IOAA 2021 — Задача 1. ALMA - Calculating photons (10 points).

Theory — Q4-1, English (Official) — ALMA - Calculating photons · 10 т.

Условие

ALMA is a radio observatory with a revolutionary design. It consists of 66 high-precision antennas, operating in the wavelength range from $0.32\ \mathrm{mm}$ to $8.60\ \mathrm{mm}$. The principal array has fifty antennas of $12\ \mathrm{m}$ diameter each that can work together as a single telescope in the so-called interferometric mode. There is also another array of four $12\ \mathrm{m}$ antennas, and twelve smaller antennas of $7\ \mathrm{m}$ diameter each.

Imagine that a single $12\ \mathrm{m}$ antenna is being calibrated, pointing to a source with a known incident flux of $1 \times 10^{-20}\ \mathrm{W/m^2}$

4.1 Assuming that all the flux arrives at the shortest wavelength of ALMA sensitivity, determine the average number of photons that would reach the detector every second. [2 т.]

4.2 Compare it to the average number of photons that would have reached the detector, if all the flux arrived at the longest wavelength of operation. [2 т.]

4.3 What is the angular resolution (in arcsec) of a single $12\ \mathrm{m}$ antenna, operating at $74.9\ \mathrm{GHz}$? [2 т.]

4.4 Imagine the principal array operating at $74.9\ \mathrm{GHz}$ in the interferometric mode. Assuming for simplicity that the spatial resolution is solely given by the longest baseline (largest distance between any pair of antennas), which turns to be $D_{\max} = 16\ \mathrm{km}$, what would be the angular resolution (in arcsec) in this case? Treat this case as a single slit aperture instead of a circular one. [2 т.]

4.5 For a radio antenna, the term SEFD refers to 'System Equivalent Flux Density', which is a characteristic energy flux density of the antenna, depending on its temperature and size. We also note that for energy estimation of radio photons, Rayleigh-Jeans approximation is valid. Assuming a system temperature of $691\ K$, what would be the SEFD of the full ALMA observatory in Jansky if all the 66 antennas could work together? [2 т.]

Решение

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Оригинал в Архива: TQ-4-Q.pdf