[论文解读] Tidal effects on brown dwarfs: Application to the eclipsing binary 2MASSJ05352184-0546085 - The anomalous temperature reversal in the context of tidal heating

René Heller, Brian Jackson+3 more|GoeScholar The Publication Server of the Georg-August-Universität Göttingen (Georg-August-Universität Göttingen)|Feb 5, 2010

Stellar, planetary, and galactic studies参考文献 48被引用 10

一句话总结

本研究探讨了潮汐加热作为解释双棕矮星系统2M0535-05中次星异常温度反转和亮度增强的潜在机制。采用恒定时间滞后和恒定相位滞后潮汐模型，研究发现仅靠潮汐加热难以解释观测结果，需假设不切实际的低$Q_{\mathrm{BD}} \sim 10^{3.5}$和高自转轨道倾角（$\gtrsim 50^\circ$），而后者已被潮汐锁定 timescales 推翻，后者暗示$\log(Q_{\mathrm{BD}}) \gtrsim 4.5$。结果表明，潮汐效应可能减缓了冷却过程，但需通过耦合演化模型加以确认。

ABSTRACT

2MASSJ05352184-0546085 (2M0535-05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as an important benchmark for models of BD formation and evolution. However, theoretical predictions of the system's properties seem inconsistent with observations: i. The more massive (primary) component is observed to be cooler than the less massive (secondary) one. ii. The secondary is more luminous (by roughly 10^{24} W) than expected. We study the impact of tidal heating to the energy budget of both components. We also compare various plausible tidal models to determine a range of predicted properties. We apply two versions of two different, well-known models for tidal interaction, respectively, (i.) the 'constant-phase-lag' model and (ii.) the 'constant-time-lag' model, and incorporate the predicted tidal heating into a model of BD structure. We find that the contribution of heat from tides in 2M0535-05 alone may only be large enough to account for the discrepancies between observation and theory in an unlikely region of the parameter space. The tidal quality factor of BDs, Q_{BD}, would have to be 10^{3.5} and the secondary needs a spin-orbit misalignment greater than 50 degrees. However, tidal synchronization time scales for 2M0535-05 restrict the tidal dissipation function Q_{BD} to values greater than 10^{4.5} and rule out intense tidal heating in 2M0535-05. We provide the first constraint on Q_{BD}. Tidal heating alone is unlikely to be responsible for the surprising temperature reversal within 2M0535-05. But an evolutionary embedment of tidal effects and a coupled treatment with the structural evolution of the BDs is necessary to corroborate or refute this result.

研究动机与目标

• 评估潮汐加热是否能解释双星系统2MASS J05352184-0546085中观测到的温度反转和光度过剩。
• 评估潮汐耗散在两个组分能量预算中的作用，特别是次星异常光度（比预测值高约$10^{24}$ W）的影响。
• 利用潮汐锁定 timescales 和自转演化约束，对棕矮星的潮汐品质因子$Q_{\mathrm{BD}}$进行限制。
• 检验自转轨道倾角或非同步自转是否能在增强次星潮汐加热的同时最小化主星的加热。
• 确定潮汐加热是否可能自约1 Myr前形成以来减缓了棕矮星的冷却与收缩过程。

提出的方法

• 应用两种潮汐模型：恒定相位滞后模型和恒定时间滞后模型，均将潮汐耗散纳入棕矮星结构模型。
• 将潮汐加热率纳入棕矮星演化模型，使用质量比、轨道周期和偏心率等观测系统参数。
• 在不同假设下评估潮汐加热：同步与非同步自转，以及自转轨道倾角$\psi$高达$\sim 50^\circ$的情况。
• 利用潮汐锁定 timescales 估计推导$Q_{\mathrm{BD}}$的下限，基于观测到的自转特性与轨道衰减约束。
• 将预测的加热率与观测到的光度过剩及温度反转进行比较，以检验模型的可行性。
• 结合Rossiter-McLaughlin效应测量结果和系外行星系统中自转轨道倾角的统计，评估高$\psi$的合理性。

Figure 1: Degeneracy parameter $\tilde{\Psi}=k_{\mathrm{B}}T/(k_{\mathrm{B}}T_{\mathrm{F}})$ (solid line) with model parameters similar to those of the 2M0535 $-$ 05 primary and radius-integrated luminosity $L$ (dashed line) as a function of radius. To fit into the plot, $L$ is normalized to 10.

实验结果

研究问题

• RQ1 在2M0535-05中，仅靠潮汐加热能否解释主星质量更大但温度更低的观测到的温度反转？
• RQ2 要使潮汐加热解释次星的光度过剩，所需的潮汐品质因子$Q_{\mathrm{BD}}$是多少？该值在物理上是否合理？
• RQ3 自转轨道倾角如何影响潮汐加热率？次星中$\gtrsim 50^\circ$的倾角是否能解释观测到的光度增强？
• RQ4 潮汐锁定 timescales 对$Q_{\mathrm{BD}}$施加了何种约束？这如何影响潮汐加热作为机制的可行性？
• RQ5 自形成约1 Myr以来，潮汐加热是否可能减缓了棕矮星的冷却与收缩过程，从而在潮汐膨胀与加热之间形成反馈？

主要发现

• 在合理物理条件下，仅靠潮汐加热不足以解释2M0535-05中观测到的温度反转与光度过剩。
• 要使潮汐加热解释光度过剩，所需潮汐品质因子$Q_{\mathrm{BD}} \approx 10^{3.5}$，与来自潮汐锁定 timescales 推导出的下限$\log(Q_{\mathrm{BD}}) \gtrsim 4.5$不一致。
• 为增强次星的潮汐加热，需存在$\gtrsim 50^\circ$的自转轨道倾角，但如此高的倾角在系统寿命内难以维持。
• 恒定相位滞后与恒定时间滞后模型结果一致，后者因假设同步自转而提供了加热率的下限。
• 次星观测到的光度过剩$\approx 2.3 \cdot 10^{24}$ W无法在合理的$Q_{\mathrm{BD}}$值下由潮汐加热解释。
• 潮汐加热可能在棕矮星形成后减缓了其冷却与收缩过程，但需通过自洽的耦合潮汐-演化模型加以确认。

Figure 2: Orbital evolution of 2M0535 $-$ 05 after model #1 going back in time for 1.5 Myr. Left: Eccentricity evolution. Depending on $\tilde{Q}$ and on the age of the system, its initial eccentricity has not been smaller than $\approx 0.3133$ , which is $\approx 97.4\%$ of its current value. Right