Dark Shadows

Change-me Charlie’s still badgering Astronomer-in-training Jim and Physicist-in-training Newt about “Dark Stuff,” though he’s switched his target from dark matter to dark energy. “OK, the expansion of the Universe is speeding up. How does dark energy do that?”

Jim steps up to bat. “At this point dark energy’s just a name. We frankly have no idea what the name represents, although it seems appropriate.”

“Why’s that?”

“Gravity pulls things together, right, and we have evidence that galaxies are flying away from each other. When you pick something up your muscles give it gravitational potential energy that becomes kinetic energy when you let go and it drops. In space, a galaxy moving away from its neighbors gains gravitational potential energy relative to them. If the Energy Conservation Law holds, that energy has to come from somewhere. ‘Dark energy’ is what we call the somewhere, but naming something and understanding it are two different things.”

Newt chips in. “Einstein came at it from a different direction. His General Relativity field equations contained two numbers for observation to fill in — G, Newton’s gravitational constant, and lambda (Λ), which we now call the Cosmological Constant. Lambda measures the energy density of empty space. The equations say the balance between lambda and gravity controls whether the Universe expands, contracts or stays static. Lambda‘s just a little bit positive so the universe is expanding.”

“Same conclusion, different name. Neither one says where the energy comes from.”

That’s my cue. “True, but Einstein’s work goes deeper. Newtonian physics maps the Universe onto a stable grid of straight lines. In General Relativity those lines are deformed and twisted under the influence of massive objects. Vinnie and I talked about how gravity’s a fictitious force arising from that deformation. Like John Wheeler said, ‘Mass tells space-time how to curve, and space-time tells mass how to move.’ Anyway, when you throw dark energy’s lambda into the mix, the grid lines themselves go into motion. Dark energy torques the spacetime fabric that pulls galaxies together.”

“So dark energy pulls things apart by spreading out the grid they’re built on? If that’s so how come I’m still in one piece?”

“Nothing personal, but you’re too small and dense to notice. So am I, so is the Earth.”

“Why should that make a difference?”

“Time for a thought experiment. Think of the Sun. The atoms inside its surface are trying to get out, right? What’s holding them in?”

“The Sun’s gravity.”

“Just like pressure on the skin of a balloon. In either case, as long as things are stable the pressure on an enclosing real or mathematical surface rises and falls with the amount of enclosed energy density and it doesn’t matter which we talk about. Energy density’s easier to think about. With me so far?”

“I guess.”

“Let’s run a few horseback numbers on Old Reliable here. Start with protons and neutrons trying to leave an atomic nucleus. Here’s the total binding energy of an iron-56 nucleus divided by its volume…”

“… so the nuclear particles would fly apart except for the inward pressure exerted by the nuclear forces. Now we’ll go up a level and consider electrons trying to leave a helium atom. They’re held in by the electromagnetic force…”

“Still a lot of inward pressure but less than nuclear by fifty-five powers of ten. Gravity next. That’s what keeps us from flying off into space. I’ll use Earth’s escape velocity to cheat-quantify it…”

“Ten billion times weaker than the electromagnetism that holds our atoms and molecules together. Dark energy’s mass density is estimated to be about 10-27 kilograms per cubic meter. I’ll use that and Einstein’s E=mc2to calculate its pull-us-apart pressure.”

“A quintillion times weaker still.”

“So what you’re saying is, dark energy tries to pull everything apart by stretching out that spacetime grid, but it’s too weak to actually do anything to stuff that’s held together by gravity, electromagnetism or the two nuclear forces.”

“Mostly. Nuclear forces are short-range so distance doesn’t matter. Gravity and electromagnetism get weaker with the square of the distance. Dark energy only gets competitive working on objects that are separated much further than even neighboring galaxies. You’re not gonna get pulled apart.”

~~ Rich Olcott

Dark Horizon

Charlie's table sign says "Dark Energy is bogus"

Change-me Charlie attacks his sign with a rag and a marker, rubbing out “Matter” and writing in “Energy.” Turns out his sign is a roll-up dry-erase display and he can update it on site. Cool. I guess with his rotating-topic strategy he needs that. “OK, maybe dark matter’s a thing, but dark energy ain’t. No evidence, someone just made that one up to get famous!”

And of course Physicist-in-training Newt comes back at him. “Lots of evidence. You know about the Universe expanding?”

“Prove it.” At least he’s consistent.

<sigh> “You know how no two snowflakes are exactly alike but they can come close? It applies to stars, too. Stars are fairly simple in a complicated way. If you tell me a star’s mass, age and how much iron it has, I can do a pretty good job of computing how bright it is, how hot it is, its past and future life history, all sort of things. As many stars as there are, we’re pretty much guaranteed that there’s a bunch of them with very similar fundamentals.”

“So?”

“So when a star undergoes a major change like becoming a white dwarf or a neutron star or switching from hydrogen fusion to burning something else, any other star that has the same fundamentals will behave pretty much the same way. They’d all flare with about the same luminosity, pulsate with about the same frequency —”

“Wait. Pulsate?”

“Yeah. You’ve seen campfires where one bit of flame coming out of a hotspot flares up and dies back and flares up and dies back and you get this pulsation —”

“Yeah. I figured that happens with a sappy log where the heat gasifies a little sap then the spot cools off when outside air gets pulled in then the cycle goes again.”

“That could be how it works, depending. Anyhow, a star in the verge of mode change can go through the same kind of process — burn one kind of atom in the core until heat expansion pushes fuel up out of the fusion zone; that cools things down until fuel floods back in and off we go again. The point is, that kind of behavior isn’t unique to a single star. We’ve known about variable stars for two centuries, but it wasn’t until 1908 that Henrietta Swan Leavitt told us how to determine a particular kind of variable star’s luminosity from its pulsation frequency.”

“Who cares?”

“Edwin Hubble cared. Brightness dies off with the distance squared. If you compare the star’s intrinsic luminosity with how bright the star appears here on Earth, it’s simple to calculate how far away the star is. Hubble did that for a couple dozen galaxies and showed they had to be far outside the Milky Way. He plotted red-shift velocity data against those distances and found that the farther away a galaxy is from us, the faster it’s flying away even further.”

“A couple dozen galaxies ain’t much.”

“That was for starters. Since the 1930s we’ve built a whole series of ‘standard candles,’ different kinds of objects whose luminosities we can convert to distances out to 400 million lightyears. They all agree that the Universe is expanding.”

“Well, you gotta expect that, everything going ballistic from the Big Bang.”

“They don’t go the steady speed you’re thinking. As we got better at making really long-distance measurements, we learned that the expansion is accelerating.”

“Wait. I remember my high-school physics. If there’s an acceleration, there’s gotta be a force pushing it. Especially if it’s fighting the force of gravity.”

“Well there you go. Energy is force times distance and you’ve just identified dark energy. But standard candles aren’t the only kind of evidence.”

“There’s more?”

“Sure — ‘standard sirens‘ and ‘standard rulers.’ The sirens are events that generate gravitational waves we pick up with LIGO facilities. The shape and amplitude of the LIGO signals tell us how far away the source was — and that information is completely immune to electromagnetic distortions.”

“And the rulers?”

“They’re objects, like spiral galaxies and intergalactic voids, that we have independent methods for connecting apparent size to distance.”

“And the candles and rulers and sirens all agree that acceleration and dark energy are real?”

“Yessir.”

~~ Rich Olcott

Dancing in The Dark

Change-me Charlie at his argument table

The impromptu seminar at Change-me Charlie’s “Change My Mind” table is still going strong, but it looks like Physicist-in-training Newt and Astronomer-in-training Jim have met his challenge. He’s switched from arguing that dark matter doesn’t exist to asking how it worked in the Bullet Cluster’s massive collision between two collections of galaxies with their clouds of plasma and dark matter. “OK, the individual galaxies are so spread out they slide past each other without slowing down but the plasma clouds obstruct each other by friction. Wouldn’t friction in the dark matter hold things back, too?”

Jim’s still standing in front of the table. “Now that’s an interesting question, so interesting that research groups have burned a bazillion computer cycles trying to answer it.”

“Interesting, yes, but that interesting?”

“For sure. What we know about dark matter is mostly what it doesn’t do. It doesn’t give off light, it doesn’t absorb light, it doesn’t seem to participate in the strong or weak nuclear forces or interact with normal matter by any means other than gravity, and no identifiable dark matter particles have been detected by bleeding-edge experiments like IceCube and the Large Hadron Collider. So people wonder, does dark matter even interact with itself? If we could answer that question one way or the other, that ought to tell us something about what dark matter is.”

“How’re we gonna do that?”

Newt’s still perched on Charlie’s oppo chair. “By using computers and every theory tool on the shelf to run what-if? simulations. From what we can tell, nearly everywhere in the Universe normal matter is embedded in a shell of dark matter. The Bullet Cluster and a few other objects out there appear to break that rule and give us a wonderful check on the theory work.”

The Bullet Cluster, 1E 0657-56 (NASA image)

“Like for instance.”

“Simple case. What would the collision would looked like if dark matter wasn’t involved? Some researchers built a simulation program and loaded it with a million pretend plasma particles in two cluster-sized regions moving towards each other from 13 million pretend lightyears apart. They also loaded in position and momentum data for the other stars and galaxies shown in the NASA image. The simulation tracked them all as pretend-time marched along stepwise. At each time-step the program applied known or assumed laws of physics to compute every object’s new pretend position and momentum since the prior step. Whenever two pretend-particles entered the same small region of pretend-space, the program calculated a pretend probability for their collision. The program’s output video marked each successful collision with a pink pixel so pinkness means proton-electron plasma. Here’s the video for this simulation.”

“Doesn’t look much like the NASA picture. The gas just spreads out, no arc or cone to the sides.”

“Sure not, which rules out virtually all models that don’t include dark matter. So now the team went to a more complicated model. They added a million dark matter particles that they positioned to match the observed excess gravity distribution. Those’re marked with blue pixels in the videos. Dark matter particles in the model were allowed to scatter each other, too, under control of a self-interaction parameter. The researchers ran the simulations with a whole range of parameter values, from no-friction zero up to about twice what other studies have estimated. Here’s the too-much case.”

“Things hold together better with all that additional gravity, but it’s not a good match either.”

“Right, and here’s the other end of the range — no friction between dark matter particles. Robertson, the video’s author/director, paused the simulation in the middle to insert NASA’s original image so we could compare.”

“Now we’re getting somewhere.”

“It’s not a perfect match. Here’s an image I created by subtracting a just-after-impact simulation frame from the NASA image, then amplifying the red. There’s too much left-over plasma at the outskirts, suggesting that maybe no-friction overstates the case and maybe dark matter particles interact, very slightly, beyond what a pure-gravity theory predicts.”

“Wait, if the particles don’t use gravity, electromagnetism or the nuclear forces on each other, maybe there’s a fifth force!”

“New Physics!”

A roar from Cap’n Mike — “Or they’re not particles!”

~~ Rich Olcott

Dark Passage

Change-me Charlie’s not giving up easily. “You said that NASA picture did three things, but you only told us two of them — that dark matter’s a thing and that it’s separate from normal matter. What’s the third thing? What exactly is in that picture? Does it tell us what dark matter is?”

The Bullet Cluster ( 1E 0657-56 )

Physicist-in-training Newt’s ready for him. “Not much of a clue about what dark matter is, but a good clue about how it behaves. As to what’s in the picture, we need some background information first.”

“Go ahead, it’s not dinner-time yet.”

“First, this isn’t two stars colliding. It’s not even two galaxies. It’s two clusters of galaxies, about 40 all together. The big one on the left probably has the mass of a couple quintillion Suns, the small one about 10% of that.”

“That’s a lot of stars.”

“Oh, most of it’s definitely not stars. Maybe only 1-2%. Those stars and the galaxies they form are embedded in ginormous clouds of proton-electron plasma that make up 5-20% of the mass. The rest is that dark matter you don’t like.”

“Quadrillions of stars are gonna make a super-super-nova when they collide!”

“Well, no. That doesn’t even happen when two galaxies collide. The average distance between neighboring stars in a galaxy is 200-300 times the diameter of a star so it’s unlikely that any two of them will come even close. Next level up, the average distance between galaxies in a cluster is about 60 galaxy diameters or more, depending. The galaxies will mostly just slide past each other. The real colliders are the spread-out stuff — the plasma clouds and of course the dark matter, whatever that is.”

Astronomer-in-training Jim cuts in. “Anyway, the collision has already happened. The light from this configuration took 3.7 billion years to reach us. The collision itself was longer ago than that because the bullet’s already passed through the big guy. From that scale-bar in the bottom corner I’d say the centers are about 2 parsecs apart. If I recall right, their relative velocity is about 3000 kilometers per second so…” <poking at his smartphone> “…the peak intersection was about 700 million years earlier than that. Call it 4.3 billion years ago.”

“So what’s with the cotton candy?”

Newt looks puzzled. “Cotton… oh, the pink pixels. They’re markers for where NASA’s Chandra telescope saw X-rays coming from.”

“What can make X-rays so far from star radiation that could set them going?”

“The electrons do it themselves. An electron emits radiation every time it collides with another charged particle and changes direction. When two plasma clouds interpenetrate you get twice as many particles per unit volume and four times the collision rate so the radiation intensity quadruples. There’s always some X-radiation in the plasma because the temperature in there is about 8400 K and particle collisions are really violent. The Chandra signal pink shows the excess over background.”

“The blue in the Jim’s picture is supposed to be what, extra gravity?”

“Basically, yeah. It’s not easy to see from the figure, but there are systematic distortions in the images of the background galaxies in the blue areas. Disks and ellipsoids appear to be bent, depending on where they sit relative to the clusters’ centers of mass. The researchers used Einstein’s equations and lots of computer time to work back from the distortions to the lensing mass distributions.”

“So what we’ve got is a mostly-not-from-stars gravity lump to the left, another one to the right, and a big cloud in the middle with high-density hot bits on its two sides. Something in the middle blew up and spread gas around mostly in the direction of those two clusters. What’s that tell us?”

“Sorry, that’s not what happened. If there’d been a central explosion the excess to the right would be arc-shaped, not a cone like you see. No, this really is the record of one galaxy cluster bursting through another one. Particle-particle friction within the plasma clouds held them back while the embedded galaxies and dark matter moved on.”

“OK, the galaxies aren’t close-set enough for them to slow each other down, but wouldn’t friction in the dark matter hold things back, too?”

“Now that’s an interesting question…”

~~ Rich Olcott

The Prints of Darkness

There’s a commotion in front of Al’s coffee shop. Perennial antiestablishmentarian Change-me Charlie’s set up his argument table there and this time the ‘establishment’ he’s taking on is Astrophysics. Charlie’s an accomplished chain-yanker and he’s working it hard. “There’s no evidence for dark matter, they’ve never found any of the stuff and there’s tons of no-dark-matter theories to explain the evidence.”

Big Cap’n Mike’s shouts from the back of the crowd. “What they’ve been looking for and haven’t found is particles. By my theory dark matter’s an aspect of gravity which ain’t particles so there’s no particles for them to find.”

Astronomer-in-training Jim spouts off right in Charlie’s face. “Dude, you can’t have it both ways. Either there’s no evidence to theorize about, or there’s evidence.”

Physicist-in-training Newt Barnes takes the oppo chair. “So what exactly are we talking about here?”

“That’s the thing, guy, no-one knows. It’s like that song, ‘Last night I saw upon the stair / A little man who wasn’t there. / He wasn’t there again today. / Oh how I wish he’d go away.‘ It’s just buzzwords about a bogosity. Nothin’ there.”

I gotta have my joke. “Oh, it’s past nothing, it’s a negative.”

“Come again?”

“The Universe is loaded with large rotating but stable structures — solar systems, stellar binaries, globular star clusters, galaxies, galaxy clusters, whatever. Newton’s Law of Gravity accounts nicely for the stability of the smallest ones. Their angular momentum would send them flying apart if it weren’t for the gravitational attraction between each component and the mass of the rest. Things as big as galaxies and galaxy clusters are another matter. You can calculate from its spin rate how much mass a galaxy must have in order to keep an outlying star from flying away. Subtract that from the observed mass of stars and gas. You get a negative number. Something like five times more negative than the mass you can account for.”

“Negative mass?”

“Uh-uh, missing positive mass to combine with the observed mass to account for the gravitational attraction holding the structure together. Zwicky and Rubin gave us the initial object-tracking evidence but many other astronomers have added to that particular stack since then. According to the equations, the unobserved mass seems to form a spherical shell surrounding a galaxy.”

“How about black holes and rogue planets?”

Newt’s thing is cosmology so he catches that one. “No dice. The current relative amounts of hydrogen, helium and photons say that the total amount of normal matter (including black holes) in the Universe is nowhere near enough to make up the difference.”

“So maybe Newton’s Law of Gravity doesn’t work when you get to big distances.”

“Biggest distance we’ve got is the edge of the observable Universe. Jim, show him that chart of the angular power distribution in the Planck satellite data for the Cosmological Microwave Background.” <Jim pulls out his smart-phone, pulls up an image.> “See the circled peak? If there were no dark matter that peak would be a valley.”

Charlie’s beginning to wilt a little. “Ahh, that’s all theory.”

The Bullet Cluster ( 1E 0657-56 )

<Jim pulls up another picture.> “Nope, we’ve got several kinds of direct evidence now. The most famous one is this image of the Bullet Cluster, actually two clusters caught in the act of colliding head-on. High-energy particle-particle collisions emit X-rays that NASA’s Chandra satellite picked up. That’s marked in pink. But on either side of the pink you have these blue-marked regions where images of further-away galaxies are stretched and twisted. We’ve known for a century how mass bends light so we can figure from the distortions how much lensing mass there is and where it is. This picture does three things — it confirms the existence of invisible mass by demonstrating its effect, and it shows that invisible mass and visible mass are separate phenomena. I’ve got no pictures but I just read a paper about two galaxies that don’t seem to be associated with dark matter at all. They rotate just as Newton would’ve expected from their visible mass alone. No surprise, they’re also a lot less dense without that five-fold greater mass squeezing them in.”

“You said three.”

“Gotcha hooked, huh?

~~ Rich Olcott

Fierce Roaring Beast

A darkish day calls for a fresh scone so I head for Al’s coffee shop. Cathleen’s there with some of her Astronomy students. Al’s at their table instead of his usual place behind the cash register. “So what’s going on with these FRBs?”

She plays it cool. “Which FRBs, Al? Fixed Rate Bonds? Failure Review Boards? Flexible Reed Baskets?”

Jim, next to her, joins in. “Feedback Reverb Buffers? Forged Razor Blades?
Fennel Root Beer?”

I give it a shot. “Freely Rolling Boulders? Flashing Rapiers and Broadswords? Fragile Reality Boundary?”

“C’mon, guys. Fast Radio Bursts. Somebody said they’re the hottest thing in Astronomy.”

Cathleen, ever the teacher, gives in. “Well, they’re right, Al. We’ve only known about them since 2007 and they’re among the most mystifying objects we’ve found out there. Apparently they’re scattered randomly in galaxies all over the sky. They release immense amounts of energy in incredibly short periods of time.”

“I’ll say.” Vinnie’s joins the conversation from the next table. “Sy and me, we been talking about using the speed of light to measure stuff. When I read that those radio blasts from somewhere last just a millisecond or so, I thought, ‘Whatever makes that blast happen, the signal to keep it going can’t travel above lightspeed. From one side to the other must be closer than light can travel in a millisecond. That’s only 186 miles. We got asteroids bigger than that!'”

“300 kilometers in metric.” Jim’s back in. “I’ve played with that idea, too. The 70 FRBs reported so far all lasted about a millisecond within a factor of 3 either way — maybe that’s telling us something. The fastest way to get lots of energy is a matter-antimatter annihilation that completely converts mass to energy by E=mc².  Antimatter’s awfully rare 13 billion years after the Big Bang, but suppose there’s still a half-kilogram pebble out there a couple galaxies away and it hits a hunk of normal matter. The annihilation destroys a full kilogram; the energy release is 1017 joules. If the event takes one millisecond that’s 1020 watts of power.”

“How’s that stand up against the power we receive in an FRB signal, Jim?”

“That’s the thing, Sy, we don’t have a good handle on distances. We know how much power our antennas picked up, but power reception drops as the square of the source distance and we don’t know how far away these things are. If your distance estimate is off by a factor of 10 your estimate of emitted power is wrong by a factor of 100.”

“Ballpark us.”

<sigh> “For a conservative estimate, say that next-nearest-neighbor galaxy is something like 1021 kilometers away. When the signal finally hits us those watts have been spread over a 1021-kilometer sphere. Its area is something like 1049 square meters so the signal’s power density would be around 10-29 watts per square meter. I know what you’re going to ask, Cathleen. Assuming the radio-telescope observations used a one-gigahertz bandwidth, the 0.3-to-30-Jansky signals they’ve recorded are about a million million times stronger than my pebble can account for. Further-away collisions would give even smaller signals.”

Looking around at her students, “Good self-checking, Jim, but for the sake of argument, guys, what other evidence do we have to rule out Jim’s hypothesis? Greg?”

“Mmm… spectra? A collision like Jim described ought to shine all across the spectrum, from radio on up through gamma rays. But we don’t seem to get any of that.”

“Terry, if the object’s very far away wouldn’t its shorter wavelengths be red-shifted by the Hubble Flow?”

“Sure, but the furthest-away one we’ve tagged so far is nearer than z=0.2. Wavelengths have been stretched by 20% or less. Blue light would shift down to green or yellow at most.”

“Fran?”

“We ought to get even bigger flashes from antimatter rocks and asteroids. But all the signals have about the same strength within a factor of 100.”

“I got an evidence.”

“Yes, Vinnie?”

“That collision wouldn’t’a had a chance to get started. First contact, blooie! the gases and radiation and stuff push the rest of the pieces apart and kill the yield. That’s one of the problems the A-bomb guys had to solve.”

Al’s been eaves-dropping, of course. “Hey, guys. Fresh Raisin Bread, on the house.”

~~ Rich Olcott

Friendly Resting Behemoths

Atoms are solar systems? Um, no…

Suddenly there’s a hubbub of girlish voices to one side of the crowd.  “Go on, Jeremy, get up there.”  “Yeah, Jeremy, your theory’s no crazier than theirs.”  “Do it, Jeremy.”

Sure enough, the kid’s here with some of his groupies.  Don’t know how he does it.  He’s a lot younger than the grad students who generally present at these contests, but he’s got guts and he grabs the mic.

“OK, here’s my Crazy Theory.  The Solar System has eight planets going around the Sun, and an oxygen atom has eight electrons going around the nucleus.  Maybe we’re living in an oxygen atom in some humongous Universe, and maybe there are people living on the electrons in our oxygen atoms or whatever.  Maybe the Galaxy is like some huge molecule.  Think about living on an electron in a uranium atom with 91 other planets in the same solar system and what happens when the nucleus fissions.  Would that be like a nova?”

There’s a hush because no-one knows where to start, then Cathleen’s voice comes from the back of the room.  Of course she’s here — some of the Crazy Theory contest ring-leaders are her Astronomy students.  “Congratulations, Jeremy, you’ve joined the Honorable Legion of Planetary Atom Theorists.  Is there anyone in the room who hasn’t played with the idea at some time?”

No-one raises a hand except a couple of Jeremy’s groupies.

“See, Jeremy, you’re in good company.  But there are a few problems with the idea.  I’ll start off with some astronomical issues and then the physicists can throw in some more.  First, stars going nova collapse, they don’t fission.  Second, compared to the outermost planet in the Solar System, how far is it from the Sun to the nearest star?”

A different groupie raises her hand and a calculator.  “Neptune’s about 4 light-hours from the Sun and Alpha Centauri’s a little over 4 light-years, so that would be … the 4’s cancel, 24 hours times 365 … about 8760 times further away than Neptune.”

“Nicely done.  That’s a typical star-to-star distance within the disk and away from the central bulge.  Now, how far apart are the atoms in a molecule?”

“Aren’t they pretty much touching?  That’s a lot closer than 8760 times the distance.”

“Yes, indeed, Jeremy.  Anyone else with an objection?  Ah, Maria.  Go ahead.”

“Yes, ma’am.  All electrons have exactly the same properties, ¿yes? but different planets, they have different properties.  Jupiter is much, much heavier than Earth or Mercury.”

Astrophysicist-in-training Jim speaks up.  “Different force laws.  Solar systems are held together by gravity but at this level atoms are held together by electromagnetic forces.”

“Carry that a step further, Jim.  What does that say about the geometry?”

“Gravity’s always attractive.  The planets are attracted to the Sun but they’re also attracted to each other.  That’ll tend to pull them all into the same plane and you’ll get a flat disk, mostly.  In an atom, though, the electrons or at least the charge centers repel each other — four starting at the corners of a square would push two out of the plane to form a tetrahedron, and so forth.  That’s leaving aside electron spin.  Anyhow, the electronic charge will be three-dimensional around the nucleus, not planar.  Do you want me to go into what a magnetic field would do?”

“No, I think the point’s been made.  Would someone from the Physics side care to chime in?”

“Synchrotron radiation.”

“Good one.  And you are …?”

“Newt Barnes.  I’m one of Dr Hanneken’s students.”

“Care to explain?”

“Sure.  Assume a hydrogen atom is a little solar system with one electron in orbit around the nucleus.  Any time a charge moves it radiates waves into the electromagnetic field.  The waves carry forces that can compel other charged objects to move.  The distance an object moves, times the force exerted, equals the amount of energy expended by the wave.  Therefore the wave must carry energy and that energy must have come from the electron’s motion.  After a while the electron runs out of kinetic energy and falls into the nucleus.  That doesn’t actually happen, so the atom’s not a solar system.”

Jeremy gets general applause when he waves submission, then the crowd’s chant resumes…

.——<“Amanda! Amanda! Amanda!”>Bohr and Bohr atom

~~ Rich Olcott

“Hot Jets, Captain Neutrino!”

“Hey, Cathleen, while we’re talking IceCube, could you ‘splain one other thing from that TV program?”

“Depends on the program, Al.”

“Oh, yeah, you weren’t here when we started on this.  So I was watching this program and they were talking about neutrinos and how there’s trillions of them going through like my thumbnail every second and then IceCube saw this one neutrino that they’re real excited about so what I’m wondering is, what’s so special about just that neutrino? How do they even tell it apart from all the others?”

“How about the direction it came from, Cathleen?  We get lotsa neutrinos from the Sun and this one shot in from somewhere else?”

SMBH jet and IceCube
Images from NASA and JPL-Caltech

“An interesting question, Vinnie.  The publicity did concern its direction, but the neutrino was already special.  It registered 290 tera-electron-volts.”

“Ter-what?”

“Sorry, scientific shorthand — tera is ten-to-the-twelfth.  A million electrons poised on a million-volt gap would constitute a Tera-eV of potential energy.  Our Big Guy had 290 times that much kinetic energy all by himself.”

“How’s that stack up against other neutrinos?”

“Depends on where they came from.  Neutrinos from a nuclear reactor’s uranium or plutonium fission carry only about 10 Mega-eV, wimpier by a factor of 30 million.  The Sun’s primary fusion process generates neutrinos peaking out at 0.4 MeV, 25 times weaker still.”

“How about from super-accelerators like the LHC?”

“Mmm, the LHC makes TeV-range protons but it’s not designed for neutrino production.  We’ve got others that have been pressed into service as neutrino-beamers. It’s a complicated process — you send protons crashing into a target.  It spews a splatter of pions and K-ons.  Those guys decay to produce neutrinos that mostly go in the direction you want.  You lose a lot of energy.  Last I looked the zippiest neutrinos we’ve gotten from accelerators are still a thousand times weaker than the Big Guy.”

I can see the question in Vinnie’s eyes so I fire up Old Reliable again.  Here it comes… “What’s the most eV’s it can possibly be?”  Good ol’ Vinnie, always goes for the extremes.

“You remember the equation for kinetic energy?”

“Sure, it’s E=½ m·v², learned that in high school.”

“And it stayed with you.  OK, and what’s the highest possible speed?”

“Speed o’ light, 186,000 miles per second.”

“Or 300 million meters per second, ’cause that’s Old Reliable’s default setting.  Suppose we’ve got a neutrino that’s going a gnat’s whisker slower than light.  Let’s apply that formula to the neutrino’s rest mass which is something less than 1.67×10-36 kilograms…”Speedy neutrino simple calculation“Half an eV?  That’s all?  So how come the Big Guy’s got gazillions of eV’s?”

“But the Big Guy’s not resting.  It’s going near lightspeed so we need to apply that relativistic correction to its mass…Speedy neutrino relativistic calculation“That infinity sign at the bottom means ‘as big as you want.’  So to answer your first question, there isn’t a maximum neutrino energy.  To make a more energetic neutrino, just goose it to go even closer to the speed of light.”

“Musta been one huge accelerator that spewed the Big Guy.”

“One of the biggest, Al.”  Cathleen again.  “That’s the exciting thing about what direction the particle came from.”

“Like the North Pole or something?”

“Much further away, much bigger and way more interesting.  As soon as IceCube caught that neutrino signal, it automatically sent out a “Look in THIS direction!” alert to conventional observatories all over the world.  And there it was — a blazar, 5.7 billion lightyears away!”

“Wait, Cathleen, what’s a blazar?”

“An incredibly brilliant but highly variable photon source, from radio frequencies all the way up to gamma rays and maybe cosmic rays.  We think the thousands we’ve catalogued are just a fraction of the ones within range.  We’re pretty sure that each of them depends on a super-massive black hole in the center of a galaxy.  The current theory is that those photons come from an astronomy-sized accelerator, a massive swirling jet that shoots out from the central source.  When the jet happens to point straight at us, flash-o!”

Duck!

“I wouldn’t worry about a neutrino flood.  The good news is IceCube’s signal alerted astronomers to check TXS 0506+056, a known blazar, early in a new flare cycle.”

“An astrophysical fire alarm!”

~~ Rich Olcott

Cube Roots

Cathleen steps into at Al’s for her morning coffee-and-scone.  “Heard you guys talking neutrinos so I’ll bet Al got you started with something about IceCube.  Isn’t it an awesome project?  Imagine instrumenting a cubic kilometer of ice, and at the South Pole!”

“Ya got me, Cathleen.  It knocked me out that anyone would even think of building it.  Where did the idea come from, anyhow?”

“I don’t know specifically, but it’s got a lot of ancestors, going back to the Wilson Cloud Chamber in the 1920s.”

“Oh, the cloud chamber!  Me and my brother did one for the Science Fair — used dry ice and some kind of alcohol in a plastic-covered lab dish if I remember right, and we set it next to one of my Mom’s orange dinner plates.  Spooky little ghost trails all over the place.”

“That’s basically what the first ones were.  An incoming particle knocks electrons out of vapor molecules all along its path.  The path is visible because the whole thing is so cold that other vapor molecules condense to form micro-droplets around the ions.  Anderson’s cloud chambers were good enough to get him a Nobel Prize for discovering the positron and muon.  But table-top devices only let you study low-energy particles — high-energy ones just shoot through the chamber and exit before they do anything interesting.”

“So the experimenters went big?”

“Indeed, Sy, massive new technologies, like bubble chambers holding thousands of gallons of liquid hydrogen or something else that reacts with neutrinos.  But even those experiments had a problem.”

“And that was…?”

FirstNeutrinoEventAnnotated 2
Adapted from public domain image
courtesy of Argonne National Laboratory

“They all depended on photography to record the traces.  Neutrino-hunting grad students had to measure everything in the photos, because neutrinos don’t make traces — you only find them by finding bigger particles that were disturbed just so.  The work got really intense when the astrophysicists got into the act, trying to understand why the Sun seemed to be giving off only a third of the neutrinos it’s supposed to.  Was the Sun going out?”

“Wait, Cathleen, how’d they know how many neutrinos it’s supposed to make?”

“Wow, Vinnie, you sure know how to break up a narrative, but it’s a fair question.  OK, quick answer.  We know the Sun’s mostly made of hydrogen and we know how much energy it gives off per second.  We’ve figured out the nuclear reactions it must be using to generate that energy.  The primary process combines four hydrogen nuclei  to make a helium nucleus.  Each time that happens you get a certain amount of energy, which we know, plus two neutrinos.  Do the energy arithmetic, multiply the number of heliums per second by two and you’ve got the expected neutrino output.”

“So is the Sun going out?”

“As usual, Al cuts to the chase.  No, Al, it’s still got 5 billion years of middle age ahead of it.  The flaw in the argument was that we assumed that our detectors were picking up all the neutrinos.”

“My mutations!”

“Yes, Vinnie.  Our detector technology at the time only saw electron neutrinos.  The Sun’s reactions emit electron neutrinos.  But the 93-million mile trip to Earth gave those guys plenty of time to oscillate through muon neutrino to tau neutrino and back again.  All we picked up were the ones that had gone through an integer number of cycles.”

“We changed technology, I take it?”

“Right again, Sy.  Instead of relying on nuclear reactions initiated by electron neutrinos, we went so spark chambers — crossed grids of very fine electrified wire in a box of argon gas.  Wherever a passing neutrino initiated an ionization, zap! between the two wires closest to that point.  Researchers could computerize the data reduction.  Turns out that all three neutrino flavors are pretty good at causing ionizations so the new tech cleared up the Solar Paradox, but only after we solved a different problem — the new data was point-by-point.  Working back from those points to the traces took some clever computer programming.”

“Ah, I see the connection with IceCube.  It doesn’t register traces, either, just the points where those sensors see the Cherenkov flashes.  It’s like a spark chamber grown big.”

“Cubic-kilometer big.”

~~ Rich Olcott

Bigger than you’d think

Al’s coffee shop, the usual mid-afternoon crowd of chatterers and laptop-tappers.  Al’s walking his refill rounds, but I notice he’s carrying a pitcher rather than his usual coffee pot.  “Hey, Al, what’s with the hardware?”

“Got iced coffee here, Sy.  It’s hot out, people want to cool down.  Besides, this is in honor of IceCube.”

“Didn’t realize you’re gangsta fan.”

“Nah, not the rapper, the cool experiment down in the Antarctic.  It was just in the news.”

“Oh?  What did they say about it?”

“It’s the biggest observatory in the world, set up to look for the tiniest particles we know of, and it uses a cubic mile of ice which I can’t think how you’d steer it.”

A new voice, or rather, a familiar one. “One doesn’t, Al.”
Neutrino swirl 1“Hello, Jennie.  Haven’t seen you for a while.”

“I flew home to England to see my folks.  Now I’m back here for the start of the Fall term.  I’ve already picked a research topic — neutrinos.  They’re weird.”

“Hey, Jennie, why are they so tiny?”

“It’s the other way to, Al.  They’re neutrinos because they’re so tiny.  Sy would say that for a long time they were simply an accounting gimmick to preserve the conservation laws.”

“I would?”

“Indeed.  People had noticed that when uranium atoms give off alpha particles to become thorium, the alpha particles always have about the same amount of energy.  The researchers accounted for that by supposing that each kind of nucleus has some certain quantized amount of internal energy.  When one kind downsizes to another, the alpha particle carries off the difference.”

“That worked well, did it?”

“Oh, yes, there are whole tables of nuclear binding energy for alpha radiation.  But when a carbon-14 atom emits a beta particle to become nitrogen-14, the particle can have pretty much any amount of energy up to a maximum.  It’s as though the nuclear quantum levels don’t exist for beta decay.  Physicists called it the continuous beta-spectrum problem and people brought out all sorts of bizarre theories to try to explain it.  Finally Pauli suggested maybe something we can’t see carries off energy and leaves less for the beta.  Something with no charge and undetectable mass and the opposite spin from what the beta has.”

“Yeah, that’d be an accounting gimmick, alright.  The mass disappears into the rounding error.”

“It might have done, but twenty years later they found a real particle.  Oh, I should mention that after Pauli made the suggestion Fermi came up with a serious theory to support it.  Being Italian, he gave the particle its neutrino name because it was neutral and small.”

“But how small?”

“We don’t really know, Al.  We know the neutrino’s mass has to be greater than zero because it doesn’t travel quite as fast as light does.  On the topside, though, it has to be lighter than than a hydrogen atom by at least a factor of a milliard.”

“Milliard?”

“Oh, sorry, I’m stateside, aren’t I?  I should have said a billion.  Ten-to-the-ninth, anyway.”

“That’s small.  I guess that’s why they can sneak past all the matter in Earth like the TV program said and never even notice.”

This gives me an idea.  I unholster Old Reliable and start to work.

“Be right with you… <pause> … Jennie, I noticed that you were being careful to say that neutrinos are light, rather than small.  Good careful, ’cause ‘size’ can get tricky at this scale.  In the early 1920s de Broglie wrote that every particle is associated with a wave whose wavelength depends on the particle’s momentum.  I used his formula, together with Jennie’s upper bound for the neutrino’s mass, to calculate a few wavelength lower bounds.Neutrino wavelength calcMomentum is velocity times mass.  These guys fly so close to lightspeed that for a long time scientists thought that neutrinos are massless like photons.  They’re not, so I used several different v/c ratios to see what the relativistic correction does.  Slow neutrinos are huge, by atom standards.  Even the fastest ones are hundreds of times wider than a nucleus.”

“With its neutrino-ness spread so thin, no wonder it’s so sneaky.”

“That may be part of it, Al.”

“But how do you steer IceCube?”

~~ Rich Olcott