A Far And Dusty Traveler

Cathleen takes the mic. “Quick coffee and scone break, folks, then Jim will continue our ‘IR, Spitzer And The Universe‘ symposium.” <pause> “OK, we’re back in business. Jim?”

“Thanks, Cathleen. Well, we’ve discussed finding astronomical molecules with infra-red. Now for a couple of other IR applications. First up — looking at things that are really far away. Everyone here knows that the Universe is expanding, right?”

<general murmur of assent, although the probably-an-Art-major looks startled>

“Great. Because of the expansion, light from a far-away object gets stretched out to longer wavelengths on its way to us. Say a sodium atom shot a brilliant yellow-gold 590-nanometer photon at us, but at the time the atom was 12.5 million lightyears away. By the time that wave reaches us it’s been broadened to 3540 nanometers, comfortably into the infra-red. Distant things are redder, sometimes too red to see with an optical telescope. The Spitzer Space Telescope‘s infra-red optics let us see those reddened photons. And then there’s dust.”

<voice from the crowd> “Dust?”

Cosmic dust, pretty much all the normal matter that’s not clumped into stars and planets. Some of it is leftovers from early times in the Universe, but much of it is stellar wind. Stars continuously spew particles in their normal day-to-day operation. There’s a lot more of that when one explodes as a nova or supernova. Dust particles come in all sizes but most are smaller than the ones in tobacco smoke.”

<same voice> “If they’re so small, why do we care about them?”

“Two reasons. First, there’s a lot of them. Maybe only a thousand particles per cubic kilometer of space, but there’s a huge number of cubic kilometers in space and they add up. More important is what the dust particles are made of and where we found them. Close inspection of the dust is like doing astronomical archaeology, giving us clues about how stars and galaxies evolved.”

<Vinnie, skeptical as always> “So what’s infra-red got to do with dust?”

“Depends on what kind of astronomy you’re interested in. Dust reflects and emits IR light. Frequency patterns in the light can tell us what that dust made of. On the other hand there’s the way that dust doesn’t interact with infra-red.”

<several voices> “Wait, what?”

The Milky Way from Black Rock Desert NV
By Steve Jurvetson via Flickr, Wikimedia Commons, CC BY 2.0

“If Al’s gotten his video system working … ah, he has and it does. Look at this gorgeous shot of the Milky Way Galaxy. See all the dark areas? That’s dust blocking the visible light. The scattered stars in those areas are simply nearer to us than the clouds. We’d like to study what’s back beyond the clouds, especially near the galaxy’s core. That’s a really interesting region but the clouds block its visible light. Here’s the neat part — the clouds don’t block its infra-red light.”

<other voices> “Huh?” “Why wouldn’t they?”

“It’s the size of the waves versus the size of the particles. Take an extreme case — what’s the wavelength of Earth’s ocean tides?”

<Silence, so I speak up.> “Two high tides a day, so the wavelength is half the Earth’s circumference or about 12’500 miles.”

“Right. Now say you’re at the beach and you’re out there wading and the water’s calm. Would you notice the tide?”

“No, rise or fall would be too gentle to affect me.”

“Now let’s add a swell whose peak-to-peak wavelength is about human-height scale.”

“Whoa, I’d be dragged back and forth as each wave passes.”

“Just for grins, let’s replace that swell with waves the same height but only a millimeter apart. Oh, and you’re wearing SCUBA equipment.”

“Have mercy! Well, I should be able to stand in place because I wouldn’t even feel the peaks and troughs as separate waves, just a foamy massage. Thanks for the breathing assistance, though.”

“You’re welcome, and thanks for helping with the thought experiment. Most cosmic dust particles are less than 100 nanometers across. Infra-red wavelengths run 100 to 1000 times longer than that. Infra-red light from those cloud-hidden stars just curves around particles that can stop visible lightwaves cold. Spitzer Space Telescope and its IR-sensitive kin provide deeper and further views than visible light allows.”

~~ Rich Olcott

Small, yes, but how small?

Another quiet summer afternoon in the office. As I’m finishing up some paperwork I hear a fizzing sound I’d not heard in a while. “Hello, Anne, welcome back. Where’ve you been?”

Her white satin looks a bit speckled somehow but her voice still sounds like molten silver. “I’m not sure, Sy. That’s what I’ve come to you about.”

“Tell me about it.”

“Well, after we figured out that I can sort of ‘push’ myself across time and probability variation I realized that the different ‘pushes’ felt like different directions, kind of. When I go backward and forward in time it feels a little like falling backward or forward. Not really, but that’s the best way I can describe it. Moving to a different probability is a little like going left or right. So I wondered, what about up and down?”

“And I gather you tried that.”

“Sure, why not? What good’s a superpower if you don’t know what you can do with it? When I ‘push’ just a little upward thIS HAPPENS.”

“Whoa, watch out for the ceiling fan! Shrink back down again before you break the furniture or something.”

“Oh, I won’t, I’ve learned to be careful when I resize. Good thing I was outside and all by myself the first time I tried it. Took some practice to control how how much my size changes by how light or heavy I ‘pushed’.”

“I think I can see where this is going.”

“Mm-hm, it’s good to know what the limits are, right? I’ve got a pretty good idea of what would happen if I got huge. What I want to know is, what’ll I be getting into if I try ‘pushing’ down as hard as I can?”

“Kinda depends on how far down you go. I’m assuming your retinas scale their sensitivity with your size. When you get bigger do green things look blue and yellow things look green and so forth?”

“Yeah, orange juice had this weird yellow color. Tasted OK, though.”

“Right. So when you get smaller the colors you perceive will shift the other way, to shorter wavelengths — at first, yellow things will look red, blue things will look yellow and you’ll see ultraviolet as blue. When you get a thousand times smaller than normal, most things will look black because there’s not much X-ray illumination unless you’re close to a badly-shielded Crookes tube.”

“Good thing this ‘push’ ability also gave me some kind of extra feel-sense that’s not sight. Sometimes when I try to ‘push’ it ‘feels’ blocked until I move around a little. After the ‘push’ I see a wall or something I would have jumped into.”

“That’s a relief. I was wondering how you’d navigate when you’re a million times smaller than normal, at the single-cell level, or a million times smaller than that when you’d be atom-sized.”

“Then what comes?”

“Mmm… one more factor of a thousand would get you down to about the size of an atomic nucleus, but below that things get real fuzzy. It’s hard to get experimental data in the sub-nuclear size range because any photon with a wavelength that short is essentially an extremely-high-energy gamma ray, better at blowing nuclei apart than measuring them. Theory says you’d encounter nuclei as roiling balls of protons and neutrons, but each of those is a trio of quarks which may or may not be composed of even smaller things.”

“Is that the end of small?”

“Maybe not. Some physicists think space is quantized at scales near 10—35 meter. If they’re wrong then there’s no end.”

“Quantized?”

Quantized means something is measured out in whole numbers. Electric charge is quantized, for instance, because you can have one electron, two electrons, and so on, but you can’t have 1½ electrons. Some physicists think it’s possible that space itself is quantized. The basic idea is to somehow label each point in space with its own set of whole numbers.  There’d be no vacant space between points, just like there’s no whole number between two adjacent whole numbers.”

“So how small can I get?”

“Darned if I know.”

~~ Rich Olcott

Thanks to Jerry Mirelli for his thoughts that inspired this post and the next.

Rhythm Method

A warm Summer day.  I’m under a shady tree by the lake, watching the geese and doing some math on Old Reliable.  Suddenly a text-message window opens up on its screen.  The header bar says 710-555-1701.  Old Reliable has never held a messaging app, that’s not what I use it for.  The whole thing doesn’t add up.  I type in, Hello?

Hello, Mr Moire.  Remember me?

Suddenly I do.  That sultry knowing stare, those pointed ears.  It’s been a yearHello, Ms Baird.  What can I do for you?

Another tip for you, Mr Moire.  One of my favorite star systems — the view as you approach it at near-lightspeed is so ... meaningful.  Your astronomers call it PSR J0337+1715.

So of course I head over to Al’s coffee shop after erasing everything but that astronomical designation.  As I hoped, Cathleen and a few of her astronomy students are on their mid-morning break.  Cathleen winces a little when she sees me coming.  “Now what, Sy?  You’re going to ask about blazars and neutrinos?”

I show her Old Reliable’s screen.  “Afraid not, Cathleen, I’ll have to save that for later.  I just got a message about this star system.  Recognize it?”

“Why, Sy, is that a clue or something?  And why is the lettering in orange?”

“Long story.  But what can you tell me about this star system?”

“Well, it’s probably one of the most compact multi-component systems we’re ever going to run across.  You know what compact objects are?”

“Sure.  When a star the size of our Sun exhausts most of its hydrogen fuel, gravity wins its battle against heat.  The star collapses down to a white dwarf, a Sun-full of mass packed into a planet-size body.  If the star’s a bit bigger it collapses even further, down to a neutron star just a few miles across.  The next step would be a black hole, but that’s not really a star, is it?”

“No, it’s not.  Jim, why not?”

“Because by definition a black hole doesn’t emit light.  A black hole’s accretion disk or polar jets might, but not the object itself.”

“Mm-hm.  Sy, your ‘object’ is actually three compact objects orbiting  around each other.  There’s a neutron star with a white dwarf going around it, and another white dwarf swinging around the pair of them.  Vivian, does that sound familiar?”

“That’s a three-body system, like the Moon going around the Earth and both going around the Sun.  Mmm, except really both white dwarfs would go around the neutron star because it’s heaviest and we can calculate the motion like we do the Solar System.”

“Not quite.  We can treat the Sun as motionless because it has 99% of the mass.  J0337+1715’s neutron star doesn’t dominate its system as much as the Sun does ours.  That outermost dwarf has 20% of its system’s mass.  Phil, what does that suggest to you?”

“It’d be like Pluto and Charon.  Charon’s got 10% of their combined mass and so Pluto and Charon both orbit a point 10% of the way out from Pluto.  From Earth we see Pluto wobbling side to side around that point.  So the neutron star must wobble around the point 20% outward towards the heavy dwarf.  Hey, star-wobble is how we find exoplanets.  Is that what this is about, Mr Moire?  Did someone measure its red-shift behavior?”PSR J0337+1715Cathleen saves me from answering.  “Not quite.  The study Sy’s chasing is actually a cute variation on red-shift measurements.  That ‘PSR‘ designation means the neutron star is a pulsar.  Those things emit electromagnetic radiation pulses with astounding precision, generally regular within a few dozen nanoseconds.  If we receive slowed-down pulses then the object’s going away; sped-up and it’s approaching, just like with red-shifting.  The researchers  derived orbital parameters for all three bodies from the between-pulse durations.  The heavy dwarf is 200 times further out than the light one, for instance.  Not an easy experiment, but it yielded an important result.”

My ears perk up.  “Which was…?”

“The gravitational force between the pulsar and each dwarf was within six parts per million of what Newton’s Laws prescribe.  That observation rules out whole classes of theories that tried to explain galaxies and galaxy clusters without invoking dark matter.”

Cool, huh?

Uh-huh.

~~ 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.”

“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

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