131 research outputs found
On the trapping of stars by a newborn stellar supercluster
Numerical experiments conducted by Fellhauer et al. (MNRAS, 372, 338, 2006)
suggest that a supercluster may capture up to about 40 per cent of its mass
from the galaxy where it belongs. Nevertheless, in those experiments the
cluster was created making appear its mass out of nothing, rather than from
mass already present in the galaxy. Here we use a thought experiment, plus a
few simple computations, to show that the difference between the dynamical
effects of these two scenarios (i.e., mass creation vs. mass concentration) is
actually very important. We also present the results of new numerical
experiments, simulating the formation of the cluster through mass
concentration, that show that trapping depends critically on the process of
cluster formation and that the amounts of gained mass are substantially smaller
than those obtained from mass creation.Comment: 6 pages, 3 figures. Submitted to MNRA
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 --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.Comment: 11 pages, 14 figures. Accepted for publication in MNRA
Models of cuspy triaxial stellar systems. II. Regular orbits
In the first paper of this series we used the N--body method to build a dozen
cuspy (gamma ~ 1) triaxial models of stellar systems, and we showed that they
were highly stable over time intervals of the order of a Hubble time, even
though they had very large fractions of chaotic orbits (more than 85 per cent
in some cases). The models were grouped in four sets, each one comprising
models morphologically resembling E2, E3, E4 and E5 galaxies, respectively. The
three models within each set, although different, had the same global
properties and were statistically equivalent. In the present paper we use
frequency analysis to classify the regular orbits of those models. The bulk of
those orbits are short axis tubes (SATs), with a significant fraction of long
axis tubes (LATs) in the E2 models that decreases in the E3 and E4 models to
become negligibly small in the E5 models. Most of the LATs in the E2 and E3
models are outer LATs, but the situation reverses in the E4 and E5 models where
the few LATs are mainly inner LATs. As could be expected for cuspy models, most
of the boxes are resonant orbits, i.e., boxlets. Nevertheless, only the (x, y)
fishes of models E3 and E4 amount to about 10 per cent of the regular orbits,
with most of the fractions of the other boxlets being of the order of 1 per
cent or less.Comment: Accepted for publication in the Monthly Notices of the Royal
Astronomical Societ
On the correct computation of all Lyapunov exponents in Hamiltonian dynamical systems
The Lyapunov Characteristic Exponents are a useful indicator of chaos in
astronomical dynamical systems. They are usually computed through a standard,
very efficient and neat algorithm published in 1980. However, for Hamiltonian
systems the expected result of pairs of opposite exponents is not always
obtained with enough precision. We find here why in these cases the initial
order of the deviation vectors matters, and how to sort them in order to obtain
a correct result.Comment: 8 pages, 3 figure
A three dimensional investigation of two dimensional orbits
Orbits in the principal planes of triaxial potentials are known to be prone
to unstable motion normal to those planes, so that three dimensional
investigations of those orbits are needed even though they are two dimensional.
We present here an investigation of such orbits in the well known logarithmic
potential which shows that the third dimension must be taken into account when
studying them and that the instability worsens for lower values of the forces
normal to the plane. Partially chaotic orbits are present around resonances,
but also in other regions. The action normal to the plane seems to be related
to the isolating integral that distinguishes regular form partially chaotic
orbits, but not to the integral that distinguishes partially from fully chaotic
orbits.Comment: Accepted for publication in CMD
Models of cuspy triaxial stellar systems. I. Stability and chaoticity
We used the N-body code of Hernquist and Ostriker (1992) to build a dozen
cuspy ({\gamma}\approx 1) triaxial models of stellar systems through
dissipationless collapses of initially spherical distributions of 10^6
particles. We chose four sets of initial conditions that resulted in models
morphologically resembling E2, E3, E4 and E5 galaxies, respectively. Within
each set, three different seed numbers were selected for the random number
generator used to create the initial conditions, so that the three models of
each set are statistically equivalent. We checked the stability of our models
using the values of their central densities and of their moments of inertia,
which turned out to be very constant indeed. The changes of those values were
all less than 3 per cent over one Hubble time and, moreover, we show that the
most likely cause of those changes are relaxation effects in the numerical
code. We computed the six Lyapunov exponents of nearly 5,000 orbits in each
model in order to recognize regular, partially and fully chaotic orbits. All
the models turned out to be highly chaotic, with less than 25 per cent of their
orbits being regular. We conclude that it is quite possible to obtain cuspy
triaxial stellar models that contain large fractions of chaotic orbits and are
highly stable. The difficulty to build such models with the method of
Schwarzschild (1979) should be attributed to the method itself and not to
physical causes.Comment: 10 pages, 5 figures, published in MNRAS (The definitive version is
available at www.blackwell-synergy.com
Large-scale study of the NGC 1399 globular cluster system in Fornax
We present a Washington C and Kron-Cousins R photometric study of the
globular cluster system of NGC 1399, the central galaxy of the Fornax cluster.
A large areal coverage of 1 square degree around NGC 1399 is achieved with
three adjoining fields of the MOSAIC II Imager at the CTIO 4-m telescope.
Working on such a large field, we can perform the first indicative
determination of the total size of the NGC 1399 globular cluster system. The
estimated angular extent, measured from the NGC 1399 centre and up to a
limiting radius where the areal density of blue globular clusters falls to 30
per cent of the background level, is 45 +/- 5 arcmin, which corresponds to 220
- 275 kpc at the Fornax distance. The bimodal colour distribution of this
globular cluster system, as well as the different radial distribution of blue
and red clusters, up to these large distances from the parent galaxy, are
confirmed. The azimuthal globular cluster distribution exhibits asymmetries
that might be understood in terms of tidal stripping of globulars from NGC
1387, a nearby galaxy. The good agreement between the areal density profile of
blue clusters and a projected dark-matter NFW density profile is emphasized.Comment: 9 pages, 9 figures. Accepted for publication in A&
Granular discharge and clogging for tilted hoppers
We measure the flux of spherical glass beads through a hole as a systematic
function of both tilt angle and hole diameter, for two different size beads.
The discharge increases with hole diameter in accord with the Beverloo relation
for both horizontal and vertical holes, but in the latter case with a larger
small-hole cutoff. For large holes the flux decreases linearly in cosine of the
tilt angle, vanishing smoothly somewhat below the angle of repose. For small
holes it vanishes abruptly at a smaller angle. The conditions for zero flux are
discussed in the context of a {\it clogging phase diagram} of flow state vs
tilt angle and ratio of hole to grain size
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