This week we dip a little deeper into Titan’s weirdness trove. Check the diagram. Two kinds of ice??!? What’s that about?
and water polymorphs
As everyone knows, diamonds and pencil lead (graphite, and I loved learning that graphite is an actual dug-from-the-ground mineral whose name came from the Greek verb “to write”) are both pure carbon, mostly. Same atoms, just arranged differently.
Graphite‘s carbon atoms are laid out in sheets of hexagons. Adjacent sheets are bonded together but not as strongly as are the atoms within each sheet. Sheets can slide past each other, which is why we use graphite as a lubricant and why pencils can write and erasers can unwrite.
Diamond‘s atoms are also laid out in sheets of (rumpled) hexagons, but now the bonds between sheets are identical to the bonds within a sheet. Turn your head sideways and you’ll see that sheets run vertical, too. In fact, each carbon atom participates in four sheets, three vertical and one horizontal. All that symmetrical bonding makes diamond one of the hardest substances we know of.
Neighboring carbon atoms form bonds by sharing electrons between their positive nuclei. Neighboring water molecules (H2O) don’t share electrons but they do tend to line up with their somewhat positive hydrogen atoms pointing towards nearby somewhat negative oxygens. That’s a loose rule in liquid water but it dominates when the molecules freeze into ice.
Most of the ice on Earth has an Ice-Ih structure, where the oxygen atoms are arranged in the same pattern as the carbons are in graphite. Water’s hexagonal sheets aren’t quite flat, but the 6-fold symmetry gives us snowflakes. There’s a hydrogen atom between each pair of oxygens, but it’s not half-way between. Instead, each oxygen tightly holds its own two hydrogens while it pulls at further-away hydrogens owned by two neighboring oxygens.
But water molecules have other ways to arrange themselves. A small fraction of Earth’s ice has a diamond-like Ice-Ic structure with each oxygen participating in four hexagon sheets. Again, hydrogens are on the lines between them.
Water’s such a versatile molecule that it doesn’t stop with two polymorphs. Ice scientists recognize seventeen distinct crystalline varieties, plus three where the molecules don’t line up neatly. (None of them is Vonnegut’s “Ice-nine.”) Each polymorph exists in a unique temperature and pressure range; each has its own set of properties. As you might expect, ices formed at high pressure are denser than liquid water. Fortunately, Ice-Ih is lighter than water and so ice cubes and icebergs float.
As cold as Titan is and as high as the pressure must be under 180 miles of Ice-Ih and watery ammonia sea (even at 10% of Earth’s gravity), it’s quite likely* that there’s a thick layer of Ice-something around Titan’s rocky core.
The primary reason we think Titan is so wet is that Titan’s density is about halfway between rock and water. We know there are other light molecules on Titan — ammonia, methane, etc. We don’t know how much of each. Those compounds don’t have water’s complex phase behavior but many can dissolve in it. That’s why that hypothetical “Ammonia sea” is in the top diagram.
But wait, there’s more. Both graphite and water ice are known to form complex polymorphs, clathrates, that host other molecules. This diagram gives a hint of how that can happen. Frozen water under pressure forms a large number of more-or-less ordered cage clathrate structures that can host Titan’s molecular multitude.
At Titan’s temperatures ice rocks would be about as hard as granite. Undoubtedly they’ll have surprising chemistry and interesting histories. We can expect clathrate geology on Titan to be as complex as silicate geology is on Earth.
Geochemist heaven, except for the space suits.
~~ Rich Olcott
* – A caveat: we know a great deal about Earth’s structure because we live here and have been studying it scientifically for centuries. On the other hand, most of what we think we know about Titan’s interior comes from mathematical models based on gravitational observations from the Cassini mission, plus 350 photos relayed back from the Huygens lander, plus experiments in Earth-bound chemistry labs. Expect revisions on some of this stuff as we learn more.
Air warmed by the equatorial Sun rises, only to sink as it heads poleward. Our packet loops between the Equator and about 30ºN (see the diagram).
Titan’s atmosphere is heavy-duty compared with Earth’s — 6 times deeper and about 1½ times the surface pressure. When I read those numbers I thought, “Huh? But Titan’s diameter is only 40% as big as Earth’s and its surface gravity is only 10% of ours. How come it’s got such a heavy atmosphere?”
Their common experimental strategy sounds simple enough — compare two beams of light that had traveled along different paths
Of all the wave varieties we’re familiar with, gravitational waves are most similar to (NOT identical with!!) sound waves. A sound wave consists of cycles of compression and expansion like you see in this graphic. Those dots could be particles in a gas (classic “sound waves”) or in a liquid (sonar) or neighboring atoms in a solid (a xylophone or marimba).
Einstein noticed that implication of his Theory of General Relativity and in 1916 predicted that the path of starlight would be bent when it passed close to a heavy object like the Sun. The graphic shows a wave front passing through a static gravitational structure. Two points on the front each progress at one graph-paper increment per step. But the increments don’t match so the front as a whole changes direction. Sure enough, three years after Einstein’s prediction, Eddington observed just that effect while watching a total solar eclipse in the South Atlantic.
We’re being dynamic here, so the simulation has to include the fact that changes in the mass configuration aren’t felt everywhere instantaneously. Einstein showed that space transmits gravitational waves at the speed of light, so I used a scaled “speed of light” in the calculation. You can see how each of the new features expands outward at a steady rate.
The second question is harder. The best the aLIGO team could do was point to a “banana-shaped region” (their words, not mine) that covers about 1% of the sky. The team marshaled a world-wide collaboration of observatories to scan that area (a huge search field by astronomical standards), looking for electromagnetic activities concurrent with the event they’d seen. Nobody saw any. That was part of the evidence that this collision involved two black holes. (If one or both of the objects had been something other than a black hole, the collision would have given off all kinds of photons.)
In contrast, a LIGO facility is (roughly speaking) omni-directional. When a LIGO installation senses a gravitational pulse, it could be coming down from the visible sky or up through the Earth from the other hemisphere — one signal doesn’t carry the “which way?” information. The diagram above shows that situation. (The “chevron” is an image of the LIGO in Hanford WA.) Models based on the signal from that pair of 4-km arms can narrow the source field to a “banana-shaped region,” but there’s still that 180o ambiguity.
The great “if only” is that the VIRGO installation in Italy was not recording data when the Hanford WA and Livingston LA saw that September signal. With three recordings to reconcile, the aLIGO+VIRGO combination would have had enough information to slice that banana and localize the event precisely.
We can investigate things that take longer than an instrument’s characteristic time by making repeated measurements, but we can’t use the instrument to resolve successive events that happen more quickly than that. We also can’t resolve events that take place much closer together than the instrument’s characteristic length.
A wave happens in a system when a driving force and a restoring force take turns overshooting an equilibrium point AND the away-from-equilibrium-ness gets communicated around the system. The system could be a bunch of springs tied together in a squeaky old bedframe, or labor and capital in an economic system, or the network of water molecules forming the ocean surface, or the fibers in the fabric of space (whatever those turn out to be).
An isolated black hole is surrounded by an intense gravitational field and a corresponding compression of spacetime. A pair of black holes orbiting each other sends out an alternating series of tensions, first high, then extremely high, then high…
Almost a century later, James Clerk Maxwell (the bearded fellow at left) wrote down his electromagnetism equations that explain how light works. Half a century later, Einstein did the same for gravity.
Gravitodynamics is completely unlike electrodynamics. Gravity’s transverse “force” doesn’t act to move a whole mass up and down like Maxwell’s picture at left. Instead, as shown by Einstein’s picture, gravitational waves stretch and compress while leaving the center of mass in place. I put “force” in quotes because what’s being stretched and compressed is space itself. See 
The experiment consists of shooting laser beams out along both arms, then comparing the returned beams.
Hard Science Ain't Hard 
