Analytic models of self-gravitating rotating gaseous tori with central black hole

In this thesis project, I present stationary models of rotating fluids with toroidal distributions that can be used to represent the active galactic nuclei (AGN) central obscurers, i.e. molecular tori (Combes et al., 2019), as well as geometrically thick accretion discs, like ADAF discs (Narayan and Yi, 1995) or Polish doughnuts (Abramowicz, 2005). In particular, I study stationary rotating systems with a more general baroclinic distribution (with a vertical gradient of the angular velocity), which are often more realistic and less studied, due to their complexity, than the barotropic ones (with cylindrical rotation), which are easier to construct. In the thesis, I compute analytically the main intrinsic and projected properties of the power-law tori based on the potential-density pairs of Ciotti and Bertin (2005). I study the density distribution and the resulting gravitational potential for different values of α, in the range 2 < α < 5. For the same models, I compute the surface density of the systems when seen face-on and edge-on. I then apply the stationary Euler equations to obtain rotational velocity and temperature distributions of the self-gravitating models in the absence of an external gravitational potential. In the thesis I also consider the power-law tori with the presence of a central black hole in addition to the gas self-gravity, and solving analytically the stationary Euler equations, I compute how the properties of the system are modified by the black hole and how they vary as a function of the black hole mass. Finally, applying the Solberg-Høiland criterion, I show that these baroclinic stationary models are linearly stable in the absence of the black hole. In the presence of the black hole I derive the analytical condition for stability, which depends on α and on the black hole mass. I also study the stability of the tori in the hypothesis that they are weakly magnetized, finding that they are always unstable to this instability.

Methodologies for attitude determination from MEMS sensors in vehicles

The focus of the thesis is the application of different attitude’s determination algorithms on data evaluated with MEMS sensor using a board provided by University of Bologna. MEMS sensors are a very cheap options to obtain acceleration, and angular velocity. The use of magnetometers based on Hall effect can provide further data. The disadvantage is that they have a lot of noise and drift which can affects the results. The different algorithms that have been used are: pitch and roll from accelerometer, yaw from magnetometer, attitude from gyroscope, TRIAD, QUEST, Magdwick, Mahony, Extended Kalman filter, Kalman GPS aided INS. In this work the algorithms have been rewritten to fit perfectly with the data provided from the MEMS sensor. The data collected by the board are acceleration on the three axis, angular velocity on the three axis, magnetic fields on the three axis, and latitude, longitude, and altitude from the GPS. Several tests and comparisons have been carried out installing the electric board on different vehicles operating in the air and on ground. The conclusion that can be drawn from this study is that the Magdwich filter is the best trade-off between computational capabilities required and results obtained. If attitude angles are obtained from accelerometers, gyroscopes, and magnetometer, inconsistent data are obtained for cases where high vibrations levels are noticed. On the other hand, Kalman filter based algorithms requires a high computational burden. TRIAD and QUEST algorithms doesn’t perform as well as filters.

Angular momentum of S0 galaxies

The aim of this thesis is to study the angular momentum of a sample of S0 galaxies. In the quest to understand whether the formation of S0 galaxies is more closely linked to that of ellipticals or that of spirals, our goal is to compare the amount of their specific angular momentum as a function of stellar mass with respect to spirals. Through kinematic comparison between these different classes of galaxies we aim to understand if a scenario of passive evolution, in which the galaxy’s gas is consumed and the star formation is quenched, can be considered as plausible mechanism to explain the transformation from spirals to S0s. In order to derive the structural and photometric parameters of galaxy sub-components we performed a bulge-disc decomposition of optical images using GALFIT. The stellar kinematic of the galaxies was measured using integral field spectroscopic data from CALIFA survey. The development of new original software, based on a Monte Carlo Markov Chain algorithm, allowed us to obtain the values of the line of sight velocity and velocity dispersion of disc and bulge components. The result that we obtained is that S0 discs have a distribution of stellar specific angular momentum that is in full agreement with that of spiral discs, so the mechanism of simple fading can be considered as one of the most important for transformation from spirals to S0s.