'Star Light, Star Bright' as Explained by Math
Selin Deniz Akdoğan​
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The changing periodicity of the brightness of certain types of stars can now be mathematically explained.
Not every star is bright all of the time. Owing to cyclical phenomena such as moving planets or the pull of other stars, some have a brightness that varies rhythmically. Others display a gradual transition in this periodicity over time, which is difficult to detect or mathematically catch.
Soumya Das and Marc Genton of KAUST have devised a mechanism for incorporating this emerging periodicity into mathematically "cyclostationary" systems. "Variations in the brightness of variable stars can be difficult to understand because they follow a normal trend over time," Das says. "In this research, we developed methods for explaining the evolution of a variable star's light, even as it deviates from strict periodicity or constant amplitude."
Classic cyclostationary systems, such as the sweep of a lighthouse beam or the annual change in solar irradiance at a given spot, provide a readily definable variation over time.
The term "stationary" refers to the periodicity's consistency over time and is used to denote highly predictable mechanisms such as a revolving shaft or a lighthouse beam. The mathematics for cyclostationary systems, on the other hand, fails as the time or amplitude varies steadily over several periods.
"We call this an EPACS (evolving time and amplitude cyclostationary) mechanism," Das explains. "Since EPACS processes are more flexible than cyclostationary processes, they can be used to model a broad range of real-life scenarios," says the researcher.
The nonstationary length and amplitude were modeled by Das and Genton as time-varying functions. They did so by broadening the concept of a cyclostationary method to better define the relationship between variables like a variable star's brightness and periodic loop.
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They then used an iterative approach to fine-tune key parameters so that the model could complement the observed method.
"We used our system to model the light emitted by R Hydrae, a variable star whose period slowed from 420 to 380 days between 1900 and 1950," Das explains. "Our method revealed that R Hydrae has a changing time and amplitude association structure that had previously gone unnoticed."
Importantly, since this methodology connects EPACS processes to classical cyclostationary theory, fitting an EPACS process allows current cyclostationary process methods to be used.
"Our approach can be extended to other phenomena like climatology and environmetrics as well as solar irradiance, which could be useful for forecasting energy harvesting in Saudi Arabia," Das says.
References
Abdullah, King. “'Star light, star bright' as explained by math”, Physc.org. 26 April, 2021. https://phys.org/news/2021-04-star-bright-math.html