The Galaxies Formed as the First Atoms were Bound
According to my galaxy formation theory, the barred spiral galaxies such as NGC 1365 in Fornax are considerably smaller than the 88,060 light-year in diameter flat spirals, the barred spirals measuring 3/2 Jeans lengths along the bar, or 48,070 light-years. I assume we start from a gas of average Milky Way density, 2.67 x 10-21 kg/m3 cooled to the He++ to He+ transition temperature of 6.31 x 105 degrees Kelvin. This temperature is determined by the ionization energy of 54.39 eV for singly ionized helium. An 88,060 light-year in diameter spiral averaging about 10,200 light-years thick is thought to have been formed from pressure waves featuring an integer number 7 of Jeans half-lengths across and 11 complete waves azimuthally around at the mass-averaged expectation radius, automatically excluding most possible initial forms in the flat spiral class by initially requiring integer numbers of pressure wavelets both radially across and azimuthally around. The numbers 7 & 11 come up, like something from a cosmic game of dice, except that all is determined by a pressure wave-mechanical process triggered by a quantum-mechanical atomic transition. It reminds us of Einstein's saying "God does not play dice with the universe". The pressure waves are due to the pressure jog induced by the phase transformation He++ to He+ in the cooling Big Bang fireball, which takes place at a well-defined temperature. On the other hand, a galaxy formation process based on the H+ to H recombination event would produce galaxies with linear dimensions reduced by 1/2 and masses down by (1/2)3 = 1/8, no longer matching observations well.
According to my model, a flattened elliptical galaxy like NGC 5195 in M51 (the whirlpool spiral is NGC 5194) always has a total thickness of about 12,494 light-years. The alternative 10,200 light-year number for flattened spirals comes from a flat coin model for producing the galactic gravitational potential. If the width of the NGC 5195 were the 12,494 flattened elliptical value, it would span the disk of NGC 5194 (a typical 88,060 light-year diameter spiral averaging 10,200 light-years thick) about 7 times instead of the observed 4 times. On the other hand, a spherical galaxy in my model always has a diameter of 17,668 light-years. If NGC 5195 were spherical, we should see 88,060/17,668 = 4.98, a closer fit. The galactic dynamics of material accreting to the elliptical NGC 5195 from the neighboring spiral probably causes it to flatten out into something resembling a flattened elliptical galaxy 12,494 light-years thick and 88,060/4 = 22,015 light-years wide, which my galaxy formation theory allows for flattened ellipticals. I note that the M51 galactic forms seem to mythically suggest revolution and counter-revolution, and the galaxy formation theory leads us to suspect that both of them are actually viewed flat side up.
Many of the results of the sophisticated theory based on pressure waves at the Jeans wavelength associated with the He++ to He+ transition phase transformation can be obtained from floccule theory based on models of gas evaporation from galactic surfaces. In floccule theory one considers the escape of a gas particle working against the gravitational potential for the cloud, and from this derives the dimensions of the cloud if the density is assumed to be the average Milky Way density. This density is assumed to be a relic of the Big Bang fireball at the He++ to He+ transition temperature. Using floccule theory, one can then derive the dimensions of spherical galaxies, elliptical galaxies, and flattened ellipticals. The results agree well with observations of galaxies in clusters, and with the predictions of the model using Jeans length pressure waves. Using the gravitational potential associated with a flat plate, one may estimate the thickness of flattened spiral galaxies using bound floccule theory, which turns out to be 10,200 light-years, although no limit is specified then for the galactic diameter, which is determined by the more elaborate model involving Jeans length pressure waves due to the jog associated with the He++ to He+ phase transformation.
Mythologically, the barred spiral swordsman NGC 1365 appears to one side of the River Eridanus, into which Orion may trip and fall down if things go poorly, so that the galactic-scale nebular sub-illustrations here show him cut down to size. I note that Aquarius falls at "88" on his way backwards to the Florida peninsula (constellation Cetus), clutching at the necktie constellation Sculptor, preparing for an interview so that things will not go poorly with an "Eridanus" washout. The clusters of galaxies seem to fit into the mythic story associated with the celestial sphere. For instance, I derived my galaxy formation theory when I was at home at Virgo-Ruth, so the huge Virgo cluster of galaxies spills out of the cup of the associated constellation, which seems to reach after Leo bounding away towards his destiny as Orion. The depth of the mythic part of the celestial sphere image extends outwards hundreds of millions of light-years.
According to the equations for a universe of constant density, the solution for the radius of the universe should vary like r = a*[t]2/3. From observations, if the universe were shrunken by a factor of Z = 100, the galaxies would all be touching. Let rB be the radius of the universe at that time. Then if r is the current radius of the universe,
Then t/tB = (100)3/2 = 1000, and
tB = t/1000 = 13.5 x 109 years/1000 = 13.5 million years.
This is on the time-scale associated with the matter-dominated era, but it shows that the galaxies formed quite early. Using radiation-dominated era models, I find that the galaxies formed at least 3.542 x 105 years after the explosion from nucleonic density, but the radiation-dominated era model was probably no longer valid when the galaxies formed, through radiation and matter were still coupled. However, we should never be able to see this far backwards in time with a telescope, but only to the maximum depth of view (3/5)t, that is, (3/5)(13.5 billion years), the theoretical limit of telescopic vision in an expanding universe due to observational time-delay τ = L/c for an object at L. Instead, we should see well-formed spiral galaxies with high red shifts near this 8.1 billion light-year limiting distance. This explains Olber's paradox very neatly. If we take a very highly red-shifted flattened spiral viewed edge-on, we expect to find approximately that
88,060 light years equals 8.1 billion light-years x (angular extent of the galaxy in radians).
Similar results should apply to the 10.2 thousand light-year predicted average thickness of the galactic disk.
Note that looking back into the Hubble Deep Field, we seem to pick up a volume of space in which very distant galaxies are exploding away from each other, some red-shifted, some blue-shifted and rushing towards us! This is probably because we are looking backwards into a time τ = L/c = nearly 8 billion years ago when that's what we'd have seen! Still, very red-shifted galaxies do not appear until the distance is cosmological. To compute the distribution of colors in galaxies near the red limit at (3/5)tuniverse = 8.1 billion light-years, one has to consider that there a mass of galaxies are rushing away from each other in all directions, then superimpose the overall cosmological redshift
Using r = a*(t)2/3 again, if we could see all the way back 8.1 billion years to the edge of telescopic visibility, then we should see
That is, at the very limit of telescopic observation, the galaxies will have come apart by a factor of 1.4, so that 0.4 galactic widths should be observed between galaxies at that 8.1 billion year depth. No matter what, we will not see galaxies at a greater depth with tighter average packing. When Z=1, the galaxies are all touching, but this time will be invisible to telescopes.
- Jim Green, alias Lovelorn Green, March 13, 2006.
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Galaxy Formation by James A. Green.