Black Holes Exist?

It’s an obvious question. How can you see something that doesn’t reflect light? At all! 

Artist conception (Ohio State University)

The idea of a black hole comes from a pretty simple high school physics calculation. There is a thing called escape velocity. If you toss up a baseball at 30 mph it comes back down. If you toss it at 100 mph it still comes down but, of course, it goes significantly higher. So, at what speed must you throw the ball (or launch the rocket) so that it goes up but never comes down? That’s escape velocity. You can calculate it by turning the question around. Ask, If I dropped a ball from rest from really, really far away, how fast will it be going when it smacks into the ground? That’s escape velocity. Starting with that velocity will get you really, really far away.

Escape velocity for Earth is about 7 miles/sec or 25,000 mph. As you might expect the escape velocity for more massive planets is larger although it depends on the diameter of the planet as well. If you had an ‘Earth’ with the same mass but twice as big the escape velocity would be smaller because you’d be starting farther from the center.

Now, ask the question, What if we put in the speed of light for the escape velocity in that little formula. Since that’s the top speed allowed in the universe what sort of object would that lead us to? Let’s do it for the sun. Let’s use the known mass of the sun, put in the speed of light and solve for R.

Doing that gets you 6 kilometers  for the diameter of the sun! That’s down from its actual 12,000 kilometer diameter! So if the sun were to shrink down to a ball only 6 kilometers in diameter it would become a black hole. A thing whose surface gravity has gotten so large that not even light can escape from it.

The formation of a black hole (btw our sun is never going to do that) requires a huge mass in a small space. Is there any mechanism for this to happen?

The life cycle of stars

Stars are born by the gravitational attraction of space dust. Just hydrogen and crap floating around perhaps from a long dead star. With enough mass the stuff squeezes itself into a ball and with enough stuff and enough pressure ignites a nuclear fire. Fusing hydrogen atoms forming helium in an ongoing chain reaction - a nuclear bomb. The bomb stays together via gravity - the outward pressure of the nuclear chain reactions balanced by the inward press of gravity and we have a star that will ‘burn’ like this for billions of years.

At some point though you just run out of fuel. You’ve fused much of the hydrogen into helium and the helium will fuse to form heavier atoms and so on up the periodic table. To iron. That’s where it stops.

Elements are heavier as you move to the right and down the table.

After iron on the periodic table it takes more energy to fuse the nuclei than will be released by the reaction.* You can’t have a chain reaction that way. As the fuel dries up the star can no longer support itself. It will grow in size due to burning heavier elements but as some point not enough outward pressure to hold back the inward crush of gravity. In stars the size of our sun and larger there comes a moment when the collapse is sudden and spectacularly violent. A nova or super nova. The rapid inward collapse followed by an outward explosion and ejection of much of the star’s mass. Usually this will leave behind a small dense thing called a neutron star or white dwarf. Super dense they are the remnants of once bright stars.

But if you start with a star much bigger than our sun, say 100 times the mass of our sun, ** when they die there is nothing to stop that inward crush of gravity. The star will shrink down to …

a point. Something with zero size and infinite density. Infinite escape velocity.

A black hole.

At some distance from this point you reach a place where the escape velocity has dropped down from infinity to the speed of light . This is the border or ‘size’ of the black hole called the event horizon or Schwarzschild radius. The more massive the black hole the larger this radius.

This is all well and good but prove it! You can’t see one because they emit no light and any light that falls into them never comes out. But, as material falls into a black hole it gets shredded to bits. Just before it passes the point of no return it will emit x-rays. So to detect a black hole you look for strong sources of x-rays coming from . . . an empty place in the sky!

You also look for speeds of stars orbiting near the center of our galaxy (and others) that are going ‘too fast’ for the observable mass around them. We then conclude that there must be a super massive black hole at the center of our galaxy and, indeed, at the center of most spiral and elliptical galaxies. The center of our own Milky Way galaxy contains a super massive black hole with about 100,000 times the mass of our sun! All that mass shrunk down to a point in space!  Interesting to note that super massive stars beyond about 120 solar masses do not exist. (with one notable exception). Stars above this mass are simply not stable. The existence of a black hole with hundreds of thousands of solar masses might be due to a black hole constantly swallowing mass from its surroundings or even merging with other black holes.

With the new LIGO gravitational wave detector we now have evidence of two black holes orbiting and then combining in a super collision event that sends out ripples in the very fabric of space and time.

* You might wonder then where we get all the elements beyond Iron on the periodic table? Since the universe started with a big bang which led to the formation of simple elements of hydrogen and some helium. Those elements glomed together forming the first stars. Super massive stars die in a supernova explosion and at that moment can fuse heavier elements forming the elements beyond Iron. Any elements on this earth or even in your body that are heavier than Iron we’re formed eons ago by the explosion of a long defunct super massive star.

You’re welcome!






 ** Star mass can be measured two ways. With a binary system, two stars orbiting each other - which is common, you can infer the mass from the orbital data of distance separating the stars and the period of rotation. Also, stars mostly lie on a graph called the ‘main sequence’. Knowing the temperature spectrum of the star will tell you its mass.