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Pulsating Beacons: Revolutionary Measurements Redefine Cepheid Variable Stars

A new study reveals deep insights into the structure and evolution of cupid stars through precise radial measurements, and offers new approaches to the study of the universe using advanced technologies

The brightness of RS Puppis, one of the brightest Cepheid variable stars, changes at a constant rate on a six-week cycle. Credit: NASA, ESA, Hubble Heritage Team (STScI/AURA)-Hubble/Europe Collaboration
The brightness of RS Puppis, one of the brightest Cepheid variable stars, changes at a constant rate on a six-week cycle. Credit: NASA, ESA, Hubble Heritage Team (STScI/AURA)-Hubble/Europe Collaboration

"Classical Cepheids" are a type of pulsating stars whose apparent brightness changes at a constant rate with time. These pulsations can help astronomers measure vast distances in space, so cupids are essential "standard candles" that help us understand the size and scope of our universe.

Despite their importance, Cepheids are difficult to study. Their pulsations and potential interactions with companion stars create complex patterns that are difficult to measure precisely. Different instruments and methods used over the years have led to inconsistent data, making it difficult for us to understand these stars.

"Tracking cupid pulsations using high-quality velocity measurements gives us insights into the structure of these stars and how they evolve," says Richard Anderson, an astrophysicist at EPFL. "In particular, measurements of the speed of expansion and contraction along the line of sight - known as radial speed - provide a critical counterpart to accurate brightness measurements from space. However, there is an urgent need for high-quality radial velocities because it is expensive to collect them and few devices can do it."

Anderson led a team of scientists that did just that through the VELOCE project, a large collaboration that over 12 years collected more than 18,000 highly precise measurements of 258 radial velocities of cupids using advanced spectrographs between 2010 and 2022. "This data will serve as an anchor to link observations of Cepheids from different telescopes over time in hopes of encouraging continued research by the community."

Velos is based on observations from the Swiss Euler telescope in Chile and the Flemish Mercator telescope in La Palma. "It is important to understand the nature and physics of cupids because they provide us with information about how stars evolved in general, and because we rely on them to determine distances and the expansion rate of the universe."

The wonderful precision and long-term stability of the measurements allowed interesting new insights into the pulsating mode of cephaloids," says doctoral student Giordano Viviani. "The pulsations cause changes in the radial velocity of up to 70 km per second or about 250,000 km per hour. We measured these changes with a typical accuracy of 120 km/h (37 meters per second), and in some cases even 7 km/h (2 meters per second), which is more or less a fast walking speed of a person."

To obtain such precise measurements, Velos researchers used two spectrographs with high resolution, which separate and measure wavelengths in AM radiation: Hermes in the northern hemisphere and Corelli in the southern. Outside of Volos, Corelli is famous for finding extrasolar planets and Hermes is a workhorse of stellar astrophysics.

Both spectrographs detected tiny changes in the light of the cupids, indicating their movements. The researchers used advanced techniques to ensure their measurements were stable and accurate, correcting for instrument drift and atmospheric changes. "We measure radial velocities using the Doppler effect", Mespir Anderson. "It's the same effect that the police use to measure speed, and also the effect you recognize from the change in tone when an ambulance approaches or moves away from us."

Velos' observations follow the expansion and contraction of cupid stars with unprecedented precision. Left: The observed spectra of the Capadian delta archetype in Caphaus with their wavelengths changing due to the pulsations. Right: the radial velocity curve measured at Volus, with the changing size of the star shown (not to scale) using star-shaped symbols (expansion to the left of the dashed line, contraction to the right of the line).
Credit: RI Anderson (EPFL)

The Velos project has revealed some fascinating details about Cepheid stars. For example, the Velos data provide the most detailed look yet at the Hertzsprung series—a pattern in stellar pulsations—that shows previously unknown double-peaked hills and will provide clues to better understand the structure of cupids compared to theoretical models of pulsating stars.

The team found that some Cepheids show complex modulated variation in their movement. This means that the star's radial velocity varies in ways that cannot be explained by simple regular pulsation patterns. In other words, although we would expect cupids to beat in a predictable rhythm, the Velos data reveal additional, unexpected changes in these movements.

These changes are inconsistent with the theoretical pulsation models traditionally used to describe cupids. "It follows that there are more complex processes taking place in these stars, such as interactions between different layers of the star, or additional (non-radial) pulsation signals that may make it possible to determine the structure of cupid stars using astroseismology," says postdoctoral student Henrika Netzel. First discoveries of such vellus-based signals are reported in a companion paper.

The study also identified 77 Cepheid stars that are part of a binary system (two stars orbiting each other) and found 14 more potential ones. A companion paper describes these systems in detail, adding to our understanding of how these stars evolve and interact. "We see that approximately one-third of the cupids have an invisible companion whose presence can be determined by the Doppler effect," says lead author Sharia Shetia.

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