Title: Star-planet tidal interaction and the limits of Gyrochronology
Authors: Florian Gallet, Phillippe Delorme
First Author’s Institution: Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
Status: Accepted for publication in A&A, open access
Stars, like their Hollywood namesakes, like to be elusive about their age. Finding ways to reliably determine how old stars are is therefore a large part of current research. One such technique is gyrochronology, the study of the relation between a star’s rotation, colour, and age. Stars of a given colour on the Main Sequence stage of their lifetime will spin more slowly (or ‘spin down’) as they evolve at a relatively reliable rate. This means if you know a star’s colour and rotation you can derive a reliable age estimate, which is especially useful in cases where other methods don’t work as well.
But what happens when a star doesn’t get to spin down in isolation; what if it is disrupted somehow? If the star was caused to spin more quickly (or ‘spun up’) (for example, by stealing material from a stellar companion), using gyrochronology to determine its age would make it look younger than it actually is. One way to change a star’s spin down rate could be due to tidal interactions with a nearby planet, creating tides on the star much like the moon creates tides on earth. Today’s authors ask the question: how close and how big does a planet need to be before it starts seriously disrupting the stellar spin and our use of gyrochronology?
Studying the tides
In order to find the type of star-planet system in which gyrochronology can be applied, the authors combine a stellar evolution model with an orbital evolution model, and link the two together using equations describing the tidal effects induced by the star and the planet. They start off each simulation at the same stellar rotation and the same orbital distance, but tweak the masses of the planet and of the star, allowing the system to evolve naturally. They then calculate the gyrochronology age based on the rotation, and compare it to the true age of the system, to see how the planet impacts the estimate. The results can be seen in Figure 1.
In Figure 1, the brightest regions at low orbital period indicate the region where the planethas caused the star’s rotation to change by more than 10% compared to if the star was isolated. Using this changed period to calculate an age with gyrochronology would give you an age that is off by 20%. From where the bright region extends on the plot, we cansee that heavy planets can have an impact when they are further away from their host star, and that this impact is larger if the star is already rotating slowly.
Riding the tides
In order to keep gyrochronology useful in systems with massive planets at small orbits, the authors develop a new gyrochronology relation that includes information about tidal interaction with planets, and dub it tidal-chronology.Using their models of star-planetsystem evolution, they investigate the relation between the rotation of the star, the period of the planet’s orbit, and the system’s age, as seen in Figure 2.
Using the information in Figure 2, we can try and calculate the age of a system if we know the rotation of its host star and the orbit of its planet. Age (as calculated) increases with increasing stellar period, as predicted by gyrochronology. The changes due to the planet’s orbit then allows us to calculate an age for a system affected by tidal forces.
So when can we use what?
The authors’ analysis shows that you can get an age estimation that is within 20% of the true value using regular gyrochronology, provided that the orbit of the planet is longer than 4 days, and the planet is less than five times the mass of Jupiter. They warn, however, that in dramatic events such as a star engulfing a planet, the planet can be gone from the system but the impact on the star’s age will remain, with no clear evidence the planet was ever there to disrupt it. Finally, they state that their tidal-chronology is a promising technique, but needs more improvement before it can be used. It looks like, for the time being, gyrochronology works, provided we apply it carefully.