Atlas of the Light Curves and Phase Plane Portraits of Selected Long-Period Variables

Abstract

For a group of the Mira-type stars, semi-regular variables and some RV Tau - type stars the limit cycles were computed and plotted using the phase plane diagrams. As generalized coordinates x and $\dot{x},$ we have used $\phi$ - the brightness of the star and its phase derivative. We have used mean phase light curves using observations of various authors from the databases of AAVSO, AFOEV, VSOLJ, ASAS and approximated using a trigonometric polynomial of statistically optimal degree. As generalized coordinates x and $\dot{x}$, we have used m - the brightness of the star and its phase derivative. For a simple sine-like light curve, 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.