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Projecte llegit

Títol: Bifurcations of equilibrium points in non-centered barred galaxies

Estudiants que han llegit aquest projecte:

Director/a: SÁNCHEZ MARTÍN, PATRICIA

Departament: MAT

Títol: Bifurcations of equilibrium points in non-centered barred galaxies

Data inici oferta: 23-01-2024     Data finalització oferta: 23-09-2024


Estudis d'assignació del projecte:
    DG ENG AERO/SIS TEL
    DG ENG AERO/TELEMÀT
Tipus: Individual
 
Lloc de realització: EETAC
 
Segon director/a (UPC): MASDEMONT SOLER, JOSEP JOAQUIM
 
Paraules clau:
Equilibrium Points, Barred Galaxies
 
Descripció del contingut i pla d'activitats:
Barred galaxies, which are characterized by a central bar composed of stars, exhibit a notable dynamical behavior wherein the equilibrium points contribute to organizing the dynamics of the system. In some galaxies, such as the Large Magellanic Cloud, the bar is displaced from its central position, which results in a bifurcation of the equilibrium points. In classical models, where the bar is centered, the model has five equilibrium points with two of them exhibiting a saddle x centre x centre behavior (with realistic parameters of the galaxy) around which the arms of the galaxy emanate. The present study aims to investigate the bifurcations of the equilibrium points depending on the position of the bar and other parameters of the system. This would allow us to explain galaxies with different numbers of arms.
 
Overview (resum en anglès):
Barred galaxies are a common type of galaxy, representing about nearly two-thirds of all spiral galaxies, including our own Milky Way. They have an elongated, bar-shaped central structure, mainly made up of stars. This bar acts as a bridge that channels gas and stars towards the center of the galaxy, promoting star formation and the evolution of the galaxy's nucleus. In the outer region, spiral arms or rings evolve, whose origin, though not yet fully understood, may be explained by the theory that they are formed by the hyperbolic invariant manifolds associated with periodic or quasi-periodic orbits around the unstable equilibrium points of the system.

This project studies the dynamical behaviour of equilibrium points in asymmetric galactic models where the center of mass is offset from the center of the galaxy's bar. By shifting galactic components, such as the bulge and the bar, and analysing the bifurcation of equilibrium points as the configuration of the system evolves, the study provides information on the stability and evolution of these equilibrium points regarding this displacement. The project employs simulations to examine in detail how the Lagrangian points shift and bifurcate when the galaxy is not symmetrical.

In order to analyse these results, the galactic system is modelled taking into account each of its components. In addition, a root-finding algorithm is set up to calculate the equilibrium points from an approximate input file. Finally, the stability of each of the equilibrium points is determined according to the eigenvalues of the Jacobian matrix.

The results of the work present a number of interesting conclusions. Firstly, we observe that a long displacement in the X-direction of the bulge with respect to the center of mass of the bar gives rise to the appearance of two new equilibrium points. One of these is stable, while the other is unstable, resulting from the reconfiguration of the system's potential.

Additionally, two scenarios are examined, where minor displacements in the X and Y directions relative to the bar's center of mass result in a modification of the behaviour of the system, reducing the number of equilibrium points from five to three, or vice versa. In these transitions where the number of equilibrium points is altered, a detailed analysis is conducted on smaller displacement steps, along with an investigation into the impact of this change on the stability of the system's equilibrium points.

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