AI 中文总结
本研究针对磁性白矮星金属污染问题，推导沉降与扩散时标之比的温度依赖关系，结合磁场计算其随磁场强度的变化，发现磁场扩展丰度斑块范围有限，提出吸积率十年尺度变化的可能解决方案。
AI 中文摘要
对被金属污染的磁性白矮星的观测表明，大多数这类白矮星的金属在极区的浓度高于低纬度地区。维持这种丰度梯度要求对流区下方的重力沉降时间$t_\text{↓}$短于对流涡旋在表面的水平扩散时间$t_\text{↔}$。我们通过解析推导得出，$t_\text{↓}/t_\text{↔}$与$T^{8/3}$成正比，其中$T$是对流区底部的温度，当对流更深地穿透大气层时，该温度会升高一个数量级以上。相应地，$t_\text{↓}/t_\text{↔}$会跃升数个数量级，从而清晰区分出存在丰度差异的热白矮星与表面均匀的冷白矮星。我们首次将磁场自洽地纳入恒星结构计算，得出沉降与扩散时标之比随磁场强度$B$的变化关系。在给定有效温度$T_{\rm eff}$下，磁性白矮星的对流区更浅，且对流的向内穿透会向更低的$T_{\rm eff}$偏移。定量来看，$B\backsim10^5\textrm{ G}$会将增强丰度斑块的范围从氦主导大气下$T_{\rm eff}\backsim30000\textrm{ K}$（氢主导大气下为$13000\textrm{ K}$）扩展到$T_{\rm eff}\backsim15000\textrm{ K}$（氢主导大气下为$6000\textrm{ K}$），但这仍不足以解释观测到的更冷的斑块状白矮星。一个可能的解决方案是吸积率在十年时间尺度上的变化，这一现象已在另一颗白矮星中被观测到。
英文摘要
Observations of magnetic polluted white dwarfs indicate that most of them have higher concentrations of metals near the poles compared to lower latitudes. Maintaining such abundance gradients requires gravitational sinking times $t_\downarrow$ below the convection zone that are shorter than the horizontal spreading time $t_\leftrightarrow$ across the surface by convective eddies. We show analytically that $t_\downarrow/t_\leftrightarrow\propto T^{8/3}$, where $T$ is the temperature at the base of the convection zone, which rises by more than an order of magnitude as convection penetrates deeper into the atmosphere. Correspondingly, $t_\downarrow/t_\leftrightarrow$ jumps by several orders of magnitude, clearly delineating between hot white dwarfs with abundance variations and cold ones with homogenous surfaces. We incorporate magnetic fields self-consistently into the stellar structure and compute for the first time the sinking to spreading time-scale ratio as a function of $B$. Magnetic white dwarfs have shallower convection zones at a given $T_{\rm eff}$, and the inward penetration of convection shifts to lower $T_{\rm eff}$. Quantitatively, $B\sim 10^5\textrm{ G}$ extends the range for enhanced abundance patches from $T_{\rm eff}\gtrsim 30\,000 \textrm{ K}$ ($13\,000\textrm{ K}$) to $T_{\rm eff}\gtrsim 15\,000 \textrm{ K}$ ($6000\textrm{ K}$) for helium (hydrogen) dominated atmospheres, which is insufficient to explain the observed patchy white dwarfs, which are even colder. A possible solution is variability in the accretion rate on a time-scale of a decade, as recently detected in another white dwarf.
Commentssubmitted to MNRAS, comments welcome
