Breaking gyrochronology through the collapse of coronal winds

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 ($\Omega$) 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 $\Omega$ 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 $T_0\propto B_{r0}^\sigma$ while retaining the ``standard'' dynamo relationship $B_{r0}\propto\Omega$, we show that reproducing the observed break in gyrochronology requires an exponent $\sigma\gtrsim 1.5$, 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.