Two Centuries of a Pulsating Giant: How R Leonis Changed Its Rhythm and Dusty Veil
In this paper, first author Mike Goldsmith studies the Mira variable star R Leonis using more than 200 years of brightness observations to ask a deceptively simple question: how stable is this star over time? Mira variables are red giant stars that brighten and fade in a regular rhythm, driven by pulsations in their outer layers. R Leonis is especially well suited for this kind of long-term study because it has been observed since the late 18th century, with tens of thousands of visual brightness estimates now archived, mainly through the American Association of Variable Star Observers. By carefully extracting the dates and brightnesses of the star’s maxima (brightest points) and minima (dimmest points), the paper looks for slow changes that unfold over decades rather than single cycles.
Physical Background: Pulsations, Molecules, and Dust
The introduction explains the physical picture behind R Leonis’s variability. Its roughly 312-day pulsation period is set by the kappa mechanism, where changes in opacity trap and release energy in the star’s atmosphere. These pulsations generate shock waves that allow molecules such as TiO and H₂O to form, along with dust grains made of silicates and oxides. Together, molecules and dust strongly dim the star at minimum light. While much of this material is destroyed as the star reheats toward maximum light, some dust survives and is pushed outward, gradually building a complex circumstellar environment. Because dust shells are known to evolve over many decades, the author argues that long historical light curves provide a rare window into these slow processes.
Extracting Reliable Maxima and Minima from Historical Data
A large part of the paper is devoted to how reliable maxima and minima values are extracted from noisy historical data. For minima, the author fits a mathematical curve to the deepest part of each cycle, carefully accounting for differences between observers. Maxima are treated differently, using a non-parametric approach that averages many measurements without assuming a fixed light-curve shape. These results are then combined with earlier published compilations to produce a final dataset of 181 maxima and 138 minima. This careful groundwork is essential, because the changes being studied are often only a few tenths of a magnitude, comparable to typical observer uncertainties.
Changes in Period and Timing over Two Centuries
The temporal analysis shows that R Leonis’s pulsation period is not perfectly constant. Over the past two centuries, the mean period has shortened by about three days, a change of roughly one percent. On top of this slow trend are clear modulations on timescales of about 35 and 98 years. Using observed-minus-calculated (O–C) diagrams, the paper shows that when one minimum or maximum arrives early or late, the following extrema tend to do the same for several cycles in a row. This timing “memory” lasts for about 10 to 12 years before fading, suggesting that the pulsation is influenced by slowly varying internal processes rather than random noise alone.
Non-Random Behavior of Minima Depths
The most striking results come from the analysis of extrema depths. Statistical tests show that the depths of minima are strongly non-random: adjacent minima are much more similar to each other than would be expected by chance. On average, neighboring minima differ by only about 0.26 magnitudes, compared to 0.38 magnitudes for randomly chosen pairs. This similarity persists for surprisingly long intervals, up to about 50 cycles or roughly 43 years. Maxima, in contrast, show much weaker and mostly insignificant evidence for such memory. Periodicity tests suggest a broad, century-scale pattern in minimum depths, but the author emphasizes that the dataset is still too short to confirm a true cycle.
Long-Term Brightness Trends and the Role of Dust
To understand what these patterns mean physically, the paper examines long-term averages of minima and maxima brightness. When the data are smoothed over windows of several dozen cycles, clear multi-decade trends emerge, including extended periods of gradual dimming or brightening. Goldsmith argues that these changes are best explained by variations in circumstellar dust rather than changes in the star’s pulsation itself. Small imbalances between dust formation and removal, amounting to only a fraction of the dust produced each year, are enough to account for the observed long-term dimming at minimum light. Because dust blocks a larger fraction of light when the star is faint, minima are more strongly affected than maxima.
Conclusions and Broader Implications
The paper paints a picture of R Leonis as a star with a long memory. Its pulsation period slowly evolves, its timings drift coherently over several cycles, and, most importantly, its dust environment changes over decades, leaving a clear imprint on the depths of its minima. While the exact physical mechanisms remain uncertain, the study shows how historical visual observations, despite their limitations, can reveal subtle evolutionary changes when analyzed with modern statistical tools. Even “regular” variable stars are far from static: over a human lifetime, and certainly over two centuries, they can change in measurable and meaningful ways.
Source: Goldsmith
