To unravel this mystery, multiple teams with diverse expertise from the Department of Astrophysics had to come together. This is because the architecture that unites a star with its planet is highly complex. It required a fine understanding of both stellar and planetary physics by exploring their interactions, and a deep knowledge of the observations made by NASA's Kepler satellite to be capable of decrypting the data.
The study shows that the observed scarcity seems to stem not from an observational bias, but rather from physical causes. Tidal effects and magnetism alone are enough to qualitatively and quantitatively explain the migration of nearby planets around fast-rotating stars. Moreover, this migration seems to depend on the spectral type of the star (which fundamentally depends on the mass). Although these results are promising, it is nonetheless necessary to enlarge the sample size to better constrain the scarcity and understand the mechanisms at play. In particular, this study underlines the importance of considering the spectral types of stars (their masses) if one wants to correctly model star-planet interactions.
This work has been published in the journal
Astronomy & Astrophysics.
A Gap in the Data: Observational Bias or Physical Reality?
Launched in 2009, the Kepler satellite observed the same portion of the sky for over 4 years, searching for exoplanets via the transit method. With over 3000 exoplanets discovered to its credit, contributing to more than half of the confirmed discoveries to date, Kepler has revolutionized our understanding of planets and their host stars.
Figure 1 - Modeling the magnetic interaction between star and planet.
Credit: CEA/A. Strugarek Science is made of discoveries, but always under the veil of uncertainties and biases, related to several factors, known or unknown. Among these are observational biases that can lead to erroneous conclusions simply because the sample being studied is not representative. Thus, researchers actively hunt for such biases, notably through statistical tests.
In the case of Kepler observations, it was noted as of 2013 (McQuillan et al. 2013) a shortage of planets as they got closer to stars, but not any stars: those that rotate rapidly on themselves, known as "fast rotators" (i.e., up to 10 times faster than our Sun). In Figure 2, this shortage is clearly visible below the magenta line. Is this gap due simply to an observational bias, linked to, for example, too few observations, or is there an underlying physical reason?
Carefully Selected Data
In order to understand this scarcity in the data, researchers compare these observed systems to a synthetic population calculated with the Star-Planet Evolution and Magnetism (ESPEM) code. This code calculates the tidal and magnetic interactions in a system composed of a single star and a single planet, from the dissipation phase of the gas disk in which the exoplanetary system forms up to the end of the main sequence.
Thus, just as a good chef carefully selects his ingredients before cooking a dish, the researchers begin by selecting the study sample in a strict manner to not introduce observational bias that could skew the results.
Figure 2 - The diagram shows the star's rotation period (Prot) in relation to the orbital period of the detected planets by the Kepler satellite (Porb). The blue dots represent a system composed of a single planet and a single star. The lower this point is in the diagram, the more rapidly the host star spins on itself. The further left the point is, the more rapidly the planet orbits its star, meaning it is closer.
Thus, a shortage of close-in planets around fast-rotating stars is observed (bottom left), represented by the dotted magenta line. The dotted gray line corresponds to a 1:1 synchronization, that is, the planet orbits its star at the same speed that the star spins on itself.
Credit: Garcia et al. 2023. For this purpose, the observational data must follow two criteria:
- Use only Kepler observations whose characteristics are very well known and controlled. A mixture of data from different telescopes could introduce observational biases.
- Systems that can be modeled by the ESPEM code. Namely: The systems must contain only one planet and one star. The latter must be in the main sequence (i.e., stars burning Hydrogen in their core), and possessing enough magnetic spots on their surface to precisely measure their rotation period (Prot).
Ultimately, 576 exoplanetary systems observed by Kepler meet these criteria.
A Shortage Confirmed by Stellar Models
The synthetic exoplanetary systems generated by the ESPEM model code also predict a scarcity of planets in close orbits around fast-rotating stars, a prediction in line with the Kepler data sample as shown in Figure 2. Furthermore, a correlation seems to emerge with the spectral type of stars, in other words, with their mass: There are more close-in planets around fast-rotating cold type K stars, thus less massive (0.436 ≤ M ≤ 0.896 M☉), than around hot type F stars, thus massive (M >= 1.015 M☉).
This trend is explained by the complex interaction between the star and the planet, mainly governed by gravitational forces and magnetic fields.
The gravitational interaction between two celestial bodies induces tidal effects, causing deformations in their structure. These deformations dissipate energy (originally in gravitational form) as heat, leading to an exchange of angular momentum that can slow down or speed up the rotation of the central star and cause the planet to migrate outward or toward the star. This is why the Moon is moving away from Earth by about 1.5 inches (3.8 cm) per year: the Earth's tides, mainly caused by the Moon, induce a slowdown in Earth's rotation, contributing to the Moon's retreat. Similarly, a planet can migrate due to the tidal effects it generates on its star, with more pronounced effects the more massive the planet is.
Then, generally of lesser intensity (but not always), magnetism comes into play. Just as a large ship disrupts the speed of a smaller one entering its wake, a star's magnetic footprint in its environment applies a magnetic drag effect on orbiting planets. The closer the planet is to the star, the more intense this drag is, potentially causing the planet to migrate over timescales of a few hundred million years.
Figure 3 - Same legend as figure 2, this time separated by the spectral type of the star, the colder ones on top, on which has been superimposed the possible star-planet distribution calculated by the ESPEM code, with red indicating the highest density. Note that there is a factor of 100 difference between the red and green colors in the density scale. The gray area corresponds to the parameter space that cannot be calculated by ESPEM.
Credit: Garcia et al. 2023 The orbits of massive planets are primarily influenced by tides, while less massive planets are mostly affected by magnetism. For hot type F stars, the predominant influence is magnetic, whereas for other colder stars, it is mainly tides that play a critical role. Therefore, depending on the spectral type of the star and the mass of the planet, a planet may migrate closer or farther from its star, explaining the planetary distribution in orbit around fast-rotating stars observed.
However, while these results are promising, it is necessary to increase the sample size to better constrain the scarcity and understand the mechanisms at play. These preliminary conclusions nevertheless demonstrate the importance of considering the spectral types of stars in future models of the interactions that bind a star to its planet.