PHASE PLANE ANALYSIS OF THE PHOTOMETRICAL VARIATIONS OF LONG-PERIOD VARIABLES
Journal Title: Odessa Astronomical Publications - Year 2017, Vol 30, Issue
Abstract
Using the phase plane diagrams, the phase light curves of a group of the Mira-type stars and semi-regular variables are analyzed. As generalized coordinates х and ẋ, we have used m – the brightness of the star and its phase derivative. We have used mean phase light curves using observations of various authors. The data typically span a large time interval (nearly a century). They were compiled from the databases of AAVSO, AFOEV, VSOLJ, ASAS and approximated using a trigonometric polynomial of statistically optimal degree. As the resulting approximation characterizes the autooscillation process, which leads to a photometrical variability, the phase diagram corresponds to a limit cycle. For all stars studied, the limit cycles were computed. For a simple sine-like light curve, in e.g., L2 Pup, the limit cycle is a simple ellipse. In a case of more complicated light curve, in which harmonics are statistically significant, the limit cycle has deviations from the ellipse. In an addition to a classical analysis, we use the error estimates of the smoothing function and its derivative to constrain an “error corridor” in the phase plane.
Authors and Affiliations
L. S. Kudashkina, I. L. Andronov
Keywords
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- EP ID EP348993
- DOI 10.18524/1810-4215.2017.30.114346
- Views 99
- Downloads 0
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