Starlight, Star Bright… as explained by Math
The evolutionary periodicity of the luminosity of certain types of stars can now be described mathematically.
All the stars do not always shine brightly. Some have a brightness that changes rhythmically due to cyclical phenomena such as the passing of planets or the towing of other stars. Others show a slow change in this periodicity over time which can be difficult to discern or to grasp mathematically. Soumya Das and Marc Genton from KAUST have developed a method to bring this evolutionary periodicity within the framework of mathematically “cyclostationary” processes.
“It can be difficult to explain the variations in the brightness of variable stars unless they follow a regular pattern over time,” Das explains. “In this study, we have created methods that can explain the evolution of the luminosity of a variable star, even if it deviates from a strict periodicity or from a constant amplitude.”
Classic cyclostationary processes have an easily definable variation over time, such as the sweep of a lighthouse beam or the annual variation in solar irradiance at a given location. Here, “stationary” refers to the constant nature of periodicity over time and describes highly predictable processes such as a rotating shaft or a headlight beam. However, when the period or amplitude changes slowly over many cycles, the mathematics of cyclostationary processes fail.
“We call such a process an evolving period and amplitude cyclostationary process, or EPACS,” says Das. “Because EPACS processes are more flexible than cyclostationary processes, they can be used to model a wide variety of real-life scenarios.”
Das and Genton modeled the non-stationary period and amplitude by defining them as functions that vary over time. In doing so, they broadened the definition of a cyclostationary process to better describe the relationship between variables, such as brightness and the periodic cycle of a variable star. They then used an iterative approach to refine the key parameters in order to adapt the model to the observed process.
“We applied our method to model the light emitted by the variable star R Hydrae, which exhibited a slowdown in its period from 420 to 380 days between 1900 and 1950,” explains Das. “Our approach has shown that R Hydrae has an evolving period and amplitude correlation structure that has not been taken into account in previous work.”
Mainly, because this approach links EPACS processes to classical cyclostationary theory, then fitting an EPACS process allows existing methods to be used for cyclostationary processes.
“Our method can also be applied to similar phenomena other than variable stars, such as climatology and the environment, and in particular for solar irradiance, which could be useful for predicting energy harvest in Saudi Arabia. », Explains Das.
Reference: “Cyclostationary processes with evolutionary periods and amplitudes” by Soumya Das and Marc G. Genton, February 4, 2021, IEEE signal processing transactions.
DOI: 10.1109 / TSP.2021.3057268