Automatic classification of stellar orbits in axisymmetric potentials

Within the classification of orbits in axisymmetric stellar systems, we present a new algorithm able to automatically classify the orbits according to their nature. The algorithm involves the application of the correlation integral method to the surface of section of the orbit; fitting the cumulative distribution function built with the consequents in the surface of section of the orbit, we can obtain the value of its logarithmic slope m which is directly related to the orbit’s nature: for slopes m ≈ 1 we expect the orbit to be regular, for slopes m ≈ 2 we expect it to be chaotic. With this method we have a fast and reliable way to classify orbits and, furthermore, we provide an analytical expression of the probability that an orbit is regular or chaotic given the logarithmic slope m of its correlation integral. Although this method works statistically well, the underlying algorithm can fail in some cases, misclassifying individual orbits under some peculiar circumstances. The performance of the algorithm benefits from a rich sampling of the traces of the SoS, which can be obtained with long numerical integration of orbits. Finally we note that the algorithm does not differentiate between the subtypes of regular orbits: resonantly trapped and untrapped orbits. Such distinction would be a useful feature, which we leave for future work. Since the result of the analysis is a probability linked to a Gaussian distribution, for the very definition of distribution, some orbits even if they have a certain nature are classified as belonging to the opposite class and create the probabilistic tails of the distribution. So while the method produces fair statistical results, it lacks in absolute classification precision.

Back-in-time void finder: dynamical detection of cosmic voids for precision cosmology

Cosmic voids are vast and underdense regions emerging between the elements of the cosmic web and dominating the large-scale structure of the Universe. Void number counts and density profiles have been demonstrated to provide powerful cosmological probes. Indeed, thanks to their low-density nature and they very large sizes, voids represent natural laboratories to test alternative dark energy scenarios, modifications of gravity and the presence of massive neutrinos. Despite the increasing use of cosmic voids in Cosmology, a commonly accepted definition for these objects has not yet been reached. For this reason, different void finding algorithms have been proposed during the years. Voids finder algorithms based on density or geometrical criteria are affected by intrinsic uncertainties. In recent years, new solutions have been explored to face these issues. The most interesting is based on the idea of identify void positions through the dynamics of the mass tracers, without performing any direct reconstruction of the density field. The goal of this Thesis is to provide a performing void finder algorithm based on dynamical criteria. The Back-in-time void finder (BitVF) we present use tracers as test particles and their orbits are reconstructed from their actual clustered configuration to an homogeneous and isotropic distribution, expected for the Universe early epoch. Once the displacement field is reconstructed, the density field is computed as its divergence. Consequently, void centres are identified as local minima of the field. In this Thesis work we applied the developed void finding algorithm to simulations. From the resulting void samples we computed different void statistics, comparing the results to those obtained with VIDE, the most popular void finder. BitVF proved to be able to produce a more reliable void samples than the VIDE ones. The BitVF algorithm will be a fundamental tool for precision cosmology, especially with upcoming galaxy-survey.

Dynamics of galaxies in the cluster environment: a resonant origin for the ISP?

The internal dynamics of elliptical galaxies in clusters depends on many factors, including the environment in which the galaxy is located. In addition to the strong encounters with the other galaxies, we can also consider the gravitational interaction with the ubiquitous Cluster Tidal Field (CTF). As recognized in many studies, one possible way in which CTF affects the dynamics of galaxies inside the cluster is related to the fact that they may start oscillating as “rigid bodies” around their equilibrium positions in the field, with the periods of these oscillations curiously similar to those of stellar orbits in the outer parts of galaxies. Resonances between the two motions are hence expected and this phenomenon could significantly contribute to the formation of the Intracluster Stellar Population (ISP), whose presence is abundantly confirmed by observations. In this thesis work, we propose to study the motion of an elliptical galaxy, modelled as a rigid body, in the CTF, especially when its center of mass traces a quasi-circular orbit in the cluster gravitational potential. This case extends and generalizes the previous models and findings, proceeding towards a much more realistic description of galaxy motion. In addition to this, the presence of a further oscillation, namely that of the entire galaxy along its orbit, will possibly increase the probability of having resonances and, consequently, the rate of ISP production nearly to observed values. Thus, after reviewing the dynamics of a rigid body in a generic force field, we will assess some physically relevant studies and report their main results, discussing their implications with respect to our problem. We will conclude our discussion focusing on the more realistic scenario of an elliptical galaxy whose center of mass moves on a quasi-circular orbit in a spherically symmetric potential. The derivation of the fundamental equations of motion will serve as the basis for future modelling and discussions.

Ephemeris generation of the Galilean moons by using VLBI observations in support to stellar occultations

Stellar occultations are the most accurate Earth-based astronomy technique to obtain the lateral position of celestial bodies, in the case of natural satellites, their accuracy also depends on the central body to which the satellite orbits. The main goal of this thesis work is to analyze if and how very long baseline interferometry (VLBI) measurements of a body like Jupiter can be used in support to stellar occultations of its natural satellites by reducing the planetary uncertainty at the time of the occultation. In particular, we analyzed the events of the stellar occultations of Callisto (15.01.2024) and Io (02.04.2021). The stellar occultation of Callisto has been predicted and simulated using the stellar occultation reduction analysis (SORA) toolkit while the stellar occultation of Io has been already studied by Morgado et al. We then simulated the VLBI data of Jupiter according to the current JUNO trajectories. The required observation were then used as input of an estimation to which then we performed a covariance analysis on the estimated parameters to retrieve the formal errors (1 − σ uncertainties) at each epoch of the propagation. The results show that the addition of the VLBI slightly improves the uncertainty of Callisto even when Jupiter knowledge is worse while for Io we observed that the VLBI data is especially crucial in the scenario of an a priori uncertainty in Jupiter state of about 10km. Here we can have improvements of the estimated initial states of Io of about 70m, 230m and 900m to the radial, along-track and cross-track directions respectively. Moreover, we have also obtained the propagated errors of the two moons in terms of right ascension and declination which both show uncertainties in the mas level at the occultation time. Finally, we simulated Io and Europa together and we observed that at the time of the stellar occultation of Europa the along-track component of Io is constrained, confirming the coupling between the two inner moons.