Led by Szilárd Kálmán (ELTE), for a period of one month staff of the Gothard Astrophysical Observatory of the Eötvös Loránd University (ELTE), the ELKH Research Centre for Astronomy and Earth Sciences (CSFK), the University of Szeged (SZTE), and the MTA-ELTE Exoplanet Systems Research Group have observed WASP-33, a planet that is 2.1 times the size of Jupiter and orbits a Delta Scuti-type pulsating variable star in 1.2 days. Hungarian researchers have shown that the WASP-33b exoplanet excites and partially tunes the star’s pulsation. This is the first time that such a phenomenon has been observed and statistically substantiated in a star-planet system. A study summarizing the findings has beeen published in the prestigious international journal Astronomy & Astrophysics.

WASP-33, the planetary-sized companion of the young mainstream star, which is heavier and hotter than the Sun, was discovered in 2006 during the SuperWASP (Wide Angle Search for Planets) program. WASP-33b, unlike the planets in the Solar System, does not orbit in the equatorial plane of the star, but in an orbit close to it, near to its pole. Because the central star rotates very quickly around its own axis, its shape has become flattened, and its brightness changes rapidly and spectacularly due to the multi-mode pulsation of the Delta Scuti type.

Proper analysis of planetary and stellar interactions requires high-precision and continuous observations, which is only possible with telescopes capable of space photometry. One such spacecraft currently in operation is the TESS (Transiting Exoplanet Survey Satellite), whose measurements of the WASP-33 system over the period of approximately one month formed the basis of the analysis. The discovery of most exoplanets known today is based on the phenomenon that when a planet passes in front of its star, and partially obscures it, the measured luminosity of the star typically decreases slightly. Such planets passing before their stars are known as transiting exoplanets. In the case observed here, the star pulsation is applied to this effect, and the gravitational darkening also occurs due to the rapid rotation. This means that we can observe that the poles of the star are significantly (1,000-1,500 Kelvin) hotter than the equator. As a result, the researchers were able to determine that the axis of rotation of the star under study and the orbit of WASP-33b were approximately perpendicular to each other. The transit of the planet thus takes place in front of the stellar surface with an uneven temperature distribution that causes an asymmetric change in light. Simultaneous analysis of transits, pulsation, and gravitational darkening has so far been limited to the WASP-33 system.

To analyze pulsation, the researchers had to break it down into the sum of sinusoidal signals of different amplitudes and frequencies. In doing so, it was found that some of the pulsation frequencies show a high degree of agreement with the circular harmonics (multiples of the circulating frequency), mainly with the 3rd, 12th, and 25th harmonics. Based on statistical studies, it is very unlikely that a random frequency distribution resulted in the current observations of the planet influencing stellar pulsation. In the case of binary stars, where much greater gravitational forces occur, such a phenomenon has been observed several times, but in the case of star-planet systems, the case of WASP-33 is the first and so far only known case of tidally perturbed pulsation. This means that although the star does not pulsate because of the planet, some components of the pulsation pattern appear as if the tidal force of the planet allows it, and the frequency of other components can be slightly tuned (or perturbed, to be precise) by the planet’s circulation. According to the researchers, the source of the tidal forces underlying the interaction is the relatively perpendicular position of the planet’s orbit and the axis of rotation.

The study summarizing the results was prepared with the professional support of the Doctoral Student Scholarship Program of the Hungarian Ministry of Innovation and Technology funded by the Hungarian National Research, Development and Innovation Fund.

Figure 1: Schematic diagram of the phenomena observed in the WASP-33 system. Due to the rapid rotation of the star about its own axis of rotation (point-line), the equator is cooler than the poles – panel a). Due to the Delta Scuti pulsation, some surface elements of the star surface are seen to be brighter than others – panel b). The planet orbiting the polar orbit excites and attenuates the star pulsation – panel c), red. (Bernadett Pál, CSFK)


Figure 2: Schematic diagram for pulsation excitation. The tidal excitation of the pulses to which the planet is closest will be more intense in those parts of the star. (Bernadett Pál, CSFK)