Toroidal star

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

p1t1o
Posts: 940
Joined: Wed Nov 10, 2010 4:32 pm UTC
Location: London, UK

Toroidal star

Postby p1t1o » Thu Nov 17, 2016 4:15 pm UTC

So, could this be possible? Obviously very improbable, but is there anything other than very specific starting conditions (involving lots and lots of angular momentum), that would prevent this?

Background:
I just saw an article about "the most spherical object ever observed in nature" which was a particularly slowly rotating star.
Stars are slightly oblate due to rotation - can this be extrapolated to the point of wholly toroidal stars?

Im guessing its not possible, but I dont know why. I can of course think of many reasons why it would be very, very improbable, but I would like to know about "possible".

User avatar
Zohar
COMMANDER PORN
Posts: 8513
Joined: Fri Apr 27, 2007 8:45 pm UTC
Location: Denver

Re: Toroidal star

Postby Zohar » Thu Nov 17, 2016 5:29 pm UTC

My first thought is the pressure wouldn't be able to build up enough for fusion to happen.
Mighty Jalapeno: "See, Zohar agrees, and he's nice to people."
SecondTalon: "Still better looking than Jesus."

Not how I say my name

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26738
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Toroidal star

Postby gmalivuk » Thu Nov 17, 2016 5:44 pm UTC

Given that Klemperer rosettes are unstable, I can't imagine why a continuous toroidal distribution of matter would be stable. I think it would either collapse into a disc or into a binary system.

Edit: Also, yeah, if it were spinning fast enough to spread out like that, it means rotation is enough to counteract gravity, which means it wouldn't be a star with any fusion happening.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: Toroidal star

Postby Soupspoon » Thu Nov 17, 2016 8:00 pm UTC

My first thoughts were how (as logical progression from slow-spinning most spherical star) you'd transition a fast-spinning star to a toroid. I doubt you would, was my conclusion.

Faster spinning (induced... somehow..?) sends your near-sphere into an more extreme oblate spheroid shape. After a while, rotation at the extremities threatens to launch equatorial matter out, as equatorial velocity becomes escape velocity. Matter on the axis has no reason to go anywhere, save that the poles find themselves at higher potential (gravity alone) than their surroundings (gravity minus a minor component of centrfugal/petal/whatever force) and thus can only 'slump' away from the pole until the potential gradient equalises. Deeper 'axial material' only gets affected when the available rotational encouragement of near-axial surface material is greater than the purely gravitational pull. To hollow out the centre of the disc and remove(/slump) the core matter out onto the inner circular equator of a toroid, the forces upon the outer circular equator of the toroid should, it seems to me, have already exceeded any practical limit for keeping the whole thing together.

(There's a complication to that. By 'shell' modeling the purely gravitational forces, the deeper within a body you are, the less (net) gravity you experience as only that mass below your depth really counts. But I think you'd need a particularly viscous (high surface gension?) material, still, to keep the outer reaches together to get past the (say) ¾-mass 'hump' and start to draw out axial material with significantly less gravitational reason to stay in 'the donut hole region'. But what kind of fusioning/excited/hot-and-bothered plasma is 'sticky' to itself? Maybe some peculiar spontaneous magneto-dynamic containment effect? Hard to say.)


With the Rosette principle in mind, perhaps both the spin and the method for pushing more donut-hole outwards without flinging donut-edge matetial out too fast might be to arrange for significant numbers/masses of 'rosette' objects to steeply dive down to punch through and brush close by the core, creating significant amounts of internal void whilst (symmetrically) drawing up and out the matter back out the other side (all sides!), carefully tuned to make this the new outer-equatorial mass, excited to velocities required to keep the ring open, whilst the original equatorial surface of the star (excepting that on or near the relatively insignificant 'puncture marks' of both entry and exit wounds by the 'rossettes') and non-voided inner forms the new internal equator and the toroid 'core' circle. But that's just a thought experiment, which relies upon engineering a surrounding rosette and then engineering the rosette components to simultaneously head towards a periapsis extremely close to the rosette/star barycentre/core-centre.

If you can do both those things, then maybe, instead:
1) Set up a standard rosette of stars, circling an empty barycentre.
2) Simultaneously bring all the stars to a lower (stable) orbit, such that their atmospheres touch and combines like the electron orbitals of a benzene ring...

More (rosette) stars than six might be necessary, for best results. But at a certain reduction of off orbit (and thefefore gap between star cores) the mutual diffusion of the outer layerss (competing solar winds pushing mass outwards from the 'core ring' zone) should settle down as a thickening toroidal atmosphere creating a corridor of fussioning core-pressure gases no longer limited to just the traditional nominal cores of the donor stars, but acting as a 1-dimensional 'centre line' rather than a set of 0-dimensional 'centre-points'.


(I had also considered a single massive object punching, pole to pole, straight through another star, evacuating the centre and effectively creating a roiling' smoke ring' of the original object, but the energies involved would be difficult to martial (or have happen purely by chance!) without getting an expanding Praxis Effect ring as donor star (and probably also our hypotical 'punch projectile', necessarily acting alone) gets scattered to the six space-winds....)

If we ever find such an artefact, we probably need to consider where the builders of it are.

ijuin
Posts: 1073
Joined: Fri Jan 09, 2009 6:02 pm UTC

Re: Toroidal star

Postby ijuin » Sun Nov 20, 2016 5:07 am UTC

The problem, as I understand it, is that maintaining a toroidal shape would require a net outward force that is greater closer to the center than it is farther away. Unfortunately, rotation and gravity do not work that way. The only force that I can imagine holding a stellar mass in such a shape is an externally imposed electromagnetic field, forming essentially an octillion-tonne tokamak.

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: Toroidal star

Postby Soupspoon » Sun Nov 20, 2016 5:56 am UTC

ijuin wrote:The problem, as I understand it, is that maintaining a toroidal shape would require a net outward force that is greater closer to the center than it is farther away. Unfortunately, rotation and gravity do not work that way. The only force that I can imagine holding a stellar mass in such a shape is an externally imposed electromagnetic field, forming essentially an octillion-tonne tokamak.

As I see it, the net gravitational force within a shell is zero. If you have gotten to the point that there is no mass in the hole of a donut then the rest of the mass of the donut only has to balance centripetal force vs the donut mass within the sphere (partial sphere, i.e curved ring-slice) and pressure. Upon the equatorial plane, this clearly allows a hollow centre. I'm a bit concerned about the northern/southern 'polar' rings having force of the (more or less, give or take an arc-bulge) core-ring to inner-equatorial ring pulling inwards to the barycentre, but the spin of the whole kaboodal makes it likely that you can treat that as moving at near-orbital speeds, with circulation1 dealing with not-quite-orbital velocities.

Or, to put it another way, in a Rosette you don't worry about the forces in the centre, the only mass you need to worry about is orbiting that centre. If all that orbiting mass is touching, in a chain, it's just a matter of balance, still.

Someone probably needs to mathcad this, I suppose. I'm not even using a back of an envelope in my own mental musings.


1 I'm trying to get my head round the coriolis effects in both 2D (torus warped-surface) and 3D (volumetric, combined with convection) within such a space. And any unlikely alien geometers whose native environment is the unlikely toroid star (or mere gas) will have a complex cartographical understanding, indeed, of their home...

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26738
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Toroidal star

Postby gmalivuk » Sun Nov 20, 2016 3:14 pm UTC

There's no force inside a spherical shell, but there are no spherical shells in a torus, so that's not really relevant. The only point with no gravitational force from a torus is at the exact center. Everywhere else, the force of gravity is approximately toward the equatorial plane vertically and toward the nearest point on the surface of the torus horizontally.

This means that both gravity *and* centrifugal force will be pushing the inner equator *away* from the axis of rotation.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

lgw
Posts: 437
Joined: Mon Apr 12, 2010 10:52 pm UTC

Re: Toroidal star

Postby lgw » Sun Nov 20, 2016 8:44 pm UTC

ijuin wrote:The problem, as I understand it, is that maintaining a toroidal shape would require a net outward force that is greater closer to the center than it is farther away. Unfortunately, rotation and gravity do not work that way. The only force that I can imagine holding a stellar mass in such a shape is an externally imposed electromagnetic field, forming essentially an octillion-tonne tokamak.


I think this summarizes the problem nicely.

It seems intuitively like it should work because our intuitions are guided by liquids with surface tension, but that doesn't work for gasses, and especially not for plasma. Plasma can be confined by a toroidal field as in a Tokamak or Stellarator, and you could certainly get fusion that way. I can't imagine any way you'd get the needed magnetic fields naturally, but as a "stellar engine" - sure, why not? Seems like a heck of a way to make an "intelligent life was here" beacon that would be detectable at quite some distance.

Also, you could cheat this I think with dark matter - does it count as a torus if the donut hole is a blob of dark matter rather than being empty? A sphere of dark matter "inhabited" by a disk of familiar matter seems to be what our galaxy is, as I understand it, so it seems much more likely you could get the appearance of a toroidal star with fast rotation of the familiar matter (not necessarily shared by the dark matter). I'm not sure you could get that dense enough to fuse, though, as gmalivuk points out.
"In no set of physics laws do you get two cats." - doogly

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: Toroidal star

Postby Soupspoon » Mon Nov 21, 2016 12:01 am UTC

I'm just trying to dust off my long-unused integration skills to work on the problem.

In replying to ijuin, I was addressing the need for a net outward force near the centre (where I'm assuming there already isn't any mass, in the pre-holed bosy), and gmalivuk then wants to talk about gravitational forces plus rotational ones pushing too much out. There's going to be a gradient, I think.

Rougly outside the major radius distance, gravity will pull inwards. Roughly inside that distance, the cross-sectional slice of the lobe nearest out-pulls (due to proximity) the equal but opposite-side lobe, and the sweep of cross-sections in/out of the page acts in a continuum between the two, and I'm guessing that this pulls it torus-coreward, but it's a similar problem to the spherical shell problem. (And forces towards the equatorial plane for all points not on it, obviously.)

For a given rotation-profile (not neccessarily the same angle/time, across the minor diameter across the major radius point, hence complications of coriolis forces) there'd be an adjustment to that, but I was going to work that out separately after the gravity gradient, and working out how to factor in a possibly necessary density gradient related to the pressures, but that'd involve some form of feedback into the equation, and if we're going that far then perhaps the side-pressures upon the off-equatorial matter would also dictate a non-circular minor cross-section, too, depending on the rotation profile.

But so far it's in my head, not on paper. (I don't have a handy physics-modelling package at hand, on any machine/device, but once I've done the maths on the formulae, I could write my own plotting script.) So it's just a general hypothesis, so far, that a toroid construct of gas/plasma can be made stable. Not, of course, that it's easy or especially not easily possible to be natural in origin.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26738
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Toroidal star

Postby gmalivuk » Mon Nov 21, 2016 2:25 am UTC

Soupspoon wrote:I'm guessing that this pulls it torus-coreward
Why are you guessing that? Rings pull things inside them to the nearest point on the ring, because inverse-square gravity combined with only a 1-dimensional massive body means proximity wins out. (The reason it balances in the sphere is you've got all that extra material in the opposite direction, spreading out in a surface behind you instead of just a line.)
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: Toroidal star

Postby Soupspoon » Mon Nov 21, 2016 2:37 am UTC

gmalivuk wrote:
Soupspoon wrote:I'm guessing that this pulls it torus-coreward
Why are you guessing that? Rings pull things inside them to the nearest point on the ring, because inverse-square gravity combined with only a 1-dimensional massive body means proximity wins out. (The reason it balances in the sphere is you've got all that extra material in the opposite direction, spreading out in a surface behind you instead of just a line.)

Yes, that's exactly why I'm guessing it.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26738
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: Toroidal star

Postby gmalivuk » Mon Nov 21, 2016 4:01 am UTC

Ah, I didn't get what you meant by "coreward".
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Soupspoon
You have done something you shouldn't. Or are about to.
Posts: 4060
Joined: Thu Jan 28, 2016 7:00 pm UTC
Location: 53-1

Re: Toroidal star

Postby Soupspoon » Mon Nov 21, 2016 6:17 am UTC

Ah, yes. Definite terminology confusion.

Not the barycentre (origin point O, x=y=z=0), but the circular 'core line' (probably not x²+y²=R² and z=0, for major radius R in a more/less-than regular toroid, but it'd be not far off within minor radius r from there), and where the highest pressures would be, by definition, as that's where converging forces, including pressures from the sheathing gasses, create the zone of greatest density.

Tub
Posts: 468
Joined: Wed Jul 27, 2011 3:13 pm UTC

Re: Toroidal star

Postby Tub » Mon Nov 21, 2016 3:16 pm UTC

lgw wrote:Also, you could cheat this I think with dark matter - does it count as a torus if the donut hole is a blob of dark matter rather than being empty?

Keep in mind that dark matter does not have an electric charge. The thing that allows you to hold stuff in your hand is electromagnetism - the electron hulls around your hand's atoms repel the electron hulls around whatever it is you're holding.

Dark matter doesn't do that. It can pass right through other dark matter or regular matter. The only thing a bunch of dark matter in the center of the torus would do is to pull the torus to it's center due to the dark matter's weight.

Bonus question: could you stabilize a torus by somehow giving the star a net electric charge? My first instinct is to assume that a charge large enough to maintain a hole in the middle would be large enough to maintain a lot of holes in the torus (i.e. the torus explodes), but that's just my instinct, not formulas.
/edit: silly me, wouldn't work. Any particle bordering the hole would feel a force towards the hole, so the hole closes up.

lgw
Posts: 437
Joined: Mon Apr 12, 2010 10:52 pm UTC

Re: Toroidal star

Postby lgw » Mon Nov 28, 2016 7:45 pm UTC

Tub wrote:
lgw wrote:Also, you could cheat this I think with dark matter - does it count as a torus if the donut hole is a blob of dark matter rather than being empty?

Keep in mind that dark matter does not have an electric charge. The thing that allows you to hold stuff in your hand is electromagnetism - the electron hulls around your hand's atoms repel the electron hulls around whatever it is you're holding.

Dark matter doesn't do that. It can pass right through other dark matter or regular matter. The only thing a bunch of dark matter in the center of the torus would do is to pull the torus to it's center due to the dark matter's weight.


That was sort of the idea, though. Start with a relatively heavy sphere pf dark matter, concentrated in the center as you'd expect from gravity alone holding it together. Now you have a central point for familiar matter to orbit. Have a spinning disk of gas of familiar matter with a hole in the middle, which wouldn't be stable on its own, but is now stable because the overall system doesn't have a hollow center, just an invisible one (and the dark matter doesn't need to rotate in step with the familiar matter).
"In no set of physics laws do you get two cats." - doogly


Return to “Science”

Who is online

Users browsing this forum: No registered users and 6 guests