# Useful Eccentricity

“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.”

~~ Rich Olcott

“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