Khagol Bulletin # 136 (Apr 2025) - ENG

| 10 | KHAG L | No. 136 - APRIL 2025 Dr. DipanjanMukherjee is an Associate Professor at IUCAA. Prof. Mukherjee's research interests are primarily on the topic of computational astrophysics with a broad region of application, from fluid flows near compact objects to galaxy evolution and physics of relativistic jets. Dynamical transitions in stars- a data driven approach Recent research at all levels is highly med i a t ed by d i g i t a l da t a , e i the r experimental or observational, and the increase in the availability of a large number of data sets makes this all the more demanding. This is especially so in the area of astronomy and astrophysics, where large amounts of observational data are waiting to be analysed for an understanding of the astrophysical sources and events that generate the data. Hence, computationally efficient and reliable algorithms that can extract knowledge out of data is the need of the day. Most often, the dynamical processes guiding the evolution of such sources like stars are not fully understood, and we have to depend on observational data to arrive at their dynamics, which necessitates a data driven approach in their study. In this context, the techniques developed in nonlinear time series analysis provide powerful methods to detect nontrivial structures in such data that will indicate the nature of the underlying dynamics. We will see how these techniques can be applied to observational data of the light curves from stars to reconstruct the dynamics, so that we can understand the variability and transitions in their dynamics. Let us start with the familiar example of a pulsating irregular variable star for which stellar pulsations result in irregular light curves. The reconstruction techniques discussed below give strong evidence that the light curves of many variable stars like R UMi, RS Cyg, UX Dra, SX Her, W Vir, R Scuti, etc. are generated by a low- d imens i ona l chao t i c pu l s a t i ona l dynamics[1,2]. To reconstruct the dynamics of a star from its light curve or intensity data, the method of time delay embedding is used by defining delay vectors on its phase space of dimensionMas, Here, τ is the delay time and M is the e m b e d d i n g d i m e n s i o n o f t h e reconstructed phase space. One of the methods to estimate τ is to look for the time when the autocorrelation C( τ ) falls to 1/e of C(0), and that for M is the method of False Nearest Neighbours [3]. The intricate dynamical structure of the reconstructed dynamics is then captured from the recurrence pattern of its trajectory points in the M-dimensional phase space. For this, the recurrences are defined as points which are closer than a chosen threshold e and a 2-d Recurrence Plot (RP) is derived from them, displaying all the recurring points. We mention two important measures defined on the RP, Determinism(DET), which comes from the distribution of diagonal line segments and Laminarity (LAM) from that of vertical line segments. These reflect the nature of the dynamics and hence can differentiate periodic, chaotic, and noisy dynamics. Sudden changes in dynamics can occur with small changes in the parameters or can be induced by stochastic effects. Such changes in the dynamics, called critical transitions, will cause variations in the phase space structure even prior to the transition and therefore can be detected and quantified by recreating the dynamics over time in windows that are shifted over the data. The corresponding changes in the pattern of recurrences can be analysed using DET and LAM, calculated in each window over time. Then the transitions in dynamics will become evident as significant changes in these measures. They can even be tailored to predict upcoming transitions or major changes in dynamics. Our recent research on the data from Betelgeuse illustrates the efficiency of this procedure [4]. Betelgeuse [ α Orionis, HD 39801, M1- of radio AGN in the local Universe. Themost massive galaxies are always switched on. A&A 2019, 622, A17. Molyneux, S.J.; Calistro Rivera, G.; et al. The Quasar Feedback Survey: characterizing CO excitation in quasar host galaxies. MNRAS2024, 527, 4420–4439. Kukreti, P.; Morganti, R.; Tadhunter, C.; Santoro, F. Ionised gas outflows over the radio AGN life cycle. A&A 2023, 674, A198.