How did hydrogen and helium gas collapse to form the first celestial object in the early universe?

[TheSameDude]

Based on the big bang theory, stellar and planetary development requires gravity to accumulate cosmic gas, but particles move too fast to coalesce. At -272.15°C, hydrogen atoms move at 158 meters/second while helium atoms move at 79 meters/second. All you need is a velocity of 4.31498e-14 meters/second to escape the gravitational pull of an H2 molecule. There’s no doubt that cosmic clouds possess a lot of gravity, but the gravity is divided by the gas particles that make up the cloud (mass = gravity). Hence, the gravitational sum doesn’t coalesce anything because it can’t get the first two gas particles to cohere. It can only move the matter to a particular direction to form very thick fog. This increases the collision frequency or makes the pressure push outward until it equalizes, so the system will grow instead of compressing. Nuclear and electromagnetic forces would still produce atoms, and atoms would still bond to make molecules, but that's as far as it would get. Helium doesn't form any molecules and hydrogen would predominantly form H2 which are filled shell molecules, so they can't bond to more hydrogen.

 

[Acme]

Mmmm....let's see. Are there celestial objects? Stars? Planets? Molecules? Are there people who don't understand how it could happen? Are there people who question people who don't understand how it could happen? Case closed.

[Greg H.]

Nuclear and electromagnetic forces would still produce atoms, and atoms would still bond to make molecules, but that's as far as it would get.

Obviously not, or we wouldn't be here to tell you how wrong you are.

 

I would start with some introductory texts on cosmology or astronomy. They should give you the basics behind the early universe as we understand it today.

 

Or you could just try Google. Apparently, that's a thing now.

[swansont]

Based on the big bang theory, stellar and planetary development requires gravity to accumulate cosmic gas, but particles move too fast to coalesce. At -272.15°C, hydrogen atoms move at 158 meters/second while helium atoms move at 79 meters/second. All you need is a velocity of 4.31498e-14 meters/second to escape the gravitational pull of an H2 molecule. There’s no doubt that cosmic clouds possess a lot of gravity, but the gravity is divided by the gas particles that make up the cloud (mass = gravity). Hence, the gravitational sum doesn’t coalesce anything because it can’t get the first two gas particles to cohere. It can only move the matter to a particular direction to form very thick fog. This increases the collision frequency or makes the pressure push outward until it equalizes, so the system will grow instead of compressing. Nuclear and electromagnetic forces would still produce atoms, and atoms would still bond to make molecules, but that's as far as it would get. Helium doesn't form any molecules and hydrogen would predominantly form H2 which are filled shell molecules, so they can't bond to more hydrogen.

 

 

emphasis added

 

Gravity doesn't work that way — it doesn't get divided up, and it's not simply the interaction between two atoms. It's a cumulative effect, so you have to look at the gravity of many times Avogadro's number (i.e. waaay more than 10^24 atoms)

 

One step you're missing is that atoms colliding at some temperature will radiate photons, which lowers the atoms' energy and thus temperature and that affects pressure and volume.

[Spyman]

...Hence, the gravitational sum doesnt coalesce anything because it cant get the first two gas particles to cohere...

This is where your train of thoughts go wrong, you can't look at individual molecules and conclude that since their gravity can't pull them together a larger cloud can't collapse either.

 

There are some general basic rules of nature that you are overlooking, the strength of gravity depends on mass and distance but the number of molecules can increase in three spatial dimension making the size growing slower than its mass when molecular clouds gets larger.

 

If we look at a sphere then when the radius doubles the volume and its mass increases with the cube of the radius:

 

[math] V = \frac {4}{3} \pi r^3 [/math]

 

And since the force of gravity decreases with the square of distance, according to Newton's law of universal gravitation:

 

[math] F = G \frac {m_1m_2}{r^2} [/math]

 

Thus the gravity of a roughly spherical molecular cloud at its edge will be approximately proportional to its radius.

 

Double the radius of the cloud and the "surface" gravity will also be doubled, at some larger size it will begin to coalesce.

Edited April 29, 2014 by Spyman

[Janus]

This is where your train of thoughts go wrong, you can't look at individual molecules and conclude that since their gravity can't pull them together a larger cloud can't collapse either.

 

There are some general basic rules of nature that you are overlooking, the strength of gravity depends on mass and distance but the number of molecules can increase in three spatial dimension making the size growing slower than its mass when molecular clouds gets larger.

 

If we look at a sphere then when the radius doubles the volume and its mass increases with the cube of the radius:

 

[math] V = \frac {4}{3} \pi r^3 [/math]

 

And since the force of gravity decreases with the square of distance, according to Newton's law of universal gravitation:

 

[math] F = G \frac {m_1m_2}{r^2} [/math]

 

Thus the gravity of a roughly spherical molecular cloud at its edge will be approximately proportional to its radius.

 

Double the radius of the cloud and the "surface" gravity will also be doubled, at some larger size it will begin to coalesce.

Another way to look at it is in terms of escape velocity. The escape velocity at the surface of the sphere is

 

[math]V_e= \sqrt{\frac{2GM}{r}}[/math]

 

For a uniformly dense sphere, M goes up by the cube of r so Ve goes up by in proportion to r. With a large enough cloud of any density, Ve will exceed the given molecular speeds. And that's for molecules at the distance of r, molecules closer to the center will have give up speed climbing to a distance of r, and thus would have to have even greater starting velocities in order to escape.

 

Thus a cloud of sufficient size will be gravitationally bound with the molecule trapped in orbits around the common center of gravity. Then add in the collision effect brought up by swansont, and these molecules will bleed away energy and velocity, forcing them into tighter and tighter orbits, eventually leading to the collapse and formation of a stellar or planetary body.

[TheSameDude]

 

One step you're missing is that atoms colliding at some temperature will radiate photons, which lowers the atoms' energy and thus temperature and that affects pressure and volume.

 

Light bulbs emit photons which increases temperature

[Orodruin]

 

 

Light bulbs emit photons which increases temperature

Light bulbs emit photons because they are hot, not the other way around. The photon emission cools the bulb by carrying away energy. However, during normal operations the same amount of energy is added by electric work. Once the electric current stops the bulb (the glow thread to be precise) quickly cools down to a temperature where it is no longer emitting visible light.

[Mordred]

To add some key points. First of to describe how stars and large scale structure formation started you must understand the thermodynamics involved. So lets start at the end of inflation. Or rather at the reheating phase at the end of inflation. During this time the temperature is too hot for stable recations to occur. Any reaction, quickly destabilizes into the reverse reaction. This is described as thermal equilibrium. The ideal gas laws decribe the relations. However the simple forms are not applicable. To describe fermions you need the fermi-dirac distribution formula, for bosons you need to use the bose-Einstein distributions. So photons which is it own anti particle and is a boson with a spin of one. Has an entropy of 2, and its distributions are described by the Bose_Einstein distributions. Now inflation reheating didn't reheat all the volume of space at the same time. Some regions reheated slighly later. This caused regions of anistropies. The cooler regions will have particle species drop out of equilibrium faster than other regions. Gravity starts to take hold of the matter forming in the cooler regions expanding the anistropy regions. As the volume of the universe continues to increase. A rough order is photons, neutrinos(including electron),protons, neutron. Once protons and neutrons drop out of equilibrium hydrgen, lithium, deuturium and lithium can start to form. They collect in the cooler regions first. Dark matter i also an early phase and contributor but its debatable how early it drop out of equilibrium. Where the cooler regions are gravity continues to collect the available plasma.

 

these two articles cover this however be prepared for intense math. hydrogen and helium formation starts at chapter 5 of the second article which also covers BBN big bang nucleosynthesis.

 

http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde
http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

[MigL]

Are you sure you want to include neutrons in that Mordred ?

All primordeal neutrons would have undergone decay as thy were not stabilized in nucleii at this time.

All present day neutrons are the product of recombination in later ( lower temp ) eras.

If that wasn't the case we'd still see massive particles around, maybe even magnetic monopoles.

 

Are you sure you want to include photons in that Mordred ?

The photons, or radiation, are what the massive particles are in thermal equilibrium with.

They would be present throughout the particle creation/destruction era in various ( decreasing ) energies.

 

One point I'd clarify is that production of massive particles actually starts earlier, but thermal equilibrium quickly ensures that just as many are destroyed as are created. It is only after they drop out of equilibrium due to cooling that that the reverse order of lighter to heavier takes over.

 

Not implying you're wrong by any means, just thought it needed some clarification and re-consideration.

Edited May 10, 2014 by MigL

[Mordred]

Evidently your misunderstanding what I am saying, so yes better clarity is needed. For one thing I chose not to break down when or what temperatures particles drop out of thermal equilibrium. I chose instead to let the OP use the article as a reference for those details.

 

" One point I'd clarify is that production of massive particles actually starts earlier, but thermal equilibrium quickly ensures that just as many are destroyed as are created. It is only after they drop out of equilibrium due to cooling that that the reverse order of lighter to heavier takes over."

 

correct some older textbooks cover pre-inflationary particle productions, such as the various epochs, planck epoch, electroweak epoch, lepton epoch, etc... The listing of epochs depend on which form of symmetry breaking is describing the process, super-symmetry vs symmetry for example. As we cannot observe this time period, much of our understanding of these era's depend on which model is being looked at. textbook examples include Weinberg's first 3 minutes, Any processes prior to inflation however is effectively washed out, or rather the energy density of any pre-inflationary particles would be so miniscule as to be negligable. Or as Liddle describes it in the first link I posted,

"Inflation comes to an end when H begins to decrease rapidly. The energy stored in the vacuum-like state is then transformed into thermal energy, and the universe becomes extremely hot. From that point onward, its evolution is described by the standard hot universe theory, with the important refinement that the initial conditions for the expansion stage of the hot universe are determined by processes which occurred at the inflationary stage, and are practically unaffected by the structure of the universe prior to inflation"

 

Now here is where things get interesting, I mentioned that inflation did not reheat the universe with uniformity. This is fairly new research after the time of Liddle's article and most textbooks and is showing that pre-inflationary thermodynamics may in fact affect post inflationary thermodynamics. The work was pointed out by a friend of mine named Brian Powell. I am in regular contact with him. The pre-inflationary vacuum in the cosmic microwave background.

http://arxiv.org/pdf/astro-ph/0612006v3.pdf his work is working on the degeneracy problems in canonical/non-canonical inflation.

" In the simple case of single field canonical inflation, the amplitudes of the scalar and tensor power spectra on CMB scales uniquely map to the parameters of the inflationary Lagrangian. However, the inflaton need not be canonically normalized, nor need it be the primary source of primordial perturbations."

http://arxiv.org/pdf/1212.4154v2.pdf

anyways he has numerous articles now on www.arxiv.com so you can follow his work,for these reasons I did not specify timelines or temperatures when particles drop out of thermal equilibrium. I prefer to leave that to the OP to discover for himself. For one thing it also depends on which inflationary model is correct. Planck data shows a better fit to the single scalar models, however that does not rule out the multi scalar models, currently there is still 60+ inflationary models that are decent observational fit, the Planch data fits 17 of them. Which one you prefer is up to you

Encyclopaedia Inflationaris

http://arxiv.org/abs/1303.3787

as far as the sequence goes I could have posted this article

http://www.maths.qmul.ac.uk/~jel/ASTM108lecture7.pdf however as I described above it depends on which inflation model, which form of symmetry breaking etc that occurs. Out of numerous searches online and dozens of articles I've seen including textbooks you will rarely see any two articles or textbooks that 100% agree with each other, when it comes to the temperature they drop out at, or the timeline/epoch. So I prefer to go with the textbooks as opposed to any other form of article.

on that note the particle physics of the early universe, matches up to Scott Dodelsons Modern Cosmology 2nd edition.

Edited May 10, 2014 by Mordred

[MigL]

As I said I agree with your earlier post and thank you for the additional references.

I just wanted to make it clearer for everyone that heavier particles, being higher energy, start being created earlier in the timeline, at higher temperature.

And I still would not have included photons and neutrons in the model due to the reasons given previously.

 

Haven't really given much thought to the eras before the symmetry breaks, but don't some models predict inflationary periods following a symmetry break due 'rolling' down from the false vacuum zero energy level. I believe Guth's original inflation made use of this mechanism.

[Mordred]

yes many of the inflationary models do, particularly after the development of the slow roll inflationary model. Coincidentally the slow roll approximation, is still one of the better fits AFAIK. Its used as a benchmark model to compare the other models in the Encyclopaedia Inflationaris.

As I said I agree with your earlier post and thank you for the additional references.

I just wanted to make it clearer for everyone that heavier particles, being higher energy, start being created earlier in the timeline, at higher temperature.

And I still would not have included photons and neutrons in the model due to the reasons given previously.

 

 

you need to be careful here, there is two contributions to a particles energy, there is an contribution arising from the particles mass and an energy contribution arising from its momentum. Hence you cannot rely on a particles rest mass in terms of your statement. You must consider both the particles rest mass and momentum, in terms of its total energy.

 

for the total energy of a particle is see equation 7.2 which is derived by a full relativistic treatment.

http://www.maths.qmul.ac.uk/~jel/ASTM108lecture7.pdf

 

here is how the total energy is derived

http://galileo.phys.virginia.edu/classes/252/energy_p_reln.html

 

for a relativistic particle its rest mass is meaningless, as its mass is dominated by its kinetic energy, hence for a photon its rest mass is treated as zero

 

now consider this in terms of the 4 bosons and GUT theories.

Photons are the force carriers of the electromagnetic field.
W and Z bosons are the force carriers which mediate the weak force.
Gluons are the fundamental force carriers underlying the strong force.

Higg's boson imparts mass

graviton?

 

 

 

for simplicity we will use this table

http://en.wikipedia.org/wiki/Graphical_timeline_of_the_Big_Bang

planck epoch the forces except gravity as its said to separate at this time and all particles are in thermal equilibrium, Higg's drops out here as well to impart mass for gravity to work. possibly....The Higg's inflation models times it with the gravity phase transition. (depends on which theory)

GUT epoch the strong force separates, so Gluons drop out of equilibrium

electroweak epoch you need the electromagnetic mediator, so photons have dropped out of equilibrium, at the end of the electroweak epoch

the weak force separates so you have your w and z bosons.

 

keep in mind there is a lot of steps missed and inflation reheating can cause certain particle species previously dropped out of equilibrium to go back into thermal equilibrium. I've yet to come across an up to date break down in terms of GUT that includes the effects of inflation lol

Edited May 11, 2014 by Mordred

[MigL]

Well if the slow roll inflationary model is still the benchmark ( didn't know there was an encyclopaedia inflationaris ), why doesn't anyone speak of multiple inflationary periods. I would think there would be one after each symmetry break. The latest would be the electroweak break where EM decouples from the weak nuclear. The previous would be where the grand unified breaks and the strong ( colour ) nuclear decouples from the electroweak at approx. 15 GeV ( IIRC ). and there may even be one where gravity decouples ( this one is still undecided depending on the nature of gravity ).

 

And if each inflationary period leads to a causal break from the previous epoch, how can we possibly proceed backwards along the timeline to get closer and closer to t=0

[Mordred]

No one knows for sure how inflation works, in most cases its not due to a thermodymanic phase transition.(possible exception Higg's inflation with its non minimal coupling to gravity during the electro-weak epoch. Most models its similar to Allen Guth's false vacuum model The original false vacuum had one major problem. Once inflation starts it had no mechanism to stop. Google "runaway inflation" Slow roll provided the hill mechanism you described. However that still didn't completely stop inflation which is where chaotic eternal inflation comes in and (bubble universes). False vacuum as I believe you understand is higher energy potential vacuum region (false vacuum,) and a (true vacuum region, minimal vacuum) where quantum tunneling occurs, and energy is transported from the higher potential region to the lower potential region.

 

The difference between the single scalar models and multi scalar models is primarily on how they stop inflation once its starts or how it controls runaway inflation. There was also a slew of models at roughly the same time so 95% of them never got announced. Keep in mind I certainly didn't study every model lol.

Edited May 12, 2014 by Mordred