Electron heat conduction in the solar wind: transition from Spitzer-H\"{a}rm to the collisionless limit

We use a statistically significant set of measurements to show that the field-aligned electron heat flux $q_\parallel$ in the solar wind at 1 AU is consistent with the Spitzer-H\"{a}rm collisional heat flux $q_{sh}$ for temperature gradient scales larger than a few mean free paths $L_T \gtrsim 3.5 ~\lambda_{fp}$. This represents about 65% of the measured data and corresponds primarily to high $\beta$, weakly collisional plasma ('slow solar wind'). In the more collisionless regime $\lambda_{fp}/L_T \gtrsim 0.28$, the electron heat flux is limited to $q_\parallel/q_0 \sim 0.3$, independent of mean free path, where $q_0$ is the 'free-streaming' value; the measured $q_\parallel$ does not achieve the full $q_0$. This constraint $q_\parallel/q_0 \sim 0.3$ might be attributed to wave-particle interactions, an interplanetary electric potential, or inherent flux limitation. We also show a $\beta_e$ dependence to these results that is consistent with a local radial electron temperature profile $T_e \sim r^{-\alpha}$ that is a function of the thermal electron beta $\alpha = \alpha(\beta_e)$ and that the $\beta$ dependence of the collisionless regulation constraint is not obviously consistent with a whistler heat flux instability. We discuss the results in a broader astrophysical context.