Answered: Problem C.2 : First Image of a Black…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

Section: Chapter Questions

Problem 1LR

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Question

Problem C.2 : First Image of a Black Hole
This problem requires you to read the following recently published scientific article:
Link: https://arxiv.org/pdf/1906.11238.pdf
Answer following questions related to this article:
(a) Calculate the photon capture radius and the Schwarzschild radius of M87∗
(in AU).
(b) Why was it not possible for previous telescopes to take such a picture of the black hole?
(c) Describe the components and functionality of the event horizon telescope.

Expert Solution

Radius of M87*

1) Photon capture radius is given as R_c = $\frac{\sqrt{27} G M}{c^{2}}$

where G = Gravitational constant = $6.67 \times 10^{- 11} N k g^{- 2} m^{2}$

M = Mass of M87* = $6.6 \times 10^{9} M O = 6.6 \times 10^{9} \times 2 \times 10^{30} k g = 1.32 \times 10^{40} k g$

c= speed of light = $3 \times 10^{8}$ m/s²

Putting the values in above formulae $R_{c} = \frac{\sqrt{27} \times 6.67 \times 10^{- 11} \times 1.32 \times 10^{40}}{{(3 \times 10^{8})}^{2}} = 1.71 \times 10^{13} m = 1.142 \times 10^{2} A U .$

2) Schwarzschild radius of M87 ( R_s) = $\frac{2 G M}{c^{2}}$

$= \frac{2 \times 6.67 \times 10^{- 11} \times 1.32 \times 10^{40}}{{(3 \times 10^{8})}^{2}} = 1.95 \times 10^{13} m = 1.306 \times 10^{2} A U$

Previous Telescopes.

Previous telescopes were not able to cope up with :

Higher Atmospheric opacity.
Increase in phase fluctuation caused by atmospheric turbulence.
Decrease efficiency in the size of the radio telescopes in the millimeter and submillimeter bands .
Array sensitivity .
Increased noise in radio receiver electronics.

Hence previous telescopes were not able to take such a picture of blackhole .