Beyond The Shadow of A…?

“Alright, Vinnie, what’s the rest of it?”

“The rest of what, Sy?”

“You wouldn’t have hauled that kid’s toy into Al’s shop here just to play spitballs with it. You’re building up to something and what is it?”

“My black hole hobby, Sy. The things’re just a few miles wide but pack more mass than the Sun. A couple of my magazines say they give off jets top and bottom because of how they spin. That just don’t fit. The stuff ought to come straight out to the sides like the paper wads did.”

“Well, umm… Ah. You know the planet Saturn.”

“Sure.”

“Are its rings part of the planet?”

“No, of course not, they go around it. I even seen an article about how the rings probably came from a couple of collided moons and how water from the Enceladus moon may be part of the outside ring. Only thing Saturn does for the rings is supply gravity to keep ’em there.”

“But our eyes see planet and rings together as a single dot of light in the sky. As far as the rest of the Solar System cares, Saturn consists of that big cloudy ball of hydrogen and the rings and all 82 of its moons, so far. Once you get a few light-seconds away, the whole collection acts as a simple point-source of gravitational attraction.”

“I see where you’re going. You’re gonna say a black hole’s more than just its event horizon and whatever it’s hiding inside there.”

“Yup. That ‘few miles wide’ — I could make a case that you’re off by trillions. A black hole’s a complicated beast when we look at it close up.”

“How can you look at a thing like that close up?”

“Math, mostly, but the observations are getting better. Have you seen the Event Horizon Telescope’s orange ring picture?”

“You mean the one that Al messed with and posted for Hallowe’en? It’s over there behind his cash register. What’s it about, anyway?”

“It’s an image of M87*, the super-massive black hole at the center of the M87 galaxy. Not the event horizon itself, of course, that’s black. The orange portion actually represents millimeter-radio waves that escape from the accretion disk circling the event horizon. The innermost part of the disk is rotating around the hole at near-lightspeed. The arc at the bottom is brighter because that’s the part coming toward us. The photons get a little extra boost from Special Relativity.”

Frames again?”

“With black holes it’s always frames. You’ll love this. From the shell’s perspective, it spits out the same number of photons per second in every direction. From our perspective, time is stretched on the side rotating away from us so there’s fewer photons per one of our seconds and it’s dimmer. In the same amount of our time the side coming toward us emits more photons so it’s brighter. Neat demonstration, eh?”

“Cute. So the inner black part’s the hole ’cause it can’t give off light, right?”

“Not quite. That’s a shadow. Not a shadow of the event horizon itself, mind you, but of the photon sphere. That’s a shell about 1½ times the width of the event horizon. Any photon that passes exactly tangent to the sphere is doomed to orbit there forever. If the photon’s path is the slightest bit inward from that, the poor particle heads inward towards whatever’s in the center. The remaining photons travel paths that look bent to a distant observer, but the point is that they keep going and eventually someone like us could see them.”

“The shadow and the accretion disk, that’s what the EHT saw?”

“Not exactly.”

“There’s more?”

“Yeah. M87* is a spinning black hole, which is more complicated than one that’s sitting still. Wrapped around the photon sphere there’s an ergosphere, as much as three times wider than the event horizon except it’s pumpkin-shaped. The ergosphere’s widest at the rotational equator, but it closes in to meet the event horizon at the two poles. Anything bigger than a photon that crosses its boundary is condemned to join the spin parade, forever rotating in sync with the object’s spin.”

“When are you gonna get to the jets, Sy?”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 1

Eddie makes great pizzas but Jeremy thinks they stay in the oven just a little too long.  As he crunched an extra-crispy wedge-edge he mused, “Gravity aside, I wonder what it’d be like to land on a black hole.  I bet it’d be real slippery if it’s as smooth as Mr Moire says.”

Jennie cut in.  “Don’t be daft, lad.  Everyone’s read about the spaceman sliding through the event horizon unaware until it’s too late.  Someone far away sees the bloke’s spacetime getting all distorted but in his local frame of reference everything’s right as rain.  Right, Sy?”

“As rain, Jennie, if all you’re concerned about is relativity.  But Spaceman Jeremy has lots of other things to be concerned about on his way to the event horizon.  Which he couldn’t stand on anyway.”

“Why not, Mr Moire?  I mean, I said ‘gravity aside’ so I ought to be able to stand up.”

“Nothing to stand on, Jeremy.  It’d be like trying to stand on Earth’s orbit.”

“Pull the other one, Sy.  How can they be alike?”

“Both of them are mathematical constructs rather than physical objects.  An orbit is an imaginary line that depicts planet or satellite locations.  An event horizon is an imaginary figure enclosing a region with such intense spacetime curvature that time points inward.  They’re abstract objects, not  concrete ones.  But let’s get back to Jeremy’s black hole evaporation quest.  He’ll have to pass three perils.”

“Ooo, a Quest with Perils —  loverly.  What are the Perils then?”

“The Roche Radius, the Photon Sphere and the Firewall.  Got your armor on, Jeremy?”Astronaut and 3xBlack hole

“Ready, Mr Moire.”

“Stand up.  The Roche effect is all about gravitational discrepancy between two points.  The two meter distance between your head and feet isn’t enough for a perceptible difference in downward pull.  However, when we deal with astronomical distances the differences can get significant.  For instance, ocean water on the day side of Earth is closer to the Sun and experiences a stronger sunward pull than water on the night side.”

“Ah, so that’s why we get tides.”

“Right.  Sit, sit, sit.  So in 1849 Édouard Roche wondered how close two objects could get until tidal forces pulled one of them apart.  He supposed the two objects were both just balls of rocks or fluid held together by gravity.  Applying Newton’s Laws and some approximations he got a formula for threshold distance in terms of the big guy’s mass and the little guy’s density.  Suppose you’re held together only by gravity and you’re nearing the Sun feet-first.  Its mass is 2×1030 kg/m³.  Even including your space armor, your average density is about 1.5 kg/m³.  According to Roche’s formula, if you got closer than 8.6×106 kilometers your feet would break away and fall into the Sun before the rest of you would.  Oh, that distance is about 1/7 the radius of Mercury’s orbit so it’s pretty close in.”

“But we’re talking black holes here.  What if the Sun collapses to a black hole?”

“Surprisingly, it’s exactly the same distance.  The primary’s operative property is its mass, not its diameter.  Good thing Jeremy’s really held together by atomic and molecular electromagnetism, which is much stronger than gravity.  Which brings us to his second Peril, the dreaded Photon Sphere.”

“Should I shudder, Sy?”

“Go ahead, Jennie.  The Sphere is another mathematical object, not something physical you’d collide with, Jeremy.  It’s a zero-thickness shell representing where electromagnetic waves can orbit a massive object like a black hole or a neutron star.  Waves can penetrate the shell easily in either direction, but if one happens to fly in exactly along a tangent, it’s trapped on the Sphere.”

“That’s photons.  Why is it a peril to me?”

“Remember that electromagnetism that holds you together?  Photons carry that force.  Granted, in a molecule they’re standing waves rather than the free waves we see with.  The math is impossible, but here’s the Peril.  Suppose one of your particularly important molecules happens to lie tangent to the Sphere while you’re traversing it.  Suddenly, the forces holding that molecule together fly away from you at the speed of light.  And that disruption inexorably travels along your body as you proceed on your Quest.”

[both shudder]

~~ Rich Olcott