2017年IOAA理论第6题-超新星1987A

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英文原题

(T6) Supernova 1987A [15 marks]

Supernova SN 1987A was at its brightest with an apparent magnitude of +3 on about 15th May 1987 and then faded, finally becoming invisible to the naked eye by 4th February 1988. It is assumed that brightness B varied with time t as an exponential decline, B=B₀e^-t/τ, where B₀ and τ are constant. The maximum apparent magnitude which can be seen by the naked eye is +6.

a) Determine the value of τ in days. [5]

b) Find the last day that observers could have seen the supernova if they had a 6-inch (15.24cm) telescope with transmission efficiency T=70%. Assume that the average diameter of the human pupil is 0.6 cm. [10]

中文翻译

超新星1987A

超新星1987A爆发于1987年5月15日，爆发最亮时的视星等达到+3等。随后，它逐渐变暗，直到1988年2月4日，减为裸眼不可见。假设它的亮度为 B，随着时间 t 的变化趋势为指数变化B=B₀e^-t/τ，其中B₀和τ是常数。裸眼的极限星等为+6等。

（a）求τ的值，以天为单位。

（b）如果观测者有一台传输效率T=70%，口径为6英寸（15.24cm）的望远镜，求他能用望远镜观测到1987A的最终日期。假设人眼的平均直径为0.6cm。