Dark Galaxy Discovered: Unbelievable Findings

[DaveC426913]

Dark Galaxy found!?

You know, I've always been secretly hoping that dark matter was an aberration of our observations or calculations, some value to be tweaked or some normalizing factor to be applied thing that was making galaxies turn faster than formulae predicted. I just couldn't believe that we are only observing 4% of the universe.
But it seems that idea has been blown apart.
They've discovered a Dark Galaxy.
http://www.space.com/scienceastronomy/050223_dark_galaxy.html"
http://www.discover.com/issues/dec-05/cover/?page=2"

It is completely invisible to light, it is only visible by its radio emissions. And even at that, only a tiny portion of it is visible even there. They can tell by its gravity that there's many, many times more mass in it than can be seen. Whatever the mass, it is completely undetectable directly. This is a galaxy that contains no (zero) stars.
Incredible. Stranger than fiction.

 

[Garth]

Well they discovered ordinary hydrogen, from its 21cm radiation emission, so that is hardly exotic DM. But they also state: "From the speed it is spinning, we realized that VIRGOHI21 was a thousand times more massive than could be accounted for by the observed hydrogen atoms alone," Minchin said."

Now in an ordinary galaxy/cluster the ordinary baryonic matter is 0.002 closure density whereas the total baryonic matter is ~ 0.04 closure, so about 95% of ordinary baryonic stuff is invisible even in the Mainstream LCDM model. In this dark galaxy it seems this 20:1 invisible/visible baryonic matter ratio is some 50 times larger. Now this could require an exotic form of DM to be invoked, but we could be more certain if we knew where that 95% invisible baryonic matter was!

It could be that here is a resevoir of exotic (totally new physics) non-baryonic DM, or that in this galaxy the ordinary baryonic stuff never got round to forming stars and becoming visible, which do you think it is?

Garth

 

[SpaceTiger]

Unfortunately, this isn't the first claim of a "dark galaxy" to hit the presses. Even more unfortunately, these claims usually turn out to be bogus or easily explained some other way. In this particular case, it looks like the object could just as easily be tidal debris from a recent interaction. See here:

http://xxx.lanl.gov/abs/astro-ph/0505580"

 

[Chronos]

Bah, ST got the scoop on me there. There was another alleged DM galaxy story about a year ago... it too did not pan either. Links:

http://www.newscientist.com/article.ns?id=dn7056
http://www.arxiv.org/abs/astro-ph/050231

 

[ubavontuba]

paradox?

SpaceTiger,

That was an interesting link. I wonder if by applying Occam's razor we might be more inclined to believe it to simply be debri, rather than jumping to the conclusion that it is a dark matter galaxy?

Also, if there really is all this dark matter floating about, what does that say for our observations regarding the expanding universe? Wouldn't "dark energy" be required to overcome it and cause the perceived acceleration in the universe, and wouldn't this dark energy nullify the effect of dark matter so we must have more dark matter to overcome dark energy? Then, wouldn't we need more dark energy to overcome the effects of the of dark matter? And then wouldn't we need more dark matter... well, I think you get the picture.

 

[matt.o]

I would be extremely skeptical of any "dark galaxy" found in a cluster environment, since we know dynamical interaction and ram pressure stripping are both effective gas removalists.

If one of these things were to be found in isolation, then that would be a different matter.

Also, in collapsed systems, the effect of the dark energy is negligible as gravity dominates.

 

[ubavontuba]

Also, in collapsed systems, the effect of the dark energy is negligible as gravity dominates.

Sure, but everyone seems to have forgotten the basic rule about action and reaction. Applying this simple rule seems to indicate that you cannot have two distinct entities (dark matter and dark energy).

Where is the dark matter's proposed position in galaxies? It is mostly confined to a halo around the visible mass. Therefore, its edges are most exposed to the ant-gravity (I hate that word) effect of dark energy, effectively meaning that dark energy should nibble away at dark matter's placement in galaxies.

Think about it. Dark energy is strong enough to push on entire galaxies. Dark matter is a loose conglomeration of mass on the edges of these galaxies. If dark energy is a force, it must extend into the gravitational field of these galaxies, thereby nullifying (to some extent) the gravity on the edges of galaxies (this effect should be strongest at the edges if gravity rules as you say). Mass on the edges should simply sling away!

Since dark energy's purported task is to separate mass from mass, it should obviously work well at separating small mass and particles from galaxy edges. I.e. nibble away at galaxies. That is it should if it's an acceleration like gravity.

In short, it seems to me that the combination of these two opposing hypothetical forces in our universe acting in this way, would cause galaxies to evaporate away into space. Therefore, there should be a more homogenous dispersal of matter in the universe.

Supposing it is only a confining or "pushing" force that doesn't disturb the gravitational attraction of dark and ordinary matter (essentially creating a demarcation line at the edges of galaxies) we should then note that galaxies are denser at the edges. In other words, galaxies would need to exhibit a ring or sphere of denser matter at the edges, due to the compression effects of dark energy. Additionally, this would tend to make galaxies collapse upon themselves!

In conclusion, if dark energy deeply penetrates galaxies in radians, galaxies should evaporate. If it only pushes on the edges of galaxies, then galaxies should show signs of compression and perhaps collapse.

 

[ubavontuba]

I've explained that dark energy cannot be a distinct force acting between the galaxies, but I haven't explained what it could be.

Many think it could be an expansion of space itself, where the galaxies only appear to be accelerating because the space inbetween them is getting larger. However, I have issues with this because an apparent acceleration caused by expansion should exhibit the same local "anti-gravity" effects I listed in the prior post. That is that it should nibble away loose matter at the edges of galaxies. This is because this hypothesized expansion is occurring everywhere, only local gravity trumps it. However, weakly contained mass orbiting on the fringes should be spun away by even the slightest imbalance between their centripetal force connections (gravity) and a weakening of centripetal force caused by the effect of expanding space between the masses, thus stretching and diminishing the centripetal connections. In short, galaxies should radiate mass and energy from the edges (evaporate).

I think it must be a more pervassive force acting not on the galaxies, but on all of space at once. I propose that this force is gravity and that the galaxies are simply falling toward the universe's cosmological event horizon. I explain this hypothesis here.

 

[matt.o]

I think you should go and read these articles and think about the scales they are talking about.

http://en.wikipedia.org/wiki/Dark_energy"

and

http://physicsweb.org/articles/world/17/5/7"

 

[ubavontuba]

matt.o,

Those are good articles (I particularly liked the physicsweb article and will cite it in the future), but they only demonstrate my point. They treat galaxies like single entities reacting to dark energy and provide no mention of possible consequences to the galaxies themselves when considering the various hypothetical versions of dark energy.

Galaxies are not single entities. They are loose conglomerations of matter held in a thin balance between dispersal and collapse. You can't simply treat them as individual entities reacting to the vagrancies of dark energy.

 

[Chronos]

Hi ubavontuba! I side with matt.o. on this one. There is a huge amount of observational and mathematical evidence he is sitting on that fits much better than the dark galaxy thing.

 

[ubavontuba]

Chronos,

Hi ubavontuba! I side with matt.o. on this one. There is a huge amount of observational and mathematical evidence he is sitting on that fits much better than the dark galaxy thing.

Actually I agree. Where matt.o and I seemed to disagree was on the local effects of dark energy on dark matter and galaxies. I then foolishly ran off on a tangent about dark energy in a dark matter thread (someone oughtta' come up with more distinctive names). Sorry.

Anyway, I think Occam's razor should lead us first to look at simpler possibilities, rather than jump to the initial conclusion that it's a dark matter galaxy. It could be a dark matter galaxy, but it could be a bunch of loose gases too. I think more study is required for a definitive solution.

I like your signature. My current favorite quote is:
"Beer is proof that God loves us and he wants us to be happy." -Ben Franklin

 

[matt.o]

Actually, it does mention that one kind of dark energy called quintessence may lead to a 'big rip'. Since in this model dark energy may get stronger with time it will eventually tear apart clusters and galaxies and it is even poostulated that it will overcome all other forces in the universe, tearing apart atoms on the way. This is a rather large extrapolation of the current data, which I believe (I may be wrong) is not good enough to distinguish different models for dark energy.

Did you notice that they only notice the effects of dark energy at about a redshhift of 1? Does that not tell you the local effects at this present time are negligible and the things you describe are not going to be observed?

 

[Garth]

Did you notice that they only notice the effects of dark energy at about a redshhift of 1? Does that not tell you the local effects at this present time are negligible and the things you describe are not going to be observed?

Or it might tell you that the GR-with-Inflation-and-DM model begins to break down when extrapolated out to z > 1.

Garth

 

[ubavontuba]

Actually, it does mention that one kind of dark energy called quintessence may lead to a 'big rip'. Since in this model dark energy may get stronger with time it will eventually tear apart clusters and galaxies and it is even poostulated that it will overcome all other forces in the universe, tearing apart atoms on the way. This is a rather large extrapolation of the current data, which I believe (I may be wrong) is not good enough to distinguish different models for dark energy.

Yeah. I kind of like this. It's about as wild as some of my own musings. It seems positively poetic that the universe which started from nothing might someday disolve back into nothing...

Did you notice that they only notice the effects of dark energy at about a redshhift of 1? Does that not tell you the local effects at this present time are negligible and the things you describe are not going to be observed?

Yes, but even if it is very weak but pervasive force throughout the universe, we should see more fog in intergalactic space. It wouldn't take much of a nudge to strip mass off of the edges of galaxies.

It is possible that dark matter is somehow viscuos and acts as a kind of glue-barrier between dark energy and normal matter, but then we'd have to come up with a bunch more new physics to explain this efffect. Perhaps it might have something to do with it's purported weak interaction with normal matter? Even so, it should still fall in gravity just the same though, right? Therefore shouldn't it also fall away the same under the influence of a separating force?

 

[ubavontuba]

Or it might tell you that the GR-with-Inflation-and-DM model begins to break down when extrapolated out to z > 1.

Yeah, or the extrenum of distance might have effects not yet anticipated in relativity.

In either case, I think dark matter is interesting. Did anyone ever get anywhere with the hypothesis that dark matter might be nuetrinos?

 

[Garth]

Yeah, or the extrenum of distance might have effects not yet anticipated in relativity.
In either case, I think dark matter is interesting. Did anyone ever get anywhere with the hypothesis that dark matter might be nuetrinos?

Yes, neutrinos have an upper limit mass that means they can only account for 1% max. of $\Omega_{total}$, not 23% as required for DM.

Garth

 

[jhe1984]

"Yes, neutrinos have an upper limit mass that means they can only account for 1% max. of , not 23% as required for DM"


Can you clarify what "upper limit mass" means?

Is it basically the calculation that, if every possible neutrino that could be produced was produced, they would still only account for 1% of the universe's total mass?

If they were all located in a certain place, say on the outskirts of galaxies, couldn't this have a fairly sizable impact?

 

[Garth]

"Yes, neutrinos have an upper limit mass that means they can only account for 1% max. of , not 23% as required for DM"
Can you clarify what "upper limit mass" means?
Is it basically the calculation that, if every possible neutrino that could be produced was produced, they would still only account for 1% of the universe's total mass?

Yes

If they were all located in a certain place, say on the outskirts of galaxies, couldn't this have a fairly sizable impact?

Neutrinos are 'hot', that is they 'zoom' everywhere at relativistic speeds and would not congregate on the outskirts of galaxies. Others have suggested that neutrinos are the exotic DM but they don't fit, their mass is too small and they are too active to explain the large scale structure and galaxy formation required by the standard theory.

I hope this helps.

 

[Chronos]

Affirmed. I agree with Garth's explanation. Neutrinos are like photons, just more abundant. They cannot clump, or possibly make up more than a few percent of the 'missing' mass in current models of the universe.

 

[matt.o]

Yes, but even if it is very weak but pervasive force throughout the universe, we should see more fog in intergalactic space. It wouldn't take much of a nudge to strip mass off of the edges of galaxies.

What do you mean by "fog"?
I think you need to go and crunch some numbers to prove to yourself that this is not the case.

It is possible that dark matter is somehow viscuos and acts as a kind of glue-barrier between dark energy and normal matter, but then we'd have to come up with a bunch more new physics to explain this efffect. Perhaps it might have something to do with it's purported weak interaction with normal matter? force?

I don't understand what you are trying to say here. Dark matter does not interact with baryonic matter apart from it's gravitational influences, which are more than enough to stop a galaxy being nibbled away at by dark energy (to use your terms).

Even so, it should still fall in gravity just the same though, right? Therefore shouldn't it also fall away the same under the influence of a separating force?

Again, I don't understand what you are trying to say here.
It sounds as though you are drawing a lot of conclusions from your own unfounded hypothesis.

 

[ubavontuba]

What do you mean by "fog"?
I think you need to go and crunch some numbers to prove to yourself that this is not the case.

By "fog," I mean that galaxies might not have such definable boundaries. That is, might they appear to be more "fuzzy?"

I don't understand what you are trying to say here. Dark matter does not interact with baryonic matter apart from it's gravitational influences, which are more than enough to stop a galaxy being nibbled away at by dark energy (to use your terms).

Right, but my point is, what's to stop the dark matter from being nibbled away, by this same separating force?

Again, I don't understand what you are trying to say here.
It sounds as though you are drawing a lot of conclusions from your own unfounded hypothesis.

It's the same point I was making regarding dark matter's interaction with dark energy above.

I am not making any speculative conclusions based on any personal theories. I am merely asking questions regarding the interactions between gravitational and dark energy forces. If dark energy reacts with baryonic matter in an antigravity sort of way and dark matter reacts with baryonic matter in a gravitational way, shouldn't dark energy also react with dark matter in an antigravity sort of way?

 

[Garth]

Both non-baryonic Dark Matter and Dark Energy are hypothetical entities that have not been discovered in a laboratory. Therefore we do not know what they are or how they behave. However they are invoked to explain some non-Newtonian behaviour of matter and the universe as a whole at galactic and larger scales.

The invoked DE is considered to be cosmological and spread out evenly throughout space whereas DM self gravitates and collapses into massive halos into which the galaxies fall and form.

Although your question is an interesting one, the behaviour of DE and DM is modeled in very large numerical calculations that do not demonstrate the sort of interactions you speculate on.

Garth

 

[ubavontuba]

Although your question is an interesting one, the behaviour of DE and DM is modeled in very large numerical calculations that do not demonstrate the sort of interactions you speculate on.

Why not?

This has been my point all along. It seems that science may have missed the interplay between these two hypothetical forces that Newtonian Mechanics would demand. Perhaps the mathematical model is incomplete or too simple?

See? Galaxologists (?) need a force to hold galaxies together, so we get dark matter. Cosmologists need a force to explain cosmic acceleration, so we get dark energy. Both of these concepts (if real) must interact with each other in the universe (since everything is relative) and I don't know if the two camps have realized this.

Therefore I ask the questions: Could one preclude the other? Can both hypothetical forces live comfortably in the same universe?

 

[Garth]

In the standard LCDM model DM & DE do live comfortably in the same universe. DE acting on a larger scale, DM on a smaller scale. The results of the numerical calculations do fit the observed features of the universe very well, although there are a few problems by playing with the equation of states of both DE (w </=/>1) and DM (non or weakly interacting) they can be made to fit better.

I have a problem in that they are not found in the laboratory even after ~ 30 years of intense investigations and they are an artefact of interpreting cosmological observations with GR. The results are theory dependent. An alternative theory may be able to duplicate the observed features of the universe without exotic DM or unknown DE, and there are several such alternatives (MOND, SCC) that are being tested at the moment, so we shall see.

Garth

 

[ubavontuba]

But why are they modeled to act on different scales? Gravity is a universally acting force above quantum and therefore is not scalable in the cosmos, right. It seems that dark energy must act on a similar scale, right (even if weakly as opposed to gravity)?

Therefore, these two forces (if real) must interact on all scales above quantum, right? That is to say that if dark energy weakens gravity (even if only a little) in the cosmos, then dark matter should exhibit this effect, right?

What I think it comes down to is a paradox of contention between the two forces. Dark matter that is weakly held in a halo around galaxies (in higher orbits) would seem to be particularly susceptible to the vagaries of dark energy and it would tend to slip away from galaxies under the influence of dark energy... essentially causing the same problem that dark matter was ostensibly supposed to fix. Simple conservation of angular momentum would speed this process along until the whole galaxy evaporated (in an infinite time model). Doesn't this sound reasonable?

So, again I ask: Could our standard model be to simple? Might the interaction of these two hypothetical cosmic forces have been missed or dampened by a too simplistic model?

 

[Garth]

First I think the standard model is anything but simple, and its get more complicated as time goes on.

However the reason DE and DM work on different scales is the same reason why universal expansion and gravitational collapse work on different scales.

In GR, where the local density increases above the cosmological 'smeared out' critical value, because of local concentrations of matter, then gravitational collapse overcomes the cosmological expansion of space.

If that cosmological expansion is actually accelerating, despite the presence of matter, then DE is at work.

In bound galaxy clusters etc. the gravitational forces, including a major part played by DM, overwhelm the effects of expansion and DE.

You have to do the numbers and solve the equations of a set theory rather than just guess.

Garth

 

[matt.o]

let's reiterate;
the dark energy is dominant on large scales, the dark matter (ie. gravity) is dominant on small scales, hence dark matter dominates in galaxies and dark energy dominates the universe.

But why are they modeled to act on different scales? Gravity is a universally acting force above quantum and therefore is not scalable in the cosmos, right. It seems that dark energy must act on a similar scale, right (even if weakly as opposed to gravity)?

see above reiteration.

What I think it comes down to is a paradox of contention between the two forces. Dark matter that is weakly held in a halo around galaxies (in higher orbits) would seem to be particularly susceptible to the vagaries of dark energy and it would tend to slip away from galaxies under the influence of dark energy...

Weakly held compared to what? On this scale dark energy is much weaker compared to gravity.

essentially causing the same problem that dark matter was ostensibly supposed to fix.

I don't see how you reach this conclusion from the above.

Simple conservation of angular momentum would speed this process along until the whole galaxy evaporated (in an infinite time model).

It depends on how dark energy evolves with time.

Doesn't this sound reasonable?
So, again I ask: Could our standard model be to simple? Might the interaction of these two hypothetical cosmic forces have been missed or dampened by a too simplistic model?

Our model may be too complex. Who knows. It fits the data reasonably well and things seem to be converging towards a lambda CDM model.

 

[SpaceTiger]

Okay, I can't promise a follow-up until thursday, but I have to make some comments on this thread.

What I think it comes down to is a paradox of contention between the two forces. Dark matter that is weakly held in a halo around galaxies (in higher orbits) would seem to be particularly susceptible to the vagaries of dark energy and it would tend to slip away from galaxies under the influence of dark energy... essentially causing the same problem that dark matter was ostensibly supposed to fix. Simple conservation of angular momentum would speed this process along until the whole galaxy evaporated (in an infinite time model). Doesn't this sound reasonable?

You can understand how this would not occur on galaxy scales by simply recognizing two facts:

1) The energy density of matter and dark energy are comparable (i.e. within the same order of magnitude) at the present epoch.
2) Galaxies represent extreme overdensities of matter.

You don't even need to crunch numbers. Just ask yourself what the condition is for the repulsive effects of dark energy to become comparable to the attractive effects of matter. The condition is that, within a given spherical volume, you would need a comparable amount of dark energy and matter. If galaxies are extreme overdensities of matter and dark energy is smoothly distributed in space (as we believe), then can you see how extreme overdensities of matter (galaxies) will have much more matter than dark energy (bullet 2, above)? Furthermore, can you see how the spherical volume at which this will no longer be true will be on cosmological scales (bullet 1, above)?

That's the simple answer. The more technical answer is that, in a $\Lambda$CDM universe, the growth of structure halts at a certain scale which is given by the value of the cosmological constant (dark energy density). It turns out that, in our universe, this scale is only relevant for the growth of galaxy clusters, not galaxies themselves. The dark matter halos occupied by the latter are much smaller, in general, and would not feel the effects of dark energy. The outer boundaries of galaxies are already fuzzy and are more likely to be determined by tidal forces from other nearby galaxies and/or the "temperature" of the dark matter.

I should emphasize that the cosmological constant only halts growth, it does not cause the clusters to evaporate. The reason for this is that, in a CDM universe (i.e. one with only dark and luminous matter), structure is forever growing, and it's doing so on larger and larger scales. This was the basic behavior of our universe prior to z~1, when the dark energy density became comparable to the matter density. When dark energy began to make itself known, this "infall" and growth was thought to have slowed and it should eventually come to a stop (if it hasn't already). The whole reason it's called the cosmological constant is that it has a constant energy density with time. Combine this with the reasoning in my "simple explanation" and you should be able to see why growth halts at a certain physical scale.

The cosmological constant is not the only possible source of the dark energy. There are some (admittedly exotic) theories in which the density of the dark energy forever increases with time. These are the "Big Rip" theories that matt.o was referring to and, in those theories, everything eventually gets torn apart by the dark energy, not just galaxies. Again, this can be understood by the arguments I give above.

Finally, it's worth noting that gravitationally bound groups of stars (like globular clusters and perhaps galaxies), can undergo a sort "evaporation" as a natural consequence of their evolution. This is not related to dark energy, however, and is not just a consequence of conservation of angular momentum, as you seemed to suggest at one point. Rather, this occurs because, when a galaxy/cluster tries to relax (i.e. reach equilibrium), it excites a few stars to speeds larger than the escape velocity of the cluster/galaxy. These few stars will then escape the cluster. In order for more stars to escape, the cluster must relax again, so the timescale for evaporation is many "relaxation times". We do observe this kind of behavior in globular clusters. However, this relaxation timescale turns out to be longer for larger objects, so we won't notice these effects in galaxies or galaxy clusters whose relaxation times are comparable to and longer than the age of the universe.

 

[ubavontuba]

Thanks for the replies. You all sound like very sophisticated and educated gentlepeople so the fact that I don't seem to be conveying my dilemma very well must (obviously) lie with me. So with that consideration, let me restate my concerns as a Mechanic's conundrum.

Beginning by first assuming that you are all very well aware of Newtonian Mechanics I will skip any lecture and go straight to the conundrum.

Let's create a universe with only two very small masses. Let's say they are bits of dark matter. Let's create a galaxy of these two bits by placing them in orbit around one another at a fixed distance.

Under ordinary Newtonian considerations, they should remain in this exact orbit... essentially forever.

Let's introduce a very weak antigravity force, we'll call "dark energy." This force is wa-a-a-a-ay weaker than gravity by many orders of magnitude, though like gravity it works on all scales (since it pushes on all matter). How might it effect our universe model?

Obviously (to me) this energy/force (regardless of how small) would tend to spread our two bits apart. Why? Because even if it is very weak, a little bit of it is inbetween the two separate but orbitting bits. They are pushed apart (however slightly). Then, since there's more space, more DE get's inbetween and pushes them apart more effectively. then more DE gets inbetween and again pushes them apart even more effectively, then... you get the idea. Now extrapolate this effect as having been happening for about 10 billion years, each orbit being slightly larger than the last.

Basically, this is a conudrum of F=ma. If the force of gravity and the force of DE are equal, then there is no net force and the two bits could never be in orbit around each other. If DE is much weaker, then an orbit can occur but it cannot be stable forever. This is because although gravity might be very strong, in this model gravity is balanced by the two particle's angular momentum. Therefore, even the weakest of force should be able to disturb the orbits. That is to say that the force of gravity minus angular momentum is less than the force of DE (in radii from the center of mass of the system).

DE would essentially be like a couple of very weak ion drives attached to both particles. Always pushing... always adding energy for incremental changes.

However, DE could never be strong enough in this model to separate single gravitational bodies as there is no room to work and insufficient angular momentum to nullify the great strength of gravity (not to mention electro-static attraction). It's only the equalizing force of angular momentum that would allow a condition of balance that can be disturbed by the DE.

Does this sound like a correct assesment? If not, where have I erred?

Sorry if this post seems to ramble a bit, I wrote it while "Malcolm in the Middle" was on.

 

[SpaceTiger]

Let's create a universe with only two very small masses. Let's say they are bits of dark matter. Let's create a galaxy of these two bits by placing them in orbit around one another at a fixed distance.

Let's introduce a very weak antigravity force, we'll call "dark energy." This force is wa-a-a-a-ay weaker than gravity by many orders of magnitude, though like gravity it works on all scales (since it pushes on all matter). How might it effect our universe model?

Ok, I think this is a good example. I'll repeat your assumptions in a different way, since they will be crucial to the arguments that follow:

1) The "repulsive force" is very weak on the scale of the system. It will eventually dominate the potential if one goes to large enough radii, but it will be many orders of magnitude larger than the separation between the masses.
2) The potential is time-independent; that is, the energy density of dark energy at a particular location in space does not change with time. Since we're talking about the cosmological constant, not some other form of dark energy, this is a required assumption.

Since we've established a time-independent potential, we can define an energy for the orbiting mass.

$$E=-V_g(r)+V_r(r)+T$$

where $V_g$ is the potential due to gravity (the usual 1/r potential), $V_r$ is the potential of the "repulsive" force, and T is the total kinetic energy of the orbiting body. The radial coordinate is measured from the center of mass of the orbiting bodies. I've pulled the minus sign out of the gravitational potential to make its attractive nature explicit. For the arguments that follow, it won't matter if the repulsive potential increases or decreases with radius, as long as it stays well below the magnitude of the gravitational potential.

Let's start by considering a purely radial orbit. In this case, the kinetic energy is just:

$$T=\frac{1}{2}mv_r^2$$

Now, the question is, can we create an orbit that is bound for all time? To answer this, let's just choose some initial condition. We don't have to think very hard on this one, let's just drop the object from some radius, r. That is, $v_r=0$ at $r=r_0$. What is the total energy of the object? To answer that, we just set the kinetic energy to zero:

$$E_{tot}=-V_g(r_0)+V_r(r_0)$$

A bound orbit has negative total energy and an unbound one has positive. Since we agreed that $V_r(r_0)$ is much less than the gravitational potential, this orbit must be bound. Since the potential is time-independent, energy conservation must always apply and the orbit must be forever bound.

We can also examine circular orbits. You seem to claim that they would be unstable in this potential, but we can examine this directly. Setting $v_r=0$, the energy is given by:

$$E=-\frac{GMm}{r}+V_r(r)+\frac{L^2}{2mr^2}=V_{eff}$$

A circular orbit is found by finding the minima and maxima of the effective potential as a function of r. The stability is determined by concavity and positive concavity means a stable orbit. Now we could solve for the first and second derivatives of this function and get explicit answers, but it should be easier to just imagine the shape of the function. In a Newtonian potential, if L is small enough, the function should look something like the red curve in this picture:

http://qonos.princeton.edu/nbond/Kepler78.gif

Disregard the blue curve, as it's not relevant here. As you can see, there's a stable circular orbit in the red curve at x=1. The question we want to now ask is whether or not this changes qualitatively when we add a small potential with positive sign; that is, does this potential change the shape of the curve? If it's very weak, I don't see how it could. You can imagine adding a very small number to every point on that curve, all it will do is shift the minimum slightly.

So what does this mean? Basically, it means that there are stable circular orbits in the presence of a cosmological constant. The dark energy does not forever push the objects apart. All of these arguments fall apart if the dark energy density is increasing with time because the potential becomes time-dependent and energy is not conserved. This, again, is the Big Rip.

Obviously (to me) this energy/force (regardless of how small) would tend to spread our two bits apart. Why? Because even if it is very weak, a little bit of it is inbetween the two separate but orbitting bits. They are pushed apart (however slightly). Then, since there's more space, more DE get's inbetween and pushes them apart more effectively. then more DE gets inbetween and again pushes them apart even more effectively, then... you get the idea. Now extrapolate this effect as having been happening for about 10 billion years, each orbit being slightly larger than the last.

You can analyze this same problem by summing the effect of an infinite number of infinitesimal forces, but you'll get the same answer. The series must, at some point, converge. If it didn't, energy and/or angular momentum would not be conserved.

However, DE could never be strong enough in this model to separate single gravitational bodies as there is no room to work and insufficient angular momentum to nullify the great strength of gravity (not to mention electro-static attraction). It's only the equalizing force of angular momentum that would allow a condition of balance that can be disturbed by the DE.

If you were to take an orbit in a Newtonian potential and then suddenly introduce a field of dark energy, you would get a perturbation in the orbit for the reasons you give. However, the orbit will quickly reach a new equilibrium that includes the effects of the dark energy (that is, the three forces will come to a balance). If you don't further change your system, it will remain in this equilibrium for all time.

 

[ubavontuba]

Ok, I think this is a good example. I'll repeat your assumptions in a different way, since they will be crucial to the arguments that follow:

1) The "repulsive force" is very weak on the scale of the system. It will eventually dominate the potential if one goes to large enough radii, but it will be many orders of magnitude larger than the separation between the masses.
2) The potential is time-independent; that is, the energy density of dark energy at a particular location in space does not change with time. Since we're talking about the cosmological constant, not some other form of dark energy, this is a required assumption.

Hmm, as I understand it (I may be mistaken), the dark energy in our universe is possibly time-dependent in that it apparently started fairly late in the cosmic evolution.

Since we've established a time-independent potential, we can define an energy for the orbiting mass.

$$E=-V_g(r)+V_r(r)+T$$

where $V_g$ is the potential due to gravity (the usual 1/r potential), $V_r$ is the potential of the "repulsive" force, and T is the total kinetic energy of the orbiting body. The radial coordinate is measured from the center of mass of the orbiting bodies. I've pulled the minus sign out of the gravitational potential to make its attractive nature explicit. For the arguments that follow, it won't matter if the repulsive potential increases or decreases with radius, as long as it stays well below the magnitude of the gravitational potential.

Let's start by considering a purely radial orbit. In this case, the kinetic energy is just:

$$T=\frac{1}{2}mv_r^2$$

Now, the question is, can we create an orbit that is bound for all time? To answer this, let's just choose some initial condition. We don't have to think very hard on this one, let's just drop the object from some radius, r. That is, $v_r=0$ at $r=r_0$. What is the total energy of the object? To answer that, we just set the kinetic energy to zero:

$$E_{tot}=-V_g(r_0)+V_r(r_0)$$

A bound orbit has negative total energy and an unbound one has positive. Since we agreed that $V_r(r_0)$ is much less than the gravitational potential, this orbit must be bound. Since the potential is time-independent, energy conservation must always apply and the orbit must be forever bound.

Actually, (so I've read) it seems apparent that dark energy might be a violation of conservation.

We can also examine circular orbits. You seem to claim that they would be unstable in this potential, but we can examine this directly. Setting $v_r=0$, the energy is given by:

$$E=-\frac{GMm}{r}+V_r(r)+\frac{L^2}{2mr^2}=V_{eff}$$

A circular orbit is found by finding the minima and maxima of the effective potential as a function of r. The stability is determined by concavity and positive concavity means a stable orbit. Now we could solve for the first and second derivatives of this function and get explicit answers, but it should be easier to just imagine the shape of the function. In a Newtonian potential, if L is small enough, the function should look something like the red curve in this picture:

http://qonos.princeton.edu/nbond/Kepler78.gif

Disregard the blue curve, as it's not relevant here. As you can see, there's a stable circular orbit in the red curve at x=1. The question we want to now ask is whether or not this changes qualitatively when we add a small potential with positive sign; that is, does this potential change the shape of the curve? If it's very weak, I don't see how it could. You can imagine adding a very small number to every point on that curve, all it will do is shift the minimum slightly.

Ah, but this "very small number" grows with distance. Shifting the curve will require you to reshift the curve for the new values and then you'll have to reshift the curve...

So what does this mean? Basically, it means that there are stable circular orbits in the presence of a cosmological constant. The dark energy does not forever push the objects apart. All of these arguments fall apart if the dark energy density is increasing with time because the potential becomes time-dependent and energy is not conserved. This, again, is the Big Rip.

Or, they move apart as the dark energy potential is increasing with distance and gravity potential is decreasing with distance. Conservation (in this case) is not firmly established. Perhaps there is an asymmetry to it that we are too small to perceive, perhaps there is a super-symmetry of multiverses that allows this apparent asymmetry to occur in our universe. Perhaps all of DE is symmetrically equivalent to all of gravity, Who knows?

You can analyze this same problem by summing the effect of an infinite number of infinitesimal forces, but you'll get the same answer. The series must, at some point, converge. If it didn't, energy and/or angular momentum would not be conserved.

Right. But conservation is questionable on large scales, the CP(T?) violation being one example.

If you were to take an orbit in a Newtonian potential and then suddenly introduce a field of dark energy, you would get a perturbation in the orbit for the reasons you give. However, the orbit will quickly reach a new equilibrium that includes the effects of the dark energy (that is, the three forces will come to a balance). If you don't further change your system, it will remain in this equilibrium for all time.

Right, but the changes wrought by DE create changes to DE and gravity potential that then cause changes to the system that then change DE and gravity potential that then... It's a vicious circle.

Conservation of momentum appears to create a convergence in your fixed DE value system, but it doesn't when one considers the gravitational potential between the two bodies also changes with distance. There shouldn't be an acceleration in a changeless potential (as you would have it), but the potential does change, even if DE potential doesn't. This is due to the inverse square law applicable to gravity potential. The orbits should steadily increase in circumference in an acceleration, should the potential of DE remain unchanged and the potential of gravity decrease with distance.

Obviously, this would be an excrutiatingly slow process of separation, but we have billions of years of its effects to observe. We should see "fuzzy," more dispersed galaxies (if it's a separating force, like space-time expansion). Or, we should see signs of compression (if it's a pushing force from between the galaxies (ZPE?)).

Does this make sense?

 

[SpaceTiger]

Hmm, as I understand it (I may be mistaken), the dark energy in our universe is possibly time-dependent in that it apparently started fairly late in the cosmic evolution.

It is possible that the dark energy has a time-dependent density, but that's not immediately derivable from its late-time dominance in the universe. If the dark energy density were constant with time, then you would get late-time dominance naturally by virtue of the fact that the matter density drops as the universe expands. The so-called "Lambda transition" occurs when the matter energy density drops to that of the cosmological constant.

The most popular theory of the universe right now is $\Lambda CDM$, where the $\Lambda$ refers to the cosmological constant. There are other theories in which the dark energy density changes with time and in these models my arguments would not apply, as I've already said. Most of them actually have the density decreasing with time, meaning that the orbits should exhibit a slight contraction.

Actually, (so I've read) it seems apparent that dark energy might be a violation of conservation.

In fact, a fully general relativistic treatment of the universe does not conserve energy, even in the absence of the dark energy. However, as you said, we were working in the Newtonian approximation. With galaxies and weak fields, this approximation should be valid. There may be higher-order relativistic corrections, but they're small, difficult to model, and not in correspondence with the arguments you gave.

Ah, but this "very small number" grows with distance. Shifting the curve will require you to reshift the curve for the new values and then you'll have to reshift the curve...

The plot is already a function of distance (r). I think you should read the argument and plots again a little more carefully. The "shifting" of the plot is only done once with the addition of the dark energy potential (which is already a function of distance). The potential does not change with time.

Conservation (in this case) is not firmly established.

In your toy model, it's very firmly established. We can modify this toy model and speculate that higher-order general relativistic corrections might produce a change in one direction or the other, but it would be an even smaller shift than has already been produced.

Perhaps there is an asymmetry to it that we are too small to perceive, perhaps there is a super-symmetry of multiverses that allows this apparent asymmetry to occur in our universe. Perhaps all of DE is symmetrically equivalent to all of gravity, Who knows?

In the real world, there are all sorts of potential complications, but the purpose of simple models is to remove those and understand the physics one bit at a time. In the purely Newtonian approximation, along with the mass distribution you've postulated, energy will be conserved and the orbits can be bound.

Right. But conservation is questionable on large scales, the CP(T?) violation being one example.

Even GR is questionable on large scales -- it's very hard to test theories of gravity on cosmological scales unless they produce major deviations from GR.

Right, but the changes wrought by DE create changes to DE and gravity potential that then cause changes to the system that then change DE and gravity potential that then... It's a vicious circle.

I don't follow you here. Are you coupling Lagrangians?

Conservation of momentum appears to create a convergence in your fixed DE value system, but it doesn't when one considers the gravitational potential between the two bodies also changes with distance. There shouldn't be an acceleration in a changeless potential (as you would have it), but the potential does change, even if DE potential doesn't. This is due to the inverse square law applicable to gravity potential. The orbits should steadily increase in circumference in an acceleration, should the potential of DE remain unchanged and the potential of gravity decrease with distance.

I suspect you've completely misunderstood my argument. On the very first step, I give both the dark energy and gravitational potential a distance dependence.

Does this make sense?

I think we should try approaching this more methodically. Go through my arguments and make sure you understand each step. If you're confused about something in particular, ask me to elaborate. Have you ever taken a class or done problems on orbital dynamics?

 

[ubavontuba]

The plot is already a function of distance (r). I think you should read the argument and plots again a little more carefully. The "shifting" of the plot is only done once with the addition of the dark energy potential (which is already a function of distance). The potential does not change with time.

In your equation $$E_{tot}=-V_g(r_0)+V_r(r_0)$$, it looks to me like you arbitrarily predetermined the outcome you wanted by supposing beforehand that there is such a stable orbit. I think you will find the distance for this orbit is zero for any non-zero mass.

I think we should try approaching this more methodically. Go through my arguments and make sure you understand each step. If you're confused about something in particular, ask me to elaborate. Have you ever taken a class or done problems on orbital dynamics?

I don't think I'm confused (yet), but I'll let you know if I feel that way. It's funny you should ask though. Another nickname of mine is "Uba confused," or "Uba confused Vontuba."

 

[SpaceTiger]

In your equation $$E_{tot}=-V_g(r_0)+V_r(r_0)$$, it looks to me like you arbitrarily predetermined the outcome you wanted by supposing beforehand that there is such a stable orbit. I think you will find the distance for this orbit is zero for any non-zero mass.

That equation is the energy of a mass starting with zero velocity at $r=r_0$. It doesn't matter what the form of the potential is, as long as it's spherically symmetric (or, alternatively, one-dimensional), that equation will be valid. If it were true that $V_r(r_0) > V_g(r_0)$, then the orbit would be unbound and the particle would be able to escape.

Think about it this way. A mass that is "free" will have only kinetic energy, which must be positive. If its total energy is negative at any point in the orbit, then conservation of energy demands that it never be "free".