How to calculate the power of a black hole collision

On the left, an optical image from the Digitized Sky Survey shows Cygnus X-1, outlined in a red box. Cygnus X-1 is located near large active regions of star formation in the Milky Way, as seen in this image that spans some 700 light years across. An artist's illustration on the right depicts what astronomers think is happening within the Cygnus X-1 system. Cygnus X-1 is a so-called stellar-mass black hole, a class of black holes that comes from the collapse of a massive star. New studies with data from Chandra and several other telescopes have determined the black hole's spin, mass, and distance with unprecedented accuracy.

After writing about the collision between two black holes that weren't "supposed to exist," I received the following email from Álvaro Díez, a particle physicist at the University of Warsaw:

Being a huge astrophysics enthusiast, I just built a Black Hole Collision Calculator that explains the after-effects of a star (or any astronomical object) being eaten by a massive black hole.

It's a tool that computes the amount of energy released and how every collision expands the size of the event horizon. Did you know?If the 'Sun' was swallowed up by this black hole it'll produce 10,725,744,303,045,181,715,760,000,000,000,000,000,000
Megajoules of energy waves that would ripple through the whole Universe? (That's 27,903,988 quintillion years of Earth's total energy consumption).

This is the kind of physics that I find endlessly fascinating and that I will spend hours digging into, even though it goes completely over my head. (My high school AP Physics teacher announced his retirement on the second day of school, so I spent the 5th period senior year just fucking around with speakers and amplifiers and thus totally bombed the AP exam and gave up on physics entirely.)

But if you, like me, are into this kind of stuff, there's lots of information to consume, and Díez does a great of explaining what, exactly, the fuck a lot of these heady astrophysical concepts even mean. For example:

When an object, typically a star or a star remnant, falls into a black hole, a huge amount of energy is dispersed into the Universe. The amount of energy in this flash of light varies from about 3% to 42% of the mass of the object, depending on the properties of the black hole it falls into.

artistic impression of a star being swallowed by a black hole
One of the most common ways in which this happens is what we call a tidal disruption event. In this case, when the star gets close to the black hole, different parts of it are attracted with different strengths, causing the star to be torn apart. Those bits that are closer to the black hole detach from the star and start spiraling around the black hole, before being "eaten" – i.e. passing into the event horizon and disappearing forever.

[…]

First, we need to describe what is happening before the collision: a star wandering the Universe, minding its own business. Oh no star! Look out for that black hole! To set up the initial conditions of this scenario, we need the mass of the object being eaten (Mfalling) and the mass of the black hole (Mblack hole). You can also use the event horizon's radius (Revent horizon) since a black hole's mass and radius are related.

I can at least wrap my head around that (even if I can't fathom any practical application for the knowledge). Pretty cool! Now to play with numbers.

Black Hole Collision Calculator [Álvaro Díez / Omni Calculator]

Image: Public Domain via NASA / Wikimedia Commons