Although numerous white dwarf stars host dusty debris disks, the temperature distribution of these stars differs significantly from the white dwarf population as a whole. Dusty debris disks exist exclusively around white dwarfs cooler than 27,000 K. This is all the more enigmatic given that the formation processes of dusty debris disks should favor younger, hotter white dwarfs, which likely host more dynamically unstable planetary systems. Here we apply a sophisticated material sublimation model to white dwarf systems to show that these statistics are actually a natural result of the interplay of thermal and tidal forces and how they define the circumstellar regions where dusty debris disks can form. We demonstrate that these processes tend to prevent stability against both sublimative destruction and reaccretion into planetesimals for rocky materials until white dwarfs cool to below ∼25,000–32,000 K, in agreement with the observed limit of ∼27,000 K. For pure water ice, this critical temperature is less than 2700 K (requiring a cooling age older the universe); this precludes pure water ice–rich debris disks forming through the accepted two-step mechanism. The critical temperature is size-dependent; more massive white dwarfs could potentially host dusty debris disks at warmer temperatures. Our model suggests that the location of the disks within the PG 0010+280, GD 56, GD 362, and PG 1541+651 systems are consistent with a forsterite-dominated olivine composition. We also find that very cool white dwarfs may simultaneously host multiple, independently formed dusty debris disks, consistent with observations of the LSPM J0207+3331 system.

尽管许多白矮星都有尘埃碎片盘，但这些恒星的温度分布与整个白矮星种群有很大不同。尘埃碎片盘只存在于温度低于 27,000 K 的白矮星周围。考虑到尘埃碎片盘的形成过程应该有利于更年轻、更热的白矮星，而这些白矮星可能拥有更动态不稳定的行星系统，这更加神秘。在这里，我们将复杂的材料升华模型应用于白矮星系统，以表明这些统计数据实际上是热力和潮汐力相互作用的自然结果，以及它们如何定义可以形成尘埃碎片盘的星际区域。我们证明了这些过程往往会阻止岩石材料的升华破坏和再吸积到小行星中的稳定性，直到白矮星冷却到~25,000-32,000 K以下，这与观察到的~27,000 K的极限一致。对于纯水冰，这个临界温度低于 2700 K（需要一个比宇宙更老的冷却年龄）；这排除了通过公认的两步机制形成纯水富含冰的碎片盘。临界温度取决于尺寸；在更高的温度下，更大质量的白矮星可能会承载尘土飞扬的碎片盘。我们的模型表明，PG 0010+280、GD 56、GD 362 和 PG 1541+651 系统内的圆盘位置与镁橄榄石为主的橄榄石成分一致。我们还发现非常酷的白矮星可能同时拥有多个，