Andrew over on "Dispatches from Turtle Island" http://dispatchesfromturtleisland.blogspot.co.uk/2013/11/a-lost-and-found-galaxy.html
has recently cited this thread.
Perhaps William drank too much Hermitage that night? Who knows?
In a more serious frame of mind we need to consider what we mean by our local place in the universe. Galaxies occur in groups, clusters and superclusters separated by space. If one googles these key words and searches images there are a plethora of examples that reveal the universe's structure. http://commons.wikimedia.org/wiki/File:Local_galaxy_filaments.gif
or view galaxy filaments.
A more technical discussion lecture 25 is here http://ircamera.as.arizona.edu/astr_250/Lectures/Lec_25sml.htm
What are galactic filaments or walls or sheets etc? Well they are morphological descriptions of what we observe- all those countless google images. I mentioned some while ago that I could see many triple junctions out there, similar to what one sees in a can of oil as it slowly warms up or global plate triple junctions as we see here on Earth. Of course I am biased, those on Earth have a failed arm, otherwise the Earth's volume would increase without limit. Again, the global plates are essentially two dimensional structures whereas in the celestial vault the galactic motions of filaments take place in a three dimensional space. At increasing distance we still see filaments but the basic units we observe or galaxies become increasingly structureless "irregular blobs" which if in close association suggests that they are merging. As we go to increasing distance we see earlier epochs(times) in the history of the universe.
Is the universe isotropic and or homogeneous and do we live at a priveleged time and position? These encompass what are referred back to as a simple cosmological principle and the Copernican viewpoint. Within the local group of our own galaxy were one to look around from the locale within a large globular or spherical starcluster within a galaxy the night sky would appear totally different than we we to change locale to the barycentre of our local group or let us say midway between Andromeda and the Milky Way. One wouldn't see any stars in the night sky and with my eyesight I might see a faint haze that would represent the core of Andromeda, about fourfold brighter than from our Earthly vantage point. Again, on the other side of the sky our Milky Way would display only a slight haze. Without a telescope to enhance our vision we wouldn't even debate the priciples central to astronomy.
Our local group is confined to a size or diameter of several million light years. Out at 52 million light years NGC 1107 probably belongs to the Virgo cluster. Is it gravitationally bound to that rather than our own local group? It doesn't really matter in that our local group is certainly bound to bigger fish. Galaxies or rather clusters of them do recede in an expanding space, the Hubble expansion and it appears incontrovertible. I see no reason to challenge that statement, that space is expanding as per lecture 25 and similar presentations.
Cosmic density or the critical density= 3*Ho2
/8*Pi*G is actually a limit. There's a straightforward derivation. One has to balance gravitational potential and kinetic energies of the total energy of the system. As one goes to greater radial distance things look more symmetric, ideal spheres with volume 4/3 *Pi*R3
and mass this factor fold cosmic critical density. The system has kinetic energy and this is related to 1/2 Ho2
. The kinetic energy also includes angular momentum that needs to be released, ultimately as heat to the voids which I do not address. No matter how irregular galaxies and ancient blobs may be, ie. I mean hugely distorted from a spherical form we need a proof to demonstrate at what R that irregular blob might collapse, a consequence of sufficient mass to be either gravitationally bound or not ie. sufficient kinetic energy to fly away to infinity. These blobs are what you observe. In this case by they represent filaments of galaxies rather than ancestral galaxy blobs that are globular or irregular, that appear to be merging. The Abell supercluster is relatively close by. By that I mean one can see an association that is irregular and elongate. It is not ideally spherical. Nevertheless draw a circle that encompasses the longest axis. The gravitational potential on the surface of this sphere is idealised as uniform and lower than what would be measured were one to measure the potential at various points along an irregular shape in proximity to the elongated blobs of galaxies.
What we observe, what I observe infact as filaments appear to be strings or ropes of galaxies with triple junctions. Of course I am biased about triple junctions, there are often four or five and in fact occasionally one observes what looks very spherical , a triple spherical cow of a junction that is representative of that famous formula for critical density with the numerical factor 3/(8*Pi). Ultimately, it comes from the first few lines of the derivation with factor 4/3* Pi *R3
. 8*Pi* G is a famous factor. It is fallacious in that it doesn't approximate what we actually observe. There's no problem with Ho
- it is empirical fact
Yet what we observe are filaments, however you so define them they are not the 4/3 Pi volume sort. As ropes or strings they are R* (Pi*R/n)2
volumes where R/n is the ratio of idealised R to rope radius. Now they are not long single ropes, they don't look like single ropes. Many are biforcated and are so becaused I am actually biased about triple junctions. You may see four junctions or more or even object that these aren't rope stuctures at all because they can be described as sheets or walls. Well! calculate the gravitational potentials along these sheets; you do need to address volume and eventually derive a critical density for homogenised mass . You will find critical densities that lies between the 3Ho2
/8*Pi*G , as a limit for for the universally accepted derivation that assumes spherical cows all on up, and irregular turtle densities all on down, to the limit of Y triple junctions or
critical density based upon filaments of Pi2
An actual averaged out cosmic density is between these limits but it doesn't exist, there's no privileged average density.
What does it mean? One could devote a whole chapter to an alternative derivation of critical density ? with numerical factors 3/8*Pi versus Pi2
/6 . Consider a sphere of galaxies where R becomes big enough to encompass... but hardly big enough to encompass the whole universe. The critical density homogenises the distribution of matter, it's idealised and extrapolated wholescale to well beyond z=2. We see out to say z=10 and to an earlier phase where irregular blobs become apparent, "obviously merging". I make no assumptions here, I describe what I see rather than infer a merging or evaporation. It's a filamentous structure of galaxies we observe along with great voids. Neglecting angular momentum which will dissipate eventually, if I inscribe a sphere around any irregular glob with the major axis incorporated therein; if there is sufficient mass within rather than inferred critical density it will collapse all the way to a black hole. The density depends upon the geometry idealised. The blobs have kinetic energy, sufficient of course to prevent collapse.
The idealised density imagines a volume big enough to describe homogenised matter and isotropic. It is expanding, the system has an entropy and it is increasing. The filamentous organistion of matter as galactic units actually has a higher entropy and as expansion occurs it will also increases but it always higher than the idealised spherical system at any time. Unlike the chemical systems in thermodynamics , agglomeration of matter gravitationally packs entropy ultimately into black holes. A filamentous structure of galaxies at its simplest appears a more likely, a more probable configuration in the evolution of structure. It works in a bath of oil , here on Earth with plate tectonics although how useful these analogies really are I do not know. Yet the newly derived critical density is huge! It's more by a factor of ten from the idealised sherical cow calculation. It depends upon how many triple junctions there are; some may prefer interconnecting membranes or more rigorous mathematical treatments. Then again it varies from region to region. Imagine if you were an observer in a large void? Well with a big enough telescope an external observer would eventually realise major scientific progress unless they were aquatics or in a save haven totally albeit shrouded in clouds of whatever- ammonia! 3/8*Pi is famous for physicists but so also is Pi2
/6 to a chemist and mathematician, infact so also a physicist. I quote it as a limit for biforcated strings, for idealised triple junction filaments. The universe appears less isotropic and less homogenous than assumed. That's a vague association and so also so are these astronomical principles. The older I get the more privileged I feel, another triumph for Pi2
/6 applications. Don't take my word for it, check it yourself.