You Can't Know the True Size of an Exoplanet Without Knowing its Star's Magnetic Field

In 2011, astronomers with the Wide Angle Search for Planets (WASP) consortium detected a gas giant orbiting very close to a Sun-like (G-type) star about 700 light-years away. This planet is known as WASP-39b (aka. “Bocaprins”), one of many “hot Jupiters” discovered in recent decades that orbits its star at a distance of less than 5% the distance between the Earth and the Sun (0.05 AU). In 2022, shortly after the James Webb Space Telescope (JWST) it became the first exoplanet to have carbon dioxide and sulfur dioxide detected in its atmosphere.

Alas, researchers have not constrained all of WASP-39b’s crucial details (particularly its size) based on the planet’s light curves, as observed by Webb. which is holding up more precise data analyses. In a new study led by the Max Planck Institute for Solar System Research (MPS), an international team has shown a way to overcome this obstacle. They argue that considering a parent star’s magnetic field, the true size of an exoplanet in orbit can be determined. These findings are likely to significantly impact the rapidly expanding field of exoplanet study and characterization.

The study was led by Dr. Nadiia M. Kostogryz and her fellow researchers from the MPS. They were joined by astronomers and astrophysicists from the Center for Astronomy (Heidelberg University), the Astrophysics Group at Keele University, the Kavli Institute for Astrophysics and Space Research at the Massachusetts Institute of Technology (MIT), and the Space Telescope Science Institute (STScI). The paper describing their research, “Magnetic origin of the discrepancy between stellar limb-darkening models and observations,” was recently published in Nature Astronomy.

A light curve is the measurement of a star’s brightness over longer periods. Using the Transit Method (Transit Photometry), astronomers monitor stars for periodic dips in brightness, which can result from an exoplanet passing (transiting) in front of their face relative to the observer. In addition to being the most widely used method for detecting exoplanets, precise observations of light curves allow astronomers to estimate the size and orbital period of the exoplanets.

These curves can also reveal information about the composition of the planet’s atmosphere based on light passing through its atmosphere as it makes a transit – a technique known as “transit spectroscopy.” Unfortunately, estimates on planet size suffer from an observational issue known as “limb darkening.” Dr. Kostogryz explained in an MPS press statement:

“The problems arising when interpreting the data from WASP-39b are well known from many other exoplanets – regardless [of] whether they are observed with Kepler, TESS, James Webb, or the future PLATO spacecraft. As with other stars orbited by exoplanets, the observed light curve of WASP-39 is flatter than previous models can explain.”

The edge of the stellar disk (or “limb”) plays a decisive role in interpreting a star’s light curve. Since the limb corresponds to the star’s outer (and cooler) layers, it appears darker to the observer than the inner area. However, the star does not actually shine less brightly further out. This “limb darkening” affects the shape of the exoplanet signal in the light curve, as the dimming determines how steeply the curve falls during a planetary transit and then rises again. Historically, astronomers have not been able to reproduce observational data using conventional stellar models accurately.

In every case, the decrease in the star’s brightness was less abrupt than model calculations predicted. Clearly, something was missing from the models that prevented astronomers from reproducing exoplanet transit signals. As Dr. Kostogryz and her team discovered, the missing piece is stellar magnetic fields, which are generated by the motion of conductive plasma inside a star. The team first noticed this when examining selected light curves obtained by NASA’s Kepler Space Telescope between 2009 and 2018.

The researchers also proved that the discrepancy between observational data and model calculations disappears if the star’s magnetic field is included in the computations. To this end, the team turned to selected data from NASA’s Kepler Space Telescope, which captured the light of thousands and thousands of stars from 2009 to 2018. To this end, they modeled the atmosphere of typical Kepler stars in the presence of a magnetic field and then simulated observational data based on these calculations. When they compared their results to real data, they found it accurately reproduced Kepler’s observations.

They also found that the strength of the magnetic field can have a profound effect, where limb darkening is more pronounced in stars with weak magnetic fields and less in stars with strong ones. Lastly, they extended their simulations to emission spectra data obtained by the JWST and found that the magnetic field of the parent star influences limb darkening differently at different wavelengths. These findings will help inform future exoplanet studies, leading to more precise estimates of the planets’ characteristics. Said Dr. Alexander Shapiro, coauthor of the current study and head of an ERC-funded research group at the MPS:

“In the past decades and years, the way to move forward in exoplanet research was to improve the hardware, the space telescopes designed to search for and characterize new worlds. The James Webb Space Telescope has pushed this development to new limits. The next step is now to improve and refine the models to interpret this excellent data.”

The researchers now plan to extend their analyses to stars different from the Sun, which could lead to refined estimates of exoplanet mass for rocky planets (similar to Earth). In addition, their findings indicate that the light curves of stars could be used to constrain the strength of stellar magnetic fields, another characteristic that is challenging to measure.

Further Reading: MPS, Nature Astronomy