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

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.