IOAA 2016, theory — Задача 8. U-Band photometry

Theoretical Examination · 20 т.

Условие

A star has an apparent magnitude $m_{\mathrm{U}} = 15.0$ 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 ($1\ \mathrm{Jy} = 1 \times 10^{-26}\ \mathrm{W\ Hz^{-1}\ m^{-2}}$) is given by

$f = 3631 \times 10^{-0.4m}\ \mathrm{Jy}$

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/arcsec$^2$.

T8.1 Approximately how many $U$-band photons, $N_0$, from this star will be incident normally on a 1 m$^2$ area at the top of the Earth's atmosphere every second? [8 т.]

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''? [8 т.]

T8.3 In practice, only 20% of U-band photons falling on the primary mirror are detected. How many photons, $N_{\mathrm{t}}$, from the star are detected per second? [4 т.]

Решение

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Оригинал в Архива: theory-qp.pdf · официални решения: theory_sol.pdf