At first the gas is transparent and the radiation escapes quite easily so the collapse is quite rapid. The radius is large, luminosity is high (thousands of times higher than L_SUN) and the effective temperature T_EFF is low.

Eventually, the temperatures in the outer layers rises to the point that the gasses become opaque, 4000K, and internal pressure slows the collapse to a state of gravitational contraction where the virial theorem becomes quite accurate, then to a state of quasistatic gravitational contraction where the radius is of order 100 R_SUN and luminosity 1000 L_SUN.

Much of the internal energy goes into ionizing hydrogen and so the internal temperature stays at about 10,000K until the H is ionized. Once the H and He have been ionized, (quasistatic) hydrostatic equilibrium is established and the physical model of the structure and further evolution is straightforeward. The star is about sixty R_SUN and only a few hundred years have elapsed.

Hayashi showed that a star contracts along a nearly vertical line in the H-R diagram (Te roughly 4000K) until it reaches the main sequence. We call such evolutionary tracks Hayashi tracks. The large luminosity and high opacity makes the star thouroughly convective so by the time the star reaches the main sequence it will be quite homogeneous.

It is important to note that gravitational contraction will provide the luminosity of a star if nuclear sources are absent or "burned out". It is very persistent. But we will see instances where for a short time the contraction of the outer few percent of the mass of a star can be reversed and nuclear energy put back into gravitational potential, the red giant phase. And then there is the final phase...

During the contraction phase which lasts about ten million years for one solar mass (a thousand years for 10 solar mass) the core heats up and the density rises. At some point any deuterium (d) present in the star will "burn" that is, a proton will combine with a deuterium nucleus to form a light isotope of helium and a gamma ray, p+dà ³He+g or d(p,g)³He. So we don't see any deuterium in the solar spectrum. (And ³He is too hard to detect.)

The real trick is to convert hydrogen to helium and/or helium to something heavier. Fortunately for us this is not an easy thing to do since p+pà ²Heà p+p and p+aà ⁵Lià p+a and a+aà ⁸Beà a+a does not work.

Hans Bethe first showed that the weak nuclear interaction p+pà d+b⁺+n was possible and this unlikely "weak" reaction is the basis of stellar energy production in stars like the sun. In the sun the lifetime of a proton is about ten billion years! If ²He were stable, we would not be around to know it.

Once the pp hurdle has been overcome, the d is "immediately" fused to ³He as it was on the Hayashi track. Over a period of time the ³He concentration builds up and the star can get energy via ³He+³Heà ⁴He+2p (PP I) or via ³He+⁴Heà ⁷Be+g (PP II,III). Here, PP I reads "pee pee one chain" and occurs when fusion equilibrium occurs in stars rather less massive than the sun.

Depending on temperature, the ⁷Be nucleus can capture an electron resulting in ⁷Li which immediately captures a proton ⁷Be+pà ⁷Li+n, ⁷Li+pà ⁴He+⁴He or ⁷Be(b,n)⁷Li(p,g)2⁴He the PP II chain which dominates for stars like the sun -- or the Be can capture a proton in a "pee-gamma reaction" resulting in ⁷Be(p,g)⁸B(b+,n)⁸Beà ⁴He+⁴He, the PP III chain which works best at higher temperatures.

In the sun, the ratio of PP II to PP III is about 400:1 but is of considerable interest since the boron neutrino is very energetic and should be detectable in Davis' neutrino telescope. To date, the results fall short of theoretical predictions by a factor of three! (Phys Rev Lett 81 #6 p.1158 (1998) gives 36% of the neutrino flux predicted by the BP95 solar model.)

The Neutrino problem (work in progress).

What about p+³He or d+d? These reactions are insignificant due to low cross section or low equilibrium abundance (d+d). In equilibrium the PP I chain dominates for a central temperature T₆<8 and the PP II chain dominates for T₆<20 where T₆ is the temperature measured in millions of degrees K.

But note that at zero age the ³He abundance is low and T_C is low so the PP I chain is favoured but cannot procede until ³He approaches its equilibrium value. When the ³He abundance is low it is actually burned (very slowly) by ³He(d,p)⁴He. Equilibrium for d, B, Be etc occurs at once but ³He is another matter. The time is very temperature dependent, a few million years at T₆=15, twenty million at T₆=12, and over a billion years at T₆=8 (about 0.5M_SUN, MK spectral class M5).

The CNO (bi-)cycle or PP IV chain.

When the central temperature rises to twenty million degrees as happens when the mass rises above 1.5 solar masses, protons can penetrate the coulomb barriers of the C, N and O nuclei so if Z is appreciable it is possible to, in essence, succesively add four protons to a ¹²C nucleus which then breaks down into an alpha particle and a new ¹²C nucleus. The carbon acts as a catalyst in the fusion of hydrogen to helium. In more detail, the reactions involved in the process are sketched below and it is readily evident why the process is often called "bi" cycle. The biggest hurdle in the cycle is the ¹⁴N Coulomb barrier so if the process is important any initial C, N and O isotopes are transformed to approximately 95% ¹⁴N, 4% ¹²C and 1% ¹³C over a wide temperature range.

Note that the rate that the CNO generates energy depends on the initial amount of C+N+O as well as temperature and no C N or O is created here. The main sequence only converts H to He. Note also that the interstellar medium (ISM) abundance is 58% O, 32% C and 10% N (by number) so this processed material does not find its way back into the ISM. And this process does not generate carbon, it merely uses any CNO present to catalyze H to He.

Note too that two weak processes are involved so two neutrinoes are produced. These neutrinoes are quite energetic and would be easy to detect in Davis' experiment.

SUMMARY:

If a collapsing object is greater than about 0.07 solar masses, the central temperature and density become high enough to initiate the fusion of four hydrogen atoms to helium with an energy release of about Q=26.730 MeV resulting in a main sequence star. Some of the energy is carried off in the form of neutrinoes which we hope to detect -- neutrino astronomy -- so the actual energy Q* ranges from 26.2 down to 19.1 for the ppIII chain.