Aplicações da disentropia da autocorrelação e da função Wq de Lambert-Tsallis em astronomia

Abstract

This thesis addresses some applications of the disentropy of the autocorrelation and the Lambert-Tsallis Wq function in astronomy. Initially, the disentropy of the autocorrelation, which is a measure of randomness, is used in three problems: I) Calculating the randomness of cosmic microwave background (CMB) maps. II) Erasing background stars in astronomical images. III) Calculating the randomness of the actual signal from a pulsar used as a random number generator. The first problem shows that the randomness in CMB maps is high and reaches its maximum value when signals from the Milky Way are erased from the map. In the second problem, the proposed algorithm erases regions of the astronomical image that have high randomness, highlighting large structures. Finally, the third problem shows that the randomness of the signal coming from the pulsar PSR J0437-4715 increases as the interval between the pulses considered increases. The maximum randomness is achieved when pulses are collected in batches of 6. In the second part of the thesis, the Lambert-Tsallis Wq function is used in two problems: I) In the analysis of the pulsar's rotation frequency from the frequency of the gravitational wave emitted by that same pulsar; II) In the approximation of the solution to Kepler's equation. In the first case, the branch point of the Wq function is used to obtain a relationship between the coefficients of the rotation frequency equation, the frequency of the emitted gravitational wave, and the Keplerian breakup frequency. In the second case, a numerical algorithm using Wq is presented that calculates the solution to Kepler's equation of celestial mechanics with an error of less than 10-4 when the eccentricity of the orbital ellipse is less than or equal to 0.3.