Tag: Doppler effect

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.

Useful Eccentricity

On By rolcottIn Astronomy: Techniques, UncategorizedLeave a comment

“Hi, Al. What’s the hubbub in the back room?”

“Cathleen’s doing another astronomy class group seminar. This one’s about exoplanets. I’d like to listen in but I’ve got to tend the cash register here. Take notes, okay?”

“Sure, no problem.”

Professor Cathleen’s at the podium. “Okay, class, settle down. I hope everyone’s ready with their presentations. Maria, you’ve got a good topic to start us off.”

“Thank you. Everyone here knows I’ve been interested in spectroscopy since I was a student intern at Arecibo. It is such a powerful thing to know that a particular kind of atom, anywhere in the Universe, absorbs or gives off exactly the same pattern of light frequencies. Suppose you are looking at the spectrum of a star or a galaxy and you recognize a pattern, like sodium’s yellow doublet or hydrogen’s Lyman series. The pattern won’t be at its normal frequencies because of the Doppler effect. That’s good because the amount of blue‑shift or red‑shift tells us how quick the object is moving toward or away from us. That was how Dr Hubble proved that most other galaxies are flying away.”

<casts a slide to Al’s video screen> “I’ll begin with a review of some class material. The spectroscopy we see in the sky is light that was emitted at some peak wavelength lambda. Lambda with the little ‘o‘ is what we see for the same emission or absorption process in the laboratory. The wavelength difference between sky and laboratory is the absolute shift. Divide that by the laboratory wavelength to get the relative shift, the z‑scale. All the light from one object should have the same z value. It is important that z also gives us the object’s velocity if we multiply by the speed of light.”

<voice from the rear> “What’s the ‘fe ka‘ stuff about?”

“I was getting to that. Those two lines describe a doublet, a pair of peaks that always appear together. This is in the X‑ray spectrum of iron which is Fe for the chemists. K-alpha is a certain process inside the iron atom. Astronomers like to use that doublet because it’s easy to identify. Yes, profesora?”

“Two additional reasons, Maria. Iron’s normally the heaviest element in a star because stellar nuclear fusion processes don’t have enough energy to make anything heavier than that. Furthermore, although every element heavier than neon generates a K-alpha doublet, the peak‑to‑peak split increases with atomic mass. Iron’s doublet is the widest we see from a normal star.”

“Thank you. So, the arithmetic on the rest of the slide shows how Dr Hubble might have calculated the speed of a galaxy. But that’s steady motion. Exoplanets orbiting a star appear to speed ahead then fall behind the star, yes? We need to think about how a planet affects its star. This next slide talks about that. My example uses numbers for the Sun and Jupiter. We say Jupiter goes around the Sun, but really, they both go around their common center of gravity, their barycenter. You see how it’s calculated here — MP is the planet’s mass, MS is the star’s mass, dSP is the star-to-planet distance and dB is the distance from the star’s center to the barycenter. I’ve plugged in the numbers. The barycenter is actually ten thousand kilometers outside the Sun!”

“So you could say that our Sun counterbalances Jupiter by going in a tight circle around that point.”

“Exactly! For my third slide I worked out whether a distant astronomer could use Doppler logic to detect Sun‑Jupiter motion. The first few lines calculate the size of the Sun’s circle and than how fast the Sun flies around it. Each Jupiter year’s blue shift to red shift totals only 79 parts per billion. The Sun’s iron K‑alpha1 wavelength varies only between 193.9980015 and 193.9979985 picometers. This is far too small a change to measure, yes?”

<dramatic pause> “I summarize. To make a good Doppler signal, a star must have a massive exoplanet that’s close enough to push its star fast around the barycenter but far enough away to pull the barycenter outside of the star.”

“Thank you, Maria.”

“X” marks the barycenter

~~ Rich Olcott

Pushing It Too Far

On By rolcottIn Astronomy: Techniques, Cosmology, UncategorizedLeave a comment

It’s like he’s been taking notes. Mr Feder’s got a gleam in his eye and the corner of his mouth is atwitch. “You’re not getting off that easy, Cathleen. You said that Earendell star’s 66 trillion lightyears away. Can’t be, if the Universe’s only 14 billion years old. What’s going on?”

“Oops, did I say trillion? I meant billion, of course, 109 not 1012. A trillion lightyears would be twenty times further than the edge of our observable universe.”

“Hmph. Even with that fix it’s goofy. Sixty-six billion is still what, five times that 14 billion year age you guys keep touting. I thought light couldn’t travel that far in that time.”

“I thought the Universe is 93 billion light years across.”
  ”That’s diameter, and it’s just the observable universe.”
    ”Forty-seven billion radially outward from us.”
      ”None of that jibes with 14 billion years unless ya got stuff goin’ faster than light.”

“Guys, guys, one thing at a time. About that calculation, I literally did it on the back of an envelope, let’s see if it’s still in my purse … Nope, must be on my office desk. Anyhow, distance is the trickiest part of astronomy. The only distance‑related thing we can measure directly is z, that redshift stretch factor. Locate a familiar pattern in an object’s spectrum and see where its wavelength lies relative to the laboratory values. The go‑to pattern is hydrogen’s Lyman series whose longest wavelength is 121 nanometers. If you see the Lyman pattern start at 242 nanometers, you’ve got z=2. The report says that the lens is at z=2.8 and Earendel’s galaxy is at z=6.2. We’d love to tie those back to distance, but it’s not as easy as we’d like.”

“It’s like radar guns, right? The bigger the stretch, the faster away from us — you should make an equation outta that.”

“They have, Mr Feder, but Doppler’s simple linear relationship is only good for small z, near zero. If z‘s greater than 0.1 or so, relativity’s in play and things get complicated.”

“Wait, the Hubble constant ties distance to speed. That was Hubble’s other big discovery. Old Reliable here says it’s something like 70 kilometers per second for every megaparsec distance. What’s that in normal language? <tapping keys> Whoa, so for every lightyear additional distance, things fly away from us about an inch per second faster. That’s not much.”

“True, Sy, but remember we’re talking distant, barely observable galaxies that are billions of lightyears away. Billions of inches add up. Like with the Doppler calculation, you get startling numbers if you push a simple linear relation like this too far. As an extreme example, your Hubble rule says that light from a galaxy 15 billion lightyears away will never reach us because Hubble Flow moves them away faster than photons fly toward us. We don’t know if that’s true. We think Hubble’s number changes with time. Researchers have built a bucketful of different expansion models for how that can happen; each of them makes different predictions. I’m sure my 66 came from one of those. Anyhow, most people nowadays don’t call it the Hubble constant, it’s the Hubble parameter.”

“Sixty-six or forty-seven or whatever, those diameters still don’t jibe with how long the light’s had a chance to travel.”

“Sy, care to take this? It’s more in your field than mine.”

“Sure, Cathleen. The ‘edge of the observable universe‘ isn’t a shell with a fixed diameter, it simply marks the take-off points for the oldest photons to reach us so far. Suppose Earendel sent us a photon about 13 billion years ago. The JWST caught it last night, but in those 13 billion years the universe expanded enough to insert twenty or thirty billion lightyears of new space between between here and Earendel. The edge is now that much farther away than when the photon’s journey started. A year from now we’ll be seeing photons that are another year older, but the stars they came from will have flown even farther away. Make sense?”

“A two-way stretch.”

“You could say that.”

~~ Rich Olcott

  • Thanks to my brother Neil, who pointed out the error and asked the question.

The Red Advantage

On By rolcottIn Astronomy: Techniques, James Webb Space Telescope, Physics: Light and Relativity, Space Travel, Uncategorized1 Comment

“OK, Cathleen, I get that JWST and Hubble rate about the same for sorting out things that are close together in the sky, and I get that they look at different kinds of light so it’s hard to compare sensitivity. Let’s get down to brass tacks. Which one can see farther?”

“An excellent question, Mr Feder. I’ve spent an entire class period on different aspects of it.”

“Narrow it down a little, I ain’t got all day.”

“You asked for it — a quick course on cosmological redshift. Fasten your seat belt. You know what redshift is, right?”

“Yeah, Moire yammers on about it a lot. Waves stretch out from something moving away from you.”

I bristle. “It’s important! And some redshifts don’t have anything to do with motion.”

“Right, Sy. Redshift in general has been a crucial tool for studying everything from planetary motion to the large‑scale structure of the Universe. Your no‑motion redshift — you’re thinking of gravitational redshift, right?”

“Mm-hm. From a distance, space appears to be compressed near a massive object, less compressed further away. Suppose we send a robot to take up a position just outside a black hole’s event horizon. The robot uses a green laser to send us its observations. Space dilates along the beam’s path out of the gravity well. The expanding geometry stretches the signal’s wavelength into the red range even though the robot’s distance from us is constant.”

“So, that’s gravitational redshift and there’s the Doppler redshift that Mr Feder referred to—”

“Is that what its name is? With p‘s? I always heard it as ‘doubler’ effect and wondered where that came from.”

“It came from Christian Doppler’s name, Al. Back in the 1840s he was investigating a star. He noticed that its spectrum was the overlap of two spectra slightly shifted with respect to each other. Using wave theory he proposed that the star was a binary and that the shifted spectra arose from one star coming towards us and the other moving away. Later work confirmed his ideas and the rest is history. So it’s Doppler, not doubler, even though the initial observation was of a stellar doublet.”

“So what’s this cosmo thing?”

“Cosmological redshift. It shows up at large distances. On the average, all galaxies are moving away from us, but they’re moving away from each other, too. That was Hubble’s big discovery. Well, one of them..”

“Wait, how can that be? If I move away from Al, here, I’m moving toward Sy or somebody.”

“We call it the expansion of the universe. Have you ever made raisin bread?”

“Nah, I just eat it.”

“Ok, then, just visualize how it’s made. You start with a flat lump of dough, raisins close together, right? The loaf rises as the yeast generates gas inside the lump. The dough expands and the raisins get further apart, all of them. There’s no pushing away from a center, it’s just that there’s an increasing amount of bubbly dough between each pair of neighboring raisins. That’s a pretty good analogy to galactic motion — the space between galaxies is expanding. The general motion is called Hubble flow.”

“So we see their light as redshifted because of their speed away from us.”

“That’s part of it, Al, but there’s also wave‑stretching because space itself is expanding. Suppose some far‑away galaxy, flying away at 30% of lightspeed, sent out a green photon with a 500‑nanometer wavelength. If the Doppler effect were the only one in play, our relative speeds would shift our measurement of that photon out to about 550 nanometers, into the yellow. Space expansion at intermediate stations along its path can cumulatively dilate the wave by further factors out into the infrared or beyond. Comparing two galaxies, photons from the farther one will traverse a longer path through expanding space and therefor experience greater elongation. Hubble spotted one object near its long‑wavelength limit with a recognizable spectrum feature beyond redshift factor 11.”

“Hey, that’s the answer to Mr Feder’s question!”

“So what’s the answer, smart guy?”

“JWST will be able to see farther, because its infrared sensors can pick up distant light that’s been stretched beyond what Hubble can handle.”

~~ Rich Olcott

Toccata for A Rubber Ruler

On By rolcottIn Astronomy: Stellar Science, Astronomy: Techniques, Cosmology, Physics: Fundamentals, UncategorizedLeave a comment

“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