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Fireworks in space? Astronomers are comparing “starbursts” from a galaxy that is in the throes of star formation to a Fourth of July fireworks display. And three particular galaxies are like my children’s favorite part of a fireworks display: the grand finale. These bursts occur at a fast and furious pace, lighting up a region for a short time before winking out. But that’s only part of the story. Archived data from the Hubble Space Telescope are showing that starbursts — intense regions of star formation — sweep across the whole galaxy and last 100 times longer than astronomers thought. The longer duration may affect how dwarf galaxies change over time, and therefore may shed light on galaxy evolution.
A group of astronomers studied three dwarf galaxies, NGC 4163, NGC 4068, and IC 4662. Their distances range from 8 million to 14 million light-years away. The trio is part of a survey of starbursts in 18 nearby dwarf galaxies.
“Our analysis shows that starburst activity in a dwarf galaxy happens on a global scale,” explains Kristen McQuinn of the University of Minnesota in Minneapolis and leader of the study. “There are pockets of intense star formation that propagate throughout the galaxy, like a string of firecrackers going off.” According to McQuinn, the duration of all the starburst events in a single dwarf galaxy would total 200 million to 400 million years.
These longer timescales are vastly more than the 5 million to 10 million years proposed by astronomers who have studied star formation in dwarf galaxies. “They were only looking at individual clusters and not the whole galaxy, so they assumed starbursts in galaxies lasted for a short time,” McQuinn says.
Dwarf galaxies are considered by many astronomers to be the building blocks of the large galaxies seen today, so the length of starbursts is important for understanding how galaxies evolve.
“Astronomers are really interested to find out the steps of galaxy evolution,” McQuinn says. “Exploring these smaller galaxies is important because, according to popular theory, large galaxies are created from the merger of smaller, dwarf galaxies. So understanding these smaller pieces is an important part of filling in that scenario.”
With the high resolution Hubble data, McQuinn and her team were able to pick out individual stars in the galaxies and measure their brightness and color, two important characteristics astronomers use to determine stellar ages. By determining the ages of the stars, the astronomers could reconstruct the starburst history in each galaxy.
Two of the galaxies, NGC 4068 and IC 4662, show active, brilliant starburst regions in the Hubble images. The most recent starburst in the third galaxy, NGC 4163, occurred 200 million years ago and has faded from view.
The team looked at regions of high and low densities of stars, piecing together a picture of the starbursts. The galaxies were making a few stars, when something, perhaps an encounter with another galaxy, pushed them into high star-making mode. Instead of forming eight stars every thousand years, the galaxies started making 40 stars every thousand years, which is a lot for a small galaxy, McQuinn says. The typical dwarf is 10,000 to 30,000 light-years wide. By comparison, a normal-sized galaxy such as our Milky Way is about 100,000 light-years wide.
About 300 million to 400 million years ago star formation occurred in the outer areas of the galaxies. Then it began migrating inward as explosions of massive stars triggered new star formation in adjoining regions. Starbursts are still occurring in the inner parts of NGC 4068 and IC 4662.
The total duration of starburst activity depends on many factors, including the amount of gas in a galaxy, the distribution and density of the gas, and the event that triggered the starburst. A merger or an interaction with a large galaxy, for example, could create a longer starburst event than an interaction with a smaller system.
McQuinn plans to expand her study to another larger sample of more than 20 galaxies. “Studying nearby dwarf galaxies, where we can see the stars in great detail, will help us interpret observations of galaxies in the distant universe, where starbursts were much more common because galaxies had more gas with which to make stars,” McQuinn explains.
McQuinn’s results appeared in the April 10 issue of The Astrophysical Journal.
Source: HubbleSite
This paper’s conclusion leads me to think of these dwarf galaxies (and possibly most others) as lighting up like Christmas trees, with various regions ‘winking’ on and of as star formation proceeds apace! The preprint paper can be found here: http://hubblesite.org/pubinfo/pdf/2009/19/pdf.pdf . Some interesting images of all three dwarfs.
It is amazing yet should not been surprizing up to about 25 years ago, astronomers thought old Globular Clusters were merely the oldest ‘original’ part of a Spiral Galaxy and all ‘Globs’ are old. It just so happened all along there was merely old ‘Dwarf Galaxies’ captured by the Milky Way but not torned apart. Today, new type future Globulars are being created, R144 in LMC and many others, how much knowledge has been gained with the international astronomy community over the last 2 decades, awesome!!! Far more will be gained and more questions will be answered in the near future.
Readers might likely say, yeah, but the paper was published in the Journal of Plasma Physics, that’s not an astrophysics journal.
Indeed, but note the authors of the paper:
H. U. Rahman, Institute of Geophysics and Planetary Physics, University of California, Riverside.
D. Bhattacharya, Institute of Geophysics and Planetary Physics, University of California, Riverside.
S. Rajpoot, Department of Physics and Astronomy, California State University, Long Beach.
P. Amendt , Lawrence Livermore National Laboratory, University of California, Livermore.
The authors all have solid astrophysics backgrounds.
Yes, the paper is over 10 years old, but more recent papers also make the same conclusions. Including this space.com article, Unknown Force Triggers Star Formation (March 1, 2005) which profiles a paper published in the Astrophysical Journal:
“Some previously unrealized energetic process, likely related to magnetic fields, is superheating parts of the cloud, nudging it to become a star, scientists said.”
“The detection of X-rays from the cold stellar precursor surprised astronomers. The observations reveal that matter is falling toward the core 10 times faster than gravity could account for.”
Magnetic fields (with supporting electric currents) are described as promoting star formation.
Could the, above, two papers be describing a process occurring in specific regions, what the paper profiled in the post is describing at the galactic scale?
This is an interesting report.
“The galaxies were making a few stars, when something, perhaps an encounter with another galaxy, pushed them into high star-making mode.”
This “something” is critical for understanding how galaxies evolve. The report, as the quote makes clear, postulates a possible encounter with another galaxy, although, how an “encounter” would set off a star burst is unstated.
I can’t help noticing Jon Hanford’s choice of descriptives for the star burst: “…these dwarf galaxies (and possibly most others) as lighting up like Christmas trees, with various regions ‘winking’ on and of as star formation proceeds apace!
The acceleration of the process is remarkable — a chain-reaction, if you will — a very dynamic process.
Is there any gravity processes that could explain the “global scale”, which “sweep across the whole galaxy and last 100 times longer than astronomers thought”?
“Then it began migrating inward as explosions of massive stars triggered new star formation in adjoining regions.”
“There are pockets of intense star formation that propagate throughout the galaxy, like a string of firecrackers going off.”
Or as in christmas tree lighting, a circuit of electromagnetic energy — electric currents, where a flow or wave of electricity, Birkeland currents, cause a chain-reaction, both of star explosions, an overload of electrical energy input, and in turn star formation depending on “the amount of gas [plasma] in a galaxy, the distribution and density of the gas [plasma, ionized particles].
This electromagnetic process of star formation has been written up before.
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=18077
This star burst dynamic seems more energetic than gravitational collapse of accretion disk matter would allow for.
An alternative theory — sure you bet, but one that seems consistent with the evidence at hand.
The paper the link takes you to is titled “Diamagnetic effects during the early stages of star formation”, and the first sentence of the abstract reads “The role of magnetic fields during the initial stages of protostellar cloud collapse is investigated, in particular with respect to the scenario where the magnetic force can be an effective compressor due to diamagnetic effects.”
I don’t know how you, Anaconda, managed to conclude, from the paper, all that stuff about Birkeland currents, star explosions, and an overload of electrical energy input. Somewhere else, in the UT story comments, someone said that you (and solrey, and others) have a tendency to string technical terms, from plasma physics, together, without, apparently, much of an idea just how meaningless the resulting sentences are. This seems like one such example.
By the way, I think you do know, don’t you, that estimates of the strength and direction of the magnetic fields which pervade the ISM (interstellar medium) have been published in dozens (if not hundreds) of papers in astrophysics journals. Do you suppose, from these estimates, you could attempt to estimate the size and strength of any field-aligned currents in the ISM, if only in principle? If not, why not?
@other readers: in my experience the use of the term Birkeland current instead of field-aligned current is a sure sign of an overexposure to the pseudo-science, or non-science, that goes by the name Electric Universe (except when Birkeland currents is used with reference to such currents in the Earth’s magnetosphere). Further, in my experience almost none of those who are entranced by this Electric Universe nonsense have any grasp of the relevant physics, beyond the qualitative, or ‘word salad’ stage, and certainly none who write so often and so widely in internet discussion fora, blogs, etc.
@ Nereid:
As you note the linked paper (abstract) discusses magnetic fields, per Maxwell’s Equations and observation & measurement, only electric currents cause magnetic fields.
In fact, the paper (abstract) makes this explicit: “This model explores the scenario where the electromagnetic forces can achieve a supercritical mass-to-flux ratio in a magnetized cloud before dynamical collapse due to gravity takes over.”
Electromagnetism has a role in star formation.
And, yes, gravity has a role in star formation as well.
The paper (abstract) goes on to state: “…in particular [it’s investigated] with respect to the scenario where the magnetic force can be an effective compressor due to diamagnetic effects.”
The paper (abstract) speaks of “compression” because of electromagnetic forces. Could this be the z-pinch or Bennet pinch process described here?
Nereid fails to mention the 2005 paper published in the Astrophysical Journal, which described a process where “matter is falling toward the core 10 times faster than gravity could account for.”
Nereid states: “I don’t know how you, Anaconda, managed to conclude, from the paper, all that stuff about Birkeland currents, star explosions, and an overload of electrical energy input.”
It’s part of the puzzle. Almost all Scientific questions and answers are constituted of various parts of a over all larger puzzle. Both papers I linked stand for the proposition that electromagnetism plays a role in star formation (along with gravity). This post is about star formation (starburst).
If electromagnetism plays a role then the component parts (processes) of electromagntism also must play a role: “Birkeland currents, star explosions, and an overload of electrical energy input.”
This is a logical construction of the dynamics involved: Over all dynamics must be build from constituent dynamical processes.
The paper profiled in the post relates observations & measurements (which are discussed in the post) that give rise to a reasonable inference (in my opinion) that the various processes mentioned, Birkeland currents, star explosions, and an overload of electrical energy input, are involved in the starburst process.
What “observations” mentioned in the profiled paper would suggest electromagnetic processes?
There is a recurrent theme in the descriptions in the paper of a movement and flow of some unknown dynamic along strings or waves washing over a region of the dwarf galaxies.
Even a directional description is given: “Then it began migrating inward as explosions of massive stars triggered new star formation in adjoining regions.” This just happens to match the hypothesis of Peratt and Alfven (both made quantitative calculations) that electrical energy is emitted out the axial plane of a galaxy and then flows back down the spiral arms of the galaxy in a large galactic circuit.
The profiled paper discusses star explosions, and how the star ages are determined: “[The] team were able to pick out individual stars in the galaxies and measure their brightness and color, two important characteristics astronomers use to determine stellar ages. By determining the ages of the stars, the astronomers could reconstruct the starburst history in each galaxy.”
Star age is normally thought to be determinative of when a star explodes. But, it seems, here, some other determinative factor is controlling when stars explode in a given region (and when stars form) independent of age.
Certainly, the paper never states explicitly (from the available docements) that age determined the star explosions, rather, the implication is that something else is at work.
I [Anaconda] made the statement: “This star burst dynamic seems more energetic than gravitational collapse of accretion disk matter would allow for.”
Nereid, you chose not to address this statement.
So, if age is not solely determinative and gravity is not solely determinative, then what other factor could contribute to the determination?
I offered the alternative hypothesis that electromagnetism, a Fundamental Force, plays a role in this starburst process.
@ Nereid:
I note that your response to my comments didn’t address the descriptive phases I quoted from the paper profiled in the post. In my opinion, that is where analysis and interpretation “grasp the nettle”. To the extent one fails to “grasp the nettle” and specifically explain why another analysis and interpretation is misinterpreting specific phrases and passages, one has failed to offer a compelling critique.
Nereid states: “Do you suppose, from these estimates, you could attempt to estimate the size and strength of any field-aligned currents in the ISM, if only in principle? If not, why not?
Yes, in principle, but only to the extent those “estimates” of magnetic field strength are quantitized. And I believe Dr. Anthony Peratt of the Los Alamos National Laboratory has “attempt[ed] to estimate the size and strength of any field-aligned currents in the ISM”, in fact, It’s my understanding Dr. Peratt has quantitized these “field-aligned currents” in order to derive a particle-in-cell computer simulation of galaxy formation.
Nereid, your “@ other readers” passage is a generalized criticism that sheds no light on the present post. Rather, sadly, in my opinion, it is an implied call to bias & prejudice in a generalized attack against any idea that can be characterized as being under the label “EU”. In essence, it means: “Anybody who uses the term “Birkeland current” is not to be listened to.”
Fine.
But that type of argument is usually resorted to by those that don’t have any specific rational for disagreement with a present opposing opinion based on the facts and evidence at hand.
Does that attempted “across the board” injunction offer one iota of rational argument or scientific evidence against my assertion that electromagnetism plays a role in the starburst process?
Nereid, I’m surprised you would engage in general, across the board attack. Science is about specifics, which you are quite facile at discussing, not appeals to generalized conclusions relying on the bias & prejudice of a given audience.
Nereid, what do you mean by the word, “entranced”?
And, Nereid, are you suggesting that none, but those that can perform complex mathematical calculations, should offer alternative opinions, analysis & interpretation about the posts, here, on UniverseToday?
If you are asking me: I’ll be unequivocal, no, I can’t do the complex mathematical equations.
Do only complex mathematical calculations constitute scientific evidence?
Surely, that would turn this website from a vehicle for popular sharing of astronomical information and theories, into a more remote website. Scientific disagreement if conducted in a respectful manner can be and often is an illuminating process that informs all parties to the discussion.
Here’s what Lawrence B. Crowell wrote, UT date April 30th, 2009 at 7:07 pm, commenting on a comment by solrey on the UT story New Mysteries Unveiled on Mercury (I highlighted one name):
And here we have Anaconda writing:
So, Anaconda, what is the electric current that causes the magnetic field in your refrigerator magnet?
In classical physics, what is the electric current that causes the magnetic fields in electromagnetic radiation, such as radio waves and x-rays?
I don’t want to say there is no content to what you wrote here (UT date May 3rd, 2009 at 10:19 am) Anaconda, but I do want to say that it is confused (and confusing) at best.
I’ll write a series of comments that try to clear up some of the worst muddles, but I’d really like to get to the source of the confusion. And to do that I’d really like you to answer my questions, in another UT story comment section, on what you see as the distinctions between direct observation, indirect observation, detection, and inference are, in astronomy. OK with you?
@Anaconda: you wrote:
The two key papers cited on that webpage are Peratt’s 1986 ones. Why are they key? Because they are the only ones which present the details of the only simulations Peratt actually performed (using codes named TRISTAN and SPLASH).
Now he certainly had an interesting idea, and no doubt the simulations were done correctly and reported accurately (you can, I think, check for yourself, because one of the codes is in the public domain).
However, his model does not describe the universe we live in, because it fails to match an enormous number and range of high quality astronomical observations (or inferences or detections, in your approach).
For starters, few, if any, spiral galaxies have the kind of double-bulge structure that Peratt’s simulations require (and which are obvious in the animation on that webpage).
Then there’s the fact that the rotation curves of spiral galaxies can be derived from the light of stars – of all ages – as well as HI emissions, and the two sets of curves are essentially identical. This is important because in Peratt’s model stars cannot possibly have the same rotational speeds as the ionised component of the ISM (which is what he models).
Add to that the fact that the galaxies Peratt models in his first 1986 paper are known to have a great many stars older than ~a billion years, yet, per Peratt’s model, they cannot even have begun to form more than a billion years ago.
The same applies to elliptical and spiral and barred spiral galaxies; in Peratt’s model, no stars can be older than ~5 billion years, yet all such galaxies, sufficiently close to us for us to determine the ages of the stars in them, have a great many stars much older than that.
But perhaps most notable of all is the complete absence of any direct observational evidence of giant, ~35 kpc wide, galactic-sized filaments (field aligned currents), let alone any interacting ones.
That’s just a few of the many fatal flaws in Peratt’s model, fatal in the sense of being strongly inconsistent with the observational evidence.
Clearing up some confusions, part I
Anaconda wrote:
In plasma physics, you can describe the dynamics of plasmas using either the magnetic field and bulk velocity (Bv) or you use the electric field and currents (Ej). (“The alternative paradigm for magnetospheric physics (J. Geophys. Res. 101, 10587 – 10626, 1996), link to follow, explains why these two are equivalent, and why the Bv paradigm is preferred, at least for magnetospheric studies).
If you limit your scope to (classical) plasma physics, because of the way that the E and B fields are coupled through the Maxwell equations, you can eliminate one or the other (my thanks to BAUT member tusenfem for this material).
Link: http://www.agu.org/pubs/crossref/1996/95JA02866.shtml
Well of course it does, just as it has a role to play in all of us remaining firmly in our chairs, rather than accelerating freely towards the centre of the Earth. And later in the star-forming process the weak and strong (nuclear) forces have roles to play as well.
If one is interested in the process of star formation, it is not helpful to say that one or other of the four (or three – electroweak) fundamental forces has a role, because they all do.
Rather, one needs to specify *how* a particular force works, via processes that are laid out in some detail. The Rahman et al. paper does that; at least it proposes a process that may be involved, even important, at one stage in at least some stars’ formation.
(to be continued)
Clearing up the confusion, Part II
No, it could not.
The abstract was quite clear and specific about the proposed mechanism; namely, “due to diamagnetic effects.”
Classical plasma physics is completely blind to diamagnetism, because the latter is due to quantum effects (while classical plasma physics completely ignores all quantum effects); the z-pinch is a classical plasma physics process (or phenomenon).
This is not so much a confusion, perhaps, as a failure of logic; after all, using this logic, the Casimir effect and hydrogen bonding must also play a role (to name just two). Or, in another version, since the strong force plays a role, then quark-gluon plasma physics (a component of the strong force) must also play a role.
The challenge, in astrophysics, is to find the dominant process (or mechanism), or the major processes, involved at each stage of the evolution of a system. Certainly since the time of Newton, the key to working out what processes dominate is fundamentally quantitative, involving math, numbers, equations, and so on. By stringing together technical terms, even if done in a logically consistent manner, gets you only a very distance towards getting a handle on the likely mechanisms involved; among other things, without ‘doing the math’ you have no way to determine how important any process on your list of ‘possibles’ actually is.
(to be continued)
This is off topic, but i think it needs to be said.
Nereid, thank you so much for taking all the time and effort into explaining the physics and cosmology to clear all of the confusion that certain members here are having. Many before you have tried to reason with them to no avail, but you seem to be doing a great job of it.
For the rest of us watching from the sidelines, all this discourse is both interesting and educational.
Keep up the good work.
Clearing up more confusions (etc), Part III
Anaconda said:
Oops, I missed a < ! Anyway, I think it’s clear what I wrote vs what I’m quoting … (if not, I’ll edit the comment and submit again).
That turned out to be easier than I had expected; this 19-page 2007 paper by Richard B. Larson seems to fit the bill well (link is to the arXiv preprint abstract): “Insights from Simulations of Star Formation” (http://arxiv.org/abs/astro-ph/0701733).
Of course, Larson’s focus is on numerical simulations (for reasons he gives in the Introduction section), but all such simulations must pass the ultimate reality test: to what extent do they explain the relevant observational and experimental results (and, for extra marks, to what extent do they permit extensive further testing, via predictions)?
You’ll see in this review that magnetic fields have been modelled, and the role played by MHD (which Alfvén invented) in star formation explored.
You’ll also see that there are many open questions, and that, as this is only a short review, there is little math, few equations, etc (the heavy lifting in that regard is done by the 123 papers Larson cites).
Anaconda wrote:
The quick answer is, no, it could not.
To see why not, in more detail, we will need to go through the McQuinn et al. paper (Jon Hanford provided a link to it, in the first comment). Is anyone interested?
Later, Anaconda also wrote (I’ve highlighted some words):
Despite the strong implication, by Anaconda, the quote comes from the UT story, not the paper (I checked, and you can too if you wish).
This is the second time I’ve come across this sort of thing; maybe it would be a good idea to be much clearer as to the source of the words you quote, Anaconda?
No papers by Alfvén or Peratt are cited by McQuinn et al.; may we have a reference or two please Anaconda to where this Alfvén-Peratt hypothesis was published? Then we can all check to see how well it matches the data presented in the McQuinn et al. paper.
I figure I’m only about half-way done in terms of clarifying confusions, mis-understandings etc in what Anaconda has written here; nevertheless, I think it should be clear to everyone that what Anaconda calls “a reasonable inference” (in his opinion) is, in fact, exactly the kind of thing which Fraser stated, in the 24th April blog entry (Comments: The Crackdown), would be verboten (“Don’t promote your personal, alternative physics theories”). Of course, it may well be that Anaconda did not set out to promote his personal alternative physics theory – just look at how much confusion and misunderstanding I’ve covered so far – but that surely is irrelevant.
More confusions.
Here the confusion seems to be with the term “starburst”, which Anaconda has interpreted as something to do with explosions of (individual) stars.
Let’s start with something boring, the SFR, or star formation rate.
This term means, strictly speaking, the number of stars which form in a year; a cluster (of stars, not galaxies) may be forming new stars at a rate of 10 per year, for example.
However, as the majority of new stars are red dwarfs, and as red dwarfs can only be directly detected, individually, out to distances of a few, or few tens of, kpc (kiloparsecs), astronomers use an indirect method to infer the SFR of extragalactic objects (e.g. dwarf galaxies, one region or another of a regular galaxy, or, for those quite distant, whole galaxies). This indirect method rests on assumptions about another TLA, the IMF, or initial mass function (no, not the International Monetary Fund); one consequence is that astronomers use ‘sols per annum’ as the unit to measure SFRs (the total mass of stars formed, expressed in units of the mass of our Sun, per year).
If you look at all the stars formed from the same giant cloud, at more or less the same time, and if you plot the number with mass M against M, you get the IMF. A great deal of work has gone into understanding the IMF – the YSO work I mentioned earlier is part of this – and it seems that the IMF is reasonably constant, with a possible (and notable) exception of the environment in and near galaxy nuclei. If anyone’s interested in more details on this, and how you can estimate the SFR using the IMF, just ask.
A starburst is an elevated SFR; a starburst region is a part of a galaxy where the SFR is much greater than normal, and a starburst galaxy is one where the SFR is high throughout the whole galaxy. The Antennae have examples of the former, M82 is an example of the latter (check out the Astronomy Picture of the Day for 24 October 2006, and 25 April 2006, respectively, for nice images).
A recent starburst appears quite spectacular in optical waveband images because lots of bright, massive, young stars will be seen in a relatively small volume (the much larger number of equally young but less bright and less massive stars are much less obvious). Now massive stars die very young, so older starbursts (regions where the SFR is much greater than average, remember) are less obvious, because the bright blue stars are now dead.
And that’s all McQuinn et al. did; they got an awful lot of data about a lot of stars in these three dwarf galaxies and analysed it to estimate the SFR in various parts of the galaxies. The estimated SFRs indicated that starbursts had taken place, and the same data enabled McQuinn et al. to estimate when each starburst ocurred.
And what the paper is about, roughly, is when and where starbursts occurred, how elevated the SFRs were in each starburst, and how long each starburst lasted.
One more thing: why starburst occur – what processes or mechanisms trigger them – is a fascinating topic, and yet another area of great contemporary interest in astronomy and astrophysics. However, the formation of individual stars (or binaries, as is more common) seems to be pretty much unrelated; what a starburst trigger does is create the conditions under which lots and lots of stars can form, in a short time.
@Anaconda, re my “@other readers’ paragraph: it was not my intention to attack anyone, nor do I think my comment did so; rather, I was giving other readers the benefit of my years of experience in internet discussion fora. Now as someone (Ignoramus?) mentioned in an earlier comment, “Nereid” has written many posts in the forum attached to this UT site (BAUT Forum), and for a time was a Moderator there; those posts are freely available for anyone with an internet connection to read (and if you join BAUT, you can access them much faster using the search feature of the site; otherwise you can proceed more slowly using Google, for example).
As to whether comments on UT stories should contain promotion of, or reference to, Electric Universe ideas, I suggest that Fraser has already stated that it shouldn’t (see the Comments: The Crackdown blog), but that’s surely something for him to decide, isn’t it?
Re Birkeland currents: if you think that this is a standard term for field-aligned currents, other than in magnetospheric studies, by all means please say so (and present some evidence). Otherwise, continuing to use a non-standard term surely impedes understanding and communication, doesn’t it?
Anaconda wrote:
I’m curious to know, Anaconda, if you think that I have grasped the nettle, in the set of comments I wrote subsequent to this one of yours I’m quoting. If you still think so, would you be kind enough to explain where, and why?
@ GekkoNZ: many thanks for the kind words.
If there’s anything that is not clear in my comments, or if you have any questions about any of it, I trust that you’ll not be shy about jumping in.
BTW, does the NZ in your handle mean you’re a kiwi? A person on whose wall hangs a map with the North Island, the South Island, and the West Island clearly labelled?
Yup, i sure am 🙂