Author: Adam

The Night Land (I)

The Night Land by William Hope Hodgson – Project Gutenberg.

A seriously creepy tale, by dint of the setting in time and space. “The Night Land” is millions of years in the future, after the Sun has become too cold to be visible to human eyes. Life on Earth has been preserved in a vast ravine a hundred miles deep into the mantle, warmed and powered by volcanism. Humanity struggles on, preserved against the “Night Land”, in the Last Redoubt, which is a huge pyramidal Arcology, several miles square on its base and projecting eight miles into the endless night. It is threatened by weird creatures, chiefly vastly old and patient “Watchers” and darker (!) forces of spiritual evil. Billennia before, it’s revealed, humans had experimented in space-time and let in “Things” – spiritual lifeforms that predate on human minds/souls.

The basic tale I’ll save for next time, but for now I wanted to examine the physics. Basically we’re talking about the Kelvin-Helmholtz timescale for the Sun’s contraction and its powering by gravitational potential energy being converted into heat energy. Essentially every mass falling into another mass will release energy and the total energy represented by all the mass of an object falling together into its current configuration is its binding energy.

Back in the 19th Century the only energy source known powerful enough to keep the Sun shining for millions of years was gravitational energy. But there was a problem – the Sun’s present configuration represented a binding energy of 18.75 million years of sunshine at present levels. Allowing for unknowns about the insides of the Sun, the total lifespan to date of the Sun was less than 100 million years and probably less than 30 million years.

That produced two problems. Firstly, geology seemed to imply Earth was at least 100 million years old and probably much older. Secondly, it meant that without a continuing infall of mass on to the Sun, it would grow cold and go out within a few million years.

The first problem is another tale, but the second inspired SF for several decades after Lord Kelvin first posed it in the 1860s. H.G.Wells visited an Earth orbitting a Sun grown cold in his “The Time Machine”, mentioning the infall of both Mercury and Venus which kept the Sun glowing hot for a bit longer. In 30 million years from his own time, his Time Traveller sees a huge red Sun over a chilled Earth which is facing its Final Winter. The Sun hasn’t grown huge like it is imagined to in present day astrophysics – instead Earth has slowly spiralled in towards it. And it is only shining like a red-hot ember, albeit a gigantic one, that’s rapidly losing its warmth.

By 1912, in William Hope Hodgson’s tale, the discovery of radioactivity was giving some geologists hope that the interior of the Earth would remain warm, but no one was too sure about the Sun and the other stars. Einstein’s work on the interconversion of mass and energy hadn’t filtered through to most fictioneers or astrophysicists, though very soon people would be talking about powering the Sun through annihilation of mass. But Hodgson doesn’t show any awareness of this, though he does indicate knowledge of speculations about non-Euclidean geometry with his “Doorways of the Night”, akin to the modern-day ‘wormhole’.

In an earlier tale Hodgson has a character visit the very end of the Cosmos as the corpse of the Sun itself collides with the “Central Star” – a speculation of the 19th Century that eventually gravity would bring everything together, at least in this “Island Universe”. But that fate is for much later than “The Night Land”…

Olaf Stapledon Online

Some utter classics of SF available c/o the Australian Project Gutenberg…

Last and First Men.

…a history of all the human species over the next two aeons. From Earth to Neptune. Written 1930.

Last Men in London.

…a visit by the Neptunian Last Men to our day via mental time-travelling. From 1932.

Star Maker.

…a history of our Cosmos, its Mind, and its ascent towards the Infinite. A glimpse across Eternity. From 1937.

Curiously the stellar physics reflects the change in understanding that astrophysicists had achieved in the 1930s. Prior to nuclear fusion being understood, the stars were believed to potentially be many trillions of years old, slowly burning away their total rest-mass energy. In “Last and First Men” the Sun’s life-span is 10 trillion years, but the planets only appear mid-way through after a James Jeans style near-collision. However by “Star Maker” the lives of the stars were seriously curtailed to mere billions of years and the ‘Big Bang’ provides the cosmic time-scale.

What about prior to Einstein? See my next post…

Iron and Oxygen: A Tale

The Iron Record Of Earth’s Oxygen / Science News.

Oxygen and iron can both exist in aqueous solution, but not together in great quantities. Instead they form insoluble oxides that precipitate out i.e. they make rust! Earth’s oceans haven’t always been as iron poor nor as oxygen rich as they are today. For about 2 billion years – from about 4.4 Gya to 2.3 Gya – they were full of dissolved iron and short on oxygen. As the Science News article, linked to above, reports new research is giving us deeper insights into the “Great Oxygenation Event” of that post-Archean, early Paleo-Proterozoic Era. For example, about 2.316 Gya enough oxygen had built up to form an ozone layer, fundamentally changing the prospects for life ever since.

Geological understanding is built on applying what we know of present day processes to past events – a maxim usually put as “the Present is the Key to the Past”. One present day key-to-the-past is an oxygen-poor lake in Indonesia. Its surface waters are oxygenated, but short on nutrients, then below ~120 metres the water is full of dissolved iron, no oxygen and alive with “photoferrotrophs” – bacteria that use photosynthesis to get energy from oxidising dissolved iron. They live by rusting the iron in the deep lake waters. A feature of the early days of oxygen’s rise are “Banded Iron Formations”, BIFs, from which most of the world’s commercial sources of iron/steel are derived. Basically BIFs are huge rust deposits and the “photoferrotrophs” of the Archean/Paleo-Proterozoic seem to be partially responsible.

What a strange, and humbling, debt we owe to such obscure bacteria. Their metabolic wastes are the ruddy feedstock of the first stage of manufacturing many of modern day industry and construction’s products. The steel skeletons of the Colossii of a modern City come from bacterial chemistry concentrating iron oxides over millennia. And frequently BIFs show a banding effect, now believed to have been caused by seasonal chemistry changes – more rust deposited in warm weather, more silica in cold. But the BIFs keep many more mysteries that geologists have yet to tease out of them…

Brightside of Meteorite bombardment & Junk DNA

Meteorite bombardment may have made Earth more habitable, says study.

Saved by Junk DNA.

The Origin of Life on Earth is a puzzle that biologists, biochemists, physicists and geologists – to name a few – have chewed on over the past 150 years since Darwin opened up the conceptual doors and let in the refreshing light of natural selection. One related question is just when was Earth first inhabited and habitable. The first study above seems to indicate that both Mars and Earth were made more clement by that last gasp of accretion, the Late Heavy Bombardment, which pounded the Inner Planets some 4.0-3.9 billion years ago.

How so? The infalling meteorites released both water and carbon dioxide, thus wetting & warming both planets, perhaps sufficiently for liquid water to remain stable on the open surface. Prior to that event, water may well have been mostly frozen. There’s good reason to think that the process of making long-chains of biomolecules, an important step before ‘Life’ itself, was via concentration of smaller sub-units within ice. Tiny channels of unfrozen liquid become increasingly concentrated in solutes as watery solutions freeze, providing an accelerated reaction environment for polymerisation. In such conditions even quite short pieces of RNA become capable of ‘ligation’, the fusing of RNA sub-units into longer chains.

Once RNA Life has given way to DNA Life what drives the evolution of ever longer strings of DNA and thus ever more complex Life? The second news piece is about evidence that so-called ‘Junk DNA’ – mostly repetitive segments of DNA with no obvious function – actually promotes faster evolution of organisms by altering the rate of gene mutation and gene expression. It seems the ‘Junk’ can make a gene’s DNA sequence more exposed and liable to change when the ‘Junk’ situated next to it has changed in length.

But there’s always a trade off. ‘Junk’ DNA is reduced in some organisms, very noticeably in birds, while it has immensely expanded in some organisms, like certain plants and slow-living creatures like amphibians and lungfish. One’s pace of life style has a distinct selective role on ‘Junk’ DNA’s quantity – fast-living reduces its presence, and perhaps its selective advantage. Birds need to rapidly churn out proteins from their DNA genes and operate at a higher blood temperature too. This might make the DNA more liable to change – birds are immensely speciose – without any ‘Junk’ DNA putting pressure on genes at all. Lungfish, and their kin, live ‘cold-blooded’ rather sedate lives, and carry around a large load of ‘Junk’ that ensures their DNA remains healthy, making the invasion of ‘DNA’ parasites, like viruses, much harder because the host DNA is already full of virus-like ‘Junk’.

Catalytic Nuclear Ramjet

Catalytic Nuclear Ramjet(application/pdf Object).

Robert Bussard first proposed the Nuclear-Fusion Interstellar Ramjet in 1960 and it caught the imagination of researchers (like Carl Sagan) and fiction writers (like Larry Niven & Poul Anderson) alike. Basically Bussard proposed to scoop up the interstellar medium and fuse it for propulsion, thus allowing a rocket to refuel for its entire journey. A 1,000 ton rocket could theoretically scoop propellant and fly at 1 g ‘forever’ – at least until drag became equal to its thrust.

A problem arose – hydrogen is very hard to fuse all by itself. The reaction rate of proton-proton fusion at “low” (i.e. an achieveable 100 million degrees) temperatures is essentially negligible and only powers the stars because they’re so gigantic. The Sun’s energy production rate is a bit more than 10 Watts per cubic metre of the fusion part of its core, which is far less than the power packed into a battery, for example. Unlike a battery, of course, that energy can trickle out for billions of years – but that’s no good for propelling a starship.

How do we make the reaction go faster? Physicist Daniel Whitmire proposed we burn the hydrogen via the well-known CNO Bi-Cycle. Basically a hydrogen fuses to a carbon-12, then another is fused to it to make nitrogen-14, then two more to make oxygen-16, which is then highly ‘excited’ and it spits out a helium nucleus (He-4) to return the nitrogen-14 back to carbon-12. Since the carbon-12 isn’t consumed it’s called a “catalytic” cycle, but it’s not chemical catalysis as we know it. Call it “nuclear chemistry”.

The CNO-cycle was first proposed by Hans Bethe as the means by which the Sun makes heat & light. It’s one means by which the Sun does so, but proton-proton fusion is dominant at the lower temperatures in the Sun and lower mass stars. Slightly bigger stars are predominantly powered by the CNO cycle and as the Sun evolves and its core contracts as helium builds up, it too will burn mostly via the CNO cycle.

Whitmire’s paper gives a rough guide to how well the CNO cycle improves a ramjet’s power-levels and shows, reasonably, that a Catalytic Nuclear Ramjet could propel a ship to the stars…

…the rest is an exercise for the student.

What the Hell is a Polytrope?

polytrop.pdf (application/pdf Object).

This little pdf file covers some interesting properties of polytropes – but what’s a polytrope? Basically it’s a sphere of gas, or some other matter, governed by a particular equation of how the pressure and the density are related.

P = K.(rho)1+1/n

…(rho) being density, P is pressure, K is a constant, and n is the polytropic index.

This equation is used to create an expression for the structure of the sphere that is converted into a differential equation, the Lane-Embden equation, which then can be integrated. Polytropes of n = 3/2 are used to model brown dwarfs and planets, for example, while polytropes of n = 3 are used to model stars like the Sun. Both need to be computed numerically as closed form solutions only exist for n = 0, 1 & 5.

The paper referenced above derives an expression for the gravitational binding energy of a polytrope of arbitary index. And it’s surprisingly easy…

(Omega) = -[3/(5-n)]*GM2/R

…thus a sphere of constant density (n=0) is -(3/5)*GM2/R,
n=3/2 case is -(6/7)*GM2/R,
and n=3 case is -(3/2)*GM2/R. What that means is that the Sun has squeezed into it about 5/2 times the potential energy that you’d expect from the Kelvin-Helmholtz solar model. If its energy derived from gravitational contraction then it has about 50 million years stored up inside it in its current configuration.

A puzzle of stellar structure, prior to the breakthrough that was relativity and quantum mechanics, was what was stopping a star from collapsing forever? Nothing seemed strong enough to hold back the inexorable squeeze of a star’s own gravity.

STEV

STEV.

The Stellar Evolution course page of Onno Pols & Matteo Cantiello at Utrecht University in the Netherlands, in English, the Universal language of Academia (at least for non-Dutch speakers like moi.)

An aside: The more I speak to non-English speakers who are learning my mongrel birth-tongue, the sillier English seems. Half Latin, half Norse/French, all arbitarily frozen-in spellings and pronounciations which probably would sound and look incomprehensible to Chaucer and Erasmus. We can’t even read Shakespeare or the 1611 King James Bible without misreading various words and turns of phrase.

That’s all natural, as language is alive and evolves… which is why it’s so frustrating that we can’t be a bit more arbitary, yet rational, about the whole damned thing.

Pulsars for interstellar navigation

Technology Review: Blogs: arXiv blog: How to use pulsars for interstellar navigation.

Thanks to the TechReview arXivBlog… a proposed means of navigating via known pulsars. Accurate to within metres, at least within the solar system, but surely it can be extrapolated to interstellar distances.

Helium-burning Puzzler

The Triple-Alpha fusion process “burns” helium-4 into carbon-12 and powers stars on the Helium Main Sequence, the short-lived and bright After-Life of a star when it has exhausted its Core hydrogen and is reborn through the Phoenix-like pyre of the Red Giant Branch. A standard Triple-alpha process code, NACRE, reproduces the Red-Giant Branch neatly and has enjoyed a lot of support, but it is only approximate. This prompted Kazuyuki Ogata, Masataka Kan, and Masayasu Kamimura (OKK) to try to compute the Triple-alpha process over a range of relevant temperatures using more exact computational tools, thus producing a new temperature-reaction rate profile for the process. Now Aaron Dotter and Bill Paxton have given the new profile a test-run by using it to compute the evolution of low-mass stars, with surprising results… basically the ‘disappearance’ of the Red-Giant Branch (RGB) and an exceptionally long-lived, cooler Helium Main Sequence (HMS).

This is a seriously wrong result because the RGB and HMS are observationally very well circumscribed stages in stellar evolution – we would’ve noticed a cooler, longer HMS by ten times more stars actually in it, and we would’ve certainly have noticed a dearth of stars in the RGB. Looking deeper at the OKK profile the authors noticed it allowed a much earlier and cooler onset of helium burning at 30 million K rather than the NACRE derived 80 million K. This has dramatic consequences as helium burning is exquisitely sensitive to the temperature, which drives the RGB stage – basically the star is in a runaway nuclear reaction as its core collapses and heats up, ending only in the “Helium Flash”. The OKK profile still produces the Flash, but with a lower peak output and milder entry onto the HMS.

So the audience are now wondering: Can the discrepancy be resolved? Can theory and observation ever meet? Stay tuned…

How much is there?

Just how much oxygen is in our atmosphere? And is it imperilled by sequestering carbon dioxide from burning fossil fuels?

Firstly, how much atmosphere is there? Earth’s surface pressure is defined as 101,325 newtons/metre2 and Earth’s surface gravity is roughly 9.78 m/s2, so the mass per unit area of air is 10,332.3 kg. The average molar mass of air is 28.96 grams, so that’s 356,778 moles of air pressing down on every square metre of Earth. Earth’s surface area is 510.072 trillion m2 so there’s 182 examoles (1 examole is 1018 moles) of air, more or less. Oxygen occupies 20.9% of the volume of air, so there’s 38 examoles of it. At 380 parts per million (ppm) there’s 69 petamoles (1015) of CO2, so it’s a minor gas with a big effect.

Just how much has to be burnt to use up all the oxygen? Depends on the fuel. Some sample reactions:

C + O2 => CO2 …one mole O2 for every mole of carbon, releasing 401,155 J/mole (O2).

CH4 + 2O2 => CO2 + 2H2O …2 moles O2 for every mole of methane, releasing 393,520 J/mole (O2).

C8H18 + 12.5O2 => 8CO2 + 9H2O …one mole of octane uses 12.5 moles of O2 to fully burn, releasing 409,294.4 J/mole (O2).

H2 + 0.5O2 => H2O …half a mole of O2 for every mole of hydrogen, releasing 483,660 J/mole (O2).

Thus you can see that burning carbon is the worst performer, so let’s burn that in a worst case scenario. How much is there to burn is the really pressing question? According to new research there might only be 600 billion tons of coal left that can feasibly be extracted, though the total in the ground that’s known might be 3 trillion tons. Sounds like a lot, but how many moles is it? One mole of carbon masses 12 grams, thus 600 billion tons is 50 petamoles – all burnt up it would produce less carbon dioxide than what’s currently present in the atmosphere and would consume (50/38,000)x100% = 0.13% of the available oxygen. All the gas and oil might double that figure, thus consuming 0.26% of the world’s oxygen. But we’d be left without fuel to burn…

Oxygen supply is the least of our worries. Energy needs to come from something other than fossil fuels – carbon, methane or octane are all very finite resources. Nuclear power could replace the coal we burn for base-load power, solar and wind could provide peak-power, and cellulosic ethanol could provide liquid fuels… but they’re ALL needed in vastly higher proportions than the present in order to replace the fossil-fuels in time.

What about fusion? Here’s one hopeful news-bite…

Ultra-dense Deuterium May Be Nuclear Fuel Of The Future

…about a super-dense deuterium, 130,000 times denser than water, which might make practical laser-ignition fusion-fuel. Details about the new deuterium phase’s stability isn’t available so I don’t know if it can be stored indefinitely, or must be made continually. But it’s a hopeful development.

Another hopeful news-bite is from Richard Nebel and the team at EMC2, who are working on the fusion reactor design bequeathed to the world by the late Robert Bussard…

Interview Dr. Richard Nebel of IEC/Bussard Fusion Project by Sander Olson

…Dr. Nebel is expecting to be making commercial fusion reactors by 2020, which will be getting close to the “Peak Coal” period of c.2025 that’s expected. Might be a massive incentive to switch to fusion if coal is going to be getting more expensive as fusion starts to be available on the market. If fusion really is as cheap as hoped – no one is too sure yet – we might be able to use it to reform hydrocarbons straight from carbon dioxide and water extracted from the air. This would accelerate the downward trend on carbon dioxide in the air, hopefully returning the world to a pre-Greenhouse condition by 2100.

Now that’s a future to hope for!