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

Technical Deep Dive: On the shape of the ascending branch of the light curves of Long Period Variables

Overview

This technical deep dive examines the relationship between the light curves of Long Period Variables (LPVs) and the evolution of these stars along the Asymptotic Giant Branch (AGB). The study focuses on analyzing the shape of the ascending branch of the light curves, using two new parameters, p and q, that describe this feature. The analysis reveals strong correlations between these shape parameters and other stellar parameters, providing new insights into how the light curve evolution is linked to the physical processes occurring within these pulsating stars.

Methodology

• The study analyzed a sample of 93 well-measured light curves of LPVs, including 25 Mno (no technetium detected), 10 Myes (technetium detected), 18 S, and 21 C-type stars.
• Each light curve's ascending branch was normalized and fit to a two-parameter function, with p representing the slope and q representing the curvature at the midpoint of the ascending branch.
• The distributions of p and q for different spectral types were analyzed, and correlations were examined between the shape parameters and other stellar properties like period, amplitude, color index, and regularity.

Results

Mno (no technetium) stars

• Mno stars show a clear correlation between q and other stellar parameters, with q increasing as the star evolves along the AGB.
• As q increases, the period, spectral type index, and width parameter W also increase, while the oscillation amplitude and regularity decrease.
• A subset of 8 "outlier" Mno stars were identified that have distinctly different ascending branch shapes compared to the other Mno stars.

Myes (technetium detected) and S stars

• Myes and S stars cover a broad region of the p-q parameter space, suggesting diverse evolutionary paths.
• Some Myes/S stars ("My1", "S1") appear to be direct successors of the warmer Mno stars, with a large increase in oscillation amplitude when transitioning from Mno to Myes.
• Other Myes/S stars ("My2", "S2") have q values similar to the warmer Mno stars, possibly indicating a separate evolutionary track.
• A distinct group of low-q S stars ("S3") may be the progeny of the My2/S2 stars, though the exact connections are uncertain.

Carbon-rich (C) stars

• The transition from S to C spectral type is marked by a significant drop in oscillation amplitude and increase in period and W.
• C stars span a wide range of q values, with lower q associated with higher temperatures, lower mass loss rates, and lower carbon isotope ratios.

Interpretation

• The results suggest a general continuity in the evolution of light curve shapes as LPVs progress along the AGB, with q serving as a useful proxy for tracking this evolution.
• However, exceptions and irregularities in the observed trends point to gaps in the current understanding of the physical mechanisms governing the transition between stable and unstable pulsation regimes.
• The identification of distinct groups and outliers, as well as the complex relationships between light curve shapes and stellar properties, highlight the need for further investigation into the detailed physics underlying these phenomena.

Limitations & Uncertainties

• The analysis relies on the assumption that continuity in stellar evolution corresponds to continuity in light curve evolution, which may not always hold true.
• The sample size, while substantial, is still limited, and the assignments of spectral types (particularly for stars with unknown technetium content) introduce some uncertainty.
• The two-parameter p-q model, while effective in many cases, does not perfectly capture all the complexities observed in the light curve shapes.
• The physical mechanisms driving the transitions between different pulsation regimes and spectral types remain poorly understood.

Future Directions

• Expand the sample size and improve spectral type classifications to further validate the observed trends and groupings.
• Investigate the physical processes responsible for the transitions between stable and unstable pulsation regimes, as well as the links between light curve shapes and the underlying stellar properties and evolutionary stages.
• Explore alternative parameterizations or analysis techniques that may reveal additional insights into the light curve-stellar evolution connection.
• Integrate these findings with other observational and theoretical work to develop a more comprehensive understanding of LPV behavior and evolution.