2023 February Monthly Notes Page

Trying to dig myself out of a pit of depression, I've got a lot of unread stuff. Doing OK on the languages front - I've started a campagn on trying to get the last two un-achieved achievements on Duolingo, since I'm well over the 2000 day streak mark. Anyway, digging through the ArXiv pile …

2023 February science readings.

Redshift- distance - age relationship, Working out distance and (light-)age from redshift.

Just about any extra-galactic observational astronomical paper you read mentions the redshift of [whatever they're observing. It's one of the first things they do, because it's a relatively simple observation to make. Assuming you've got a telescope whose light you can defelct into a spectroscope, set the spectroscope's inlet slit across the object, get a spectrum, find some lines (that may be a bit more difficult!, particularly for the dimmer objects), work out what they are (again, not necessarily simple, they're not actually labelled, but there are tools to help) compare to lab numbers ; calculate the redshift.

Then you quote the object's distance, and how "old" the light is (how long it has been since the light entering your telescope left the object), and frequently how old the universe was when the image we're seeing was generated. Now, that's a more complicated question, in large part because the calculation also requires you to have a model of how the universe's expansion rate has changed over the period in which the light has been "in flight". And there are genuine reasons to differ over those choices.

Nevertheless, I've long harboured the wish to be able to do those calculations for myself - an implicitly to have at least a better idea of what those choices arem and why you'd make them. And that gets into some mathematically hairy territory. (Well, hairy by my standards ; I got my Maths A-level, but at S-level, I was getting lost. Maybe if I'd gone for Maths in first year at Uni, I'd have cleared what was blocking me, but I cohose to go for Stats instead of "pure" Maths, and that has been useful. Choices, choices …).

The paper linked to above reinvigorated my hope for this project. Nomograms are useful things, though out-dated in this wonderful online world. But the particular style here is encouraging - all the lines are presented parallel, so the relationship between the elements is relatively simple. Better, there is associated source code to generate the PostScript for the pages. So the problem can't be that hard. Even better - the source code allows for adjusting one of the important parameters (the proportion of gravitating material (dark matter plus bright matter) to non-gravitating inflating matter ("Cosmological constant", "Einstein's blunder", "dark energy", whatever you want to call it) making for a "cosmological model" with a useful degree of flexibility. So, back to the grindstone of trying to work out what the relevant equations are, from lots of Wikipedia and wherever else.

Several days of Wikiing and RTFPing ... and the problem really is one of integration over your model of the universe. Which is more complicated than I really want to go. So ... I investigated the several online calculators linked to from the paper. Of those four, two are dead links, and one is limited to z <e; 10. Which simplifies matters. They agree with each other to better than 1%, which is good enough for me. So I'll just do it as a look-up table. Wright's calculator (https://astro.ucla.edu/~wright/CosmoCalc.html) produces more parameters, without the z <e; 10 constraint, so I'll use that one.

Well, I've got that working adequately (to my purposes). I'll put it up onto GoogleDocs. And here it is!

Duolingo Cheat Sheet Update

I've been working on Duo plenty. I've discovered a tool for "drawing down" my stock of those "lingot" things which are a metric of some sort, and that's leading me to revisit some of the earlier sections. It's also prompted me to try hitting the last couple of "challenges" in the Owl's imventory.

So at month-end, I need to update the French cheat sheet - which I won't have finished by then. Also any other cheat sheets, but I'm concentrating on (re-finishing) the French course. Which also means producing (slight) entried for the earlier parts of the course. THAT's tomorrow's job - I've been finishing the Redshift stuff first.

Slightly off left of the field, I realised that I'd got my keyboard (standard EN_GB) set up with the "Compose" key mapped to "Scroll Lock" - which is itslef a 3-key composite character on my (laptop) keyboard. Re-mapped it to look at the (physical) CapsLock key, and I acquire the œŒ key, and a number of others which I couldn't get with AltGr+… (or even "…"). ·₀⁰·₁¹·₂²·₃³

WEIT, on "Earth Layers"

I was writing a comment on WEIT in response to Jerry mentioning a story about discovering a "new layer of the Earth". That lead me to think how many layers I could come up with. It all got a bit too geological for Jerry's website-not-blog, but I've saved it here.

Off the top of my head, there are :

1. this paper's innermost core
2. an "outer inner" core. People have been trying to identify the core's shape for decades, but the tools available would struggle to differentiate between a non-spherical inner core, and an inner core with a transition zone to the liquid outer core. We're getting a reasonable deconvolution of arrival-time into velocities along different directions in the inner core (and other layers - it all adds to make the whole. But whether those velocity differences are the result of shape differences (it's not necessarily spherical!) or material properties, and are those materials isotropic (same properties in all directions)? After 3 years of optical mineralogy, you should be thoroughly disabused of the idea that most materials are isotropic, but that's not a common mindset.
3. the liquid (and probably stirred, but is it well stirred?) outer core
4. the D''S'' layer of high density, high velocity material at the base of the mantle (maybe the "relics" of oceanic crust slabs, after secondary reheating after subduction). Which is definitely variable in thickness, also definitely variable in velocity, and probably mineralogy.
5. the lower mantle - where the variations vary fairly steadily with depth, but not too much laterally. We think.
6. the asthenosphere (a relatively weak, "fast-flowing" layer) from about 600km up to about 300km.
7. the upper mantle (which may move relative to the plates above, or may be fixed to the plates)
8. the uppermost mantle (about 100km of material definitely welded under the bottom of plates
9. then the Mohorovičić discontinuity (a 2~4km/s jump in seismic velocity, very noticeable!)
10. then the crust proper starts - basaltic/ gabbroic under ocean basins (judging from slices brought up to the surfacce in ophiolites), an unidentified but probably also gabbroic "lower" crust under the continents and finally a granitic/ tonalitic (plus sediments) crust from between 30 and 90km depth and daylight (very dependent on local topography).

I make that 8 or 9 layers (the lower crust is fairly continuous under both continents and oceans, with only minor differences in seismic velocity, but whether it is compositionally similar ... hard question). The Kola Superdeep borehole was attempted to reach this under the Karelian Shield, and that was both record-breaking and unsuccessful. (Was this film "Superdeep" unsuccessful?). Whether you consider the Moho a layer or a discontinuity ... generally it's modelled as a distinct surface of change, but in some parameters it's "foggy", which could be a transition zone. Or multiple faults spaced by ≲λ_sound(in these rocks).

Reading The Friendly (!) Paper ... well there's not a huge amount more. By stacking multiple recordings of the same earthquake (and so, source waveform) from different stations at differing angular distances from the earthquakes' focus, to get a display comparable to CDP stacking in shallow seismography. There's some deep maths to that, but the outcome seems fairly clear. They try to get out from the data estimates of the anisotropy (fast- versus slow- directions) in the innermost core. It's not very well defined - which would argue against the occasionally-expressed "single crystal inner core" model. But maybe that will resolve with more data.

It's a nice result. Far from complete, but it does seem that seismography is homing in on an objective reality, through the mists of 5000+km of solid rock.

What is it about Croatia that produces lots of seismologists? Mohorovičić was bad enough, but this author Hrvoje Tkalčić may push me to learning how to do keyboard composition of ĉaron symbols.

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Labels: Arxiv, Astronomy, Science, Slashdot, WEIT

# posted by A. Karley FGS, BSc : February 24, 2023

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