Tag: Cal’s Coffee

Through The Looking Glass, Darkly

On By rolcottIn General: Fun Stuff, Mathematics: Dimensions, Physics: Entropy and Thermodynamics, Uncategorized1 Comment

The Acme Building is quiet on summer evenings.  I was in my office, using the silence to catch up on paperwork.  Suddenly I heard a fizzing sound.  Naturally I looked around.  She was leaning against the door frame.

White satin looked good on her, and she looked good in it.  A voice like molten silver — “Hello, Mr Moire.”White satin and chessboard 1

“Hello yourself.  What can I do for you?”

“I’m open to suggestions, but first you can help me find myself.”

“Excuse me, but you’re right here.  And besides, who are you?”

“Not where I am but when I am.  Anne.”

“You said it right the first time.”

“No, no, my name is Anne.  At the moment.  I think.  Oh, it’s so confusing when your memory works in circles but not very well.  Do you have the time?”

“Well, I was busy, but you’re here and much more interesting.”

“No, I mean, what time is it?”

I showed her my desk clock — date, time, even the phase of the moon.

“Half past gibbous already?  Oh, bread-and-butter…”

“Wait — circles?  Time’s one-dimensional.  Clock readings increase or decrease, they don’t go sideways.”

“You don’t know Time as well as I do, Mr Moire.  It’s a lot more complicated than that.  Time can be triangular, haven’t you noticed?”

“Can’t say as I have.”

“That paperwork you’re working on, are you near a deadline?”

“Nah.”

“And given that expanse of time, you feel free to permit distractions.  There are so many distractions.”

“You’re very distracting.”

“Thank you, I guess.  But suppose you had an important deadline coming up tomorrow.   That broad flow of possibilities at the beginning of the project has narrowed to just two — finish or don’t finish.  Your Time has closed in on you.”

“So you’re saying we can think of Time as two-dimensional.  The second dimension being…?”

“I don’t know.  I just go there.  That’s the problem.”

“Hmm… When you do, do you feel like you’re turning left or right?”

“No turning or moving forward or backward.  Generally I have to … umm… ‘push’ like I’m going uphill, but that only works if there’s a ‘being pushed’ when I get past that.  Otherwise I’m back where I started, whatever that means.”

“What do you see?  What changes during the episode?”

“Little things. <brief fizzing sound.  She … flickered.>  Like ‘over there’ you’re wearing a bright green T-shirt instead of what you’re wearing here.  And you’re using pen-and-paper instead of that laptop.  Green doesn’t suit you.”

“I know, which is why there’s nothing green in my wardrobe, here.  But that gives me an idea.  Did you always have to ‘push’ to get ‘over there’?”

“Usually.”

“Fine.  OK, I’m going to flip this coin.  While it’s in the air, ‘push’ just lightly and come back to tell me which way the coin fell.”

<fizzing> “Heads.”

“It’s tails here.  OK, we’re going to do that again but this time ‘push’ much harder.”

<louder fizzing> “That was weird.  Your coin rolled off the desk and landed on edge in a crack in the floor so it’s not heads or tails.”

“AaaHAH!”Coins 1

“?”

“Your ‘over theres’ have different levels of probability than ‘over here.’  They’re different realities.  Actually, I’ll bet you travel across ranges of probability.  Or tunnel through them, maybe.  That’d why you have to ‘push’ to get past something that’s less probable in order to get to something that’s more probable.  Like getting past a reality where the coin can just hang in the air or fly apart.”

“I’ve done that.  Once I sneezed while ‘pushing’ and wound up sitting at a tea party where the cream and sugar just refused to stir into the tea.  When I ‘pushed’ from there I practically fell into a coffee shop where the coffee was well-behaved.”

“Case closed.  Now I can answer your question.  Spacewise, you’re in my office on the twelfth floor.  Timewise, I just showed you my clock.  As for which reality, you’re in one with a very high probability because, well, you’re here.”

“So provincial.  Oh, Mr Moire, how little you know.” <fizzing>

On the 12th floor of the Acme Building, high above the city, one man still tries to answer the Universe’s persistent questions — Sy Moire, Physics Eye.

~~ Rich Olcott

Twinkle, Twinkle, Tabby’s Star

On By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Astronomy: Techniques, Uncategorized2 Comments

Al was carrying his coffee pot past our table.  “Refills?  Hey, I heard you guys talking about Tabby’s Star.  Have you seen the latest?”

“Ohmigawd, there’s more?”

“Yeah, Cathleen.  They’ve finally found something that’s periodic.”

“Catch us up, Al.  Cathleen said that the dimmings are irregular.”

“They’ve been, Sy.  But remember Cathleen’s chart that showed big dips in 2011 and 2013, about 750 days apart?  Well, guess what?”

“They’ve seen more dips at 750-day intervals, in 2015 and 2017.”

“Well, not quite.  Nobody was looking in 2015.  But Kickstarter funding let the team buy observing time in 2017.  A dip came in right on schedule.  Here’s the picture. [shows smartphone around]”

WTF 2017 peak after day 5
Visible-light photometry of Tabby’s Star
14-28 May 2017
Image from Dr Boyajian’s blog

Cathleen snorted.  “Damn shame we need crowd-funding to support Science these days.”

“True,” I agreed, “but the good news is that the support is there.  Suddenly you’re scribbling on the back of that envelope.  So what does this chart tell us?”

“I’m sure every astronomer out there will tell you, ‘It’s too soon to say anything for sure.‘  This is raw data, which means it’s hasn’t gone through the usual clean-up process to account for instrumental issues, long-term trending, things like that.  The timing is great, though.  The bottom of this dip is at 18May2017.  The first dip bottomed out 2267 days earlier on 4March2011.  Counting the 2015 case that no-one saw, there’d be three intervals from first to most recent.  2267÷3 makes the average 756 days.  Add 756 to the first date and we’re at 28Mar2013, right in the midst of that year’s complex mess.  It does fit together.”

“So whatever’s causing it has a 756-day orbit?”

“Could be.  I know your next question.  If the eclipsing material were in our Solar System, it’d be a bit outside the 687-day orbit of Mars.  But we’ve already ruled out causes near our solar system.  Tabby’s Star is about 1½ times our Sun’s mass.  That 756-day orbit around Tabby, if it is one, is maybe 30% wider than the orbit of Mars.  But.”

[both] “But?”

“But the dip profiles don’t match up from one cycle to the next.  This dip’s only 2% or so, a tenth of the ones in 2011 and 2013.  Of course, the 2013 event spanned multiple dips so Heaven knows which one we should match to.  Even 2011 and 2017 don’t look the same.  The usual quick-and-dirty way to compare dips is to pair up widths at half depth.  That statistic for 2011 is about a day.  This one is twice that or more.  If the absorber is orbiting the star, it’s changing shape and can’t be a planet.”Tabby in orbit
“So what do we got, Sy?”

“Damifino, Al.  Everything Cathleen just told us points to something like an enormous comet loaded with loose rocks that go flying along random paths away from the star.”

“Sorry, Sy, the infrared data rules out the comet dust that would have to be spewed out along with the rocks.  Besides, someone calculated just how much rocky material would be required to reproduce the dimming we’ve seen already.  You’d need a ‘comet’ somewhere between Earth-size and Jupiter-size, and maybe more than one, and with that much mass the rocks wouldn’t fly apart very well.  Oh, and there’s that long-term fading, which the comet idea doesn’t account for.”

“So we’re down to…”

[sigh] “The explanation of last resort, which astronomers are very reluctant to talk about because journalists tend to go overboard.  Maybe, just maybe, we’re witnessing an advanced civilization at work, constructing a Dyson sphere around a star 1500 light years away.  People have talked about such things for decades.  Think about it — the Sun sends out light in all directions.  Earth intercepts only a billionth of that.  If we could completely surround the Sun with solar panels we’d have access to a billion times more energy than if we covered our own planet with panels.  Better yet, it’s all renewable and producing 24 hours a day.  But even with advanced technology, panels around Tabby’s Star would still radiate in the infrared and we don’t see that.”

My smartphone chirped that same odd ringtone and it was that same odd number, 710-555-1701. “Hello, Ms Baird.”

“The Universe is not only stranger than you imagine, Mr Moire, it’s stranger than you can imagine.”

~~ Rich Olcott

Tabby’s Star — Weird Or Really Weird?

On By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

I needed some time to mull over what Cathleen had told me about Tabby’s Star, so I went to the counter to replenish our coffee and scones. When I returned I said, “OK, let’s recap.  Dr Boyajian’s Planet Hunters citizen scientists found a star that dims oddly.  But I understand there’s lots of variable stars out there.  What’s so special about this one that the SETI project got interested?”

“There’s variable stars and variable stars, but this one shouldn’t vary.  Look, one of the triumphs of 20th-century science is that we pretty much understand how stars work.  You tell me a handful of a star’s properties, things like radius, surface temperature, iron/hydrogen ratio, a couple more, and I can give you its whole life story from light-up to nova.  We’ve catalogued about 70,000 variable stars.  Virtually all of them do episodic brightening — pulsating or flaring up.  There’s about a hundred that dim more or less regularly, but they’re supergiants with cool, sooty atmospheres.  Tabby’s Star is a flat-out normal F-type main sequence star, about 1½ times the Sun’s mass and a little bit warmer.  Like the clean-cut kid next door — no reason to expect trouble from it.”

“So if it’s not the star itself that’s dimming, then something must be getting between it and us.”

“Well, yeah.  The question is what.  There’s so many theories that one pair of authors wrote a 15-page paper just classifying and rating them.”

“Gimme a few.”
Multi-Tabby Star

“Clouds of interstellar dust, for starters.  Sodium’s sparse in stars and the interstellar medium, but it’s got two easily recognized strong absorption lines in the yellow part of the visible spectrum.  Tabby’s sodium lines are broad and weak like you’d expect in a star’s atmosphere, but in the data they’re overlain by sharp, intense absorption peaks that can only come from sodium-bearing gas or dust in the nine-quadrillion-mile journey from there to here.  So there’s dispersed matter in the line of sight, but it can account for at most 35% of the dimming.  Furthermore, an interstellar cloud would have a hard time maintaining structures small enough to produce the sharp dim-and-recover pattern Boyajian found.  Loosely-bound stuff like dust clouds and gas tends to smear out in space.”

“How about comets, or rings, or clumps of asteroids orbiting the star?”

“There’s evidence against all those, but I guess I haven’t mentioned it yet.  You’ve seen the heat lamps over Eddie’s pizza bar?”

“Sure.  Infrared radiation heats things up.”

“And warm things give off infrared radiation.  ‘Warm’ meaning anything above absolute zero.  Better yet, there’s a well-known relation between an object’s temperature and its infrared spectrum.  Rocks or dust anywhere near the star would absorb energy from whatever kind of light and re-radiate it as heat infrared we could see.  The spectrum would show more infrared than you’d expect from the star itself.  And there isn’t any extra infrared.”

“None?”

“Not so’s our technology can detect.  If there’s any there, it’s less than 0.2% of the total coming from the star, nowhere near enough to account for those 8%, 16% and 22% dips.  So no, no comets or rings or asteroid clumps orbiting Tabby’s Star.”

“How about something orbiting our Sun, way far out where we’ve not found it yet?”

“Any light-blocking object near us, like maybe in the Oort Cloud that sends us long-term comets, should produce the same sort of weirdness from Tabby’s near neighbors.  We don’t see that.  One astronomer studied a star only 25 arc-seconds away — steady as a rock.  So whatever’s causing the dimming is probably close to Tabby’s star.  Oh, wait, here’s one more weirdness.  I just saw a report…” [twiddles on tablet] “Yeah, here it is.  Check out this chart.”Dimming montage“You’ll have to unravel that for me.”

“Sure.  The Planet Hunter team was looking for transits, which generally take at most a few days, so the Kepler science team filtered out slow variations before passing the data along.  After Boyajian’s report came out, two Keplerians looked back at the raw data.  I told you about the 3-6% dimming (estimates vary) since 1890.  The raw Kepler data show a 3% drop in four years!”

“I’m starting to think about Dyson Spheres and Larry Niven’s Ringworld.”

“Now you know why SETI got excited.”

~~ Rich Olcott

The Weirdest, And Naughtiest, Star in The Galaxy

On By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Astronomy: Techniques, UncategorizedLeave a comment

It was an interesting ringtone — aggressive but feminine, with a hint of desperation.  And it was a ringtone I hadn’t programmed into my phone.  The number was intriguing, too — 710-555-1701.  It didn’t add up, so I answered the ring. “Moire here.”

“Hello, Mr Moire, this is Victoria Baird.”

“It’s been a long time, Ms Baird.  What can I do for you?”  Her voice and the memory of her pointed ears sent chills down my spine.

“This time it’s what I can do for you, Mr Moire.  Here’s a tip — Tabby’s star.”  I could hear the italics.  I wanted to ask questions but the line went dead.

Considering the context, I called my Astronomy Department source.  “Morning, Cathleen.  It’s break time, can I buy you some of Al’s coffee and a scone?”

“You’re going to ask me questions, aren’t you?  What am I going to have to bone up on?  I know, it’s Tabby’s Star, right?”

“Got it in one, Cathleen.  Meet you at Al’s?”

“Yeah, give me 15 minutes.”Tabbystar 400

A quarter-hour later we had a table, two mugs of coffee and a plate of scones in front of us.  “So how’d you know I’d be asking about Tabby’s star?  And what is it?  And who is Tabby?”

“Tabby is Tabetha (she spells it with an ‘e’) Boyajian, PhD.  She teaches Astronomy at Louisiana State, does research specializing in high-precision star measurement.  In her spare time she manages a citizen-scientist project called Planet Hunters.  The Hunters get their kicks combing through databases from the Kepler satellite telescope.  They get all excited if the records indicate that a star’s been transited.”

“Oh, like that star-dimming that found the TRAPPIST-1 planets?”

“Exactly.  I think they’ve got over a hundred candidate planetary systems and a couple-dozen confirmed ones to their credit by now.  Anyhow, 2012 was a banner year for them, ’cause they raised an alert on what’s now being called the weirdest star in the galaxy.”

“Which would be Tabby’s Star.  Got it.  But what’s weird about it?”

“Poets like to write about ‘the constant stars.’  This star is world-champion not-constant.  You know how stars seem to flicker when you look at them?”

“Yeah, that’s how I tell them apart from planets.”

“Then you know that the flickering comes from starlight getting messed up going through our turbulent atmosphere.  Astronauts don’t see the flickering.  Neither does Kepler up there, so it can reliably detect miniscule variations in a star’s output.  Virtually all of the 150,000 stars it tracked for four years had rock-steady production.  A few of them occasionally dimmed or flared by maybe a percent, but Tabby’s Star (formally known as KIC 8462852) got the Hunters’ attention when it dimmed by 16%.”

“Twenty times a normal dimming!  Did it stay that way or did the light come back up again?”

“Oh, it came back all right, but the curve on the way up didn’t match the curve on the way down.  That was even weirder.  So the team scoured through the star’s 4-year record and found a dozen events on the 0.05-2% scale, plus one at 8% and another at 21%.”

“21%?  That’s a big shadow.”

“Ya think?  Especially since the between-event timing was seriously irregular and some of those events were complex with three or more separate components.  But that’s not all the weirdness. Those dips lasted for hours or even days, longer than most planetary transits.  After Boyajian and her 48 collaborators published their initial report, which has to have one of the naughtiest titles in the astronomical literature, some other —”

“Wait, a naughty title?  C’mon, don’t tease.”

“OK <sigh>.  The technical term for a star’s light output is flux.  That paper was half about the observations and half about what might be causing the variation.  Assuming the star’s real output is constant, the question becomes, ‘What happened to that missing light?‘  Or as the authors put it, ‘Where’s The Flux?‘  Since then both the paper and the star have been informally referred to as WTF.  OK?”

“OK <sigh>.  So you were saying there’s something else.”

“Yeah.  Some other astronomers went digging in the archives.  WTF has been dimming gradually for at least the past 100 years.  Weird, eh?”

“Yeah.  So what’s causing it?”

“We don’t even have good guesses.”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 2

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

Eddie came over to our table.  “Either you folks order something else or I’ll have to charge you rent.”  Typical Eddie.

“Banana splits sound good to you two?”

[Jeremy and Jennie] “Sure.”

“OK, Eddie, two banana splits, plus a coffee, black, for me.  And an almond biscotti.”

“You want one, that’s a biscotto.”

“OK, a biscotto, Eddie.  The desserts are on my tab.”

“Thanks, Mr Moire.”

“Thanks, Sy.  I know you want to get on to the third Peril on Jeremy’s Quest for black hole evaporation, but how does he get past the Photon Sphere?”

“Yeah, how?”

“Frankly, Jeremy, the only way I can think of is to accept a little risk and go through it really fast.  At 2/3 lightspeed, for instance, you and your two-meter-tall suit would transit that zero-thickness boundary in about 10 nanoseconds.  In such a short time your atoms won’t get much out of position before the electromagnetic fields that hold your molecules together kick back in again.”

“OK, I’ve passed through.  On to the Firewall … but what is it?”

“An object of contention, for one thing.  A lot of physicists don’t believe it exists, but some claim there’s evidence for it in the 2015 LIGO observations.  It was proposed a few years ago as a way out of some paradoxes.”

“Ooo, Paradoxes — loverly.  What’re the paradoxes then?”

“Collisions between some of the fundamental principles of Physics-As-We-Know-It.  One goes back to the Greeks — the idea that the same thing can’t be in two places at once.”

“Tell me about it.  Here’s your desserts.”

“Thanks, Eddie.  The place keeping you busy, eh?”

“Oh, yeah.  Gotta be in the kitchen, gotta be runnin’ tables, all the time.”

“I could do wait-staff, Mr G.  I’m thinking of dropping track anyway, Mr Moire, 5K’s don’t have much in common with base running which is what I care about.  How about I show up for work on Monday, Mr G?”

“Kid calls me ‘Mr’ — already I like him.  You’re on, Jeremy.”

“Woo-hoo!  So what’s the link between the Firewall and the Greeks?”

“Link is the right word, though the technical term is entanglement.  If you create two particles in a single event they seem to be linked together in a way that really bothered Einstein.”

“For example?”Astronaut and biscotti
“Polarizing sunglasses.  They depend on a light wave’s crosswise electric field running either up-and-down or side-to-side.  Light bouncing off water or road surface is predominately side-to-side polarized, so sunglasses are designed to block that kind.  Imagine doing an experiment that creates a pair of photons named Lucy and Ethel.  Because of how the experiment is set up, the two must have complementary polarizations.  You confront Lucy with a side-to-side filter.  That photon gets through, therefore Ethel should be blocked by a side-to-side filter but should go through an up-and-down filter.  That’s what happens, no surprise.  But suppose your test let Lucy pass an up-and-down filter.  Ethel would pass a side-to-side filter.”

“But Sy, isn’t that because each photon has a specific polarization?”

“Yeah, Jennie, but here’s the weird part — they don’t.  Suppose you confront Lucy with a filter set at some random angle.  There’s only the one photon, no half-way passing, so either it passes or it doesn’t.  Whenever Lucy chooses to pass, Ethel usually passes a filter perpendicular to that one.  It’s like Ethel hears from Lucy what the deal was — and with zero delay, no matter how far away the second test is executed.  It’s as though Lucy and Ethel are a single particle that occupies two different locations.  In fact, that’s exactly how quantum mechanics models the situation.  Quite contrary to the Greeks’ thinking.”

“You said that Einstein didn’t like entanglement, either.  How come?”

“Einstein published the original entanglement mathematics in the 30s as a counterexample against Bohr’s quantum mechanics.  The root of his relativity theories is that the speed of light is a universal speed limit.  If nothing can go faster than light, instantaneous effects like this can’t happen.  Unfortunately, recent experiments proved him wrong.  Somehow, both Relativity and Quantum Mechanics are right, even though they seem to be incompatible.”

“And this collision is why there’s a problem with black hole evaporation?”

“It’s one of the collisions.”

“There’s more?  Loverly.”

~~ Rich Olcott

How Many Ways Can You Look at The Sky?

On By rolcottIn Astronomy, Astronomy: Techniques, Mathematics, Uncategorized2 Comments

Cathleen and I were discussing her TRAPPIST-1 seminar in Al’s coffee shop when a familiar voice boomed over the room’s chatter.

“Hey, Cathleen, I got questions.”

“Vinnie?”

“Yeah, Sy, he hangs out with the Astronomy crew sometimes.  You know him, too, huh?”

“From way back.  Long story.”

“What’re your questions, Vinnie?”

“I missed the start of your talk, Cathleen, but why so much hype about this TRAPPIST-1 system?  We’ve already found 3,500 stars with planets, right, and some of them have several.  What’s so special here?”

“You’re right, Vinnie, Kepler-90 has seven planets, just like TRAPPIST-1. (brandishes a paper napkin)  But that star’s more than 60 times further from us than TRAPPIST-1 is.  It’s just too far away for us to be able to learn much more about the planets than their masses and orbital characteristics.  This new system’s only 40 lightyears away, close enough that we’ve got a hope of seeing what’s in the planetary atmospheres.”

(another paper napkin)  “That ties in with the second thing that’s special.  The star’s surface temperature, 2550ºK, is so low that even though its planets orbit very close in, three of them are probably in the Goldilocks Zone.  They’re not too hot and not too cold for liquid water to exist on their surface.  IF there’s liquid water on one of them and IF there’s something living there, we should be able to detect traces of that biochemistry in the planet’s atmosphere.”

Star demographics
Observational data (dots) and four different models
of star count (vertical axis) versus temperature.
Hotter stars are to the left.

(napkin #3)  “The third special thing is that TRAPPIST-1 is the first-known planet-hosting star in its category — ultra-cool dwarf stars burning below 2700°K.  Finding those stars is hard — they’re small and dim.  No-one really knows how many there are compared to the other categories.  Some models say they should be rare, other models suggest they could be as common as G-type stars like our Sun.  IF there’s lots of ultra-cool dwarfs and IF they generally have planets like G-type stars do, then the category’s a new prime target for exoplanet hunters seeking life-signs.”

“Why’s that?”

“Because it’s easier to spot a small planet around a small star than around a big one.  Transits across TRAPPIST-1 dim its light by 1% or so.  A TRAPPIST-1 planet transiting our Sun would dim it by 1/100th of that.  The same problem hinders planet-finding methods fishing for stars that wobble because a planet’s orbiting around it.”

“Alright, I get that TRAPPIST-1 is special.  My other question is, I heard the part of your talk where you figured the odds on seeing its transits, but you lost me with the word steradian.  My dictionary says that’s an area on a sphere divided by the square of the sphere’s radius. What would that get me?  Where’d your numbers come from?”

“You need one additional piece of information.  If you take any sphere’s total surface area and divide that by r², you’ll always get 4π steradians.  You can use that to convert between absolute surface area and fraction of the sphere.  Mmm…  Sy, you own some land outside of town, yes?”

“A little.”

“And you have mineral rights?”

“Oh, yeah, that’s why I bought it.”

“And they go how far down?”

“All the way to the center of the Earth.”

“So your claim’s actually a pyramid 6370 kilometers deep.  When I moved here I learned it’s impolite to ask how much land someone has.  For round numbers I’ll assume 40 acres, which is about 1,000 square meters.  (tapping keys on her smartphone)  The Earth’s radius is 6.37×106 meters, so Sy’s claim is 1,000/(6.37×106)2 = 2.47×10-11 steradians.  Divide 4π by that and you get … 5.08×1011.  So Earth’s entire surface has room for 5.08×1011 patches matching Sy’s.  Visualize 5.08×1011 pyramids pointing in every direction from Earth’s center.  Now extend each pyramid outward to define a separate patch of sky.  Got that picture, Vinnie?”viewing cones

“Sort of.”

“TRAPPIST-1 is 3.74×1017 meters away.  TRAPPIST-1h’s orbit is a near-circle whose radius is 9.45×109 meters.  It covers π(9.45×109)2/(3.74×1017)2 = 2.00×10-15 steradians on a sphere centered on us. Divide 4π by 2.00×10-15 …  6.27×1015 sky-patches the size of TRAPPIST-1h’s orbit.  They had to pick the right patch to find TRAPPIST-1.”

“Long odds.”

“Yep.”

~~ Rich Olcott

The Luck o’ The (insert nationality here)

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

“Afternoon, Al.  What’s the ruckus in the back room?”

“Afternoon, Sy.  That’s the Astronomy crew and their weekly post-seminar coffee-and-critique session.  This time, though, they brought their own beer.  You know I don’t have a beer license, just coffee, right?  Could you go over there and tell ’em to keep it covered so I don’t get busted?”

“Sure, Al.  … Afternoon, folks.  What’s all the happy?”

“Hey, Sy, welcome to the party.  Trappist beer, straight from Belgium!”

“Don’t mind if I do, Cathleen, but Al sure would like for you to put that carton under the table.  Makes him nervous.”

“Sure, no problem.”

“Thanks.  I gather your seminar was about the new seven-planet system.  How in the world do the Trappists connect to that story?”

“Patriotism.  The find was announced by a team from Belgium’s University of Liege.  They’ve built a pair of robotic telescopes tailored for seeking out rocks and comets local to our Solar System.  Exoplanets, too.  Astronomers love tying catchy acronyms to their projects.  This group’s proudly Belgian so they called their robots TRAnsiting Planets and Planetesimals Small Telescopes, ergo TRAPPIST, to honor the country’s 14 monasteries.  And their beer.  Mainly the beer, I’ll bet.”

“So the planets are a Belgian discovery?”

“Well, the lead investigator, Michaël Gillon, is at Liege, and so are half-a-dozen of his collaborators.  Their initial funding came from the Belgian government.  But by the time the second paper came out, the one that claimed a full seven planets spanning a new flavor of Goldilocks Zone, they’d pulled in support and telescope time from over a dozen other countries — USA, India, UK, France, Morocco, Saudi Arabia… the list goes on.  So it’s Belgian mostly but not only.”

“I love international science.  Next question — I see the planets are listed as TRAPPIST-1b, TRAPPIST-1c, and so on up to TRAPPIST-1h.  What happened to TRAPPIST-1a?”

“Rules of nomenclature, Sy.  TRAPPIST-1a is the star itself.  Actually, the star already had a formal name, which I just happen to have written down in my seminar notes somewhere … here it is, 2MASS J23062928 – 0502285.  You can see why TRAPPIST-1 is more popular.”

“I’m not even going to ask how that other name unwinds.  So what was the seminar topic this week?”

7 planets
TRAPPIST-1’s planets,
drawn to scale against their star. The
green ones are in the Goldilocks Zone.

“The low probability for us ever noticing those planets blocking the star’s light.”

“I’d think seeing a star winking on and off like it’s sending Morse code would attract attention.”

“That’s not close to what it was doing.  It’s all about the scale.  You know those cartoons that show planets together with their host sun?”

(showing her my smartphone) “Like this one?”

“Yeah.  It’s a lie.”

“How is it lying?”

“It pretends they’re all right next to the star.   7 planets perspectiveThis image is a little better.”  (showing me her phone)  “This artist at least tried to build in some perspective.  Even in this tiny solar system, about 1/500 the radius of ours, the star’s distance to each planet is hundreds to a thousand times the size of the planet.  You just can’t show planets AND their orbits together in a linear diagram.  Now, think about how small these planets are compared to their sun.”

“Aaaa-hah!   When there’s an eclipse, only a small fraction of the light is blocked.”

“That’s part of it.  Each eclipse (we call them transits) dims the measured brightness by only a percent or so.  But it’s worse than that.”

eclipses“How so?”

“All those orbits lie in a single plane.  We can’t see the transits unless our position lines up with that plane.  If we’re as little as 1½° out of the plane, we miss them.  But it’s worse than that.”

“How so?”

“During a transit, each planet casts a conical shadow that defines a patch in TRAPPIST-1’s sky.  You can tile TRAPPIST-1’s sky with about 150,000  patches that size.  There’s one chance in 150,000 of being in the right patch to see that 1% dimming.  In our sky there are over 6×1015 patches the size of TRAPPIST-1h’s orbit.  The team had to inspect the just right patch to find it.”

“With odds like that, no wonder TRAPPIST uses robots.”

“Yep.”

~~ Rich Olcott

The New System’s in Tune

On By rolcottIn Astronomy: Stellar Science, UncategorizedLeave a comment

<We interrupt our running story line to bring you this important development…>

“Morning, Sy.  What can I get you?”

“My usual mugfull of black, Al.  What’s the Scone-of-The-Day?”

“I’m calling this The Trappist.  It’s got raspberry jam!”

“Why that name?”

“In honor of TRAPPIST-1, you know, that star they just found a bunch of planets around.”

“Your coffee shop being right next to the Astronomy building, I guess you’ve heard a lot about it.”

“Sy, you couldn’t believe.  The planetologists are going nuts of course, even though no-one’s actually seen the planets, and the astrometrics folks are lining up for telescope time ’cause they’ve got a whole new class of stars to monitor and of course the astrophysicists get to figure out how the system even works.”

“Astrometrics folks?  New class of stars?”

“Yeah, the high-precision star-measurers.  They didn’t used to pay attention to the small, dim stars because why bother.  But now … woo-hoo, whole new ballgame.”

“Nobody’s seen those planets?  How do they know they’re there?”

“Process of elimination, Sy.  The TRAPPIST telescopes picked up repetitive dark blips in the light coming from that star.  It’s a close, fast-moving star so there’s no sense supposing it’s like going behind or in front of a regular array of rocks or stars or something.  It’s not wobbling side-to-side like it would if it was a binary so it’s not traveling along with another star.  If the blips were sunspots going around as the star rotates there’d be only one rhythm, but these blips come in too complicated for that.  Besides, the star’s low-activity, too cool for lotsa sunspots.  Gotta be planets eclipsing it.”

trappist-1-system-450
NASA’s artistic (and cute) rendition
of the TRAPPIST-1 system
Note the close-in steam and the frost further out

“Sounds pretty good, but…”

“Hey Sy, there was something else, maybe you could explain it.  One astrophysics guy was real impressed that the planets had residences.  I didn’t understand that.”

“Residences?  That’s a new one on me.”

“Had something to do with the blip periods.  Yeah, here’s the paper napkin he wrote ’em all down on.”

Object
TRAPPIST-1x
Period, days
Resonance
Actual /
Expected
b
1.51
c
2.42
5c:8b
1.002
d
4.05
3d:5c
1.004
e
6.10
2e:3d
1.004
f
9.20
2f:3e
1.006
g
12.35
3g:4f
1.007
h
20?
5h:8g
1.012?

“Oh, resonances! That I recognize, and yeah, those numbers are much more convincing.  Remember my post about gear logic?”

“Sorry, Sy, that must’ve been a long time ago and who has time to read?”

“I understand.  OK, that post explained how planets that survive the early chaos of a forming solar system tend to wind up in orbits whose relative year-lengths form ratios of small whole numbers.  In our system, for instance, the length of Pluto’s year is exactly 3/2 of Neptune’s, Neptune’s year is twice that of Uranus, and so on.  If a planet doesn’t synch up with its neighbors, it’ll collide with someone or be flung out of the system.  Put another way, a system’s not stable if its planetary orbit periods are just any old numbers.  Make sense?”

“I suppose, so…?”

“So look at this guy’s table.  The periods of each pair of adjacent objects follow that rule almost exactly.  Five times c‘s period is less than 0.25% away from eight times b‘s, and so on all the way out to h, which I take it has an uncertain period because the guy put in that question mark.  In fact, I think this system follows the rule more tightly than our Solar System does.  As far as I’m concerned that regularity in the periods makes the case for TRAPPIST-1 having planets.  You hear anything else?”

“Yeah, there was a lot of excitement about the middle three planets being in some kind of Goldilocks zone.  What’s that about?”

“Hah, I’d be excited, too.  If a planet’s too close to the star, like Mercury is to ours, it’ll be too hot for liquid water.  If the planet’s too far, any water it has would be frozen stiff.  Either way, not good for life to grow there.  In the Goldilocks zone, it’s…”

“Just right, huh, Sy?”

“On the nose, Al.  I’m going to have to read up on TRAPPIST-1.”

~~ Rich Olcott

Three Body Problems

On By rolcottIn Astronomy: Stellar Science, Gravitational astronomy, Physics: Black Holes and Relativity, UncategorizedLeave a comment

The local science museum had a showing of the Christopher Nolan film Interstellar so of course I went to see it again.  Awesome visuals and (mostly) good science because Nolan had tapped the expertise of Dr Kip Thorne, one of the primary creators of LIGO.  On the way out, Vinnie collared me.

“Hey, Sy, ‘splain something to me.”

“I can try, but first let’s get out of the weather.  Al’s coffee OK with you?”

“Yeah, sure, if his scones are fresh-baked.”

Al saw me walking in.  “Hey, Sy, you’re in luck, I just pulled a tray of cinnamon scones out of the oven.”  Then he saw Vinnie.  “Aw, geez, there go my paper napkins again.”

Vinnie was ready.  “Nah, we’ll use the backs of some ad flyers I grabbed at the museum.  And gimme, uh, two of the cinnamons and a large coffee, black.”

“Here you go.”

At our table I said, “So what’s the problem with the movie?”

“Nobody shrank.  All this time we been talking about how things get smaller in a strong gravity field.  That black hole, Gargantua, was huge.  The museum lecture guy said it was like 100 million times as heavy as the Sun.  When the people landed on its planet they should have been teeny but everything was just regular-size.  And what’s up with that ‘one hour on the planet is seven years back home’ stuff?”

“OK, one thing at a time.  When the people were on the planet, where was the movie camera?”

“On the planet, I suppose.”

“Was the camera influenced by the same gravitational effects that the people were?”

“Ah, it’s the frames thing again, ain’t it?  I guess in the on-planet inertial frame everything stays the relative size they’re used to, even though when we look at the planet from our far-away frame we see things squeezed together.”

(I’ve told you that Vinnie’s smart.)  “You got it.  OK, now for the time thing.  By the way, it’s formally known as ‘time dilation.’  Remember the potential energy/kinetic energy distinction?”

“Yeah.  Potential energy depends on where you are, kinetic energy depends on how you’re moving.”

“Got it in one.  It turns out that energy and time are deeply intertwined all through physics.  Would you be surprised if I told you that there are two kinds of time dilation, one related to gravitational potential and the other to velocity?”

“Nothing would surprise me these days.  Go on.”

“The gravity one dropped out of Einstein’s Theory of Special Relativity.  The velocity one arose from his General Relativity work.”  I grabbed one of those flyers.  “Ready for a little algebra?”

“Geez.  OK, I asked for it.”gargantua-3
“You certainly did.  I’ll just give you the results, and mind you these apply only near a non-rotating sphere with no electric charge.  Things get complicated otherwise.  Suppose the sphere has mass M and you’re circling around it at a distance r from its geometric center.  You’ve got a metronome ticking away at n beats per your second and you’re perfectly happy with that.  We good?”

“So far.”

“I’m watching you from way far away.  I see your metronome running slow, at only n√[1-(2 G·M/r·c²)] beats per my second.  G is Newton’s gravity constant, c is the speed of light.  See how the square root has to be less than 1?”

“Your speed of light or my speed of light?”

“Good question, considering we’re talking about time and space getting all contorted, but Einstein guarantees that both of us measure exactly the same speed.  So anyway, in the movie both the Miller’s Planet landing team and that poor guy left on good ship  Endurance are circling Gargantua.  Earth observers would see both their clocks running slow.  But Endurance is much further out (larger r, smaller fraction) from Gargantua than Miller’s Planet is.  Endurance’s distance gave its clock more beats per Earth second than the planet gets, which is why the poor guy aged so much waiting for the team to return.”

“I wondered about that.”

Then we heard Ramona’s husky contralto.  “Hi, guys.  Al said you were back here talking physics.  Who wants to take me dancing?”

We both stood up, quickly.

“Whee, this’ll be fun.”

~~ Rich Olcott

Gravity’s Real Rainbow

On By rolcottIn Astronomy: Multi-messenger, Astronomy: Stellar Science, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Waves, UncategorizedLeave a comment

Some people are born to scones, some have scones thrust upon them.  As I stepped into his coffee shop this morning, Al was loading a fresh batch onto the rack.  “Hey, Sy, try one of these.”

“Uhh … not really my taste.  You got any cinnamon ones ready?”

“Not much for cheddar-habañero, huh?  I’m doing them for the hipster trade,” waving towards all the fedoras on the room.  “Here ya go.  Oh, Vinnie’s waiting for you.”

I navigated to the table bearing a pile of crumpled yellow paper, pulled up a chair.  “Morning, Vinnie, how’s the yellow writing tablet working out for you?”

“Better’n the paper napkins, but it’s nearly used up.”

“What problem are you working on now?”

“OK, I’m still on LIGO and still on that energy question I posed way back — how do I figure the energy of a photon when a gravitational wave hits it in a LIGO?  You had me flying that space shuttle to explain frames and such, but kept putting off photons.”

“Can’t argue with that, Vinnie, but there’s a reason.  Photons are different from atoms and such because they’ve got zero mass.  Not just nearly massless like neutrinos, but exactly zero.  So — do you remember Newton’s formula for momentum?”

“Yeah, momentum is mass times the velocity.”

“Right, so what’s the momentum of a photon?”

“Uhh, zero times speed-of-light.  But that’s still zero.”

“Yup.  But there’s lots of experimental data to show that photons do carry non-zero momentum.  Among other things, light shining on an an electrode in a vacuum tube knocks electrons out of it and lets an electric current flow through the tube.  Compton got his Nobel prize for that 1923 demonstration of the photoelectric effect, and Einstein got his for explaining it.”

“So then where’s the momentum come from and how do you figure it?”

“Where it comes from is a long heavy-math story, but calculating it is simple.  Remember those Greek letters for calculating waves?”

(starts a fresh sheet of note paper) “Uhh… this (writes λ) is lambda is wavelength and this (writes ν) is nu is cycles per second.”

“Vinnie, you never cease to impress.  OK, a photon’s momentum is proportional to its frequency.  Here’s the formula: p=h·ν/c.  If we plug in the E=h·ν equation we played with last week we get another equation for momentum, this one with no Greek in it:  p=E/c.  Would you suppose that E represents total energy, kinetic energy or potential energy?”

“Momentum’s all about movement, right, so I vote for kinetic energy.”

“Bingo.  How about gravity?”

“That’s potential energy ’cause it depends on where you’re comparing it to.”

light-in-a-gravity-well“OK, back when we started this whole conversation you began by telling me how you trade off gravitational potential energy for increased kinetic energy when you dive your airplane.  Walk us through how that’d work for a photon, OK?  Start with the photon’s inertial frame.”

“That’s easy.  The photon’s feeling no forces, not even gravitational, ’cause it’s just following the curves in space, right, so there’s no change in momentum so its kinetic energy is constant.  Your equation there says that it won’t see a change in frequency.  Wavelength, either, from the λ=c/ν equation ’cause in its frame there’s no space compression so the speed of light’s always the same.”

“Bravo!  Now, for our Earth-bound inertial frame…?”

“Lessee… OK, we see the photon dropping into a gravity well so it’s got to be losing gravitational potential energy.  That means its kinetic energy has to increase ’cause it’s not giving up energy to anything else.  Only way it can do that is to increase its momentum.  Your equation there says that means its frequency will increase.  Umm, or the local speed of light gets squinched which means the wavelength gets shorter.  Or both.  Anyway, that means we see the light get bluer?”

“Vinnie, we’ll make a physicist of you yet.  You’re absolutely right — looking from the outside at that beam of photons encountering a more intense gravity field we’d see a gravitational blue-shift.  When they leave the field, it’s a red-shift.”

“Keeping track of frames does make a difference.”

Al yelled over, “Like using tablet paper instead of paper napkins.”

~~ Rich Olcott