IOAA 2019, Теория — Задача 3. The supermassive black hole in the centre of Milky Way Galaxy and M87

a) (6 т.)

How large an instrument would be needed to resolve the shadow (in effect the photon capture radius, which is three times the size of event horizon) of a supermassive black hole in the centre of a galaxy? Express the result as a function of the distance $d$ and the mass $M$ of the black hole.

b)

Give the size of the instrument in units of Earth radius for

i. the supermassive black hole in the centre of M87, ($d_{\text{BH-M87}} = 5.5 \times 10^7\ \mathrm{ly}$, $M_{\text{BH-M87}} = 6.5 \times 10^{9}\ M_{\odot}$) [1 т.]

ii. and Sgr A*, the supermassive black hole of our own galaxy, Milky Way.
($d_{\text{Sgr A*}} = 8.3\ \mathrm{kpc}$, $M_{\text{Sgr A*}} = 3.6 \times 10^{6}\ M_{\odot}$) [1 т.]

c) (2 т.)

What type of technology is needed for the development of such an instrument? Mark the letter of your answer with × on the answer sheet.

(A) Gravitational lensing by dark matter (B) Interferometry with an array of radio telescopes (C) Photon deceleration in a dense environment (D) Reducing the effect of incoming wavefront distortions (E) Neutrino focusing with strong electromagnetic fields