2016年IOAA理论第8题-U波段测光
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?
