2019年IOAA数据分析第2题-三重掩星的等级三星系统 - 版本历史

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 '''2. Triply eclipsing hierarchical triple stellar system (90 p)'''
 HD 181068 was one of the brightest targets which was continuously observed during the almost 4-
 year-long primary mission of NASA’s exoplanet-hunter Kepler space telescope. The spacecraft

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 !stars
 !BJD
-!$$\phi_1$$
+!𝜑<sub>1</sub>
-!$$\phi_2$$
+!𝜑<sub>2</sub>
 |-
 | rowspan="4" |1

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 b) Determine, whether star A, or the close binary (i.e. stars B and C) were closer to the
-observer during each eclipsing event. '''Write your answer in the table on the answer'''
+observer during each eclipsing event. '''Write your answer in the table on the answer sheet.'''(5 p)
 c) Using the table above, calculate (1) the dimensionless radius of each star relative to the
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 d) Based on the results obtained above, calculate the outer mass ratio (𝑞<sub>2</sub> = 𝑚<sub>BC</sub>⁄𝑚<sub>A</sub>). (8 p)
-''ii. Dynamical determination of the stellar masses using radial velocity (RV) and eclipse timing''
+''ii. Dynamical determination of the stellar masses using radial velocity (RV) and eclipse timing variations (ETV) measurements''
 To obtain RV data, ground-based spectroscopic follow up observations were carried out with four

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 as the photometric phases of the inner and outer binaries respectively. {𝑥} denotes the
 decimal part of the real number 𝑥. If {𝑥} < 0, use {𝑥} + 1 instead. Calculate the phases for
-the times of the tabulated contact events and '''write the answers in the appropriate'''
+the times of the tabulated contact events and '''write the answers in the appropriatecolumns of the table on the answer sheet Round your answers to four decimal places.'''
 (10 p)

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 Define
-$$\phi_1(t)=\{(t-T_{01})/P_1\},and\ \phi_2(t)=\{(t-T_{02})/P_2\}$$
+𝜑<sub>1</sub> (𝑡) = {(𝑡 − 𝑇<sub>01</sub>)⁄𝑃<sub>1</sub> }, and 𝜑<sub>2</sub> (𝑡) = {(𝑡 − 𝑇<sub>02</sub>)⁄𝑃<sub>2</sub> }
 as the photometric phases of the inner and outer binaries respectively. {𝑥} denotes the
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 measurements against time, the RV curve was nicely fitted in the following form:
-$$V_{rad,A}=V_\gamma +K_Asin\phi_RV$$,
+𝑉<sub>rad,A</sub> = 𝑉<sub>𝛾</sub> + 𝐾<sub>A</sub> sin𝜙<sub>RV</sub>
 where 𝑉<sub>𝛾</sub> is the systemic velocity and 𝐾<sub>𝐴</sub> is the velocity amplitude:

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 the inner system significantly larger (usually orders of magnitude) than the semi-major axis of the inner
 system. The schematic view of an example of a triple star system is illustrated in Fig. 2.1.
 Mathematically, the motion of a hierarchical triple system can be well approximated with two