New theory explains how Earth’s inner core remains solid despite extreme heat | Hacker News Reader

New theory explains how Earth’s inner core remains solid despite extreme heat

kth.se

87 pointsrenafowler34 comments

Something I've been wondering. Does the earth's core have negative heat capacity?[1]

I've read that it is usually modeled as a self-gravitating system[2], and that such systems can end up in states with negative heat capacity [3].

[1] > "If the system loses energy, for example by radiating energy away into space, the average kinetic energy actually increases." https://en.wikipedia.org/wiki/Heat_capacity#Negative_heat_ca...

[2] > "The Earth’s outer core is a rotating ellipsoidal shell of compressible, stratified and self-gravitating fluid." https://www.uleth.ca/dspace/handle/10133/3672

[3] > "Negative heat capacities can only occur in isolated or nearly isolated systems. They are impossible in truly extensive systems in canonical ensembles or for that matter in grand canonical ensembles. However, far from being a strange phenomenon only found in the thermodynamics of black holes they occur widely on a macroscopic scale in astrophysics and with less precision on a microscopic scale throughout physics and chemistry. They are the origin of the large fluctuations that occur at phase transitions and we speculate that they cause those transitions." http://adsabs.harvard.edu/full/1977MNRAS.181..405L

Edit: Also, the link to the paper leads to a 404 page... Stabilization of body-centred cubic iron under inner core conditions, Nature Geosciences, nature.com/articles/doi:10.1038/ngeo2892

If you look at the Wikipedia article in more detail, you will see that the negative heat capacity of a self-gravitating, isolated system arises from the virial theorem. Heuristically, as a self-gravitating system radiates energy away into space, it becomes more tightly bound; that means it contracts. But as it contracts, the "orbital speeds" of its constituents increase (because decreasing orbital radius means increasing orbital speed), meaning its average kinetic energy increases, meaning it heats up.

Technically, the virial theorem argument only applies to systems whose constituents are in free-fall orbits. But I believe you can do a similar analysis for an isolated self-gravitating system that is in hydrostatic equilibrium--basically, as it radiates energy away into space, the hydrostatic equilibrium changes to one in which the radius is smaller and pressure and temperature are higher. Unfortunately I don't have a handy link to such an analysis right now, though.

As far as whether any of the above would apply to the Earth's core, I don't think it would since the Earth's core is not isolated; but it might apply to the Earth as a whole, to the extent that the Earth can be viewed as being in hydrostatic equilibrium (i.e., pressure balancing gravity everywhere). AFAIK it is common in astronomy to treat stars this way.

Interesting, thanks. I still am not sure what the technical meaning of "isolated" is here. But wouldn't such an object continue heating up "infinitely" (maybe stopping at some phase-transition temperature) without constant input of energy?

> I still am not sure what the technical meaning of "isolated" is here.

Technically, it means an object of finite spatial extent surrounded by vacuum, and nothing else in the entire universe. Obviously that's an idealization. :-) But it makes the mathematical model tractable.

> wouldn't such an object continue heating up "infinitely"

Not necessarily; it might reach a stable state where it can't radiate any more energy. Cold white dwarfs, cold neutron stars, and cold planets are possible examples of such states. ("Cold" here basically means "at absolute zero", i.e., in the ground state for its configuration of particles.)

> Technically, it means an object of finite spatial extent surrounded by vacuum, and nothing else in the entire universe. Obviously that's an idealization.

Reminds me of Fritz Zwicky's "spherical bastards". Although unrelated, my physics prof that taught thermo introduced spherical bastards as an aside after stating we'd basically assume all bodies are spherical when calculating thermo transfers. This prof was where I learned that Zwicky often referred to some colleagues as "spherical bastards", and when when questioned why, he responded: "because no which way you look at them, they're a bastard." I'm sad I can't remember the prof's name; he was quite a character, a short, squat old man. Just add a beard and appropriate clothing, he'd have played a good Santa Clause. He had a minor role in the Manhattan Project, and would often share stories. Lectures were always fun. One of the few classes I never skipped.

"Cold" in astrophysical settings tends to mean T << µ (the chemical potential) which usually justifies a low temperature expansion in T/µ, although thermal effects can be qualitatively important.

> "Cold" in astrophysical settings tends to mean T << µ (the chemical potential)

Yes, I know, but this in itself does not preclude energy being emitted by radiation. To preclude that, the object needs to be in a genuine ground state--no internal transitions possible that can reduce its total energy. That's a considerably stronger condition than T << µ.

This headline seems a bit overzealous, as if this new theory is the final answer.

This new theory, noted as contradicting one from 2014 and 30 years of previous conventional scientific wisdom, came after researchers "looked into larger computational samples of iron than studied previously". What will be the headline and tone in several more years, when someone comes along and studies an even higher number of samples and coming to an entirely different conclusion?

Doesn't it seem more appropriate and useful for the scientific community and publishers of these studies to be careful not to state their findings as conclusive and act as if their most recent study does much more than to estimate what might be happening?

I expect the article itself is more carefully worded than the press release.

I don't think people in the scientific community in general really care much about the press releases. The publicity is more something that the funding organizations and universities have started to require in recent years --- you may even get some quantified "career points" of some sort from them depending on the grant. The press releases are at best an afterthought for the researchers. As they are also often edited by the PR staff of the university, there may be some standardized level of hype injected.

There are many researchers who are eager to have their work publicized, both for reasons of pride and grant-writing. They often are far from diligent in working with the journalist to make sure the article is written with sufficient modesty. Yes, universities and funders have began directly soliciting hype journalism, but the researchers themselves still benefit, and follow incentives.

Like other content on this site, it's just ripped from the original publisher and author, with the author credit cut out. The title is the same on the original:

https://www.kth.se/en/forskning/artiklar/new-theory-explains...

> The ultimate goal of Earth Sciences is to understand the past, present and future...

That is the ultimate goal of all science.

You are right, science is not bound to Earth and also even "the past, present and future" seem too narrow to me. Science is about understanding anything which we are curious about, and that may include alternative timelines which do not lay neither in the "the past, present nor the future" and also the time itself.

Without a way to access those alternate timelines, no science can be done there, because no hypothesis will be falsifiable.

But what of the scientists working to improve lives? You dont have to do blue sky research in a shiny tower. Some scientists are in the trenches looking not to discover but to apply discoveries in the real world.

Right but all of these discoveries aim to predict the future through modeling. In other words, they seek a model which says that if this and this occur than we can expect this result with some probability.

Well, it's to use evidence and inductive reasoning to objectively prove that you understand those things.

You can understand lots of things without being able to prove them or explain their underlying mechanisms.

How do they know that it is solid?)

Seismic waves traveling through the earth refract for the same reason that light refracts when entering different substances (e.g. air, water). The inner core has a different density from the outer core, and this difference in density tells us that it is solid. Of course the density difference could be due to something we don't know yet, but this is out current best guess.

To the first order it is the fact that a liquid only propagates pressure waves while a solid can propagate shear and pressure waves (which propagate a different speeds).

That's true, but can shear waves be transmitted to the earth's solid core through the liquid iron surrounding it?

Pressure waves go through the liquid part, hit the solid part, some of their energy is converted into shear waves which go through the solid core, convert back to pressure waves on the other side, and eventually hit the surface again. By measuring propagation time, direction, etc, the full picture is only compatible with the pressure / shear / pressure double conversion.

TLDR: It's complicated.

By measuring how quickly seismic waves travel between different points on the earth's surface. Seismic waves travel at different speeds depending on the density and type of material they pass through, which lets us determine the composition of the Earth.

Measuring earthquake wave propagation?

Yes. And to add a missing piece, seismic waves radiate out from the point of vibration. Some of these waves pass through the core of the earth and are received on measurement equipment on the other side. Some of these waves pass through the mantle or the crust. If we know the epicenter of the quake, then we can estimate how long these waves should take to reach our different measuring stations assuming different densities.

Given that we can know how long they actually do take, we can turn around and estimate the mean density along the straight-line path they took. When we determine that the mean density is significantly higher for paths through the center of the earth, that tells us that the material there is much denser, and so we suppose that it could be solid.

Funniest ad placement seen in a while:

"Spinning within Earth’s molten core is a crystal ball"

... with the Canadian Foreverspin.com ad just above this. I want one, and please, keep on spinning.

If you ever want to f' with TSA in a completely legal way: carry lead crystal in your carry-on luggage. I've done it a number of times carrying Christmas gifts to/from family. My favorite was when my parents gifted me a set of lead crystal tumblers from Waterford. The cut on the crystal sorta makes them look like a pineapple grenade. Thing is, they're opaque on TSA scanners, so they make you pull them out (and they're really cautious at this point), then they pull the items out, and they're completely transparent. Their minds: blown. If you're lucky, you get one you can explain it to, if you're unlucky, you get a doofus that has to call for backup.

Haha. :) Thing is, I'd probably have to show my HN credentials and whatever an^T^T digital probing they do to let you in, so they'd know it was all premeditated and then I'd be in real trouble. (I'm in Straya).

>I want one, and please, keep on spinning.

Really? When they first came out I figured they were tailgating on inception, but it's been a few years and they're still around. What's the attraction?

Just haven't seen them before (i.e. a high quality machined spinners), and I reckon my 6y son would love it too.

Blogspam of:

https://www.kth.se/en/forskning/artiklar/new-theory-explains...

Ok, we changed to that from http://sciencebulletin.org/archives/10367.html.

I'm pretty sure most of these are press releases intended to be republished, which isn't exactly the same as blogspam (where one site rips off another). Still, original URLs are preferable.

I never comment against actual press releases, because, hey, that's what they're meant for.

"Blogspam" is appropriate for literally ripped content without specific attribution; to then proceed to edit out a byline or other author credit is simple plagiarism.

Press Releases always have either an embargo date/time or "For Immediate Release" and a press contact for the originator, in my experience.

I'm not sure that's right. We see countless articles, usually originating on university websites, that are PR pieces about research studies. These get reprinted across a wide range of science-content farm sites, which tend to be pretty low quality, but I'm not sure they're copying without permission. It seems more that the system is designed to work this way.

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