Breaking gyrochronology through the collapse of coronal winds

TL;DR

This work addresses the observed breakdown of gyrochronology for middle-aged solar-type stars by testing whether a collapse of coronal winds, triggered by reduced coronal heating, can reproduce the break. Using the Weber–Davis magnetized wind framework with a polytropic wind and a dynamo-like relation $B_{r0} \propto Ω$, it shows that wind dynamics near the hydrostatic corona limit produce non-monotonic and complex dependencies of mass and angular momentum loss on coronal base temperature $T_0$ and heating parameter $α$. However, reproducing the observed break requires a steep $T_0(Ω)$ coupling with exponent $σ \gtrsim 1.5$, which implies a power input decrease by more than three orders of magnitude that current observations do not support, making wind collapse alone an unlikely explanation. The results therefore point to additional dynamo-related processes, such as a shutdown or topological shift of the large-scale coronal magnetic field, to fully account for the gyrochronology break and emphasize the need for integrated constraints on coronal heating and magnetic topology in aging solar-type stars.

Abstract

Gyrochronology, a method for dating aged field stars ($\gtrsim$ a few Gyr) based on their rotation rate, has recently been shown to fail for many stars older than the sun. The explanation most often put forth is that a shutdown or mode change in the stellar dynamo leads to a sharp decrease in angular momentum loss in magnetized coronal winds. In this paper, we explore an alternate possibility, namely a collapse of the wind itself through a reduction of coronal heating. We show that in the low coronal temperature ($T_0$) limit, even at solar-like low rotation rates ($Ω$) and coronal magnetic field strength ($B_{r0}$), magnetocentrifugal effects are important and preclude expression of the mass and angular momentum loss rates as power-laws of $T_0$ or $Ω$ when $T_0$ drops below $\simeq 1.5\,$MK. Mass loss is found to scale linearly with power input into the wind at all coronal temperatures. Introducing an ad hoc power law relationship $T_0\propto B_{r0}^σ$ while retaining the ``standard'' dynamo relationship $B_{r0}\proptoΩ$, we show that reproducing the observed break in gyrochronology requires an exponent $σ\gtrsim 1.5$, with which is associated a drop by over 3 orders of magnitude in power input into the quiet corona. This appears physically unrealistic, given current observations of chromospheric and coronal non-thermal emission in aged solar-type stars.

Figures (9)

• Figure 1: Radial profiles of wind (solid lines) and Alfvén (dashed) speed from WD solutions with rotation rates $\Omega/\Omega_\odot=0.6$ (blue), 1 (green) and 2 (orange). In all cases $r_0/R_\odot=1.15$, $T_0=1.5\times 10^6\,$K, $\alpha=1.1$, and $B_{r0}\propto\Omega$.
• Figure 2: Two representative simulation runs of the MacGregorBrenner1991 spindown model, for fixed coupling timescale $\tau_c=10^7\,$yr and initial conditions on the ZAMS $\Omega/\Omega_\odot=5$ and $25$. Solid (dash-dotted) lines give the angular velocities of the convective envelope (radiative core) in each case. The dashed line is the Skumanich $t^{-1/2}$ Law pinned to the present day sun.
• Figure 3: Variations of the Alfvén radius $r_A$ (red), base flow speed $u_{r0}$ (blue), and angular momentum loss rate ${\dot J}$ (green), versus coronal base temperature, as obtained from a sequence of $\alpha=1.1$ WD wind solutions at fixed solar rotation rate and surface magnetic field strength.
• Figure 4: Top panel: Radial profiles of wind variables for a $\alpha=1.125$ WD solution with solar rotation and magnetic field strength, and a "low" coronal base temperature $T_0=1.23\times 10^6\,$K. The black dashed line shows the $u_r(r)$ profile for a non-rotating, unmagnetized coronal wind of the same base temperature and polytropic index. The two solid dot indicates the corresponding Alfvén points. The bottom panel shows the corresponding acceleration terms in the momentum equation: gravity, pressure, centrifugal, and magnetic force, as labeled. The solid blue line gives the resulting Lagrangian acceleration. Note how centrifugal and magnetic forces dominate beyond the sonic point (blue inverted triangle).
• Figure 5: Angular momentum loss rate (top panel) and mass loss rate (bottom panel) as a function of coronal base temperature in WD wind solutions with various values of the polytropic index $\alpha$, as color-coded. The vertical dashed lines indicate the corresponding hydrostatic corona limiting temperature. In all cases the rotation rate and magnetic field strength are held at their solar values, and the coronal base density is fixed at $\rho_0=10^{14} m_p\,$m$^{-3}$ in calculating the mass loss rate.