Rick's Critique of the Cosmic Coincidences: Chapter 9C

The Fine Tuned Strong Force?: (4)The Implications of a Stable Diproton

In this Chapter we investigate the consequences of the nuclear force being increased sufficiently to bind the diproton. With the aid of the pp capture cross section evaluated in Appendix 4 of the Tutorial we can determine whether the pp capture reaction rate is sufficiently fast to affect, (a)the outcome of Big Bang nucleosynthesis, or, (b)the luminosity and lifetime of stars. We find that Big Bang nucleosynthesis is unaffected whereas stars are greatly affected. However, contrary to the claims that have generally been made in the literature, it does appear that stable stars could form. They would be quite different from the stars of this universe, but would be capable of forging the chemical elements, and be sufficiently hot and luminous to nurture life.

In Appendix A4 of the Tutorial we showed that the pp capture rate is much slower than the np capture rate as a result of pp capture involving identical particles. In this Chapter we show that the pp capture rate is sufficiently slow that no significant numbers of diprotons are formed during Big Bang nucleosynthesis, and the stability of the diproton is irrelevant. Only when stars form does the stability of the diproton make a difference to the universe. This is contrary to the impression given in the literature. The scenario commonly depicted is that diproton stability would lead to an all-helium primordial universe, forever devoid of hydrogen and hence incapable of forming water, hydrocarbons, proteins, or anything with a hydrogen bond. Life based on anything remotely like familiar biochemistry would not be possible in such a universe - but this is not the true outcome of diproton stability.

In this Chapter we use the single-energy cross sections of Appendix A4 to find the pp reaction rate at a given temperature. The latter involves the usual integral over the product of the tail of the Maxwell distribution and the energy-sensitive cross-section (i.e. the Gamow peak). To estimate the Gamow peak we use a simple analytic approximation for the cross-section based on that with no Coulomb barrier, times a Coulomb barrier factor. This rough estimate is then subject to a simple 'empirical' correction factor by comparing it to the numerical solutions of the Tutorial Appendix A4.

A reaction is frozen out by cosmic expansion when its rate drops below the Hubble parameter. Thus we estimate the time (temperature) for freeze-out of diproton formation. We can also estimate the earliest time at which diprotons become stable to photodisintegration, simply by equating the number of photons with energy sufficient to cause photodisintegration with the maximum possible number of diprotons. We find that the diproton formation reaction is frozen-out before diprotons become stable. Consequently, no significant numbers of diprotons survive the period of Big Bang nucleosynthesis.

It is also shown that no significant numbers of dineutrons would be produced either.

The second half of this Chapter investigates how stars might behave in a universe with a stable diproton. This changes the initial nuclear reaction in stars in a crucial way. Rather than the first reaction being the weak-force mediated proton-proton capture to form deuterium, which is extremely slow, we have the electro-strong capture reaction to form a diproton. This is followed by the weak decay of the diproton to deuterium. Overall, the new reaction pathway is perhaps about 10 orders of magnitude faster at typical stellar temperatures and densities than the conventional reaction. It is entirely false to conclude that stars would, as a consequence, be explosively unstable. The reason is very simple: the typical temperature and density of stars are not the same in the two universes. Nuclear reaction rates are so very sensitive to temperature (exponentially so) that a relatively modest reduction in temperature can bridge this enormous reaction rate difference and produce stars which are not so very different from those in our universe.

This is demonstrated here by constructing an explicit example. We cannot claim that this is conclusive. To do so, a detailed stellar model including all the relevant opacities, heat transfer mechanisms, spatial variations of the field variables, etc, would be required. Moreover, it is not clear that mechanisms leading to the formation of such a star would necessarily exist. Nevertheless, by considering elementary requirements for stellar stability the claim is made plausible and the burden of proof shifted to those who claim otherwise.

Thus, we claim that a stable star with a central temperature of 10^6 K appears to be credible in a universe with stable diprotons. The properties of such a star would be:-

Hence, stars in such a universe would be larger, more massive and more luminous, than stars with a similar lifetime in this universe. Whether they would be cooler or hotter cannot be determined without a complete stellar model.

Most importantly, stars are feasible with lifetimes in the region of billions of years, as required for biological evolution. The luminosity and surface temperature may well be of the correct order to support biological life based on conventional molecular chemistry.

The import of this Chapter is that a universe with a strong nuclear coupling constant, gs, increased by 10% - 40% or so, and hence with a stable diproton, would still contain hydrogen and still be capable of chemical diversity and supporting life. Thus, whilst nuclear stability imposes a lower bound on gs, there is no 'diproton disaster' to provide an upper bound on gs. The 'fine tuning' of gs remains single-sided, and hence far less convincing as a ‘coincidence’, than would be the case if an upper bound also applied.

However, if gs is increased significantly beyond a factor of x1.4, deuterium becomes stable at times before 1 second, and hence when the leptonic reactions which inter-convert neutrons and protons are still active. At sufficiently early times the prevailing ambient energies are sufficiently great that neutron and proton numbers are virtually the same. Thus, for a sufficiently large gs, all the neutrons and protons will combine to form helium-4 with no excess protons left over. The disastrous all-helium universe with no hydrogen would then occur. The upper bound on gs to avoid this 'second deuteron disaster' will be evaluated in Chapter 9D.

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Cassini Flyby Shows Saturn's Moon Enceladus Venting: Enormous ice jets are erupting. That Enceladus vents fountains of ice was first discovered on Cassini images in 2005. Continued study of the ice plumes may yield further clues as to whether underground oceans, candidates for containing life, exist on this distant ice world. These ice jets are believed to be the origin of material which coats the surface of thge ice moon Tethys (see Chapter 4). [Credit: NASA/JPL/SSI; Mosaic: Emily Lakdawalla]