发表机构
The Hebrew University（希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究超大质量白矮星的德拜冷却，通过解析和数值计算冷却时间，发现冷却加速由德拜效应与对流耦合共同导致，并探讨了磁场及微观物理不确定性对冷却曲线的影响。
AI 中文摘要
近期对冷且大质量白矮星的观测开始探测到德拜冷却：一种由低温下结晶内部热容 $C_V(T)$ 消失所驱动的加速冷却阶段，这是由于声子振荡的量子性质所致。我们通过解析和数值两种方式分析了这一阶段，计算了瞬时冷却时间 $\tau(L)\equiv -\textrm{d}t/\textrm{d}\ln L$，该量是给定光度 $L$ 下白矮星数量密度的代理。我们发现，在 $L\lesssim 10^{-4}\\\\,\textrm{L}_{\odot}$ 时，由于德拜冷却与简并核心与表面同时发生的对流耦合的共同作用，冷却加速（$\tau$ 缩短），而单独任一过程都不会导致显著加速。具体而言，强磁场会抑制对流耦合，导致近乎平坦的 $\tau\propto L^{1/7}$。我们通过推广亥姆霍兹自由能来参数化固体微观物理的不确定性，使得低温下 $C_V\propto T^\delta$。目前观测到的德拜区域递减的光度函数与非磁性白矮星在 $\delta=3$（对应标准德拜模型）时的 $\tau(L)$ 大致一致。更大的样本除了探测磁性外，还能探测 $\delta<3$ 的偏差，对于质量 $M\gtrsim 1.0\\\\,\textrm{M}_{\odot}$ 的白矮星，这些偏差在银河系盘年龄 $t\approx 10\textrm{ Gyr}$ 之前会显著发散。相比之下，对于 $\delta>3$，冷却曲线收敛，因为热容由简并电子主导，$C_V\propto T$。
英文摘要
Recent observations of cold and massive white dwarfs are beginning to probe Debye cooling: an accelerated cooling phase driven by the vanishing heat capacity $C_V(T)$ of the crystallized interiors at low temperatures $T$, due to the quantum nature of phonon oscillations. We analyse this regime by calculating, both analytically and numerically, the instantaneous cooling time $τ(L)\equiv -\textrm{d}t/\textrm{d}\ln L$, which is a proxy for the number density of white dwarfs at a given luminosity $L$. We find that cooling accelerates ($τ$ shortens) at $L\lesssim 10^{-4}\,\textrm{L}_{\odot}$ due to a combination of Debye cooling and the simultaneous convective coupling of the degenerate core to the surface, with neither process causing significant acceleration on its own. Specifically, strong magnetic fields can inhibit convective coupling, leading to an almost flat $τ\propto L^{1/7}$ instead. We parametrize the uncertainty in the solid microphysics by generalizing the Helmholtz free energy such that $C_V\propto T^δ$ at low temperatures. The currently observed decreasing luminosity function in the Debye regime is tentatively consistent with $τ(L)$ of non-magnetic white dwarfs with $δ=3$, corresponding to the standard Debye model. Larger samples could probe, in addition to magnetism, deviations $δ<3$, which diverge appreciably before the Galactic disc's age $t\approx 10\textrm{ Gyr}$ for masses $M\gtrsim 1.0\,\textrm{M}_{\odot}$. For $δ>3$, in contrast, the cooling curves converge because the heat capacity becomes dominated by the degenerate electrons $C_V\propto T$.
Comments9 pages, 6 figures. Submitted to MNRAS, comments are welcome
