Title: Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and τ Cet
Authors: Travis S. Metcalfe, Klaus G. Strassmeier, Ilya V. Ilyin, Jennifer L. van Saders, Thomas R. Ayres, Adam J. Finley, Oleg Kochukhov, Pascal Petit, Victor See, Keivan G. Stassun, Sandra V. Jeffers, Stephen C. Marsden, Julien Morin, Aline A. Vidotto
First Author’s Institution: White Dwarf Research Corporation, Golden, Colorado, USA
Status: Accepted to ApJ Letters [open access]
How to Brake a Star
You might be familiar with the classic example of conservation of angular momentum where an ice skater is spinning on a (frictionless) piece of ice with their arms tucked in. When they extend their arms, they increase their moment of inertia. Conservation of angular momentum then requires that the rotation rate of the skater reduces– the skater “spins down”.
However, conservation of angular momentum is only valid if the system (the spinning ice skater) is isolated. Things are a little different if, for instance, the skater is holding weights as they spin. When they extend their arms, they again increase their moment of inertia and slow their rotation rate. Then, the skater can drop the weights. The instant that the skater drops the weights, the system is no longer isolated, and angular momentum is no longer conserved. The reduction in moment of inertia caused by dropping the weights also reduces the angular momentum.
This same principle is at work in stars. Instead of a figure skater holding weights, there is a stellar magnetic field holding plasma. Winds from the star can push the plasma further and further out, causing the star to spin down like when the skater extended their arms. Eventually, the plasma is pushed so far away that the magnetic field isn’t strong enough to contain it anymore, and the plasma is lost along with some of the star’s angular momentum. This is called magnetic braking.
Because magnetic braking gradually removes the star’s angular momentum and slows down the star’s rotation rate, a star’s rotation rate can be used to estimate its age. This principle drives a field of study called gyrochronology. More specifically, stars’ ages are characterized by their Rossby number– the ratio between the star’s rotation period and convective overturn timescale (the time it takes for a bubble of plasma to move through the convective zone). As a star ages and its rotation rate decreases, its Rossby number increases. Eventually, a star’s rotation slows down so much that a critical Rossby number is reached. At this point, the star experiences weakened magnetic braking (WMB) and the star spins down at a slower rate than it had previously experienced.
The authors of this paper investigate this transition to WMB for stars cooler than the Sun– the first time this has been done before. This is an important distinction; cooler stars have deeper convective zones and thus longer overturn timescales. This means their Rossby number is smaller than it is for hotter stars with the same rotation period. It also means that at the critical Rossby number, their rotation period will be longer than hotter stars’ periods.
For this work, they look at two G8 dwarf stars– these are stars a few hundred Kelvin cooler than the Sun. In order to investigate the transition to WMB, they chose two stars of very different ages: the younger of the two stars is named 61 UMa and is about 1 billion years old. The older star is named tau Ceti and is ~9 billion years old– about twice the age of the Sun! To figure out the effects of magnetic braking on these stars, there are two major parameters besides age to consider: the stellar magnetic field shape and strength and the mass loss rate of the wind. Stronger magnetic fields can hold plasma out to greater distances and hence provide a larger torque than weak fields do. Additionally, the higher the mass loss rate is, the faster the angular momentum is lost.
For 61 UMa, they determine the magnetic field properties from previously-collected Zeeman Doppler Imaging data and calculate the mass loss rate from its x-ray luminosity. For tau Ceti, they collected data with the PEPSI instrument on the Large Binocular Telescope to estimate its magnetic field and determined its mass loss rate from previously-collected Lyman alpha measurements. With all of this information, they can estimate the torques from the fields and winds that are braking the stars.
The results of their calculations show that 61 UMa experiences a torque about 300 times stronger than tau Ceti’s torque. This is consistent with the idea that older stars, especially those with Rossby numbers above the critical Rossby number, are much less efficient at braking than younger stars that haven’t yet reached the critical Rossby number. The torque they calculated is plotted against the Rossby number in Figure 1, along with hotter stars that had been previously studied. Besides a trend for stars with higher Rossby numbers to have weaker torques, this figure shows that this work extended the stellar sample to include both smaller and larger Rossby numbers and torques than had previously been investigated in this context.
Aside from the magnetic field and mass loss rate parameters, other stellar parameters like rotation period and stellar size are also used to determine torque. The authors were able to investigate the contributions of the various evolutionary model parameters by varying them, one at a time. What this work confirmed is that, by far, the evolutionary change in mass-loss rate and magnetic-field properties dominate the effects of braking. Changing other parameters like the evolution of the rotation period, the stellar mass, and stellar radius contribute about 2-10 times less to the decrease in torque with time.
This research serves as an important expansion to our understanding of stellar spin evolution as a function of spectral type. This is crucial for understanding both stellar histories and futures and provides important insight to the environment of young and old stars alike. It also represents the beginning of work dedicated to understanding these cooler stars and solar analogs; the authors have plans to collect spectropolarimetric data to map magnetic fields on cooler, K-dwarf stars so that they can extend their analysis to a broader sample. Although these stars are slowing down, the authors are moving full-speed ahead!
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