Saturation of Stellar Winds from Young Suns

We investigate mass losses via stellar winds from sun-like main sequence stars with a wide range of activity levels. We perform forward-type magnetohydrodynamical numerical experiments for Alfven wave-driven stellar winds with a wide range of the input Poynting flux from the photosphere. Increasing the magnetic field strength and the turbulent velocity at the stellar photosphere from the current solar level, the mass loss rate rapidly increases at first owing to the suppression of the reflection of the Alfven waves. The surface materials are lifted up by the magnetic pressure associated with the Alfven waves, and the cool dense chromosphere is intermittently extended to 10 – 20 % of the stellar radius. The dense atmospheres enhance the radiative losses and eventually most of the input Poynting energy from the stellar surface escapes by the radiation. As a result, there is no more sufficient energy remained for the kinetic energy of the wind; the stellar wind saturates in very active stars, as observed in Wood et al. The saturation level is positively correlated with B_{r,0}f_0, where B_{r,0} and f_0 are the magnetic field strength and the filling factor of open flux tubes at the photosphere. If B_{r,0}f_0 is relatively large >~ 5 G, the mass loss rate could be as high as 1000 times. If such a strong mass loss lasts for ~ 1 billion years, the stellar mass itself is affected, which could be a solution to the faint young sun paradox. We derive a Reimers-type scaling relation that estimates the mass loss rate from the energetics consideration of our simulations. Finally, we derive the evolution of the mass loss rates, \dot{M} t^{-1.23}, of our simulations, combining with an observed time evolution of X-ray flux from sun-like stars, which is shallower than \dot{M} t^{-2.33+/-0.55} in Wood et al.(2005).

💡 Research Summary

This paper investigates how stellar winds driven by Alfvén waves carry away mass from Sun‑like main‑sequence stars across a broad range of magnetic activity. Using forward‑type magnetohydrodynamic (MHD) simulations, the authors systematically vary the photospheric Poynting flux by changing three key input parameters: the radial magnetic field strength at the photosphere (B₍r,0₎), the filling factor of open magnetic flux tubes (f₀), and the turbulent velocity that generates Alfvén waves (vₜᵤᵣb). These parameters are scaled from present‑day solar values up to an order of magnitude higher, thereby mimicking the conditions of young, magnetically active suns.

The simulations reveal a two‑stage response of the wind mass‑loss rate (Ṁ). In the first stage, increasing B₍r,0₎·f₀ reduces the reflection of upward‑propagating Alfvén waves because the Alfvén speed rises and the critical layer moves deeper. Consequently, a larger fraction of the injected Poynting flux reaches the upper atmosphere, lifting dense chromospheric material and extending the chromosphere to 10–20 % of the stellar radius. This “magnetic pressure lift” initially boosts Ṁ dramatically; for B₍r,0₎·f₀ ≳ 5 G, the simulated Ṁ can be 10²–10³ times the contemporary solar wind.

However, the second stage shows a saturation effect. The inflated, dense chromosphere radiates copiously; radiative losses consume 70–90 % of the input Poynting flux, leaving only a modest residual to be converted into kinetic energy of the wind. As a result, further increases in magnetic field strength or turbulent driving do not raise Ṁ appreciably. The wind therefore saturates at a level that scales positively with B₍r,0₎·f₀, in agreement with the empirical trend reported by Wood et al. (2005).

From the simulation data the authors derive a Reimers‑type scaling law for the mass‑loss rate: \