Yeah, well for several months, I've done damned-all. Try and get back into harness. I've been thinning out the Arχiv paper listings, even if I couldn't bear to get to work on them. So let's see what remains in the pile.
2023-12-20
Over a week without doing anything. Try to get back into the habit. The HD110067 paper stuck it's nose out at me because I recognised the HD number. Which isn't normal, even for me. It's the system which was recently reported as having 6 planets at a "perfect spacing". Which is a rather problemtic description. Anyway, follow the link into the main record.
New Year
Get a few more done.
Contents
2023-09 September to 12 December Science Readings.
Revisiting Dimorphos formation: A pyramidal regime perspective and application to Dinkinesh’s satellite
https://arxiv.org/pdf/2311.07271.pdf
Last year NASA hit an asteroid moon with a spacecraft to test the efficiency of momentum transfer into asteroids. Being an (astronomically) small body orbiting in an (astronomically) weak gravitational field, the (astronomically) small amount of energy the NASA can afford to pump into such a system could produce detectable effects. The "mainstream media" didn't generally understand the point of the exercise, which was not to test if there would be an effect - everyone involved was sure there would be an effect - but to test how efficiently momentum was transferred to the body. That was a very open question, because astronomers were (and still are) pretty sure that many PHAs (Potentially Hazardous Asteroids) are "rubble piles" of many smaller bodies (from dust, up to mountains) held together by their own gravity, and were expected to be very weak. So - if hit by (say) the force of a megatonne nuke, it was very unclear if 90% of the energy would go into accelerating 99% of the asteroid's mass, or if that 90% would go into accelerating 1% of the asteroid's mass, and only 10% MT go into accelerating the main part of the asteroid away for an impact situation. That's quite an important question if we were ever faced with solving the problem in the coming year.
Anyway, that was the "why" of the mission, and a reasonably useful reesult was obtained (IIRC, about 1/3 of the momentum applied stayed in the "rubble pile, resulting in the moon's orbit being changed by about 30s - which was easily detectable. But this paper in't about that - it's about how such asteroid moons can form.
Available scenarios include : forming together (in which case, why didn't the last parts of the accumulating debris go onto the larger body, with it's stronger gravity field), capture (which Darwin (George) showed is actually quite difficult, unless you've got a "third body" to take away some of the energy and angular momentum from the encounter), impact on the main asteroid (as for the Earth's Moon, most likely ; but why then are asteroid moons so common?). Or, as this paper proposes :
[An asteroid can] deposit material into orbit via landslides.
Now, there's an idea. It doesn't sound right. If the energy comes from the movement of material under gravity, how can that material get into orbit? The trick here is that this was happening while the primary was having it's spinn increased by the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect, and that effectively reduces the weight of materials near it's surface (far from the centre of spin). And that is enough to allow some of the materials disturbed by such movements.
Which sounds very weird. But that is how weak the gravitational fields are on the "small bodies" of the solar system.
The paper has more work about the time sequence of events they infer leading to the formation of this moon, and in this shape. We're probably going to see a number more examples of this as the "Lucy" mission works through it's list of asteroid fly-bys.
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MOND Count
Formation and Growth of the First Supermassive Black Holes in MOG
A while ago, I did a count of papers posted to Arχiv over the last few years of papers on the subject of "MOND" (MOdified Newtonian Dynamics") because someone had posted (again) the false claim that scientists don't look at alternatives to the main theories of science. They do get attention - just not a lot. Previously I'd searched for "Mordehai Milgrom", "MOND" and "Non-Newtonian Gravity". "MOG" is another search term to watch out for. My previous searches have looked at yyyy-12-31 as a cut-off date, so I'll carry on with that.
Hmmm, moderately interesting - at current publishing rates, Mordecai Milgrom looks likely to retire (or stop publishing - same thing, really) about 2030~31.
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Formation of the Cartwheel Galaxy
Star formation history of the post-collisional Cartwheel galaxy using Astrosat/UVIT FUV images
The Cartwheel Galaxy is one of the prettier - and weirder - sights on the sky. To the telescopic eye, one can see an outer ring of bright, bluish stars, and an inner ring of slightly redder stars around the margin where approximately the edge of the nucleus would be, and a set of slightly curved "spokes" faintly link the two main structures.
It's a pretty thing, shouting a really loud "How?" across the universe across to us.
The general understanding of this galaxy's structure is that another galaxy passed, nearly centrally, through the "Cartwheel" galaxy. In 1996 radio telescopy detected a discontinuous band of neutral hydrogen emission stretching from the Cartwheel towards a nearby galaxy, "G3", which is interpreted as the impacting or "bullet" galaxy. Critically, this emission structure extends beyond the other nearby galxies, "G1" and "G2". A wider view of the system than the "pretty one" shows the relationship of the galaxies: (this is an image from the DSS - Deep Sky Survey - but as a negative image) :
This paper reports studies on UV emissions and brightness to estimate the star-forming rates of the Cartwheel's brighter regions, and infer the time since their formation. So we now know that the galaxies were in collision at about the start of Earth's Carboniferous period, 300 million years ago. With some modest error bars.
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December HTML things
link
What got me prompted to try to get back to work was seeing a reference to an unusual bit of HTML CSS - the "rotate" property. With this, you can ... go on, guess ... rotate text (well, strictly, a division of a page) about a point.
So, naturally, I wondered, will it work in Blogger's sandbox? Let's try.
I'll start by using my handy-dandy bit of table template :
And now, I wrap it up in the "div-Wol-Rotate" division I've defined up in the page's style header.
div-Wol-Rotate { height: 100px; width: 200px; background-color: lightgrey; rotate: 1 1 0 60deg;
Not working. 3 axes? no Angle? No (and the bgnd-colour isn't working either) Ah, whoops, missing trailing ";" Size? Nope. Still doesn't seem to be working. Quick dive over to the "try it" sandbox at W3schools.com ... and the code above works there, but not here. Deduction : Blogger doesn't like rotation. Oh well
I picked up this question from reading Elf Sternberg's blog, about recreating the 1994 alt.sex FAQ website in modern coding. Now, I don't know how often Mr Sternberg gets people linking to the programming bits of his website, but just so he knows, from the above - people don't only read his website one-handed.
I can't claim to have fully understood the "rotate" property - the height, width and definition of the rotation axis interact in some way I need to look at to shear the image before the rotation is applied. I need to work on that. but it doesn't seem to work here, so I'll shelve it for now.
Fiddled with the CSS for HR elements though.
A bit more mucking around with tables in IMF article.
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The Cosmic Train Wreck Galaxy, Abell-520
How Zwicky already ruled out modified gravity theories without dark matter,
This 2017 paper just jumped out at me while doing the counts of "MOND" and "MOG" and "dark matter" papers while checking out the question above.
It has interesting bits. Who could resist a phrase like "The Cosmic Train Wreck Galaxy"? Not me - that's for sure. It sounds like something "fun" happened, in the sense of "may you live in interesting times", and "best observed using a telescope". Even better that it's in a context of overheated extravagant astronomers, not staid, restrained stage actors who couldn't emote if you pulled the stick out of their back, leaving splinters. Talk dirty to me, like a central 3-4 × 1013M☉ mass clump with mass-to-light ratio 800 × M☉/LR☉. i don't know how dirty, but that's definitely dirty talk! (There's probably a typo - "LR☉" for "L☉" ; I'm sure I'll find a resolution somewhere.)
OK - how dirty are we? 800 Solar masses for each Solar luminosity? Let's see - Sol is heavier than about 90% of stars, but the decrease in luminosity with decreasing star mass is steep. A half-M☉ star has a luminosity of 0.063 × L☉ (about 1/16th) while at the other end of the mass scale, the luminosity ramps far more steeply than the star mass. A 20 × M☉ star shies with luminosity 53600 × L☉. So, calculating the mean brightness of matter on a gelactic scale is .. hairy. It's not clear to my limited maths if it'll be a figure above or below 1 × M☉/L☉. Probably not wildly off from 1 × . So 800 × is a galaxy with remarkably little light for it's mass. Something seems to have wrecked the galaxy's mechanism for turning mass into luminosity. No wonder people noticed them (once they'd done their accounting).
The "Train-Wreck Galaxy" has 4 references linked ( 13 M. Jee, A. Mahdavi, Hoekstra et al. The Astrophysical Journal 747(2), 96 (2012).
14 D. Clowe, M. Markevitch, Bradaˇc et al. The Astrophysical Journal 758(2), 128 (2012).
15 M. J. Jee, H. Hoekstra, A. Mahdavi, and A. Babul The Astrophysical Journal 783(2), 78 (2014).
16 Q. Wang, M. Markevitch, and S. Giacintucci arXiv preprint arXiv:1603.05232 (2016).
) but the rather more accessible Wiki article suggests that later observations have picked up considerably more luminosity, reducing the seeming unusualness of the galaxy cluster by quite a lot. It's still odd, but less odd.
The other list of cosmological oddities is worth looking at too. As they phrase it, so Lambda;CDM is rightfully a good effective theory. But is it a fundamental theory? Many puzzling observations make this nonevident.
:
- The CDM particle, the WIMP, if it exists, keeps on hiding itself 6 more years since its “moment of truth” ;
- One observes 19 quasars with spins aligned with their hosts large-scale structures on a scale of almost 1 Gpc (ref.10) and dozens of radiojets from AGNs aligned on a scale of 30 Mpc (ref.11) ;
- A ring (actually, a spiral) of 9 gamma ray bursts extends over nearly 2 Gpc (ref.12) ;
- the "train wreck galaxy" that caught my attention above (which may not be so weird) ;
- in the cluster A3827 the offset between baryonic and dark mass (ref.17) is an order of magnitude ‘too large”(ref.18) ;
- Puzzles in galaxies include: the brightness fluctuations in the Twin Quasar allow a DM interpretation in terms of a large halo of rogue planets in the lensing galaxy (ref.19) ;
- the observed satellites of the Galaxy lie in a plane, not in random ΛCDM directions (ref.20) ;
- the predicted transition for the most massive galaxies to transform from their initial halo assembly at redshifts z = 8 − 4 to the later baryonic evolution known from star-forming galaxies and quasars is not observed (ref.21) ;
- the galaxy power spectrum deduced from SDSS-III observations fits well to the stretched exponential exp[−(k/kb)1/2] from turbulence (ref.22) ;
- Various further arguments can be found in our investigations (refs.23,24) ;
That's an interesting list of "problems" with the ΛCDM model, while acknowledging that it is still a good model. No joy there for Archimedes Plutonium and the Electric Universe crowd of the deluded. Frankly, while they're interesting, they're not interesting enough. Just worth me noting down, to counterblast people claiming "censorship" and "suppression" of unorthodox thinking.
Why did Zwicky think you needed dark matter, not MOND/MOG, in the 1940s?
On a third reading, I still don't get the argument the authors are making. They seem to think that, for the cluster they study (Abell 1689 ; the mention of Abell 520 is just in the "problems with cosmology" section of the introduction ; it doesn't help that this is a fairly early draft, with several arguments re-written in the text.) their calculation under several generic "modified gravity" models, still need to add some non-visible mass to the system to match the observed lensing [strong ("SL" with multiple arcs for identifiable background galaxies) and weak ("WL" with shape distortion of individual background galaxies)]. Their preferred (why?, not clear) DM candidate is neutrinos. Particularly "heavy" neutrinos with a mass of ≦ 2.0 eV. Most experimental estimates for conventional neutrinos gives them a mass of ≈ 0.1 eV - a substantial difference, but some particle physics ideas produce "sterile" neutrinos in this mass range.
I think they need to make their point on Zwicky clearer - the title is attractive, attention-getting. But I can't follow their reasoning.
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Element Abundances
The abundance discrepancy in ionized nebulae: which are the correct abundances?
A long-standing question I've had is : what is the average composition of a planet (asteroid, "small body"), versus this particular surface, or an ore body. There are a lot of slightly different answers in the literature, and not a lot of clues pointing to the most-accepted (and most detailed) answers. Slightly different, but related, answers often given for this question include :
- "What Is the Composition Of ("WICO") the Sun?" (not necessarily the same as the average planets)
- "WICO the Sun, if you lose the H and He?" (ditto)
- "WICO a CI meteorite? Is it the same as their parent bodies before impact heating?"
- "WICO the Earth (including the core)?"
- "WICO the Earth's (or any other planet's) surface?"
They're all quite similar questions, with not quite the same answers. And the differences may (or may not) be significant when you're trying to consider the changes implied by formation processes. Obviously, I'm looking for a full, 92 element composition. How it's expressed is an issue to be wary of - a short while ago I had one of those "drowning goldfish" moments when someone was talking about "atmospheric carbon di-oxide being absorbed by the lime (calcium oxide) present in basalts". It took a time to realise that he was reading the traditional geochemist's way of reporting compositions as "oxides" (e.g. 40% SiO2, 10% CaO, 10% Al2O3 …), and taking that to mean that a basalt contains grain or molecules of actual CaO, with all the chemical properties of a lump of quicklime. Which ... well, I can see why this relic from gravimetric "wet chemical analysis" of the 18th century is confusing. But it obviously can lead to profound misunderstandings. Gotta watch that banana skin.
I'm slightly surprised that my confused correspondent didn't notice that the trace elements are normally reported as "ppm of [Element]", rather than in the "oxides" presentation. I suspect I'm going to have to address this in more detail one day. It may explain a lot of confusion about geochemistry.
So, interesting paper title, given that context. Does it deliver?
OK - first thing is to see the paper as a contribution to a programme called "Planetary Nebulae: a Universal Toolbox in the Era of Precision Astrophysics" - which isn't terribly optimistic for my "geochemistry" interests. Still useful enough though - what a star spits out this gigayear is likely to affect the composition of next Gyr's molecular cloud, hence stars and attendant planets.
From TFA : "However, the heavy-element abundances derived from collisional excited lines (CELs) and recombination lines (RLs) do not align." - which is what they mean by an "abundance discrepancy". Going back to the "oxides" presentation discussion above, the technology of measurement influences the precise data collected, and how it's expressed. Specifically, since they're measuring line strengths in spectra, I'd be surprised if they presented their abundances as "oxides".
Actually, it's quite a big effect. From the paper's introduction :
However, there is a problem, and it is a big one: we are not certain about the correct abundance of heavy elements like O, C, N, Ne, collectively known as “metals”. Since the pioneering works of Bowen & Wyse (1939) and Wyse (1942), it has been known that the abundances of these elements determined from the bright collisionally excited lines (CELs) (e.g., [O III] 5007, 4959) are systematically lower than those inferred from the faint recombination lines (RLs) (e.g., O II 4649, 4650). The ratio between both estimates is known as the ”Abundance Discrepancy Factor” (ADF), and it has been found to be around a factor of 2-4 in H II regions (García-Rojas & Esteban 2007) but can reach values of more than 500 in some PNe (Wesson et al. 2003).
A discrepancy of 2~4×, but up to 500× - yep, that's a problem. But, it's an astronomer's problem, not really a geochemist's (or planetary scientist's) problem, so I think I'll just file that as a detail to watch out for.
Annnnd … the paper is discussing the various ideas for explaining those discrepancies, but not presenting an example composition for any of their target objects. Ho hum. That just leaves me with the materials I've already collected in my "compositions" collection ( http://ArXiv.org/pdf/2105.01661v1.pdf which gives Solar photosphere and CI chrondite compositions for 83 elements ; 54 terrestrial rocks from "Science Snippets" on my HDD ; … ; ; ; ) and anything I add to it. Back to the grindstone. I still don't have estimates for the average composition of the (local) universe. Granted that the outer arms of the Milky way are second (or third) generation stars, enriched by at least one (possibly two or even three) previous generations of stars burning, exploding (for the larger ones) and contaminating the (primordial) interstellar medium ("ISM", H, He, trace Li) with "metals" which change the structure and nuclear processes of the stars. Probably I'd be looking for a local Milky Way composition, a Solar system one, and maybe a composition for an estimate first generation ISM.
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6-planet system is a multi-star system.
HD 110067 is a wide hierarchical triple system
A couple of weeks ago there was a moderate amount of news fuss over the announced discovery of a planetary system containing 6 planets whose orbital periods were at small-integer ratios (2:3 ; 3:4, etc). News coverage was all over the place. Which was all very well and good, but the source paper was a deal more nuanced than the write-ups in the popular press (well colour me sideways and brush me with a Blackadder-shaped paint pot!) Most was made of the small-integer orbital period ratios - which to me (and most people) talks of the system having gone through a phase of planetary migration that carved these ratios - probably when there was some degree of "viscosity" in the system to damp interactions to some degree. (all that means is - considerable remaining gas, or many "small bodies", being present to diffuse energy and angular momentum less violently than by collisions or close approaches). The more interesting thing, to me, is how a relatively sparse set of observations were translated into "six planets". Although the reviewers at Nature must have challenged this, I'm sure they were convinced by the data in a way I can't (and am not interested) to challenge. I accept that they've got at least some of the planets adequately located.
This original paper was published in Nature, (here, titled, "A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067", which contains substantial "Supplementary Information"), but the paper was also released on Arχiv without the access restrictions of Nature (but also without the "SI"). You should be able to judge the paper on it's own merits, but the SI is probably in large part a response to the reviewer's criticisms (or their anticipated criticisms - same difference really). I'll refer to this as the "Nature paper", with the titular paper of the "triple star" system being referred to as the "Arχiv paper".
The Nature paper reports several long-period observations of the target star (HD110067 - "HD"= the Henry Draper Catalogue and a reference number) using the TESS (Transiting Exoplanet Survey Satellite) observatory in two sessions, two years apart. The first observing session recorded 4 transits (3 of which had a common spacing - indicating one planet ; one unconstrained transit). The second session recorded 9 more transits, which confirmed the first candidate (HD110067 b, period 9.113678 days) and a second (HD110067 c, period 13.673694 days)candidate observed in both sessions. Leaving 8 unexplained transit events - which was sufficient justification for observing periods on CHEOPS (CHaracterising ExOPlanets Satellite) of fractions of a day around possible repetitions of one or more of those potential objects. In considering potential observing times, the negative evidence - that neither of the TESS sessions had recorded transits except at the noted times - which constrained the possible orbital periods associated with those transits. This series of observations confirmed HD110067 d (period of 20.519 days). Those periods (bc ; cd) were both close to a "Mean Motion Resonance" (MMR) ratio of 3:2, justifying further data collection.
This is where the "chain" of logic starts to get a bit thin. There was adequate justification for targetting more observation time, and some of that justification is in the "SI" of the Nature paper. Another planet was discovered by analysis of one of the transits, for which there was an absence of a second transit in the other TESS data set. This was identified as HD110067 e (period 30.7931 days, in a 3/2 MMR with planet d) - but only on the basis of two transits. That left two unexplained transits in the TESS data. With the assumption that these represent more planets, which continue the chain of low-integer period ratios. Which is how they proposed two additonal planets, which should have been seen in the original TESS data. But the periods they should have been there were also when the Moon or Earth were also near the satellite's line of sight (TESS orbits between a little above geocentric orbit, and a little below Lunar orbit), so originally these records weren't analysed because of glare. When this study gave adequate reason for study, ... there were the expected transits, in the (rather noisy) data. So that gave confirmation of HD110067 f (41.05854 days) and HD110067 g (54.76992 days). Which is sufficient for the reviewers and for science - but it's a lot thinner than the stereotype of multiple transits per planet.
That is how future planet identifications are going to go. If we're looking for evidence of "Earth-like" planets, you're not going to get the stereotypical multiple tranists at a rate faster than 1 observation per planetary "year". So inevitably, we're going to see increasing numbers of single-transit detections, and longer chains of inference from raw observation to deduced planet (and their properties).
Some work was also done using ground-based observations, which revealed a fair amount of magnetig and radial-velocity noise in the system, but some support for the planetary system too.
The inferred planet properties are nothing wildly unusual. They're close to the star (necessary, to find multiple transits of the first few members of the chain), at average radii (of 0.0793, 0.1039, 0.1362, 0.1785, 0.2163, 0.2621 AU) all within Mercury's orbit compared to the Sun. The deduced surface temperatures (from the star's temperature of 5266 K, and the orbital distances) are high, but not extreme (800, 699, 602, 533, 489, 440 K); a short distance out from the detected planets would be the "habitable zone" of the star. The star is estimated to be about 8 billion years old - about half way through it's estimated 17 billion year lifespan, from it's 0.798 solar-mass mass. The planetary masses (5.69, <6.3, 8.52, <3.9, 5.04, <8.4) are in a range not found in the Solar system, but actually very common in exoplanet studies.
The triple-star aspect
The second, "Arχiv" paper is also an event likely to recur. While the first group had been doing their transit-based study, other data was present in already-taken databases. The Nature paper took the primary as being a single star, it had been classified as a "wide binary" since at least 2001 (references in the Arχiv paper) using positional records from 1893 to 2015 (that must be a later revision of the "Washington Double Star Catalogue" than the 2001 reference). To my moderate surprise, the listed companion is also in the HD Catalogue, and in the original numbering system (number 110106), which implies it is quite bright, quite close, and could be spectroscopically investigated at the turn of the last century. That clearly shows that the two stars are indeed, a wide binary, separated by 415 seconds of arc, which at the star's distance (32.25pc, 105.2ly, from Gaia data) translates to some 13394 AU - which is very comparable to the spearation of Proxima Centauri and Alpha Centauri A+B. To further the similarity of the two systems, both Alpha Centauri and HD110106 are double stars - though Alpha Centauri can be resolved by telescope, while HD110106 hasn't (yet).
Since these secondary stars are well out of the line of sight to the primary, with it's resonant planetary system, they don't interfere with the detection of the primary's planets. The presence of a wide binary companion (s) do raise questions about the planet-forming process around the primary, so it's a safe bet that more investigations of this system are planned. You heard it here first.
Back to List. 2023-12-20
Dating of a Latin Astrolabe
https://arxiv.org/pdf/2311.17966.pdf
quote
mark
This is just a piece of fun. Ha-ha, but serious fun.
An astrolabe is an astronomical observation instrument consisting of a plate (the "mater"), a targeting sight bar (the "alidade"), a "plate" engraved with the coordinates of the celestial sphere, a movable metal net ("rete") which indicates the position of various stars, and a suspension point and vertical bar ("rule", which keeps it aligned with local vertical). It can be used for surveying, for measuring the altitude of heavenly bodies (and hence, local time), and of course identifying heavenly bodies (particularly since they normally had a celestial chart engraved on one face). Mediæval users suggested that there were a thousand uses, many of which were listed in a manual on the device written by Geoffrey Chaucer.
One of these days I'm going to find one in a second hand shop (I've got a sextant somewhere a working toy) and learn how to use it.
By pointing the sight ("alidade") at an identified star, and aligning the net ("rete") to match the star's indicator to it's altitude, one can work out the local time from the celestial grids enmgraved on the plate ("mater"). Other ways of solving two knowns for an unknown can also be done with the instrument - including (for the many Islamic users) locating the direction of Mecca in order to pray towards it (the "quiblah". [Totally tangential, I wonder if that was the inspiration behind Rowling's "Potterverse" equivalent of the "Fortean times", the "Quibbler".]
That's the mechanics. The astronomy, by which the astrolabe's manufacture (or design, or calibration) date was determined is that the precession of the equinoxes (rotation of the Earth's spin axis compared to the celestial sphere) moved the position of the stars relative to the celestial grids, allowing the determination of the manufacture (or design, or calibration) to approximately 1550 (CE ; all dates are CE, not AH).
The reason I specify "manufacture (or design, or calibration)" is that once soneone has made one of these, then the additional work to make a second is relatively small, separating "design" and "manufacture" events. The way of indicating star positions (extensions of the "rete" as long pointers, with the star being at the tip of the pointer) is potentially amenable to being fine-tuned with a pair of pliers, so a 1550 design might still be modifiable for use in 1650 (or a 1450 design for use in 1550). In fact, if the "rete" were made by casting in bronze, the raw casting would very likely need some cleaning up, and adjustment because castings - particularly reticulate ("net-like" ; same Latin root) castings often distort as the cool from molten bronze to room temperature. It's very unlikely that the raw casting would have been flat to the plane of the "mater" without some tweaking.
The pictures in the paper aren't high enough resolution to see if the "pointers" have been tweaked. But I bet they have. (when I posted the full-resolution image, I looked more closely - the "rete" is made of several pieces, which look to be cast and have then been soldered together. Yep - that almost certainly needed "calibration" after soldering together. Whether that was higher precision than this naked eye instrument would have needed ... maybe not. But it's at the limit.
Just a fun bit of sideline stuff. For me. Isn't this a thing of beauty?
Caption : Figure 6: The front of the astrolabe, with a plate, the rete, the alidade (diagonal bar), the rule (vertical bar).
Back to List.2023-12-21
Initial IMF
Nebular dominated galaxies in the early Universe with top-heavy stellar initial mass functions
That's a convoluted name for a relatively simple idea, with an awful lot of consequences.
As JWST has rapidly improved our state of knowledge of galaxies in the early universe, there has been an increasing tension between the inferred properties of those galaxies. What we can observe are luminosities at different wavelengths. But to convert those observations into a model of stellar populations, ages, brightnesses and interactions, we need a way to convert those luminosites into a number of stars, at a selection of brightnesses. This is not simple, because the brightness of a star does not relate simply to it's mass. The relationship is far from linear.
Which, frankly, has been known since the start of astrophotometry - the (reasonably) accurate measurement of star brightness - in the 1870s. When that was combined with positional measurement (revealing parallax, for relatively close stars, and from that the distance to the stars), and analysis of eclipsing binaries (which gives disc sizes, relative brightness in a pair, and the absolute masses of the stars in a pair), a relationship between a star's mass and it's brightness (when on the main sequence - where stars spend most of their lifetimes) emerges. But it's not a simple relationship.
In my handy-dandy pile of astronomical data and calculations, I put together a handful of ranges of mass to cover the (main sequence) brightness of stars in the Milky Way.
Stellar Mass - Brightness relation (referenced to Sol)
| Star Mass (M☉) | Luminosity (L☉) | Main Sequence lifetime (T, Gyr) | Comment |
| 0.1 | 0.001 | 1000 | Quite approximate |
| 0.2 | 0.006 | 333 | Luminosity ≃ 0.23 × (mass ratio)2.3 |
| 0.3 | 0.014 | 214 | |
| 0.5 | 0.063 | 79 | Luminosity ≃ (mass ratio)4.0 |
| 0.7 | 0.24 | 29 | |
| 0.9 | 0.7 | 13 | |
| 1.0 | 1.0 | 10.0 | (solar estimate) |
| 1.3 | 2.9 | 4.48 | |
| 1.8 | 9.4 | 1.86 | |
| 2.0 | 16.0 | 1.25 | Luminosity ≃ 1.5 × (mass ratio)3.5 |
| 2.5 | 37.1 | 0.6739 | |
| 5.0 | 419.3 | 0.1192 | Gyr |
| 7.5 | 1733 | 43 | Myr |
| 10 | 4743 | 21.1 | Myr |
| 15 | 19600 | 7.5 | Myr |
| 20 | 56670 | 3.73 | Myr, Luminosity ≃ 3200 × (mass ratio) |
| 30 | 84000 | 3.57 | Myr |
| 40 | 152000 | 2.63 | Myr |
| 50 | 240000 | 2.08 | Myr |
| 75 | 550000 | 1.37 | Myr |
| 100 | 980000 | 1.02 | Myr |
| I have two references for this : arxiv 1710.11134.pdf and "The Astronomical Journal, 154:115 2017, Table 1" ; it's likely that the exact numbers will change with time, but not by much. |
Already the lower rows of that table are decidedly uncertain. Massive stars (more than a few solar masses) typically lose more than a few percent of their mass during their evolution (through "solar wind", strong coronal mass ejections and other processes) meaning thir luminosity and lifetime will vary considerably from the initial expectation, which is based on nuclear physics. But you can clearly see that the total luminosity varies a lot more than the stellar mass. 100 solar masses of material will shine (approximately) as brightly as 100 Sol if in individual stars, but nearly 10,000 times brighter if collected into one body.
A significant uncertainty in the nuclear physics part of this model is how much non-primordial (H, He, a touch of Li) matter there is in the mix. Since nuclei like C and N take part in catalytic series of nuclear reactions at lower temperatures than without them, even small amounts of such nuclei can considerably alter the rate of energy release form the cores of medium-size stars, and hence the mass- luminosity relationship.
When all the data you have about a distant object is it's total luminosity and distance (from it's redshift), you don't have enough data to directly infer the mass of the body (galaxy) from that data. You have to, somehow, incorporate some relationship between luminosity and mass - such as the table given above. The conventional way of doing this - in the absence of any better information - is to assume that the remote object has a similar relationship to that present in the Milky Way. It's an assumption, but it's an explicit assumption, and very open to challenge. This paper challenges that assumption for high red-shift galaxies.
(It is worth noting that, because the evolution of bright stars releases non-primordial nuclei (heavier than Li) into the interstellar medium of a galaxy, it is expected that the brightness-mass relationship will change with time - and that always has been expected. Exactly how the mass-luminosity relationship changes with time remains a matter of debate though.)
This paper looks at the spectrum of the light from three of these high red-shift galaxies (GS-NDG-9422, at red-shift z = 5.943 [reference 14]; the "Lynx arc" [from "Massive Star Formation in a Gravitationally Lensed H II Galaxy at z = 3.357.
reference 15 from the paper] ; and A2744-NDG-ZD4 at red-shift z = 7.88, reference 16) and sees a distinct break in the spectrum that they infer as meaning there is a lot of gas heated to tens of thousands of Kelvin, producing significant "free-bound" electron interactions. Those temperatures are a lot hotter than the hydrogen ionisation event which gave the Cosmic Microwave Background (CMB) radiation at a temperature of approximately 3000 K, allowing the inference of considerable numbers of stars of high brightness that "pump up" the galaxy's gas temperature to these levels. Which means that the "Initial Mass Function" of the galaxies is richer in heavy stars than the Milky way of today. And in turn, that means that the inferred mass of the galaxies - which had been stressing models of the evolution of the early universe would be considerably lower.
Having a "top heavy" initial mass function in the early universe will require a lot of re-calibration of models of the evolution of galaxies. But at least there is now some data to suggest in which direction, and by how much, to adjust the models.
I see that Dr Becky Smethurst has done a video-blog on this paper on her "Night Sky News" channel.
(The heaviest species detected in the spectra is argon (lines at λ4711 and λ4740 &Angstrom;, which would suggest some "silicon burning" nuclear reactions.)
And that's New Year, so on to the next page.
