The expansion of the universe is a manifestation of the principle of Conservation of Energy.

Thread Index of Key Points
Introduction (below)
The Actual Expansion Rate #7
Cosmic "Sea-level" #15
Dealing With Infinity #24
The Basic Picture #27
The Crux of the Matter #55, p2
The Big Picture #56
Einstein's Sublest Error #57
Contraction Energy Estimate #33 p3
Expansion Energy Est. (revised) #256 p 9
On-going Discussion page 3 +

Figure 1 & Figure 2[Print these two figures to follow along in the text. The original urls no longer work , and the printed versions are easier to understand anyway]

Everywhere in the universe, matter is "falling together," radiating energy "into space" as it does so. What happens to all this energy radiated "into space"? It causes "space" to expand! General Relativity allows for this. In GR, space can bend and stretch, and it does so in such a way that the total energy content of the universe is constant. Space expands in GR as naturally as water flows downhill.

Except for the trivial case of a cold, collapsed body, all gravitational systems either expand or contract. Contraction always tends to occur near "centers of mass," and expansion tends to occur away from the center. The sun's core is contracting, but its outer envelope expanding. Satellites near to earth spiral in; those beyond the geosynchronus orbit spiral away. The cores of globular clusters contract; their outer halos expand or get torn apart by tidal forces. The core of a supernova collapses, the outer parts blown away.

Since all gravitational systems are unstable, either contracting or expanding, and since all contraction tends to take place "locally," it logically follows that on the largest scales, the residual effect must be expansion. The universe is in almost perfect balance...but not quite. Locally, the net effect is contraction, accompanied by the release of energy. Cosmically, the net effect is expansion. The expansion of the universe, acceleration and all, is due to "balancing the books" on energy.

You seem to have made a multitude of poorly qualified statements, even assuming a lot of what you are debunking/agreeing with is theory.

...or entropy, or chaos theory. Einstein's Special Relativity goes a good way towards properly defining how the conservation laws should be applied.

Space is expanding, this is not in debate. And unless you believe in parallel universes or magic, yes, the energy output must equal the energy input. Space can be said to be both "ripping" and agglomerating into black holes at the same time though. This is only if you are concerned with physical mass, and properties exerted through weak forces, such as gravity. Since the matter calculation is short some 96% of known "visible" matter, theories turn to discussions of dark matter and dark energy, which is what I thought this thread would be about.

Cold, collapsed bodies will do something too, as they posess mass. Reactions in the sun are not good examples either. Total mass due to loss of photons & radiation don't truly represent an "expansion" over time. Nearly 100% of all radiated energy from Sol will be captured by other celestial bodies. Eventually the sun will "contract", as you say- it will become a black hole on its own or in conjunction with another massive body. Stars have been seen thus far to merge with others, via black holes, while spinning further outwards into the fringes of the Universe. New galaxies aren't exactly spontaneously forming in the middle of intergalactic space.

"Unstable" is a subjective term. The visible universe agglomerates locally, as I have said, while at the same time, being spun outwards. You are correct that the net result is expansion of the Universe. I don't see how the perfect balance result you claim is arrived at. Gravitational effects are largely unexplained without the benefit of theoretical "dark matter" and "dark energy".

An example will help clarify.

The earth-moon system, like the universe, is expanding. Both are expanding at about the same rate: the universe at about 72 parts-per-trillion-per-year (ppt/yr) and the moon's orbit at about 100 ppt/yr. (1 km/sec/mpc = 1 ppt/yr) Both are "almost perfectly" balanced (not "perfectly"!), but not quite. The expansion rate of the cosmos and the earth-moon system are both "almost zero." Neither is in "perfect" balance, but both are very close.

Is "dark energy" causing the moon's orbit to expand? No, it is rotational energy of the earth. The earth's rotational energy is being transformed into gravitational energy of an expanding earth-moon system. Is dark energy causing the universe to expand? No, it is "light energy." More specifically, radiation eneregy in all forms (radio waves to gamma rays; neutrinos; gravitational waves; & cosmic rays). Visible matter radiates energy, which is why it is visible, and this energy drives the expansion, according to the principle of Conservation of Energy.

In other words, Dark Energy is light energy!

Isn't that a poor example ? Astrophysicists agree that that the Moon will eventually achieve escape velocity, and be hurled off somewhere else in the solar system.

But the dark matter / dark energy discussion has typically revolved around the unexplained high velocity of galaxies and galactic clusters. Gravity is actually a very weak force in atomic terms. It takes significantly large bodies to see and measure these effects.

The high velocity of remote galaxies is easily explained: space is expanding in proportion to itself. The more space there is, the faster it expands. This is what Hubble discovered. Consider the national debt. It is "expanding" at the rate of about $1300 per second! Phenomenal! How do you explain the United States' debt expanding at $1300/sec? It is easily explained: its just billions of $25 savings bonds compounding at $0.00000003/s, or 4% APR.

Likewise, the high velocity of remote galaxies is easily explained: it is just gargantuan volumes of space expanding expanding at an infinitesimal rate. The velocity is high when you go to billions of light-years distance (just as 4% APR comes out to a lot when the debt is in the trillions of dollars), but the rate of expansion is infinitesimal. The rate of expansion is so small, 0.000000000073/yr, that the energy involved is also very small. And the energy emitted by visible matter easily explains energy involved in the infinitesimal expansion.

When astronomers report on distant galaxies, they come up with a lot of "gee-whiz" numbers. Don't let the numbers fool you: the rate of expansion is infinitesimal, and so is the rate of energy gain, and so it is easily explained.

Have you worked on this idea, Peter Wilson, to the point where you have some equations, numbers, maths and stuff to describe it?

If you haven't, do you expect that you will, sometime in the next three months (say)?

If you don't, perhaps you'd be kind enough to let us know how you think BAUT members could attack your idea, with glee and fervour (per the BAUT rules, ATM section)?

For example, what - in principle - could anyone present that could show your non-quantitative description is inconsistent (internally, with GR or QFT, with good observational or experimental results)?

Yes…I welcome the gleeful fusillade of BAUT members! I have worked on this for so long and from so many angles, the problem is what to leave in, and what to leave out. So rather than trying to explain everything at once, in this forum I have laid out the basic premise, and will respond to attacks/questions/criticisms as they arise.

Numbers are hard to come by, because astrophysicists are using a different paradigm. I know that sounds like a lame excuse, but I have asked many a PhD professor for the numbers, and they mostly ignore the question; the kinder ones tell me, “Sorry, you’re wrong.” I do not know how a question can be “wrong,” but that is the response I get when I ask for the numbers! So let me start with the “easy” one, the Hubble constant.

Suppose you ask your broker, “What is the bond rate today?” Your broker replies, “Its at 72 Lira per second per ton of gold.” What would you do with this information? It is utterly useless, because the units are so arcane. So it is with the Hubble expansion, expressed in kilometers per second per megaparsec (km/sec/mpc). These units are misleading, to say the least. They make it sound like the universe is coming apart at the seams! But it is not; the rate of expansion is sub-sub-sub-microscopic.

To convert into meaningful units, we must first divide by the number of kilometers per megaparsec, to get rid of the confusing distance-per-distance. Using the “accepted” value of Hubble constant, 72 km/sec/mpc:

(72 km/sec/mpc) * 1 mpc/(3.09 x 10^19 km/mpc) = 2.3 x 10^-18/sec. This number is so small, out of mercy, we multiply it by the number of seconds in a year, to get the expansion on an annual rate, like interest on a bond:

(2.3 x 10^-18/sec) * (3.15 x 10^7 sec/yr) = 7.3 x 10^-11/yr = 73 ppt/yr

Since the place-value for the number of kilometers-per-megaparsec (3.09) and the number of seconds-per-year (3.15) are almost the same, and their exponents differ by 12 (a factor of one trillion), it is handy to “round-down” the conversion factor to: 1 km/sec/mpc = 1 ppt/yr. In ordinary, scientific terms, the universe is expanding at a rate of about 72 ppt/yr, or 73 ppt/yr if you insist on accuracy. This is a small number. Very small. But I didn’t just pull it out of a hat. Is it clear now where this number comes from? And is it clear that the universe is expanding at a very, very small rate?

To what extent, if any, does your idea incorporate the physics which astronomers and cosmologists use in their work?

Specifically, QED (which incorporates a quantum theory of 'light', and includes 'energy'), and GR (which differs immeasurably from Newtonian theory in most regimes).

Also, I didn't see where you answered this question of mine:Would you care to take a stab at answering it please?

ppt= part per trillion , "what is part defined as? " - just an interested observer.

"Part" is any measure you want to use. Think interest rate. 4% APR means "4 parts per hundred per year." The "parts" could be dollars, Euros, Lira, Pesos...whatever. 4% is 4%, no matter the currency. So it is with the expansion of space: use miles, kilometers or furlongs, it is all the same. For every trillion units of distance there are this year, next year there will be 1,000,000,000,073. [Note: the "parts" cannot be light-years, because the observable universe is less than a trillion light-years across. Think of the expansion rate as a proportionality constant. If a galaxy is 50 million light-years away today, this time next year it will be: 50 Mlyr*1.000000000073 = 50,000,000.0037 lyr away. That is what 73 ppt/yr means.]

OK that's a fair upper limit for parts. Does it have any lower limit?

My idea incorporates the usual fare. What is different is the starting assumption. Present models assume a universe exploding into existance, then use GR to track how the explosion evolves. My model begins with with the universe as we see it: matter more-or-less evenly distributed in space from here to infinity, more-or-less uniformly radiating away energy.

In Newtonian gravity, this creates a paradox: where does the energy "radiated into space" go? General Relativity resolves this paradox by allowing space itself to expand. While the difference between Newtonian and GR is "immeasurable," do not forget that the expansion itself is infinitesimal.

As for how anyone could show that my non-quantitative description is inconsistent...I have no idea. GR and CE (conservation of energy) are consistent, as far as I know. The universe we see, radiating energy at the rate we observe, will expand at a residual rate, according to GR. The only question, as you suggest, is this one: What is the rate? At what rate does GR say our universe should expand? That is the $100,000 question.

what is this again?

Thanks for the clarifications Peter Wilson.

Earlier in this thread you said:... and in your clarification you acknowledged that there's "no new physics" in your idea (well, that's my summary).

Perhaps a first step to testing your idea would be to find out how much 'light energy' there is, throughout the universe?

Let's start with our solar system. An utterly trivial fraction of the solar system is occupied by stuff that's opaque to (most) electromagnetic frequencies - TeV (and higher energy) gammas from AGNs are detected smashing up (Earth's) atmosphere molecules, COMPTON detected lots of gammas of lesser energies (from even further away), XMM-Newton regularly produces lovely pictures of distant galaxies, ... and so on. There are, of course, some obstacles - Jupiter, the Sun, and the IPM below the plasma frequency, but 'light' finds our solar system essentially empty.

So we can add up all the photons, of all the frequencies, that come from all over the sky, to see how much 'light energy' there is. Right?

What would such an investigation conclude? (An OOM - order of magnitude - answer would be just fine).

Yes, and that is an excellent question!

Below about 5 Mpc—I am not sure of the exact distance—the Hubble relation “doesn’t work,” due to local motions. Case in point, the Andromeda galaxy (M31) is about 1 Mpc away, and would be receding at 72 km/sec per the Hubble expansion, but instead is coming at us at 100 km/sec (and gaining!)

Contraction and expansion in the cosmos are complementary, in the same way that erosion and sedimentation are complementary in geology. Every square foot of the earth’s surface is generally either in the process of being eroded-away or “sedimented”-in. On the surface, the two processes mix and match endlessly. Yet below sea-level, there is net sedimentation, and above sea-level, there is net erosion.

Likewise, in the cosmic dance, expansion and contraction intermingle endlessly. I already mentioned the space between the earth and moon is expanding at 100 ppt/yr. On the other hand, the space between earth and man-made satellites contracts (they spiral back down). The height of geosynchronous orbit (GESO), about 24,000 miles above the equator, is the dividing line or “inflection point” between expansion and contraction. Below GESO, satellites spiral in, above it, they spiral away. Right at GESO, they are at a quasi-static orbit, but eventually—without adjustment—a satellite at GESO will drift into one bin or the other: expansion or contraction.

All astronomical systems are rife with such inflection points, of all character, where things either fall in or fall away. As with the “sea-level” on earth that provides the dividing line between net-erosion and net-expansion, this 5 Mpc dimension, while not as clear-cut as the shoreline, nonetheless provides a conceptual divide: within a 5 Mpc “volume” there is net-contraction; beyond it, there is net expansion. So this 5 Mpc distance represents the “minimum” below which, as you asked, the Hubble relation does not apply.

1 mpc/(3.09 x 10^19 km/mpc)

Sorry about the confustion; its hard to do math in text format, and I messed that one up. The Hubble constant is traditonally expressed ("Bad Astronomy" if there ever was!) in km/mpc (per second), instead of ppt/yr. To get rid of the km/mpc, we multiply by the # of mpc/km, which is the same as dividing by the # of km/mpc, which is what I did there.

I think I understand your effort: to simply. But multiplying by 1/x/y is not the same as dividing by 1/y/x. I do like your train of thought but the switch to ppt still baffles me. Give me some time to re-think your proposal- 12 hours.

That has been my thinking. I’ve made some OOM estimates, but that is jumping ahead a little. Allow me to diverge here just a bit. As an “outsider” (no PhD; no association with an Institute), I am “pointing the way,” not providing an answer. I know “the sign” (positive, i.e. expansion), but I do not know the magnitude. It will take “real scholars” in their ivory towers to do the calculation in a way that everyone will accept, but recent work gives me hope.

Fred Cooperstock and Steven Tieu (C&T) have submitted calculations for journal publication that show galactic “dark matter” is explained simply by properly applying GR to galaxy rotation.

http://www.space.com/scienceastronom...rk_matter.html

Their calculations have met with a lot of skepticism, but as Einstein would say, “The theory is correct,” and their work will surely be accepted. It will certainly go down in history as a turning-point in our understanding of the cosmos. “Dark matter” has been an enigma for about 7 decades. Ironically, GR has been around for about 8. Why did no one previously turn to GR as an explanation for dark matter? As far as I know, Einstein was as baffled as anyone by the mystery of dark matter, and he would surely be pleased to know that yet another long-standing observational mystery is explained by his venerable theory.

In the narrow, conservative manner of academics, C&T only claim to explain dark matter within spiral galaxies, but I am betting that when the dust settles, GR will explain intergalactic dark matter as well. And of course, I’m betting that when the dust settles, GR will explain “dark energy,” in a round-about sort of way. Take the observed distribution of visible matter in the universe, and the rate at which it is radiating energy; model the observed distribution of matter and the energy radiation using GR, and you will find that “space” expands at some rate in such a model. My central contention is that when this calculation is done, the predicted rate of expansion will be close to or equal the observed rate of expansion, 73 ppt/yr.

72 km/sec/mpc * 1 year = 2.27 x 10^9 km/yr/mpc is this a wrong step?

Re-hashing this a couple of times will not hurt, because the misconception regarding the expansion rate is so deeply ingrained. Here is the conversion, one more time:

1) H = 72 km/sec/Mpc = 72 km/(Mpc-sec)
(seconds and megaparsecs are both "down-stairs")

2) [72 km/(Mpc-sec)] * [1 Mpc/(3.09 x10^19 km)] = 23 x 10^-19/sec
(km & Mpc are both cancelled out)

3) [23 x 10^-19/sec] * [3.15 x 10^7 sec/yr] = 73 x 10^-12/yr
(seconds are cancelled out)

4) 73 x 10^-12/yr = 73 ppt/yr

Again, to a first approximation, 1 km/sec/Mpc = 1 ppt/yr. They are, for all intents and purposes, the same, but "kilometers per second" creates the totally wrong impression of what is going on. The expansion rate is truly infinitesimal, and using "parts per trillion per year" paints more "accurate" picture.

{typo removed for clarity}

As I understand it, correct me if I'm wrong, this constant is a unit of expansion for Mps distances based on the red shift formula. Any use of it in smaller parts, even lys or km is outside the limit of its purpose. If other words the farther away it is, the more additional expansion needs to be applied. To see this in terms of trillions of parts where parts are less that a trillionth of a Mps, for instance, IS infintesimal and not appropriate for the constant's purpose. Yes, I like your argument for the small expansion rate. But when considered in all directions it isn't so puny to me. Thank you for bearing with my learning curve and best wishes in the success of your model.

A quick dimensional analysis ... km/s/Mpc has dimensions of (L/T)/L = T^-1 (L = length, T = time).

Or, in ordinary words, frequency. Which is measured in Hertz (Hz = inverse seconds).

Peter Wilson said as much, in line 2) above (though I get 2.3 x 10^-18 Hz, not -19).

It's a pretty deep frequency, wouldn't you say? About one beat per 13 billion years (if I've done my arithmetic right). Hmm, now where have I seen that number before?

As a frequency device yes the Hubble constant can be translated into Hz. Having fun with harmonics of frequencies : cosmic rays attain 10^21. Could one find support that 10^-21 hz is more likely the beat of the Universe. And that H may only represent when the weak force, atoms (e.i. light) was formed? Leaving a horizon shell which expands or contracts based on black hole intake? (No response nec. Just trying to conceptualize both of your math wizardry.)

Well…technically…you’re correct. An infinitesimal expansion rate viewed over infinite distance comes out to mind-boggling velocity! Recession velocity at 14 Bly approaches the speed of light, and then what?

The problem is, the human mind cannot take-in infinity. The best we can do is to look at the 14 Bly bubble of universe that is visible, and assume that beyond 14 Bly is more of the same.

Here’s the deal: the expansion of the universe is a manifestation of the yin-yang principal on the largest scale. Remember the debate in the 19th century over whether light was particle or wave? Well, it’s both. How about the fuss in the 20th century over whether human behavior is Nature or Nurture? Of course, it’s both. And poor Einstein nearly tore his hair out, because his equations of GR seemed to say that space must either expand or contract, yet it was observed to be doing neither!

Hubble and big telescopes came to Einstein’s rescue, however, when it was discovered that space is expanding after all. You just have to look half-way to infinity to really see it. But the complete answer to Einstein’s puzzlement is that space is actually doing both. It is another "duality of nature." Space contracts on “local” scales, and “expands” on cosmic scale. While this cannot be pictured in a Newtonian space-time coordinate system, GR allows it.

Within the 5 Mpc distance mentioned earlier—a more precise figure has been published somewhere, but I cannot recall where—there is net contraction. Stuff “falls in,” radiating energy as it does so. Beyond the 5 Mpc mark, stuff “falls away.” The energy released by contraction supplies the energy of expansion. You could say gravity is “causing” expansion, because the expansion is the flip-side of local gravitational contraction. Expansion is a reaction to contraction. It is balancing the energy books. Local contraction is the yin, and cosmic expansion is the yang.

Dooh!

You're right...it shoulda' been 23 x 10^-19/sec. But the end result is the same.

The Hubble constant is not in units of frequency, which is cycles per unit time. H is just "per unit time" (w/o cycles).

A better way to think of it is in terms of a "time-constant." We say a radioactive sample has a "half-life" of so-many years. The universe is not shrinking, like a sample of radioactive material, it is expanding. The universe therefore has a "doubling-time," about 10^10 years. If the expansion rate is constant, which it has been for at least the past 5 billion years (about as far as we can presently see), then it will double in size in 10 billion years.

How about the horizon shell yin-yang'in but always beyond our x-ray sight? Say a definite thickness like an orange peel but until a frequency beyond cosmic rays is discovered, a finite outside skin with an adjustable lower epidermis? Still I truly have enjoyed both of your excellent insights, and as I have yet to read Our Living Multiverse by Fred Adams, I'm just about out of thoughts. May some observations on harmonic cosmic radiation diffusion patterns, as for what is beyond our orange? That would be a discovery indeed!

I have no idea what is beyond our orange...our grapefruit?

Jedi Knight, you wish to be? Know what lies beyond the dark side, can you? Go within first, you must. (Aw heck, I never could do Yoda very well...)

Excellent question!

Alright...back to the topic

Before I toss some numbers out, let me describe the problem qualitatively a little more clearly. And let me begin with some observations: We are gravitationally bound to the earth. The earth is gravitationally bound to the sun. The sun is bound to the galaxy. The galaxy is bound within the Local Group of galaxies. The Local Group is orbiting about some super-cluster, which itself is...wait. At some point, things go from bound, to unbound. We find, as we look around, that we are gravitationally bound within larger and larger groupings, but at some point, everything is "unbound," or falling away.

At what scale does this transition occur, and why?

I have already answered the scale-part: it occurs @ +/- 5 Mpc. The "why" part is subtle, however, and can be looked at from several angles.

Start by considering the solar-system. Imagine a bubble of space, centered on the sun, extending to the outer fringes. Clearly, as the sun burns its hydrogen fuel and shines, more energy leaves this bubble than enters it. But now, what if we expand the bubble to 10 parsecs? Well, in that case, the surface area of the bubble becomes pretty big, but now there are other stars radiating away energy, and we can still be pretty sure that more energy is being radiated away from the volume of space than is entering it. Now imagine a bubble 100 kpc in diameter, this time centered on the center of our galaxy. Such a bubble would now encompass a lot of empty space, but being centered on our galaxy (a relatively bright beacon in our neck of the universe), it would still radiate away more energy than enters it.

But when the size of the bubble gets to about 5 Mpc, a funny thing happens. The surface area of the sphere becomes so large, and the amount of radiative matter within the sphere becomes so small in proportion to it, that the amount of energy leaving the bubble and the amount of energy entering it become equal. Then what? What does that mean to say the amount of energy entering and leaving the bubble is the same?

What it means is that the energy balance has to be taken into consideration. When we considered just the solar-system, we could say, "The sun's energy is radiated into space," and be done with it. There is no accounting for it: energy goes "into space," and that is that. But when we get to 5 Mpc, because the surface area of the sphere is so large, as much energy is "coming in from space" as is being radiated "into space," so we arrive at a paradox. If as much energy is entering as is leaving, what is chainging?

What is changing is the distance between things. Within the 5 Mpc bubble, things tend to get closer together, i.e contract. Beyond it, things get further away, i.e. expand. Within the bubble, matter "loses energy" by radiating it "into space." With respect to matter beyond the bubble, however, matter "gains energy" on account of the expansion.

As for the rate at which matter radiates energy "into space," we can express it in joules/kilogram/year. Visible matter in our universe can be observed to be radiating, on-average, so-many j/kg/yr. Likewise, due to the expansion, matter can be said to be gaining so-many j/kg/yr. Determining the average rate that matter radiates energy is a matter of culling observational data. Calculating the energy gain due to expansion using GR...that gives me a headache just thinking about it!

Figure 1 graphically illustrates the concept of the expansion being an energy balance. An artist I’m not, so you have to use your imagination a little. Picture the cube shown in the top repeating to infinity in all directions, like one of those fantastic Escher drawings.

What happens from top to bottom is that matter clumps together locally, radiating energy in the process. In "the real universe," these clumps are visible as stars, star clusters, galaxies, black holes, etc. Because the grid repeats to infinity, there is radiation coming from everywhere, going to everywhere. The result is a uniform glow in all directions. As much radiant energy enters each cube as leaves it.

Thus, the total energy content of the universe, from top to bottom, never changes. What changes is the way this energy is distributed. In the top, gravitational energy is uniformly distributed among all particles. In the bottom, energy has been “lost” by matter within each clump. Yet with respect to other clumps, the matter within each clump has “gained energy” by moving apart.

Keep in mind, it is not just the cube shown that has expanded; every cube all the way to infinity has done likewise. So the distance between all clumps has increased, and the greater the starting distance, the greater the increase in ending distance, i.e. Hubble’s law. The time-scale from top to bottom is about a billion years. Also, it is the bizarre tenets GR that allow space to stretch, as depicted (and observed), but it is the more mundane principal of Conservation of Energy that drives the expansion.

I'm not sure this is entirely correct. For example, there are objects which are not bound to stellar systems, nor to galaxies, nor to clusters, nor to super-clusters (the most obvious are UHE cosmic rays and neutrinos). Further, the nature of structure at the ~5 Mpc+ level is rather more complex than you've outlined - what are 'cold' objects in voids (e.g. the Bootes void) bound to? what sort of 'binding' is there for objects in sheets (e.g. the Great Wall) and filaments?True. But why consider only a bubble centred on the Sun? Leaving aside the feeble net energy radiated by Jupiter and Saturn, almost all bubbles of sizes up to ~1 pc will have more energy entering them than leaving (just as long as a bubble does not include a chunk of the Sun, they pretty much all will). There are vastly more of such bubbles than ones with net energy leaving.This is only true, of course, if there are stars in such a bubble (and none, for example, just on the fringes).

You could create a pathological case of a 10 pc bubble, with a brown dwarf in it, and a large number of O stars just 1 au outside the bubble - I'm pretty sure in this case there would be vastly more energy (in the form of photons) entering than leaving.And again, if the 100 kpc bubble were such that it included just a few halo stars, and maybe one or two dozen in the outer bulge, then it would 'absorb' more energy than it radiates.Well, I think you can see from the other bubbles I've painted that your idea needs some more work. At the least, you have to address the apparent arbitrariness in how you choose to 'draw' your bubbles.