starform

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Star Formation

Some Theorising

Sr. No	Some Interesting Points
1	We start with an assumption that a homogenous gas cloud that was to result in a star the size of our present sun existed at a temperature that of the Cosmic Background Radiation (CMB), at some point of time in the past.
2	We further assume that Its Diameter was 1 lightyear. And because we are playing God here in this thought experiment, it did not start any thing until it had reached a perfect state of thermodynamic equilibrium as well as a uniform density everywhere inside it, and also the cloud had zero spin, and zero initial velocity. (just because we desired it so. How else to cater for the initial conditions?). On our saying so, Gravitation took hold and it started to collapse. We then could study the collapse at our ease.
3	Surprisingly contrary to our opinion, we discovered (with a Gods all percieving vision ofcourse) that the cloud was collapsing faster at its periphery than at its core, half a lightyear away from its outer skin, where things had hardly even started to register the fury we had unleashed. SPECIFICS:- That was because the way gravitational intensity of acceleration "g" is defined. g = GM/rr ---- eqn - (1). But the mass of the containing sphere, M = (the initial uniform density D(0) ) (the volume of the containing sphereof radius r) or M = D0{ (4/3)Pirrr } ---eqn (2) or g = (4/3)D(0)GPi*r ---- eqn - (3) at any point in the star, at a radius r units from the center. Because at any point r units away from the center, the containing sphere radius would be r , and the layers lying beyond would add up to zero force on it anyway.(But that is another subject). Consequently the outer layer of the star would start to collapse inward at an ever increasing speed that would be limited only by the "SONIC SPEED" of the matter in the vicinity of the skin. Also the value of "g" being greater in layers at greater distances, the outermost layers would be collapsing faster than the inner ones, sort of overtaking and absorbing them.
4	Eventually, the continuous assimilation of fresh material in this rapidly evolving shell would start to become denser and hotter by the moment. The buildup of pressure due to accreted material as well as rise in temperature due to friction / turbulence would begin to temporarily halt / slow down the collapse.
5	In all probability due to the excessive build up of kinetic energy by the collapsing layers, it would be some time before the collapse was halted and eventually reversed even, resulting in the outer shell oscillating and going thru progressive cycles of heating and cooling till the loss of sufficient amount of heat and radiant energy made the collapse to progress anew. However meanwhile the inner layers that escaped being gobbled up, had been continuing with their but nevertheless inexorable journey towards the center of our wouldbe star, resulting for the first time in a clear void space between the rebounding outer and the still collapsing inner layers. (no doubt slower and less dramatic due to smaller starting radii). The PROTO PLANETS WERE FORMING ALREADY. Needless to say, there was nothing to prevent more such occurances in the inner collapsing sphere now, resulting in the end in a gaseous onion so to speak.But in the absence of a SPIN all these layers were doomed to merge violently at the surface of the new star sooner or later. Such a Star would have no Planets!!
6	Introduction of a SPIN would however changes that picture quite a bit. First, the spin would imply an initial tangential component of velocity v(t). All points in the cloud with v(t) such that the centrifugal acceleration was greater than the centripetal acceleration would tend to move out towards the outer reaches of the cloud. [v(t)v(t) / r] > g --- eqn (4) And points where g predominated the centrifugal tendency would migrate inwards under the influence of gravity. [v(t)v(t)/ r] < g --- eqn (5) Also points where both g and the centrifugal tendency matched, would remain in a radial equilibrium. [v(t)*v(t) / r] = g --- eqn (6) Ofcourse the rdial components of velocity would have their effects added on, thru the application of the princople of Superposition.
7	Somewhere along the line, in this chaotic whirling, as matter met matter coming from opposite direction, an AXIS would emerge. No doubt randomly oriented, and still subject to random re-orientation, as dictated by the lumpy gaseous overlord of the moment. ( The maths enabling me to put that down in equations is beyond me clearly! But it is not so difficult to visualise / imagine that as a logical consequence of the goings on so far ! We are afterall Gods here remember? Albeit Gods with some constraints!!)
8	One fallout of para 7 would be that matter above and below the emerging orbital plane would have only two ways to go. Join the matter in the orbital plane or fall inward. It is difficult to predict clearly howmuch of that matter would reach the stellar body at the center (still as yet an undisturbed and ,low density and temperature "tranquil" area of space.). But in the end we would be left with a whirling disc of gas. With many clear voids in it, not unlike the rings of saturn!
9	The rings on the outside would be showing more activity than the ones inside, due to a longer history of collapse and accretion and heating and rebounding. The inner rings in time would be catching up with the outer ones also in terms of activity. The most important consequence for planet formation would be that as each ring accreted more matter, became denser, and hotter, it would in time either be gobbled up by a faster inward moving outer ring or a rebounding inner ring. In the end we would be left with a handful of survivers, that would eventually fit equation 6 and fall into orbits never to reach the stellar center.
10	One more interesting consequence of all the above is that if we SEED the initial cloud with Solid dusty matter, we get something closer to reality. Though the gaseous rings are free to rebound and go about their unruly business, their brethren of the solid variety will be having only 2 choices. Lump together and tumble about, till eqn 6 is satisfied, or fall inward. Also, all the time the solid matter will be dissipating their tangential orbital speed faster thru friction, to the surrounding gaseous medium, and gaining inward radial velocities. This matter as a consequence will be always found "below" the outer gaseous rings. (Is that the reason why solid planets are ""inside"" the orbits of the gaseous ones in our solar system? And is it a rule?)
11	Other consequences of above are:- (1) - Possiblities of more than one planets in one and the same stable orbit. (2) - Possibility of "arcs" instead of complete rings due to random clumpiness accreting to itself adjoining matter in a ring, thus breaking the ring and slowly starting planet formation. (3) - The period of rotation of a planet about its axis will be determined by the difference in orbital speeds of the innermost and outermost parts of the initial planet forming ring. (One interesting spinoff of this would be that all the planets [undisturbed by external disturbances] would be found to be turning about their axes in same directions. Also, their surface velocities on the "day side" would be opposite to the direction of their orbital velocities.)
12	Now to get on with our story, if we focus on the tranquil center, we notice that it is encircled by a collosal shock wave of SOUND" (what else does one call a disturbance in a gaseous medium?). I am really unable to describe what is easy to visualise. An inward continuous streaming of matter that long ago became TRANSONIC in its velocity of free fall.
13	The paradox here is that at the center, for values of r = 100,000 km or so, the mass of the containing sphere is so small, as to make one wonder why the remote layers are making so much haste to reach there at all.
14	But in the end inspite of 13 above, the shock wave reaches the center first, then slowly the surrounding shell of radiant matter turns the center into an ever heating up Hell. (Only influx of radiation, from all sides without letup). This effect should be observable in areas such as the Eagle Nebula, where many newly forming Accretion discs are being observed by "HUBBLE SPACE TELESCOPE" . A sudden explosive burst at the center of a planetary nebula. The fireworks would soon die down, drowned in the deluge of matter as it cascaded in, by its sheer kinetic energy. Depending on the amount of matter that thus "falls" on the gravitational center, The star would evolve into white hot star whose surface would soon cool by radiating heat away till an inner thermodynamic temperature gradient was stabilised, due to any fusion reactions sustained within. The initial higher surface emperature would be mainly due to the Kinetic aspect of its energy.
15	Also from 10 above, significant quantities of the solid dust will reach the stellar center first, before most of the star buildup is completed. Thus we might come up with intriguing situation where the disc of planetary gas might be observed to have an inconsequential planetoid as its center! Of course in due course that planetoid would be completely swamped by overlying layers of gas as the star builds up. Soon we would have the fusion reactions started, but the star would have a core not cooked from its nucleosynthesis, but made of matter inherited from its formative Nebula.
16	Eqn - (6) yields one more result that the orbital velocity v(t) = sqrt{gr} = sqrt{GM/r} eqn - (7) or THE ORBITAL VELOCITY VARIES AS THE INVERSE OF THE ROOT OF IT'S ORBITAL RADIUS. The Orbital Period T = (orbital periphery) / (orbital velocity) or T = 2pir / sqrt(GM/r) or T = [2pi / sqrt(GM)][sqrt(r)r] eqn - (8) or T T =[ 4pipirr] [r / GM] or T squared = K * [r cubed] where K = {[4pipi] / [G*M]} eqn - (9) THIS IS THE FAMED KEPLER'S LAW THAT THE SQUARE OF A PLANET'S ORBITAL PERIOD VARIES AS THE CUBE OF IT'S MEAN ORBITAL RADIUS!!
17	One important consequence of this (16) above is that :- As in a flat disk for all points to be steady wrt each other ,the first derivative of the v(t) wrt r which is angular velocity omega , must be independent of radius r at any point of the disk. In such disks, v(t) = {[2pi] / T}r eqn - (10) where T is not a variable dependent on r, but an arbitrary constant. In our "PLANETARY DISC" and most probably in the disk around Saturn, every point in the disk will be going about its orbit at a faster and faster pace as we reduce the orbital radius r.
18	Also there exists a possibility that just as there can be 2 or 3 satellites in stable orbit around a planet, so can rings, then WHY NOT ARCS or SEMI COMPLETE RINGS? (This is just a point of no contest, as arcs have already been found to exist around the outer GAS GIANTS of our solar system.)
19	One important consequence of the above arguments especially point 3 above, is that the velocity distribution of the stars in the central bulge of the spiral galaxies, which in many ways is like the "containing sphere" of point 3, does show that their v(t) increases with increasing radius from the galactic center! Instead of falling off as the inverse of the root of their orbital radius as expected in ring systems. Combining eqn - (3) and eqn - (6), [v(t)v(t) / r] = (4/3)D(0)GPir or v(t) = sqrt[(4/3)D(0)GPi]r eqn - (11) Since T (orbital period) is defined as [2Pir] / v(t) = T , substituting v(t) by rhs of eqn - (11) yields a result T =[2Pi] / sqrt[(4/3)D(0)G*Pi] - eqn (12) Very Important result! IT MEANS THAT IN SUCH CASES HAVING ONCE DERIVED THE ORBITAL PERIOD OF THE HUB OF A SPIRAL GALAXY, WE CAN DIRECTLY CALCULATE THE INITIAL DENSITY OF THE CLOUD OUT OF WHICH IT FORMED! As all the other constants are known. That applies to GLOBULAR CLUSTERS also. The orbital periods of all the stars in globular clusters must be the same.

Last Updated on 6/18/00
By upadhye_js You may mail me more and I will put them up here.

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