Category: Astronomy

A Non-political Polarizing Topic

On By rolcottIn Astronomy: Techniques, Physics: Black Holes and Relativity, Physics: Waves, UncategorizedLeave a comment

Vinnie gets the deck next, but first thing he does is plop a sheet of paper onto the table. “Topic is black holes, of course. Everybody’s seen this, right?”

“Sure, it’s the new view of the Milky Way’s super-massive black hole with the extra lines. So deal already.”

“Hold your horses, Cal.” <Vinnie starts dealing.> “I’m looking for explanations. Where’d those lines come from? They swirl across the accretion disk like so much rope, right? Why aren’t they just going straight in orderly‑like? The whole thing just don’t make sense to me.”

Susan bets a few chips. “I saw a similar pop‑sci article, Vinnie. It said the lines trace out polarization in the light waves the Event Horizon Telescope captured. Okay, radio waves — same thing just longer wavelength. Polarized radio waves. I’ve measured concentrations of sugar and amino acid solutions by how much the liquid rotates polarized light, but the light first went through a polarizing filter. How does a black hole make polarized waves?”

Kareem matches Susan’s bet. “Mm‑hm. We use polarized light passing through thin sections of the rocks we sample to characterize the minerals in them. But like Susan says, we don’t make polarized light, we use a filter to subtract out the polarization we don’t want. You’re the physicist, Sy, how does the black hole do the filtering?”

Plane‑polarized electromagnetic wave
 Electric (E) field is red
 Magnetic (B) field is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)

My hand’s good so I match the current ante. “It doesn’t. There’s no filtering, the light just comes out that way. I’d better start with the fundamentals.” <displaying Old Reliable> “Does this look familiar, Vinnie?”

“Yeah, Sy, you’ve used it a lot. That blue dot in the back’s an electron, call it Alice, bobbing straight up and down. That’s the polarization it’s puttin’ on the waves. The red lines are the force that another electron, call it Bob, feels at whatever distance away. Negative‑negative is repelling that so Bob goes down where the red line goes up but you get the basic idea.”

“The blue lines are important here.”

“I’m still hazy on those. They twist things, right?”

“That’s one way to put it. Hendrik Lorentz put it better when he wrote that Bob in this situation experiences one force with two components. There’s the red‑line charge‑dependent component, plus the blue‑line component that depends on the charge and Bob’s motion relative to Alice. If the two are moving in parallel—”

“The same frame, then. I knew frames would get into this somehow.”

“It’s hard to avoid frames when motion’s the subject. Anyway, if the two electrons are moving in parallel, the blue‑line component has zero effect. If the two are moving in different directions, the blue‑line component rotates Bob’s motion perpendicular to Alice’s red‑line polarization plane. How much rotation depends on the angle between the two headings — it’s a maximum when Bob’s moving perpendicular to Alice’s motion.”

“Wait, if this is about relative motion, then Bob thinks Alice is twisting, too. If she thinks he’s being rotated down, then he thinks she’s being rotated up, right? Action‑reaction?”

“Absolutely, Vinnie. Now let’s add Carl to the cast.”

“Carl?”

Alice and Bob’s electromagnetic interaction
begets motion that generates new polarized light.

“Distant observer at right angles to Alice’s polarization plane. From Carl’s point of view both electrons are just tracking vertically. Charges in motion generate lightwaves so Carl sees light polarized in that plane.”

Cathleen’s getting impatient, makes her bet with a rattle of chips. “What’s all this got to do with the lines in the EHT image?”

“The hole’s magnetic field herds charged particles into rotating circular columns. Faraday would say each column centers on a line of force. Alice and a lot of other charged particles race around some column. Bob and a lot of other particles vibrate along the column and emit polarized light which shows up as bright lines in the EHT image.”

“But why are the columns twisted?”

“Orbit speed in the accretion disk increases toward its center. I’d bet that’s what distorts the columns. Also, I’ve got four kings.”

“That takes this pot, Sy.”

~~ Rich Olcott

New Volcano, Old Crater

On By rolcottIn Astronomy: Planetary Science, UncategorizedLeave a comment

Now Eddie’s dealing the cards and the topic choice. “So I saw something on TV about a new volcano on Mars. You astronomy guys have been saying Mars is a dead planet, so what’s with a new volcano? Pot’s open.”

Vinnie’s got nothing, throws down his hand. So does Susan, but Kareem antes a few chips. “I doubt there’s a new volcano, it’s probably an old one that we just realized is there. We find a new old caldera on Earth almost every year. Sy, I’ll bet your tablet knows about it.”

I match Kareem’s bet and fire up Old Reliable. A quick search gets me to the news item. “You’re right, Kareem, it’s a new find of an old volcano. This article’s a puff‑piece but the subject’s in your bailiwick, Cathleen.”

Cathleen puts in her bet and pulls out her tablet. “You’re right, Kareem. It’s a volcano we all saw but no‑one recognized until this two‑person team did. Here’s a wide‑angle view of Mars to get you oriented. North is up top, east is to the right just like usual.”

“Gaah. Looks like a wound!”

“We’ll get to that. The colors code for elevation, purple for lowlands up through the rainbow to red, brown and white. Y’all know about Olympus Mons, the 22‑kilometer tallest volcano in the Solar System, and there’s Valles Marineris, at 4000 kilometers the longest canyon. The Tharsis bulge is red‑to‑pink because it’s higher than most all the rest of the planet’s surface. Do you see the hidden volcano?”

“It’s hard to tell the volcanos from the meteor craters.”

“Understandable. Let me switch to a closer view of the canyon’s western end. This one’s in visible light, no color‑coding games. The middle one of the three Tharsis volcanos is to the left, no ginormous meteor craters in the view. Noctis labyrinthus, ‘the Labyrinth of Night.’ is that badlands region left of center. Lots of crazy canyons that go helter‑skelter.”

“That’s more Mars‑ish, but it’s still unhealthy‑looking.”

“It is a bit rumpled. Do you see the volcano?”

“Mmm, no.”

“This should help. It’s a close-up using the elevation colors to improve contrast.”

“Wow, the area inside that circle sure does look like it’s organized around its center, not higgledy-piggledy like what’s west of it. That brown image had something peaky right about there. What’s ‘prov’?”

“Good eye, Susan. The ‘prov’ means ‘provisional‘ because names aren’t real until the International Astronomical Union blesses them. The peak is nine kilometers high, almost half the height of Olympus Mons. The concentric array of canyons and mesas around it certainly make it look like a collapsed and eroded volcano. But IAU demands more evidence than just ‘look like.’ Using detailed spectroscopic data from two different Mars orbiters, the team found evidence of hydrated minerals plus structural indications that their proposed volcano either punched through a glacier or flowed onto one. Better yet, the mesas all tilt away from the peak, and the minerals are what you’d expect from water reacting with fresh lava.”

“Did they use the word ‘ultramafic‘?”

“I don’t think so, Kareem, just ‘mafic‘.”

“From underground but not deep down, then.”

“I suppose.”

Cal bets. “You said we’d get back to wounds. What was that about?”

“Well, just look at all that mess related to the Tharsis bulge — higher than all its surroundings, massive volcanos nearby, the Noctis badlands, Valles Marineris that doesn’t look water‑carved but has that delta at its eastern end. Why is all of that clustered in just one part of the planet? Marsologists have dozens of hypotheses. My own favorite centers on Hellas basin. It’s the third largest meteor strike in the Solar System and just happens to be almost exactly on the opposite side of Mars.”

Eddie looks a bit gobsmacked. “A wallop like that would carry a lot of momentum. Kareem, can a planet’s interior just pass that along in a straight line?”

“Could be, depending. If it’s solid or high‑viscosity, I guess so. If it’s low‑viscosity you’d get a doughnut‑shaped circulatory pattern inside that’d turn the energy into heat and vulcanism. How long was Mars cooling before the hit?”

“We don’t know.”

Cal’s pair of jacks apologetically takes the pot.

~~ Rich Olcott

Soggy Euclid

On By rolcottIn Astronomy, UncategorizedLeave a comment

It’s Cal’s turn to deal the cards and topic. “Water, water everywhere, especially where you wouldn’t expect it.”

Eddie bets a few chips. “Say what, Cal?”

“Oh, this article in one of my Astronomy magazines, says Euclid has an ice problem.”

“None of Euclid’s problems are nice. I barely got out of Geometry class alive.”

“Not that Euclid, Eddie. The European Space Agency’s Euclid space telescope that’s gonna catalog whatever it can see in a third of the sky. They’re looking to pick up everything out to 10 billion lightyears. S’posed to help us chase down dark energy, get a better handle on really big structures and voids, stuff like that. Anyhow, it’s in a potato‑chip orbit around the Earth‑Sun L2 point like JWST does but twice as far out. The ESA engineers noticed that Euclid‘s readings of some calibration stars were dropping and they figured out it was ice getting in the way.”

“Ice? In space?”

“Yeah, that’s what I said. Turns out all our space missions bring water out with ’em even if they don’t want to.”

Vinnie’s bet doubles the pot. “Ain’t gonna happen. Every ounce of payload gotta have a good excuse or they don’t let it ride.”

“No, really. This ain’t payload, it’s like a stowaway. Mostly in the thermal insulation which has a lot of surface area inside with nooks and crannies where water molecules can stick. Makes no difference to most missions, but when you’ve got world‑class optics that you’re pushing to their limits, a layer of ice a few dozen molecules thick in the wrong place can hurt.”

“Okay, I get there’s problems if the ice is in the optics but you said it was in the insulation. And what’s it even doing there in the first place? If they know it’s gonna be a problem they can just bake it out during construction.”

Chemist Susan chucks a handful of chips into the pot. “Water molecules are small and sneaky. They always surprise you, especially when you don’t want them to. When they’re frozen‑solid ice you’d think they’d stay there, right? Oh, no, they evaporate without going through a liquid phase which lets them migrate around. It’s called sublimation. And do they migrate — just try to keep them out of somewhere. Pour absolute ethanol through humid air, it’s not absolute any more. Dry solids? If the substance has any surface oxygens you’re guaranteed to have water molecules hanging onto them even after you bake the stuff. So, Vinnie — that insulation wrap in the telescope? If it ever saw humidity the fibers are carrying water that could migrate to the optics.”

“Oh yeah, there’ll be humidity. Okay, Baikonur’s pretty much in the middle of a near‑desert, but the Guiana Space Center that France uses is right by the ocean and have you ever looked at a map of Cape Canaveral? That insulation’ll be soggy enough to spew water molecules onto the optics even at space temperatures. C’mon, Kareem, you gonna bet or what?”

“I’m deciding whether to talk about watery moons or the deep‑down Earth water we’re discovering. Jupiter’s moon Europa, for instance. We now know it has a kilometers‑thick shell of ice surrounding an ocean with twice as much water as our oceans put together. Meanwhile,” <meets Susan’s bet> “there’s another huge ocean beneath our feet.”

“Not our feet. This place is built on bedrock.”

“Think below the bedrock, Cal. We live on top of crust, maybe a couple dozen kilometers thick, floating on molten magma. You guys know about subduction, right, where chunks of sea-bottom crust are forced under the edges of continental crust. The further down you go, the hotter things get. The sea‑bottom stuff eventually melts to form lighter magma that ultimately rises to make volcanoes. Thing is, the sinking crust drags water with it, either in cracks or as water of crystallization. A melting chunk releases its water into a kilometers‑thick layer of steamy silicate slurry roughly 400 kilometers below us. That water ‘rains’ upward into our oceans, completing the cycle. Full house, queens and aces. Any challengers?”

Kareem’s surprisingly impatient for a geologist. Nobody counters so the pot’s his. Eddie gets next deal.

~~ Rich Olcott

No Symphony on Mars

On By rolcottIn Astronomy: Planetary Science, Physics: Waves, Uncategorized2 Comments

“Evening, Jeremy, a scoop of your pistachio gelato, please. What’re you reading there?”

“Hi, Mr Moire. It’s ‘A City on Mars‘ by Kelly and Zach Weinersmith. One of my girlfriends read it and passed it along to me. She said it’s been nominated for a Hugo even though it’s non‑fiction and it argues against the kind of go‑to‑Mars‑soon planning that Mr Musk is pushing.”

“Is she right about the argument?”

“Pretty much, so far, but I’m not quite done. You get a clue, though, from the book’s subtitle — ‘Can we settle space, should we settle space, and have we really thought this through?‘ Here’s your gelato.”

“Thanks. Not just Mars, space also?”

“That’s right. It’s about the requirements and implications for people living in space and on the Moon and on Mars. The discussion starts with making and raising babies.”

“That first part sounds like fun.”

“Well, you’d think so, but apparently you need special equipment. Hard to stay in contact if there’s no gravity to key on. But that’s only the start of a problem cascade. Suppose the lady gets pregnant. The good news is in zero gravity it’s easy for her to move around. The bad news is we don’t know whether Earth gravity’s important for making babies develop the way they’re supposed to. Also, delivering a baby isn’t the only medical procedure that’d be a real challenge in zero‑g where you need to keep fluid droplets from bouncing around the cabin and into the air system.”

“Whoa. Hmm, never thought about it in this context before, but babies leak. Diapers can help, but babies burp up stuff along with the air. Yuck! Tears they cry in space would just stay on their eyes instead of rolling down cheeks. So … we’d need OB/GYN clinics and nurseries somewhere down a gravity well.”

“For sure, although no‑one knows whether even the Moon’s 1/6‑g is strong enough for good development. I know my little cousins burn up a lot of energy just running around. Can’t give a toddler resistance bands or trust it on a treadmill.”

“So we need an all‑ages gym down there, too, with enough room for locals and visiting spacers.”

“You’re coming round to the Weinersmiths’ major recommendation — don’t go until you can go big! Don’t plan on growing from a small colony, plan on starting with a whole city that can support everything you need to be mostly self‑sufficient.”

“So you’re young, Jeremy. Are you looking forward to being a Mars explorer?”

“I’ll admit all that rusty landscape reminds me of Navajoland, but I think I’d rather stay here. On Mars I’d be trapped in tunnels and domes and respirators and protective coveralls. I wouldn’t be able to just go out and run under the sky the way I was brought up to do.”

“Wouldn’t be able to do a lot of things. Concerts would sound weird, according to a paper I just read.”

“Sure, wind instruments wouldn’t work with bubble helmets. We could still have strings, percussion and electronics, though, right?”

“Sure you could have them. But it’s worse than that. Mars atmosphere is very different from Earth’s. Its temperature measured in kelvins is 25% colder. The pressure’s 99% lower. Most important, molecule for molecule Mars’ mostly‑CO2 atmosphere’s is 50% heavier than Earth’s N2‑O2 mixture. Those differences combine to muffle sounds so they don’t carry near as far as they would on Earth. Most sounds travel about 30% more slowly, too, but that’s where a CO2 molecule’s internal operation makes things weird.”

“Internal? I thought molecules in sound waves just bounced off each other like little billiard balls.”

“That’s usually the case unless you’re at such high pressures that molecules can start sticking to each other. CO2 under Mars conditions is different. If there’s enough time between bounces, CO2 can convert some of its forward kinetic energy into random heat. The threshold is about 4 milliseconds. A sound wave frequency longer than that travels noticeably slower.”

“Four milliseconds is 250 Hertz — that’s a middle B.”

“Mm-hm. Hit a cymbal and base drum simultaneously, your audience hears the cymbal first. Terrible acoustics for a band.”

~~ Rich Olcott

A Million Times Weaker Than Moonlight

On By rolcottIn Cosmology, Gravitational astronomy, Physics: Waves, UncategorizedLeave a comment

Big Vinnie’s getting downright antsy, which is something to behold. “C’mon, Sy. We get it that sonication ain’t sonification and molecules bumping into each other can carry a sound wave across space if the frequency’s low enough and that can maybe account for galaxies having spiral arms, but you said the Cosmic Hum is a sound, too. That’s a gravity thing, not molecules, right?”

“Not quite what I said, Vinnie. The Hum’s sound‑related, but it’s not ‘sound’ even by our extended definition.”

“Then what’s the connection?”

“Waves.”

“Not frames like always?”

“Not frames, for a change.”

“So it’s waves, but they go though empty space. Can’t happen like sound waves from molecules bumping into each other ’cause molecules are too small to have enough gravity do that when they’re so far apart. What’s carrying the waves?”

“Good question. Einstein figured out one answer. A whole cohort of mid‑20th‑century theoreticians came to a slightly different conclusion.”

“Okay, I’ll bite. What was Einstein’s answer?”

“Relativity, of course. Gravity’s the effect we see from mass deforming nearby space. Moving a mass drives corresponding changes in the shapes of space where it was and where it has moved to. The shape‑changes generate follow‑on gravitational effects that propagate outward over time. Einstein even showed that the gravitational propagation speed is equal to lightspeed.”

“Gimme a sec … Okay, that black hole collision signal LIGO picked up back in 2015, the holes lost a chunk of their combined mass all of a sudden. Quick drop in the gravity thereabouts. You’re saying it took time for the missing gravity strength to get noticed where we’re at. If I remember right, the LIGO people said the event was something like a billion lightyears away so that tells me it happened about a billion years ago and what the LIGO gadget picked up was space waves, right?”

“Right, but it wasn’t just the mass loss, it was the rapid and intense waggles in the gravitational field as those two enormous bodies, each 30 times as massive as the Sun, whirled around each other multiple times per second. The ever‑faster whirling shook the field with a frequency that swept upward to the ‘POP‘ when your mass‑loss happened. LIGO eventually picked up that signal. Einstein would say there’s no ‘action at a distance‘ in the collision‑LIGO interaction, because the objects acted on the gravitational field which acted on the LIGO system.”

“Like using a towel to pop someone in the locker room. The towel’s just transmi– ulp.”

“An admission of guilt if I ever heard one. Yes, like that, except a towel pop carries all the initial energy to its final destination. Gravitational waves spread their energy across the surface of an expanding sphere. The energy per unit area goes down as the square of the distance.” <keying a calculation on Old Reliable> “Suppose the collision releases 10 solar masses worth of energy, we’re a billion lightyears away, and the ‘POP‘ signal is delivered in a tenth of a second. We’d see a signal power … about a millionth as strong as moonlight.”

“Not much there.”

“Right, which is why LIGO and its kin have been such pernickety instruments to build and run. LIGO’s sensors are mirrors roughly a meter across. You get a million times more power sensitivity if your detector’s diameter is a mile across. That was part of the NANOGrav team’s strategy, but they went much bigger.”

“Yeah, that’s the multi-telescope thing, so NANOGrav faked a receiver the size of the Earth, like the Event Horizon Telescope.”

“Much bigger. Their receiver is the entire Milky Way. Instead of LIGO’s mirrors, NANOGrav’s signal generators are neutron stars a dozen or more miles wide scattered across the galaxy.”

“Gotcha, Sy. Two ways. Neutron stars are billions heavier than a LIGO mirror so they’d be less power‑sensitive, not more. Then, power is about moving stuff closer or farther but if I got you right these space waves don’t really do that anyway, right?”

“Right and right, Vinnie, but not relevant. What NANOGrav’s been watching for is pulsar beams being twitched by a gravitational wave. A waltzing black hole pair should generate years‑long or decades‑long wavelengths. NANOGrav may have found one.”

~~ Rich Olcott

Sounds, Harsh And Informative

On By rolcottIn Astronomy: Techniques, Chemistry, Physics: Waves, UncategorizedLeave a comment

Vinnie’s frowning. “Wait, Sy. I get how molecules bumping into each other can carry a sound wave across space if the frequency’s low enough and that can maybe account for galaxies having spiral arms. So what’s that got to do with the Sonication Project?”

Now Jeremy’s frowning. “What’s sonication got to do with Astronomy? One of my girl friends uses sonication in Biology lab when she’s studying metabolism in plant cells.”

“Whoa! Sonification, not sonication — they could have called it soundify‑cation but sonification‘s classier. ‘Sonication‘ uses high‑intensity ultrasound to jiggle a sample so roughly that cell walls can’t take the stress. They break open and spill the cell’s internal soup out where your friend’s probes can get to it. Tammy, the chemist down the hall from my lab, uses sonication, too.”

“Whoa, Susan, wouldn’t sonication break up molecules?”

“Depends on the frequency and intensity, Vinnie. Sonication can mess up big floppy proteins and DNA, but chemists who play with little peptides and such don’t care. Tammy does solid‑state chemistry. She’s looking for superconductors and she actually does want to break things. The field’s hot category these days is complex copper oxides doped with other metals. You synthesize those compositions by sintering a mix of oxide powders. To maximize contact for a good reaction you need really fine‑grained powders. Sonication does a great job of shattering brittle oxide grains down to bits just a few‑score atoms wide. But Tammy’s technique is even more elegant than that.”

“Elegant sneezes from the powder?”

Susan wallops my shoulder. “No, Sy, the powders are so small they’d be a lung hazard and some of them are toxic. Everything’s done behind respiratory protection.” <Susan doesn’t joke about lab safety.> “There’s evidence that some of these materials are only superconductive if they have the right kind of layered structure. Turns out that if Tammy has her sonicator setup just right when she preps a sample for sintering, the sound wave peaks and valleys inside the machine make the shattered particles settle out in interesting layers.”

“Like Chladni figures.”

“Oh, you know about them.”

“Yeah, I wrote about them a few years ago. Waves do surprising things.”

The Bullet Cluster (1E 0657-56)
Sonification Credit: NASA/CXC/SAO/K.Arcand,
SYSTEM Sounds (M. Russo, A. Santaguida), based on X-Ray image by NASA/CXC/CfA/M.Markevitch,
Optical and lensing map: NASA/STScI, Magellan/U.Arizona/D.Clowe,
Lensing map: ESO WFI

Vinnie’s getting impatient. “So what’s sonification then?”

Tinkly music bursts from Cathleen’s tablet. “This one’s listenable, Susan, and it’s a nice demonstration of what sonification’s about and how arbitrary it can be. You start with complicated multi‑dimensional data and use some process to turn it into audible signals. The process algorithm can use any sound characteristics you like — loudness, pitch, timbre, whatever. This example started with the famous Bullet Cluster image that most people accept as the first direct confirmation of dark matter. All the white‑ish thingies are galaxies except for the ones with pointy artifacts — those are stars. The pink haze is X‑ray light from the same region. The blue haze comes from a point‑by‑point assessment of how badly the galaxy images have been distorted by gravitational lensing — that’s an estimate of the dark matter mass between us and that region of sky. Got all that?”

“And that vertical line is like a scan going across the picture?”

“It’s not like a scan, it is a scan. Imagine a collection of tiny multi‑spectral cameras arranged along a carrier bar. As the bar travels across the picture, each camera emits three signals proportional to the amount of white, pink and blue light it sees. If you look close, just to the right of the line, you’ll see moving white, red and blue line‑charts of the respective signals.”

“That’s fine, but what’s with the sound effects?”

“The Project’s sonification processing generated hiss and rumble sounds whose loudness is proportional to the red and blue signals. Each white‑ish peak became a ping whose pitch indicates position along that bar.”

“Why go to all that trouble?”

“The sounds encode the picture for vision‑challenged people. Beyond that, the Project participants hope that with the right algorithms, their music will reveal things the pictures don’t.”

“They should avoid screamy sounds.”

~~ Rich Olcott

Galaxies Sing In A Low Register

On By rolcottIn Astronomy, Physics: Waves, UncategorizedLeave a comment

Jeremy gets a far‑away look. ”It’s gotta be freakin’ noisy inside the Sun.” just as our resident astronomer steps into Cal’s Coffee.

“Wouldn’t bet that, Jeremy. Depends on where you are in the Sun and on how you define noise.”

Vinnie booms, quietly. ”We just defined it, Cathleen. Atoms or molecules bumping each other in compression waves. Oh, wait, that’s ‘sound,’ you said ‘noise.’ Is that different?”

Susan slurps the last of her chocolate latte. ”Depends on your mood, I guess. All noise is sound, but some sound can be signal. Some people don’t like my slurping so for them it’s noise but Cal hears it as an order for another which makes him happy.”

“Comin’ up, Susan. Hey, Cathleen, maybe you can slap down Sy. He said spiral galaxies have something to do with sound which don’t make sense. Set him straight, okay?”

“Sy, have you all settled that sound isn’t limited to what humans hear?”

“Sure. Everybody’s agreed that infrasound and ultrasound are sound, and that Bishop Berkeley’s fallen tree made a sound even though nobody heard it. That’s probably what got Jeremy thinking about sound inside the Sun.” Jeremy nods.

“Then Vinnie’s definition is too limited and Sy’s statement is correct. Probably.”

That gets a reaction from everyone, though mine is a smile. ”Let ’em have it, Cathleen.”

“Okay. Let’s take Jeremy’s idea first and then we’ll get to galaxies.” <fetches her tablet from her purse and a display on her tablet> “Here’s a diagram of the Sun I did for class. If you restrict ‘sound‘ to mean only coherent waves borne by atoms and molecules, there’s no sound in the innermost three zones. The only motion, if Sy grants I can call it that, is photons and subnuclear particles randomly swapping between adjacent nuclei that are basically locked into position by the pressure. Not much actual atomic motion until you’re up in the Convection Zone where rising turbulence is the whole game. Even there most of the particles are ions and electrons rather than neutral atoms. Loud? You might say so but it’d be a continuous random crackle‑buzz, not anything your ears would recognize. Sound waves as such don’t happen until you reach the atmospheric layers. Up there, oh yes, Jeremy, it’s loud.”

Geologist Kareem is a quiet guy, normally just sits and listens to our chatter, but Cathleen’s edging onto his turf. ”How about seismic waves? If there’s a big flare or CME up top, won’t that send vibrations all the way through?”

“Good point, Kareem. Yes, the Sun has p and s waves just like Earth does, but they travel no deeper than the Convection Zone. A different variety we may not have, g waves, would involve the core. Unfortunately, theory says g waves are so weak that the Convection Zone’s chaos swamps them. Anyway, the Sun’s s, p and g waves wouldn’t contribute to what Jeremy would hear because their frequencies are measured in hours or days. Can I get to galaxies now?”

“Please do.”

A Hubble view of NGC 5457, the Pinwheel Galaxy. Credit: NASA, ESA.

“Thanks.” <another display on her tablet> “Here’s a classic spiral galaxy. Gorgeous, huh? The obvious question is, is it winding in or spraying out? The evidence says ‘No‘ to both. The stars are neither pulled into a whirlpool nor flung out from a central star‑spawner. By and large, the stars or clusters of them are in perfectly good Newtonian orbits around the galactic center of gravity. So why are they collected into those arms? Here’s a clue — most of the blue stars are in the arms.”

“What’s special about blue stars?”

“In general, blue stars are large, hot and young. Our Sun is yellow, about halfway through a 10‑million‑year lifetime. The blue guys burn through their fuel and go nova in a tenth of that time. Blue stars out there tell us that the arms serve as stellar nurseries. It’s not stars gathering into arms, it’s galaxy‑wide rotating waves of gas birthing stars there. There’s argument about whether the wave rotation is intrinsic or whether there’s feedback as each wave is pulled along by star formation at the leading edge and pushed by novae at the trailing edge. Sy’s point, though, is that an arm‑dwelling old red star would experience the spinning gas density pattern as a basso profundo sound wave with a frequency even lower than the million‑year range. Right, Sy?”

“As always, Cathleen.”

~~ Rich Olcott

  • More thanks to Alex.

Screams And Thunders

On By rolcottIn Astronomy: Techniques, Physics: Waves, UncategorizedLeave a comment

Coffee time. I step into Cal’s shop and he’s all over me. ”Sy, have you heard about the the NASA sonification project?”

Susan puts down her mocha latte. “I didn’t like some of what they’ve released. Sounds too much like people screaming.”

Jeremy looks up from the textbook he’s reading. ”In space, no-one can hear you scream.”

Vinnie rumbles from his usual table by the door. “Any of these got anything to do with the Cosmic Hum?”

“They have nothing to do with each other, except they do. Spiral galaxies, too.”

“Huh?”
 ”Huh?”
  ”Huh?”
   ”Huh?”

“A mug of my usual, Cal, please, and a strawberry scone.”

“Sure, Sy, here ya go, but you can’t say something like that around here without you tellin’ us how come.”

“Does the name Bishop Berkeley ring a bell with anyone?”

Vinnie’s on it. ”That the ‘If a tree falls in the forest…‘ guy, right? Claimed there’s no sound unless somebody’s there to hear it?”

“And by extension, no sound outside human hearing range.”

“But bats and them use sound we can’t hear.”
 ”So do elephants and whales.”

“Well there you go. So are we agreed that he was wrong?”

“Not quite, Mr Moire. His definition of ‘sound‘ was different from one you’d like. He was a philosopher theorizing about perception, but you’re a physicist. You two don’t even define reality the same way.”

Vinnie’s rumble. ”Good shot, Jeremy. Sound is waves. Sy and me, we talked about them a lot. One molecule bangs into the next one and so on. The molecules don’t move forward, mostly, but the banging does. Sy showed me a video once. So yeah, people listening or not, that tree made a sound. There’s molecules up in space, so there’s sound up there, too, right, Sy?”

“Mmm, depends on where you are. And what sounds you’re equipped to listen for. The mechanism still works, things advancing a wave by bouncing off each other, but the wave’s length has to be longer than the average distance between the things.” <drawing Old Reliable, pulling up display> “Here’s that video Vinnie saw. I’ve marked two of the particles. You see them moving back and forth over about a wavelength. Suppose a much shorter wave comes along.”

“Umm… Each one would get a forward kick before they got back into position. They wouldn’t oscillate, they’d just keep moving in that direction. No sound wave, just a whoosh.”

“Right, Jeremy. Each out‑of‑sync interaction converts some of the wave’s oscillating energy into one‑way motion. The wave doesn’t get energy back. A dozen wavelengths along, no more wave. So the average distance between particles, we call it the mean free path, sets limits to the length and frequency of a viable wave. Our ears would say it filters out the treble.”

“Space ain’t quite empty so it still has a few atoms to bump together. What kinds of limits do we get out there?”

“Well, there’s degrees of empty. Interplanetary space has more atoms per cubic meter than interstellar which is more crowded than intergalactic. Nebulae and molecular clouds can be even less empty. Huge range, but in general we’re talking wavelengths longer than a million kilometers. Frequencies measured in months or years — low even for your voice, Vinnie.”

Jeremy gets a look on his face. ”One of my girlfriends is a soprano. We tested her in the audio lab and she could hit a note just under two kilohertz, that’s two thousand cycles per second. My top screech was below half that. I could scream in space, but I guess not low enough to be heard.”

“Yeah, keep that spacesuit helmet closed and be sure your radio intercom’s working.”

“Wait, what about screaming over the radio?”

“Radio operates with electromagnetic waves, not bumping atoms. Mean free path limits don’t apply. Radio’s frequency range is around a hundred megahertz, screeching’s no problem. Your broadcast equipment’s response range would set your limits.”

“Sy, those screamy sounds I objected to — you say they can’t have traveled across space as sound waves. Was that a radio transmission?”

“Maybe, Susan. From what I’ve read, we’ve picked up beaucoodles of radio sources, all different types and all over the sky. Each broadcasts a spectrum of different radio frequencies. Some of them are constant radiators, some vary at different rates. You may have heard a recording of a kilohertz variable source.”

<shudder> “All nasty treble, no bass or harmony.”

~~ Rich Olcott

  • Thanks to Alex, who raised several questions.

A Spherical Bandstand

On By rolcottIn Astronomy: Planetary Science, Mathematics, Mathematics: Spherical Harmonics, UncategorizedLeave a comment
Radial harmonics Rn = Ln e-nr

“Whoa, Sy, something’s not right. Your zonal harmonics — I can see how latitudes go from pole to pole and that’s all there are. Your sectorial harmonic longitudes start over when they get to 360°, fine. But this chart you showed us says that the radius basically disappears crazy close to zero. The radius should keep going forever, just like x, y and z do.”

“Ah, I see the confusion, Susan. The coordinate system and the harmonic systems and the waves are three different things, um, groups of things. You can think of a coordinate system as a multilevel stage where chords of harmonic musicians can interact to play a composition of wave signals. The spherical system has latitude and longitude levels for the brass and woodwind players, plus one in back for the linear percussion section. Whichever direction the brass and woodwinds point, that’s where the signals go out, but it’s the percussion that determines how far they get. Sure, radius lines extend to infinity but except for R0 radial harmonics damp out pretty quickly.”

“Signals… Like Kaski’s team interpreted Juno‘s orbital twitches as a signal about Jupiter’s gravitational unevenness. Good thing Juno got close enough to be inside the active range for those radial harmonics. How’d they figure that?”

“They probably didn’t, Cathleen, because radial harmonics don’t fit easily into real situations. First problem is scale — what units do you measure r in? There’s an easy answer if the system you’re working with is a solid ball, not so easy if it’s blurry like a protein blob or galaxy cluster.”

“What makes a ball easy?”

“Its rigid surface that doesn’t move so it’s always a node. Useful radial harmonics must have a node there, another node at zero and an integer number of nodes between. Better yet, with the ball’s radius as a natural length unit the r coordinate runs linearly between zero at the center and 1.0 at the surface. Simplifies computation and analysis. In contrast, blurries usually don’t have convenient natural radial units so we scrabble around for derived metrics like optical depth or mixing length. If we’re forced into doing that, though, we probably have worse challenges.”

“Like what?”

“Most real-world spherical systems aren’t the same all the way through. Jupiter, for instance, has separate layers of stratosphere, troposphere, several chemically distinct cloud‑phases, down to helium raining on layers of hydrogen in liquid, maybe slushy or even solid form. Each layer has its own suite of physical properties that put kinks into a radial harmonic’s smooth curve. Same problem with the Sun.”

“How about my atoms? The whole Periodic Table is based on atoms having a shell structure. What about the energy level diagrams for atomic spectra? They show shells.”

“Well, they do and they don’t, Susan. Around the turn of the last Century, Lyman, Balmer, Paschen, Brackett and Pfund—”

“Sounds like a law firm.”

“<ironically> Ha, ha. No, they were experimental physicists who gave the theoreticians an important puzzle. Over a 40‑year period first Balmer and then the others, one series at a time, measured the wavelengths of dozens of lines in hydrogen’s spectrum. ’Okay, smarties, explain those!‘ So the theoreticians invented quantum mechanics. The first shot did a pretty good job for hydrogen. It explained the lines as transitions between discrete states with different energy levels. It then explained the energy levels in terms of charge being concentrated at different distances from the nucleus. That’s where the shell idea came from. Unfortunately, the theory ran into problems for atoms with more than one electron.”

“Give us a second… Ah, I get why. If one electron avoids a node, another one dives in there and that radius isn’t a node any more.”

“Got it in one, Cathleen. Although I prefer to think of electrons as charge clouds rather than particles. Anyhow, when an atom has multiple charge concentrations their behavior is correlated. That opens the door to a flood of transitions between states that simply aren’t options for a single‑electron system. That’s why the visible spectrum of helium, with just one additional electron, has three times more lines than hydrogen does.”

“So do we walk away from spherical harmonics for atoms?”

“Oh, no, Susan, your familiar latitude and longitude harmonics fit well into the quantum framework. These days, though, we mostly use combinations of radial fade‑aways like my Sn00 example.”

~~ Rich Olcott

Jupiter And The Atoms

On By rolcottIn Astronomy: Planetary Science, Mathematics: Spherical Harmonics, UncategorizedLeave a comment

“Okay, Sy, what’s your third solution?”

“Solution to what, Susan?”

“These harmonic thingies. They’re about angles so it makes sense to chart them in polar or spherical coordinates, but when they take on negative values the radius goes the wrong way. You said one solution was to chart the negatives in a different color. That’s confusing, though. Another solution is to square all the values to get everything into positive territory. That’s okay for chemists like me because the peaks and nodes we care about stay in the same places. What’s the third option?”

“One that gets to why these ‘harmonic thingies’ are interesting at all. When Juno‘s orbiting Jupiter, does it feel each of Kaspi’s Jn shapes individually?”

“No, of course not, she just reacts to how they all add togethherrr … Oh! So you’re saying we can handle negative values from one harmonic by adding it to another one that’s more positive and plotting the combination.”

<pointing to paper napkin> “Bingo! Remember this linear plot of J2 where I colored its negative section pink?” <pointing to display on Old Reliable> “When you multiply J2 by C0 you get S220. I added that to four helpings of Sn00 to get this combination.”

“Ah, that negative region in S220‘s middle shaves back the equator on Sn00‘s sphere while the positive part adds bumps top and bottom.” <Susan gives me the side‑eye> “Why’d you pick that 4‑to‑1 ratio, and what’s with those n subscripts instead of numbers?”

“Getting a little ahead of myself. For the moment let’s concentrate on Juno‘s experience with Jupiter’s gravity. One reason I chose that ratio was that it’s pretty easy to see in the picture. In real cases the physical system determines the ratios. Kaspi’s team derived their ratios experimentally. They used math to fit a model to Juno‘s very slightly wobbly orbit. Their model of Jupiter’s gravity field started from the spherical J0 shape. They tweaked that by adding different ratios of J2 through J40, adjusting the ratios until the model’s total gravity field predicted an orbit that matched the real‑world one. J2‘s share was about 15 parts per thousand but most of the rest contributed less than a part per million. Jupiter probably uses multiple mass blobs to make the J2 shape. The point is, the planet’s really a mess but we can analyze the mess in terms of the harmonics.”

“So that’s how you drew what Cal called your wiggle-waggles — you followed Kaski’s Jn recipe and then added some constant to push the polar plot out far enough that the negatives didn’t poke out the wrong side. That constant — what value did you use and why that one?”

“That’s exactly what I did do, Cathleen. Frankly, I don’t even remember what constant I added, just something that was big enough to make the negatives behave nicely, not so large that the peaks vanished by comparison. Calibrating accurately to Jupiter’s J0 would shrink the peaks down to parts‑per‑thousand invisibility. After all, I was more concerned with peak position than peak size.”

“Now we’re back to your 4‑to‑1 ratio. Was that arbitrary, too?”

“No, it wasn’t, Susan. Would it have been closer to Chemistry if I’d labeled that figure as 1s22s22p1?”

“Two electrons in the 1s‑shell, two in the 2s‑shell plus one 2p electron … that’s a boron atom? But you’re showing only one radial shell, not two separate ones.”

“True, but that’s to make another point. There isn’t an electron in the 1s shell, or even a pair of them nicely staying on opposite sides. The atom’s charge, all five electrons‑worth of it, is smeared out as a wave pattern across the entire structure. The Sn00 pattern captures everything that’s spherical. The S220 pattern gets what’s left.”

“But what about the radial nodes? Isn’t that the difference between 1s and 2s, that 2s has a node?”

“Oh there are nodes, alright, but they don’t have much effect. Each radial harmonic is the product of two factors — a polynomial and an exponential. The exponential part squeezes the polynomial so hard that adjacent peaks and valleys are barely bumps and dents.”

“So Jupiter and atoms use the same math, huh?”

“So does the Sun.”

~~ Rich Olcott