Velocity Isotropy Research Articles

The Origin of Young Stellar Populations in NGC 1783: Accretion of External Stars

The presence of young stellar populations in the Large Magellanic Cloud cluster NGC 1783 has caught significant attention, with suggestions ranging from it being a genuine secondary stellar generation to a population of blue straggler stars or simply contamination from background stars. Thanks to multiepoch observations with the Hubble Space Telescope, proper motions for stars within the field of NGC 1783 have been derived, thus allowing accurate cluster membership determination. Here, we report that the younger stars within NGC 1783 indeed belong to the cluster and their spatial distribution is more extended compared to the bulk of the older stellar population, consistent with previous studies. Through N-body simulations, we demonstrate that the observed characteristics of the younger stars cannot be explained solely by blue straggler stars in the context of the isolated dynamical evolution of NGC 1783. Instead, accretion of the external, low-mass stellar system can better account for both the inverse spatial concentration and the radial velocity isotropy of the younger stars. We propose that NGC 1783 may have accreted external stars from low-mass stellar systems, resulting in a mixture of external younger stars and blue straggler stars from the older bulk population, thereby accounting for the characteristics of the younger sequence.

The dynamical structure of broken power-law and double power-law models for dark matter haloes

ABSTRACT Galaxy kinematics and gravitational lensing are two complementary ways to constrain the distribution of dark matter on galaxy scales. The typical dark matter density profiles adopted in dynamical studies cannot easily be adopted in lensing studies. Ideally, a mass model should be used that has the global characteristics of realistic dark matter distributions, and that allows for an analytical calculation of the magnifications and deflection angles. A simple model with these properties, the broken power-law (BPL) model, has very recently been introduced. We examine the dynamical structure of the family of BPL models. We derive simple closed expressions for basic dynamical properties, and study the distribution function under the assumption of velocity isotropy. We find that none of the BPL models with realistic parameters has an isotropic distribution function that is positive over the entire phase space, implying that the BPL models cannot be supported by an isotropic velocity distribution, or models with a more radially anisotropic orbital structure. This result limits the attractiveness of the BPL family as a tool for lensing studies to some degree. More generally, we find that not all members of the general family of double power-law or Zhao models, often used to model dark matter haloes, can be supported by an isotropic or radially anisotropic distribution function. In other words, the distribution function may become negative even for spherically symmetric models with a well-behaved density profile.

The Gaia-ESO Survey: asymmetric expansion of the Lagoon Nebula cluster NGC 6530 from GES and Gaia DR2

The combination of precise radial velocities from multi-object spectroscopy and highly accurate proper motions from Gaia DR2 opens up the possibility for detailed 3D kinematic studies of young star forming regions and clusters. Here, we perform such an analysis by combining Gaia-ESO Survey spectroscopy with Gaia astrometry for ~900 members of the Lagoon Nebula cluster, NGC 6530. We measure the 3D velocity dispersion of the region to be $5.35^{+0.39}_{-0.34}$~km~s$^{-1}$, which is large enough to suggest the region is gravitationally unbound. The velocity ellipsoid is anisotropic, implying that the region is not sufficiently dynamically evolved to achieve isotropy, though the central part of NGC 6530 does exhibit velocity isotropy that suggests sufficient mixing has occurred in this denser part. We find strong evidence that the stellar population is expanding, though this is preferentially occurring in the declination direction and there is very little evidence for expansion in the right ascension direction. This argues against a simple radial expansion pattern, as predicted by models of residual gas expulsion. We discuss these findings in the context of cluster formation, evolution and disruption theories.

Models of cuspy triaxial stellar systems – III. The effect of velocity anisotropy on chaoticity

In several previous investigations we presented models of triaxial stellar systems, both cuspy and non cuspy, that were highly stable and harboured large fractions of chaotic orbits. All our models had been obtained through cold collapses of initially spherical $N$--body systems, a method that necessarily results in models with strongly radial velocity distributions. Here we investigate a different method that was reported to yield cuspy triaxial models with virtually no chaos. We show that such result was probably due to the use of an inadequate chaos detection technique and that, in fact, models with significant fractions of chaotic orbits result also from that method. Besides, starting with one of the models from the first paper in this series, we obtained three different models by rendering its velocity distribution much less radially biased (i.e., more isotropic) and by modifying its axial ratios through adiabatic compression. All three models yielded much higher fractions of regular orbits than most of those from our previous work. We conclude that it is possible to obtain stable cuspy triaxial models of stellar systems whose velocity distribution is more isotropic than that of the models obtained from cold collapses. Those models still harbour large fractions of chaotic orbits and, although it is difficult to compare the results from different models, we can tentatively conclude that chaoticity is reduced by velocity isotropy.

The masses of the Milky Way and Andromeda galaxies

We present a family of robust tracer mass estimators to compute the enclosed mass of galaxy haloes from samples of discrete positional and kinematical data of tracers, such as halo stars, globular clusters and dwarf satellites. The data may be projected positions, distances, line of sight velocities or proper motions. Forms of the estimator tailored for the Milky Way galaxy and for M31 are given. Monte Carlo simulations are used to quantify the uncertainty as a function of sample size. For the Milky Way, the satellite sample consists of 26 galaxies with line-of-sight velocities. We find that the mass of the Milky Way within 300 kpc is ~ 0.9 x 10^12 solar masses assuming velocity isotropy. However, the mass estimate is sensitive to the anisotropy and could plausibly lie between 0.7 - 3.4 x 10^12 solar masses. Incorporating the proper motions of 6 Milky Way satellites into the dataset, we find ~ 1.4 x 10^12 solar masses. The range here if plausible anisotropies are used is still broader, from 1.2 - 2.7 x 10^12 solar masses. For M31, there are 23 satellite galaxies with measured line-of-sight velocities, but only M33 and IC 10 have proper motions. We use the line of sight velocities and distances of the satellite galaxies to estimate the mass of M31 within 300 kpc as ~ 1.4 x 10^12 solar masses assuming isotropy. There is only a modest dependence on anisotropy, with the mass varying between 1.3 -1.6 x 10^12 solar masses. Given the uncertainties, we conclude that the satellite data by themselves yield no reliable insights into which of the two galaxies is actually the more massive.

COMPARING X-RAY AND DYNAMICAL MASS PROFILES IN THE EARLY-TYPE GALAXY NGC 4636

We present the results of an X-ray mass analysis of the early-type galaxy NGC 4636, using Chandra data. We have compared the X-ray mass density profile with that derived from a dynamical analysis of the system's globular clusters (GCs). Given the observed interaction between the central active galactic nucleus and the X-ray emitting gas in NGC 4636, we would expect to see a discrepancy in the masses recovered by the two methods. Such a discrepancy exists within the central ~10kpc, which we interpret as the result of non-thermal pressure support or a local inflow. However, over the radial range ~10-30kpc, the mass profiles agree within the 1-sigma errors, indicating that even in this highly disturbed system, agreement can be sought at an acceptable level of significance over intermediate radii, with both methods also indicating the need for a dark matter halo. However, at radii larger than 30kpc, the X-ray mass exceeds the dynamical mass, by a factor of 4-5 at the largest disagreement. A Fully Bayesian Significance Test finds no statistical reason to reject our assumption of velocity isotropy, and an analysis of X-ray mass profiles in different directions from the galaxy centre suggests that local disturbances at large radius are not the cause of the discrepancy. We instead attribute the discrepancy to the paucity of GC kinematics at large radius, coupled with not knowing the overall state of the gas at the radius where we are reaching the group regime (>30kpc), or a combination of the two.

MASS DISTRIBUTION IN THE CENTRAL FEW PARSECS OF OUR GALAXY

We estimate the enclosed mass profile in the central 10 pc of the Milky Way by analyzing the infrared photometry and the velocity observations of dynamically relaxed stellar population in the Galactic center. HST/NICMOS and Gemini Adaptive Optics images in the archive are used to obtain the number density profile, and proper motion and radial velocity data were compiled from the literature to find the velocity dispersion profile assuming a spherical symmetry and velocity isotropy. From these data, we calculate the enclosed mass and density profiles in the central 10 pc of the Galaxy using the Jeans equation. Our improved estimates can better describe the exact evolution of the molecular clouds and star clusters falling down to the Galactic center, and constrain the star formation history of the inner part of the Galaxy.

Constraints on grain size and stable iron phases in the uppermost inner core from multiple scattering modeling of seismic velocity and attenuation

We propose to model the uppermost inner core as an aggregate of randomly oriented anisotropic “patches”. A patch is defined as an assemblage of a possibly large number of crystals with identically oriented crystallographic axes. This simple model accounts for the observed velocity isotropy of short period body waves, and offers a reasonable physical interpretation for the scatterers detected at the top of the inner core. From rigorous multiple scattering modeling of seismic wave propagation through the aggregate, we obtain strong constraints on both the size and the elastic constants of iron patches. In a first step, we study the phase velocity and scattering attenuation of aggregates composed of hexagonal and cubic crystals, whose elastic constants have been published in the mineral physics literature. The predicted attenuations for P waves vary over two orders of magnitude. Our calculations demonstrate that scattering attenuation is extremely sensitive to the anisotropic properties of single crystals and offers an attractive way to discriminate among iron models with e.g. identical Voigt average speeds. When anisotropy of elastic patches is pronounced, we find that the S wavespeed in the aggregate can be as much as 15% lower than the Voigt average shear velocity of a single crystal.In a second step, we perform a systematic search for iron models compatible with measured seismic velocities and attenuations. An iron model is characterized by its symmetry (cubic or hexagonal), elastic constants, and patch size. Independent of the crystal symmetry, we infer a most likely size of patch of the order of 400 m. Recent bcc iron models from the literature are in very good agreement with the most probable elastic constants of cubic crystals found in our inversion. Our study (1) suggests that the presence of melt may not be required to explain the low shear wavespeeds in the inner core and (2) supports the recent experimental results on the stability of cubic iron in the inner core, at least in its upper part.

Dynamical insight into dark matter haloes

We investigate, using the spherical Jeans equation, self-gravitating dynamical equilibria satisfying a relation ρ/σ 3 ∝ r −α , which holds for simulated dark matter haloes over their whole resolved radial range. Considering first the case of velocity isotropy, we find that this problem has only one solution for which the density profile is not truncated or otherwise unrealistic. This solution occurs only for a critical value of αcrit = 35/18 = 1.94, which is consistent with the empirical value of 1.9 ± 0.05. We extend our analysis in two ways: first, we introduce a par ,

Geometrical conditions for the design of partial or full isotropic hexapods

This paper presents a methodology for the design of PKMs (parallel kinematic machines) with defined isotropy and stiffness. Partial isotropy or full isotropy can be achieved by suitable design choices. The former is useful for five axis applications, while the latter for six axis manipulators. The paper summarizes the concept of full and partial isotropy, and for a wide class of hexapods defines in analytical form the conditions to achieve it exactly. These conditions can be used to design isotropic parallel manipulators. The methodology requires that the six legs have to be divided into two groups (terns). The legs belonging to one tern are mutually identical and are positioned with radial symmetry with respect to the TCP (tool center point). The paper shows that the manipulator structure can be defined in term of 13 design parameters, the value of six of them are chosen in order to achieve the required isotropy and stiffness properties, while the remaining seven parameters can be used to optimize the structure. The design criterion here presented assures that stiffness isotropy, force, and velocity isotropy are all achieved contemporarily. This methodology can be practically applied to a large family of hexapods. © 2005 Wiley Periodicals, Inc.

Velocity performance indices for parallel mechanisms with actuation redundancy

This paper analyses the concept of velocity isotropy for Parallel Mechanisms with Actuation Redundancy (PMAR). The limits of classical indices based on the Jacobean matrix condition number are shown. It is proposed to use either the largest ellipsoid included in the operational polytop, or the operational polytop itself, as better representations of a PMAR capabilities. The polytop is studied because it is actually the accurate representation of a machine capability, while the largest ellipsoid remains similar to the classical tool roboticists are dealing with for decades. Velocity performance indices are proposed, and the ways to compute them efficiently are given.

Dynamics of the Globular Cluster System Associated with M49 (NGC 4472): Cluster Orbital Properties and the Distribution of Dark Matter

Using the Low Resolution Imaging Spectrometer on the Keck I and II telescopes, we have measured radial velocities for 196 globular clusters (GCs) around M49 (NGC 4472), the brightest member of the Virgo Cluster. Combined with published data, they bring the total number of GCs with measured radial velocities in this galaxy to 263. In terms of sample size, spatial coverage, velocity precision, and the availability of metallicity estimates from Washington photometry, this radial velocity database resembles that presented recently for M87 (NGC 4486), Virgo's cD galaxy and its second-ranked member. We extract the projected kinematics of the full sample of GCs and of separate subsamples of 158 metal-poor and 105 metal-rich GCs. In agreement with previous results for the global GC kinematics based on smaller data sets, we find that the GC system as a whole exhibits a slow overall rotation that is due almost entirely to a net rotation of the metal-poor GC subsystem alone. In a spatial average, the metal-rich GCs show essentially no rotation. As a function of galactocentric position, the metal-poor GCs rotate roughly about the photometric minor axis of M49 and at an approximately constant level of ΩR ~ 100-150 km s-1 out to R 2Reff. The metal-rich GC system shows some evidence (at roughly 1 σ significance) for weak rotation (ΩR ~ 50 km s-1) beyond R 0.5Reff, also about the galaxy's minor axis, but in the opposite direction from the metal-poor GCs. Outside of R ~ Reff, the line-of-sight velocity dispersion of the metal-poor GCs exceeds that of their metal-rich counterparts by ~50%. We also note the presence of a well-defined grouping of 10 metal-rich GCs that are located at opposite poles along the galaxy's major axis and that appear to be rotating at nearly 300 km s-1 about the minor axis. This grouping may be the relic of a past merger or accretion event. The dynamics of the GC system is modeled by using published catalogs and number counts to define three-dimensional GC density distributions as input to a Jeans equation analysis. We show that the GC radial velocities alone point unequivocally, and independently of X-ray observations, to the need for a massive dark halo associated with M49 and the Virgo B subcluster around it. We then use a mass model for M49/Virgo B, constructed without reference to any GC data and described in detail in a forthcoming paper, to infer the orbital properties of the M49 globulars. The GC system as a whole is shown to be consistent with an almost perfectly isotropic velocity ellipsoid. It is more difficult to draw any firm conclusions on the orbital (an)isotropy of the two metallicity subsamples, as a result of the large uncertainties in their individual spatial density profiles and the poorly observationally defined kinematics of the metal-rich GCs in particular. After M87, M49 is the second elliptical galaxy for which we have been able to demonstrate velocity isotropy in the GC system overall, when no division based on GC color or metallicity is attempted. Thus, the data for these two galaxies lend support to the general assumption of isotropy when using GC kinematics to study the dark matter distribution in early-type galaxies. We also compare the kinematic properties of the GC system of M49 to those of M87, M31, and the Milky Way, the other galaxies for which samples of 100 or more GC velocities have been accumulated. We argue that, contrary to the traditional view of GCs as nonrotating, or slowly rotating, systems, rotation may in fact be a common by-product of the formation of GC systems. However, the quantitative details of the rotation are still not clear, particularly with regard to the question of possible differences between metal-poor and metal-rich globulars.

Borehole seismic profiles in the Ekofisk Field

In October 1983 a major borehole seismic survey was carried out in the Ekofisk oil field in the Norwegian sector of the North Sea on behalf of the Phillips Petroleum Licence 018 group of companies. A vertical seismic profile with the source vertically above the geophone in the highly deviated wellbore and three multilevel walk‐away borehole profiles were acquired in an area showing very poor surface seismic returns owing to gas charging in the overlying sediments. The processing of the data through to a series of conventional common‐midpoint sections has permitted detailed interpretation of the top of the Ekofisk formation and the top of the Tor formation apart from well control. Both formations are producers separated by a tight zone. The Tor formation is the primary horizon to waterflood. Information as to its lateral continuity is important in the location of proposed waterflood injector wells. Prior to the survey, the field was considered effectively unfaulted. An apparent graben lying subparallel to the borehole was detected by the surveys. Reflections from below the reservoir formations are evident. A byproduct of the survey is strong evidence for the existence of lateral velocity gradients or apparent transverse velocity isotropy associated with the overlying gas‐charged sediments. Subsequent to the oral presentation of this paper, the graben was drilled and found to have a 41 m fault throw, in its western flank.

Superclusters as Nondissipative Pancakes

The formation of aspherical superclusters (SC's) is studied by 3-D N-body simulations that are confronted with the Local SC (LSC), and a simple model is developed. A nondissipative scenario, in which galaxies are formed from perturbations on smaller scales prior to the collapse of SC's, is found to be successful. It explains the disk-halo structure of SC's, their flattening and their low dispersions, which are nontransient because of the expansion along the long axes. The LSC has collapsed at z≤0.5. The large-scale velocity isotropy and the local 1-D infall indicate Ω<1. The correlation of galaxies on a few Mpc scales grows nonselfsimilarly due to recent pancaking rather than gradual clustering. This may be tested by the lack of clustering among objects at z>1.