36 research outputs found
Properties of quasi-relaxed stellar systems in an external tidal field
In a previous paper, we have constructed a family of self-consistent triaxial
models of quasi-relaxed stellar systems, shaped by the tidal field of the
hosting galaxy, as an extension of the well-known spherical King models. For a
given tidal field, the models are characterized by two physical scales (such as
total mass and central velocity dispersion) and two dimensionless parameters
(the concentration parameter and the tidal strength). The most significant
departure from spherical symmetry occurs when the truncation radius of the
corresponding spherical King model is of the order of the tidal radius, which,
for a given tidal strength, is set by the maximum concentration value admitted.
For such maximally extended (or "critical") models the outer boundary has a
generally triaxial shape, given by the zero-velocity surface of the relevant
Jacobi integral, which is basically independent of the concentration parameter.
In turn, the external tidal field can give rise to significant global
departures from spherical symmetry (as measured, for example, by the quadrupole
of the mass distribution of the stellar system) only for low-concentration
models, for which the allowed maximal value of the tidal strength can be
relatively high. In this paper we describe in detail the intrinsic and the
projected structure and kinematics of the models, covering the entire parameter
space, from the case of sub-critical (characterized by "underfilling" of the
relevant Roche volume) to that of critical models. The intrinsic properties can
be a useful starting point for numerical simulations and other investigations
that require initialization of a stellar system in dynamical equilibrium. The
projected properties are a key step in the direction of a comparison with
observed globular clusters and other candidate stellar systems.Comment: 13 pages, 11 figures, uses emulateapj.cls with apjfonts.sty. Accepted
for publication in The Astrophysical Journa
A dynamical study of Galactic globular clusters under different relaxation conditions
We perform a systematic combined photometric and kinematic analysis of a
sample of globular clusters under different relaxation conditions, based on
their core relaxation time (as listed in available catalogs), by means of two
well-known families of spherical stellar dynamical models. Systems
characterized by shorter relaxation time scales are expected to be better
described by isotropic King models, while less relaxed systems might be
interpreted by means of non-truncated, radially-biased anisotropic f^(\nu)
models, originally designed to represent stellar systems produced by a violent
relaxation formation process and applied here for the first time to the study
of globular clusters. The comparison between dynamical models and observations
is performed by fitting simultaneously surface brightness and velocity
dispersion profiles. For each globular cluster, the best-fit model in each
family is identified, along with a full error analysis on the relevant
parameters. Detailed structural properties and mass-to-light ratios are also
explicitly derived. We find that King models usually offer a good
representation of the observed photometric profiles, but often lead to less
satisfactory fits to the kinematic profiles, independently of the relaxation
condition of the systems. For some less relaxed clusters, f^(\nu) models
provide a good description of both observed profiles. Some derived structural
characteristics, such as the total mass or the half-mass radius, turn out to be
significantly model-dependent. The analysis confirms that, to answer some
important dynamical questions that bear on the formation and evolution of
globular clusters, it would be highly desirable to acquire larger numbers of
accurate kinematic data-points, well distributed over the cluster field.Comment: 18 pages, 7 figures. Accepted for publication in Astronomy &
Astrophysic
Rotating Globular Clusters
Internal rotation is considered to play a major role in the dynamics of some
globular clusters. However, in only few cases it has been studied by
quantitative application of realistic and physically justified global models.
Here we present a dynamical analysis of the photometry and three-dimensional
kinematics of omega Cen, 47 Tuc, and M15, by means of a recently introduced
family of self-consistent axisymmetric rotating models. The three clusters,
characterized by different relaxation conditions, show evidence of differential
rotation and deviations from sphericity. The combination of line-of-sight
velocities and proper motions allows us to determine their internal dynamics,
predict their morphology, and estimate their dynamical distance. The
well-relaxed cluster 47 Tuc is very well interpreted by our model; internal
rotation is found to explain the observed morphology. For M15, we provide a
global model in good agreement with the data, including the central behavior of
the rotation profile and the shape of the ellipticity profile. For the
partially relaxed cluster omega Cen, the selected model reproduces the complex
three-dimensional kinematics; in particular the observed anisotropy profile,
characterized by a transition from isotropy, to weakly-radial anisotropy, and
then to tangential anisotropy in the outer parts. The discrepancy found for the
steep central gradient in the observed line-of-sight velocity dispersion
profile and for the ellipticity profile is ascribed to the condition of only
partial relaxation of this cluster and the interplay between rotation and
radial anisotropy.Comment: 19 pages, 14 figures, accepted for publication in the Astrophysical
Journa
Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era
The structural and dynamical properties of star clusters are generally
derived by means of the comparison between steady-state analytic models and the
available observables. With the aim of studying the biases of this approach, we
fitted different analytic models to simulated observations obtained from a
suite of direct N-body simulations of star clusters in different stages of
their evolution and under different levels of tidal stress to derive mass, mass
function and degree of anisotropy. We find that masses can be
under/over-estimated up to 50% depending on the degree of relaxation reached by
the cluster, the available range of observed masses and distances of radial
velocity measures from the cluster center and the strength of the tidal field.
The mass function slope appears to be better constrainable and less sensitive
to model inadequacies unless strongly dynamically evolved clusters and a
non-optimal location of the measured luminosity function are considered. The
degree and the characteristics of the anisotropy developed in the N-body
simulations are not adequately reproduced by popular analytic models and can be
detected only if accurate proper motions are available. We show how to reduce
the uncertainties in the mass, mass-function and anisotropy estimation and
provide predictions for the improvements expected when Gaia proper motions will
be available in the near future.Comment: 14 pages, 8 figures, accepted for publication by MNRA
On the density profile of the globular cluster M92
We present new number density and surface brightness profiles for the
globular cluster M92 (NGC 6341). These profiles are calculated from optical
images collected with the CCD mosaic camera MegaCam at the
Canada-France-Hawaii-Telescope and with the Advanced Camera for Surveys on the
Hubble Space Telescope. The ground-based data were supplemented with the Sloan
Digital Sky Survey photometric catalog. Special care was taken to discriminate
candidate cluster stars from field stars and to subtract the background
contamination from both profiles. By examining the contour levels of the number
density, we found that the stellar distribution becomes clumpy at radial
distances larger than about 13 arcminutes, and there is no preferred
orientation of contours in space. We performed detailed fits of King and Wilson
models to the observed profiles. The best-fit models underestimate the number
density inside the core radius. Wilson models better represent the
observations, in particular in the outermost cluster regions: the good global
agreement of these models with the observations suggests that there is no need
to introduce an extra-tidal halo to explain the radial distribution of stars at
large radial distances. The best-fit models for the number density and the
surface brightness profiles are different, even though they are based on the
same observations. Additional tests support the evidence that this fact
reflects the difference in the radial distribution of the stellar tracers that
determine the observed profiles (main sequence stars for the number density,
bright evolved stars for the surface brightness).Comment: 18 pages, 10 figures, Accepted by A
Ongoing hierarchical massive cluster assembly: the LISCA II structure in the Perseus complex
We report on the identification of a massive ( M)
sub-structured stellar system in the Galactic Perseus complex likely undergoing
hierarchical cluster assembly. Such a system comprises nine star clusters
(including the well-known clusters NGC 654 and NGC 663) and an extended and
low-density stellar halo. Gaia-DR3 and available spectroscopic data show that
all its components are physically consistent in the 6D phase-space (position,
parallax, and 3D motion), homogeneous in age (14 44 Myr), and chemical
content (half-solar metallicity). In addition, the system's global stellar
density distribution is that of typical star clusters and shows clear evidence
of mass segregation. We find that the hierarchical structure is mostly
contracting towards the center with a speed of up to km s,
while the innermost regions expand at a lower rate (about km
s) and are dominated by random motions. Interestingly, this pattern is
dominated by the kinematics of massive stars, while low-mass stars (
M) are characterized by contraction across the entire cluster. Finally,
the nine star clusters in the system are all characterized by a relatively flat
velocity dispersion profile possibly resulting from ongoing interactions and
tidal heating. We show that the observational results are generally consistent
with those found in -body simulations following the cluster violent
relaxation phase strongly suggesting that the system is a massive cluster in
the early assembly stages. This is the second structure with these properties
identified in our Galaxy and, following the nomenclature of our previous work,
we named it LISCA II.Comment: 21 pages, 24 figures, 1 table; accepted for publication in A&
First Phase Space Portrait of a Hierarchical Stellar Structure in the Milky Way
We present the first detailed observational picture of a possible ongoing
massive cluster hierarchical assembly in the Galactic disk as revealed by the
analysis of the stellar full phase-space (3D positions and kinematics and
spectro-photometric properties) of an extended area ( diameter)
surrounding the well-known and Persei double stellar cluster in
the Perseus Arm. Gaia-EDR3 shows that the area is populated by seven co-moving
clusters, three of which were previously unknown, and by an extended and quite
massive () halo. All stars and clusters define a complex
structure with evidence of possible mutual interactions in the form of
intra-cluster over-densities and/or bridges. They share the same chemical
abundances (half-solar metallicity) and age ( Myr) within a small
confidence interval and the stellar density distribution of the surrounding
diffuse stellar halo resembles that of a cluster-like stellar system. The
combination of these evidences suggests that stars distributed within a few
degrees from and Persei are part of a common, sub-structured
stellar complex that we named LISCA I. Comparison with results obtained through
direct -body simulations suggest that LISCA I may be at an intermediate
stage of an ongoing cluster assembly that can eventually evolve in a relatively
massive (a few ) stellar system. We argue that such cluster
formation mechanism may be quite efficient in the Milky Way and disk-like
galaxies and, as a consequence, it has a relevant impact on our understanding
of cluster formation efficiency as a function of the environment and redshift.Comment: 19 pages, 8 figures, 1 table; accepted for publication in Ap
Forward and Back: Kinematics of the Palomar 5 Tidal Tails
The tidal tails of Palomar 5 (Pal 5) have been the focus of many
spectroscopic studies in an attempt to identify individual stars lying along
the stream and characterise their kinematics. The well-studied trailing tail
has been explored out to a distance of 15^\text{o} from the cluster centre,
while less than four degrees have been examined along the leading tail. In this
paper, we present results of a spectroscopic study of two fields along the
leading tail that we have observed with the AAOmega spectrograph on the
Anglo-Australian telescope. One of these fields lies roughly 7^\text{o} along
the leading tail, beyond what has been previously been explored
spectroscopically. Combining our measurements of kinematics and line strengths
with Pan-STARRS1 photometric data and Gaia EDR3 astrometry, we adopt a
probabilistic approach to identify 16 stars with high probability of belonging
to the Pal 5 stream. Eight of these stars lie in the outermost field and their
sky positions confirm the presence of ``fanning'' in the leading arm. We also
revisit previously-published radial velocity studies and incorporate Gaia EDR3
astrometry to remove interloping field stars. With a final sample of 109 {\it
bona fide} Pal 5 cluster and tidal stream stars, we characterise the 3D
kinematics along the the full extent of the system. We provide this catalogue
for future modeling work.Comment: 13 pages, 8 figures, accepted for publication in MNRAS. The extended
version of Table 4 is available as an ancillery file, and will be
supplementary material in MNRA
The construction of non-spherical models of quasi-relaxed stellar systems
Spherical models of collisionless but quasi-relaxed stellar systems have long
been studied as a natural framework for the description of globular clusters.
Here we consider the construction of self-consistent models under the same
physical conditions, but including explicitly the ingredients that lead to
departures from spherical symmetry. In particular, we focus on the effects of
the tidal field associated with the hosting galaxy. We then take a stellar
system on a circular orbit inside a galaxy represented as a "frozen" external
field. The equilibrium distribution function is obtained from the one
describing the spherical case by replacing the energy integral with the
relevant Jacobi integral in the presence of the external tidal field. Then the
construction of the model requires the investigation of a singular perturbation
problem for an elliptic partial differential equation with a free boundary, for
which we provide a method of solution to any desired order, with explicit
solutions to two orders. We outline the relevant parameter space, thus opening
the way to a systematic study of the properties of a two-parameter family of
physically justified non-spherical models of quasi-relaxed stellar systems. The
general method developed here can also be used to construct models for which
the non-spherical shape is due to internal rotation. Eventually, the models
will be a useful tool to investigate whether the shapes of globular clusters
are primarily determined by internal rotation, by external tides, or by
pressure anisotropy.Comment: AASTeX v5.2, 37 pages with 2 figures, accepted for publication in The
Astrophysical Journa