Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic models, fully incorporating the time-dependent nature of the systems. Here we aim at analysing the fractions of chaotic motion within different morphological components of the galaxy. We wish to investigate how the presence of chaotic orbits evolves with time, and how their spatial distribution is associated with morphological features of the galaxy. We employ a time-dependent analytical potential model that was derived from an N-body simulation of a strongly barred galaxy. With this analytical potential, we may follow the dynamical evolution of ensembles of orbits. Using the Generalized Alignment Index (GALI) chaos detection method, we study the fraction of chaotic orbits, sampling the dynamics of both the stellar disc and of the dark matter halo. Within the stellar disc, the global trend is for chaotic motion to decrease in time, specially in the region of the bar. We scrutinized the different changes of regime during the evolution (orbits that are permanently chaotic, permanently regular, those that begin regular and end chaotic, and those that begin chaotic and end regular), tracing the types of orbits back to their common origins. Within the dark matter halo, chaotic motion also decreases globally in time. The inner halo (r $łt$ 5 kpc) is where most chaotic orbits are found and it is the only region where chaotic orbits outnumber regular orbits, in the early evolution.

{We present a weak-lensing and dynamical study of the complex cluster Abell 1758 (A175

Context. The stellar metallicity gradients of disc galaxies provide information on disc assembly, star formation processes, and chemical evolution. They also might store information on dynamical processes that could affect the distribution of chemical elements in the gas phase and the stellar components. Understanding their joint effects within a hierarchical clustering scenario is of paramount importance. Aims: We studied the stellar metallicity gradients of simulated discs in a cosmological simulation. We explored the dependence of the stellar metallicity gradients on stellar age and on the size and mass of the stellar discs. Methods: We used a catalogue of galaxies with disc components selected from a cosmological hydrodynamical simulation performed including a physically motivated supernova feedback and chemical evolution. Disc components were defined based on angular momentum and binding energy criteria. The metallicity profiles were estimated for stars with different ages. We confront our numerical findings with results from the Calar Alto Legacy Integral Field Area (CALIFA) Survey. Results: The simulated stellar discs are found to have metallicity profiles with slopes in global agreement with observations. Low stellar mass galaxies tend to have a larger variety of metallicity slopes. When normalized by the half-mass radius, the stellar metallicity gradients do not show any dependence and the dispersion increases significantly, regardless of the galaxy mass. Galaxies with stellar masses o f around 10$^10$M$_⊙$ show steeper negative metallicity gradients. The stellar metallicity gradients correlate with the half-mass radius. However, the correlation signal is not present when they are normalized by the half-mass radius. Stellar discs with positive age gradients are detected to have negative and positive metallicity gradients, depending on the relative importance of recent star formation activity in the central regions. Conclusions: Our results suggest that inside-out formation is the main process responsible for the metallicity and age profiles. The large dispersions in the metallicity gradients as a function of stellar mass could be ascribed to the effects of dynamical processes such as mergers, interactions and/or migration as well as those regulating the conversion of gas into stars. The fingerprints of the inside-out formation seem better preserved by the stellar metallicity gradients as a function of the half-mass radius.

The current standard cosmological scenario predicts that rich clusters of galaxies are still accreting mass. This dynamical activity is reflected on the intracluster plasma surface brightness, which often shows substructures. A remarkable feature observed in cool-core clusters is the presence of a spiral arm (eg., Laganá et al. 2010). The origin of this arm is probably the sloshing of the cool central gas by the off-axis collision of a passing group or cluster (Ascasibar \amp Markevitch 2006).The rich cluster Abell 2052 was extensively studied in X-ray by Blanton et al. (2011). They show the presence of a spiral structure extending more than 250 kpc, which is comprised of cool gas. Using hydrodynamical N-body simulations of cluster collision, we have recovered the dynamical history of Abell 2052 and reproduced the broad morphology of the spiral feature, as compared with newly computed hardness ratio map and X-ray imaging.We obtain two regimes that reproduce the desired features: (I) a close encounter and a recent event (0.8 Gyr since pericentric passage), and (II) a scenario with a larger impact parameter and older event (almost 2.6 Gyr since pericentric passage). Interestingly, in the second case, we were able to identify an observed optical counterpart - based on the light distribution obtained from the SDSS - at the same redshift of the perturbing galaxy group, with M$_500$ = (1.16\plusmn0.43)x10$^13$ M$_sun$ at about 2 Mpc from the centre of the major cluster.

Major mergers between massive clusters have a profound effect in the intracluster gas, which may be used as a probe of the dynamics of structure formation at the high end of the mass function. An example of such a merger is observed at the northern component of Abell 1758, comprising two massive sub-clusters separated by approximately 750 kpc. One of the clusters exhibits an offset between the dark matter and the intracluster gas. We aim to determine whether it is possible to reproduce the specific morphological features of this cluster by means of a major merger. We perform dedicated SPH (smoothed particle hydrodynamics) N-body simulations in an attempt to simultaneously recover several observed features of Abell 1758, such as the X-ray morphology and the separation between the two peaks in the projected galaxy luminosity map. We propose a specific scenario for the off-axis collision of two massive clusters. This model adequately reproduces several observed features and suggests that Abell 1758 is seen approximately 0.4 Gyr after the first pericentric passage, and that the clusters are already approaching their maximum separation. This means that their relative velocity is as low as 380 km s$^-1$. At the same time, the simulated model entails shock waves of \tilde4500 km s$^-1$, which are currently undetected presumably due to the low-density medium. We explain the difference between these velocities and argue that the predicted shock fronts, while plausible, cannot be detected from currently available data.

The intracluster plasma of Abell 2052 exhibits in X-rays a spiral structure extending more than 250 kpc, which is comprised of cool gas. This feature is understood to be the result of gas sloshing caused by the off-axis collision with a smaller subcluster. We aim to recover the dynamical history of Abell 2052 and to reproduce the broad morphology of the spiral feature. To this end, we perform hydrodynamical N-body simulations of cluster collisions. We obtain two regimes that adequately reproduce the desired features. The first scenario is a close encounter and a recent event (0.8 Gyr since pericentric passage), while the second scenario has a larger impact parameter and is older (almost 2.6 Gyr since pericentric passage). In the second case, the simulation predicts that the perturbing subcluster should be located approximately 2 Mpc from the centre of the major cluster. At that position, we are able to identify an observed optical counterpart at the same redshift: a galaxy group with M$_500$ = (1.16 \plusmn 0.43) \times 10$^13$ M$_⊙$.

Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global phase space properties, which are the underlying cause of observed structures. The potentials needed to describe self-consistent models are time dependent. Here, we aim to investigate dynamical properties (regular/chaotic motion) of a non-autonomous galactic system, whose time-dependent potential adequately mimics certain realistic trends arising from N-body barred galaxy simulations. We construct a fully time-dependent analytical potential, modelling the gravitational potentials of disc, bar and dark matter halo, whose time-dependent parameters are derived from a simulation. We study the dynamical stability of its reduced time-independent 2-degrees of freedom model, charting the different islands of stability associated with certain orbital morphologies and detecting the chaotic and regular regions. In the full 3-degrees of freedom time-dependent case, we show representative trajectories experiencing typical dynamical behaviours, i.e. interplay between regular and chaotic motion for different epochs. Finally, we study its underlying global dynamical transitions, estimating fractions of (un)stable motion of an ensemble of initial conditions taken from the simulation. For such an ensemble, the fraction of regular motion increases with time.

We will discuss here how structures observed in clusters of galaxies can provide us insight on the formation and evolution of these objects. We will focus primarily on X-ray observations and results from hydrodynamical $N$-body simulations. This paper is based on a talk given at the School of Cosmology Jose Plinio Baptista – `Cosmological perturbations and Structure Formation' in Ubu/ES, Brazil.

We follow the formation and evolution of bars in N-body simulations of disc galaxies with gas and/or a triaxial halo. We find that both the relative gas fraction and the halo shape play a major role in the formation and evolution of the bar. In gas-rich simulations, the disc stays near-axisymmetric much longer than in gas-poor ones, and, when the bar starts growing, it does so at a much slower rate. Because of these two effects combined, large-scale bars form much later in gas-rich than in gas-poor discs. This can explain the observation that bars are in place earlier in massive red disc galaxies than in blue spirals. We also find that the morphological characteristics in the bar region are strongly influenced by the gas fraction. In particular, the bar at the end of the simulation is much weaker in gas-rich cases. The quality of our simulations is such as to allow us to discuss the question of bar longevity because the resonances are well resolved and the number of gas particles is sufficient to describe the gas flow adequately. In no case did we find a bar which was destroyed. Halo triaxiality has a dual influence on bar strength. In the very early stages of the simulation it induces bar formation to start earlier. On the other hand, during the later, secular evolution phase, triaxial haloes lead to considerably less increase of the bar strength than spherical ones. The shape of the halo evolves considerably with time. We confirm previous results of gas-less simulations that find that the inner part of an initially spherical halo can become elongated and develop a halo bar. However we also show that, on the contrary, in gas-rich simulations, the inner parts of an initially triaxial halo can become rounder with time. The main body of initially triaxial haloes evolves towards sphericity, but in initially strongly triaxial cases it stops well short of becoming spherical. Part of the angular momentum absorbed by the halo generates considerable rotation of the halo particles that stay located relatively near the disc for long periods of time. Another part generates halo bulk rotation, which, contrary to that of the bar, increases with time but stays small. Thus, in our models there are two non-axisymmetric components rotating with different pattern speeds, namely the halo and the bar, so that the resulting dynamics have strong similarities to the dynamics of double bar systems.

Context. The ESA Gaia mission, to be launched during 2013, will observe billions of objects, among which many galaxies, during its 5 yr scanning of the sky. This will provide a large space-based dataset with unprecedented spatial resolution. Aims: Because of its natural Galactic and astrometric priority, Gaia's observational strategy was optimized for point sources. Nonetheless, it is expected that \~10⁶ sources will be extragalactic, and a large portion of them will be angularly small galaxies. Although the mission was designed for point sources, an analysis of the raw data will allow the recovery of morphology of those objects at a \~0.2'' level. This may constitute a unique all-sky survey of such galaxies. We describe the conceptual design of the method adopted for the morphological analysis of these objects as well as first results obtained from data simulations of low-resolution highly binned data. Methods: First, the raw Gaia 1D observations are used to reconstruct a 2D image of the object - this image is known to contain artifacts and reconstruction signatures. Then, parameters characteristic of the reconstructed image are measured, and used for a purely morphological classification. Finally, based on the classification, a light profile is selected (pure-disk, disk+bulge, pure bulge, point source+disk, etc.) and fitted to all Gaia 1D observations simultaneously in a global process using forward modeling. Results: Using simulations of Gaia observations from official Gaia Data Processing and Analysis Consortium tools, we were able to obtain the preliminary classification of the simulated objects at the \~83% level for two classes (ellipticals, spirals/irregulars) or at the \~79%, \~56%, and \~74% levels for three classes (E, S, and I). The morphological parameters of simulated object light profiles are recovered with errors at the following levels: -9 \plusmn 36% for the bulge radius, 11 \plusmn 53% for the bulge intensity, 1 \plusmn 4% for the disk radius, and -1 \plusmn 7% for the disk intensity. From these results, we conclude that it is possible to push the limits of the Gaia space mission by analysing galaxy morphology.

In large scale structure formation, massive systems assemble through the hierarchical merging of less massive ones. Galaxy clusters, being the most massive and thus the most recent collapsed structures, still grow by accreting smaller clusters and groups. In order to investigate the dynamical evolution of the intracluster medium, we perform a set of adiabatic hydrodynamical simulations of binary cluster mergers.

Observed galaxy clusters often exhibit X-ray morphologies suggestive of recent interaction with an infalling subcluster. A3376 is a nearby (z = 0.046) massive galaxy cluster whose bullet-shaped X-ray emission indicates that it may have undergone a recent collision. It displays a pair of Mpc-scale radio relics and its brightest cluster galaxy is located 970 h$^- 1$$_70$ kpc away from the peak of X-ray emission, where the second brightest galaxy lies. We attempt to recover the dynamical history of A3376. We perform a set of N-body adiabatic hydrodynamical simulations using the smoothed particle hydrodynamics (SPH) code GADGET-2. These simulations of binary cluster collisions are aimed at exploring the parameter space of possible initial configurations. By attempting to match X-ray morphology, temperature, virial mass and X-ray luminosity, we set approximate constraints on some merger parameters. Our best models suggest a collision of clusters with mass ratio in the range 1/6-1/8, and having a subcluster with central gas density four times higher than that of the major cluster. Models with small impact parameter (b $łt$ 150 kpc), if any, are preferred. We estimate that A3376 is observed approximately 0.5 Gyr after core passage, and that the collision axis is inclined by i \ap 40\deg with respect to the plane of the sky. The infalling subcluster drives a supersonic shock wave that propagates at almost 2600 km s$^-1$, implying a Mach number as high as mathcal $\$M$\$\tilde 4; but we show how it would have been underestimated as mathcal $\$M$\$\tilde 3 due to projection effects.

The baryonic discs of galaxies are believed to alter the shapes of the dark matter haloes in which they reside. We perform a set of hydrodynamical N-body simulations of disc galaxies with triaxial dark matter haloes, using elliptical discs with a gaseous component as initial conditions. We explore models of different halo triaxiality and also of different initial gas fractions, which allows us to evaluate how each affects the formations of the bar. Due to star formation, models of all halo shapes and of all initial gas fractions reach approximately the same gas content at the end of the simulation. Nevertheless, we find that the presence of gas in the early phases has important effects on the subsequent evolution. Bars are generally weaker for larger initial gas content and for larger halo triaxiality. The presence of gas, however, is a more efficient factor in inhibiting the formation of a strong bar than halo triaxiality is.

Cosmological N-body simulations indicate that the dark matter haloes of galaxies should be generally triaxial. Yet, the presence of a baryonic disc is believed to alter the shape of the haloes. Here we aim to study how bar formation is affected by halo triaxiality and how, in turn, the presence of the bar influences the shape of the halo. We perform a set of collisionless N-body simulations of disc galaxies with triaxial dark matter haloes, using elliptical discs as initial conditions. Such discs are much closer to equilibrium with their haloes than circular ones, and the ellipticity of the initial disc depends on the ellipticity of the halo gravitational potential. For comparison, we also consider models with initially circular discs, and find that the differences are very important. In all cases, the mass of the disc is grown quasi-adiabatically within the haloes, but the time-scale of growth is not very important. We study models of different halo triaxialities and, to investigate the behaviour of the halo shape in the absence of bar formation, we run models with different disc masses, halo concentrations, disc velocity dispersions and also models where the disc shape is kept artificially axisymmetric. We find that the introduction of a massive disc, even if this is not circular, causes the halo triaxiality to be partially diluted. Once the disc is fully grown, a strong stellar bar develops within the halo that is still non-axisymmetric, causing it to lose its remaining non-axisymmetry. In triaxial haloes in which the parameters of the initial conditions are such that a bar does not form, the halo is able to remain triaxial and the circularization of its shape on the plane of the disc is limited to the period of disc growth. We conclude that part of the circularization of the halo is due to disc growth, but part must be attributed to the formation of a bar. Bars in the halo component, which have already been found in axisymmetric haloes, are also found in triaxial ones. We find that initially circular discs respond excessively to the triaxial potential and become highly elongated. They also lose more angular momentum than the initially elliptical discs and thus form stronger bars. Because of that, the circularization that their bars induce on their haloes is also more rapid. We also analyse halo vertical shapes and observe that their vertical flattenings remain considerable, meaning that the haloes become approximately oblate by the end of the simulations. Finally, we also analyse the kinematics of a subset of halo particles that rotate in disc-like manner. These particles occupy a layer around the plane of the disc and their rotation is more important in the spherical halo than in triaxial ones. We also find that, even though the final shape of the halo is roughly independent of the initial shape, the initially triaxial ones are able to retain the anisotropy of their velocity dispersions.