Holes in The Ground — Big Ones

Al’s stacking chairs on tables, trying to close his coffee shop, but Mr Richard Feder (of Fort Lee, NJ) doesn’t let up on Jim.  “What’s all this about Gale Crater or Mount Sharp that Curiosity‘s running around?  Is it a crater or a mountain?  How about it’s a volcano?  How do you even tell the difference?”

That’s a lot of questions but Jim’s got game.  “Gale is an impact crater, about three and a half billion years old.  The impacting meteorite must have hit hard, because Mount Sharp’s in the middle of Gale.”

Mud drop
Adapted from a photo
by Davide Restivo, Aarau, Switzerland
[CC BY-SA 2.0] via Wikimedia Commons
“How’s that follow?”

“Have you ever watched a rain drop hit a puddle?  It forces the puddle water downward and then the water springs back up again to form a peak.  The same general process  happens when a meteorite hits a rocky surface except the solid peak doesn’t flatten out like water does.  We know that’s the way many meteor craters on the Moon and here on Earth were formed.  We’re pretty sure it’s what happened at Gale — the core of Mount Sharp (formal astronomers call it Aeolis Mons) is probably that kind of peak.”

“Only the core?  What about the rest of it?”

“That’s what Curiosity has been digging into.”  <I have to smile — Jim’s not one to do puns on purpose.>  “The rover’s found evidence that the core’s wrapped up in lots of sedimentary clays, sulfates, hematites and other water-derived minerals of a sort that wouldn’t be there unless Gale had once been a lake like Oregon’s Crater Lake.  That in turn says that Mars once had liquid water on its surface.  That’s why everyone got so excited when those results came in.”

“Oregon’s Crater Lake was from a meteorite?”

“Oops, bad example.  No, that one’s a water-filled volcanic caldera.”

“How do you know?  Any chance its volcano will blow?”

“The best evidence, of course, is the mineralogy.  Volcanoes are made of igneous rocks — lava, tefra and everything in between.  Impact craters are made of whatever was there when the meteorite hit, although the heat and the pressure spike transform a lot of it into some metamorphic form.”

“But you can’t check for that on Mars or the Moon.”

“Mostly not, you’re right, so we have to depend on other clues.  Most volcanoes, for instance, are above the local landscape; most impact structures are below-level.  There are other subtler tests, like the pattern and distance that ejecta were thrown away from the event.  In general we can be 95-plus percent sure whether we’re looking at a volcano or an impact crater.  And no, it won’t any time soon.”

“What won’t do what?”

“You asked whether Crater Lake’s volcano will erupt.  Mount Mazama blew up 7700 years ago and it’s essentially been dormant ever since.”

“There’s some weasel-wording back there — most volcanoes do this, most impacts do that.  What about the exceptions?”

“Those generally have to do with size.  The really enormous features are often hard to even recognize, much less classify.  On Mars, for instance the Northern Lowlands region is significantly smoother than most of the rest of the planet.  Some people think that’s because it’s a huge lava flow that obliterated older impact structures.  Other people think the Lowlands is old sea bottom, smooth because meteorites would have splashed water instead of raising rocky craters.”

Labeled Mars map 420
Mars map from NASA/JPL/GSFC

“I’ll bet ocean.”

“There’s more.  You’ve heard about Olympus Mons on Mars being the Solar System’s biggest volcano, but that’s really only by height.  Alba Mons lies northeast of Olympus and is far huger by volume — 600 million cubic miles of rock but it’s only 4 miles high.  Average slope is half a degree — you’d never notice the upward grade if you walked it.  Astronomers thought Alba was just a humungous plain until they got detailed height data from satellite measurements.”

“The other one’s more than 4 miles high?”

“Oh, yeah.  Olympus Mons rises about 13.5 miles from the base of its surrounding cliffs.  That’s more than the jump from the bottom of the Mariana Trench to the top of Mount Everest.”

“Things on Mars are big, alright.”

~~ Rich Olcott

 

Why Is Mars Red But Earth Is Blue?

The grad students’ Crazy Theory Contest event at Al’s coffee shop is breaking up.  Amanda’s flaunting the Ceremonial Broom she won with her ‘Spock and the horseshoe crabs‘ theory.  Suddenly a voice from behind me outroars the uproar.  “Hey, Mars guy, I got questions.”

Jim looks up and I look around.  Sure enough, it’s Mr Richard Feder.  I start with the introductions but he barrels right along.  “People call Mars the Red Planet, but I seen NASA pictures and it’s brown, right?  All different kinds of brown, with splotches.  There’s even one picture with every color in the rainbow.  What’s with that and what color is Mars really?”

Jim’s a newly-fledged grad student so I step in to give him a chance to think.  “That rainbow picture, Mr Feder, did it have a circular purple spot about a third of the way up from the bottom and was it mostly blue along the top?”

“Yeah, sounds about right.”

“That’s a NASA topographic map, color-coded for relative elevations, purple for low areas to red high-up.  The blue area is the Northern Lowlands surrounding the North Pole, and that purple spot is Hellas Basin, a huge meteor crater billions of years old.  It’s about 5 miles deep which is why they did it in purple.  The map colors have nothing to do with the color of the planet.”

“About your question, Mr …. Feder is it?”

“Yeah, kid, Richard Feder, Fort Lee, New Jersey.”

“Good to meet you, sir.  The answer to your question is, ‘It depends.’  Are you looking down from space or looking around on the surface?  And where are you looking?  Come to think of it, when are you looking?”

“All I’m asking is, is it red or not?  Why make it so complicated?”

“Because it is complicated.  A few months ago Mars had a huge dust storm that covered the whole planet.  At the surface it was far darker than a cloudy moonless night on Earth.  From space it was a uniform butterscotch color, no markings at all.”

“OK, say there’s no dust in the air.”

“Take away all the floating dust and it almost wouldn’t be Mars any more.  The atmosphere’s only 1% of Earth’s and most of that is CO2 — clear and colorless.”

“So what would we see looking down at the surface?”

“Uh … you’re from New Jersey, right?  What color is New Jersey’s surface?”

<a little defensively> “We got a lot of trees and farms, once you get away from all the buildings along the coast and the Interstates, so it’s green.”

“Mars doesn’t have trees, farms, buildings or roads.  What color is New Jersey underneath all that?”

“The farmland soil’s black of course, and the Palisades cliffs near me are, too.  Down-state to the south we got sand-colored sand on the beaches and clay-colored clay.”

“Mars has clay, the Curiosity rover confirmed that, and it’s got basalt like your cliffs, but it has no soil.”

“Huh? How could it not have soil?  That’s just ground-up rocks, right, and Mars has rocks.”

“Soil’s way more then that, Mr Feder.  If all you have is ground-up rocks, it’s regolith.  The difference is the organic material that soil has and regolith doesn’t — rotted vegetable matter, old roots, fungus, microorganisms.  All that makes the soil black and helps it hold moisture and generally be hospitable to growing things.  So far as we know, Mars has none of that.  We’ve found igneous, sedimentary and metamorphic rocks just like on Earth; we’ve found clays, hematites and gypsum that had to have been formed in a watery environment.  But so far no limestone — no fossilized shelly material like that would indicate life.”

“What you’re saying is that Mars colors look like Earth colors except no plants.  So why do astronomers call Earth a ‘pale blue marble’ but Mars is ‘the red planet’?”

“Earth looks pale blue from space.  The blue is the dominant color reflected from the 70% of Earth’s surface that’s ocean-covered.  It’s pale because of white light reflected from our clouds of water vapor.  Mars lacks both.  What Mars does have is finely-divided iron oxide dust, always afloat above the surface.”

“Mars looks red ’cause it’s atmosphere is rusty?”

“Yessir.”Earth and Mars

~~ Rich Olcott

A Force-to-Force Meeting

The Crazy Theory contest is still going strong in the back room at Al’s coffee shop. I gather from the score board scribbles that Jim’s Mars idea (one mark-up says “2 possible 2 B crazy!“) is way behind Amanda’s “green blood” theory.  There’s some milling about, then a guy next to me says, “I got this, hold my coffee,” and steps up to the mic.  Big fellow, don’t recognize him but some of the Physics students do — “Hey, it’s Cap’n Mike at the mic.  Whatcha got for us this time?”

“I got the absence of a theory, how’s that?  It’s about the Four Forces.”

Someone in the crowd yells out, “Charm, Persuasiveness, Chaos and Bloody-mindedness.”

“Nah, Jennie, that’s Terry Pratchett’s Theory of Historical Narrative.  We’re doing Physics here.  The right answer is Weak and Strong Nuclear Forces, Electromagnetism, and Gravity, with me?  Question is, how do they compare?”

Another voice from the crowd. “Depends on distance!”

“Well yeah, but let’s look at cases.  Weak Nuclear Force first.  It works on the quarks that form massive particles like protons.  It’s a really short-range force because it depends on force-carrier particles that have very short lifetimes.  If a Weak Force carrier leaves its home particle even at the speed of light which they’re way too heavy to do, it can only fly a small fraction of a proton radius before it expires without affecting anything.  So, ineffective anywhere outside a massive particle.”

It’s a raucous crowd.  “How about the Strong Force, Mike?”

.  <chorus of “HOO-wah!”>

“Semper fi that.  OK, the carriers of the Strong Force —”

.  <“Naa-VY!  Naaa-VY!”>

.  <“Hush up, guys, let him finish.”>

“Thanks, Amanda.  The Strong Force carriers have no mass so they fly at lightspeed, but the force itself is short range, falls off rapidly beyond the nuclear radius.  It keeps each trio of quarks inside their own proton or neutron.  And it’s powerful enough to corral positively-charged particles within the nucleus.  That means it’s way stronger inside the nucleus than the Electromagnetic force that pushes positive charges away from each other.”

“How about outside the nucleus?”

“Out there it’s much weaker than Electromagnetism’s photons that go flying about —”

.  <“Air Force!”>

.  <“You guys!”>

“As I was saying…  OK, the Electromagnetic Force is like the nuclear forces because it’s carried by particles and quantum mechanics applies.  But it’s different from the nuclear forces because of its inverse-square distance dependence.  Its range is infinite if you’re willing to wait a while to sense it because light has finite speed.  The really different force is the fourth one, Gravity —”

.  <“Yo Army!  Ground-pounders rock!”>

“I was expecting that.  In some ways Gravity’s like Electromagnetism.  It travels at the same speed and has the same inverse-square distance law.  But at any given distance, Gravity’s a factor of 1038 punier and we’ve never been able to detect a force-carrier for it.  Worse, a century of math work hasn’t been able to forge an acceptable connection between the really good Relativity theory we have for Gravity and the really good Standard Model we have for the other three forces.  So here’s my Crazy Theory Number One — maybe there is no connection.”

.  <sudden dead silence>

“All the theory work I’ve seen — string theory, whatever — assumes that Gravity is somehow subject to quantum-based laws of some sort and our challenge is to tie Gravity’s quanta to the rules that govern the Standard Model.  That’s the way we’d like the Universe to work, but is there any firm evidence that Gravity actually is quantized?”

.  <more silence>

“Right.  So now for my Even Crazier Theories.  Maybe there’s a Fifth Force, also non-quantized, even weaker than Gravity, and not bound by the speed of light.  Something like that could explain entanglement and solve Einstein’s Bubble problem.”

.  <even more silence>

“OK, I’ll get crazier.  Many of us have had what I’ll call spooky experiences that known Physics can’t explain.  Maybe stupid-good gambling luck or ‘just knowing’ when someone died, stuff like that.  Maybe we’re using the Fifth Force in action.”

.  <complete pandemonium>
four forces plus 1

~ Rich Olcott


Note to my readers with connections to the US National Guard, Coast Guard, Merchant Marine and/or Public Health Service — Yeah, I know, but one can only stretch a metaphor so far.

Helios versus Mars, Planetary Version

Al waves me over the moment I step through the door of his coffee shop.  “Sy, ya gotta squeeze into the back room.  The grad students are holding another Crazy Theory contest and they’re having a blast.  I don’t know enough science to keep up with ’em but you’d love it.  Here’s your coffee.”

“Thanks, Al.  I’ll see what’s going on.”

The Crazy Theory contest is a hallowed Al’s Coffee Shop tradition — a “seminar” where grad students present their weirdest ideas in competition.  Another tradition (Al is strong on this one) is that the night’s winner has to sweep up the thrown spitballs and crumpled paper napkins at the end of the presentations.  I weave my way in just as the girl at the mic finishes her pitch with, “… and that’s why Spock and horseshoe crabs both have green blood!”

Some in the crowd start chanting “Amanda!  Amanda!  Amanda!”  She’s already reaching for the Ceremonial Broom when Jim steps up to the mic and waves for quiet.  “Wanna hear how the Sun oxidized Mars and poisoned it for us?”

Helios and Mars
Helios and Mars
Mars image adopted from photo by Mark Cartwright
Creative Commons license
Attribution-NonCommercial-ShareAlike

Voice from the crowd — <“The Sun did what?”>

“You remember titration from school chem lab?”

.——<“Yeah, you put acid in a beaker and you drip in a base until the solution starts to turn red.”>

“What color is Mars?”

.——<“Red!”>

“Well, there you are.”

.——<“Horse-hockey!  What’s that got to do with the Sun or what you said about poison?”>

“Look at what our rovers and orbiters found on Mars — atmosphere only 1% of Earth’s but even that’s mostly CO2, no liquid water at the surface, rust-dust everywhere, soil’s loaded with perchlorate salts.  My Crazy Theory can explain all of that.”

.——<“Awright, let’s hear it!”>

“Titration’s all about counting out chemical species.  Your acid-base indicator pinked when you’d neutralized your sample’s H+ ions by adding exactly the right number of OH ions to turn them all into H2O, right?  So think about Mars back in the day when it had liquid water on the ground and water vapor in the atmosphere.  Along comes solar radiation, especially the hard ultra-violet that blows apart stratospheric H2O molecules.  ZOT!  Suddenly you’ve got two free hydrogen atoms and an oxygen floating around.  Then what happens?”

It’s a tough crowd.  <“We’re dying to hear!  Get on with it!”>

“The hydrogens tie up as an H2 molecule.  The escape velocity on Mars is well below the speed of H2 molecules at any temperature above 40K, so those guys abandon Mars for the freedom of Space.  Which leaves the oxygen atom behind, hungry for electrons and ready to oxidize anything it can get close to.”

They’re starting to come along.  <“Wouldn’t the oxygen form O2 and fly away too?”>

“Nowhere near as quickly.  An O2 molecule is 16 times heavier than an H2 molecule.  At a given temperature it moves 1/4 as fast and mostly stays on-planet where it can chew up the landscape.”

.——<“How could an atom do that?”>

“It’s a chain process.  First step for the O is to react with something else in the atmosphere — make an oxidizing molecule like ozone or hydrogen peroxide.  That diffuses down to ground level where it can eat rocks.”

.——<“Wait, ‘eat rocks’!!?!  How does that happen?”>

“Look, most rocks are basically lattices of double-negative oxide ions with positive metal ions tucked in between to balance the charge.  Surface oxide ions can’t be oxidized by an ozone molecule, but they can transmit electron demand down to the metal ions immediately underneath.  An iron2+ ion gets oxidized to iron3+, one big step towards rust-dust.  The charge change disrupts the existing oxide lattice pattern and that piece of the rock erodes a little.”

.——<“What about the poison?”>

“Back when Mars had oceans, they had to have lots of chloride ions floating around to be left behind when the ocean dried up.  Ozone converts chloride to perchlorate, ClO4, which is also a pretty good oxidizer.  Worse, it’s the right size and charge to sneak into your thyroid gland and mess it up.  Poison for sure.  Chemically, solar radiation raised the oxidation state of the whole planet.”

One lonely voice — “Nice try, Jim” — but then the chant returns…

.——<“Amanda!  Amanda!  Amanda!”>

~~ 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

Rhythm Method

A warm Summer day.  I’m under a shady tree by the lake, watching the geese and doing some math on Old Reliable.  Suddenly a text-message window opens up on its screen.  The header bar says 710-555-1701.  Old Reliable has never held a messaging app, that’s not what I use it for.  The whole thing doesn’t add up.  I type in, Hello?

Hello, Mr Moire.  Remember me?

Suddenly I do.  That sultry knowing stare, those pointed ears.  It’s been a yearHello, Ms Baird.  What can I do for you?

Another tip for you, Mr Moire.  One of my favorite star systems — the view as you approach it at near-lightspeed is so ... meaningful.  Your astronomers call it PSR J0337+1715.

So of course I head over to Al’s coffee shop after erasing everything but that astronomical designation.  As I hoped, Cathleen and a few of her astronomy students are on their mid-morning break.  Cathleen winces a little when she sees me coming.  “Now what, Sy?  You’re going to ask about blazars and neutrinos?”

I show her Old Reliable’s screen.  “Afraid not, Cathleen, I’ll have to save that for later.  I just got a message about this star system.  Recognize it?”

“Why, Sy, is that a clue or something?  And why is the lettering in orange?”

“Long story.  But what can you tell me about this star system?”

“Well, it’s probably one of the most compact multi-component systems we’re ever going to run across.  You know what compact objects are?”

“Sure.  When a star the size of our Sun exhausts most of its hydrogen fuel, gravity wins its battle against heat.  The star collapses down to a white dwarf, a Sun-full of mass packed into a planet-size body.  If the star’s a bit bigger it collapses even further, down to a neutron star just a few miles across.  The next step would be a black hole, but that’s not really a star, is it?”

“No, it’s not.  Jim, why not?”

“Because by definition a black hole doesn’t emit light.  A black hole’s accretion disk or polar jets might, but not the object itself.”

“Mm-hm.  Sy, your ‘object’ is actually three compact objects orbiting  around each other.  There’s a neutron star with a white dwarf going around it, and another white dwarf swinging around the pair of them.  Vivian, does that sound familiar?”

“That’s a three-body system, like the Moon going around the Earth and both going around the Sun.  Mmm, except really both white dwarfs would go around the neutron star because it’s heaviest and we can calculate the motion like we do the Solar System.”

“Not quite.  We can treat the Sun as motionless because it has 99% of the mass.  J0337+1715’s neutron star doesn’t dominate its system as much as the Sun does ours.  That outermost dwarf has 20% of its system’s mass.  Phil, what does that suggest to you?”

“It’d be like Pluto and Charon.  Charon’s got 10% of their combined mass and so Pluto and Charon both orbit a point 10% of the way out from Pluto.  From Earth we see Pluto wobbling side to side around that point.  So the neutron star must wobble around the point 20% outward towards the heavy dwarf.  Hey, star-wobble is how we find exoplanets.  Is that what this is about, Mr Moire?  Did someone measure its red-shift behavior?”PSR J0337+1715Cathleen saves me from answering.  “Not quite.  The study Sy’s chasing is actually a cute variation on red-shift measurements.  That ‘PSR‘ designation means the neutron star is a pulsar.  Those things emit electromagnetic radiation pulses with astounding precision, generally regular within a few dozen nanoseconds.  If we receive slowed-down pulses then the object’s going away; sped-up and it’s approaching, just like with red-shifting.  The researchers  derived orbital parameters for all three bodies from the between-pulse durations.  The heavy dwarf is 200 times further out than the light one, for instance.  Not an easy experiment, but it yielded an important result.”

My ears perk up.  “Which was…?”

“The gravitational force between the pulsar and each dwarf was within six parts per million of what Newton’s Laws prescribe.  That observation rules out whole classes of theories that tried to explain galaxies and galaxy clusters without invoking dark matter.”

Cool, huh?

Uh-huh.

~~ Rich Olcott

Quartetto for Rubber Ruler

Suddenly Al’s standing at our table.  “Hey guys, I heard you talking about spectroscopy and stuff and figured you could maybe ‘splain something I read.  Here’s some scones and I brought a fresh pot of coffee..”

“Thanks, Al.  What’s the something?  I’m sure Cathleen can ‘splain.”

“Syyy…”

“It’s this article talking about some scientists going down to Australia to use really old light to look for younger light and it’s got something to do with dark matter and I’m confused.”

“You’re talking about the EDGES project, right?”

“Yeah, I’m pretty sure they said ‘EDGES’ in the article.”

“OK, first we need some background on the background, that really old light you mentioned.  The Cosmic Microwave Background is the oldest light in the Universe, photons struggling out of the white-hot plasma fog that dominated most of the first 377,000 years after the Big Bang.”

“Wait a minute, ‘plasma fog’?”

“Mm-hm.  In those early years the Universe was all free electrons and nuclei colliding with photons and each other.  No photon could travel more than a few centimeters before being blocked by some charged particle.  The Universe had to expand and cool down to 4,000K or so before electrons and nuclei could hold together as atoms and the fog could lift.”

“Cathleen showed me an intensity-frequency plot for those suddenly-free photons.  It was a virtually perfect blackbody curve, identical within a couple parts per million everywhere in the sky.  The thing is, the curve corresponds to a temperature of only 2.73K.  Its peak is in the microwave region, hence the CMB moniker, nestled in between far infrared and HF radio.”

“I thought she said that the fog lifted at 4,000K, Sy.  That’s a lot different from 2-whatever.”

Wavelength-stretching, Vinnie, remember?  Universe expansion stretches the photon waves we measure temperatures with, the further the longer just like Hubble said.  The CMB’s the oldest light in the Universe, coming to us from 13.4 billion lightyears away.  The stretch factor is about 1100.”

“Vinnie, that 2.7K blackbody radiation is the background to the story.  Think of it as a spherical shell around the part of the Universe we can see.  There are younger layers inside that shell and older layers beyond it.”

“What could be outside the Universe, Cathleen?”

“Hey, Al, I carefully said, ‘the part of the Universe we can see.’  I’m quite sure that the Universe extends beyond the spatial volume we have access to, but light from out there hasn’t had a chance to get to us yet.  Going outward from our CMB sphere there’s that 337,000-year-deep shell of electron-nucleus fog.  Beyond that, 47,000 years-worth of quark soup and worse, out to the Big Bang itself.  Coming inward from the CMB we see all the things we know of that have to do with atoms.”

“Like galaxies?”

“Well, not immediately, they took a billion years to build up.  First we had to get through the Dark Ages when there weren’t any photons in the visible light range.  We had huge clouds of hydrogen and helium atoms but virtually all of them were in the ground state.  The CMB photons running around were too low-energy to get any chemistry going, much less nuclear processes.  The Universe was dark and cooling until gravitational attraction made clumps of gas dense enough to light up and become stars.  That’s when things got going.”

“How’d that make a difference?”Blackbody spectrum with notch

“A ground state hydrogen atom’s lowest available empty energy level is way above what a CMB photon could supply.  Those Dark Age atoms were essentially transparent to the prevailing electromagnetic radiation.  But when starlight came along it excited some atoms so that they could also absorb CMB light.  See the notch on the long-wavelength side of this blackbody curve?  It marks the shadow of starlit hydrogen clouds against the CMB’s glow.  The notch wavelength indicates when the absorption started.  Its position suggests that some stars lit up as early as 180 million years after the Big Bang.”

“Suggests, huh?”

“Mm-hm.  There are other interpretations.  That’s where the fun comes in, both on the theory side and the get-more-data side.  Like looking at different times.”

“Different times?”

“Every wavelength represents a different stretch factor and a different depth into the past.”

~~ Rich Olcott

Zarzuela for Rubber Ruler

“Hey, Cathleen, if the expansion of the Universe stretches light’s wavelengths, how do you know when you see a color in a star what you’re looking at?”

“Excuse me, Professor, but your office-mate said you’d be here at the coffee shop and I have a homework question.”

“Good heavens, look at the time!  It’s my office hours, I should be over there.  Oh well, you’re here, Maria, what’s the question?”

“You showed us this chart and asked us to write an essay on it.  I don’t know where to begin.”Temp and BB peak

“Ah.  Hang on, Vinnie, this bears on your question, too.  OK, Maria, what can you tell me about the chart?”

“Well, there are five peaked curves, labeled with different temperatures.  Can I assume the green curve peaks, too, not continuing straight up?”

“Yes.  What else?”

“The horizontal axis, sorry I don’t know the word —”

“abscissa”

“Oh, we have almost the same word in Spanish!  Anyhow, the abscisa says it shows wavelengths.  It goes from a tenth of a nanometer to maybe 10 micrometers.  The chart must have to do with light, because sound waves can’t get that short.  The … ordinada…?”

“Ordinate”

“Thank you.  The ordinate says ‘Intensity’ so the chart must show light spectra at different temperatures.  But there’s only one peak at each temperature.”

“Is that Kirchhoff’s ‘continuous spectrum,’ Cathleen?”

“Right, Vinnie, a smoothly-varying cascade of every wavelength, photons arising from heat-generated motion of charged particles.”

Ah, ya lo veo — this is blackbody spectra given off by hot objects.  You showed us one in class and here we have several.”

“Good, Maria.  Now —”

“But all the peaks look exactly the same, Cathleen.  The hot objects ought to be brighter.  A really hot flame, you can’t even look at it.  Something’s phony.”

“Good eye, Vinnie.  I divided each curve in the graph by its peak height to put them all on an even footing.  That’s why the axis is labeled ‘Intensity profile‘ instead of ‘Intensity.'”

“I’ve got a different issue, Cathleen.  Hot objects have more energy to play with.  Shouldn’t the hotter peaks spread over a wider wavelength range?  These are all the same width.”

“I think I know the answer to that one, Mr Moire.  In class la profesora showed us how the blackbody curve’s equation has two factors, like B=W*X.  The W factor depends only on wavelength and grows bigger as the wavelength gets smaller.  That’s the ‘ultraviolet catastrophe,’ right, ma’am?”

“Mm-hm.  Go on, Maria.”

“But the X factor gets small real fast as the wavelength gets small.  In fact, it gets small so fast that it overpowers W‘s growth — the W*X product gets small, too.  Do you have that movie you showed us on your laptop there, ma’am?”

“Sure.  Here it is…”Blackbody peaks 1

“OK, the blue line is that W factor.  Oh, by the way, the ordinate scale here is logarithmic, so the value at the left end of the blue line is 1027/106 or about 1021 times bigger than it is at the right end even though it looks like a straight line.  The green line is that temperature-dependent factor.  See how it pulls down the orange lines’ values for cold objects, but practically goes away for very hot objects?”

“Yeah, that shows it real good, right, Sy?  That orange peak moves to the left just like Cathleen’s picture shows.  It answers your question, too.”

“It does, Vinnie?  How so?”

“‘Cause the peaks get broader as they get higher.  It’s like the intensity at the, umm, microwave end hardly changes at all and the whole rest of the curve swings up and out from there.”

“Keep in mind, guys, that we’re talking really large numbers here.  Vinnie’s ‘hardly changes at all’ is actually a factor of 40,000 or so.  Those pretty peaks in my homework chart are only pretty because the spread-out tails are so small relative to the peaks.”

“Alright, Cathleen, but how does Maria’s question tie in with mine?”

“They both hinge on wavelength.  The blackbody equation lets us measure a star’s temperature by looking at its color.  Do you have enough to start on that essay, Maria?”

“Yes, ma’am.  Gracias.”

De nada.  Now run along and get to work on it.”

~~ Rich Olcott

Trio for Rubber Ruler

“It’s all about how lightwaves get generated and then what happens.”

Sy and me talked about that, Cathleen.  Lightwaves come from jiggling electrons, right?”

“Any kind of charged particles, Vinnie, but there’s different ways that can happen.  Each leads to its own kind of spectrum.”

“Different kinds of spectrum?  Do you mean like visible versus infrared and ultraviolet, Cathleen?”

“No, I don’t, Sy.  I’m referring to the thing’s overall appearance in every band.  A hundred and fifty years ago Kirchoff pointed out that light from a source can have lines of color, lines without color, or a smooth display without lines.”

“Like that poster that Al put up between the physicist and astronomer corners?”  (We’re still chatting at a table in Al’s coffee shop.  I’m on my fourth scone.)

Astroruler with solar spectrum
Based on N.A.Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF

“Kind of.  That’s based on a famous image created at Kitt Peak Observatory.  In the background there you see a representation of what Kirchoff called a continuous or black-body spectrum, where all the colors fade smoothly into each other in classic rainbow order.  You’re supposed to ignore the horizontal dark lines.”

“And the vertical lines?”

“They form what Kirchoff called an absorption spectrum.  Each dark vertical represents an isolated color that we don’t get from the Sun.”

“You’re saying we get all the other colors but them, right?”

“Exactly, Vinnie.  The Sun’s chromosphere layer filters those specific wavelengths before they get from the deeper photosphere out into space.”

“Complicated filter.”

“Of course.  The Sun contains most of the elements lighter than nickel.  Each kind of atom absorbs its own collection of frequencies.”

“Ah, that’s the quantum thing that Sy and me talked about, right, Sy?”

“Mm-hm.  We only did the hydrogen atom, but the same principles apply.  An electromagnetic wave tickles an atom.  If the wave delivers exactly the right amount of energy, the atom’s chaotic storm of electrons resonates with the energy and goes a different-shaped storm.  But each kind of atom has a limited set of shapes.  If the energy doesn’t match the energy difference between a pair of levels, there’s no absorption and the wave just passes by.”

“But I’ll bet the atom can’t hold that extra energy forever.”

“Good bet, Vinnie.  The flip side of absorption is emission.  I expect that Cathleen has an emission spectrum somewhere on her laptop there.”Emission spectrum“You’re right, Sy.  It’s not a particularly pretty picture, but it shows that nice strong sodium doublet in the yellow and the broad iron and hydrogen lines down in the green and blue.  I’ll admit it, Vinnie, this is a faked image I made to show my students what the solar atmosphere would look like if you could turn off the photosphere’s continuous blast of light.  The point is that the atoms emit exactly the same sets of colors that they absorb.”

“You do what you gotta do, Cathleen.  But tell me, if each kind of atom does only certain colors, where’s that continuous rainbow come from?  Why aren’t we only getting hydrogen colors?”

“Kirchoff didn’t have a clue on that, Vinnie.  It took 50 years and Einstein to solve it.  Not just where the light comes from but also its energy-wavelength profile.”

“So where does the light come from?”

“Pure heat.  You can get a continuous spectrum from a hot wire, molten lava, a hole through the wall of a hot oven, even the primordial chaos of the Big Bang.  It doesn’t matter what kind of matter you’re looking at, the profile just depends on the temperature.  You know that temperature measures the kinetic energy stored in particle random motion, Vinnie?”

“Well, I wouldn’t have put it that way, but yeah.”

“Well, think about the Sun, just a big ball of really hot atoms and electrons and nuclei, all bouncing off each other in frantic motion.  Every time one of those changes direction it affects the electromagnetic field, jiggles it as you say.  The result of all that jiggling is the continuous spectrum.  Absorption and emission lines come from electrons that are confined to an atom, but heat motion is unconfined.”

“How about hot metal?”

“The atoms are locked in their lattice, but heat jiggles the whole lattice.”

~~ Rich Olcott