April science readings.
I guess I should look for Acta Primae Aprila, but I can't say I'm really bothered. See this post for a trip down April Fool Road.
The Origin and Evolution of Multiple Star Systems
https://arxiv.org/pdf/2203.10066.pdf
FTFA : Most stars are born in multiple stellar systems.
Is this true? I knew it was getting close, but was it over the 50% line? I guess, it's easier to disrupt a multiple star system to form a single and a (lower-)multiple, or two singles, while it's much harder to form two singles into a double, or a single and a multiple into a (higher-) multiple, so the multiple:single ratio should decrease over time. Even in a relatively densely packed molecular cloud, it's still going to be harder.
Corollary, and this is my own thought, hence date - when disrupting a multiple star system to form a multiple and a single, wouldn't most of the Oort cloud and Kuiper belt stay with the larger star, potentially giving a way to distinguish single which were born as singles from singles which were ejected from multiples? So, finding a Sun-like star with a much smaller Oort cloud (and/ or Kuiper Belt) than the Sun's, might be a flag that this newly-characterised system is an ejectee? Do we have observational techniques which could survey to this depth? (2022-04-09 13:22)
OK, back from that rabbit hole.
RoTFA : In this review, we compile the results of observational and theoretical studies of stellar multiplicity. We summarize the population statistics spanning system evolution from the protostellar phase through the main-sequence phase and evaluate the influence of the local environment.
[See, I did notice the impact of nearby (proto-)stars above!]
We describe current models for the origin of stellar multiplicity and review the landscape of numerical simulations and assess their consistency with observations. We review the properties of disks and discuss the impact of multiplicity on planet formation and system architectures. Finally, we summarize open questions and discuss the technical requirements for future observational and theoretical progress.
Those last sections sound like a useful review.
Introduction Observational data is catching up with theoretical models.
Observed Stellar Multiplicity- Multiplicity changes a lot during formation and early evolution of systems. A significant increase in multiplicity happens at star (system?) masses greater than 0.5 M⊙ (see figure 4). That bears a lot on the question I pose above. Does that represent a mass at which collapsing molecular clouds become more likely to have complex turbulance that can fragment the cloud? The decline in multiplicity continues down towards and possibly into the brown dwarf regime, but detectability biases become challenging. (Table 1, in Astronomy notebook, 13columns, does not render well.) "Moving toward earlier spectral types, we find that the trend of an increasing MF with primary mass continues" and that trend continues to O-type stars - the biggest and brightest, where 90% are multiples, and most are triples or higher (companion frequency (CF) is 2.1 ± 0.3 for O-B stars)
Definitions : MF, CF
My question above remains in play when the authors say "The multiplicity fraction increases monotonically with primary mass from MF ≈ 20% for [brown dwarves] and late-M dwarfs to ≈ 50% for solar-type stars to MF > 90% for OB stars. The triple fraction increases even more dramatically from THF ≈ 2% for late-M dwarfs to 14% for FGK dwarfs to nearly 70% for O-type stars." because more than half of all stars are in the M class. There are also moderate (but significant) trends in metallicity, separation of stars within a system, and the ratio of star masses between primary and subsidiary stars in a system. For M stars, there doesn't seem to be much reduction in multiplicity in the first few hundred million years of life (which bears on my corollary above).
Models For Multiple Star Formation - Well, I didn't know that Fred Hoyle had his finger in the pie of star formation processes. "Hoyle F., 1953 ApJ, 118, 513. On the Fragmentation of Gas Clouds Into Galaxies and Stars" Hoyle studied the radiation of heat from contracting (self-gravitating) gas clouds and showed that they were unstable to separation into smaller, denser, faster-contracting clumps. Which leads naturally to a hierarchical system of collapse. More recent treatments add in the effects of turbulence and magnetic fields, for a fuller but inherently stochastic model (due to the turbulence, if nothing else).
Current ideas for multiple formation can be divided into three main categories: theories in which multiples form via fragmentation of a core or filament (§3.1), via fragmentation of a massive accretion disk (§3.2) or through dynamical interactions (§3.3). This third mode can also rearrange the hierarchy and multiplicity of systems formed via the prior fragmentation channels.[...] Due to their wide initial separations, multiples formed from turbulent fragmentation accrete gas with different net angular momentum. This frequently produces misaligned stellar spins, accretion disks and protostellar outflows.
There's a lot more, but it boils down to we/ve got several ways which could lead to the story of star system formation that we do see, and distinguishing between them is unlikley to be clear statisitcally. It's not a recipe for "this model works, and no other", more likely "this that and the other model all work, and any could have formed this system". That's for systems which have settled into Main Sequence tedium for a few tens to hundreds of million years. High mass, bright stars don't live long enough for the evidence of their birth environment to have dissipated, but that doesn't necessarily reflect the conditions under which low mass stars form.
Martian meteorites reflectance and implications for rover missions
https://arxiv.org/pdf/2203.10051.pdf
Obviously you need to do the legwork before trying to interpret what you see with your rover/ helicopter/ Musk-0-nought. So you look at what samples of Mars you do have using instruments as similar as possible to the ones being flown. If that means putting a Martian meteorite into a sock and beating Musk round the head with it, well, it's a dirty job, but someone's got to do it. Please remember that Musk wants to "die on Mars, but not on impact". Maybe hit him about the torso and limbs instead?
The problem (FTFA) is
the current spectral database available for these [Martian meteorite] samples does not represent their diversity and consists primarily of spectra acquired on finely crushed samples, albeit grain size is known to greatly affect spectral features.
Yeah, legwork definitely needed.
The spectrometers in question are VNIR (Visible and Near-Infrared) instruments. So while some classroom/ Mark-1 Eyeball experience is helpful, you do need to characterise the behaviour of real minerals and mineral mixtures (rocks) to have confidence in their interpretation.
the physical state of the sample, and especially its grain size, have been shown to significantly influence both the absolute reflectance and the shape of the absorption bands
Geologists know this from thier thousands of hours in the laboratory and field. (No lab-work? Not a geologist.) Non-geologists may need to be reminded of it. In theory you can do it from a book. But in theory there is no difference between theory and practice, whereas in practice there is. (Ref : "Oldies but Goodies", Chthulhu & Ugg, Gobekli Tepe Publications, 10000 BCE
In addition, in situ measurements by the SuperCam instrument [on the Mars 2020 rover, currently on Mars as "Perseverance"] will be achieved remotely and without any sample grinding
I wasn't paying close attention, but I had noticed repeated references to "pew-pew-pew"-ing various rock surfaces before drilling a hole, then later collecting the rock dust, or "pew-pew-pew"-ing the dust pile after drilling. I'd been taking that as getting spot measures versus a bulk-rock, but it would also address the grains size issue above. The rock dust pile would represent the mixed (to some degree) minerals of the rock interior, while the surface readings would be measuring the oxidised, UV+cosmic-ray-blasted surface minerals - which are not necessarily the same. Then there is the fact that soft minerals (interstitial carbonates, weathering clays ("phyllosilicates")) would express different surface area in the powder than in the bulk rock. It may be hard to differentiate these effects from the data collected in each drilling procedure, but if you didn't collect the data, then it would be impossible to differentiate these effects.
11 Martian meteorite had previously been IR-sperctrogrammed (mostly as powders, e.g. cutting debris) ; this study add 16 more meteorites in IR, and 11 of these were also studied with hyperspectral imaging.
Petrology
Most of the samples were mafic to ultramafic rocks, often showing cumulate textures. One polymict breccia (NWA 7034, explosive or sedimentary?) and several basalts and phenocrystic lavas were also in the suite examined. The shergottites in general yeild three ages : cosmic-ray exposure ages (indicating duration of interplanetary flight before a relatively recent impact on Earth) of 0-5 to 20 Ma ; mineral separates show Rb-Sr, Sm-Nd, Lu-Hf and U-Pb ages of 175-475 Ma (possibly a metamorphism age, or a re-melting?) and whole-rock Pb-Pb and Rb-Sr ages of about 4.1 Ga (original intrusion, or a protolith later re-melted?). That's a nice example that will go into the isotope geochemistry text books - if it's not there already.
Contamination of the meteorite samples by weathering on Earth's surface (or possibly during interplanetary transport) is quite common. It is more reported in finds from hot deserts than from cold deserts - Antarctica - but that 40-60 °ree;C storage temperature difference is sufficient to account for that. Carbonate mineals in Martian meteorites are mostly in vein-fills, and typically interpreted as terrestrial weathering products. (The presence of carbonates in distinct "rosette" concentric discs in specimen ALH84001 is one of the arguments for this feature having been formed on Mars.)
The zoning in the cpx in some of the shergottites looks really nice. But I doubt I'd ever afford a big enough sample for a thin section. Is there a sample in the BGS files? (No, but a reasonable number elsewhere. and some of them are pretty!)
Chemical Habitability: Supply and Retention of Life’s Essential Elements During Planet Formation
https://arxiv.org/pdf/2203.10056.pdf
This paper is part of the proceedings of conference "Protostars and Planets VII".
Which elements ? Well, they're sticking with "life as we know it" (Star Trek quote?), so CHONPS - Carbon Hydrogen, Oxygen, Nitorgen, Phosphorus, Sulphur. Some terrestrial lifeforms require a bit of other elements (humans a few ppb of molybdenum, IIRC), but for the structures of living things, you need that lot, in about that order. It's a choice, which could be challenged, but in itself it's a perfectly reasonable choice.
The fact that they're most of the commonest elements in the universe, is also probably part of the reason that life uses them. My data bucket (taken from http://www.kayelaby.npl.co.uk/chemistry/3_1/3_1_3.html, but you'll probably have to drill through the site to get to the table) tells me the commonest elements in the Sun are (in descending order) H, He, O, C, N, Ne, Mg, Si, Fe, S, Ar, Al, Ca, Na, Ni, Cr, Cl, and eventually P. Removing the nobel gasses, chlorine, silicon and the metallic elements (which are mostly combined with oxygen), the list is H, O, C, N, S, and P. And that, in itself is ample justification for choosing to concentrate on these elements.
From a physiological/ metabolism point of view, they're the elements used to make carbohydrates, amino acids, and energy-labile phosphates - the major structural components of biochemistry. (Sulphur is most important in cross-linking proteins into meshes as chains are folded and bring sulphur-containing amino acids into proximity, when they can cross-link.
Why is this a question? Well, it's reasonably easy to model the accumulation of high-melting point materials (metal oxides, silicate minerals) into planets, and to model the accumulation of hydrogen and helium onto a body in a condensing stellar nebula. But it's not so easy to understand how moderately volatile (boiling point a few hundred Kelvin) compounds (carbon oxides, ammonia, sulphur hydrides and oxides) accumulated onto a planetaty core, since the accumulation of the planet probably heated materials to lava-like temperatures - around a thousand (Kelvin or Centigrade). (Phosphates compounds are the least troublesome in this respect - magmas can directly crystallise phosphate minerals such as apatite from the melt, as anyone who has studied mineralogy under the polarizing microscope will remember it as one of the first minerals you are taught to diagnose (rounded crystals, moderate relief, low birefringence, optically negative, uniaxial if you can get an indicatrix). The substantially different volatire inventories of the Solar "rocky" planets, and the range of properties inferred for exoplanets show that the volatile content of planets is something that varies, a lot, even within one system, so might be a distinguishing factor etween which planets develop life and which don't.
The availability of these volatile materials influences whether a planet is considered in the "habitable zone", as the presence of "greenhouse gases" in a planets atmosphere can considerably alter the surface properties. If the Earth didn't have a lot of water available on it's surface - and therefore in the atmosphere in amounts approaching a percent - it's surface temperature would be sitting near the freezing point of water. The FUD around anthropogenic global warming is about whether people want to live on a planet with 15 degrees (Kelvin or centigrade) of global warming, or 16, 17, even 20 degrees of warming. Geologically, that experiment has been done, recently : algal blooms in the Arctic Ocean, Scandinavian crocodile-infested swamps, unbearale tropics.
The authors define "chemically habitability" in terms of
- 1) a supply of carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur (”CHONPS”), and other bio-essential elements that
are accessible to prebiotic chemistry, and
- 2) is capable of maintaining the availability of the CHNOPS elements over relevant geologic timescales.
As observational techniques improve, and the planetary examples and systems which need to be explained increase and diversify, the range under which models of chemical habitability will be tested also increases.
Section 2. Tracing The Earth’s Ingredients Back Through Time The main constraint on this is understanding when life originated on Earth. From the (body) fossil record, we know it originated before the oldest fossils at 3.5 Gyr ago, but more controversial arguments (for example, Moizjies Akilia graphite-in-apatite at 3.9 Gyr and Bell's graphite in a Jack hills zircon of 4.1 Gyr) interpret negative carbon-13 isotope ratios as evidence of a functioning biosphere consideraly before then. This is only a few hundred Myr after the Moon-forming impact, and well into the period of the Late Heavy Bombardment (if that happened, and isn't an artefact of the distribution of rocks around the Imbrium crater). If (again, a real "if") the Moon-forming impact stripped Earth's preimordial atmosphere off (alternative : formed a synestia) then the final accretion of the Earth included the volatiles for the atmosphere/ hydrosphere in it's (relatively) undifferentiated (i.e. unheated) components. With the exception of P, and the special case of O, the CHONPS are fairly uniformly distributed in the Earth's various zones (core, lower & upper mantle, lithosphere, crust, hydrosphere, atmosphere, biosphere) and can affect the systems at part per million levels (e.g. CO2 in the atmosphere). Generally, they don't form distinct minerals (though #TeamIce keep having that argument in the annual #MineralCup on @Twitter, and winning it.) and mostly are fluids. There is a lot of cycling of CHONPS between the Earth's lithosphere, hydrosphere, atmosphere and biosphere, a lot of it mediated (on Earth) by plate tectonic activities. On other worlds, that may be different - cases of "Waterworld" and "Stagnant Lid" worlds (example Venus) are considered. (Venus, being a neighbour, is obviously a prime example for examining the variations in CHONPS behaviour and other aspects of planetary science). Via it's role in reducing fault friction and enabling (or enhancing) plate tectonics, the presence of water may be very inportant in altering fluxes of other CHONPS components. But further, the role of plate tectonics-mediated heat flux in mantle may be an important point in altering the convection in the liquid core which is responsible (most likely) for producing the Earth's magnetic field, which itself is a part of the system reducing water loss from the upper atmosphere by solar wind fluxes. That may (or may not) be a general condition for habitability.
Carbon Through it's role as a greenhouse gas, even at ppm levels, the cycling of C as CO and/or CO2 between atmosphere and crust/ lithosphere/ hydrosphere has whole-planet consequences, but remember that H2O is also a significant greenhouse gas at surface temperatures above about 250K. These effects probably also constrain the levels of N (as NH3, NOx), though P and S are thought to be less effected. At high (core) pressures, C is a siderophile element, and most of Earth's C inventory is thought to reside in the core (about 4 times the amount in the atmosphere, hydrosphere and biosphere). If Earth's crustal and mantle inventories of C were to be put into the atmosphere as CO2, the resultant atmosphere would be broadly comparable to that of Venus.
Hydrogen is more evenly distributed between Earth's surface and deep interior, with an uncertain amount in the core, several "oceans" worth in the mantle (as mineral defects, which has a considerable effect o nmineral viscosity, and of course one ocean on the surface. Hydrogen that makes it ot the upper atmosphere is prone to loss via photodissociation to form monatomic hydrogen. However the current structure of the atmosphere is such that there is a "cold trap" in the stratosphere which effectively prevents water from getting above the UV-absorbing tri-oxygen layer.
Oxygen is the commonest element in the Earth - but almost all as oxide and silicate minerals, not di-oxygen gas (let alone tri-oxygen - ozone - and hypothetical higher allotropes of interest to the explosives chemists). The oxidation state of the whole Earth is dominated by the metallic oron in the core, ut that is effectively isolated from the mantle by it's density contrast. The oxidation state of the mantle is more managed by the QFM - quartz-fayalite-magnetite - reaction system than interaction with the metallic iron of the core. A similar interaction barrier exists between the mantle (and crust) and the atmosphere, with the atmosphere having a thermodynamically delicate store of 21% di-oxygen which is maintained by photosynthesis. This state has only existed since (approximately) the second to third Gyr of the Earth's existance, when the development of life, and then of photosynthesis, led to surface reservoirs of reducing power (e.g. Fe2+ minerals) being oxidised before di-oxygen started to accumulate in the atmosphere in the "Great Oxidation Event" (GOE). There is some debate over whether the GOE is due mainly to biological events, or to changes in mantle properties or circulation leading to less reducing power at the surface. This is considered problematic for the development of biological (or proto-biological) chemistry, which mostly reacts to di-oxygen by falling apart. Only small parts of biochemistry can tolerate the presence of di-oxygen, and there are considerable biochemical complications to keep it in it's place (in mitochondria and chloroplasts, for eukaryotes; prokaryotes are more variable). In a more general situation than just Earth, it is not at all clear if a "GOE" is necessary. Compared to other planets (where there is evidence), the Earth's mantle seems to be relatively oxidised (have a low free iron content) - whether this is a cause or an effect of habitability is unclear.
Nitrogen distribution between the atmosphere and the body of the Earth is strongly influenced by the oxygen fugacity of the atmosphere. As such it is then dependent on the details of the early atmosphere in contact with a post-formation magma ocean, or synestia if that was the path taken. The pressure of the Earth's atmosphere at different stages in it's history is an open question.
Phosphorus Tyrrell (1999 Nature, v400, p525, "The relative influences of nitrogen and phosphorus on oceanic primary production") considers P to be the ultimate limiting nutrient on Earth. Since there is no significant gaseous reservoir of phosphorus, it is primarily available through aqueous solution replenished by rock weathering. Currently, phosphorus is mostly released from granite/ granitoid rocks into which it is significantly segregated in igneous differentiation. However on Early Earth, there probably wasn't as much granite/ granitoid rocks at surface today and smaller amounts of phosphorus would have been released from basaltic/ mafic rocks. Very early, schreibersite ((Fe, Ni)3P), a mineral found in some meteorites may also have been a source. (The discovery of 4-4.3 Gyr zircons from the Jack Hills (Australia) and Acasta (Canada) gneisses challenges ideas of an early paucity of granite/ granitoid rocks in the very early Earth.)
Sulphur is degassed from the mantle as SO2 and H2S, but rapidly converts to sulphate and rains out into the hydrosphere. Sulphur cycles back inot the mantle via subduction, primarily as sulphide minerals (which are often processed biologically). In surface ultramafic rocks - and presumably in the mantle too - separate liquid sulphide phases (a "matte")can separate out and segregate core-wards due to it's density, taking chalcophilic elements with it. Other elements don't seem to have an effective sink to the core operating to this day. This matte process probably also operated during the Earth's assembly and after the Moon-forming impact. After the GOE, cycling between sulphide and sulphate minerals happened near the surface, which can lead to some very high degrees of isotopic differentiation.
During the accretion of the Earth (or any other planet under consideration) there were several phases, with differing processes and rates of CHONPS loss or segregation. The earliest event that can be clearly dated in the Solar system was the formation of Calcium-Aluminium Inclusions (CAIs) which are now found in chondrittic meteorites. That dates quite precisely to the memorable 4.567 Gyr ago. Rapidly, about 4~5 Myr, the gaseous component of the nebula dispersed, by which time Jupiter and Saturn had of necessity formed, and probably the cores of the terrestrial planets had reached considerable size - maybe half their current masses - which were capable of holding their own primordial atmospheres. Addition of material to the terrestrial planets continued, possibly stimulated by rearrangements of the gas giants and ice giants accreting the last of the gaseous nebula, with the hierarchical accretion of nearly similar-size bodies including the "Moon forming impact" (roughly dated to 50-150 Myr after the formation of CAIs). It remains somewhat unclear how much accretion was driven by interaction with Jupiter (including bringing in outer Solar system material to the terrestrial planets), and from where the Earth's volatile inventory came. The stable isotope ratios of meteorites (and their parent bodies) suggest formation in different parts of the Solar nebula, at different times, but the story seems complex and mixed up. Possibly by the Jovian "Grand Tack", if that happened. Possibly by the (relatively) long distance movement of "protoplanets" before their mutual collision to form "planets". It is still unclear if the Solar nebular disc remained effectively segregated by isotopic composition. One of the recent discoveries is how highly siderophile elements on Earth, which should have gone into the core during the core-forming event, and the Moon-forming impact, remain accessible on the Earth's surface, where they shouldn't be. Hence ideas of a late "veneer" on the Earth's surface.
Is this a situation that numerical scientists would describe as "ill-conditioned"? Where the models are looking for the crossing points of relationships whith very low closing angles (if you plotted them graphically), so that unavoidable noise leads to numerical results which are outside the range of the possible.
There's a huge amount more in this. Which I don't have time to go into in the necessary depth. We have a good understanding of the processes involved, but which processes are important isn't clear, and may be different in different places. And our data sources are not of the best - unavoidable because of distance and the contrast ratio between stars and planets. Frankly, "more data!" - which means visiting more planetary systems as soon as possible.
Why tyrannosaurid forelimbs were so short: An integrative hypothesis
Acta Palaeontologica Polonica
A change from astronomy. APP has been a trail-blazer for Open Access publication in the field of palaeontology for a long time (well over a decade?) The journal has a tendency towards publishing material from Eastern European researchers, but it is global in it's spread. (Follow the link for the abstract ; the PDF is linked from that page.
Padian is a well-known palaeontologist, aprticularly in the cretaceous dinosaurs of Canada and their close relatives in Mongolia.
So waht's his big idea? People have puzzled over why the forelimbs of Tyrannosaurus species (rex, and others) are so relatively small since the species was recognised in the early years of the 20th century, and has been a staple of popular (vertebrate) palaeontology ever since. What is less well known outside the field, is that similar developments happen in multiple other types of large dinosaurian carnivores through both Jurassic and Cretaceous (tyrannosaurids, albertosaurids, abelisaurids, carcharodontosaurids). Something repeatedly propelled large dinosaurian carnivores towards relative reduction in the size of their arms.
Padian's proposal is that this is a passive but recurrent process. The genera which develop the small-arms feature have previously adapted their hunting and feeding strategies to using only the mouth (and it's scary set of teeth) to catch, kill, and consume their prey. This leaves the arms with, literally, nothing to do, so energy conservation tends to reduce their size. So much isn't particularly new, but Padian adds that many of these species show evidence of group or cooperative hunting (aligned trackways, mass mortality assemblages), and proposes that the presence of these arms dangling uselessly where multiple carnivores are tearing apart a prey item is an invitation to inadvertent biting, bleeding and infection, which provides an amplification to the passive drift to reducing arm size.
Padian adds a lot more detail to the argument, but that's the basic argument. Interesting idea, and Padian discusses the ways it could be falsified, which is a good sign. We'll never know witout a time machine, so we'll never know.
Weak versus Strong Chaos
PNAS QnAs with Renu Malhotra
Does any reader (not me) need introduction to Renu Malhotra? A celestial dynamicist, she studies the variation and interrelationship of the orbits of bodies in the Solar system. That PNAS chose to do a Q'n'A with her affirms her status in the field.
What struck me here was the distinction between "weak" and "strong" chaos. Many people falsely think that "chaotic" means "anything can happen" ; what it actually means is more like that "future events can't be accurately predicted far into the future".
Also, as people did more accurate computer simulations of the orbits of the planets over the age of the Solar System, they learned that Pluto’s orbit is chaotic on the long time scale. Interestingly, it’s chaotic in a mathematical sense only; it doesn’t actually translate into any dramatic consequences for Pluto’s orbit. Pluto still remains more or less very close to its current orbit, the resonance with Neptune is preserved, and nothing terrible happens to Pluto over billions of years. So, there was this understanding that Pluto’s orbit is chaotic, but only weakly so. [...] We now understand that with the orbital arrangement of Jupiter, Saturn, and Uranus, there’s only a small range of their effective quadrupole moment over which Pluto-like orbits are stable for billions of years. If that quadrupole moment were not in that narrow range, then Pluto would be very strongly chaotic. So, Pluto is much closer to strong chaos than had been previously understood.
What is the distinction between "weak" chaos and "strong" chaos?
Google Is My Friend. But I use DDG, so here are the search results. A number of discussing systems that move between weak and strong chaos, which aren't very likely to discuss the meaning of the phrase, which one would be expected to know if you're in the field. A lot of this work is done in electronics type labs - relatively easy to do experimentally, I guess.
"We start by reminding the reader of fundamental chaos quantities (https://webspace.maths.qmul.ac.uk/r.klages/papers/klages_wchaos.pdf)" ... [Contents] "2.3 A generalized hierarchy of chaos"
Sounds useful. It does help, by bringing in a thing called the Lyapunov exponent λ but there's a lot more background. "The Lyapunov time mirrors the limits of the predictability of the system. By convention, it is defined as the time for the distance between nearby trajectories of the system to increase by a factor of e." (https://en.wikipedia.org/wiki/Lyapunov_time)
Which isn't terribly helpful, since the time varies over many orders of magnitude. There are hints that people use the time-behaviour of Lyupanov exponents - if they're increasing, the chaos is strong (gets worse with time ; if they're decreasing, the chaos is weak. But otherwise, I don't find anything resembling a simple measure of chaotic-ness.
Aha! Malhotra and colleagues seem to be using the Lyupanov exponent as a discriminant. It's in the paper that prompted the Q'n'A - Doh! "Sussman & Wisdom (6) propagated the orbital motion of the outer four giant planets and Pluto for 845 million years, and found that its nearby trajectories diverge exponentially with an e-folding time of only about 20 million years"
What numbers they attach to "Strong" or "Weak" chaos though ... Or maybe not? "The detection of positive Lyapunov exponents notwithstanding, Pluto’s and the planets’ perihelion and aphelion distances and their latitudinal variations remain well bounded on multi-gigayear timescales, indicating that the chaos detected in the above investigations is very weak indeed."
This still isn't well defined. They use the J2 parameter as a probe for examining the influence of the guiant (and inner) planets on the outer bodies, and at values of J2 somewhat less than what we actually have, the evolution of eccentricity * cos(argument of perihelion) changes from attaining all values (circling the Sun) to having values restricted to one quadrant (only a partial arc) That may be what she means by "strong" versus "weak" chaos, but I wish it was clearer.
I think that's enough on this question. If I ever meeet her, I'll ask.
Freeze-thaw cycles enable a prebiotically plausible and continuous pathway from nucleotide activation to nonenzymatic RNA copying
https://www.pnas.org/doi/10.1073/pnas.2116429119
Another sideline from the usual arXivery.
The Faint Young Sun Paradox (or Problem) is the problem that the steady accumulation of helium in the core of the Sun leads (via the increasing mean particle mass) to higher fusion pressures, temperatures and so power outputs. Power increases at something like 5% per gigayear, or about 22% increase from the origin of the Solar systems to today. That implies that the surface of the Earth would have been frozen regularly and repeatedly during the Hadean and Archean. This is very sympathetic to the "Smowball Earth" hypothesis, but also suggests that Darwin's "warm little pond" may actually have had ice crusting it and sometimes covering it at frequent intervals during the O(s)OL period.
That's not necessarily a bad thing. Growing ice crystals in a pond of dilute organic soup is a good way of getting round the "concentration problem" - a growing ice crystal would have had a far higher concentration of "soup" on it's growing surface than the bulk liquid. So there are good justifications for looking at the influnece of ice crystals, even if it's not necessarily the perfect soilution. Of course, ice-crusted pools in one place are not incompatible with the products flowing down hill to ice-free pools, nor to the pools having hydrothermal heating X days in Y, and ice the other Y-X days.
Ooops, end of the month, and time to start the next batch.
