On the shape of the ascending branch of the light curves of Long Period Variables

Abstract

The present article is written in the wake of a recently published study of the relation between the light curves of Long Period Variables and their evolution along the Asymptotic Giant Branch (AGB). It introduces a pair of new parameters that describe the shape of the ascending branches of such light curves. This parameterization reveals strong correlations with other parameters describing the evolution of the star on the AGB: periods, regularity and amplitudes of the oscillations, effective temperatures, mass loss rates, carbon and oxygen isotopic ratios, colour indices. It sheds new light on the occasional presence of humps on the ascending branches and on the distinction between stars that have not experienced strong Third Dredge Up (TDU) events and those that have as well as between oxygen-rich and carbon-rich stars. One of the new parameters, referred to as q, is particularly efficient at tracking the evolution of the star along the AGB. Globally, a simple picture can be drawn in the plane spanned by the period and by q. Yet, many details remain unexplained when looking at this picture in finer details. Overall, the results presented in the article help significantly with clarifying the complex set of observations that have been made in this domain and should inspire new considerations on their relation with the underlying physical mechanisms at stake inside the stars.

Figures (22)

• Figure 1: Schematic evolution of the light curves in parameter space ($W$ vs $A$ projection in the left panel and $W$ vs $P$ projection in the right panel) as depicted in Paper II. Crosses show mean and rms values of the samples listed in the inserts, where Table 2 stands for Mno spectral types split in three groups of temperature increasing with decreasing $W$, Table 3 and Table 4 for other M spectral types and S spectral types evolving toward lower, and respectively larger, values of $W$, and Table 5 for carbon-rich stars. Coloured ellipses approximate the regions covered by these samples. Arrows show the suggested evolution as described in the text: black for Mno stars, blue and red for stars experiencing strong TDU events, the former stopping pulsating regularly while possibly transiting to the carbon-rich stars of the sample.
• Figure 2: Mean normalized ascending branches of the light curves of V CrB (left) and of chi Cyg (right). Averaging is made either on magnitude (black) or on luminosity (red).
• Figure 3: From left to right: Dependence on $x$ of the three terms of the fit function $S(x)$; for clarity, $h(x)$ has been scaled down by a factor 10. Definition of four directions in the $p$ vs $q$ plane used to illustrate the evolution of the ascending branch profiles when spanning across it, which is done in the four rightmost panels.
• Figure 4: Left: $\chi^2$ distributions (in blue for $\varepsilon_1$=$\varepsilon_2$=0, in red for $\varepsilon_1$ and $\varepsilon_2$ free to vary). Centre-left: distributions of the best-fit values of $\varepsilon_1$ and $\varepsilon_2$. Centre-right: distribution of the improvement in $\chi^2$ due to the freedom given to $\varepsilon_1$ and $\varepsilon_2$ to vary. Right: distribution of the resulting shifts in $p$ and $q$, $\Delta{p}$ and $\Delta{q}$.
• Figure 5: Six examples of $\chi^2$ maps. The level of the white contour is twice that of the minimal value.