Earth’s Closed Eye

Question in the chat box, Maria, and I paraphrase to preserve anonymity — ‘So the Arecibo telescope won’t work any more. Why should we care? There’s lots of other telescopes that could so the same job.‘”

“But profesora, there aren’t. Arecibo is special in many ways. First, it is a very good telescope. That means it has high sensitivity and high resolution. Compare two radio telescopes with different‑size dishes and the same kinds of antennas and everything else. The one with the bigger dish is more sensitive because it can capture more photons. Arecibo’s 300‑meter dish used to be the largest in the world. China activated their FAST instrument five years ago. Its 500‑meter dish should make it more than 200 times as sensitive as Arecibo, but it doesn’t because neither telescope is designed to use the entire dish surface at once except for looking straight up. Their active areas are about the same.”

Is FAST another one of those goofy acronyms?

“Of course. It stands for ‘Five‑hundred‑meter Aperture Spherical radio Telescope‘ but in Chinese its name is Tianyan, which means ‘Heaven Eye.’ I think that is more pretty. FAST and Arecibo overlap their wavelength ranges, although FAST can receive some longer wavelengths and Arecibo can receive some shorter ones. Oh, there is also a big Russian radio telescope, RATAN‑600, with an even bigger diameter. But it is a ring, not a disk, so not as sensitive as Arecibo or FAST.”

A ring? Why did they build it that way?

“Because of the other thing you need in a good telescope, resolution. If you have good resolution in an image, you can see points that are very close together. The how‑close limit angle comes from dividing the light wavelength by the dish diameter. The diameter of RATAN’s ring is 600 meters, so RATAN’s resolving power is twice as good as Arecibo’s 300‑meter disk. RATAN doesn’t need to be sensitive, though, because it is used mostly for looking close at the Sun, not at stars and galaxies. That is OK because RATAN is so far north.”

What difference does that make?

“No telescope can see what is below its horizon. RATAN is at 43° north, almost 1400 miles north of Arecibo. It has a good view of the northern sky but cannot see down to the Equator where many asteroids and all the planets are.”

Sorry, Maria, that’s not quite correct. Earth is tilted relative to the orbital plane by 23° so even Arecibo only sees the northern portion of planetary orbits. While I’ve got the mic I’ll add some background on RATAN‑600. RATAN is the acronym for ‘Academy of Sciences Radio Telescope’ in Russian. It was built in the Cold War era when that part of the world was the USSR. Although I don’t believe it’s ever been publicly confirmed, many people think that RATAN‑600‘s original purpose was detection of ICBMs coming in over the North Pole. However, over the decades it has been a productive source of information for the solar physics community. Back to you, Maria.

“That is good to know, profesora. Thank you. So, Arecibo is — was —special because of its sensitivity and its resolution. It is also about 500 miles further south than FAST. But Arecibo has one additional feature that FAST cannot have — radar. Arecibo has high-powered transmitters that can send out terawatt pulses to things in the Solar System that are closer than Saturn. The dish gathers echoes that give us detailed knowledge of those objects. For instance, Arecibo’s radar echoes from Mercury showed us that the planet is not tidally locked to the Sun. We used to think Mercury’s day was 88 days long, like its year, but now we know it rotates in only 59 days.”

Why can’t the Chinese just add transmitters to FAST?

“The Chinese designers gave FAST a light‑weight antenna carriage to hang over its dish. Arecibo’s 900‑ton carriage can handle massive transmitters, but FAST’s cannot. There is one other radio telescope with radar, at Goldstone, California, but it has less than one‑millionth the power of Arecibo’s transmitters. Without Arecibo’s sensitivity, resolution, location and high-powered radar capability we cannot find near‑Earth asteroids on track to hit us.”

~~ Rich Olcott

Author’s note — Early in the morning of 1 December, after I completed last week’s and this post, the National Science Foundation reported that Arecibo’s central instrument platform has fallen onto the dish as a result of further cable failures.
“Vale, nostri servi boni et fidelis”
Farewell, our good and faithful servant.

Arecibo ¡que lástima!

Hello, Astronomy video class. I’ve made room in the syllabus schedule for a quick talk from someone with a personal connection to a timely topic. You may know we’ve lost one of Astronomy’s premier radio telescopes, Puerto Rico’s Arecibo Observatory. I’ve asked Maria to fill us in on the what and the why. If you have a question, type it into your chat window and I’ll relay it to her. Maria, you’re on.”

“Thank you, profesora. Yes, I do know Arecibo because I have worked there. I grew up in Hatillo, a small city on the north coast about half an hour away from the Observatory. My teacher of science in high school, somehow he got me a summer job there. Sometimes I worked in the gift shop, sometimes I helped the guided tours, but my best thing was running errands because then I could visit the science offices and chat with people about what they were doing. There I fell in love with Astronomy and that is why I came here to study.

“When people think of Arecibo they think of the big 300 meter dish, about 1000 feet across. Sharing my screen for you… there. This picture I got from Wikipedia:

The Arecibo Observatory
photo by JidoBG, licensed under the Creative Commons Attribution-Share Alike 4.0 International

“The installation sits in very rough mountains. They are so rough because they are mostly limestone that slowly dissolves in water. The water seeps in through cracks to attack the rock and make cliffs and holes and caves. The Arecibo observatory is where it is because water eroded a cavern close to the surface. The topmost material fell into the empty space to make a huge round sinkhole like very few other places in the world.”

Question from the chat, Maria. Did the rock actually dissolve into that convenient smooth reflector shape?

“¡Por Dios no! The circular shape, yes, but the sinkhole floor is nearly flat. The dish itself is many aluminum panels fixed to a floating steel grid. Here is a picture Mr Phil Perillat took from beneath the dish. I don’t know Mr Perillat’s title but he is always very busy keeping things running.

“Above you see the grid, five meters or more above the ground. The grid is supported by concrete all around the edges. Coming down from the grid you see cables leading to those round concrete piers. These cables pull the grid down into its curved shape which is actually a piece of a sphere.”

A sphere, not a parabola?

“No, profesora, and that is important. A fixed dish with a parabola shape like most telescope mirrors always would aim straight up. It would see targets at the top of the sky but for only a few minutes as the Earth turns through the day. With a sphere‑shaped dish and the antennas mounted where the center of the sphere would be, then the whole sky is in focus. The scientists aim the telescope by moving the antennas to point at different parts of the dish like you look at different parts of one of those funny mirrors in, sorry I don’t know the word, una casa de la diversión.”

A funhouse.”

“Thank you. The antenna carriage is so complicated because it must look at different parts of the dish. Here you see the carriage:

The Arecibo receiver mounting and dome
Photo by Phil Perillat, National Astronomy and Ionosphere Center

“The antennas point downward from inside that dome. When motors swing the dome along that crescent‑shaped arc, the antennas scan along an arc of the dish. More motors can rotate the arc around that circular track. By swinging and rotating together, the antennas can follow the reflection of any object that moves through the sky.”

All those motors and tracks and antennas must be heavy.”

“Yes, 900 tons hanging 500 feet above the grid. Eighteen cables hold it up. Each is many strands of steel braided together. Compressed air blows through the braids to prevent corrosion, but the storms won out in the end. Three cables have failed and it is too dangerous for repair. So sad.”

~~ Rich Olcott

Author’s note — Early in the morning of 1 December, after I completed this and next week’s posts, the National Science Foundation reported that Arecibo’s central instrument platform had fallen onto the dish as a result of further cable failures.
“Vale, nostri servi boni et fidelis”
Farewell, our good and faithful servant.

Only a H2 in A Gilded Cage

“OK, Susan, you’ve led us through doing high-pressure experiments with the Diamond Anvil Cell and you’ve talked about superconductivity and supermagnetism. How do they play together?”

“It’s early days yet, Sy, but Dias and a couple of other research groups may have brought us a new kind of superconductivity.”

“Another? You talked like there’s only one.”

“It’s one of those ‘depends on how you look at it‘ things, Al. We’ve got ‘conventional‘ superconductors and then there are the others. The conventional ones — elements like mercury or lead, alloys like vanadium‑silicon — are the model we’ve had for a century. Their critical temperatures are generally below 30 kelvins, really cold. We have a 60‑year‑old Nobel‑winning theory called ‘BCS‘ that’s so good it essentially defines conventional superconductivity. BCS theory is based on quantum‑entangled valence electrons.”

“So I guess the unconventional ones aren’t like that, huh?”

“Actually, there seem to be several groups of unconventionals, none of which quite fit the BCS theory. Most of the groups have critical temperatures way above what BCS says should be the upper limit. There are iron‑based and heavy‑metals‑based groups that use non‑valence electrons. There are a couple of different carbon‑based preparations that are just mystical. There’s a crazy collection of copper oxide ceramics that can contain five or more elements. Researchers have come up with theories for each of them, but the theories aren’t predictive — they don’t give dependable optimization guidelines.”

“Then how do they know how to make one of these?”

“Old motto — ‘Intuition guided by experience.’ There are so many variables in these complex systems — add how much of each ingredient, cook for how long at what temperature and pressure, chill the mix quickly or anneal it slowly, bathe it in an electrical or magnetic field and if so, how strong and at what point in the process… Other chemists refer to the whole enterprise as witch’s‑brew chemistry. But the researchers do find the occasional acorn in the grass.”

“I guess the high‑pressure ploy is just another variable then?”

“It’s a little less random than that, Sy. If you make two samples of a conventional superconductor, using different isotopes of the same element, the sample with the lighter isotope has the higher critical temperature. That’s part of the evidence for BCS theory, which says that electrons get entangled when they interact with vibrations in a superconductor. At a given temperature light atoms vibrate at higher frequency than heavy ones so there’s more opportunity for entanglement to get started . That set some researchers thinking, ‘We’d get the highest‑frequency vibrations from the lightest atom, hydrogen. Let’s pack hydrogens to high density and see what happens.'”

“Sounds like a great idea, Susan.”

“Indeed, Al, but not an easy one to achieve. Solid metallic hydrogen should be the perfect case. Dias and his group reported on a sample of metallic hydrogen a couple of years ago but they couldn’t tell if it was solid or liquid. This was at 5 megabars pressure and their diamonds broke before they could finish working up the sample. Recent work has aimed at using other elements to produce a ‘hydrogen‑rich’ environment. When Dias tested H2S at 1.5 megabar pressure, they found superconductivity at 203 kelvins. Knocked everyone’s socks off.”

“Gold rush! Just squeeze and chill every hydrogen‑rich compound you can get hold of.”

“It’s a little more complicated than that, Sy. Extreme pressures can force weird chemistry. Dias reported that shining a green laser on a pressurized mix of hydrogen gas with powdered sulfur and carbon gave them a clear crystalline material whose critical temperature was 287 kelvins. Wow! A winner, for sure, but who knows what the stuff is? Another example — the H2S that Dias loaded into the DAC became H3S under pressure.”

“Wait, three hydrogens per sulfur? But the valency rules—”

“I know, Sy, the rules say two per sulfur. Under pressure, though, you get one unattached molecule of H2 crammed into the space inside a cage of H2S molecules. It’s called a clathrate or guest‑host structure. The final formula is H2(H2S)2 or H3S. Weird, huh? Really loads in the hydrogen, though.”

“Jupiter has a humungous magnetic field and deep‑down it’s got high‑density hydrogen, probably metallic. Hmmm….”

~~ Rich Olcott

Futile? Nope, Just Zero

“Megabar superconductivity.”

“Whoa, Susan. Too much information, too few words. Could you unpack that, please?”

“No problem, Sy. A bar is the barometric pressure (get it?) at sea level. A megabar is—”

“A million atmospheres, right?”

“Right, Al. So Ranga Dias and his crew were using their Diamond Anvil Cells to put their chemical samples under million-atmosphere pressures while they tested for superconductivity—”

“Like Superman uses?”

“Is he always like this, Sy?”

“Just when he gets excited, Susan. The guy loves Science, what can I say?”

“Sorry, Susan. So what makes conductivity into superconductivity?”

“Excellent question, Al. Answering it generated several Nobel Prizes and we still don’t have a complete explanation. I can tell you the what but I can’t give you a firm why. Mmm… what do you know about electrical resistance?”

“Just what we got in High School General Science. We built a circuit with a battery and a switch and an unknown resistor and a meter to measure the current. We figured the resistance from the voltage divided by the current. Or maybe the other way around.”

“You got it right the first try. The voltage drop across a resistor is the current times the resistance, V=IR so V/I=R. That’s for ordinary materials under ordinary conditions. But early last century researchers found that for many materials, if you get them cold enough the resistance is zero.”

“Zero? But … if you put any voltage across something like that it could swallow an infinite amount of current.”

“Whoa, Al, what’s my motto about infinities?”

“Oh yeah, Sy. ‘If your theory contains an infinity, you’ve left out physics that would stop that.’ So what’d stop an infinite current here?”

“The resistor wasn’t the only element in your experimental circuit. Internal resistance within the battery and meter would limit the current. Those 20th-century researchers had to use some clever techniques to measure what they had. Back to you, Susan.”

“Thanks, Sy. I’m going to remember that motto. Bottom line, Al, superconductors have zero resistance but only under the right conditions. You start with your test material, with a reasonable resistance at some reasonable temperature, and then keep measuring its resistance as you slowly chill it. If it’s willing to superconduct, at some critical temperature you see the resistance abruptly drop straight down to zero. The critical temperature varies with different materials. The weird thing is, once the materials are below their personal critical temperature all superconductors behave the same way. It’s seems to be all about the electrons and they don’t care what kind of atom they rode in on.”

“Wouldn’t copper superconduct better than iron?”

“Oddly enough, pure copper doesn’t superconduct at all. Iron and lead both superconduct and so do some weird copper-containing oxides. Oh, and superconductivity has another funny dependency — it’s blocked by strong magnetic fields, but on the other hand it blocks out weaker ones. Under normal conditions, a magnetic field can penetrate deep into most materials. However, a superconducting piece of material completely repels the field, forces the magnetic lines to go around it. That’s called the Meissner effect and it’s quantum and—”

“How’s it work?”

“Even though we’ve got a good theory for the materials with low critical temperature, the copper oxides and such are still a puzzle. Here’s a diagram I built for one of my classes…”

“The top half is the ordinary situation, like in a copper wire. Most of the current is carried by electrons near the surface, but there’s a lot of random motion there, electrons bouncing off of impurities and crystal defects and boundaries. That’s where ordinary conduction’s resistance comes from. Compare that with the diagram’s bottom half, a seriously simplified view of superconduction. Here the electrons act like soldiers on parade, all quantum‑entangled with each other and moving as one big unit.”

“The green spirals?”

“They represent an imposed magnetic field. See the red bits diving into the ordinary conductor? But the superconducting parade doesn’t make space for the circular motion that magnetism tries to impose. The force lines just bounce off. Fun fact — the supercurrent itself generates a huge magnetic field but only outside the superconductor.”

“How ’bout that? So how is megabar superconductivity different?”

~~ Rich Olcott

Diamonds in The Tough

“Excuse me, they said there’s a coffee shop over here somewhere. Could you please point me to it?”

“Sure. Al’s place is right around the next corner, behind the Physics building. I’ll walk you over there.”

“Oh, I don’t want to bother you.”

“No bother, it’s my coffee time anyway. Hi, Al, new customer for you.”

“Hi, Sy. What’ll it be, Ms … ?”

“I’m Susan, Susan Kim. A mocha latte, please, Al. And you’re Sy …?”

“Moire. Sy Moire, Consulting Physicist. Who’s the ‘they’ that told you about Al’s?”

“An office staffer in the Chemistry Department. I just joined the research faculty over there.”

Al’s ears perk up. “A chemist, at last! For some reason they don’t show up over here very much.”

“Hah, I bet it’s because they’re used to drinking lab coffee from beakers.”

“As a matter of fact, Sy, I do have a coffee beaker. A glass‑worker friend added a very nice handle to a 500‑milliliter beaker for me. It’s not unpacked yet which is why I was looking for a coffee shop. This latte is very good, Al, better than lab coffee any day.”

“Thanks. So what’s the news in Science, guys?”

“Mmm… On Mars, the Insight mission‘s ‘mole’ thermal probe has finally buried itself completely, on its way down we hope to its targeted 5‑meter depth. And the OSIRIS‑REx mission to Asteroid Bennu successfully collected maybe a little too much asteroid sample. One rock fragment blocked the sampler’s lid like a bit of souvenir sticking out of a tourist’s carry‑on bag. Fortunately the engineers figured out how to stow the stuff more neatly for the two‑year trip back home. How about in the Chemistry world, Susan?”

“Hmm… Ranga Dias and his team at the University of Rochester used a diamond anvil cell to—”

“Wait — a diamond anvil? Like the Village Blacksmith but made of diamond?”

“No, Al, nothing like that. Diamond is the hardest substance we know of, right? A DAC uses a pair of quarter‑carat gem‑quality diamonds pushing against each other to create a small volume of crazy high pressure in the space between them, up into the million‑atmosphere range. Here, I’ve got a gorgeous photo of one on my phone…

Diamond anvil cell, photo by J. Adam Fenster / University of Rochester

“To give you an idea of the scale, that square black gasket between the two diamonds is a piece of rhenium metal foil that’s a quarter of a millimeter thick. The reaction vessel itself is a hole they spark-drilled through the gasket. This is teeny, nanoliter chemistry.”

“OK, they’re small diamonds, but .. DIAMONDS! I bet they crack some of them. That’s got to be ex‑PENsive, our tax dollars going CRUNCH!.”

“Not really. You’re right, some do crack, up around the seven million atmosphere mark. But here’s the fun part — the researchers don’t pay market price for those diamonds. They come from the government’s stock of smuggled goods that Customs agents have confiscated at the border.”

“Why go to all that trouble? What’s wrong with test tubes and beakers?”

“Because not all chemistry takes place at atmospheric pressure, Sy. High pressure crams molecules closer together. They get in each other’s way, maybe deform each other enough to react in ways that they wouldn’t under conditions we’d call ‘normal.’ Even water has something like 17 different forms of ice under different pressure‑temperature conditions. The whole discipline of high‑pressure chemistry got started because the seismologists needed to know how minerals transform, melt, flow and react under stress. The thing about diamond is that it doesn’t transform, melt, flow or react.”

“Oo, oo, you can see through a diamond, sorta. I’ll betcha people pipe laser beams down them, right?”

“Absolutely, Al. Before lasers came along researchers were using regular light and optics to track events in a pressurized DAC. Lasers and fiber optics completely changed the game. Not just for observation — you can use intense light to heat things up, get them even closer to deep‑Earth conditions.”

“I suppose chemists are like physicists — once a new tool becomes available everybody dives in to play.”

“You know it. There’s thousands of papers out there detailing work that used a DAC.”

“So what did Dias report on?”

~~ Rich Olcott

Zeroing In on Water

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s me, Vinnie. I just heard this news story about finding water on the Moon. I thought we did that ten years ago. You even wrote about it.”

“The internet never forgets, does it? That post wasn’t quite right but it wasn’t wrong, either.”

“How can it be both?”

“There’s an old line in Science — ‘Your data’s fine but your conclusions are … nuts.’ They use a different word in private. Suppose you land on a desert island and find a pirate’s treasure chest. Should the headlines say you’d found a treasure?”

“Naw, the chest might be empty or full of rocks or something.”

“Mm-hm. So, going back to that post… I was working from some reports on NASA’s Lunar Reconnaissance Orbiter. Its LAMP instrument mapped how strongly different Moon features reflected a particular frequency of ultraviolet light. That frequency’s called ‘Lyman‑alpha.’ Astronomers care about it because it’s part of starlight, it’s reflected by rock, and it’s specifically absorbed by hydrogen atoms. Sure enough, LAMP found some places, typically in deepshadow craters, that absorbed a lot more Lymanalpha than other places.”

“And you wrote about how hydrogen atoms are in water molecules and the Moon’s deep crater floors near the poles are sheltered from sunlight that’d break up water molecules so LAMP’s dark spots are where there’s water. And you liked how using starlight to find water on the Moon was poetical.”

“Uhh… right. All that made a lot of sense at the time and it still might be true. Scientists leapt to the same hopeful conclusion when interpreting data from the MESSENGER mission to Mercury. That one used a neutron spectrometer to map emissions from hydrogen atoms interacting with incoming cosmic rays. There again, the instrument identified hydrogen collected in shaded craters at the planet’s poles. Two different detection methods giving the same positive indication at the same type of sheltered location. The agreement seemed to settle the matter. The problem is that water isn’t geology’s only way or even its primary way to accumulate hydrogen atoms.”

“What else could it be? Hydrogen ions in the solar wind grab oxide ions from Moon rock and you’ve got water, right?”

“But the hydrogens arrive one at a time, not in pairs. Any conversion would have to be at least a two‑step process. The Moon’s surface rocks are mostly silicate minerals. They’re a lattice of negative oxide ions that’s decorated inside with an assortment of positive metal ions. The first step in the conversion would be for one hydrogen ion to link up with a surface oxide to make a hydroxide ion. That species has a minus‑one charge instead of oxide’s minus‑two so it’s a bit less tightly bound to its neighboring metal ions. Got that?”

“Gimme a sec … OK, keep going.”

“Some time later, maybe a century maybe an eon, another hydrogen ion comes close enough to attack our surface hydroxide if it hasn’t been blasted apart by solar UV light. Then you get a water molecule. On balance and looking back, we’d expect most of the surface hydrogen to be hydroxide ions, not water, but both kinds would persist better in shadowed areas.”

“OK, two kinds of hydrogen. But how do we tell the difference?”

“We evaluate processes at lower‑energies. Lyman‑alpha photons pack over 10 electronvolts of energy, enough to seriously disturb an atom and blow a molecule apart. O‑H and H‑O‑H interact differently with light in the infra‑red range that just jiggles molecules instead of bopping them. For instance, atom pairs can stretch in‑out. Different kinds of atom bind together more‑or‑less tightly. That means each kind of atom pair resonates at its own stretch energy, generally around 6 microns or 0.41 electronvolts. NASA’s Cassini mission had a mapping spectrometer that could see down into that range. It found O‑H stretching activity all over the Moon’s surface.”

“But that could be either hydroxyls or water.”

“Exactly. The new news is that sensors aboard NASA’s airborne SOFIA mission map light even deeper into the infra‑red. It found the 3‑micron, 0.21‑electronvolt signal for water’s V‑shape scissors motion. That’s the water that everybody’s excited about.”

“Lots of it?”

“Thinly spread, probably, but stay tuned.”

~~ Rich Olcott

A Star’s Tale

It’s getting nippy outside so Al’s moved his out‑front coffee cart into his shop. Jeremy’s manning the curbside take‑out window but I’m walking so I step inside. Limited seating, of course. “Morning, Al. Here’s my hiking mug, fill ‘er up with high‑test and I’ll take a couple of those scones — one orange, one blueberry. Good news that the Governor let you open up.”

“You know it, Sy. Me and my suppliers have been on the phone every day. Good thing we’ve got long‑term relationships and they’ve been willing to carry me but it gets on my conscience ’cause they’re in a crack, too, ya know?”

“Low velocity of money hurts everybody, Al. Those DC doofuses and their political kabuki … but don’t get me started. Hey, you’ve got a new poster over the cash register.”

“You noticed. Yeah, it’s a beaut. Some artist’s idea of what it’d look like when a star gets spaghettified and eaten by a black hole. See, it’s got jets and a dust dusk and everything.”

“Very nice, except for a few small problems. That’s not spaghettification, the scale is all wrong and that tail-looking thing … no.”

Artist’s impression of AT2019qiz. Credit: ESO/M. Kornmesser
Under Creative Commons Attribution 4.0 International License

“Not spaghettification? That’s what was in the headline.”

“Sloppy word choice. True spaghettification acts on solid objects. Gravity’s force increases rapidly as you approach the gravitational center. Suppose you’re in a kilometer-long star cruiser that’s pointing toward a black hole from three kilometers away. The cruiser’s tail is four kilometers out. Newton’s Law of Gravity says the black hole pulls almost twice as hard on the nose as on the tail. If the overall field is strong enough it’d stretch the cruiser like taffy. Larry Niven wrote about the effect in his short story, Neutron Star.”

“The black hole’s stretching the star, right?”

“Nup, because a star isn’t solid. It’s fluid, basically a gas held together by its own gravity. You can’t pull on a piece of gas to stretch the whole mass. Your news story should have said ‘tidal disruption event‘ but I guess that wouldn’t have fit the headline space. Anyhow, an atom in the star’s atmosphere is subject to three forces — thermal expansion away from any gravitational center, gravitational attraction toward its home star and gravitational attraction toward the black hole. The star breaks up atom by atom when the two bodies get close enough that the black hole’s attraction matches the star’s surface gravity. That’s where the scale problem comes in.”

Al looks around — no waiting customers so he strings me along. “How?”

“The supermassive black hole in the picture, AT2019qiz, masses about a million Suns‑worth. The Sun‑size star can barely hold onto a gas atom at one star‑radius from the star’s center. The black hole can grab that atom from a thousand star‑radii away, about where Saturn is in our Solar System. The artist apparently imagined himself to be past the star and about where Earth is to the Sun, 100 star‑radii further out. Perspective will make the black hole pretty small.”

“But that’s a HUGE black hole!”

“True, mass‑wise, not so much diameter‑wise. Our Sun’s about 864,000 miles wide. If it were to just collapse to a black hole, which it couldn’t, its Event Horizon would be about 4 miles wide. The Event Horizon of a black hole a million times as massive as the Sun would be less than 5 times as wide as the Sun. Throw in the perspective factor and that black circle should be less than half as wide as the star’s circle.”

“What about the comet‑tail?”

“The picture makes you think of a comet escaping outward but really the star’s material is headed inward and it wouldn’t be that pretty. The disruption process is chaotic and exponential. The star’s gravity weakens as it loses mass but the loss is lop‑sided. Down at the star’s core where the nuclear reactions happen the steady burn becomes an irregular pulse. The tail should flare out near the star. The rest should be jagged and lumpy.”

“And when enough gets ripped away…”


~~ Rich Olcott

  • Thanks to T K Anderson for suggesting this topic.
  • Link to Technical PS — Where Do Those Numbers Come From?.

A Beetled Brow

Vinnie’s brow was wrinkling so hard I could hear it over the phone. “Boltzmann, Boltzmann, where’d I hear that name before? … Got it! That’s one of those constants, ain’t it, Sy? Molecules or temperature or something?”

“The second one, Vinnie. Avagadro was the molecule counter. Good memory. Come to think of it, both Boltzmann and Avagadro bridged gaps that Loschmidt worked on.”

“Loschmidt’s thing was the paradox, right, between Newton saying events can back up and thermodynamics saying no, they can’t. You said Boltzmann’s Statistical Mechanics solved that, but I’m still not clear how.”

“Let me think of an example. … Ah, you’ve got those rose bushes in front of your place. I’ll bet you’ve also put up a Japanese beetle trap to protect them.”

“Absolutely. Those bugs would demolish my flowers. The trap’s lure draws them away to my back yard. Most of them stay there ’cause they fall into the trap’s bag and can’t get out.”

“Glad it works so well for you. OK, Newton would look at individual beetles. He’d see right off that they fly mostly in straight lines. He’d measure the force of the wind and write down an equation for how the wind affects a beetle’s flight path. If the wind suddenly blew in the opposite direction, that’d be like the clock running backwards. His same equation would predict the beetle’s new flight path under the changed conditions. You with me?”

“Yeah, no problem.”

“Boltzmann would look at the whole swarm. He’d start by evaluating the average point‑to‑point beetle flight, which he’d call ‘mean free path.’ He’d probably focus on the flight speed and in‑the‑air time fraction. With those, if you tell him how many beetles you’ve got he could generate predictions like inter‑beetle separation and how long it’d take an incoming batch of beetles to cross your yard. However, predicting where a specific beetle will land next? Can’t do that.”

“Who cares about one beetle?”

“Well, another beetle might. …
Just thought of a way that Statistical Mechanics could actually be useful in this application. Once Boltzmann has his numbers for an untreated area, you could put in a series of checkpoints with different lures. Then he could develop efficiency parameters just by watching the beetle flying patterns. No need to empty traps. Anyhow, you get the idea.”

Japanese Beetle, photo by David Cappaert,
under Creative Commons BY 3.0

“Hey, I feel good emptying that trap, I’m like standing up for my roses. Anyway, so how does Avagadro play into this?”

“Indirectly and he was half a century earlier. In 1805 Gay‑Lussac showed that if you keep the pressure and temperature constant, it tales two volumes of hydrogen to react with one volume of oxygen to produce one volume of water vapor. Better, the whole‑number‑ratio rule seemed to hold generally. Avagadro concluded that the only way Gay‑Lussac’s rule could be general is if at any temperature and pressure, equal volumes of every kind of gas held the same number of molecules. He didn’t know what that number was, though.”

“HAW! Avagadro’s number wasn’t a number yet.”

“Yeah, it took a while to figure out. Then in 1865, Loschmidt and a couple of others started asking, “How big is a gas molecule?” Some gases can be compressed to the liquid state. The liquids have a definite volume, so the scientists knew molecules couldn’t be infinitely small. Loschmidt put numbers to it. Visualize a huge box of beetles flying around, bumping into each other. Each beetle, or molecule, ‘occupies’ a cylinder one beetle wide and the length of its mean free path between collisions. So you’ve got three volumes — the beetles, the total of all the cylinders, and the much larger box. Loschmidt used ratios between the volumes, plus density data, to conclude that air molecules are about a nanometer wide. Good within a factor of three. As a side result he calculated the number of gas molecules per unit volume at any temperature and pressure. That’s now called Loschmidt’s Number. If you know the molecular weight of the gas, then arithmetic gives you Avagadro’s number.”

“Thinking about a big box of flying, rose‑eating beetles creeps me out.”

  • Thanks to Oriole Hart for the story‑line suggestion.

~~ Rich Olcott

Bridging A Paradox

<chirp, chirp> “Moire here.”

“Hi, Sy. Vinnie. Hey, I’ve been reading through some of your old stuff—”

“That bored, eh?”

“You know it. Anyhow, something just don’t jibe, ya know?”

“I’m not surprised but I don’t know. Tell me about it.”

“OK, let’s start with your Einstein’s Bubble piece. You got this electron goes up‑and‑down in some other galaxy and sends out a photon and it hits my eye and an atom in there absorbs it and I see the speck of light, right?”

“That’s about the size of it. What’s the problem?”

“I ain’t done yet. OK, the photon can’t give away any energy on the way here ’cause it’s quantum and quantum energy comes in packages. And when it hits my eye I get the whole package, right?”

“Yes, and?”

“And so there’s no energy loss and that means 100% efficient and I thought thermodynamics says you can’t do that.”

“Ah, good point. You’ve just described one version of Loschmidt’s Paradox. A lot of ink has gone into the conflict between quantum mechanics and relativity theory, but Herr Johann Loschmidt found a fundamental conflict between Newtonian mechanics, which is fundamental, and thermodynamics, which is also fundamental. He wasn’t talking photons, of course — it’d be another quarter-century before Planck and Einstein came up with that notion — but his challenge stood on your central issue.”

“Goody for me, so what’s the central issue?”

“Whether or not things can run in reverse. A pendulum that swings from A to B also swings from B to A. Planets go around our Sun counterclockwise, but Newton’s math would be just as accurate if they went clockwise. In all his equations and everything derived from them, you can replace +t with ‑t to make run time backwards and everything looks dandy. That even carries over to quantum mechanics — an excited atom relaxes by emitting a photon that eventually excites another atom, but then the second atom can play the same game by tossing a photon back the other way. That works because photons don’t dissipate their energy.”

“I get your point, Newton-style physics likes things that can back up. So what’s Loschmidt’s beef?”

“Ever see a fire unburn? Down at the microscopic level where atoms and photons live, processes run backwards all the time. Melting and freezing and chemical equilibria depend upon that. Things are different up at the macroscopic level, though — once heat energy gets out or randomness creeps in, processes can’t undo by themselves as Newton would like. That’s why Loschmidt stood the Laws of Thermodynamics up against Newton’s Laws. The paradox isn’t Newton’s fault — the very idea of energy was just being invented in his time and of course atoms and molecules and randomness were still centuries away.”

“Micro, macro, who cares about the difference?”

“The difference is that the micro level is usually a lot simpler than the macro level. We can often use measured or calculated micro‑level properties to predict macro‑level properties. Boltzmann started a whole branch of Physics, Statistical Mechanics, devoted to carrying out that strategy. For instance, if we know enough about what happens when two gas molecules collide we can predict the speed of sound through the gas. Our solid‑state devices depend on macro‑level electric and optical phenomena that depend on micro‑level electron‑atom interactions.”


“As in, ‘we don’t know exactly how it’ll go but we can figure the odds…‘ Suppose we’re looking at air molecules and the micro process is a molecule moving. It could go left, right, up, down, towards or away from you like the six sides of a die. Once it’s gone left, what are the odds it’ll reverse course?”

“About 16%, like rolling a die to get a one.”

“You know your odds. Now roll that die again. What’s the odds of snake‑eyes?”

“16% of 16%, that’s like 3 outa 100.”

“There’s a kajillion molecules in the room. Roll the die a kajillion times. What are the odds all the air goes to one wall?”

“So close to zero it ain’t gonna happen.”

“And Boltzmann’s Statistical Mechanics explained why not.”

“Knowing about one molecule predicts a kajillion. Pretty good.”

San Francisco’s Golden Gate Bridge, looking South
Photo by Rich Niewiroski Jr. / CC BY 2.5

~~ Rich Olcott

Breaking Up? Not So Hard

<transcript of smartphone dictation by Sy Moire, hard‑boiled physicist>
Day 173 of self‑isolation….
Perfect weather for a brisk solitary walk, taking the park route….
There’s the geese. No sign of Mr Feder, just as well….

Still thinking about Ms Baird and her plan for generating electric power from a black hole named Lonesome….
Can just hear Vinnie if I ever told him about this which I can’t….
“Hey, Sy, nothin’ gets out of a black hole except gravity, but she’s using Lonesome‘s magnetic field to generate electricity which is electromagnetic. How’s that happen?”
Good question….

Hhmph, that’s one angry squirrel….
Ah, a couple of crows pecking the ground under its tree. Maybe they’re too close to its acorn stash….

We know a black hole’s only measurable properties are its mass, charge and spin….
And maybe its temperature, thanks to Stephen Hawking….
Its charge is static — hah! cute pun — wouldn’t support continuous electrical generation….
The Event Horizon hides everything inside — we can’t tell if charge moves around in there or even if it’s matter or anti‑matter or something else….
The no‑hair theorem says there’s no landmarks or anything sticking out of the Event Horizon so how do we know the thing’s even spinning?

Ah, we know a black hole’s external structures — the jets, the Ergosphere belt and the accretion disk — rotate because we see red- and blue-shifted radiation from them….
The Ergosphere rotates in lockstep with Lonesome‘s contents because of gravitational frame-dragging….
Probably the disk and the jets do, too, but that’s only a strong maybe….
But why should the Ergosphere’s rotation generate a magnetic field?

How about Newt Barnes’ double‑wheel idea — a belt of charged light‑weight particles inside a belt of opposite‑charged heavy particles all embedded in the Ergosphere and orbiting at the black hole’s spin rate….
Could such a thing exist? Can simple particle collisions really split the charges apart like that?….

OK, fun problem for strolling mental arithmetic. Astronomical “dust” particles are about the size of smoke particles and those are about a micrometer across which is 10‑6 meter so the volume’s about (10‑6)3=10‑18 cubic meter and the density’s sorta close to water at 1 gram per cubic centimeter or a thousand kilograms per cubic meter so the particle mass is about 10‑18×103=10‑15 kilogram. If a that‑size particle collided with something and released just enough kinetic energy to knock off an electron, how fast was it going?

Ionization energy for a hydrogen atom is 13 electronvolts, so let’s go for a collision energy of at least 10 eV. Good old kinetic energy formula is E=½mv² but that’s got to be in joules if we want a speed in meters per second so 10 eV is, lemme think, about 2×10‑18 joules/particle. So is 2×2×10‑18/10‑15 which is 4×10‑3 or 40×10‑4, square root of 40 is about 6, so v is about 6×10‑2 or 0.06 meters per second. How’s that compare with typical speeds near Lonesome?

Ms Baird said that Lonesome‘s mass is 1.5 Solar masses and it’s isolated from external gravity and electromagnetic fields. So anything near it is in orbit and we can use the circular orbit formula v²=GM/r….
Dang, don’t remember values for G or M. Have to cheat and look up the Sun’s GM product on Old Reliable….
Ah-hah, 1.3×1020 meters³/second so Lonesome‘s is also near 1020….
A solar‑mass black hole’s half‑diameter is about 3 kilometers so Lonesome‘s would be about 5×103 meters. Say we’re orbiting at twice that so r‘s around 104 meters. Put it together we get v2=1020/104=1016 so v=108 meters/sec….
Everything’s going a billion times faster than 10 eV….
So yeah, no problem getting charged dust particles out there next to Lonesome….

Just look at the color in that tree…
Weird when you think about it. The really good color is summertime chlorophyll green when the trees are soaking up sunlight and turning CO2 into oxygen for us but people get excited about dying leaves that are red or yellow…

Well, now. Lonesome‘s Event Horizon is the no-going-back point on the way to its central singularity which we call infinity because its physics are beyond anything we know. I’ve just closed out another decade of my life, another Event Horizon on my own one‑way path to a singularity…

Hey! Mr Feder! Come ask me a question to get me out of this mood.

Author’s note — Yes, ambient radiation in Lonesome‘s immediate vicinity probably would account for far more ionization than physical impact, but this was a nice exercise in estimation and playing with exponents and applied physical principles.

~~ Rich Olcott