrast capabilities. This upgrade includes the implementation of wide-field off-axis fringe-tracking, new adaptive optics systems on all Unit Telescopes, and laser guide stars in an upgraded facility. GRAVITY+ will open up the sky to the measurement of black hole masses across cosmic time in hundreds of active galactic nuclei, use the faint stars in the Galactic centre to probe General Relativity, and enable the characterisation of dozens of young exoplanets to study their formation, bearing the promise of another scientific revolution to come at the VLTI.

astro-ph.IM↗

arXiv2022

The young stars in the Galactic Center

We present a large ${\sim 30" \times 30"}$ spectroscopic survey of the Galactic Center using the SINFONI IFU at the VLT. Combining observations of the last two decades we compile spectra of over $2800$ stars. Using the Bracket-$γ$ absorption lines we identify $195$ young stars, extending the list of known young stars by $79$. In order to explore the angular momentum distribution of the young stars, we introduce an isotropic cluster prior. This prior reproduces an isotropic cluster in a mathematically exact way, which we test through numerical simulations. We calculate the posterior angular momentum space as function of projected separation from Sgr~A*. We find that the observed young star distribution is substantially different from an isotropic cluster. We identify the previously reported feature of the clockwise disk and find that its angular momentum changes as function of separation from the black hole, and thus confirm a warp of the clockwise disk ($p \sim 99.2\%$). At large separations, we discover three prominent overdensities of angular momentum. One overdensity has been reported previously, the counter-clockwise disk. The other two are new. Determining the likely members of these structures, we find that as many as $75\%$ of stars can be associated with one of these features. Stars belonging to the warped clockwise-disk show a top heavy K-band luminosity function, while stars belonging to the larger separation features do not. Our observations are in good agreement with the predictions of simulations of in-situ star formation, and argue for common formation of these structures.

astro-ph.GA↗

arXiv2022

The Fornax3D project: discovery of ancient massive merger events in the Fornax cluster galaxies NGC 1380 and NGC 1427

We report the discovery of ancient massive merger events in the early-type galaxies NGC 1380 and NGC 1427, members of the Fornax galaxy cluster. Both galaxies have been observed by the MUSE IFU instrument on the VLT, as part of the Fornax3D project. By fitting recently-developed population-orbital superposition models to the observed surface brightness as well as stellar kinematic, age, and metallicity maps, we obtain the stellar orbits, age and metallicity distributions of each galaxy. We then decompose each galaxy into multiple orbital-based components, including a dynamically hot inner stellar halo component which is identified as the relic of past massive mergers. By comparing to analogues from cosmological galaxy simulations, chiefly TNG50, we find that the formation of such a hot inner stellar halo requires the merger with a now-destroyed massive satellite galaxy of $3.7_{-1.5}^{+2.7} \times 10^{10}$ Msun (about $1/5$ of its current stellar mass) in the case of NGC 1380 and of $1.5_{-0.7}^{+1.6} \times10^{10}$ Msun (about $1/4$ of its current stellar mass) in the case of NGC 1427. Moreover, we infer that the last massive merger in NGC 1380 happened $\sim10$ Gyr ago based on the stellar age distribution of the re-grown dynamically cold disk, whereas the merger in NGC 1427 ended $t\lesssim 8$ Gyr ago based on the stellar populations in its hot inner stellar halo. The major merger event in NGC 1380 is the first one with both merger mass and merger time quantitatively inferred in a galaxy beyond the Local Volume. Moreover, it is the oldest and most massive merger uncovered in nearby galaxies so far.

astro-ph.GA↗

arXiv2019

Scalar field effects on the orbit of S2 star

Precise measurements of the S-stars orbiting SgrA* have set strong constraints on the nature of the compact object at the centre of the Milky Way. The presence of a black hole in that region is well established, but its neighboring environment is still an open debate. In that respect, the existence of dark matter in that central region may be detectable due to its strong signatures on the orbits of stars: the main effect is a Newtonian precession which will affect the overall pericentre shift of S2, the latter being a target measurement of the GRAVITY instrument. The exact nature of this dark matter (e.g., stellar dark remnants or diffuse dark matter) is unknown. This article assumes it to be an scalar field of toroidal distribution, associated with ultra-light dark matter particles, surrounding the Kerr black hole. Such a field is a form of "hair" expected in the context of superradiance, a mechanism that extracts rotational energy from the black hole. Orbital signatures for the S2 star are computed and shown to be detectable by GRAVITY. The scalar field can be constrained because the variation of orbital elements depends both on the relative mass of the scalar field to the black hole and on the field mass coupling parameter.

astro-ph.GA↗

arXiv2019

Constraining nuclear star cluster formation using MUSE-AO observations of the early-type galaxy FCC47

Nuclear star clusters (NSCs) are found in at least 70% of all galaxies, but their formation path is still unclear. In the most common scenarios, NSCs form in-situ from the galaxy's central gas reservoir, through merging of globular clusters (GCs), or through a combination of the two. As the scenarios pose different expectations for angular momentum and stellar population properties of the NSC in comparison to the host galaxy and the GC system, it is necessary to characterise the stellar light, NSC and GCs simultaneously. The large NSC (r$_\rm{eff} = 66$ pc) and rich GC system of the early-type Fornax cluster galaxy FCC47 (NGC1336) render this galaxy an ideal laboratory to constrain NSC formation. Using MUSE science verification data assisted by adaptive optics, we obtained maps for the stellar kinematics and for stellar-population properties of FCC47. We extracted the spectra of the central NSC and determined line-of-sight velocities of 24 GCs and metallicities of five. FCC47 shows two decoupled components (KDCs): a rotating disk and the NSC. Our orbit-based dynamical Schwarzschild model revealed that the NSC is a distinct kinematic feature and it constitutes the peak of metallicity and old ages in the galaxy. The main body consists of two counter-rotating populations and is dominated by a more metal-poor population. The GC system is bimodal with a dominant metal-poor population and the total GC system mass is $\sim 17\%$ of the NSC mass ($\sim$ 7 $\times$ $10^8 M_\odot$). The rotation, high metallicity and high mass of the NSC cannot be uniquely explained by GC-inspiral and most likely requires additional, but quickly quenched, in-situ formation. The presence of two KDCs most probably are evidence of a major merger that has altered the structure of FCC47 significantly, indicating the important role of galaxy mergers in forming the complex kinematics in the galaxy-NSC system.

astro-ph.GA↗

arXiv2019

A metal-poor ultra compact dwarf galaxy at a kiloparsec distance from the low-mass elliptical galaxy FCC47

Photometric surveys of galaxy clusters have revealed a large number of ultra compact dwarfs (UCDs) around predominantly massive elliptical galaxies. Their origin is still debated as some UCDs are considered to be the remnant nuclei of stripped dwarf galaxies while others seem to mark the high-mass end of the star cluster population. We aim to characterise the properties of a UCD found at very close projected distance (1.1 kpc) from the centre of the low-mass (M~10^10 M_sun) early-type galaxy FCC47. This is a serendipitous discovery from MUSE adaptive optics science verification data. We explore the potential origin of this UCD as either a massive cluster or the remnant nucleus of a dissolved galaxy. We use archival Hubble Space Telescope data to study the photometric and structural properties of FCC47-UCD1. In the MUSE data, the UCD is unresolved, but we use its spectrum to determine the radial velocity and metallicity. FCC47-UCD1's surface brightness is best described by a single King profile with low concentration C = R_t/R_c ~ 10 and large effective radius (r_e = 24pc). Its integrated magnitude and a blue colour (G = -10.6 mag, g-z = 1.46 mag) combined with with a metallicity of [M/H] = -1.12+-0.10 dex and an age > 8 Gyr obtained from the full fitting of the MUSE spectrum suggests a stellar population mass of M_star = 4.87x10^6 M_sun. The low S/N of the MUSE spectrum prevents detailed stellar population analysis. Due to the limited spectral resolution of MUSE, we can only give an upper limit on the velocity dispersion (sig < 17km/s), and consequently on its dynamical mass (M_dyn < 1.3x10^7 M_sun). The origin of the UCD cannot be constrained with certainty. The low metallicity, old age and magnitude are consistent with a star cluster origin, whereas the extended size is consistent with an origin as the stripped nucleus of a dwarf galaxy with a initial stellar mass of a few 10^8 M_sun.

astro-ph.GA↗

arXiv2018

Multiple Star Systems in the Orion Nebula

This work presents an interferometric study of the massive-binary fraction in the Orion Trapezium Cluster with the recently comissioned GRAVITY instrument. We observe a total of 16 stars of mainly OB spectral type. We find three previously unknown companions for $θ^1$ Ori B, $θ^2$ Ori B, and $θ^2$ Ori C. We determine a separation for the previously suspected companion of NU Ori. We confirm four companions for $θ^1$ Ori A, $θ^1$ Ori C, $θ^1$ Ori D, and $θ^2$ Ori A, all with substantially improved astrometry and photometric mass estimates. We refine the orbit of the eccentric high-mass binary $θ^1$ Ori C and we are able to derive a new orbit for $θ^1$ Ori D. We find a system mass of 21.7 $M_{\odot}$ and a period of $53$ days. Together with other previously detected companions seen in spectroscopy or direct imaging, eleven of the 16 high-mass stars are multiple systems. We obtain a total number of 22 companions with separations up to 600 AU. The companion fraction of the early B and O stars in our sample is about 2, significantly higher than in earlier studies of mostly OB associations. The separation distribution hints towards a bimodality. Such a bimodality has been previously found in A stars, but rarely in OB binaries, which up to this point have been assumed to be mostly compact with a tail of wider companions. We also do not find a substantial population of equal-mass binaries. The observed distribution of mass ratios declines steeply with mass, and like the direct star counts, indicates that our companions follow a standard power law initial mass function. Again, this is in contrast to earlier findings of flat mass ratio distributions in OB associations. We exclude collision as a dominant formation mechanism but find no clear preference for core accretion or competitive accretion.

astro-ph.SR↗

arXiv2017

MUSE observations of the counter-rotating nuclear ring in NGC 7742

We present results from MUSE observations of the nearly face-on disk galaxy NGC 7742. This galaxy hosts a spectacular nuclear ring of enhanced star formation, which is unusual in that it is hosted by a non-barred galaxy, and also because this star formation is most likely fuelled by externally accreted gas that counter-rotates with respect to its main stellar body. We use the MUSE data to derive the star-formation history (SFH) and accurately measure the stellar and ionized-gas kinematics of NGC7742 in its nuclear, bulge, ring, and disk regions. We map the previously known gas counter-rotation well outside the ring region and deduce the presence of a slightly warped inner disk, which is inclined ~6 degrees compared to the outer disk. The gas-disk inclination is well constrained from the kinematics; the derived inclination 13.7 $\pm$ 0.4 degrees agrees well with that derived from photometry and from what one expects using the inverse Tully-Fisher relation. We find a prolonged SFH in the ring with stellar populations as old as 2-3 Gyr and an indication that the star formation triggered by the minor merger event was delayed in the disk compared to the ring. There are two separate stellar components: an old population that counter-rotates with the gas, and a young one, concentrated to the ring, that co-rotates with the gas. We recover the kinematics of the old stars from a two-component fit, and show that combining the old and young stellar populations results in the erroneous average velocity of nearly zero found from a one-component fit. The superior spatial resolution and large field of view of MUSE allow us to establish the kinematics and SFH of the nuclear ring in NGC 7742. We show further evidence that this ring has its origin in a minor merger event, possibly 2-3 Gyr ago.

astro-ph.GA↗

arXiv2017

The ESO Spectroscopic facility

We present the concept of a novel facility dedicated to massively-multiplexed spectroscopy. The telescope has a very wide field Cassegrain focus optimised for fibre feeding. With a Field of View (FoV) of 2.5 degrees diameter and a 11.4m pupil, it will be the largest etendue telescope. The large focal plane can easily host up to 16.000 fibres. In addition, a gravity invariant focus for the central 10 arc-minutes is available to host a giant integral field unit (IFU). The 3 lenses corrector includes an ADC, and has good performance in the 360-1300 nm wavelength range. The top level science requirements were developed by a dedicated ESO working group, and one of the primary cases is high resolution spectroscopy of GAIA stars and, in general, how our Galaxy formed and evolves. The facility will therefore be equipped with both, high and low resolution spectrographs. We stress the importance of developing the telescope and instrument designs simultaneously. The most relevant R\&D aspect is also briefly discussed.

astro-ph.IM↗

arXiv2017

Integral-field kinematics and stellar populations of early-type galaxies out to three half-light radii

We observed twelve nearby HI -detected early-type galaxies (ETGs) of stellar mass $\sim 10^{10}M\odot \leq M_* \leq \sim 10^{11}M\odot$ with the Mitchell Integral-Field Spectrograph, reaching approximately three half-light radii in most cases. We extracted line-of-sight velocity distributions for the stellar and gaseous components. We find little evidence of transitions in the stellar kinematics of the galaxies in our sample beyond the central effective radius, with centrally fast-rotating galaxies remaining fast-rotating and centrally slow-rotating galaxies likewise remaining slow-rotating. This is consistent with these galaxies having not experienced late dry major mergers; however, several of our objects have ionised gas that is misaligned with respect to their stars, suggesting some kind of past interaction. We extract Lick index measurements of the commonly-used H$β$, Fe5015, Mg\, b, Fe5270 and Fe5335 absorption features, and we find most galaxies to have flat H$β$ gradients and negative Mg, b gradients. We measure gradients of age, metallicity and abundance ratio for our galaxies using spectral fitting, and for the majority of our galaxies find negative age and metallicity gradients. We also find the stellar mass-to-light ratios to decrease with radius for most of the galaxies in our sample. Our results are consistent with a view in which intermediate-mass ETGs experience mostly quiet evolutionary histories, but in which many have experienced some kind of gaseous interaction in recent times.

astro-ph.GA↗

arXiv2017

Reaching New Heights in Astronomy - ESO Long Term Perspectives

A comprehensive description of ESO in the current global astronomical context, and its plans for the next decade and beyond, are presented. This survey covers all aspects of the Organisation, including the optical-infrared programme at the La Silla Paranal Observatory, the submillimetre facilities ALMA and APEX, the construction of the 39-metre European Extremely Large Telescope and the science operation of these facilities. An extension of the current optical/infrared/submillimetre facilities into multi-messenger astronomy has been made with the decision to host the southern Cherenkov Telescope Array at Paranal. The structure of the Organisation is presented and the further development of the staff is described within the scope of the long-range financial planning. The role of Chile is highlighted and expansion of the number of Member States beyond the current 15 is discussed. The strengths of the ESO model, together with challenges as well as possible new opportunities and initiatives, are examined and a strategy for the future of ESO is outlined.

astro-ph.IM↗

arXiv2016

A low upper mass limit for the central black hole in the late-type galaxy NGC 4414

We present our mass estimate of the central black hole in the isolated spiral galaxy NGC 4414. Using natural guide star adaptive optics assisted observations with the Gemini Near-Infrared Integral Field Spectrometer (NIFS) and the natural seeing Gemini Multi-Object Spectrographs-North (GMOS), we derived two-dimensional stellar kinematic maps of NGC 4414 covering the central 1.5 arcsec and 10 arcsec, respectively, at a NIFS spatial resolution of 0.13 arcsec. The kinematic maps reveal a regular rotation pattern and a central velocity dispersion dip down to around 105 km/s. We constructed dynamical methods using two different methods: Jeans anisotropic dynamical modeling and axisymmetric Schwarzschild modeling. Both modeling methods give consistent results, but we cannot constrain the lower mass limit and only measure an upper limit for the black hole mass of Mbh= 1.56 x 10^6 Msun(at 3 sigma level) which is at least 1 sigma below the recent Mbh-sigma_e relations. Further tests with dark matter, mass-to-light ratio variation and different light models confirm that our results are not dominated by uncertainties. The derived upper limit mass is not only below the Mbh-sigma_e relation, but is also five times lower than the lower limit black hole mass anticipated from the resolution limit of the sphere of influence. This proves that via high quality integral field data we are now able to push black hole measurements down to at least five times less than the resolution limit.

astro-ph.GA↗

arXiv2015

A re-evaluation of the central velocity-dispersion profile in NGC 6388

Recently, two independent groups found very different results when measuring the central velocity dispersion of the galactic globular cluster NGC 6388 with different methods. While Lützgendorf et al. (2011) found a rising profile and a high central velocity dispersion (23.3 km/s), measurements obtained by Lanzoni et al. (2013) showed a value 40% lower. The value of the central velocity dispersion has a serious impact on the mass and possible presence of an intermediate-mass black hole at the center of NGC 6388. We use a photometric catalog of NGC 6388 to create a simulated SINFONI and ARGUS dataset. The construction of the IFU data cube is done with different observing conditions reproducing the conditions reported for the original observations as closely as possible. In addition, we produce an N-body realization of a 10^6 M_SUN stellar cluster with the same photometric properties as NGC 6388 to account for unresolved stars. We find that the individual radial velocities, i.e. the measurements from the simulated SINFONI data, are systematically biased towards lower velocity dispersions. The reason is that due to the wings in the point spread function the velocities get biased towards the mean cluster velocity. This study shows that even with AO supported observations, individual radial velocities in crowded fields are likely to be biased. The ARGUS observations do not show this kind of bias but were found to have larger uncertainties than previously obtained. We find a bias towards higher velocity dispersions in the ARGUS pointing when fixing the extreme velocities of the three brightest stars but find those variations are within the determined uncertainties. We rerun Jeans models and fit the kinematic profile with the new uncertainties. This yields a BH mass of M_BH = (2.8 +- 0.4) x 10^4 M_SUN and M/L ratio M/L = (1.6 +- 0.1) M_SUN/L_SUN, consistent with our previous results.

astro-ph.GA↗

arXiv2015

Intermediate-mass black holes in globular clusters: observations and simulations

The study of intermediate-mass black holes (IMBHs) is a young and promising field of research. Formed by runaway collisions of massive stars in young and dense stellar clusters, intermediate-mass black holes could still be present in the centers of globular clusters, today. Our group investigated the presence of intermediate-mass black holes for a sample of 10 Galactic globular clusters. We measured the inner kinematic profiles with integral-field spectroscopy and determined masses or upper limits of central black holes in each cluster. In combination with literature data we further studied the positions of our results on known black-hole scaling relations (such as M_bh - sigma) and found a similar but flatter correlation for IMBHs. Applying cluster evolution codes, the change in the slope could be explained with the stellar mass loss occurring in clusters in a tidal field over its life time. Furthermore, we present results from several numerical simulations on the topic of IMBHs and integral field units (IFUs). We ran N-body simulations of globular clusters containing IMBHs in a tidal field and studied their effects on mass-loss rates and remnant fractions and showed that an IMBH in the center prevents core collapse and ejects massive objects more rapidly. These simulations were further used to simulate IFU data cubes. For the specific case of NGC 6388 we simulated two different IFU techniques and found that velocity dispersion measurements from individual velocities are strongly biased towards lower values due to blends of neighbouring stars and background light. In addition, we use the Astrophysical Multipurpose Software Environment (AMUSE) to combine gravitational physics, stellar evolution and hydrodynamics to simulate the accretion of stellar winds onto a black hole.

astro-ph.GA↗

arXiv2010

Early-type galaxies in different environments: an HI view

We present an analysis of deep WSRT observations of the HI in 33 nearby early-type galaxies selected from a sample studied earlier at optical wavelengths with the SAURON integral-field spectrograph. The sample covers both field environments and the Virgo cluster. Our analysis shows that gas accretion plays a role in the evolution of field early-type galaxies, but less so for those in clusters. For detection limits of a few times 10^6 Msun, HI is detected in about 2/3 of the field galaxies, while <10% of the Virgo objects are detected. In about half of the detections, the HI forms a regularly rotating disc or ring. All HI discs have counterparts of ionised gas and inner HI discs are also detected in molecular gas. The cold ISM is dominated by molecular gas (M_H2/M_HI ~ 10). We conclude that accretion of HI is common for field early-type galaxies, but the amount of material involved is usually small. Cluster galaxies appear not to accrete HI. The few galaxies with a significant young sub-population all have inner gas discs, but for the remaining galaxies there is no trend between stellar population and HI. Some early-type galaxies are very gas rich, but only have an old population. The stellar populations of field galaxies are typically younger than those in Virgo. This is likely related to differences in accretion history. In about 50% of the galaxies we detect a central continuum source. In many objects this emission is from a low-luminosity AGN, in some it is consistent with the observed star formation. Galaxies with HI in the central regions are more likely detected in continuum. This is due to a higher probability for star formation to occur in such galaxies and not to HI-related AGN fuelling. (Abridged)

astro-ph.CO↗

arXiv2009

The SAURON project - XIII. SAURON-GALEX study of early-type galaxies: the ultraviolet colour-magnitude relations and Fundamental Planes

We present GALEX far (FUV) and near (NUV) ultraviolet imaging of 34 nearby early-type galaxies from the SAURON representative sample of 48 E/S0 galaxies, all of which have ground-based optical imaging from the MDM Observatory. The surface brightness profiles of nine galaxies show regions with blue UV-optical colours suggesting recent star formation. Five of these show blue integrated UV-optical colours that set them aside in the NUV integrated colour-magnitude relation. They also have other properties confirming they have had recent star formation, in particular H_beta absorption higher than expected for a quiescent population and a higher CO detection rate. NUV-blue galaxies are generally drawn from the lower stellar velocity dispersion and thus lower dynamical mass part of the sample. We have also constructed the first UV Fundamental Planes and show that NUV blue galaxies bias the slopes and increase the scatters. If they are eliminated the fits get closer to expectations from the virial theorem. Although our analysis is based on a limited sample, it seems that a dominant fraction of the tilt and scatter of the UV Fundamental Planes is due to the presence of young stars in preferentially low-mass early-type galaxies. Interestingly, the UV-optical radial colour profiles reveal a variety of behaviours, with many galaxies showing signs of recent star formation, a central UV-upturn phenomenon, smooth but large-scale age and metallicity gradients, and in many cases a combination of these. In addition, FUV-NUV and FUV-V colours even bluer than those normally associated with UV-upturn galaxies are observed at the centre of some quiescent galaxies. Four out of the five UV-upturn galaxies are slow rotators. These objects should thus pose interesting challenges to stellar evolutionary models of the UV-upturn.

astro-ph.GA↗

arXiv2008

Two-component galaxies with flat rotation curve

Dynamical properties of two-component galaxy models whose stellar density distribution is described by a gamma-model while the total density distribution has a pure r^(-2) profile, are presented. The orbital structure of the stellar component is described by Osipkov-Merritt anisotropy, while the dark matter halo is isotropic. After a description of minimum halo models, the positivity of the phase-space density (the model consistency) is investigated, and necessary and sufficient conditions for consistency are obtained analytically as a function of the stellar inner density slope gamma and anisotropy radius. The explicit phase-space distribution function is recovered for integer values of gamma, and it is shown that while models with gamma>4/17 are consistent when the anisotropy radius is larger than a critical value (dependent on gamma), the gamma=0 models are unphysical even in the fully isotropic case. The Jeans equations for the stellar component are then solved analytically; in addition, the projected velocity dispersion at the center and at large radii are also obtained analytically for generic values of the anisotropy radius, and it is found that they are given by remarkably simple expressions. The presented models, even though highly idealized, can be useful as starting point for more advanced modeling of the mass distribution of elliptical galaxies in studies combining stellar dynamics and gravitational lensing.

astro-ph↗