The Black Hole Solar System

Planets are kind of my thing.  But black holes are awesome too. I mean, they can just suck you right in…  (I will never apologize for my bad jokes!)

I want to bring black holes and planets together.  In this post, I’ll first introduce black holes.  Then we’ll build the Black Hole Solar System. In future posts I’ll write separate posts about other black hole planetary systems.

To start off, a dumb question: what happens when you throw a ball in the air? The ball goes up and comes back down. As my son likes to say, “well, duh!”.

But humans are pretty wimpy. The fastest-throwing pitchers in the world can only throw a ball about 100 miles per hour. If you could launch a ball in the air at 25,000 miles per hour it never come back down. The ball would reach Earth’s escape speed (“escape velocity” if you’re not into the whole brevity thing).

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Escape speed is a measure of a body’s gravity. Stronger gravity, higher escape speed.

A fast-throwing pitcher can throw a ball clear off a rocky asteroid about 60 km (40 miles) across. The asteroid Vesta‘s escape speed is 360 meters per second, about 800 miles an hour. The Moon’s escape speed is 2.4 kilometers per second, about 5,000 miles per hour.  Jupiter has the strongest gravity of any Solar System planet, with an escape speed of 60 km/s (133,000 mph).  The Sun’s escape speed is ten times higher, 618 km/s.  The white dwarf star Sirius B has an escape speed ten times higher still, at 5,200 km/s (more than 11 million miles per hour).

These escape speeds are getting awfully fast. What is the highest escape speed you can imagine?  Well, nothing can go faster than light. Wouldn’t it be wild if there was an object with such strong gravity that its escape speed was the speed of light?

That’s what a black hole is. An object with so much gravity that even light can’t escape.

Any object can be a black hole if its escape speed is higher than the speed of light.   You could turn anything into a black hole by increasing its gravity, either by cranking up its mass or by shrinking it down. An object’s gravity depends on just two factors: mass and size.  Higher mass, stronger gravity.  Smaller size, stronger gravity. Without changing its size, Earth would be a black hole if its mass was 700 million times larger (more than 2000 times more massive than the Sun!). Or, without changing its mass Earth would be a black hole it was squished to the size of a small pebble.  The Sun would be a black hole if it was squished to the size of a football stadium.  The entire galaxy would be a black hole if it was the size of the Solar System.  You yourself would be a black hole if you were squished to about one ten-billionth the size of a proton.

The size of a black hole is typically measured by its Schwartzschild radius, or “event horizon”.  That was also the name of a pretty bad but fun movie from 1997 with Laurence Fishburne and Sam Neill.  (Side note: I have a memory of Laurence Fishburne’s character reaching into a black hole and pulling something out but I can’t find anyone on the internet to corroborate that, so I may have made it up…).  The event horizon is simply the distance from the center of the black hole where the escape speed is exactly the speed of light.

event-horizon

An illustration of the event horizon, the closest distance to a black hole from which light can escape. Credit: Answers magazine.

There are two kinds of black holes that we know best: stellar black holes and supermassive black holes. Stellar black holes are what you get if you squish a star. This happens when a massive enough star collapses on itself.  When the star’s gravity takes over and pulls in on itself with nothing to push back.

In a normal star, gravity is balanced by pressure generated by fusion.  As a star evolves, it eventually runs out of fuel for fusion.  Then there is nothing to stop the star collapsing on itself.  As massive stars collapse they trigger a supernova.  The center of the star keeps collapsing on itself and ends up as either a neutron star or a black hole.

stellar_evolution_BH.jpg

Stellar evolutionary paths.  Only very massive stars go supernova and can become black holes.  From this website.

Supermassive black holes lurk at the centers of galaxies and clusters of galaxies.  They are millions to billions times more massive than the Sun. Our own Milky Way has a black hole of about 4 million Suns. We think that supermassive black holes grew from stellar black holes.  Stellar black holes that form in large galaxies eat up neighboring stars, gas and other black holes and sink to the center of the galaxy. Supermassive cannibalized black holes!  This probably happened very early in the Universe’s history, because even extremely distant galaxies show signs of having supermassive black holes.

There are other types of black holes.  One very dense globular clusters of stars shows evidence for an intermediate-mass black hole of about 1000 Suns.  Other astronomical objects may also have black holes in this range, and theories expect them to exist, but they are hard to find.

Now let’s re-build our Solar System with a black hole. 

A common thought experiment in physics classes is to imagine that the Sun was replaced with a black hole of exactly the same mass. What would change?  The answer is that nothing would change regarding the planets’ orbits. All that orbits care about is mass, and the black hole has the same mass as the Sun. But I think we would all miss the Sun pretty quickly for other reasons…

In adding a black hole to the Solar System, we basically treat the black hole like dark matter.  That is, extra mass that doesn’t provide any light. But we still need light because we want to maintain Earth’s habitability.

The simplest way to make this happen is to replace the Sun with a black hole-Sun binary system. Our only real choice is the black hole mass.  For simplicity let’s use a black hole that has the same mass as the Sun.  We’ll put the Sun and the black hole on a close orbit. Let’s say, an orbit with diameter of 0.1 Astronomical Units (semimajor axis 0.05 AU).  That’s plenty big to avoid anything weird.

The Sun and black hole orbit each other every 2.9 days.  The planets’ orbits do not change noticeably.  Maintaining the same orbital distances, they orbit a little bit faster to compensate for the larger total mass of the “Sun”.  A year on Earth decreases from 365 days to 258.  Apart from that there is little change (technical detail: so-called secular frequencies related to long-term oscillations in the planets’ orbits would be affected).

BlackHolePlanets.001.jpg

The Earth-Sun distance now has an extra modulation. Of the course of 2.9 days the Sun and black hole complete one orbit. This makes the Earth-Sun distance oscillate between 95% and 105% of its average value. The amount of energy received by the Earth oscillates between 90% and 110% of its average every 2.9 days. That is a 20% difference between the extremes in the energy received between Earth’s closest and farthest approaches.  That is like bouncing between New York and Miami and back every 2.9 days. The average energy received over Earth’s orbit would not change appreciably.

What happens when the black hole passes in front of the Sun? As viewed from Earth, the black hole passes in front of the Sun once 3-day every Sun-black hole orbit.  It takes the black hole about 3 minutes to cross the Sun.

It turns out that not that much happens. The black hole itself is tiny — its event horizon is just 6 km across, about one thousandth the size of Earth.  The black hole blocks about one ten-billionth of the Sun’s light.

The black hole’s gravity does bend some light that passes close to it, but not by much.  This is called gravitational lensing.  This can make life more interesting in systems with more massive black holes, and we will go there in later posts. In this case it’s minimal.

There you have it: the Black Hole Solar System.

 

Questions?  Comments?  Words of wisdom?

 

 

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16 thoughts on “The Black Hole Solar System

  1. I guess you’re assuming that the Black Hole is just *there*, without going through all the evolution to get there too – otherwise there would have had to be a very massive star there beforehand that then evolved into a supergiant and exploded, which wouldn’t have been good for the planets in the solar system!

    (In the Event Horizon movie there is a point where one of the characters – not Fishburne’s – pokes at the exposed ‘black hole’ (or portal or whatever it was) in the engine room and gets suck into it (before getting pulled back out again, but now insane), maybe that’s what you’re thinking of?)

  2. it is worth noting that astronomers do not know whether supermassive blackholes formed from stellar mass ones or not. We have experimentally found active quasars with billions of solar masses at redshifts well over 7 early reionization epoch and scientists have found some galaxies that “break the mass to bulge ratio rule by having Blackholes at the center that are far more massive than the ratio expects.

    Evidence of this sort has led to an alternative hypothesis that the supermassive blackholes might have actually formed first by direct collapse of primordial material into blackholes with thousands of solar masses that then served as seeds for the formation of the first galaxies.

    It thus is a chicken or the egg question that currently needs better telescopes that can see further back in time to try an pin down the answer.

    And as others stated the progenitor system for such a arrangement would be quite ugly with respect to getting habitable planets. Not impossible but certainly ugly odds but I’m sure it can be worked around 😉

    • Thanks for the info, I appreciate it. That will be relevant in a few upcoming posts with much more complex planetary systems orbiting black holes (first one tomorrow, then friday)

  3. Sean, a Solar Mass Black Hole has an Event Horizon that’s just 6 km across – not the size of the Earth! That’d be a ~4,250 Solar Mass Black Hole, which would be pretty impressive for the Solar System to whizz around. At 0.1 AU, the Sun would be doing ~0.02 c. Can’t imagine what the tidal forces would be like…

  4. Pingback: The Black Hole Ultimate Solar System | PLANETPLANET

  5. Doh! My figure was off by a factor of 2… *sigh* One Solar Mass Schwarzschild radius is 2,953.7 metres. About 3 km. Thus a 6,378 km radius Black Hole (Earth Size) masses about ~2,160 Solar Masses. Thus a speed of just 0.0146 c for the Sun.

  6. Pingback: The Million Earth Solar System | PLANETPLANET

  7. Pingback: The Black Hole Ultimate Solar System: a Supermassive Black Hole, 9 Stars and 550 Planets | Astronomers and Star Gazers

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