# Star light, star bright…as explained by math

Not all stars shine brilliantly all the time. Some have a brightness that alters rhythmically due to cyclical phenomena like passing worlds or the yank of other stars. Others reveal a sluggish modification in this periodicity gradually that can be tough to recognize or record mathematically. KAUST’s Soumya Das and Marc Genton have actually now established an approach to bring this progressing periodicity within the structure of mathematically “cyclostationary” procedures.

“It can be difficult to explain the variations of the brightness of variable stars unless they follow a regular pattern over time,” states Das. “In this study we created methods that can explain the evolution of the brightness of a variable star, even if it departs from strict periodicity or constant amplitude.”

Classic cyclostationary procedures have a quickly definable variation gradually, like the sweep of a lighthouse beam or the yearly variation in solar irradiance at an offered place. Here, “stationary” describes the consistent nature of the periodicity gradually and explains extremely foreseeable procedures like a turning shaft or a lighthouse beam. However, when the duration or amplitude modifications gradually over numerous cycles, the mathematics for cyclostationary procedures stops working.

“We call such a process an evolving period and amplitude cyclostationary, or EPACS, process,” states Das. “Since EPACS processes are more flexible than cyclostationary processes, they can be used to model a wide variety of real-life scenarios.”

Das and Genton designed the nonstationary duration and amplitude by specifying them as functions that differ gradually. In doing this, they broadened the meaning of a cyclostationary procedure to much better explain the relationship amongst variables, such as the brightness and routine cycle for a variable star. They then utilized an iterative method to improve essential criteria in order to fit the design to the observed procedure.

“We applied our method to model the light emitted from the variable star R Hydrae, which exhibited a slowing of its period from 420 to 380 days between 1900 and 1950,” states Das. “Our approach showed that R Hydrae has an evolving period and amplitude correlation structure that was not captured in previous work.”

Importantly, due to the fact that this method links EPACS processes back to classical cyclostationary theory, then fitting an EPACS procedure makes it possible to utilize existing approaches for cyclostationary procedures.

“Our method can also be applied to similar phenomena other than variable stars, such as climatology and environmetrics, and particularly for solar irradiance, which could be useful for predicting energy harvesting in Saudi Arabia,” Das states.

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