Category: Uncategorized

Noodles or A Sandwich?

On By rolcottIn Cosmology, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Wait, Sy, your anti-Universe idea says there are exactly two um, sub‑Universes. Even the word ‘multiverse‘ suggests more than that.”

“You’re right, Susan, most of the multiverse proposals go to the other extreme. Maybe the most extreme version grew in reaction to one popular interpretation of quantum theory. Do you know about the ‘Many Worlds‘ notion?”

“Many Worlds? Is that the one about when I decide between noodles for lunch or a sandwich, the Universe splits and there’s one of me enjoying each one?”

“That’s the popular idea. The physics idea is way smaller, far bigger and even harder to swallow. Physicists have been arguing about it for a half‑century.”

“Come again? Smaller AND bigger?”

“Smaller because it’s a quantum‑based idea about microscopic phenomena. Doesn’t say anything about things big enough to touch. Remember how quantum calculations predict statistics, not exact values? They can’t give you anything but averages and spreads. Einstein and Bohr had a couple of marquee debates about that back in the 1930s. Bohr maintained that our only path to understanding observations at the micro‑scale was to accept that events there are random and there’s no point discussing anything deeper than statistics. Einstein’s position was that the very fact that we’re successfully using an average‑based strategy says that there must be finer‑grained phenomena to average over. He called it ‘the underlying reality.’ The string theory folks have chased that possibility all the way down to the Planck‑length scale. They’ve found lots of lovely math but not much else. Hugh Everett had a different concept.”

“With that build‑up, it’d better have something to do with Many Worlds.”

“Oh, it does. Pieces of the idea have been lying around for centuries, but Everett pulled them all together and dressed them up in a quantum suit. Put simply, in his PhD thesis he showed how QM’s statistics can result from averaging over Universes. Well, one Universe per observation, but you experience a sequence of Universes and that’s what you average over.”

“How can you show something like that?”

“By going down the rabbit hole step by step and staying strictly within the formal QM framework. First step was to abstractify the operation of observing. He said it’s a matter of two separate systems, an observer A and a subject B. The A could be a person or electronics or whatever. What’s important is that A has the ability to assess and record B‘s states and how they change. Given all that, the next step is to say that both A and B are quantized, in the sense that each has a quantum state.”

“Wait, EACH has a quantum state? Even if A is a human or a massive NMR machine?”

“That’s one of the hard‑to‑swallows, but formally speaking he’s okay. If a micro‑system can have a quantum state then so can a macro‑system made up of micro‑systems. You just multiply the micro‑states together to get the macro‑state. Which gets us to the next step — when A interrogates B, the two become entangled. We then can only talk about the combined quantum state of the A+B system. Everett referred to an Einstein quote when he wrote that a mouse doesn’t change the Moon by looking at it, but the Moon changes the mouse. The next step’s a doozy so take a deep breath.”

“Ready, I suppose.”

“B could have been in any of its quantum states, suppose it’s #10. After the observation, A+B must be an entangled mixture of whatever A was, combined with each of B‘s possible final states. Suppose B might switch to #42. Now we can have A+B(#42), separate from a persisting A+B(#10), plus many other possibles. As time goes by, A+B(#42) moves along its worldline independent of whatever happens to A+B(#10).”

“If they’re independent than each is in its own Universe. That’s the Many Worlds thing.”

“Now consider just how many worlds. We’re talking every potential observing macro‑system of any size, entangled with all possible quantum states of every existing micro‑system anywhere in our Observable Universe. We’re a long way from your noodles or sandwich decision.”

“An infinity of infinities.”

“Each in its own massive world.”

“Hard to swallow.”

~~ Rich Olcott

A Two-Way Stretch, Maybe

On By rolcottIn Uncategorized, Cosmology1 Comment

“Okay, Moire, I guess I gotta go with the Big Bang happening, but I still have a problem with it making everything come from a point full of nothing.”

“Back at you, Mr Feder. I have problems with your problem. To begin with, forget about your notion of a point with zero size. There’s some reason to think the Bang started with an event sized on the order of the Planck length, 10-35 meter. That’s small, but it’s not zero.”

“I suppose, but with the whole mass of the Universe crammed in there, ain’t that a recipe for the ultimate black hole? Nothing could get outta there.”

“Nothing needs to. What’s inside is already everything, remember? Besides, there isn’t an outside — space simply doesn’t exist outside of the spacetime the Bang created. Those bell‑shaped ‘Evolution of The Universe‘ diagrams are so misleading. I say that even though I’ve used the diagram myself. It’s just a graph with Time running along the central axis and Space expanding perpendicular to that. People have prettied it up to make it cylindrical and added galaxies and such. The lines just represent how much Space has expanded since the Bang. Unfortunately, people look at the bell as a some kind of boundary with empty space outside, but that’s so wrong.”

“No outside? Hard to wrap your head around.”

“Understandable. Only physicists and mathematicians get used to thinking in those terms and mostly we do it with equations instead of trying to visualize. Our equations tell us the Universe expands at the speed of light plus a bit.”

“Wait, I thought nothing could go faster than the speed of light.”

“True, nothing can traverse space faster than light or gravity, but space itself expands. At large distances it’s doing that faster than light. We actually had to devise two different definitions of distance. ‘Co‑moving distance‘ includes the expansion. ‘Proper distance‘ doesn’t. In another couple billion years, the farthest things we can see today will be co‑moving away so fast that the photons they emit will be carried away faster than they can fly towards us. Those objects will leave our Observable Universe, the spherical bubble that encloses the objects whose light gets a chance to reach us.”

“My head hurts from the expanding. Get back to the Bang thing ’cause it was small. Too small to hold atoms I guess so how can it explode to be everything?”

“‘Expand’, not ‘explode‘ — they’re different — but good guess. The Bang’s singularity was smaller than an atom by at least a factor of 1024, but conditions were far too hot in there for atoms to exist, or nuclei, or even protons and neutrons. Informally we call it a quark soup, which is okay because we think quarks are structureless points that can cram to near‑infinite density. We don’t yet know enough Physics for good calculations of temperature, density or much of anything else.”

“That’s a lot of energy, even if it’s not particles. Which is what I’m getting at. I keep hearing you can’t create energy, just transform it, right? So where did the energy come from?”

“That’s a deep question, Mr Feder, and we don’t have an answer or hypothesis or even a firm guess. It gets down to what energy even is — we’re just barely nibbling at the edges of that one. One crazy idea I kind of like is that creating our Universe took zero energy because the process was exactly compensated for by creating an anti‑Universe whose total anti‑energy matches our total energy.”

“Whaddaya mean, anti‑Universe and anti‑energy?”

<deep breath> “You know an atom has negatively‑charged electrons bound to its positively‑charged nucleus, right? Well, the anti‑Universe I’m thinking of has that situation and everything else reversed. Positive electrons, negative nucleus, but also flipped left‑right parities for some electroweak particle interactions. Oh, and time runs backwards which is how anti‑energy becomes a thing. Our Universe and my crazy anti‑Universe emerge at Time Zero from the singularity. Then they expand in opposite directions along the Time axis. Maybe the quarks and their anti‑quarks got sorted out at the flash‑point, I dunno.”

“So there’s an anti‑me out there somewhere?”

“I wouldn’t go that far.”

~~ Rich Olcott

Everything Everywhere All at Once

On By rolcottIn Uncategorized, CosmologyLeave a comment

It’s either late Winter or early Spring, the weather can’t make up its mind. The geese don’t seem to approve of my walk around the park’s lake but then I realize it’s not me they object to. “Hey, Moire, wait up, I got a question for you!”

“Good morning, Mr Feder. What can I do for you?”

“This Big Bang thing I been hearing about. How can it make everything from nothing like they say?”

“You’re in good form, Mr Feder, lots of questions buried within a question.”

“Oh yeah? Seems pretty simple to me. How do we even know it happened?”

“Well, there you go, one buried question up already. We have several lines of evidence to support the idea. One of them is the CMB.”

“Complete Monkey Business?”

“Very funny. No, it’s the Cosmic Microwave Background, long‑wavelength light that completely surrounds us. It has the same wavelength profile and the same intensity within a dozen parts per million no matter what direction we look. The best explanation we have for it is that the light is finally arriving here from the Big Bang roughly 14 billion years ago. Well, a couple hundred thousand years after the Bang itself. It took that long for things to cool down enough for electrons and protons to pair up as atoms. The photons had been bouncing around between charged particles but when the charges neutralized each other the photons could roam free.”

“Same in all directions so we’re in the center, huh? The Bang musta been real close‑by.”

“Not really. Astronomers have measured the radiation’s effects on a distant intergalactic dust cloud. The effect is just what we’d expect if the cloud were right here. We’re not in a special location. From everything we can measure, the Bang happened everywhere and all at once.”

“Weird. Hard to see how that can happen.”

“We answered that nearly a century ago when Edwin Hubble discovered that there are other galaxies outside the Milky Way and that they’re in motion.”

“Yeah, I heard about that, too, with everything running away from us.”

“Sorry, no. We’re not that special, remember? On the average, everything’s running away from everything else.”

“Whaddaya mean, ‘on the average‘? Why the wishy-washy?”

“Because things cluster together and swirl around. The Andromeda galaxy is coming straight toward us, for instance, but it won’t get here for 5 billion years. The general trend only shows up when you look at large volumes, say a hundred million lightyears across or bigger. The evidence says yeah, everything’s spreading out.”

“But how can everything be moving away from everything? You run away from something, you gotta be running toward something else.”

“That’d be true if your somethings are all confined in a room whose walls don’t move. The Universe doesn’t work that way. The space between somethings continually grows new space. The volume of the whole assemblage increases.”

“Is that why I just hadda buy new pants?”

“No, that’s just you gaining weight from all that beer and bar food. The electromagnetism that holds your atoms and molecules together is much stronger than what’s driving the expansion. So is the gravitation that holds solar systems and galaxies together. Expansion only gets significant when distances get so large that the inverse square laws diminish both those forces to near zero.”

“What’s this got to do with the CMB?”

“The CMB tells us that the Bang happened everywhere, but expansion says that at early times when stars and galaxies first formed, ‘everywhere‘ was on a much smaller scale than it is now. Imagine having a video of the expansion and playing it backwards. Earendel‘s the farthest star we’ve seen, but if we and it existed 12 billion years ago we’d measure it as being close‑by but still all the way across the observable Universe. Carry that idea the rest of the way. The Big Bang is expansion from a super‑compressed everywhere.”

“Okay, what’s driving the expansion?”

“We don’t know. We call it ‘dark energy‘ but the name’s about all we have for it.”

“Aaaa-HAH! At last something you don’t know!”

“Science is all about finding things we don’t know and working to figure them out.”

~~ Rich Olcott

The Sky’s The Limit

On By rolcottIn Astronomy: Planetary Science, Space Travel, UncategorizedLeave a comment

Another meeting of the Acme Pizza and Science Society, at our usual big round table in Pizza Eddie’s place on the Acme Building’s second floor. (The table’s also used for after‑hours practical studies of applied statistics, “only don’t tell nobody, okay?“) It’s Eddie’s turn to announce the topic for the evening. “This one’s from my nephew, guys. How high up is the sky on Mars?”

General silence ensues, then Al throws in a chip. “Well, how high up is the sky on Earth?”

Being a pilot, Vinnie’s our aviation expert. “Depends on who’s defining ‘sky‘ and why they did that. I’m thinking ‘the sky’s the limit‘ and for me that’s the highest altitude I can get up to legal‑like. Private prop planes generally stay below 10,000 feet, commercial jets aren’t certified above 43,000 feet, private jets aren’t supposed to go above 51,000 feet.”

Eddie counters. “How about the Concorde? And those military high-flyers?”

“They’re special. The SST has, um, had unique engineering to let it go up to 60,000 feet ’cause they didn’t want sonic boom complaints from ground level. But it don’t fly no more anyhow. I’ve heard that the Air Force’s SR-71 could hit 85,000 feet but it got retired, too.”

Al’s not impressed. “All that’s legal stuff. There’s a helicopter flying on Mars but the FAA don’t make the rules there. What else we got?”

Geologist Kareem swallows his last bite of cheese melt. “How about the top of the troposphere? That’s the lowest layer of our atmosphere, the one where most of our weather and sunset colors happen. If you look at clouds in the sky, they’re inside the troposphere.”

“How high is that?”

“It expands with heating, so the top depends where you’re measuring. At the Equator it can be as high as 18½ kilometers; near a pole in local winter the top squeezes down to 6 kilometers or so. And to your next question — above the troposphere we’ve got the stratosphere that goes up to 50 kilometers. What’s that in feet, Sy?”

<drawing Old Reliable and screen-tapping…> “Says about 31.2 miles or 165,000 feet. Let’s keep things in kilometers from here on, okay?”

“Then you’ve got the mesosphere and the exosphere but the light scattering that gives us a blue sky happens below them so I’d say the sky stops at 50 kilometers.”

Al’s been rummaging through his astronomy magazines. “I read somewhere here that you’re not an astronaut unless you’ve gone past either 80 or 100 kilometers, which is weird with two cut‑offs. Who came up with those?”

Vinnie’s back in. “Who came up with the idea was a guy named von Kármán. One of the many Hungarians who came to the US in the 30s to get away from the Nazis. He did a bunch of advanced aircraft design work, helped found Aerojet and JPL. Anyway, he said the boundary between aeronautics and astronautics is how high you are when the atmosphere gets too thin for wings to keep you up with aerodynamic lift. Beyond that you need rockets or you’re in orbit or you fall down. He had equations and everything. For the Bell X‑2 he figured the threshold was around 52 miles up. What’s that in kilometers, Sy?”

“About 84.”

“So that’s where the 80 comes from. NASA liked that number for their astronauts but the Europeans rounded it up to 100. Politics, I suppose. Do von Kármán’s equations apply to Mars as well as Earth?”

“Now we’re getting somewhere, Vinnie. They do, sort of. It’s complicated, because there’s a four‑way tug‑of‑war going on. Your aircraft has gravity pulling you down, lift and centrifugal force pulling you up. Lift depends on the atmosphere’s density and your vehicle’s configuration. The fourth player is the kicker — frictional heat ruining the craft. Lift, centrifugal force and heating all get stronger with speed. Von Kármán based his calculations on the Bell X‑2’s configuration and heat‑management capabilities. Problem is, we’re not sending an X‑2 to Mars.”

“Can you re‑calibrate his equation to put a virtual X‑2 up there?”

“Hey, guys, I think someone did that. This magazine says the Karman line on Mars is 88 kilometers up.”

“Go tell your nephew, Eddie.”

~~ Rich Olcott

Well, well, well

On By rolcottIn Chemistry, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s Susan Kim. I’m at a break point while this experiment runs. Do you want to check the scones at Al’s?”

“I’ve got a bad case of February, feel like just hibernating somewhere. Can’t get started on anything so I might as well head over there.”

“You need Al’s patented Morning Dynamite brew. See you in a couple of minutes.”

“Hi, Al. My usual mocha latte, please, and your special wake-up potion for Sy. He’s got the Februaries.”

“Here you go, Susan. Bottom of the pot coming at ya, Sy. It’ll get ya lively, for sure.”

<We grab a table.> “So, Susan, what’s this experiment that you can just let alone for a while?”

“One of your blog posts inspired it. Do you remember the one about warm water freezing faster than cold?”

“Sometimes it does that, but the point of the post was how it’s only randomly sometimes in some experiments and not at all in others. Are you experimenting with water freezing?”

“No, but I’m working on a related problem. I can’t say much about it other than that there’s an industrial process that depends on recovering a crystalline product from a hot, concentrated solution. The problem is that if the solution is too weak nothing crystallizes when it cools but if it’s too concentrated the whole batch solidifies in one big mass. The industry wants to find the right conditions for making lots of small crystals. I’ve got a grant to research ways to do that.”

“That does sound a little like water freezing. How did my blog post help?”

“I was thinking about how crystals form. We know a lot about how ions or molecules come in from solution to attach to the surface of a growing crystal. Either they’re electrostatically pulled to just the right spot or they bounce on and off the surface until they find a place they fit into. But how does that surface get started in the first place?”

“Well, I imagine it happens when two molecules love each other very mu— OW!”

“Sy Moire, get your mind back on Science! … Sorry, did it really hurt that much?”

“It wouldn’t have but that’s the same spot on the same shoulder that Cathleen got me on.”

“Actually, your flip remark isn’t that far from what we think happens except the correct verb is ‘attract,’ not ‘love.‘ Some researchers even call the initial speck ‘the embryo‘ but most of us say ‘nucleus.’ Nucleation might start with only a few molecules clicking into the right configuration, or it might require a cluster of hundreds being mostly right. The process might even require help from short‑lived solvent structures. So many variables. Nobody has a good predictive theory or even broadly useful models. It’s all by art and rule of thumb.”

“Sounds like a challenge.”

“Oh, it is. Here’s the tip I took from your blog post. You mentioned that some of the freezing studies used hundreds of trials and reported what percent of them froze. Most of the industrial crystallization studies work at pilot plant scale, with liters or gallons of solution going into each trial. I decided to go small instead. Lab supply companies sell culture plates for biological work. Typically they’re polystyrene trays holding up to a hundred one‑milliliter wells. I bought a bunch of those, and I also bought a machine that can automatically load the wells with whatever solutions I like. I’ve positioned it next to a temperature‑controlled cabinet with a camera to photograph a batch of trays at regular intervals.”

“Nice, so you can set up many duplicates at each chemical concentration and keep statistics on how many form crystals at each temperature.”

“At high concentrations I expect all the wells to show crystals. The obvious measurement will be crystal size range at each temperature. But with no change in apparatus I can go to lower and lower concentrations to where crystallization itself is random like the freezing experiments. Some wells will crystallize, some won’t. Statistics on those trays may tell us things about nucleation. It’s gonna be fun.”

“D’ya suppose the planets are culture plate wells for creation’s life experiments?”

~~ Rich Olcott

Visionaries Old And New

On By rolcottIn Astronomy, UncategorizedLeave a comment

Cathleen’s back at the mic. “Let’s have a round of applause for Maria, Jeremy, Madison and C‑J. Thank you all. We have a few minutes left for questions… Paul, you’re first.”

“Thanks, Cathleen. A comment, not a question. As you know, archeoastronomy is my specialty so I applaud Jeremy’s advocacy for the field. I agree with his notion that the Colorado Plateau’s dry, thin air generally lets us see more stars than sea‑level Greeks do. When I go to a good dark sky site, it can be difficult to see the main stars that define a constellation because of all the background dimmer stars. However, I don’t think that additional stars would change the pictures we project into the sky. Most constellations are outlined from only the brightest stars up there. Dimmer stars may confuse the issue, but I very much doubt they would have altered the makeup of the constellations a culture defines. Each culture uses their own myths and history when finding figures among the stars.”

“Thanks for the confirmation from personal experience, Paul. Yes, Sy?”

“Another comment not a question. I’m struck by how Maria’s Doppler technique and Jeremy’s Astrometry complement each other Think of a distant stellar system like a spinning plate balanced on a stick. Doppler can tell you how long the stick is. Astrometry can tell you how wide the plate is. Both can tell you how fast it’s spinning. The strongest Doppler signal comes from systems that are edge‑on to us. The strongest Astrometry signal comes from systems we see face‑on. Those are the extreme cases, of course. Most systems are be at some in‑between angle and give us intermediate signals.”

“That’s a useful classification, Sy. Madison’s and C‑J’s transit technique also fits the edge‑on category. Jim, I can see you’re about to bust. What do you have to tell us about?”

“How about a technique that lets you characterize exoplanets inside a galaxy we see as only a blurry blob? This paper I just read blew me away.”

“Go ahead, you have the floor.”

“Great. Does everyone know about Earendel?” <blank looks from half the audience, mutters about ‘Lord Of The Rings?’ from several> “OK, quick refresher. Earendel is the name astronomers gave to the farthest individual star we’ve ever discovered. It’s either 13 or 28 billion lightyears away, depending on how you define distance. We only spotted it because of an incredible coincidence — the star happens to be passing through an extremely small region of space where light in our general direction is concentrated thousands‑fold into a beam towards us. Earendel may be embedded in a galaxy, but the amplification region is so narrow we can’t see stars that might be right next to it.”

<Feder’s voice> “Ya gonna tell us what makes the region?”

“Only very generally, because it’s complicated. You know what a magnifying lens does in sunlight.”

“Sure. I’ve burnt ants that way.”

“… Right. So what you did was take all the light energy hitting the entire surface of your lens and concentrate it on a miniscule spot. The concentration factor was controlled by the Sun‑to‑lens‑to‑spot distances and the surface area of the lens. Now bring that picture up to cosmological distances. The lens is the combined gravitational field of an entire galaxy cluster, billions of lightyears away from us, focusing light from Earendel’s galaxy billions of lightyears farther away. Really small spots at both ends of the light path and that’s what isolated that star.”

“That’s what got you excited?”

“That’s the start of it. This new paper goes in the other direction. The scientists used brilliant X‑ray light from an extremely distant quasar to probe for exoplanets inside a galaxy’s gravitational lens. Like one of your ants analyzing sunlight’s glare to assess dust flecks on your lens. Or at least their averaged properties. A lens integrates all the light hitting it so your ant can’t see individual grains. What it can do, though, is estimate numbers and size ranges. This paper suggests the lensing galaxy is cluttered with 2000 free‑floating planets per main‑sequence star — stars too far for us to see.”

~~ Rich Olcott

  • Thanks to Dave Martinez and Dr Ka Chun Yu for their informative comments.

To See Beneath The Starlight

On By rolcottIn Astronomy, James Webb Space Telescope, UncategorizedLeave a comment

C‑J casts an image to Al’s video screen. “This is new news, just came out a couple of weeks ago. It’s the lead figure from NASA’s announcement of JWST’s first exoplanet examination. We’re picked this study because the scientists used the transit technique. I’ve added the orange stuff so we can make a point. Each blue dot is one measurement from JWST’s Near‑Infrared Spectrograph while it looked at a star named LHS 457. Even though the telescope is outside Earth’s atmosphere and operating at frigid temperatures, you can see that the numbers scatter. Surely the star’s light isn’t changing that quickly – the dots are about 9 seconds apart – the spread has to come from noise in JWST’s electronics.”

Adapted from image by NASA Credit: NASA, ESA, CSA, L. Hustak (STScI).

“We’re just partway through our statistics class but we know to expect 95% of noise to be within 2 standard deviations either way of the average. With about 400 dots per hour, C‑J drew his lines to put about 10 dots per hour each above and below.”

“Right, Madison, and the point we want to make is how small that range is. Only about 0.04% difference. That’s like one drop in a 2500‑drop titration. Professor Kim’s samples in our Chem lab generally take around 20 milliliters which is about 400 drops.”

“So anyway, look at that dip in the light curve. That’s way out of the noise range. The starlight really did dim, even though it wasn’t by much.”

“By the way, NASA’s press release is a little misleading and in fact missed the point of the research. JWST didn’t find this exoplanet, the TESS satellite system did. JWST looked where TESS said to and yup, there it was. This report was really about what JWST could tell us about the exoplanet’s atmosphere.”

“There’s a bunch of possibilities that the researchers can now eliminate. C‑J, please cast the next slide to the screen. We need to be clear, this isn’t the spectrum that JWST recorded during a transit.”

Adapted from image by NASA (Credit: NASA, ESA, CSA, L. Hustak (STScI)), and Figure 2 in Lustig-Yeager, et al.

“No, that would have been simply the star’s light after some of it was filtered through the planet’s atmosphere. The researchers used a lot of computer time to subtract out the right amount of the star’s own spectrum. This is what’s left — their estimate of the spectrum of the planet’s atmosphere if it has one. I added the orange error bar on each point and for the sake of comparisons I traced in that dotted curve marked ‘Metallicity‘ from the scientists’ paper. The other lines are models for four possible atmospheres.”

“Why orange again? And why are the bars longer to the right of that gap?”

“I like orange. I had to trace the bars for this slide because NASA’s diagram used dark grey that doesn’t show up very well. The dots in the wavelength range beyond 3.8 microns are from a noisier sensor. Professor O’Meara, we need some help here. What’s metallicity and why did the paper’s authors think it’s important?”

“We haven’t touched on that topic in class yet. ‘Metallicity’ is the fraction of a star’s material made up of atoms heavier than hydrogen and helium. A star could have high metallicity either because it was born in a dust cloud loaded with carbons and oxygens, or maybe it’s old and has generated them from its own nuclear reactions. Either way, a planet in a high‑metallicity environment could have an atmosphere packed with molecules like O2, H2O, CH4 and CO2. That doesn’t seem to be the case here, does it?”

“No, ma’am. The measured points don’t have this model’s peaks or valleys. Considering the error bars, the transmission spectrum is pretty much flat. Most of the researchers’ other models also predict peaks that aren’t there. The best models are a tight cloud deck like Venus or Titan, or thin and mostly CO2 like Mars, or no atmosphere at all.”

“Even a null curve tells us more than we knew.”

~~ Rich Olcott

Significant Twinkles

On By rolcottIn Astronomy, UncategorizedLeave a comment

Cathleen’s got a bit of fire in her eye. “Good exposition, Jeremy, but only just barely on‑assignment. You squeezed in your exoplanet search material at the very end. <sigh> Okay, for our next presentation we have two of our freshmen, Madison and C‑J.”

“Hello, everybody, I’m Madison. I fell in love with Science while watching Nova and Star Trek with my family. Doctor O’Meara’s Astronomy class is my first step into the real thing. C‑J?”

“Hi, I’m C‑J, like she said. What started me on Astronomy was just looking at the night sky. My family’s ranch is officially in dark sky country, but really it’s so not dark. Jeremy’s also from the High Plateau and we got to talking. We see a gazillion stars up there, probably more stars than the Greeks did because they were looking up through humid sea-level air. On a still night our dry air’s so clear you can read by the light of those stars. I want to know what’s up there.”

“Me, too, but I’m even more interested in who‘s up there living on some exoplanet somewhere. How do we find them? We’ve just heard about spectroscopy and astrometry. C‑J and I will be talking about photometry, measuring the total light from something. You can use it even with light sources that are too dim to pick out a spectrum. Photometry is especially useful for finding transits.”

“A transit is basically an eclipse, an exoplanet getting between us and its star—”

“Like the one we had in 2017. It was so awesome when that happened. All the bird and bug noises hushed and the corona showed all around where the Sun was hiding. I was only 12 then but it changed my Universe when they showed us on TV how the Moon is exactly the right size and distance to cover the Sun.”

“Incredible coincidence, right? Almost exactly 100% occultation. If the Moon were much bigger or closer to us we’d never see the corona’s complicated structure. We wouldn’t have that evidence and we’d know so much less about how the Sun works. But even with JWST technology we can’t get near that much detail from other stars.”

“Think of trying to read a blog post on your computer, but your only tool is a light meter that gives you one number for the whole screen. Our nearest star, Alpha Centauri, is 20% larger than our Sun but it’s 4.3 lightyears away. I worked out that at that distance its image would be about 8½ milliarcseconds across. C‑J found that JWST’s cameras can’t resolve details any finer than 8 times that. All we can see of that star or any star is the light the whole system gives off.”

“So here’s where we’re going. We can’t see exoplanets because they’re way too small and too far away, but if an exoplanet transits a star we’re studying, it’ll block some of the light. The question is, how much, and the answer is, not very. Exoplanets block starlight according to their silhouette area. Jupiter’s diameter is about a tenth the Sun’s so it’s area is 1% of the Sun’s. When Jupiter transits the Sun‑‑‑”

“From the viewpoint of some other solar system, of course—”

“Doesn’t matter. Jupiter could get in between the Sun and Saturn; the arithmetic works out the same. The maximum fraction of light Jupiter could block would be its area against the Sun’s area and that’s still 1%.”

“Well, it does matter, because of perspective. If size was the only variable, the Moon is so much smaller than the Sun we’d never see a total eclipse. The star‑planet distance has to be much smaller than the star‑us distance, okay?”

“Alright, but that’s always the way with exoplanets. Even with a big planet and a small star, we don’t expect to measure more than a few percent change. You need really good photometry to even detect that.”

“And really good conditions. Everyone knows how atmospheric turbulence makes star images twinkle—”

“Can’t get 1% accuracy on an image that’s flickering by 50%—”

“And that’s why we had to get stable observatories outside the atmosphere before we could find exoplanets photometrically.”

~~ Rich Olcott

Astrometers Are Wobble-Watchers

On By rolcottIn Astronomy, UncategorizedLeave a comment

letter A Hi, Sy, what’s going on in Cathleen’s seminar?

You were right, Al.
It’s about exoplanets and how to find them.
Jeremy’s pitching astrometry.
That’s about measuring star locations in the sky.
I’ll fill you in later.

“So that’s my cultural colonialism rant, thanks for listening. On to the real presentation. Maria showed us how to look for exoplanets when they wobble along our line of sight. But what if they wobble perpendicular to that? Careful measurement should show that, right? The ancients thought that holy forces had permanently set the positions of all the stars except for the planets so they didn’t measure that close. Tycho Brahe took meticulous measurements with room‑sized instruments—”

<voice from the back> “Room‑sized? What difference does that make?”

“What if I told you that two stars are 3 millimeters apart in the sky?”

<another voice> “How far out’s your ruler? Sky stuff, you need to talk angles because that’s all you got.”

“Well there you go. That’s why Tycho went for maximum angle‑measuring accuracy. He built a sextant with a 5‑foot radius. He used an entire north‑south wall as a quadrant. His primary instrument was an armillary sphere three yards across.”

<first voice again> “Wait, a sphere, like a big bubble? Why north‑south? What’s a quadrant?”

  • I give him a nudge. “He’s just a kid, Mr Feder. Be nice. One question at a time.”
  • “But I got so many!”

“Think about Tycho’s goal. Like astrometers before him, he wanted to build an accurate map of the heavens. Native Americans a thousand years or more ago carved free‑hand star maps on cave ceilings and turtle shells. Tycho followed the Arabic and Chinese quantitative mapping traditions. There’s two ways to do that. One is to measure and map the visual angles between many pairs of stars. That strategy fails quickly because errors accumulate. Four or five steps along the way you’re plotting the same star in two different locations.”

<Feder’s voice again> “There’s a better way?”

“Yessir. Measure and map each star relative to a standard coordinate system. If your system’s a good one, errors tend to average out. The latitude‑longitude system works well for locating places on Earth. Two thousand years ago the Babylonians used something similar for places in the crystal sphere they thought supported the stars above us. Where the equinoctial Sun rose on the horizon was a special direction. Their buildings celebrated it. Starting from that direction the horizontal angle to a star was its longitude. The star’s latitude was its angle up from the horizon towards the zenith straight above. But those map coordinates don’t work for another part of the world. Astrometers needed something better.”

<Feder again> “So what did they do already?”

“They may or may not have believed the Earth itself is round, but they recognized the Pole Star’s steady position that the rest of the sky revolved around. They also noticed that as each month went by the constellations played ring‑a‑rosie in a plane perpendicular to the north‑south axis. Call that the Plane of The Ecliptic. Pick a star, measure its angle away from the Ecliptic and you’ve got an ecliptic latitude. Measure its angle around the Ecliptic away from a reference star and you’ve got a ecliptic longitude. Tycho’s instruments were designed to measure star coordinates. His quadrant was a 90° bronze arc he embedded in that north‑south wall, let him measure a star’s latitude as it crossed his meridian. His ‘Sphere’ was simply a pair of calibrated metal rings on a gimbal mounting so he could point to target and reference stars and measure the angle between them. If his calibration used degree markings they’d be about 25 millimeters apart. His work was the best of his time but the limit of his accuracy was a few dozen arcseconds.”

“Is that bad?”

“It is if you’re looking for exoplanets by watching for stellar wobble. Maria’s Jupiter example showed the Sun wobbling by 1½ million kilometers. I worked this example with a bigger wobble and a star that would be mid‑range for most of our constellations. Best case, we’d see its image jiggling by about 90 microarcseconds. Tycho’s instruments weren’t good enough for wobbles.”

~~ Rich Olcott

The Stars from A Different Viewpoint

On By rolcottIn Astronomy, UncategorizedLeave a comment

“Thank you, Maria, nice job showing us why the Doppler method had such a hard time finding exoplanets. Next up, Jeremy. You’re not going to talk about black holes, are you?”

“No, ma’am, my subject today is astrometry, but that’s useful for both exoplanets and black holes. I have to be careful when I say the word because it sounds so much like astronomy but they’re different things. It helped when I looked the words up. Turns out that ‘astronomy‘ means ‘naming stars‘ but ‘astrometry‘ means ‘measuring‘ them. Not weighing one or any of that, just measuring accurately where that star is in the sky at a certain moment. Everyone on Earth has the sky above. In the days before city life and city lights brought their eyes down, cultures all over the world were doing astronomy and astrometry. Professional astronomers generally use Greek and Arabic names, but that’s Eurocentrism and it got silly.”

<voice from the back> “Like how?”

“The Greeks couldn’t name constellations in the southern hemisphere’s skies because they never saw those stars. Polynesian navigators and Indigenous Australians saw them. Those cultures had their own perfectly good constellations. Did official Astronomy ask any of those people? Of course not, so we’ve got contrived designations like The Microscope and The Air Pump. Some of you know that I’m doing a research project with Professor Begaye to correlate constellations from different cultures. I’ve found some surprises.”

<voice from the back> “Like what?”

“Practically everyone in the northern hemisphere has a special image for the Pole Star and the stars close to it. Europeans picked out Ursa Minor, the Little Bear. For us Navajos the same stars make up The Northern Fire in the sky’s dome like the fire in our traditional domed hogan homes. Staying close to the Northern Fire we see two human figures, a woman and a man. One surprise for me was that the woman’s most prominent stars are the same ones the Greeks chose for Cassiopeia, also a female. The man’s image includes many of the same stars that Europeans call Ursa Major, the Big Bear. Did you know that the word ‘Artic‘ comes from the Greek word ‘arktos‘ which means ‘bear‘? Anyway, further out there’s a winter constellation containing three bright stars in a straight line plus a few more that could be shoulders and knees.”

<voice from the back> “Orion!”

“Mm-hm. We have almost exactly the same constellation. It’s also a hunter, except that the Greeks picture the three stars as his belt and we say it’s the quiver for his arrows. Right in front of the hunter are—”

<voice from the back> “The Pleaides!”

“But for us they’re Dilyehe, the Planting Stars. When they go below the horizon it’s time to plant corn. Which gets me to astrometry. The stars and constellations have always been clocks and calendars for the world’s cultures. Typically they compare the position of the Sun or certain stars with special structures.”

<voice from the back> “Like Stonehenge and the Pyramids!”

“There’s claims and doubts about both of those. People have searched out apparent special locations, like ‘This doorway and that window were placed to show a certain star rising on Midsummers Eve,’ but without explicit markings there’s no way to be sure it wasn’t just accidental. Besides, both structures were built with huge stone blocks, a real challenge to place accurately enough to pick out just one star on one day. We Navajos don’t build structures to track special times. We use mountains.”

<voice from the back> “What, you move mountains around?”

“No, we honor and respect the natural landscape for its beauty. What we do is find the special places that help the mountains and other landmarks tell us what time of year it is. My favorite example is the Double Sunset.”

<voice from the back> “Can’t have two!”

“Yes, you can, if the mountains are sharp and stand close to one another. On the right day of the year, the Sun sets behind one mountain, then peeks for just a minute through the cleft between the two. You just have to know where to stand to see that.”

~ Rich Olcott