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Register a new userThe Mass and Radius of the Unseen M-Dwarf Companion in the Single-Lined Eclipsing Binary HAT-TR-205-013
الجسم الشامل والشعاع لصديق المصغر M الغير مرئي في الثنائي المغطى الواحد HAT-TR-205-013
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نحن نستخرج الأحجام والقطر لكلا المكونين في الثنائي المغطى بالظل HAT-TR-205-013، الذي يتكون من برامج الأولى الف7V والثانية الأخيرة الأخضر الصغير. يحتوي النظام على فترة قصيرة، $P = 2.230736 pm 0.000010$ يوم، مع مدار لا يمكن التمييز منها، $e = 0.012 pm 0.021$. نحن نظهر بشكل عام أن جرعة الأرضية للنجم الثاني في الثنائي المغطى بالظل الذي يعاني من الظلال الكاملة يمكن أن يستخرج من خصائص المنحنى الضوئي والمدار البصري. وهذا يقيد الثاني إلى خط مميز في مخطط الحجم-القطر مع $M/R^2$ = الثابت. ل HAT-TR-205-013، نحن نفترض أن المدار قد تم تحويله إلى دائرة، وأن دوران الأولى قد تم مزامنته ومحاذاةه مع محور المدار. يعطي توسع الخط الملتقط منا، $V_{rm rot} sin i_{rm rot} = 28.9 pm 1.0$ كم/ثانية، قطرا للأولى $R_{rm A} = 1.28 pm 0.04$ رسون. يؤدي تحليل المنحنى الضوئي إلى قطر الثاني، $R_{rm B} = 0.167 pm 0.006$ رسون، والمحور النصفي للمدار، $a = 7.54 pm 0.30 rsun = 0.0351 pm 0.0014$ يو آر. وبالتالي، يعطي المدار البصري المغطى بالظل والمحور النصفي الأحجام الفردية، $M_{rm B} = 0.124 pm 0.010$ مشون و$M_{rm A} = 1.04 pm 0.13$ مشون. يقع نتيجتنا ل HAT-TR-205-013 B فوق الأنظمة النموذجية الحجم-القطر من مجموعة ليون، متوافقة مع النتائج من الثنائيات المغطى بالظل المزدوج الخط. يقدم الأسلوب الذي نصحبه فرصة لدراسة نهاية القاعدة الضئيلة من علاقة الحجم-القطر للنجوم.
We derive masses and radii for both components in the single-lined eclipsing binary HAT-TR-205-013, which consists of a F7V primary and a late M-dwarf secondary. The systems period is short, $P=2.230736 pm 0.000010$ days, with an orbit indistinguishable from circular, $e=0.012 pm 0.021$. We demonstrate generally that the surface gravity of the secondary star in a single-lined binary undergoing total eclipses can be derived from characteristics of the light curve and spectroscopic orbit. This constrains the secondary to a unique line in the mass-radius diagram with $M/R^2$ = constant. For HAT-TR-205-013, we assume the orbit has been tidally circularized, and that the primarys rotation has been synchronized and aligned with the orbital axis. Our observed line broadening, $V_{rm rot} sin i_{rm rot} = 28.9 pm 1.0$ kms, gives a primary radius of $R_{rm A} = 1.28 pm 0.04$ rsun. Our light curve analysis leads to the radius of the secondary, $R_{rm B} = 0.167 pm 0.006$ rsun, and the semimajor axis of the orbit, $a = 7.54 pm 0.30 rsun = 0.0351 pm 0.0014$ AU. Our single-lined spectroscopic orbit and the semimajor axis then yield the individual masses, $M_{rm B} = 0.124 pm 0.010$ msun and $M_{rm A} = 1.04 pm 0.13$ msun. Our result for HAT-TR-205-013 B lies above the theoretical mass-radius models from the Lyon group, consistent with results from double-lined eclipsing binaries. The method we describe offers the opportunity to study the very low end of the stellar mass-radius relation.
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