2020年GeCAA理论第4题-光变曲线

英文题目

The light curve A shown below, shows a fictional edge-on eclipsing binary system containing stars X (radius $$r_{X}$$ , luminosity $$L_{X}$$ ) and Y (radius $$r_{Y}$$ , Luminosity $$L_{Y}$$ ) . Assume that star X is brighter, but star Y is hotter.

(a) (1 point) Which of the two stars is likely to be on the main sequence? (Write “X”or “Y”)

(b) Based on light curve A, estimate:

(I) (2 points) $$\frac{r_{X} }{r_{Y}} $$, the ratio of the radii of the two stars.

(II) (2 points)$$\frac{L_{X} }{L_{Y}} $$, the ratio of the Luminosity of the two stars.

(c) (15 points) For light curves B to F, in each case only one parameter of the binary system has been changed from the case in light curve A. For each case, choose the description from the following list that best corresponds to the change (Write the appropriate roman numeral in the answer sheet).

(i) Star X increased in size.

(ii) Star X increased in luminosity.

(iii) Star X decreased in size.

(iv) Star X decreased in luminosity.

(v) Star Y increased in size.

(vi) Star Y increased in luminosity.

(vii) Star Y decreased in size.

(viii) Star Y decreased in luminosity.

(ix) Star X is a variable star.

(x) Star Y is a variable star.

(xi) The inclination of the system relative to the Earth has changed.

(xii) The distance of the system from the Earth has decreased.

(xiii) The distance of the system from the Earth has increased.

(xiv) The orbital period of the system increased.

(xv) The orbital period of the system decreased.

中文翻译

下图所示的光变曲线 A 展示了一个虚构的边缘视角食双星系统，包含恒星 X（半径 $$r_{X}$$，光度 $$L_{X}$$）和 Y（半径 $$r_{Y}$$，光度 $$L_{Y}$$）。假设恒星 X 更亮，但恒星 Y 更热。

(a) (1 point) 这两颗恒星中哪一颗可能在主序星上? ( “X” or “Y”)

(b) 基于光变曲线A，估算：

(I) (2 points) $$frac{r_{X} }{r_{Y}} $$，两个恒星半径的比值。

(II) (2 points) $$frac{L_{X} }{L_{Y}} $$，两颗恒星的光度比。

(c) (15 points) 对于光变曲线 B 到 F，在每种情况下，双星系统只有一个参数与光变曲线 A 的情况不同。对于每种情况，从下列列表中选择最能对应变化的描述（在答题纸上写下相应的罗马数字）。

(i) 恒星X增大了。

(ii) 恒星X亮度增加。

(iii) 恒星X缩小了。

(iv) 恒星X亮度下降。

(v) 恒星Y增大了。

(vi) 恒星Y亮度增加。

(vii) 恒星Y缩小了。

(viii) 恒星Y亮度下降。

(ix) 恒星X是一颗变星。

(x) 恒星Y是一颗变星。

(xi) 系统相对于地球的倾角发生了变化。

(xii) 系统离地球的距离减小了。

(xiii) 系统离地球的距离增加了。

(xiv) 系统的轨道周期增加了。

(xv) 系统的轨道周期减小了。