[论文解读] Eclipsing binaries observed with the WIRE satellite. II. beta Aurigae and non-linear limb darkening in light curves

J. Southworth, H. Bruntt+1 more|arXiv (Cornell University)|Mar 25, 2007

Stellar, planetary, and galactic studies被引用 75

一句话总结

本研究基于WIRE卫星获得了比 Aurigae双星系统迄今为止最精确的光曲线，采用改进的ebop代码对非线性边缘暗化效应和光谱光度比进行建模。结果表明，非线性边缘暗化显著提升了拟合质量，并使恒星半径相比线性定律提高了0.4%；当引入光谱数据时，半径测量精度达到0.5%。

ABSTRACT

We present the most precise light curve ever obtained of a detached eclipsing binary star and use it investigate the inclusion of non-linear limb darkening laws in eclipsing binary light curve models. This light curve, of the bright system beta Aurigae, was obtained using the star tracker aboard the WIRE satellite and contains 30000 datapoints with a scatter of 0.3 mmag. We analyse it using a version of the EBOP code modified to include non-linear limb darkening and to directly incorporate observed times of minimum light and spectroscopic light ratios into the solution as individual observations. We also analyse the dataset with the WD code to ensure that the two models give consistent results. EBOP provides an excellent fit to the WIRE data. Whilst the fractional radii are only defined to a precision of 5%, including an accurate published spectroscopic light ratio improves this dramatically to 0.5%. Using non-linear limb darkening improves the quality of the fit significantly and causes the measured radii to increase by 0.4%. It is possible to derive all of the limb darkening coefficients from the light curve, although they are strongly correlated with each other, and they agree with theoretical predictions. The radii and masses of the components of beta Aur are R_A = 2.762 +/- 0.017 Rsun, R_B = 2.568 +/- 0.017 Rsun, M_A = 2.376 +/- 0.027 Msun and M_B = 2.291 +/- 0.027 Msun. Theoretical stellar models can match these parameters for a solar metal abundance and an age of 450-500 Myr. The Hipparcos trigonometric parallax and an interferometrically-derived orbital parallax give distances to beta Aur which are in excellent agreement with each other and with distances derived using surface brightness relations and several sets of empirical and theoretical bolometric corrections (abridged).

研究动机与目标

• 利用WIRE卫星的星跟踪仪获取分离开双星系统最精确的光曲线。
• 研究非线性边缘暗化定律对分离开双星光变曲线光度建模的影响。
• 通过引入光谱光度比和观测到的最小光时刻，提高恒星半径和质量测量的精度。
• 通过高精度积分验证非线性边缘暗化下的ebop代码与Wilson-Devinney代码的一致性。
• 检验经验恒星参数与理论演化模型及多种距离指示器的一致性。

提出的方法

• 采用改进的ebop代码版本，包含非线性边缘暗化定律（二次和平方根形式），并直接将观测到的最小光时刻和光谱光度比作为约束条件。
• 通过广泛的蒙特卡洛模拟推导所有拟合参数的稳健不确定性。
• 将ebop结果与使用最高积分精度和长迭代时间的Wilson-Devinney代码（wd2003）结果进行比较，以检测系统误差。
• 以Smith（1948）的光谱轨道和NJ94的光谱光度比作为光度解的锚定依据。
• 结合Hipparcos三角视差和干涉测量轨道视差，交叉验证距离。
• 评估拟合的边缘暗化系数与理论模型大气的符合程度。

实验结果

研究问题

• RQ1 在高精度分离开双星光曲线中，引入非线性边缘暗化定律是否显著改善光度拟合质量？
• RQ2 引入光谱光度比在多大程度上降低了恒星半径测量的不确定性？
• RQ3 拟合的边缘暗化系数与理论模型大气预测结果相比如何？
• RQ4 当应用于超精密数据时，Wilson-Devinney代码能否与ebop产生一致结果？其计算需求如何？
• RQ5 β Aurigae的推导物理参数是否与太阳金属丰度和特定年龄范围的理论恒星演化模型一致？

主要发现

• WIRE卫星对β Aurigae的光曲线包含30,015个数据点，点对点散差为0.3 mmag，是迄今最精确的分离开双星光曲线。
• 引入非线性边缘暗化显著提升了拟合质量，与线性边缘暗化定律相比，测得的恒星半径增加了0.4%。
• 引入NJ94提供的光谱光度比后，恒星半径的不确定性从5%降低至0.5%，凸显其在高精度光度测量中的关键作用。
• 二次和平方根形式的边缘暗化系数拟合结果与理论预测在误差范围内一致，尽管两者高度相关。
• Wilson-Devinney代码仅在高精度积分和大量迭代下产生一致解，所得的总辐射反照率为0.6，与对流包层一致。
• 推导的物理参数——半径分别为2.762±0.017 R☉ 和 2.568±0.017 R☉，质量分别为2.376±0.027 M☉ 和 2.291±0.027 M☉——与450–500 Myr年龄和太阳金属丰度的理论模型一致。