Dynamical Model for Spindown of Solar-Type Stars

Abstract

After their formation, stars slow down their rotation rates by the removal of angular momentum from their surfaces, e.g., via stellar winds. Explaining how this rotation of solar-type stars evolves in time is currently an interesting but difficult problem in astrophysics. Despite the complexity of the processes involved, a traditional model, where the removal of angular momentum by magnetic fields is prescribed, has provided a useful framework to understand observational relations between stellar rotation, age, and magnetic field strength. Here, for the first time, a spindown model is proposed where loss of angular momentum by magnetic fields evolves dynamically, instead of being prescibed kinematically. To this end, we evolve the stellar rotation and magnetic field simultaneously over stellar evolution time by extending our previous work on a dynamo model which incorporates nonlinear feedback mechanisms on rotation and magnetic fields. We show that our extended model reproduces key observations and is capable of explaining the presence of the two branches of (fast and slow rotating) stars which have different relations between rotation rate Ω versus time (age), magnetic field strength B | | versus rotation rate, and frequency of magnetic field w cyc versus rotation rate. For fast rotating stars we find that: (i) there is an exponential spindown W µ -e t 1.35 , with t measured in Gyr; (ii) magnetic activity saturates for higher rotation rate; (iii) w µ W cyc 0.83 . For slow rotating stars we find: (i) a power-law spindown W µ -t 0.52 ; (ii) that magnetic activity scales roughly linearly with rotation rate; (iii) w µ W cyc 1.16 . The results obtained from our investigations are in good agreement with observations. The Vaughan-Preston gap is consistently explained in our model by the shortest spindown timescale in this transition from fast to slow rotators. Our results highlight the importance of self-regulation of magnetic fields and rotation by direct and indirect interactions involving nonlinear feedback in stellar evolution.

Mass, energy, and momentum capture from stellar winds by magnetized and unmagnetized planets: implications for atmospheric erosion and habitability

“…The magnetic field strength and X-ray activity of solarlike stars increase with rotation rate for slow rotators and then saturate for very fast rotators (Noyes et al 1984;Schrijver & Zwaan 2000;Pizzolato et al 2003;Mamajek & Hillenbrand 2008;Wright et al 2011;Vidotto et al 2014;Reiners, Schüssler & Passegger 2014). Relationships between stellar activity, rotation, and magnetic field strength are all connected to the dynamo origin of these fields within the stars; it is an ongoing enterprise of research to understand these connections and make them quantitative (Karak, Kitchatinov & Choudhuri 2014;Kitchatinov & Olemskoy 2015;Sood, Kim & Hollerbach 2016;Blackman & Owen 2016). In the absence of significant cooling, the winds from solar-like stars, which also draw from the coronal magnetic and thermal energy, are also likely significantly stronger for younger stars.…”

The Solar Twin Planet Search

“…It also dictates the dependence of the angular momentum on the rotation rate and, in practice, it determines how early the effects of braking are felt by a model. Such prescriptions for rotational evolution have a general agreement for young ages up to the solar age (see Sood et al 2016;Amard et al 2016, and references therein), but the evolution for older ages still poses an open question. In particular, van Saders et al (2016) suggested that stars undergo a weakened magnetic braking after they reach a critical value of the Rossby number, thus explaining the stagnation trend observed on the rotational periods of older Kepler stars.…”