Black holes are some of the strangest, if not the strangest, entities in the universe due to their ability to absorb light, rendering them “invisible” to human-made observation devices for distant cosmic objects. The first modern solution for general relativity characterizing black holes was discovered by Karl Schwarzschild in 1916, and the concept of a black hole as a region from which nothing can escape was first proposed by David Finkelstein in 1958. (Hawking 1988)
There are four types of black holes:
Miniature
Stellar
Intermediate
Supermassive
Supermassive black holes reside at the centers of galaxies, continuously accreting matter from their host galaxies. Their immense size and power defy imagination. The nearest supermassive black hole to us is located at the center of our own galaxy, the Milky Way, known as Sagittarius A. It is four million times more massive than our sun. The closest supermassive black hole that has been directly imaged is located in the galaxy Messier 87, which is 2.4 billion times more massive than our sun and is situated 53 million light-years away from Earth. The image is represented at Figure 1. [(Tyson 2017; “First Image of a Black Hole,” n.d.)
Figure 1: The Messier 87 Black Hole
Why are black holes “black”?
Schwarzschild Radius
Viewed from a mathematical aspect, any object with mass can be turned into a black hole if compressed to a certain dimension called the Schwarzschild radius. This quantity represents a certain size of space in which, if a body is squeezed with a constant mass, its density would become so great that its gravitational pull or escape velocity would exceed the speed of light, meaning that nothing, not even light, could escape from the body. In this case, the body would turn into a black hole.
If you were to compress the Earth to the radius of a grape seed, while keeping its mass unchanged, it would turn into a black hole. Obviously, this is impossible, but the Schwarzschild radius of a massive star is much larger, and when it explodes into a supernova, all that remains is a gravitational singularity with infinite density, and the event horizon (Figure 2) a region around the singularity which is essentially the boundary beyond which nothing can travel without being pulled into the black hole. (Hawking 2018)
Figure 2: Singularity, Event Horizon and the Schwarzchild Radius
This so-called event horizon is a space where if light passes, it cannot reflect back, and no one knows what actually happens inside it. The radius of the event horizon is equal to the Schwarzschild radius of the black hole, and the more the black hole “feeds,” the larger its event horizon, or Schwarzschild radius becomes. There is a Schwarzschild radius for every object with mass, so we could calculate, using the given equation, the minimum radius of an object to turn it into a black hole:
As mentioned in the introduction, there are four main types of black holes:
Miniature Black Holes: Miniature black holes which are hypothesized to have formed shortly after the Big Bang. Their mass can be as low as the Planck Mass.
Stellar Black Holes: Stellar-mass black holes form from the remnants of massive stars that undergo gravitational collapse at the end of their life cycles. Their mass ranges from 3 to 20 times the mass of the Sun (M⊙).
Intermediate-Mass Black Holes: Intermediate-mass black holes occupy a mysterious gap between stellar-mass and supermassive black holes. Their formation mechanism is uncertain, but theoretical predictions suggest that their masses could range from hundreds to thousands of solar masses.
Supermassive Black Holes: These types of black holes are the most massive ones, with masses ranging from millions to billions of times that of our sun.
As you can see, the mass of black holes is measured using solar masses. Since supermassive black holes can get insanely massive, we use \(log_{10}\ M_{BH}\) to display their mass, as shown in the table in the next heading. This would mean that a black hole would have \(10^{log_{10}\ M_{BH}}\) solar masses. (Sagan 1980)
The following is a data set of all published studies of supermassive black holes in galactic centers (active galactic nuclei).
To put things into perspective, the mass of our Sun is equal to 333.000 Earths. Now, taking the “lightest” black hole (NGC4395) from our data set, when we do the logarithm math, it would consist of 281.345 Suns.
The formula used to calculate the mass of the black holes is the following:
\[
M_{BH}= <f> \frac{RV^2}{G}
\]
\(M_BH\) : Black hole mass.
\(<f>\): Scale factor, the population-average multiplicative scaling factor required to bring the \(M-σ*\) relationship for AGNs into agreement with the relationship for quiescent galaxies. In this dataset, \(<f>\) is equal to 4.3(+/- 1.1).
\(R\): Speed of light times the emission-line time delay measured from the centroid of the cross-correlation function around the peak, which is a measure of the light-crossing time between the broad emission line region and the (much smaller) accretion disk.
\(V\): Second moment of the emission line profile in the variable part of the spectrum, which is a measure of the line-of-sight velocity of the gas responding to the continuum variations.
The data set of these black holes consists of Right Ascension and Declination, as mentioned earlier. Using these properties, one can precisely track and find each black hole on the night sky. A sample graph displaying the location of some of the black holes is shown below:
