PHASE PLANE ANALYSIS OF THE PHOTOMETRICAL VARIATIONS OF LONG-PERIOD VARIABLES

Apply

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

Mira-type stars semi-regular variables limit cycle phase plane diagrams

EP ID EP348993
DOI 10.18524/1810-4215.2017.30.114346
Views 75
Downloads 0