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.Comment: 11 pages, 14 figures. Accepted for publication in MNRA

Orbit classification in the meridional plane of a disk galaxy model with a spherical nucleus

We investigate the regular or chaotic nature of star orbits moving in the meridional plane of an axially symmetric galactic model with a disk and a spherical nucleus. We study the influence of some important parameters of the dynamical system, such as the mass and the scale length of the nucleus, the angular momentum or the energy, by computing in each case the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families. Some heuristic arguments to explain and justify the numerically derived outcomes are also given. Furthermore, we present a new method to find the threshold between chaos and regularity for both Lyapunov Characteristic Numbers and SALI, by using them simultaneously.Comment: Published in Celestial Mechanics & Dynamical Astronomy (CMDA) journa

LP-VIcode: a program to compute a suite of variational chaos indicators

An important point in analysing the dynamics of a given stellar or planetary system is the reliable identification of the chaotic or regular behaviour of its orbits. We introduce here the program LP-VIcode, a fully operational code which efficiently computes a suite of ten variational chaos indicators for dynamical systems in any number of dimensions. The user may choose to simultaneously compute any number of chaos indicators among the following: the Lyapunov Exponents, the Mean Exponential Growth factor of Nearby Orbits, the Slope Estimation of the largest Lyapunov Characteristic Exponent, the Smaller ALignment Index, the Generalized ALignment Index, the Fast Lyapunov Indicator, the Othogonal Fast Lyapunov Indicator, the dynamical Spectra of Stretching Numbers, the Spectral Distance, and the Relative Lyapunov Indicator. They are combined in an efficient way, allowing the sharing of differential equations whenever this is possible, and the individual stopping of their computation when any of them saturates.Comment: 26 pages, 9 black-and-white figures. Accepted for publication in Astronomy and Computing (Elsevier

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

On a possible origin for the lack of old star clusters in the Small Magellanic Cloud

We model the dynamical interaction between the Small and Large Magellanic Clouds and their corresponding stellar cluster populations. Our goal is to explore whether the lack of old clusters ($\gtrsim 7$ Gyr) in the Small Magellanic Cloud (SMC) can be the result of the capture of clusters by the Large Magellanic Cloud (LMC), as well as their ejection due to the tidal interaction between the two galaxies. For this purpose we perform a suite of numerical simulations probing a wide range of parameters for the orbit of the SMC about the LMC. We find that, for orbital eccentricities $e \geq 0.4$, approximately 15 per cent of the SMC clusters are captured by the LMC. In addition, another 20 to 50 per cent of its clusters are ejected into the intergalactic medium. In general, the clusters lost by the SMC are the less tightly bound cluster population. The final LMC cluster distribution shows a spatial segregation between clusters that originally belonged to the LMC and those that were captured from the SMC. Clusters that originally belonged to the SMC are more likely to be found in the outskirts of the LMC. Within this scenario it is possible to interpret the difference observed between the star field and cluster SMC Age-Metallicity Relationships for ages $\gtrsim 7$ Gyr.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letter

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

And yet it moves: The dangers of artificially fixing the Milky Way center of mass in the presence of a massive Large Magellanic Cloud

Motivated by recent studies suggesting that the Large Magellanic Cloud (LMC) could be significantly more massive than previously thought, we explore whether the approximation of an inertial Galactocentric reference frame is still valid in the presence of such a massive LMC. We find that previous estimates of the LMC's orbital period and apocentric distance derived assuming a fixed Milky Way are significantly shortened for models where the Milky Way is allowed to move freely in response to the gravitational pull of the LMC. Holding other parameters fixed, the fraction of models favoring first infall is reduced. Due to this interaction, the Milky Way center of mass within the inner 50 kpc can be significantly displaced in phase-space in a very short period of time that ranges from 0.3 to 0.5 Gyr by as much as 30 kpc and 75 km/s. Furthermore, we show that the gravitational pull of the LMC and response of the Milky Way are likely to significantly affect the orbit and phase space distribution of tidal debris from the Sagittarius dwarf galaxy (Sgr). Such effects are larger than previous estimates based on the torque of the LMC alone. As a result, Sgr deposits debris in regions of the sky that are not aligned with the present-day Sgr orbital plane. In addition, we find that properly accounting for the movement of the Milky Way around its common center of mass with the LMC significantly modifies the angular distance between apocenters and tilts its orbital pole, alleviating tensions between previous models and observations. While these models are preliminary in nature, they highlight the central importance of accounting for the mutual gravitational interaction between the MW and LMC when modeling the kinematics of objects in the Milky Way and Local Group.Comment: Accepted for publication in ApJ; 16 pages, 11 figure

Weyl type theorems for restrictions of bounded linear operators

In this paper we give sufficient conditions for which Weyl’s theorems for a bounded linear operator T, acting on a Banach space X, can be reduced to the study of Weyl’s theorems for some restriction of T.peerReviewe

Weyl type theorems for restrictions of bounded linear operators

In this paper we give sufficient conditions for which Weyl’s theorems for a bounded linear operator T, acting on a Banach space X, can be reduced to the study of Weyl’s theorems for some restriction of T.peerReviewe