非接觸型與半接觸型食雙星光變曲線合成與分析

Abstract

食雙星的光變曲線合成可以幫助我們得到雙星系統的物理參數包括了恆星質量、半徑等資訊，有助於瞭解雙星系統的結構及演化過程。針對非接觸型雙星系統，我們模型使用簡單球體模型搭配三角幾何運算並加入臨邊昏暗效應的修正來合成光變曲線；而對於半接觸型雙星系統，則基於Kopal的方法計算系統的洛希重力等位面並以線性關係式對臨邊昏暗效應做修正。我們選擇XY Cet 和DD Mon 這兩個分別是非接觸與半接觸型雙星系統來做模型的測試與驗證，它們的星等觀測資料均來自All Sky Automated Survey (ASAS)，物理參數則參考Gazeas、Southworth等人的研究。從光變曲線合成的結果來看，我們使用的方法的確可以成功建立食雙星的光變曲線模型，同時也可以藉由對觀測資料的擬合得出系統的物理參數。我們也分析了CQ Ser 這個食雙星系統的光變曲線，它的星等觀測資料部份來自於ASAS，另一部份則使用我們自己以台師大RC16望遠鏡觀測所得到的資料，而擬合過程所需的模型初始參數則是直接從光變曲線估計得出。擬合的結果成功給出了CQ Ser的物理參數同時也顯示了這個雙星系統的狀態可能是兩個成員星都幾乎脹滿了洛希瓣的半接觸型雙星系統。

Light curve synthesis of eclipsing binaries can help us build a physical model of the binary systems and get the physical parameters of them. For detached binaries, we use the simple spherical model with the concepts of trigonometry and linear limb-darkening law to synthesize the light curve; on the other hand, for semi-detached systems, the model we used is base on Kopal’s methods that assuming the systems have circular orbits and using Roche model with considering the limb-darkening effect. We synthesized and analyzed the light curve of XY Cet and DD Mon which are detached and semi-detached system respectively with the photometric data taken from All Sky Automated Survey (ASAS) and the parameters used in our model were obtained from Gazeas (2010) and Southworth (2011). The results of synthetic light curves show that the methods we used have ability to construct a physical model of eclipsing binaries with certain reliability and could derive the system parameters by light curve fitting process. Then we analyzed the light curve of CQ Ser using photometric data combining with ASAS and our observation which observed with RC16 telescope at FRO of NTNU. The initinal parameters used in the fitting process were estimated from the light curve directly. The result of light curve fitting shows some system parameters and indicates that the system may be a semi-detached system with the both components almost filling the critical Roche lobe.