Advance notice

Today's science news involves something called the Chandrasekhar Limit.

Stars live for most of their lives in an equilibrium between two forces; the inward pull of their own gravity, and the outward pressure from the heat generated by fusion in their cores.  As long as there is plenty of hydrogen left to power fusion, those forces are equal and opposing, and the star is stable.

When the hydrogen is depleted, though, the balance shifts.  The core cools, and the gravitational collapse resumes.  This, however, heats things up -- recall the "ideal gas law" from high school chemistry, and that temperature and pressure are inversely proportional -- and the star begins to fuse the helium "ash" left over from hydrogen burning into carbon.  Eventually that runs out, too, and the process repeats -- carbon to oxygen and silicon, and on up the scale until finally it gets to iron.  At that point, there's nowhere to go; after iron, fusion begins to be an endothermic (energy-requiring) reaction, and the star is pretty much out of gas.

What happens at this point depends on one thing: the star's initial mass.  For a star the size of the Sun, the later stages liberate enough energy to balloon the outer atmosphere into a red giant, and when the final collapse happens, it blows off that atmosphere into a wispy bubble called a planetary nebula.  

The Cat's Eye Nebula (NGC 6543) [Image is in the Public Domain courtesy of NASA]

What's left at the center is the exposed core of the star -- a white dwarf, still glowing from its residual heat.  It doesn't collapse further because its mass is held up by electron degeneracy pressure -- the resistance of electrons to occupying the same quantum state, something known as the Pauli Exclusion Principle.  But it's no longer capable of fusion, so it will simply cool and darken over the next few billion years.

For heavier stars -- between two and ten times the mass of the Sun -- electron degeneracy is not sufficient to halt the collapse.  The electrons are forced into the nuclei of the atoms, and what's left is a densely-packed glob of neutrons called, appropriately enough, a neutron star.  So much energy is liberated by this process that the result is a supernova; the atmosphere is blown away completely, and the collapsed core, which is made of matter dense enough that a teaspoonful would weigh as much as Mount Everest, spins faster and faster because of the Law of Conservation of Angular Momentum, in some cases reaching speeds of thirty rotations per second.  This whirling stellar core is called a pulsar.

For stars even larger than that, though, the pressure of neutron star matter isn't enough to stop the gravitational collapse.  In fact, nothing is.  The supernova and subsequent collapse lead to the formation of a singularity -- a black hole.

So that's the general scheme of things, but keep in mind that this is the simplest case.  Like just about everything in science, reality is more complex.

Suppose you had an ordinary star like the Sun, but it was in a binary system.  The Sun-like star reaches the end of its life as a white dwarf, as per the above description.  Its partner, though, is still in stable middle age.  If it's close enough, the dense, compact white dwarf will begin to funnel material away from its partner, siphoning off the outer atmosphere, and -- this is the significant part -- gaining mass in the process.

Artist's conception of the white dwarf/main sequence binary AE Aquarii [Image is in the Public Domain courtesy of NASA]

The brilliant Indian physicist Subrahmanyan Chandrasekhar figured out that this process can only go on so long -- eventually the white dwarf gains enough mass that its gravity exceeds the outward pressure from electron degeneracy.  At a mass of 1.4 times that of the Sun -- the Chandrasekhar Limit -- the threshold is reached, and the result is a sudden and extremely violent collapse and explosion called a type 1a supernova.  This is one of the most energetic events known -- in a few seconds, it liberates 10^44 Joules of energy (that's 1, followed by 44 zeroes).

So this is why I got kind of excited when I read a paper in Nature Astronomy about a binary star system only 150 light years away made of two white dwarf stars, which are spiraling inward and will eventually collide.

Because that would be the type 1a supernova to end all type 1a supernovas, wouldn't it?  No gradual addition of little bits of mass at a time until you pass the Chandrasekhar Limit; just a horrific, violent collision.  And 150 light years is close enough that it will be a hell of a fireworks show.  Estimates are that it will be ten times brighter than the full Moon.  But at that distance, it won't endanger life on Earth, so it'll be the ideal situation -- a safe, but spectacular, event.

The two stars are currently orbiting their common center of mass at a distance of about one-sixtieth of that between the Earth and the Sun, completing an orbit every fourteen hours.  Immediately before collision, that orbital period will have dropped to the frantic pace of one revolution every thirty seconds.  After that...

... BOOM.

But this was the point where I started thinking, "Hang on a moment."  Conservation of energy laws suggest that to go from a fourteen-hour orbit with a radius of around 2.5 million kilometers, to a thirty-second orbit with a radius of close to zero, would require an enormous loss of energy from the system.  That kind of energy loss doesn't happen quickly.  So how long will this process take?

And there, in the paper, I found it.

This spectacular supernova isn't going to happen for another 23 billion years.

This was my expression upon reading this:

I don't know about you, but even in my most optimistic moments I don't think I'm going to live for another 23 billion years.  So this whole thing gives new meaning to the phrase "advance notice."

You know, I really think y'all astrophysicists need to step up your game, here.  You get our hopes up, and then say, "Well, of course, you know, astronomical time scales..."  Hell, I've been waiting for Betelgeuse to blow up since I was like fifteen years old.  Isn't fifty years astronomical enough for you?

And now, I find out that this amazing new discovery of two madly-whirling white dwarf stars on an unavoidable collision course is going to take even longer.  To which I say: phooey.

I know your priority isn't to entertain laypeople, but c'mon, have a heart.  Down here all we have to keep our attention is the ongoing fall of civilization, and that only gets you so far.  Back in the day, stuff like comets and supernovas and whatnot were considered signs and portents, and were a wonderful diversion from our ancestors' other occupations, such as starving, dying of the plague, and being tortured to death by the Inquisition.  Don't you think we deserve a reason to look up, too?  In every sense of the phrase?

So let's get a move on, astrophysicists.  Find us some imminent stellar hijinks to watch.  I'll allow for some time in the next few months.  A year at most.  I think that's quite generous, really.

And if you come up with something good, I might even forgive you for getting my hopes up about something amazing that won't happen for another 23 billion years.

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Crown jewel

A white dwarf is the remnant of an average-to-small star at the end of its life.  When a star like our own Sun exhausts its hydrogen fuel, it goes through a brief period of fusing helium into carbon and oxygen, but that too eventually runs out.  This creates an imbalance between the two opposing forces ruling a star's life -- the outward thermal pressure from the heat released by fusion, and the inward compression from gravity.  When fusion ceases, the thermal pressure drops, and the star collapses until the electron degeneracy pressure becomes high enough to stop the expansion.  The Pauli Exclusion Principle states that two electrons can't occupy the same quantum state, and the force generated in order to prevent this happening is sufficient to counterbalance the gravitational pressure.  (At higher masses, even that's not enough to stop the collapse; the electrons are forced to fuse with protons, generating a neutron star, or at higher masses still, a black hole.)

For a star like our Sun, in a single-star system, that's pretty much that.  The outer layers of the star's atmosphere get blown away to form a ghostly shell called a planetary nebula, and the white dwarf -- actually the star's core -- remains to slowly cool down and dim over the next billion-odd years.  But in multiple-star systems, something far more interesting happens.

White dwarfs, although nowhere near as dense as neutron stars, still have a strong gravitational field.  If the white dwarf is part of a close binary system, the gravitational pull of the white dwarf is sufficient to siphon off gas from the upper atmosphere of its companion star.  The material from the companion is heated and compressed as it falls toward the white-hot surface of the white dwarf, and once enough of it builds up, it suddenly becomes hot enough to fuse, generating a huge burst of energy in a runaway thermonuclear reaction.

The result is called a nova -- a "new star," even though it's not new at all, it has merely flared up enough to see from a long way away.  (The other name for this phenomenon is a cataclysmic binary, which I like better not only because it's more accurate but because it sounds badass.)  Once the new fuel gets exhausted, it dims again, but the process merely starts over.  The siphoning restarts, and depending on the rate of accretion, there'll eventually be another flare-up.

Artist's concept of a nova flare-up [Image courtesy of NASA Conceptual Image Lab/Goddard Flight Center]

The topic comes up because there is a recurrent nova that is due to erupt soon, and when it does, a "new star" will be visible in the Northern Hemisphere.  It's in the rather dim, crescent-shaped constellation of Corona Borealis, between Boötes and Hercules, which can be seen in the evening in late spring to midsummer.  The star T Coronae Borealis is ordinarily magnitude +10, and thus far too dim to see with the naked eye; most people can't see anything unaided dimmer than magnitude +6, and that's if you've got great eyes and it's a completely clear, dark night.  But in 1946 this particular star started to dim even more, then suddenly flared up to magnitude +2 -- about as bright as Polaris -- before gradually dimming over the next days to weeks back down to its previous near-invisibility.

And the astrophysicists are seeing signs that it's about to repeat its behavior from 78 years ago.  The best guesses are that it'll flare some time before September, which is perfect timing for seeing it if you live in the Northern Hemisphere.  If you're a star-watcher, keep an eye on the usually unremarkable constellation of Corona Borealis -- at some point soon, there will be a new jewel in the crown, albeit a transient one.

You have to wonder, though, if at some point the white dwarf in the T Coronae Borealis binary system will pick up enough extra mass from its companion to cross the Chandrasekhar Limit.  This value -- about 1.4 solar masses -- was determined by the brilliant Indian physicist Subrahmanyan Chandrasekhar as the maximum mass a white dwarf can have before the electron degeneracy pressure is insufficient to halt the collapse.  At that point, it falls inward so fast the entire star blows itself to smithereens in a type-1a supernova, one of the most spectacular events in the universe.  If T Coronae Borealis did this -- not that it's likely any time soon -- it would be far brighter than the full Moon, and easily visible in broad daylight, probably for weeks to months.

Now that I would like to see.

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A cataclysmic pirouette

Hamlet famously states to his friend, "There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy," and every time we look into the night sky, we're reminded how true that is.

In the last hundred years astronomers have discovered deadly gamma-ray bursters and black holes, neutron stars for which a teaspoon of their material would weigh as much as a mountain, planets made of stormy swirls of ammonia, methane, and hydrogen, ones made of super-hot molten metal, water-worlds completely covered with deep oceans.  We've seen newborn stars and stars in their violent death throes, looked out in space and back in time to the very beginning, when the universe itself was in its infancy.

Even with all these wonders, new and bizarre phenomena are still being discovered every time our technology improves.  Take, for example, the "cataclysmic variable" that was the subject of a paper in Nature this week, a pair of stars locked in such a tight dance that they whirl around their common center of gravity in only fifty-one minutes.

Given the euphonious name ZTF J1813+4251, this pair of stars is comprised of a white dwarf -- the burnt-out core of a low-mass star like the Sun -- and an even more lightweight star not much bigger than the planet Jupiter.  The white dwarf has been swallowing (the astronomical term is "accreting") the hydrogen fuel from its partner, and they're drawing closer together, meaning that the process will speed up.  Eventually all that will be left of the partner star will be its core, and astronomers predict that at that point, they will have an orbital period of eighteen minutes.  But once the accretion process ends, drag in the pair's movement will rob energy from the system, the wild stellar pirouette will slow down, and they will gradually start to move apart again.

It's fortunate that the partner star is as light as it is; if it had more mass, it would be headed toward one of the most violent fates a star can have -- a type 1a supernova.  White dwarfs are the remnants of stars that have exhausted all their fuel, and they shrink until the inward pull of gravity is counterbalanced by the mutual repulsion of the negatively-charged electrons that surround the atoms they're made of.  There's a limit, though, to how much this repulsive force can withstand; it's called the Chandrasekhar limit, after its discoverer Subrahmanyan Chandrasekhar, and is equal to 1.44 solar masses.  For a lone white dwarf -- as our Sun will one day be -- this is not a problem, as there won't be anything substantial adding to its mass after it reaches that point.

The situation is different when a low-mass star is in a binary system with a giant star.  When the low-mass star burns out and becomes a white dwarf, it begins to rob its partner of matter -- just as ZTF J1813+4251 is doing.  But in this case, there is a lot more mass there to rob.  Eventually, the white dwarf steals enough matter from its companion to go past the Chandrasekhar limit, and at that point, the mutual repulsion of the electrons in the stars atoms lose their contest with the inward pull of gravity.  The white dwarf's core collapses completely, making the temperature skyrocket so high that its helium ash can fuse into carbon and other heavier elements, suddenly releasing catastrophic amounts of energy.  The result is...

... boom.

In the process, the matter from the exploded dwarf star is scattered around the cosmos, and becomes the parent material for forming planets.  It is, in fact, how most of the carbon, oxygen, and nitrogen in our bodies were formed.

As Carl Sagan famously said, "We are made of starstuff."

A type 1a supernova remnant [Image is in the Public Domain courtesy of NASA/JPL]

But ZTF J1813+4251 isn't headed for such a dramatic exit -- eventually the white dwarf will pull away the outer layers of the partner star's atmosphere, and after that the two will just spiral around each other wildly for a few million years, gradually cooling and slowing from their current frenetic pace.  So maybe "cataclysmic" isn't the right word for this pair; their crazy tarantella will simply wind down, leaving two cold clumps of stellar ash behind.

Honestly, if I were a star, I think I'd rather go out with a bang.

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Homing in on Tatooine

I remember the first time I ran into the concept that the Earth's relatively circular orbit might not be universal amongst the planets out there in the universe.

I shudder to admit that it was on the generally abysmal 1960s science fiction series Lost in Space.  The brave crew of the Jupiter 2 are stranded on a strange planet, and initially the whole place seems to be a frozen wasteland.  But after a journey via their "chariot" (as they call their tank-like wheeled transport vehicle), they find the temperature is seesawing wildly -- at first it seems to be heading to cold temperatures that will eliminate all possibility of life, but unexpectedly the mercury begins to rise, and what was a crossing on solid ice turns into a treacherous sea voyage (the chariot, fortunately, has amphibious capabilities).

The explanation we're given is that the planet they're on has a very elliptical orbit, so it experiences huge temperature changes.  Unfortunately, the writers of the show apparently did not understand that there's a difference between a planet's rotation and its revolution, so they depict the excruciatingly hot temperatures when the planet is at its perigee as only lasting a minute or two, so all the Robinsons had to do was hide under a reflective shelter for a little bit to avoid getting cooked.

So good idea, lousy execution, which can be said of much of that series.

A more fundamentally startling change in my perception of what it'd look like on another planet occurred when I saw Star Wars for the first time, and hit the iconic scene where Luke is looking toward the horizon as sunset occurs on Tatooine -- and there are two suns in the sky.  Tatooine, it seems, orbits a binary star -- something I'd honestly never thought about before then.

Being a science nerd type, I wondered what the shape of a planet's orbit would be if it were moving around two centers of gravity, and found pretty quickly that my rudimentary knowledge of Newton's Laws and Kepler's Law were insufficient to figure it out.

Turns out I wasn't alone; physicists have been wrestling with the three-body problem for a couple of hundred years, and there is no general solution for it.  Three objects orbiting a common center of gravity results in a chaotic system, where the paths of each depend strongly on initial conditions (and some configurations are unstable and result in either collisions or one of the objects being ejected from the system).

It is known, however, that there are points in a three-body system called Lagrange points (after their discoverer, the French mathematician and astronomer Joseph-Louis Lagrange) which result in a stable configuration in which each of the orbiting bodies stays in the same locked position relative to the other, so the entire system seems to turn as one.  Some of the moons of Jupiter (the so-called Trojan moons) sit at the Lagrange points for that system, a pattern that seems to be stable indefinitely.  (Note that from the Earth perspective, an object at the L3 Lagrange point would never be visible -- leading conspiracy wackos to postulate that it could be a place for alien spacecraft to be hiding.)

[Image licensed under the Creative Commons Xander89, Lagrange points simple, CC BY 3.0]

Things only get worse when you add additional objects.  The only way to approximate the configuration of the orbits is to input the specific initial parameters and use computer modeling software to determine a solution; there is no general set of equations to predict what it will look like.

What brings this up is a paper this week in The Astrophysical Journal that went beyond the theoretical, and found actual data from binary star systems with planets to see what the various orbits looked like.  In "The Degree of Alignment between Circumbinary Disks and Their Binary Hosts," by a team led by Ian Czekala of the University of California - Berkeley, we read about new observations from the Atacama Large Millimeter/submillimeter Array (ALMA), which tells us that not only might objects orbiting a binary star exhibit chaotic paths, they might not all orbit in the same plane.

Because of the way planets form -- coalescence of dust and debris from a flat ring surrounding the host star -- planetary systems seem mostly to be aligned with each other.  In our own Solar System, the eight planets all orbit within seven degrees of the Earth's orbital plane (excluding, sadly, Pluto, which still hasn't recovered its planet status, and has an orbital tilt of just over seventeen degrees).

But apparently there are exceptions.  Some binary stars have planets that orbit in a highly tilted ellipse with respect to the orbit of the two stars around their own center of mass.  How this could happen -- whether the planets condensed from a ring that was already tilted for some reason, or that the three-body chaos warped the orbits after formation -- isn't known.  "We want to use existing and coming facilities like ALMA and the next generation Very Large Array to study disk structures at exquisite levels of precision," study lead author Czekala said, "and try to understand how warped or tilted disks affect the planet formation environment and how this might influence the population of planets that form within these disks."

Which is pretty cool.  While it won't solve the more general difficulty of the three-body problem (and the four-, five-, six-, etc. body problems), it will at least give some empirical data to go on with which to analyze other systems ALMA finds.

So we're homing in on Tatooine.  For what it's worth, it looks like the overall situation might be more similar to Star Wars than it is to Lost in Space.

Which is a good thing in a variety of respects.

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Any guesses as to what was the deadliest natural disaster in United States history?

I'd speculate that if a poll was taken on the street, the odds-on favorites would be Hurricane Katrina, Hurricane Camille, and the Great San Francisco Earthquake.  None of these are correct, though -- the answer is the 1900 Galveston hurricane, that killed an estimated nine thousand people and basically wiped the city of Galveston off the map.  (Galveston was on its way to becoming the busiest and fastest-growing city in Texas; the hurricane was instrumental in switching this hub to Houston, a move that was never undone.)

In the wonderful book Isaac's Storm, we read about Galveston Weather Bureau director Isaac Cline, who tried unsuccessfully to warn people about the approaching hurricane -- a failure which led to a massive overhaul of how weather information was distributed around the United States, and also spurred an effort toward more accurate forecasting.  But author Erik Larson doesn't make this simply about meteorology; it's a story about people, and brings into sharp focus how personalities can play a huge role in determining the outcome of natural events.

It's a gripping read, about a catastrophe that remarkably few people know about.  If you have any interest in weather, climate, or history, read Isaac's Storm -- you won't be able to put it down.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]