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.”

“OK…?”

“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

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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

Toccata for A Rubber Ruler

“How the heck do they know that?”

“Know what, Vinnie?”

“That the galaxy they saw with that gravitational lens is 13 billion years old?  I mean, does it come with a birth certificate, Cathleen?”

“Mm, it does, sort of — hydrogen atoms.  Really old hydrogen atoms.”

“Waitaminit.  Hydrogen’s hydrogen — one proton, one electron per atom.  They’re all the same, right?  How do you know one’s older than another one?”

“Because they look different.”

“How could they look different when they’re all the same?”

“Let me guess, Cathleen.  These old hydrogens, are they far far away?”

“On the button, Sy.”

“What where they’re at got to do with it?”

“It’s all about spectroscopy and the Hubble constant, Vinnie.  What do you know about Edwin Hubble?”

“Like in Hubble Space Telescope?  Not much.”

“Those old atoms were Hubble’s second big discovery.”

“Your gonna start with the other one, right?”

“Sorry, classroom habit.  His first big discovery was that there’s more to the Universe than just the Milky Way Galaxy.  That directly contradicted Astronomy’s Big Names.  They all believed that the cloudy bits they saw in the sky were nebulae within our galaxy.  Hubble’s edge was that he had access to Wilson Observatory’s 100-inch telescope that dwarfed the smaller instruments that everyone else was using.  Bigger scope, more light-gathering power, better resolution.”

“Hubble won.”

“Yeah, but how he won was the key to his other big discovery.  The crucial question was, how far away are those ‘nebulae’?  He needed a link between distance and something he could measure directly.  Stellar brightness was the obvious choice.  Not the brightness we see on Earth but the brightness we’d see if we were some standard distance away from it.  Fortunately, a dozen years earlier Henrietta Swan Leavitt found that link.  Some stars periodically swing bright, then dim, then bright again.  She showed that for one subgroup of those stars, there’s a simple relationship between the star’s intrinsic brightness and its peak-to-peak time.”Astroruler

“So Hubble found stars like that in those nebulas or galaxies or whatever?”

“Exactly.  With his best-of-breed telescope he could pick out individual variable stars in close-by galaxies.  Their fluctuation gave him intrinsic brightness.  The brightness he measured from Earth was a lot less.  The brightness ratios gave him distances.  They were a lot bigger than everyone thought.”

“Ah, so now he’s got a handle on distance.  Scientists love to plot everything against everything, just to see, so I’ll bet he plotted something against distance and hit jackpot.”

“Well, he was a bit less random than that, Sy.  There were some theoretical reasons to think that the Universe might be expanding.  The question was, how fast?  For that he tapped another astronomer’s results.  Vesto Slipher at Lowell Observatory was looking at the colors of light emitted by different galaxies.  None had light exactly like our Milky Way’s.  A few were a bit bluer, but most were distinctly red-shifted.”

“Like the Doppler effect in radar?  Things coming toward you blue-shift the radar beam, things going away red-shift it?”

“Similar to that, Vinnie, but it’s emitted light, not a reflected beam. To a good approximation, though, you can say that the red shift is proportional to the emitting object’s speed towards or away from us.  Hubble plotted his distance number for each galaxy he’d worked on, against Slipher’s red-shift speed number for the same galaxy.  It wasn’t the prettiest graph you’ve ever seen, but there was a pretty good correlation.  Hubble drew the best straight line he could through the points.  What’s important is that the line sloped upward.”

“Lemme think … If everything just sits there, there’d be no red-shift and no graph, right?  If everything is moving away from us at a steady speed, then the line would be flat — zero slope.  But he saw an upward slope, so the farther something is the faster it’s going further from us?”

“Bravo, Vinnie.  That’s the expansion of the Universe you’ve heard about.  Locally there are a few things coming toward us — that’s those blue-shifted galaxies, for instance — but the general trend is away.”

“So that’s why you say those far-away hydrogens look different.  By the time we see their light it’s been red-shifted.”

“93% redder.”

~~ Rich Olcott