Revisitando a problemática da medição da rotação estelar em sistemas planetários via fotometria - Rios, Luiz Daniel Alves (2024)
The present thesis aims to shed light on the problem of measuring the surface differential rotation (RD) of stars with solar characteristics. In this regard, we present a set of techniques to infer a lower limit of the RD amplitude from photometric time series extracted from the Kepler space mission (especially the star Kepler-17) and light curves of the Sun in different filters. As part of our sample, we conducted a blind test on 10 simulated light curves generated using a MATLAB code that creates time series with differential rotation in two groups: with and without planetary transit. To investigate stellar variability, we used various statistical tools, such as autocorrelation function, wavelet analysis, the Lomb-Scargle Generalized Periodogram (GLS), as well as a two-spot model proposed in the work of Lanza, Chagas e de Medeiros (2014), based on the Monte Carlo technique using Markov Chain (MCMC). As a result, we estimated an Absolute shear for K-17 out of transit of ΔΩ = 0.075 ± 0.005 rad/day and a relative differential rotation amplitude ΔΩ/Ω ≈ 14.6 ± 0.3%. For its autocorrelated light curve with a scale factor n = 8, we found ΔΩ = 0.107 ± 0.007 rad/day and ΔΩ/Ω ≈ 20.1 ± 0.3%. In the case of the Sun, where we used the Lyman-α curve, we found ΔΩ = 0.048 ± 0.002 rad/day and ΔΩ/Ω ≈ 20.6 ± 0.2%. These values are in good agreement with those known in the literature, highlighting the reliability of our approach. The blind test was important to test some parameters (such as transit in the modeling), and we observed that our methods can recover the RD of these curves. In summary, this doctoral thesis makes a significant contribution to the discussion and investigation of RD through the analysis of photometric time series, as our approach yields consistent results and opens new perspectives for analysis, questioning whether using stellar spots as tracers is indeed more suitable for inferring surface RD, which is still a matter of debate in the community. Additionally, we discuss the impact of rotation indicator evolution on the reliability of the measurement.