Why does the dephasing time saturate in open semiconductor quantum dots?

In open GaAs/AlGaAs quantum dots, $\tau_\phi$ extracted from weak-localization and conductance-fluctuation statistics saturates at low $T$; Huibers et al. (Physical Review Letters 83, 5090, 1999) studied this saturation together with the dephasing caused by applied microwave radiation. Identify the limiting source (residual electron heating, external radiation, charge fluctuators in the heterostructure, nuclear spins) from the dependence of the saturated $\tau_\phi$ on dot size, lead coupling and independently measured electron temperature.

$\tau_\phi$ versus on-chip-measured electron temperature in dots of varied size and filtering, showing which candidate source scales as predicted.