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Asteroseismology is the study of oscillations in stars, which aids in understanding the interior structure and dynamics of stars. In the last two decades, NASA's Kepler and TESS space missions have revolutionized the field of asteroseismology by providing a vast dataset of photometric time series of hundreds of thousands of stars. In this talk, I will be discussing the application of asteroseismology in studying the differential rotation in stars, and our machine learning technique that we use to measure the differential rotation. The envelope of the stars doesn't rotate with a constant rate along the latitude. The latitudinal differential rotation and the magnetic activity on the star's surface are believed to be interrelated. The differential rotation between the equator and poles of the Sun is 30% cent of the average rotation rate. It is difficult to detect differential rotation in red giants compared to main-sequence stars, as the envelope rotation rates in these stars are comparatively lower, and also, because of the presence of mixed modes (resulting from the coupling of g-modes and p-modes), their spectra are more complex and hence, in most of the red giants, the mixed modes are overlapped with the higher degree p-modes. I will be presenting our results of detecting non-zero differential rotation in 5 red giants from the Kepler's dataset. We use a machine learning algorithm to infer the important seismic parameters of a star, and then we use the machine inferences as the prior probability distributions to fit the spectra by either of these two methods - one is a standard Bayesian approach, combined with a Markov chain Monte Carlo(MCMC) algorithm, which takes from a few days to a few weeks to fit the spectrum of a single star, and the other is the Gradient Descent method, which only takes a few hours to fit a spectrum.
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