  When an ideal insulator is cooled, four regimes of thermal conductivity are
expected to emerge one after another. Two of these, the Ziman and the
Poiseuille, are hydrodynamic regimes in which collision among phonons are
mostly Normal. It has been difficult to observe them, save for a few insulators
with high levels of isotopic and chemical purity. Our thermal transport
measurements, covering four decades of temperatures between 0.1 K and 900 K,
reveal that sapphire displays all four regimes, despite its isotopic impurity.
In the Ziman regime, the thermal conductivity exponentially increases attaining
an amplitude as large as 35,000 W/Km. We show that the peak thermal
conductivity of ultra-pure, simple insulators, including diamond, silicon and
solid helium, is set by a universal scaling depending on isotropic purity. The
thermal conductivity of sapphire is an order of magnitude higher than what is
expected by this scaling. We argue that this may be caused by the proximity of
optical and acoustic phonon modes, as a consequence of the large number of
atoms in the primitive cell.
