A Recourse to Pastry

There’s something wrong about the displays laid out on Al’s pastry counter — no symmetry.  One covered platter holds eight pinwheels in a ring about a central one, but the other platter’s central pinwheel has only a five-pinwheel ring around it.  I yell over to him.  “What’s with the pastries, Al?  You usually balance things up.”

“Ya noticed, hey, Sy?  It’s a tribute to the Juno spacecraft.  She went into orbit around Jupiter on the 5th of July 2016 so I’m celebrating her anniversary.”

“Well, that’s nice, but what do pinwheels have to do with the spacecraft?”

“Haven’t you seen the polar pictures she sent back?  Got a new poster behind the cash register.  Ain’t they gorgeous?”Jupiter both poles“They’re certainly eye-catching, but I thought Jupiter’s all baby-blue and salmon-colored.”

Astronomer Cathleen’s behind me in line.  “It is, Sy, but only in photographs using visible sunlight.  These are infrared images, right, Al?”

“Yeah, from … lemme look at the caption … Juno‘s JIRAM instrument.”

“Right, the infrared mapper.  It sees heat-generated light that comes from inside Jupiter.  It’s the same principle as using blackbody radiation to take a star’s temperature, but here we’re looking at a planet.  Jupiter’s way colder than a star so the wavelengths are longer, but on the other hand it’s close-up so we don’t have to reckon with relativistic wavelength stretching.  At any rate, infrared wavelengths are too long for our eyes to see but they penetrate clouds of particulate matter like interstellar dust or the frigid clouds of Jupiter.”

Jupiter south pole 1

NASA mosaic view of Jupiter’s south pole by visible light

“So this red hell isn’t what the poles actually look like?”

“No, Al,  the visible light colors are in the tops of clouds and they’re all blues and white.  These infrared images show us temperature variation within the clouds.  Come to think of it, that Hell’s frozen over — if I recall correctly, the temperature range in those clouds runs from about –10°C to –80°C.  In Fahrenheit that’d be from near zero to crazy cold.”

“Those aren’t just photographs in Al’s poster?”

“Oh, no, Sy, there’s a lot of computer processing in between Juno‘s wavelength numbers and what the public sees.  The first step is to recode all the infrared wavelengths to visible colors.  In that north pole image I’d say that they coded red-to-black as warm down to white as cool.  The south pole image looks like warmest is yellow-to-white, coolest is red.”

“How’d you figure that?”

“The programs fake the apparent heights.  The warmest areas are where we can see most deeply into the atmosphere, which would be at the center or edge of a vortex.  The cooler areas would be upper-level material.  The techs use that logic to generate the perspective projection that we interpret as a 3-D view.”

Vinnie’s behind us in line and getting impatient.  “I suppose there’s Science in those pretty pictures?”

“Tons of it, and a few mysteries.  JIRAM by itself is telling the researchers a lot about where and how much water and other small molecules reside in Jupiter’s atmosphere.  But Juno has eight other sensors.  Scientists expect to harvest important information from each of them.  Correlations between the data streams will give us exponentially more.”

He’s still antsy.  “Such as?”

“Like how Jupiter’s off-axis magnetic field is related to its lumpy gravitational field.  When we figure that out we’ll know a lot more about how Jupiter works, and that’ll help us understand Saturn and gas-giant exoplanets.”GRS core

Al breaks in.  “What about the mysteries, Cathleen?”

“Those storms, for instance.  They look like Earth-style hurricanes, driven by upwelling warm air.  They even go in the right direction.  But why are they crammed together so and how can they stay stable like that?  Adjacent gears have to rotate in opposite directions, but these guys all go in the same direction.  I can’t imagine what the winds between them must be like.”

“And how come there’s eight in the north pole ring but only five at the other pole?”

“Who knows, Vinnie?  The only guess I have is that Jupiter’s so big that one end doesn’t know what the other end’s doing.”

“Someone’s gonna have to do better than that.”

“Give ’em time.”

~~ Rich Olcott


Zwicky Too Soon

Big Vinnie barrels into the office, again. “Hey, Sy, word is you been short-changing Fritz Zwicky. What’s the story?”

“Hey, I never even met the guy.  He died in 1974.  How could I do him a bad deal?”

“Not giving him full credit.  I read an article about him.  He talked about ‘dark matter’ almost fifty years before Vera Rubin.”

“You’ve got a point there.  Like Vera Rubin he had a political problem, but his was quite different than hers.”

“Political?  I thought all you had to do was be right.”

“No, you have to be right and you have to have people willing to spend time validating or refuting your claims.  Rubin wasn’t a self-advertiser, so it took a while for people to realize why her results were important.  They did look at them, though, and they did give her credit.  Zwicky’s was a different story.”

“Wasn’t he right?”

“Sometimes right, often wrong.  Thing was, he generated too many ideas for people to cope with.  Worse, he was one of those wide-ranging intellects who adds one plus one to make two.  Trouble was, Zwicky got his ones from different specialties that don’t normally interact.  When people didn’t immediately run with one of his claims he took it personally and lashed out, publicly called ’em fools or worse.  Never a good tactic.”

“Gimme a f’rinstance.”

“OK.  Early 1930’s, Zwicky’s out in the still-raw wilds of California, practically nothing out there but movie studios and oil wells, using a manual blink-comparator like the one Clyde Tombaugh used about the same time to find Pluto.  He’s scanning images taken with Palomar’s new wide-angle telescope to search out novae, stars that suddenly get brighter.  He’s finding dozens of them but a few somehow get orders of magnitude brighter than the rest.  He and his buddy Walter Baade call the special ones ‘supernovae.'”

“Ain’t that novas?”

“Novae — we’re being proper astronomers here and it’s a Latin word.  Anyway, Zwiky’s trying to figure out where a supernova’s enormous luminosity comes from.  He got his start in solid-state physics and he still keeps up on both Physics and Astronomy.  Just a year earlier, James Cavendish over in atomic physics had announced the discovery of the neutron.  Zwicky sees that neutrons are the solution to his problem — gravity can pack together no-charge neutrons to a much higher density than it can pack positive-charge protons.  He proposes that a supernova happens when a big-enough star uses up its fuel and collapses to the smallest possible object, a neutron star.  Furthermore, he says that the collapse releases so much gravitational energy that supernovae give off cosmic rays, the super-high-energy photons that were one of the Big Questions of the day.”

“Sounds reasonable, I suppose.”

“Well, yeah, now.  But back then most astronomers had never heard of neutrons.  To solve at a stroke both cosmic rays and supernovae, using this weird new thing called a neutron, and with the proposal coming from somewhere other than Europe or Ivy League academia — well, it was all too outlandish to take seriously.  No-one did, for decades.”

“He didn’t like that, huh?”Zwicky inspecting dark matter

“No, he did not.  And he railed about it, not only in private conversations but in papers and in the preface to one of the two galaxy catalogs he published.  Same thing with galaxy clusters.”

“Wait, you wrote that Rubin found clusters.”

“I did and she did.  Actually, I wrote that she confirmed clustering.  We knew for 150 years that galaxies bunch together in our 2-D sky, but it took Zwicky’s measurements to group the Coma Cluster galaxies in 3-D.  Problem was, they were moving too fast.  If star gravity were the only thing holding them together they should have scattered ages ago.”

“Dark matter, huh?”

“Yup, Zwicky claimed invisible extra mass bound the cluster together.  More Zwicky outlandishness and once again his work was ignored for years.”

“Even though he was right.”

“Mm-hm.  But he could be wrong, too.  He didn’t like Hubble’s expanding Universe idea so he came up with a ‘tired light’ theory to explain the red-shifts.  He touted that idea heavily but there was too much evidence against it.”

“One of those angry ‘lone wolf’ scientists.”

“And bitter.”

~~ Rich Olcott

Symphony for Rubber Ruler

“But Mr Moire, first Vera Rubin shows that galaxies don’t spread out like sand grains on a beach…”

“That’s right, Maria.”

“And then she shows that galaxy streams flow like rivers through the Universe…”


“And then she finds evidence for dark matter!  She changed how we see the Universe and still they don’t give her the Nobel Prize??!?”

“All true, but there’s a place on Mars that’s named for her and it’ll be famous forever.”

“Really?  I didn’t know about that.  Where is it and why did they give it her name?”

“What do you know about dark matter?”

Rubin inspecting dark matter“Not much.  We can’t see it, and they say there is much more of it than the matter we can see.  If we can’t see it, how did she find it?  That’s a thing I don’t understand, what I came to your office to ask.”

“It all has to do with gravity.  Rubin’s studies of dozens of galaxies showed that they really shouldn’t exist, at least on the basis of the physics we knew about at the time.  She’d scan across a galaxy’s image, measuring how its red-shifted spectrum changed from the coming-toward-us side to the going-away-from-us side.  The red-shift translates to velocity.  The variation she found amazed the people she showed it to.”Pinwheel Galaxy NGC 5457 reduced

“What was amazing about it?”

“It was a flat line.  Look at the galaxy poster on my wall over there.”

“Oh, la galaxia del Molinete.  It’s one of my favorites.”

“We call it the Pinwheel Galaxy.  Where would you expect the stars to be moving fastest?”

“Near the center, of course, and they must move slower in those trailing arms.”

“That’s exactly what Rubin didn’t find.  From a couple of reasonable assumptions you can show that a star’s speed in a rotating galaxy composed only of other stars should be proportional to 1/√R, where R is its distance from the center.  If you pick two stars, one twice as far out as the other, you’d expect the outermost star to be going 1/√2 or only about 70% as fast as the other one.”

“And she found…?”

“Both stars have the same speed.”

“Truly the same?”

“Yes!  It gets better.  Most galaxies are embedded in a ball of neutral hydrogen atoms.  With a different spectroscopic technique Rubin showed that each hydrogen ball around her galaxies rotates at the same speed its galaxy does,  even 50% further out than the outermost stars.  Everything away from the center is traveling faster than it should be if gravity from the stars and gas were the only thing holding the galaxy together.  Her galaxies should have dispersed long ago.”

“Could electrical charge be holding things together?”

“Good idea — electromagnetic forces can be stronger than gravity.  But not here.  Suppose the galaxy has negative charge at its center and the stars are all positive.  That’d draw the stars inward, sure, but star-to-star repulsion would push them apart.  Supposing that neighboring stars have opposite charges doesn’t work, either.  And neutral hydrogen atoms don’t care about charge, anyway.  The only way Rubin and her co-workers could make the galaxy be stable is to assume it’s surrounded by an invisible spherical halo with ten times as much mass as the matter they could account for.”

“Mass that doesn’t shine.  She found ‘dark matter’ with gravity!”


“What about planets and dust?  Couldn’t they add up to the missing mass?”

“Nowhere near enough.  In out Solar System, for instance, all the planets add up to only 0.1% of the Sun’s mass.”

“Ah, ‘planets’ reminds me.  Why is Vera Rubin’s name on Mars?”

“Well, it’s not strictly speaking on Mars, yet, but it’s on our maps of Mars.  You know the Curiosity rover we have running around up there?”

“Oh yes, it’s looking for minerals that deposit from water.”

“Mm-hm.  One of those minerals is an iron oxide called hematite.  Sometimes it’s in volcanic lava but most of the time it’s laid down in a watery environment.  And get this — it’s often black or dark gray.  Curiosity found a whole hill of the stuff.”

Vera Rubin Ridge labeled

Adopted from a Curiosity Mastcam image from NASA

“Yes, so…?”

“What else would the researchers name an important geologic feature made of darkish matter?”

~~ Rich Olcott

Intermezzo for Rubber Ruler

¡Dios mio!  Vera Rubin confirms that galaxies cluster and no-one thinks that’s important?”

“That was in the 1950s, Maria.  Her report was just a degree thesis and a minor paper.  Her advisor, who should have pushed her case but didn’t, was a cosmologist instead of an observational astronomer.  At the time, many considered cosmology to be just barely not metaphysics.  What she reported didn’t bear on what the astronomers of the day considered the Big Questions, like how do stars work and is the expansion of the Universe accelerating.”

“That’s political, ¿no?

“That’s part of how science works — if observations  look important, other people work to invalidate them.  If results look important, other people work to rebut them.  The claims that are validated and can’t be rebutted survive.  But the verifiers and rebutters only work on what their colleagues consider to be important.  Deciding what’s important is a political process.  The history of science is littered with claims that everyone dismissed as unimportant until decades later when they suddenly gained the spotlight.  Galaxy clustering is one of those cases.  All things considered, I think clustering’s initial obscurity had more to do with the current state of the science than with her being a woman.”

“So how did Vera Rubin react to the nada?”

“She went back to her observing, which is what she was happiest doing anyway.  Especially when computers came along and her long-time colleague Kent Ford built a spiffy electronic spectrograph.  No more gear-calculating all day for a single number, no more peering down that measuring engine microscope tube.  Results came more quickly and she could look at larger assemblies out there in the Universe.  Which led to her next breakthrough.”

Rubin inspecting metagalaxy
“Dark matter, yes?”

“No, that came later.  This one was about streams.”

“Of water?”

“Of galaxies.  At the time, most astronomers thought that galaxy motion was a solved problem.  You know about Hubble Flow?”

“No.  Is that the streaming?”

“It’s the background for streaming.  Hubble Flow is the overall expansion of the Universe, all the galaxies moving away from each other.  But it’s not uniform motion.  We know, for instance, that the Andromeda and Milky Way galaxies are going to collide in about five billion years.  Think of galaxies like gas molecules in an expanding balloon.  On the average every molecule gets further away from its neighbors, but if you watched an individual molecule you’d see it bouncing back and forth.  Astronomers call that extra movement ‘peculiar motion.'”

“‘Peculiar’ like ‘odd?'”

“It’s an old-fashioned use of the word — ‘peculiar’ like ‘distinctive’ or ‘unique.’  Anyway, the community’s general notion was you could account for galaxy movement as a simple random motion laid on top of the Hubble Flow.”

“Again Occam’s Razor cuts too close?”

“For sure.  Rubin and Ford looked at data for almost a hundred distant galaxies all over the sky.  Not just any galaxies.  They carefully picked a set of one kind of galaxy, known in the trade as ScI, all of which have about the same ratio of absolute brightness to diameter.  Measure the diameter, you get the absolute brightness.  A distant light appears dimmer as the square of its distance.  Measure the brightness we see on Earth, make a few corrections, and the inverse square law lets you calculate how far the galaxy is from here.  Then Hubble’s distance-speed law tells you how fast you expect the galaxy to be receding.  That’s half of it.”


“The other half is how fast the galaxies are really moving.  For that Rubin and Ford turned to spectroscopy.  From the red/blue-shift of each galaxy they had an independent measure of its speed relative to us.  Guess what?  They didn’t match the Hubble Flow speeds.”

Galactic velocity anisotropy

Adapted from
Astronomical Journal 81, 719-37 (1976).

“Faster or slower?”

“Both!  In one half the sky these distant galaxies appear to be fleeing faster than the Hubble Flow, and in the other half they’re going slower.  The simplest explanation is that our entire Local Group is streaming towards the ‘slowest’ part of the sky.  Rubin and company had discovered a large-scale, third kind of galactic motion — rivers of galaxies streaming through the Universe.”

“Did the people get excited?”

“Not for a while, of course.”

~~ Rich Olcott

Concerto for Rubber Ruler

An unfamiliar knock at my office door — more of a tap than a knock. “C’mon in, the door’s open.”

¿Está ocupado?

“Hi, Maria. No, I’m not busy, just taking care of odds and ends. What can I do for you?”

“I’m doing a paper on Vera Rubin for la profesora. I have the biographical things, like she was usually the only woman in her Astronomy classes and she had to make her own baño at Palomar Observatory because they didn’t have one for señoras, and she never got the Nobel Prize she deserved for discovering dark matter.

“Wait, you have all negatives there.  Her life had positives, too.  What about her many scientific breakthroughs?”

“That’s why I’m here, for the science parts I don’t understand.”

“I’ll do what I can. What’s the first one?”

“In her thesis she showed that galaxies are ‘clumped.’  What is that?”

“It means that the galaxies aren’t spread out evenly.  Astronomers at the time believed, I guess on the basis of Occam’s Razor, that galaxies were all the same distance from their neighbors.”

“Occam’s Razor?  Ah, la navaja de Okcam.  Yes, we study that in school — do not assume more than you have to.  But why would evenly be a better assumption than clumpy?”

“At the time she wrote her thesis the dominant idea was that the Big Bang’s initial push would be ‘random’ — every spot in the Universe would have an equal chance of hosting a galaxy.  But she found clusters and voids.  That made astronomers uncomfortable because they couldn’t come up with a mechanism that would make things look that way.  It took twenty years before her observations were accepted.  I’ve long thought part of her problem was that her thesis advisor was George Gamow.  He was a high-powered physicist but not an observational astronomer.  For some people that was sufficient excuse to ignore Rubin’s work.”

“Another excuse.”

“Yes, that, too.”

“But why did she have to discover the clumpy?  You can just look up in the sky and see things that are close to each other.”

“Things that appear to be close together in the sky aren’t necessarily close together in the Universe.  Look out my window.  See the goose flying there?”

“Mmm…  Yes!  I see it.”

“There’s an airplane coming towards it, looks about the same size.  Think they’ll collide?”

“Of course no.  The airplane looks small because it’s far away.”

“But when their paths cross, we see them at the same point in our sky, right?”

“The same height up, yes, and the same compass direction, but they have different distances from us.”

“Mm-hm.  Geometry is why it’s hard to tell whether or not galaxies are clustered.  Two galaxy images might be separated by arc-seconds or less.  The objects themselves could be nearest neighbors or separated by half-a-billion lightyears.  Determining distance is one of the toughest problems in observational astronomy.”

“That’s what Vera Rubin did?  How?”

“In theory, the same way we do today.  In practice, by a lot of painstaking manual work.  She did her work back in the early 1950s, when ‘computer’ was a job title, not a device.  No automation — electronic data recording was a leading-edge research topic.  She had to work with images of spectra spread out on glass plates, several for each galaxy she studied.  Her primary tool, at least in the early days, was a glorified microscope called a measuring engine.  Here’s a picture of her using one.” Vera Rubin

“She looks through the eyepiece and then what?”

“She rotates those vernier wheels to move each glass-plate feature on the microscope stage to the eyepiece’s crosshairs.  The verniers give the feature’s x– and y-coordinates to a fraction of a millimeter.  She uses a gear-driven calculating machine to turn galaxy coordinates into sky angles and spectrum coordinates into wavelengths.  The wavelengths, Hubble’s law and more arithmetic give her the galaxy’s distance from us.  More calculations convert her angle-angle-distance coordinates to galactic xy-z-coordinates.  Finally she calculates distances between that galaxy and all the others she’s already done.  After processing a few hundred galaxies, she sees groups of short-distance galaxies in reportable clusters.”

“Wouldn’t a 3-D graphic show them?”

“Not for another 50 years.”

~~ Rich Olcott

Quartetto for Rubber Ruler

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

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


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

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

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

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

“Wait a minute, ‘plasma fog’?”

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

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

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

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

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

“What could be outside the Universe, Cathleen?”

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

“Like galaxies?”

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

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

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

“Suggests, huh?”

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

“Different times?”

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

~~ Rich Olcott

Terzetto for Rubber Ruler

ruler and sodium lines“So you’re telling me, Cathleen, that you can tell how hot a star is by looking at its color?”

“That’s right, Vinnie.  For most stars their continuous spectrum is pretty close to the blackbody equation tying peak wavelength to temperature.”

“But you can’t do that with far-away stars, right, because the further they are, the more stretched-out their lightwaves get.  Won’t that mess up the peak wavelength?”

“The key is Kirchhoff’s other kinds of spectrum.”

“You’re talking the bright-line and dark-line kinds.”

“Exactly.  Each kind of spectrum comes from a different process — each is affected differently by the object in question and the environment it’s embedded in.  A continuous spectrum is all about charged particles moving randomly in response to the heat energy they’re surrounded by.  It doesn’t matter what kind of particles they are or even whether they’re positive or negative.  Whenever a particle changes direction, it twitches the electromagnetic field and gives off a wave.”

“Right — the higher the temperature the less time between twitches; the wave can’t move as far before things change so the wavelength’s shorter; any speed’s possible so you can turn that dial wherever; I got all that.  So what’s different with the bright-line and dark-line spectrums?”

Cathleen and I both blurt out, “Spectra!” at the same time and give each other a look.  We’re grown-ups now.  We don’t say, “Jinx!” to each other any more.

“Alright, spectra.  But how’re they different?”

I pick up the story.  “Like Cathleen said, continuous spectra from same–temperature stuff look identical no matter what kind of stuff’s involved because heat is motion and each particle moves as a unit  The other kinds of spectrum are about transitions within particles so they’re all about which kind of stuff.  A given kind of atom can only absorb certain wavelengths of light and it can only relax by giving off exactly the same wavelengths.  There’s no in-betweens.”

She cuts in.  “Sodium, for instance.  It has two strong lines in the yellow, at 588.995 and 589.592 nanometers.  Whether in a star or a meteor or fireworks, sodium gives off exactly those colors.  Conversely, in an interstellar cloud or in a star’s outermost layers sodium absorbs exactly those colors from any continuous-spectrum light passing through.”

I’m back in.  “And there’s the key to your unmixing question, Vinnie.  We’ve talked about frames, remember?  Your far-away star’s light-generating layers emit a continuous spectrum that describes its temperature.  If we were right next to it, that’s the spectrum we’d see.  But as you say, we’re a long way away and in our frame the light’s been stretched.  It still looks like the black-body curve but it’s red-shifted because of our relative motion.”

Cathleen’s turn.  “But if there are sodium atoms in the star’s upper layers, their absorptions will cut a pair of notches in that emitted spectrum.  It won’t be a smooth curve, there’ll be two sharp dips in it, close together, with the blue-side one twice as strong as the other one.  Easy to recognize and measure the redshift.  The blackbody peak is redshifted by exactly the same amount so with some arithmetic you’ve got the peak’s original wavelength and the star’s temperature.”

Mine.  “See, because we know what the sodium wavelengths were in the star’s frame, we can divide the dip wavelengths we measure by the rest-frame numbers we know about.  The ratios give us the star’s redshift.”

Spectrum with only blackbody and sodium Cathleen turns to her laptop and starts tapping keys.  “Let’s do an example.  Suppose we’re looking at a star’s broadband spectrogram.  The blackbody curve peaks at 720 picometers.  There’s an absorption doublet with just the right relative intensity profile in the near infra-red at 1,060,190 and 1,061,265 picometers.  They’re 1,075 picometers apart.  In the lab, the sodium doublet’s split by 597 picometers.  If the star’s absorption peaks are indeed the sodium doublet then the spectrum has been stretched by a factor of 1075/597=1.80.  Working backward, in the star’s frame its blackbody peak must be at 720/1.80=400 picometers, which corresponds to a temperature of about 6,500 K.”

“Old Reliable calculates from that stretch factor and the Hubble Constant the star’s about ten billion lightyears away and fleeing at 240,000 km/s.”

“All that from three peaks.  Spectroscopy’s pretty powerful, huh?”

Cathleen and me: “For sure!    Jinx!”

~~ Rich Olcott