“2016年IOAA理论第8题-U波段测光”的版本间的差异
（创建页面，内容为“==英文题目== '''(T8) U-Band photometry''' A star has an apparent magnitude 𝑚<sub>U</sub> = 15.0 in the U-band. The U-band filter is ideal, i.e., it has perfe…”） |
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==英文题目== | ==英文题目== | ||
'''(T8) U-Band photometry''' | '''(T8) U-Band photometry''' | ||
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𝑓 = 3631 × 10<sup>−0.4𝑚</sup>Jy | 𝑓 = 3631 × 10<sup>−0.4𝑚</sup>Jy | ||
| − | (T8.1) Approximately how many U-band photons, | + | (T8.1) Approximately how many U-band photons, 𝑁<sub>0</sub> |
, from this star will be incident normally on a | , from this star will be incident normally on a | ||
1 m<sup>2</sup> | 1 m<sup>2</sup> | ||
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(T8.2) What is the ratio, 𝑅, of number of photons received per second from the star to that received | (T8.2) What is the ratio, 𝑅, of number of photons received per second from the star to that received | ||
from the sky, when measured over a circular aperture of diameter 2′′? | from the sky, when measured over a circular aperture of diameter 2′′? | ||
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(T8.3) In practice, only 20% of U-band photons falling on the primary mirror are detected. How many | (T8.3) In practice, only 20% of U-band photons falling on the primary mirror are detected. How many | ||
photons, 𝑁<sub>t</sub> | photons, 𝑁<sub>t</sub> | ||
, from the star are detected per second? | , from the star are detected per second? | ||
| + | ==中文翻译== | ||
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| + | '''(T8) U波段测光''' | ||
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| + | 恒星在U波段的视星等为$$m_{\rm U} = 15.0$$。U波段是理想的，也就是说，这一波段的透明度是完美的（100%）并且在该波段外完全不透光（透明度0%）。滤波器的中心是$$360 \rm{nm}$$，宽度为$$80 \rm{nm}$$。假设恒星在这一频率的能谱是平坦的。在任意波段下，星等$$m$$和恒星通量密度$$f$$（单位为央斯基，$$1 \rm{Jy} = 1\times 10^{-26} \rm{W} \cdot \rm{Hz}^{-1} \cdot \rm{m} ^{-2} $$）的转换关系为 | ||
| + | \[ | ||
| + | f = 3631 \times 10^{-0.4m} \rm{Jy} | ||
| + | \] | ||
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| + | (T8.1) 每秒来自这颗恒星的U波段光子垂直入射到地球大气层顶部$$1 \rm m^2$$的区域的数目$$N_0$$大约为多少？ | ||
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| + | 这颗恒星是用一台直径为$$2.0 \rm m$$的地面望远镜在U波段观测到的。观测期间U波段的大气消光率为50%。假设视宁度达到衍射极限。实测U波段夜空表面平均亮度为22.0等。 | ||
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| + | (T8.2) 当从一个直径为2"的圆形小孔中观测时，每秒从恒星接收到的光子数与从天空接收到的光子数之比$$R$$是多少？ | ||
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| + | (T8.3) 实际上，只有20%的U波段光子落在主镜上。每秒检测到的来自恒星的光子的数目$$N_{\rm t}$$是多少？ | ||
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[[分类:星等]] | [[分类:星等]] | ||
2019年9月15日 (日) 19:11的最新版本
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英文题目
(T8) U-Band photometry
A star has an apparent magnitude 𝑚U = 15.0 in the U-band. The U-band filter is ideal, i.e., it has perfect (100%) transmission within the band and is completely opaque (0% transmission) outside the band. The filter is centered at 360 nm, and has a width of 80 nm. It is assumed that the star also has a flat energy spectrum with respect to frequency. The conversion between magnitude, 𝑚, in any band and flux density, 𝑓, of a star in Jansky (1 Jy = 1 × 10−26 W Hz −1 m−2 ) is given by
𝑓 = 3631 × 10−0.4𝑚Jy
(T8.1) Approximately how many U-band photons, 𝑁0 , from this star will be incident normally on a 1 m2 area at the top of the Earth's atmosphere every second?
This star is being observed in the U-band using a ground based telescope, whose primary mirror has a diameter of 2.0 m. Atmospheric extinction in U-band during the observation is 50%. You may assume that the seeing is diffraction limited. Average surface brightness of night sky in U-band was measured to be 22.0 mag/arcsec2 .
(T8.2) What is the ratio, 𝑅, of number of photons received per second from the star to that received from the sky, when measured over a circular aperture of diameter 2′′?
(T8.3) In practice, only 20% of U-band photons falling on the primary mirror are detected. How many photons, 𝑁t , from the star are detected per second?
中文翻译
(T8) U波段测光
恒星在U波段的视星等为$$m_{\rm U} = 15.0$$。U波段是理想的，也就是说，这一波段的透明度是完美的（100%）并且在该波段外完全不透光（透明度0%）。滤波器的中心是$$360 \rm{nm}$$，宽度为$$80 \rm{nm}$$。假设恒星在这一频率的能谱是平坦的。在任意波段下，星等$$m$$和恒星通量密度$$f$$（单位为央斯基，$$1 \rm{Jy} = 1\times 10^{-26} \rm{W} \cdot \rm{Hz}^{-1} \cdot \rm{m} ^{-2} $$）的转换关系为 \[ f = 3631 \times 10^{-0.4m} \rm{Jy} \]
(T8.1) 每秒来自这颗恒星的U波段光子垂直入射到地球大气层顶部$$1 \rm m^2$$的区域的数目$$N_0$$大约为多少？
这颗恒星是用一台直径为$$2.0 \rm m$$的地面望远镜在U波段观测到的。观测期间U波段的大气消光率为50%。假设视宁度达到衍射极限。实测U波段夜空表面平均亮度为22.0等。
(T8.2) 当从一个直径为2"的圆形小孔中观测时，每秒从恒星接收到的光子数与从天空接收到的光子数之比$$R$$是多少？
(T8.3) 实际上，只有20%的U波段光子落在主镜上。每秒检测到的来自恒星的光子的数目$$N_{\rm t}$$是多少？
