Betelgeuse going Critical

Betelgeuse may explode any moment, between now and a 100 000 years from now. Which is almost the same as ‘now’ in astrophysical terms. Of course, in human lifespan terms, the chances of me witnessing this great event are slim. Nonetheless, Betelgeuse caused quite a fuss in 2019, when it suddenly dimmed so much that the difference was noticeable to the naked eye (see Fig. 1). Later, it began brightening again. One specific explanation of dust blocking off part of the star’s light in our direction has since manifested itself. Compared to our sun, Betelgeuse truly is a giant. It’s radius is somewhere between 600 to 880 times larger than the sun and if Betelgeuse were our host star in place of the sun, the orbit of Jupiter would still be below its surface. But, while outdoing our local star in almost every aspect, there is one way our sun comes out on top: age. Betelgeuse is merely 8 million years old and already considered a case for the stellar grim reaper. For comparison, the sun has existed for around 4 billion years and is thought to be at roughly the half point of its life. The size of Betelgeuse causes the fuel necessary for the nuclear fusion inside it to be used up quicker and forebodes a violent end, when its massive gravitational forces win the struggle against the radiation energy and come crashing down. This violent death of massive stars such as Betelgeuse is called a supernova. 

Early Warning

The authors of today’s paper have taken a look at the long term development of Betelgeuse, from the beginning of modern observations of the star in the 1980s.

Early warnings for an impending change within a dynamical system (stars are no unvarying objects, they are subjected to constant changes and motion within them) can be noted when observing the long term light curve of an object preceding an event, in this case, the dimming episode.

Previous works have pointed out that if dust were responsible, there should have been an excess of infrared light observed close to the dimming as well as a reduction in polarized light due to it passing the dust. Both conditions could not be met according to detailed measurements and analysis.

Any dynamical system can exist in several possible states. These states evolve in a specific pattern and exist for a particular parameter combination. Certain transitions between states- called critical transitions-involve major changes to the dynamical behaviour of the system. They may be caused by only small changes to the parameters of the system.

The authors argue that the dimming event could have occurred due to a critical transition in the pulsation dynamics of Betelgeuse. This means that the nature of the system dynamics underwent a drastic change.

Winds of Change

Other works have shown that several quantities of a time series (such as the light curve) increase leading up to a critical transition of the system. Three of these quantities explored in this work are the autocorrelation, the variance and the so-called detrended fluctuation analysis (DFA). If the change in Betelgeuse’s brightness was indeed due to a critical transition in pulsation dynamics, then that should be imprinted on these quantifiers.

Autocorrelation is, simply speaking, the similarity of a signal observed at different times as a function of the time lag between them. This allows for the detection of repeating patterns, such as periodic signals which would otherwise be buried by noise. 

The variance measures the scatter of the data points around their mean value.
The DFA initially turns the data into a cumulative (so each measurement added on top of the previous) amplitude time series. The root mean square of the deviation is the fluctuation of the linear trend and is expected to rise as a power-law with respect to time. The exponent of this is called the Hurst exponent .

Examining these three quantifiers has also been applied in fields outside astronomy, such as ecology, engineering and psychiatry. The authors of today’s paper thus come from a diverse set of fields, including medicine, complex systems, physics and astrophysics, to optimally apply expertise.

Since there is a large number of gaps within the data between 1980 and 1990, the trends for the autocorrelation, variance, and ⍺ are analyzed for the data from 1990 onwards. The resulting plots are shown in Fig. 2.

Fig. 2: Autocorrelation Function, variance and Hurst exponent of Betelgeuse’s light curve over time. Indicated in gray are measurements before 1990, in green after 1990.
(Fig. 1 in the author’s paper)

For all three quantifiers, the values increase over time before the dimming event begins. This implies that a dynamical transition within Betelgeuse led to the decreasing subsequently increasing brightness in 2019/2020.

Other works point out another possible dimming event in the mid to late 1980s, which might explain the change of the general trend of the quantifiers at that point.
Further analysis based on the number of repeating states of the system, how deterministic the dynamics appear to be and the extent of laminar (i.e. non-turbulent) phases has been conducted by the authors. These measures show again a gradual increase leading up to the dimming phase.

A new Era for Betelgeuse

The authors conclude that the signature of the impending change in the dynamic system of Betelgeuse had been observable a long time preceding the event.

While there is evidence against a dust cloud being responsible for the dimming of Betelgeuse, it has also been shown before that the effective temperature of the star was not decreased significantly during the event, which most likely eliminates convection driven dimming, i.e. a temporary cooler period of the surface.

The authors stress that the final remaining option is a change in the pulsation dynamics of Betelgeuse, causing the 2019-2020 change in brightness.
It is still not proven decisively what caused the dimming, but the authors mention that such a critical transition would imply lasting changes for the system, detectable in the future. Thus, continuous observation of Betelgeuse could give us important new information and help to solve this puzzle.

Betelgeuse is the 10th brightest star in our night sky, so easy to spot. I would suggest, keep an eye on it. Just in case.