Black hole calculations, the "Event Horizon Telescope"

In summary, astronomers are on the verge of imaging the "shadow" of light from the event horizons of black holes, despite the seemingly impossible task of capturing images of such small objects. This is made possible by three factors: the large event horizons of supermassive black holes, the use of radio wavelengths which are not affected by interstellar dust, and the construction of a radio telescope as large as the Earth to achieve high angular resolution. Calculations were performed to determine the Schwarzschild radii of the supermassive black holes associated with our Milky Way galaxy and the giant elliptical galaxy M87, and the expected angular diameters of the innermost circular orbits were estimated. Finally, it was shown that radio astronomers can resolve
  • #1
Ellie Snyder
8
1

Homework Statement


Soon astronomers will be imaging the “shadow” of light from the event horizons of black holes. Since black holes are very small, this achievement seems impossible. Nevertheless, it is possible for three reasons:

1. Supermassive black holes have large event horizons.
2. Radio wavelengths of light are not affected by interstellar dust and can explore regions close to the black holes.
3. By building a radio telescope effectively as large as the Earth, astronomers can overcome the relatively poor resolution associated with long wavelengths and achieve high angular resolution.

a. Calculate the Schwarzschild radii (in kilometers) of the supermassive black holes associated with our Milky Way galaxy (4x10^8 M_Sun) and the giant elliptical galaxy M87 (3.5x10^9 M_Sun).

b. The distances of these black holes are 8.4 kpc and 16.4 mega-parsecs, respectively. What are the expected angular diameters of the innermost circular orbits, assuming a non-rotating black hole?

c. Show that radio astronomers can resolve (1.22*(wavelength/D)) these objects at =0.7 mm (c=wavelength*f; f=450 GHz) if they combine separate radio telescopes over the diameter of the Earth (12,742 km).

Homework Equations


a. R_Sch=(2GM)/c^2=(2.95 km/M_Sun)*M
b. Diam.=2arctan(d/2D)
c. Angular resolution=1.22*(wavelength/D)

The Attempt at a Solution


a. Using the eqn with 2.95/solar mass I calculated Schwarzschild Radii of 1.18*10^9 km for our galaxy's black hole, and 1.0325*10^10 km for M87.
b. Would I plug in the calculated radii for the variable d and the given distances for D to calculate the angular diameter?
c. Just convert the 0.7 mm and 12,742 km into similar units, then plug them into the angular resolution eqn?
 
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  • #2
Ellie Snyder said:

The Attempt at a Solution


a. Using the eqn with 2.95/solar mass I calculated Schwarzschild Radii of 1.18*10^9 km for our galaxy's black hole, and 1.0325*10^10 km for M87.
Our Milky Way BH is only 4x10^6 Msun, not 4x10^8.
b. Would I plug in the calculated radii for the variable d and the given distances for D to calculate the angular diameter?
Yes.
c. Just convert the 0.7 mm and 12,742 km into similar units, then plug them into the angular resolution eqn?
Yes. Make sure an keep track of your units and whether you are working in radians or degrees/minutes/seconds.
 

1. What is a black hole?

A black hole is a region in space with such strong gravitational pull that nothing, including light, can escape it. This happens when a massive star dies and collapses under its own gravity, creating a singularity - a point of infinite density and zero volume.

2. How do scientists calculate the size of a black hole?

Scientists use various methods to calculate the size of a black hole, including studying its effects on surrounding matter and using mathematical equations such as the Schwarzschild radius. The Event Horizon Telescope also uses interferometry techniques to directly image the event horizon of a black hole.

3. What is the Event Horizon Telescope?

The Event Horizon Telescope (EHT) is a global network of radio telescopes that work together to create a virtual Earth-sized telescope. It is specifically designed to capture images of the event horizon of black holes, including the famous image of the supermassive black hole at the center of the galaxy M87.

4. How does the Event Horizon Telescope capture images of a black hole?

The EHT uses a technique called Very Long Baseline Interferometry (VLBI), which combines data from multiple telescopes around the world to create a high-resolution image. This allows the EHT to effectively create a virtual telescope with a diameter as large as the Earth, providing enough resolution to capture the event horizon of a black hole.

5. Why is it important to study black holes and their event horizons?

Studying black holes and their event horizons helps us better understand the laws of physics and the nature of gravity. It also allows us to test Einstein's theory of general relativity and potentially discover new insights about the universe. The EHT's images can also provide valuable information about the formation and evolution of galaxies and the role of black holes in their centers.

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