A Three-dog Night Would Be So Cool

“So we’ve got three fundamentally different messengers from the stars, Mr Feder.  The past couple of years have given us several encouraging instances of receiving two messengers from the same event.  If we ever receive all three messengers from the same event, that might give us what we need to solve the biggest problem in modern physics.”

“That’s a pretty deep statement, Moire.  Care to unpack it?  The geese here would love to hear about it.”

“Lakeside is a good place for thoughts like this.  The first messenger was photons.  We’ve been observing starlight photons for tens of thousand of years.  Tycho Brahe and Galileo took it to a new level a few centuries ago with their careful observation, precision measurements and Galileo’s telescope.”

“That’s done us pretty good, huh?”

“Oh sure, we’ve charted the heavens and how things move, what we can see of them.  But our charts imply there’s much we can’t see.  Photons only interact with electric charge.  Except for flat-out getting absorbed if the wavelength is right, photons don’t care about electrically neutral material and especially they don’t care about dark matter.”

“So that’s why we’re interested in the other messengers.”

“Exactly.  Even electrically neutral things have mass and interact with the gravitational field.  You remember the big news a few years ago, when our brand-new LIGO instruments caught a gravitational wave signal from a couple of black holes in collision.  Black holes don’t give off photons, so the gravitational wave messenger was our only way of learning about that event.”

“No lightwave signal at all?”

“Well, there was a report of a possible gamma-ray flare in that patch of sky, but it was borderline-detectable.  No observatory using lower-energy light saw anything there.  So, no.”

“You’re gonna tell me and the geese about some two-messenger event now, right?”

“That’s where I’m going, Mr Feder.  Photons first.  Astronomers have been wondering for decades about where short, high-energy gamma-ray bursts come from.  They seem to happen randomly in time and space.  About a year ago the Fermi satellite’s gamma-ray telescope detected one of those bursts and sent out an automated ‘Look HERE’ alert to other observatories.  Unfortunately, Fermi‘s resolution isn’t wonderful so its email pointed to a pretty large patch of sky.  Meanwhile back on Earth and within a couple of seconds of Fermi‘s moment, the LIGO instruments caught an unusual gravitational wave signal that ran about a hundred times slower than the black-hole signals they’d seen.  Another automated ‘Look HERE’ alert went out.  This one pointed to a small portion of that same patch of sky.  Two messengers.”

“Did anyone find anything?”

“Seventy other observatories scrutinized the overlap region at every wavelength known to Man.  They found a kilonova, an explosion of light and matter a thousand times brighter than typical novae.  The gravitational wave evidence indicated a collision between two neutron stars, something that had never before been recorded.  Photon evidence from the spewed-out cloud identified a dozen heavy elements theoreticians hadn’t been able to track to an origin.  Timing details in the signals gave cosmologists an independent path to resolving a problem with the Hubble Constant.  And now we know where those short gamma-ray bursts come from.”

“Pretty good for a two-messenger event.  Got another story like that?”

“A good one.  This one’s neutrinos and photons, and the neutrinos came in first.  One neutrino.”

One neutrino?”

“Yup, but it was a special one, a super-high-powered neutrino whose incoming path our IceCube observatory could get a good fix on.  IceCube sent out its own automated ‘Look HERE’ alert.  The Fermi team picked up the alert and got real excited because the alert’s coordinates matched the location of a known and studied gamma-ray source.  Not a short-burster, but a flaring blazar.  That neutrino’s extreme energy is evidence for blazars being one of the long-sought sources of cosmic rays.”

“Puzzle solved, maybe.  Now what you said about a three-messenger signal?”grebe messenger pairs“Gravitational waves are relativity effects and neutrinos are quantum mechanical.  Physicists have been struggling for a century to bridge those two domains.  Evidence from a three-messenger event could provide the final clues.”

“I’ll bet the geese enjoyed hearing all that.”

“They’re grebes, Mr Feder.”

~~ Rich Olcott

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“Hot Jets, Captain Neutrino!”

“Hey, Cathleen, while we’re talking IceCube, could you ‘splain one other thing from that TV program?”

“Depends on the program, Al.”

“Oh, yeah, you weren’t here when we started on this.  So I was watching this program and they were talking about neutrinos and how there’s trillions of them going through like my thumbnail every second and then IceCube saw this one neutrino that they’re real excited about so what I’m wondering is, what’s so special about just that neutrino? How do they even tell it apart from all the others?”

“How about the direction it came from, Cathleen?  We get lotsa neutrinos from the Sun and this one shot in from somewhere else?”

“An interesting question, Vinnie.  The publicity did concern its direction, but the neutrino was already special.  It registered 290 tera-electron-volts.”

“Ter-what?”

“Sorry, scientific shorthand — tera is ten-to-the-twelfth.  A million electrons poised on a million-volt gap would constitute a Tera-eV of potential energy.  Our Big Guy had 290 times that much kinetic energy all by himself.”

“How’s that stack up against other neutrinos?”

“Depends on where they came from.  Neutrinos from a nuclear reactor’s uranium or plutonium fission carry only about 10 Mega-eV, wimpier by a factor of 30 million.  The Sun’s primary fusion process generates neutrinos peaking out at 0.4 MeV, 25 times weaker still.”

“How about from super-accelerators like the LHC?”

“Mmm, the LHC makes TeV-range protons but it’s not designed for neutrino production.  We’ve got others that have been pressed into service as neutrino-beamers. It’s a complicated process — you send protons crashing into a target.  It spews a splatter of pions and K-ons.  Those guys decay to produce neutrinos that mostly go in the direction you want.  You lose a lot of energy.  Last I looked the zippiest neutrinos we’ve gotten from accelerators are still a thousand times weaker than the Big Guy.”

I can see the question in Vinnie’s eyes so I fire up Old Reliable again.  Here it comes… “What’s the most eV’s it can possibly be?”  Good ol’ Vinnie, always goes for the extremes.

“You remember the equation for kinetic energy?”

“Sure, it’s E=½ m·v², learned that in high school.”

“And it stayed with you.  OK, and what’s the highest possible speed?”

“Speed o’ light, 186,000 miles per second.”

“Or 300 million meters per second, ’cause that’s Old Reliable’s default setting.  Suppose we’ve got a neutrino that’s going a gnat’s whisker slower than light.  Let’s apply that formula to the neutrino’s rest mass which is something less than 1.67×10-36 kilograms…”Speedy neutrino simple calculation“Half an eV?  That’s all?  So how come the Big Guy’s got gazillions of eV’s?”

“But the Big Guy’s not resting.  It’s going near lightspeed so we need to apply that relativistic correction to its mass…Speedy neutrino relativistic calculation“That infinity sign at the bottom means ‘as big as you want.’  So to answer your first question, there isn’t a maximum neutrino energy.  To make a more energetic neutrino, just goose it to go even closer to the speed of light.”

“Musta been one huge accelerator that spewed the Big Guy.”

“One of the biggest, Al.”  Cathleen again.  “That’s the exciting thing about what direction the particle came from.”

“Like the North Pole or something?”

“Much further away, much bigger and way more interesting.  As soon as IceCube caught that neutrino signal, it automatically sent out a “Look in THIS direction!” alert to conventional observatories all over the world.  And there it was — a blazar, 5.7 billion lightyears away!”

“Wait, Cathleen, what’s a blazar?”

“An incredibly brilliant but highly variable photon source, from radio frequencies all the way up to gamma rays and maybe cosmic rays.  We think the thousands we’ve catalogued are just a fraction of the ones within range.  We’re pretty sure that each of them depends on a super-massive black hole in the center of a galaxy.  The current theory is that those photons come from an astronomy-sized accelerator, a massive swirling jet that shoots out from the central source.  When the jet happens to point straight at us, flash-o!”

Duck!

“I wouldn’t worry about a neutrino flood.  The good news is IceCube’s signal alerted astronomers to check TXS 0506+056, a known blazar, early in a new flare cycle.”

“An astrophysical fire alarm!”

~~ Rich Olcott

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

The Biggest Telescope in The Universe

Vinnie rocks back in his chair.  “These gravitational lenses, Cathleen.  How do you figure their apertures and f-numbers, space being infinite and all?”

She takes a breath to answer, but I cut in.  “Whoa, I never got past a snapshot camera.  How about you explain Vinnie’s question before you answer it?”Bird and lenses

“You’re right, Sy, most people these days just use their cellphone camera and have no clue about what it does inside.  Apertures and f-numbers are all just simple geometry.  Everything scales with the lens’ focal length.”

“That’s how far away something is that you’re taking a picture of?”

“No, it’s a characteristic of the lens itself.  It’s the distance between the midpoint of the lens and its focal plane, which is where you’d want to put the sensor chip or film in a camera.  The aperture is the diameter of the light beam entering the lens.  The optimal aperture, the image size, even the weight of the lens, all scale to the lens focal length.”

“I can see image size thing — the further back the focal plane, the bigger the image by the the time it gets there.  It’s like a lever.”

“Sort of, Vinnie, but you’ve got the idea.”

“The aperture scales to focal length?  I’d think you could make a lens with any diameter you like.”

“Sure you could, Sy, but remember you’d be using a recording medium of some sort and it’s got an optimum input level.  Too much light and you over-expose, too little and you under-expose.  To get the right amount of light when you take the shot the aperture has to be right compared to the focal length.”

“Hey, so that’s the reason for the old ‘Sunny 16‘ rule.  Didn’t matter if I had a 35mm Olympus or a big ol’ Rollei, if it was a sunny day I got good pictures with an f/16 aperture.  ‘Course I had to balance the exposure time with the film’s speed rating but that was easy.”

“Exactly, Vinnie.  If I remember right, the Rollei’s images were about triple the size of the little guy’s.  Tripled focal length meant tripled lens size.  You could use the same speed-rated film in both cameras and use the same range of f-stops.  The rule still works with digital cameras but you need to know your sensor’s ISO rating.”

“Ya got this, Sy?  Can we move on to Cathleen’s gravity lenses?”

“Sure, go ahead.”

“Well, they’re completely different from … I’ll call them classical lenses. That kind has a focal plane and a focal length and an aperture and only operates along one axis.  Gravitational lenses have none of that, but they have an infinite number of focal lines and rings.”

Gravitational lens and galaxy“Infinite?”

“At least in principle.  Any observation point in the Universe has a focal line running to a massive object’s center of gravity.  At any point along the line, you could look toward an object and potentially see all or part of a ring composed of light from some bright object behind it.  Einstein showed that a completed ring’s  visual angle depends on the deflector’s mass and the three distances between the observer, the deflector and the bright object.”

“The way you said that, there could be a bunch of rings.”

“Sure, one for each bright object shining onto the lens.  For that matter, the deflector itself could be complex — the gravity of a whole cluster of galaxies rather than the single black hole we’ve been assuming as an example.”

“That diagram reminds me of Galileo’s telescope, just a three-foot tube with an objective lens at the far end and an eyepiece lens to look through.  But it was enough to show him the rings of Saturn and the moons of Jupiter.”

“Right, Sy.  His objective lens was maybe a couple of inches across.  If its focal point was halfway down the tube, his scope’s light-gathering power would match an f/9 camera lens.  Gravitational lenses don’t have apertures so not an issue.”

“So here we are like Galileo, with a brand new kind of telescope.”

“Poetic, Vinnie, and so right.  It’s already shown us maybe the youngest galaxy, born 13 billion years ago.  We’re just getting started.”

~~ Rich Olcott

The Fellowship of A Ring

Einstein ring 2018

Hubble photo from NASA’s Web site

Cathleen and I are at a table in Al’s coffee shop, discussing not much, when Vinnie comes barreling in.  “Hey, guys.  Glad I found you together.  I just saw this ‘Einstein ring’ photo.  They say it’s some kind of lensing phenomenon and I’m thinking that a lens floating out in space to do that has to be yuuuge.  What’s it made of, and d’ya think aliens put it there to send us a message?”

Astronomer Cathleen rises to the bait.  I sit back to watch the fun.  “No, Vinnie, I don’t.  We’re not that special, the rings aren’t signals, and the lenses aren’t things, at least not in the way you’re thinking.”

“There’s more than one?”

“Hundreds we know of so far and it’s early days because the technology’s still improving.”

“How come so many?”

“It’s because of what makes the phenomenon happen.  What do you know about gravity and light rays?”

Me and Sy talked about that a while ago.  Light rays think they travel in straight lines past a heavy object, but if you’re watching the beam from somewhere else you think it bends there.”

I chip in.  “Nice summary, good to know you’re storing this stuff away.”Gravitational lens 1

“Hey, Sy, it’s why I ask questions is to catch up.  So go on, Cathleen.”

She swings her laptop around to show us a graphic.  “So think about a star far, far away.  It’s sending out light rays in every direction.  We’re here in Earth and catch only the rays emitted in our direction.  But suppose there’s a black hole exactly in the way of the direct beam.”

“We couldn’t see the star, I get that.”

“Well, actually we could see some of its light, thanks to the massive black hole’s ray-bending trick. Rays that would have missed us are bent inward towards our telescope.  The net effect is similar to having a big magnifying lens out there, focusing the star’s light on us.”

“You said, ‘similar.’  How’s it different?”Refraction lens

“In the pattern of light deflection.  Your standard Sherlock magnifying lens bends light most strongly at the edges so all the light is directed towards a point.  Gravitational lenses bend light most strongly near the center.  Their light pattern is hollow.  If we’re exactly in a straight line with the star and the black hole, we see the image ‘focused’ to a ring.”

“That’d be the Einstein ring, right?”

“Yes, he gets credit because he was the one who first set out the equation for how the rays would converge.  We don’t see the star, but we do see the ring.  His equation says that the angular size of the ring grows as the square root of the deflecting object’s mass.  That’s the basis of a widely-used technique for measuring the masses not only of black holes but of galaxies and even larger structures.”

“The magnification makes the star look brighter?”

“Brighter only in the sense that we’re gathering photons from a wider field then if we had only the direct beam.  The lens doesn’t make additional photons, probably.”

Suddenly I’m interested.  “Probably?”

“Yes, Sy, theoreticians have suggested a couple of possible effects, but to my knowledge there’s no good evidence yet for either of them.  You both know about Hawking radiation?”

“Sure.”

“Yup.”

“Well, there’s the possibility that starlight falling on a black hole’s event horizon could enhance virtual particle production.  That would generate more photons than one would expect from first principles.  On the other hand, we don’t really have a good handle on first principles for black holes.”

“And the other effect?”

“There’s a stack of IFs under this one.  IF dark matter exists and if the lens is a concentration of dark matter, then maybe photons passing through dark matter might have some subtle interaction with it that could generate more photons.  Like I said, no evidence.”

“Hundreds, you say.”

“Pardon?”

“We’ve found hundreds of these lenses.”

“All it takes is for one object to be more-or-less behind some other object that’s heavy enough to bend light towards us.”

“Seein’ the forest by using the trees, I guess.”

“That’s a good way to put, it, Vinnie.”

~~ Rich Olcott

RIP, Dr Hawking

Today I depart from my normal schedule and the current story line and science line.  A giant has left us and I want to pay proper tribute.

Dr Stephen Hawking enjoyed telling people of his fortunate birth date, exactly 300 years after Galileo Galilei passed away.  He liked a good joke, and I think he’d be tickled with this additional connection to the man whose work made Hawking’s work possible:
RIP Hawking

The equation in the center of this cut is Hawking’s favorite result, which he wanted to be carved on his gravestone.  It links a black hole’s entropy (S) to its surface area (A).  The other letters denote a collection of constants that have been central to the development of theoretical Physics over the past century and a half:

  • k is Boltzmann’s constant, which links temperature with kinetic energy
  • c is the speed of light, the invariance of which led Einstein to Relativity
  • G is Newton’s universal gravitational constant
  • h is Planck’s constant, the “quantum of action”

Hawking spent much of his career thinking deeply about the implications of Einstein’s concepts.  Newton’s equations support excellent descriptions of everyday physical motions, from the fall of raindrops to the orbits of solar systems.  Einstein’s equations led to insights about conditions at the most extreme — velocities near lightspeed, masses millions of times the Sun’s but packed into a volume only a few dozen miles wide.

But Hawking also pondered extremes of the ultimately large and the ultimately small — the edge of the Universe and distances far smaller than atomic nuclei.  Because his physical condition prohibited speech or quick jottings, he was forced to develop extraordinary powers of concentration and visualization that enabled him to encapsulate in a few phrases insights that would take others books to develop and communicate.

Hawking wrote books, too, of course, of a quality and clarity that turned his name and Science into watchwords for the general public as well as the physics community.  By his life and how he lived it he was an inspiration to many, abled and otherwise.  Science needs its popularizers, though some in the field deprecate them as hangers-on.  Hawking managed to bridge that gap with ease and grace, a giant with standing on either side.

Requiescat in pace, Dr Hawking.  Thank you.

~~ Rich Olcott

Gravity from Another Perspective

“OK, we’re looking at that robot next to the black hole and he looks smaller to us because of space compression down there.  I get that.  But when the robot looks back at us do we look bigger?”

We’re walking off a couple of Eddie’s large pizzas.  “Sorry, Mr Feder, it’s not that simple.  Multiple effects are in play but only two are magnifiers.”

“What isn’t?”

“Perspective for one.  That works the same in both directions — the image of an object shrinks in direct proportion to how far away it is.  Relativity has nothing to do with that principle.”

“That makes sense, but we’re talking black holes.  What does relativity do?”

“Several things, but it’s complicated.”

“Of course it is.”

“OK, you know the difference between General and Special Relativity?”

“Yeah, right, we learned that in kindergarten.  C’mon.”

“Well, the short story is that General Relativity effects depend on where you are and Special Relativity effects depend on how fast you’re going.  GR says that the scale of space is compressed near a massive object.  That’s the effect that makes our survey robot appear to shrink as it approaches a black hole.  GR leaves the scale of our space larger than the robot’s.  Robot looks back at us, factors out the effect of perspective, and reports that we appear to have grown.  But there’s the color thing, too.”

“Color thing?”

“Think about two photons, say 700-nanometer red light, emitted by some star on the other side of our black hole.  One photon slides past it.  We detect that one as red light.  The other photon hits our robot’s photosensor down in the gravity well.  What color does the robot see?”

“It’s not red, ’cause otherwise you wouldn’t’ve asked me the question.”

“Check.”

“Robot’s down there where space is compressed…  Does the lightwave get compressed, too?”

“Yup.  It’s called gravitational blue shift.  Like anything else, a photon heading towards a massive object loses gravitational potential energy.  Rocks and such make up for that loss by speeding up and gaining kinetic energy.  Light’s already at the speed limit so to keep the accounts balanced the photon’s own energy increases — its wavelength gets shorter and the color shifts blue-ward.  Depending on where the robot is, that once-red photon could look green or blue or even X-ray-colored.”

“So the robot sees us bigger and blue-ish like.”Robots and perspective and relativity 2“But GR’s not the only player.  Special Relativity’s in there, too.”

“Maybe our robot’s standing still.”

“Can’t, once it gets close enough.  Inside about 1½ diameters there’s no stable orbit around the black hole, and of course inside the event horizon anything not disintegrated will be irresistibly drawn inward at ever-increasing velocity.  Sooner or later, our poor robot is going to be moving at near lightspeed.”

“Which is when Special Relativity gets into the game?”

“Mm-hm.  Suppose we’ve sent in a whole parade of robots and somehow they maintain position in an arc so that they’re all in view of the lead robot.  The leader, we’ll call it RP-73, is deepest in the gravity well and falling just shy of lightspeed.  Gravity’s weaker further out — trailing followers fall slower.  When RP-73 looks back, what will it see?”

“Leaving aside the perspective and GR effects?  I dunno, you tell me.”

“Well, we’ve got another flavor of red-shift/blue-shift.  Speedy RP-73 records a stretched-out version of lightwaves coming from its slower-falling followers, so so it sees their colors shifted towards the red, just the opposite of the GR effect.  Then there’s dimming — the robots in the back are sending out n photons per second but because of the speed difference, their arrival rate at RP-73 is lower.  But the most interesting effect is relativistic aberration.”

“OK, I’ll bite.”

“Start off by having RP-73 look forward.  Going super-fast, it intercepts more oncoming photons than it would standing still.”

“Bet they look blue to it, and really bright.”

“Right on.  In fact, its whole field of view contracts towards its line of flight.  The angular distortion continues all the way around.  Rearward objects appear to swell.”

“So yeah, we’d look bigger.”

“And redder.  If RP-73 is falling fast enough.”

~~ Rich Olcott

  • Thanks to Timothy Heyer for the question that inspired this post.