2023-07 July Science Readings

Well, I didn't do damned-all last month. Other things.

There seems to be a lot of work on stellar dimmings going on at the moment.

Articles studied this July- some of which might go to Slashdot.
A first great dimming.Betelgeuse Misbehaviour
Beware of Hubris : World Is Not Enough - WINE
Discovery of Gaia17bpp, a Giant Star with The Deepest and Longest Known [Stellar] Dimming Event
Astrophysics observatories as seismographs
Great Dimming But RW Cephei, not Betelgeuse
Potential Supernova Candidates
Exponential distance relation (aka Titius-Bode "Law") in extra solar planetary systems
End of document

Betelgeuse Misbehaviour

The evolutionary stage of Betelgeuse inferred from its pulsation periods

(Further discussion from Molńar, Meridith and Leung appended to original article.)

About a year ago, I posted on the unusual behaviour (misbehaviour, even) of Betelgeuse over the last few years, with the "Great Dimming" superimposed on it's semi-regular brightness variations. My "laughing price" thesis was that by extreme extrapolation of diameter estimates for the star, one could "predict" [sic, my tyops] simplistically, the expected "zero diameter [tyop, "] date range for Betelgeuse is 2030 to about 2040. That was from a 2009 paper, well before the "Great Dimming". Totally unreasonable from any statistical point of view, and I knew it as I calculated it.

So, another paper has come out, also pointing in the same sort of date range, but predicting a supernova not a disappearence up the stellar jacksy. Meh, I can live with that. They've probably approached the question more seriously than I did.

These authors are using a slightly more realistic stellar model than mine, and also new interpretations of old data which suggest (Neuhäuser R., Torres G., et al, 2022, MNRAS, 516, 693) that in the pre-instrumental period, Betelgeuse was yellower (and so, hotter) then than it is today. They put this - the colour change ; the semi-periodic pulsations - together to come up with a revised model for Betelgeuses fundamental parameters thar are a bit different to generally accepted models, but not wildly so. And which, these authors suggest, means that Betelgeuse is teetering on the point of experiencing a core collapse supernova in the imminent future - within a few tens of years.

Well, that'd be fun, for almost everybody. An end most devoutly to be hoped for. And on an "I told you so, young whipper-snapper Grasshopper!" timescale.

Now for the inevitable back-pedalling :

Modelling like this is pretty uncertain. Sure, we've now got a mass estimate that is 19 solar masses (M_☉ hereafter) compared to previous mass estimates of 11~14 M_☉. That has a lot of consequence for the stars expected main sequence (MS) lifetime (16~9 Myr for the lower mass range, 4Myr for the higher mass range). The post-MS lifetimes also become much shorter as the star mass goes up, and the variability and the dust clouds and mass outflows visible in and around Betelgeuse rather suggest it's already in it's post-MS phase.
It's almost unrelated to the "Great Dimming", which is most likely (IMHO) a previous dust emission, thinning and dispersing. That could easily happen on multiple century time scales, and could also affect the stars colour (as discussed by Neuhäuser et al, 2022, marked above). Which would weaken at least one major plank in this paper's estimate of Betelgeuise's mass. Since the invention of the telescope, we may never have seen Betelgeuse/s un-dimmed state.
Dr Becky had doubts too, expressed on her "Night Sky News" vlog (timestamps 06:50 ~ 14:30) - but they're pretty similar to mine. I'd add to her "general principles" concerns that we also don't know the metallicity of the core of Betelgeuse terribly well, and thats … somewhere between likely to have an effect, and unlikely to have no effect. We think that the heat transfer from the core outwards is by radiation, not by convection, so the surface (photosphere) composition is decoupled from the core composition. How decoupled ... aye, there's the rub. (Smaller stars than the Sun, "M dwarfs", may be "fully convective", where convection stirs the core material into the main body of the star, but this takes time, and in the latter stages of evolution, things happen in the core on a matter of years, while mixing may be on much longer timescales.
She was probably wrong about one thing though - the last supernova in the Milky Way wasn't "Kepler's Supernova" of 1604, but a previously unremarked star in Sagittarius, which went supernova between about 1890 and 1908 producing the radio feature G1.9+0.3. That was invisible from Earth behind dust clouds, but the supernova remenant (SNR) is obvious (and visibly growing) in radio wavelengths. Kepler's was the last naked-eye supernova in the Milky Way. It's very likely that humans will see Betelgeuse going supernova when it goes, because it's so close (450~650 ly, 150~200 pc) that it'll be naked-eye even during daylight hours (unless it happens when in conjunction with the Sun - approximately May to August, depending somewhat on the observer's latitude). Whether it happens before humans lose telescope technology is a more open question.
Of course, all this attention on Betelgeuse deflects attention from other stars which have a good chance of being the next Milky Way supernova. There's Eta Carinae, trembling away like a Hollywood child actor's lower lip; a list of 31 candidates within 800 ly of Earth (OK, Deneb/ α Cygni is 802 ly, plus or minus error bars), and a lot of other runners and riders. (After writing this, a paper concerning recent strong dimming in the "hypergiant star RW Cephei" has added another, distant, name to the "runners and riders" list. See discussion below.
It's almost inevitable in discussions like this that we have to re-stress that all the times mentioned in this topic are in Earth's reference frame, not Betelgeuse's reference frame. Yes, of course the star could have gone SN already, and the light (and neutrinos) from the event are on their way to us. But we won't know that until they get here. making the point moot. Astronomers understand this well enough that since before SN 1987A people have been plotting to observe "light echoes" from SNs (and ordinary novæ) bouncing off dust clouds behind or to one side of the (super)nova, including looking for the arival (at Earth) of light from flares and outbursts of the progenitor star before the "main event". (Eta Carinae has been a notable success in such searches, IIRC. I didn't make notes.)
(Including this caveat won't mean that nobody re-flogs the bones of this particular flayed horse. Suffer, dead Dobbin, suffer!)

Routinely, when discussing "the big one", along with the dead horse flogging over reference frames (really guys, we get it. Why is it always guys who flog this flensed Equus?) there are questions along the lines of "are we all going to die?"

The answer is "almost certainly not". When we get a "big one", it'll be the 3rd or 4th in a millennium. One going off about every 250 years, that we see. Seriously, outside astronomers, almost nobody notices. Horses chowing grass might riase head from sward for a few seconds, then go back to grazing and worrying about internet trolls and temporal reference frames. Late night taxi drivers might ask "what's that light?". At the right time of the year, daytime people might repeat the question. And almost everyone will forget about it in a few days or weeks. Alart form astronomy nerds, who will be boring people to absolute death about it. Boredom by an astronomy nerd (or bludgoning of the same nerds) is likely to be the biggest death toll consequent on the next "big one".

Specifically, for Betelgeuse, there is one potential "everybody is dead" scenario which is very unlikely. Supernovae remain potential sources of Gamma Ray Bursts ("GRB", possibly also sourced by "compact body" (neutron stars and black holes) mergers, now visible to our gravity-wave telescopes), and one of those going off 600-odd ly away could be a potential bad hair day for a lot of people. Depending on how long it lasts, Homo sapiens mighte be depending on the crews of steel-hulled ships, oil rigs & submarines to bounce back from being hit by such. Which might be game over for the species, and certainly a rough time. But probably not either. Living organisms in the open might die. But all seeds below the soil's surface, nope. Ditto some organisms living in cave entrances facing in the right direction should get enough protection. It's very unlikely to be an "end of life" situation - a mass extinction scenario more likely (hint : 6 of the 7 biggest mass extinctions have obvious non-GRB causes). Even if it happens.

But for that - the Earth to be hit by the beamed energy from a GRB - to happen, we would need to be very closely aligned with the progenitor's rotation axis. Various imaging campaigns from the mid-1990s to the present see noticeable variation in Betelgeuse's brightness from epoch (date of observation) to epoch, which suggest that we're not on the stars rotation axis (the longer-established overall brightness variations argue similarly). A 1998 paper ("Spatially Resolved Hubble Space Telescope Spectra of the Chromosphere of alpha-Orionis". The Astronomical Journal. 116 (5): 2501–2512. Bibcode:1998AJ....116.2501U. doi:10.1086/300596. S2CID 117596395.) suggested that we're about 20° off the star's axis. Which is probably enough to protect us from the "relativistic beaming" of a full-on GRB, and reduce the radiation from a pulsar to about 1 second in 5 - which the atmosphere will reduce further. I just don't see Betelgeuse being much of a (realistic) GRB threat.

Besides, Betelgeuse is probably too small ; if you really want to worry about a GRB, worry about Eta Carinae - but that is around 10 times further away, which factor alone would reduce the radiation dose about 100-fold. And we're 30~45° from the axis of that system. So that's a big fat nothing-burger too.

That's enough Betel-juicing for now.

That was last night

This morning's IArXiv (summary of today's ArXiv postings, weighted by my responses to previous IArXiv listings; though I'm actually somewhat behind on drinking from this particular hosepipe) brings this comment paper : "Comment on the feasibility of carbon burning in Betelgeuse: a response to “The evolutionary stage of Betelgeuse inferred from its pulsation periods”, arXiv:2306.00287", which is various credentialled astronomers responding from Hungary and America. I've dropped the link to Dr Becky, since she's posted on this tool. What are they saying?

These people assert (to be evaluated) that Saio et al's interpretation of Betelgeuse's brightness variation as solely a consequence of pulsations in the diameter of the star is incorrect. "However, the angular diameter measurements of the star are in conflict with the stellar radius required by their models". So, are these objections justified?

I recall thinking, as I read Saio et al's estimate of the radius of Betelgeuse - derived from their pulsation model - as being "higher than normally suggested". But an inflated radius for red giant and red supergiant stars is, as the name suggests, rather normal, so I wasn't wildly upset about it.

From The Friendly Paper (FTFP), on the subject of the star's diameter, "However, measurements do not necessarily detect the visible-light photosphere of the star directly. They are affected by factors like limb darkening, spots, molecular layers and circumstellar dust." Which, yes, that's a large part of why I wasn't terribly upset by the difference between Saio et al's radius and previous estimates. These authors present a considerable compilation of "Visual", "V-band" (an astronomical wavelength-range filter) and "SMEI" ("Solar Mass Ejection Imager" ? Why would a solar telescope be pointed at Betelgeuse? From the first light photos, it can image the Milky Way, but … ) measurements that show Betelgeuse's 380~430 day variation very well, and less distinctly, the 2200 day period. These authors interpret the "Great Dimming" as a sporadic, out of phase event (such as release of a dusty cloud from the star's surface). Which might be an important point, if Saio et al's had relied on it. They mention it, say it was about a minimum of the "~400 day vairation", and then leave it aside as just another event in that cycle.

So basically the dispute here is whether the 380~430 signal is the star's radial pulsation, or if the 2200 day pulsation fits that rôle. The "Great Dimming" doesn't really come into it - it's a random event on top of the informative variation cycles.

The new authors then "work outwards" from the photosphere into interactions of the photosphere and the star's atmosphere. Which they say, prefectly correctly, are likely to have a significant effect on the star's external appearence - as the whole "Great Dimming", and observation of other stars would agree. However ...

A major point of Saio et al's work was to introduce into the discussion "Neuhäuser et al. (2022) …, marked above] interpretation of pre-telescopic records which reveal that this star exhibited significantly higher temperatures [up to] two millennia ago." (as I quoted in the first version of this article). And Molńar, Meridith and Leung don't look at that, they look only at essentially atmospheric effects, while Saio et al's work primarily addresses the internal heat engine that drives the photospheric effects which Molńar, Meridith and Leung are looking at.

Molńar, Meridith and Leung may have valid points about the "atmospheric" effects, but they don't really invalidate Saio et al's discussion of the internal power-source of the star. We're just going to have to wait to find out.

Now, does Dr Becky have owt to say?

See also the discussion of RW Cephei below. I can't get away from the topic.

The World Is Not Enough - WINE - spacecraft ; hubris for those lacking in Classical scholarship.

https://arxiv.org/pdf/2306.03776.pdf

Boringly, the paper title is "Thermal Extraction of Volatiles from Lunar and Asteroid Regolith in Axisymmetric Crank-Nicholson Modeling", but I just love the idea of "the World Is Not Enough (WINE) spacecraft concept". Clearly someone has either not heard of the concept of hubris, and how various pantheons of gods have punished humans showing this characteristic. The designers will have to be tunr widdershins at the right moment, and perform their functional sacrifices with appropriate chanting burning of incense and prayer to the Gods of spaceflight.

What are they actually doing? Well, with Philip T. Metzger (on Twitter, @DrPhilTill on Twitter, while it's still alive) involved, you can guess its' something to do with the regolith on space bodies. In this specific case, they'ere looking at the (theoretical) efficiency of extracting volatiles (in general, water in particular) from regoliths on the Moon, asteroids and (potentially) Mars.

Previous work has shown (unsurprisingly) that in a vacuum, as you heat a sample of regolith the volatiles move away from the heat source, but the details depend on the vacuum, the temperatures, temperature gradients and many other details. A particular construction of mining machine could collect voatiles efficiently in one nevironment, and very inefficiently in another. So, there is a need to do multiple tests in various environments. Which is where the WINE (hubristic name expanded above) spacecraft comes in. In their words, WINE will be a small spacecraft, approximately 27U in CubeSat dimensions (3 by 3 by 3 cubes), with legs for walking short distances and a steam propulsion system for hopping multiple kilometers. […] WINE will drive a corer into the regolith to extract water and perform science and prospecting measurements on the regolith. The water will be extracted thermally by heating the material in the corer. Vapor will travel into a collection chamber where it is frozen onto a cold finger. After multiple coring operations have collected enough water, the tank will be heated to high pressure and vented through a nozzle to produce hopping thrust Which is a fairly ballsy set of optimisms.

They then follow with a lot of mathematical modelling, which really just serves to show that we don't have a large amount of experimental data on physical and chemical properties of regoliths, apart from a small amount of Apollo data density/ strength obtained by using core penetrometers (tube, hammer, measuring stick, notepaper) to collect soil samples. Some properties (thermal conductivity, density) were measured after several days transport and re-warming in the returning spacecraft, plus a sea landing. Yeah, I'm not going to put too much faith on those values without some "ground truthing" measurements. (These authors don't mention it, but if the "mole" of Mars Insight had worked, it would have provided at least one log of some of these parameters in Martian soil. possibly including sub-surface ice.)

The table of products form the LCROSS impact mission is interesting.

Volatiles in LCROSS Ejecta (from https://arxiv.org/pdf/2306.03776.pdf)
Compound	Symbol	Concentration (wt%)
Water	H₂0	5.50
Hydrogen sulfide	H₂S	1.73
Sulfur dioxide	Si [sic, typo] SO₂	0.61
Ammonia	NH₃	0.32
Carbon dioxide	CO₂	0.29
Ethylene	C₂H₄	0.27
Methanol	CH₃OH	0.15
Methane	CH₄	0.03
Hydroxyl	OH	0.0017
Carbon monoxide	CO	0.000003
Calcium	Ca	0.0000008
Hydrogen gas	H₂	0.0000007
Mercury	Hg	0.0000006
Magnesium	Mg	0.0000002

I hadn't particularly paid attention to that previously. But having 1.73% of the ejecta mass as hydrogen sulphide is ... challenging. If you were to pump this mix into a chemical plant to make atmosphere, rocket fuel, whatever, you're going to want to either dump that stuff, or move the sulphur to a differentl, less hazardous, oxidation state. The simple process of oxidising it to sulphurous acid (H₂SO_{2 or 3}, which is relatively innocuous) would help, but would account for something like 1/3 of the potential oxygen output from electrolysing the water. Hmmm. That's a problem. Maybe just bring the sulphur up from oxidation state -1 to state 0 would be better. "Flowers of sulphur" is a damned sight less horrible a chemical to have near living quarters then H₂S. Someone is going to have to look at that.

There's a lot more work in this paper, modelling temperature changes in lunar soils through a day-night cycle, considering temperature profiles in the corer of the "WINE" spacecraft proposal. Lots of theory. Really, some of this needs ground-truth, and I'm sure this paper will be fairly heavily drawn-upon in arguments over which next missions to launch to the Moon (or various asteroids, or Mars) to evaluate their soils physical and chemical properties. There are a lot of free parameters in these models which need pinning down to something more closely constrained by reality.

Not a very "fun" paper, but probably quite important for actually building humanity into a space-dwelling civilisation, if not necessarily a Mars dwelling one. Who would want to live at the bottom of a hole? (Known Space reference.

Stars with really long dimming events

Discovery of Gaia17bpp, a Giant Star with the Deepest and Longest Known Dimming Event

Do you remember where you were when Tabetha Boyajian said "Where's The FLux?" about star KIC 8462852 (KIC - Kepler Input Catalog)? That was a lot of a surprise (and still remains somewhat puzzling), but with the rapidly increasing completeness, cadence and sensitivity of astronomical survey programmes the number of - and extremes of magnitude and duration of - dimmings of stars recorded have beceom a commoner thing.

This is a new record-breaker. Until the next record-breaker. This star has spent about 6.5 years (2000-some days) in it's dimmed state - the start is somewhat uncertain between surveys which serendipitously covered this field in 2012 and 2013 - before which the star exhibited no obvious brightness changes. However with up to 11 or 12 year gaps in observation in the 1950s and 60s, other dimmings are plausible.

The interpretation - as for a number of other dimming events - is that the star's light has been dimmed by passing through an approximately neutrally-coloured disk of material orbiting a companion (or possibly independent, if this dimming is a one-off event). The modelled disc is at a small angle to our line of sight - if the disc had been inclined closer to face-on, the depth of dimming would have been less.

Similar explanations have been put forward for other "dimming" stars such as Epsilon Aurigae, though it's dimming recurs on a period of some 27 years, with each dimming lasting around 2 years.

We're going to see more of these. Lots more of these. Following the same arguments as justified the Kepler Observatory, around 1% of multiple star systems where one component has a significant absoebing disc will be detectable from Earth, given sufficient numbers of observations. Similar biases to close-in dust disk carrying companions will exist.

This model doesn't explain "Tabby's Star" KIC 8462852 - or at best, not very well. There are hints of periodicity in that one's dimmings, but there is a lot more stochastic noise.

Astrophysics observatories as Seismographs

Status of the GINGER (Gyroscopes IN GEneral Relativity) project.

After the successes of gravity-wave telescopes (LIGO, to a lesser extent KANGA and Virgo ; and now the various *PTA "NANAOgrav discoveries.), people are naturally looking to turn it up to 11. s. GINGER (Gyroscopes IN GEneral Relativity) is a proposal to build a number of ring laser gyroscopes (a technology that has been used in surveying since almost the invention of the lasers) to "measure general relativity effects and Lorentz Violation in the gravity sector". Which I'm sure would be terribly exciting for physicists and astronomers everywhere. But the other stipulation, that the devices be "rigidly connected to the Earth", also means that these would both be subject to non-trivial levels of seismic noise, and would also serve as a remarkably broadband seismograph. The seismic noise they've got a technique for, as deployed by LIGO Hanford and LIGO Livingstone, by having two (or more) more-or-less identical machines at considerable separation, and having some degree of appropriate coincidence detection and rejection to differentiate between GW signals and seismic signals.

That is going to be more challenging with two sensors at one location.

schematic of two rectangular frames inclined with respect to each other ; human-for-scale indicates the frames to be about two person-heights on edge, roughly square

(The proximal part of "GINGER", time wise, is about building two "technology demonstrators" in the existing deep underground lab at Grand Sasso, which is currently used for low-radiation-background experiments, neutrino detection, dark matter telescopes, that sort of thing.) They'd have to interface with more conventional seismic networks to reject the "understood" noise sources, which would leave the not-understood signals in the noise. Or for that matter, in the not-previously-"understood" signal. But I'm sure that's do-able, before building a second site. Or fully interfacing with one of the various other high-sensitivity ring gyro systems under development.

That's viewing the seismic noise as noise. But of course, it's also going to be an exquisitely sensitive seismograph. If they're looking at sensitivities in the order of 1 part in 10⁹ to 10¹¹ that would imply a bandwidth down to around millisecond or microsecond signals (since they're looking towards astronomical sources from an Earht that rotates in approximately 10⁵ s. That's a pretty good step up for seismography. And the physicists pay for it! What's not to like?

The project already has, they report (references in original paper), collapborations with high-precision observatories in Germany (G9 at Wettzell and ROMY in Bavaria), New Zealand (U.o.Canturbury) and China (HUST, Wuhan)). That Wuhan connection is going to bring the anti-vaxx freaks out of the woodwork, though I'd be moderately amused to see how they get from Length-of-Day and Earthquake measurements to Bill Gates' 5G mind control chips in the COVID vaccines. After all, it can't be coincidence. Those pre-existing collaborations are proof positive of nefarious and long-standing plans.

I see, checking those co-project's references, that several of the paper's titles include reference to siesmic and seismological results. Evidently they too have seen this ... interdisciplinary link. So they're probably touching the seismology community for some contributions of "folding" already.

As a footnote, this is a contender for the DOOFAAS project. If you like it, mail that project's instigator. It is not known if ACRONYM software was used to construct this ... "name". Or if it is natural talent on someone's behalf.

Another Great Dimming - not Betelgeuse

The Great Dimming of the hypergiant star RW Cephei

It seems as if this month's recurring theme is the dimming of Beteleuse, but many other intrinsically bright stars also have irregular dimmings, as well as more regular periodicities in brightness. RW Cephei is another such. Although it is a lot brighter intrinsically than Betelgeuse, it's not so well known because it's further away. We can't actually tell how far away to within a factor of 2 - estimates on Wiki give it at 3,416 or 6,666 pc (11,100 - 21700 ly) - an eighth to a quarter of the way around the Galaxy. It's not clear why the distance is uncertain, but the presence of an extended envelope of emissions around the star probably doesn't help. That's 10 to 20 times the distance to Betelgeuse, so it's not a bright star in our sky.

Cepheus is a circumpolar constellation from the UK, but it's not terribly well known because it's not got many bright stars. As seen on the sky, it is to the west (anticlockwise, widdershins, centred on Polaris) from the bright "W" asterism of Cassiopeia. RW Cephei is in the Cassiopeia corner of the constellation, though actually closer to the border with the dim constellation of Lacerta. It's well below naked-eye visibility during the current dimming, but at it's brightest should just be visible under excellent conditions.

Despite being a lot further away from us than Betelgeuse (which has been subject to interferometric disc-size measurement since the 1920s, and more recent actual disc imaging), RW Cephei is such a large star thet it too has a disc capable of being imaged. This paper reports on the imaging results. THe observations were carried out with the CHARA telescope array, comprised of six 1m telescopes with delay lines so that act as an interferometer with a resolving power of 200 µas. These results couples with the distance estimates given above indicate a stellar radius of 900 to 1760 R_☉, making it one of the largest stars measured, to date.

The report also includes AAVSO data for RW Cephei's visual brightness (with Betelgeuse for comparison) as figure 1 :

Caption :

If you want, you can get updated data from here. At the report's writing, the dimming event had lasted about 1100 days (compared to about 200 days for Betelgeuse's recent dimming and 2000+ days for Gaia17bpp described above). At points in the deepest part of the dimming, the magnitude was being reported as 8 (visual), compared to the normal range of brightness of 6.0 to 7.6 . The most recent (late July 2023) AAVSO data has the brightness back to about M 7.0, well within the normal range of variation.

But that's not the exciting thing in this report. What this has, which most reports like this don't have, is that with the telescopes set up for interferometry, the observers could map variations in the brightness of the star's surface and reconstruct the image of the star's surface. Which has been done before (with Betelgeuse, for example). But this is on a star an eighth to a quarter of the way across the galaxy, and a considerably more luminous star too. RW Cephei is about 300,000 times the Sun's luminosity (300,000 L_☉) while Betelgeuse is less than half that (90000 - 105000 L_☉.

The first level of reconstruction produces these images (fig 5 upper) :

But those images combine both changes in colour and intensity, which include the effects of limb darkening. If you account for that effect, you get a better impression of what is happening to the star itself. (fig 5 lower, and caption)

The colour and/ or shape variations of these images probably reflect variations in the temperature of the star's surface, which for a large star is thought to be dominated by convection cells bringing heat from the interior to the surface. But the largest stars have a competing process of mass loss with both material jetting off the surface into space (which implies cooling, with spectroscopic consequences, which can be seen) and also the release of dust to form obscuring clouds between us and the staR - a process thought to be happening with Betelgeuse.

Section 3 of the paper reports near-infrared spectroscopy taken during the dimming. Through most of the spectrum the intensity is lower than in archived (normal brightness) IR spectra, but the change is greater at shorter wavelengths. With some well established physics this can be turned into mean surface temperatures

And now the end-of-month tidy-up. Only 3 overhangs.

Red Supergiant Candidates for Multimessenger Monitoring of the Next Galactic Supernova

https://arxiv.org/pdf/2307.08785.pdf

Science wise, this is just a catalogue of these candidates. But it’s also a public bet. 677 public bets. The justification is to shorten the list of candidates for pointing “light buckets” at, in the event of an early detection of a likely supernova by neutrino telescopy. If (“if”) one or several of the operating neutrino telescopes (French ANTARES, Antarctican ICECUBE, Russian BDUNT, Japan’s SuperKamiokaNDE …) detect a burst of neutrinos incoming, and can get a directional fix (some are more directional than others) then we may have an approximate detection.

The neutrino burst from a star's core collapse (or potentially, a gravitational wave signal) should escape from the core of a star in seconds (about 5 seconds for the Sun) to the surface where we can see it, while the explosion shock wave can take hours to days to emerge (“shock breakout”). Thus, a prompt observing campaign could capture brightness, spectroscopic or even compositional data on the star as close as possible before the actual supernova. Hence, a catalogue of “usual suspects” could help with prioritising candidates. It’s a numbers game, but with a reasonable chance of prompt payoff. The 1987A supernova in the Large Magellanic Cloud was accompanied by a burst of 20 (or maybe 25 - 1 of the 4 detector instruments involved is discordant) neutrinos and antineutrinos 2 to 3 hours before the first optical detection of the star's brightening. That's a very useful amount of warning.

Probably major observatories are already incorporating this into their “Target Of Opportunity” (TOO) decision process. To a significant degree, time and date are going to affect each observatory’s listing, day by day and hour by hour, but also which instruments are deployed, the slewing time from [current target] to [TOO] to [next target] … it’s not something the night shift operators would want to have to do “on the fly” without prior planning.

The criteria used for inclusion in the catalogue are luminosity (absolute, obviously, which requires a reasonably good distance from the Gaia stellar catalogue), temperature (requiring at least multiple filter measurements, if not full-blown spectroscopy, so not all potential targets have this data available, to this date ; that'll change), and chemical contamination (also requiring spectroscopy).

Obviously there’s a lot more detail in the selection process. But the core idea is there.

The catalogue is online on GitHub , but is also already incorporated into VizieR, a standard astronomical database collection. (I need to improve my VizieR-fu! Ditto the “Jupyter notebook” mentioned on GitHub, which I’ve heard of but never needed to use.)

I’d already got a catalogue of 112 RSGs and B binaries in my astronomy workbook, so I’ve added this lot. Plus a list of 31 potential progenitors from https://arxiv.org/pdf/2004.02045.pdf - which list is of suspect stars within a kiloparsec (3200 ly, approx) whereas this more spectroscopic list has nothing closer than about 250 pc (it gives parallaxes in mas, not pc). The lists use different sets of names, so are hard to compare directly, but at least three stars (HD 17958 (HR 861 in Cassiopeia, Gaia DR3 ID 467907038749283000, DR2 ID 467907038747132000, 2MASS ID J02562466+6419563), HD 80108 (HR 3692 in Vela, DR3 ID 5423960064637140000, DR2 ID 5423960064637140000, 2MASS ID J09162303-4415564) and HD 205349 (HR 8248 in Cygnus, DR3 ID 1971358279140130000, DR2 ID 1971358279140130000, 2MASS ID J21331788+4551142 ) appear on both lists.

Ye gods, and by gods I mean Cthulhu and the FSM , I'd forgotten how bad star names were. It was bad enough with AB Doradus and ZZ UMajor a decade ago, but these Gaia ones are a factor of several worse. If only they were comprehensive catalogues. But that's not really feasible this side of 102,023 CE. Sorry, 1,102,023 CE, because we'd need to geet to the other end of the galaxy. and get the signal back. That's assuming an average human expansion rate of 0.1C, and a speciation rate of zero - both of which are rather implausible.

If you can find any more "duplicates", you're welcome to. And you deserve a chocolate biscuit.

Exponential distance relation (aka Titius-Bode "Law") in extra solar planetary systems

https://arxiv.org/abs/2307.06070

Titus and Bode’s “Law” was an exercise in applied numerology which became popular once the geometry of the Solar system became calculable, using Newton’s dynamics, plus measurements of the Astronomical Unit (AU) by observation of parallaxes, and specifically transits of Venus across the Sun’s disc. Per Wiki, the first statement was in 1715, with variations and various authors (including Titus and Bode, and others) until 1772. When Uranus was discovered in 1781, which fitted reasonably closely to the “Law”, it became more popular. And when Ceres (now classified as a dwarf planet) was discovered in 1801, further numerology ensued. And again, with the discovery of Neptune, in “not-quite” the right place, more flogging of the never-alive horse happened. Pluto, also not being in quite the right place, further encouraged the numerologists. With 3 (or 4) parameters (for different ways of expressing the idea) and 7, 8, or 9 data points (for planets, dwarf or not), anyone could join in the fun of trying to make a better-fitting model. However, no “universal” solution of free parameters has been found – every system has different parameters.

If the Solar system had formed by natural processes (potentially a question in the 1700s, not so these-centuries) then it’s appealing to expect that there should be some relationship between the orbits of the planets. Unfortunately, “appealing to shaved apes on a mud-ball” isn’t a particularly compelling argument to planets in other stellar systems or scientists anywhere. It would be harsh to call it “not even wrong”, but it’s not very well founded in physical reality for a number of reasons :

as generally presented, the Titus-Bode “Law” looks for relation in the semi-major axes of bodies orbits ; but basic Newtonian gravitation (Einsteinian too, not that it matters) shows that the biggest forces between planets would occur when the outer planet is at perihelion (nearest point in the orbit to the Sun) and the inner planet at aphelion (furthest point from the Sun), when they’re in the appropriate phase relationship. And on a significant time scale (I’m a geologist – the mega-year is a convenient unit) phase relationships do change.
orbits evolve with time. They evolve significantly. Today’s measurements of orbital parameters are good for predicting what they will be next year, and not bad for predicting a million years hence. But a billion years … nope, you’ve got no real choice but to calculate it numerically because those 10th decimal places really do add up over time. If you do a lot of calculation of models there is, for example, about a 1% chance that Earth will be hit by Mercury before the Sun goes red giant. That’s a consequence of Mercury – the second least circular planetary orbit, if you include Pluto as a planet – occasionally approaching Venus relatively closely, which increases Mercury’s eccentricity leading to closer approaches … and 1% of the time, Mercury gets ejected from the Solar system, but finds Earth in the right place at the wrong time. (Don’t worry, the Earth’s oceans boil and the Sun goes red giant with pretty much 100% probability. Even if another star hits the Sun (less than a billion-to one chance, even when the Andromeda galaxy hits the Milky Way), that’s only going to bring the red giant date forward.)
there seems to be quite a lot of randomness in the development of planets. If our best model of planetary formation is right, little things (dust grains, sand grains, dirt balls, asteroids, big asteroids) meet to form bigger things until they run out of bigger things crossing their orbits. At all stages similarly-sized bodies are colliding and merging– which is a sensitively random process. When people tried modelling the “Moon-forming impact” in the late 1980s (when supercomputer power became affordable), they discovered that it was exquisitely sensitive to the impact factor (distance between proto-Earth centre and projected path of the impactor), and to the rotation rate of both bodies. I’ve got a compendium of evidences for “late giant impacts” in the Solar system, and the only planet without good reasons for believing there to have been a “late giant impact” is Saturn – the one with the recent debris rings and the “Death Star Moon” Mimas
). Yeah, not a lot of evidence for giant impacts and hierarchical growth around Saturn.
Would you really expect a Titus-Bode like "Law" in the satellites of a planet within a stellar system? That’s quite unintuitive to me – surely the gravitational influences of the other planets would be have an effect, particularly on the outermost satellites where the statistically greatest influence on a “Law” would happen, per satellite. You could view the satellites of a planet in a multi-planet system as being somewhat similar to the planets orbiting one star in a (widely-separated) multiple-star system.

So, yeah, it’s maybe not so obvious that there should be a Titus-Bode-like "Law" for planetary systems. Certainly not to me.

FTFA, the authors find that an exponential (“Titus-Bode-like”) model fits the 32 reasonably-sized (i.e. 5 or more planets) planetary systems known to date. They use “R²” and “Median” comparison statistics – (I know “R²”- Pearson’s correlation coefficient. Their “Median” test test though is the https://en.m.wikipedia.org/wiki/Average_absolute_deviation which is a moderately well-known description of clustering in a data set around it’s central point. Here they’re using the mean as a measure of central tendency: ) $Mean Average Error (MAE) = \frac{1}{N} \sum_{i} | y_{i} - \hat{y_{i}} |$ (y-hat being the sample mean).

Historically, the Titus-Bode “Law” expression started from Earth’s orbit, and went both in- and out- wards. These authors (like many others) simplify matters by working from the smallest known orbit and just working outwards. Which makes for a simpler expression :

r (n) = {ae}^{2 λ n} n = 1,2,3 \dots

The authors are careful to exclude multi-star systems from their consideration. That suggests (to me) that the effects of the lighter star being closer to the inner planets some times - but not others - would be an issue.

By generating naïve artificial planetary systems and analysing them similarly to the actual star systems they get average regression values of 0.905 while for the Kepler poly-planet set it’s 0.966 – appreciably better. It’s unsettling that they find the (generalised) Titus-Bode "Law" to be a good descriptor of planetary systems, when I’m so disparaging of it. But they agree with me that the lack of a physical basis is problematical.

An interesting sideline is that by introducing a physically realistic constraint on placing of their “pseudo planets” in their pseudo-systems (separating planets by several Hill radii https://en.m.wikipedia.org/wiki/Hill_sphere ), their pseudo-systems approach the statistics for Titus-Bode models. That’s … suggestive. But far from convincing.

The authors spend some pages discussing the use of the Titus-Bode "Law" (originally, and in more recent formulations) to predict the positions (well, semi-major axes ; equivalently periods) of as-yet undiscovered planets. As always, the example of the discovery of Ceres is touted, and indeed, the search that yielded Ceres does actually fit the original Titus-Bode "Law". The surprising thing is that the search didn’t find Neptune, with over three times the angular diameter (though something like 1/10th of the overall brightness, so maybe not that surprising). However, Ceres itself, and the whole asteroid belt adds up to really, really little. People get this wrong. They think the asteroid belt is much more significant than it really is. By mass it is about 0.004 that of Mars (proportionally less than half the size of Earth's Moon), and 0.0004 (count the zeros! I did.) of the mass of Earth. The lack of mass in the asteroid belt has long been a problem for people trying to work out a reasonable scheme for building the Solar system from a circumstellar disc (such as we see around protostars and young stars today). Considering that, really we should do calculations about the Titus-Bode “Law” excluding both Ceres and Pluto, since they’re so small and almost massless that they can’t greatly influence anything of significant size at significant range.

While I’m worrying about Ceres’ mass, the next section of the paper comes along … suggesting the Titus-Bode “Law” may in some way be related to the age of a planetary system, as if it had been “running in” like a coarsely-machined engine. Problematically for this thesis, what you need for shuffling the components of a planetary system around is, bluntly, mass. But by including Ceres in their considerations as a “planet”, they’re also saying that, in their opinion, mass is unimportant. Fortunately, their correlation is no correlation. “Correlation is not causality” may be a mantra of statistics lecturers (even if the students tend to forget it), but “No correlation means no causality” is a considerably more firmly based claim. The authors dug this pit for themselves, then chose to not climb into it. Well done.

But then the next section they choose to throw themselves back into this pit. After a not-unreasonable discussion of the mutual influence of neighbouring planets on each other’s periods and spacing (see above comments about mass), they go on to say It is in fact well-known that “small” objects, like comets, small asteroids, debris, etc. do not follow, singularly, any particular pattern in the size of their orbits, and can be found at any distance (allowed by classical mechanics) from the central body. and then they go on to consider Ceres to be significant in the dynamics of the Solar system. Dodging a bullet is a skill, but getting hit by it after dodging it is a really difficult skill.

There may be something to the “Harmonic Resonances (HR) method”. But not by using this argument. Not if they’re considering Ceres to be throwing Mars around. Their subsequent point is that the "HR method" generally uses distinct “small number” ratios between neighbouring planetary neighbours, so the system effectively has approximately two free parameters per planet – which would practically guarantee a fairly good fit. That's well-founded. So, why pay much attention to the "method"?

Apparently the journal Icarus refuses to accept papers purporting to improve the Titus-Bode “Law”. I can understand why. Archaeology journals probably don’t accept many papers on von Daniken blurb or, latterly, Hancockian ink-waste. There may be something behind the (“a”, generalised) Titus-Bode “Law”, but it still has no theoretical basis, and it is (IMO) very problematic that real planetary systems (at least, the Solar system, and several young extra-Solar systems which have large excesses of dust) seem to have had significant but essentially stochastic (random) events. You might end up with a Titus-Bode-like "Law" from some filtering or damping of an initially random system, but that is a connection that hasn’t yet, to my knowledge, been made. And this paper doesn’t do it either. It’s probably worthwhile trying it, but this sort of numerology isn’t likely to do it. Numerical modelling of evolving systems in silicio is more likely (IMHO) to get somewhere in the right direction.

One thing that worries me is how all this depends on counting planets (gravitationally significant bodies) out from the star. If you’ve got a “hot Jupiter” in a 3-day orbit so close to the star that it's tidally locked, there probably isn’t room for a stable inner un-detected planet. But in the Solar system the innermost planet is also the smallest, and therefore the hardest to detect (by most methods). So surely, when looking at “adding planets” to an observationally based model, the case of an undiscovered small innermost planet is one that should be considered before messing around adding planets further out.

And no, Ceres still is not a gravitationally significant planet. Pluto is over twice the diameter and 13-odd times the mass, and I’m not screaming for it’s re-inclusion as a planet. (For the record, I’d have gone for a gravitational rounding + orbiting the star(s) definition rather than the IAU's “clearing the orbit” method. But I’m a geologist not an astronomer. And I’m definitely not going to get into that fight.)

And finally I'm caught up!

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2023-07-07