The sun is shining from a blue sky, delivering a thousand watts of power to every square meter on the earth. It has been doing so since time immemorial, with no notable changes. The only reasonable energy source that we know of, that can keep the sun going like that, is nuclear fusion. One unavoidable by-product of fusion is a copious flux of particles called neutrinos. Neutrino detectors on earth do find neutrinos coming from the sun, and the observed flux is of the right order of magnitude, confirming that fusion is actually taking place in the sun.
But when detailed calculations of the expected neutrino flux were confronted with measurements, about 30 years ago, a significant discrepancy was found. Only about half of the expected neutrinos could be found. This anomaly persisted until quite recently, and is known as the "solar neutrino problem". For all the nitty-gritty details of the solar neutrino problem as it appeared before being solved, see John Bahcall's authoritative book Neutrino Astrophysics (Bahcall 1989), complemented by his more recent updates (Bahcall 1997a; Bahcall & Krastev & Smirnov 1998), and with a more accessible introduction in Bahcall (1990).
As with many other anomalies in science, creationists (e.g. Oard 1995, Snelling 1997, Sarfati 2000) have invoked the solar neutrino problem as evidence of more fundamental problems in orthodox "uniformitarian" science. It is argued, in brief, that since the neutrino flux is wrong, there can't be enough fusion in the sun, in which case the sun can't keep shining for billions of years, so it must be recently created.
In this FAQ, I will first describe the standard view of the sun's internal workings, and then go on to neutrinos, what they are, and what we expect of them from the sun. After that I will discuss various possible solutions to the solar neutrino problem. Finally, the creationist arguments concerning solar neutrinos, and other solar anomalies, real and fictional, will be treated. This final section, with answers to creationist claims, is rather short; the bulk of the faq is in the lengthy introductory sections, containing all the background knowledge needed to understand the answers.
We have today a coherent picture of the sun's internal structure and function, supported by several independent lines of evidence. But this solar model is a fairly recent construction, and the supporting evidence even more so.
Speculations about the nature of the sun are as old as recorded history, but I shall not dwell on the more fanciful versions of old, as they are not pertinent to the solar neutrino issue. If we restrict ourselves to serious study of the sun, the mid-19th-century is a good place to start, with three important discoveries:
One of the leading theories of the formation of the sun
was (and is) the 18th-century nebular theory of Kant and
Laplace, in which the sun formed through the gravitational
contraction of a large gas cloud. The potential
gravitational energy of the cloud would be released as
heat, as it contracted, and Hermann Helmholtz realized that
this was a possible energy source for the sun, provided
that it was still in the contracting phase. William Thomson
(better known as Lord Kelvin) elaborated and promulgated
this theory during the last decades of the 19th
century. It was clear, however, that this energy source,
while ample by human standards, couldn't last forever.
Various calculations gave limits on the order of a few tens
of millions of years of steady sunshine: "...
it would, I
think, be exceedingly rash to assume as probable anything
more than twenty million years of the sun's light in the
past history of the earth, or to reckon on more than five
or six million years of sunlight for time to come" (Thomson 1889, p 369).
This age was troublesome for many; it was too long for Biblical literalists, but too short for geologists and biologists, who could see that the earth and its fauna had a far longer history. Physicists like Lord Kelvin did not, however, care about the opinion of either literalists or biologists, so their arguments had little impact. But this age for the sun was troublesome also in astronomy; the sun was only one star among many, and if it was assumed, reasonably enough, that all stars worked the same way, contradictions followed. For one thing, the timescale for gravitational contraction varies strongly with the size of the star (Eddington 1916, 1917; Hayashi 1961); larger stars collapse and cool down much faster than sun-sized ones. After twenty million years, all large stars should be gone, if they had been created at the same time as the sun.
Alternatively, one might assume that star birth is an ongoing process, so that the sky is filled with stars of all different ages. But in that case, there should be no particular pattern if one compared star sizes, temperatures, and luminosities. Stars of all sizes should start out cool, get hotter and denser, and then finally cool off again and end up as cold compact objects. Larger, more massive stars should generally be more luminous than smaller ones, but there is no reason to expect a relation with temperature. This stands in stark contradiction with the discovery by Hertzsprung and Russell (Hertzsprung 1905; Russell 1914) that the vast majority of stars do give such a pattern, when plotted in what is now known as a Hertzsprung-Russell diagram (e.g. here). Eddington (1924) developed these ideas further, and showed that the only reasonable conclusion is that stars start out contracting (and shining from gravitational energy), but that they then reach equilibrium along what is now known as the "main sequence". Gravitational energy cannot account for that equilibrium; a new energy source is needed.
Another argument comes from variable stars (Eddington 1920). Many stars oscillate regularly, but an ongoing contraction would measurably change the oscillation frequency, in a matter of decades. Such changes had not been observed, leading to strong upper limits on the possible contraction rate, inconsistent with what the gravitational-energy theory predicts.
Thus, the quest for a new energy source for the sun did not, as is commonly believed, stem primarily from a desire to provide sufficient time for biological evolution. To the contrary, Kelvin and others were quite adamant about their opinion that biology and geology would have to adapt to the timescale given by 19th century physics, and forget about billions of years (Barnes 1974). But, as we have seen, in the early 20th century it was found that a new energy source was needed on astronomical grounds alone. The internal structure of stars had been worked out by Eddington and others (Eddington 1920), well before the discovery of nuclear fusion, and found to be consistent with astronomical observations only if a new energy source was postulated.
In the quest for a new energy source that took place in the early 20th century, radioactivity (discovered serendipitously by Henri Becquerel in 1896) played a prominent role. Eddington (1920) speculated about the possibility of transmutation of elements, after the pattern of Rutherford's then-recent experiments. Many others, notably George Gamow, contributed to this discussion through the 1920s and 30s, but Bethe (1939) is generally regarded as the seminal work, establishing fusion as a viable energy source for stars.
Through the work of Bethe and others, it was rapidly realized that fusion was eminently suitable as the desired energy source for stars. All the various patterns and relationships between mass, temperature, luminosity and so on, that were known at the time, were nicely explained by postulating fusion in the stellar interior. And the conditions prevailing inside the sun and other stars (calculated by Eddington (1916, 1917) and others long before Bethe's work) were precisely those at which fusion reactions proceeded at an appropriate rate. Quite coincidentally, it also turned out that the lifetime of a fusion-driven sun is the same order of magnitude as the age of the earth, solving the geologists' problem.
The status of the standard solar model today can't be described as other than in excellent health. Just about everything fits neatly together, even the neutrinos nowadays. The sun is a huge sphere of ionized gas, mostly hydrogen and helium, with a percent or so of all other elements together mixed in. What is directly observable are the surface conditions, and the total mass and luminosity. These observables, together with the assumption that physics as we know it applies also in the interior, are sufficient to calculate in considerable detail what goes on inside the sun as well. It is not necessary to make any specific assumptions about either the sun's age, or its energy source.
Early (pre-computer) calculations were done assuming that the sun is close to equilibrium, shining in a steady state. This is still a pretty good approximation, but does require the assumption that the sun is old enough to have attained equilibrium. More complete models start instead from a zero-age sun (or even from just a collapsing gas cloud), and then follow the sun's development until calculated surface conditions match those observed today. These models make less assumptions, but the equations cannot be solved other than numerically, and even so require considerable amounts of computer time.
The equilibrium equations are described and derived in any decent astrophysics textbook, such as Karttunen et al (1994), which is the one I'm following here. There are four main equilibrium conditions:
The energy flow equation is further complicated by the fact that there are two competing energy transport mechanisms of comparable magnitude in stars: radiation and convection (heat conduction is negligible). Radiative energy transport occurs when radiation is emitted by hotter material, and reabsorbed by cooler material further from the center; this process is always operative, but its efficiency is strongly dependent upon the transparency of the material. Convection, the familiar upwelling motion that can be seen when heating soup in a pot, occurs whenever the density of the underlying material is less than the density of the stuff on top. It is a very efficient mode of energy transport, but is operative only in certain parts of the sun, where the density gradient is right. One crucial difference between radiation and convection is that the solar material is mixed and homogenized throughout those parts where convection occurs, but is not mixed by radiative transport. The exact balance between radiation and convection is different in different types of stars; in our sun convection occurs in the outermost 30%, whereas only radiative transport is operative in the core. But energy production takes place almost exclusively in the core, so any new elements formed through nuclear processes stay where the are, and are not spread throughout the sun.
Solving this system of four differential equations gives the internal state of the sun (or any other star) in terms of pressure, temperature and density, using standard laboratory physics, assuming only that it is shining in a steady state.
Going to the next step, with a full-blown stellar-development numerical model, will give additional information concerning the age and composition and internal processes of the star. A very similar set of equations are used, with equilibrium conditions relaxed, and the star is followed through its development from birth to the present day (or further, if so desired), taking into account all known processes and energy sources that may be operative. The Helmholtz contraction energy is taken into account, as are the various possible nuclear processes, whenever the conditions are right for them.
When the calculations are done, it is found that the Helmholtz energy dominates during the initial collapse, until the temperature and density in the center get high enough for fusion ignition. After a very brief period of deuterium fusion, the main fusion reaction kicks in (in the sun's case proton-proton fusion), and the star settles down in a near-equilibrium state where it stays for the bulk of its lifetime. During this stable phase, the luminosity of the star slowly increases, on the order of five percent per billion years in the case of the sun, a fact to which we shall return under the heading "Faint young sun". Stars of different initial mass reach equilibrium at different temperatures and luminosities, along what astronomers call "The Main Sequence". This equilibrium sequence neatly reproduces, and explains, the pattern found by Hertzsprung and Russell (Hertzsprung 1905; Russell 1914). However, if fusion were not operative for some reason, no equilibrium would be reached, and no pattern should be observed.
This process can be used to calculate the age of a star. In the sun's case the result conforms nicely to expectations from radioactive dating of the rest of the solar system (around 4.55 billions of years (Strahler 1987), leading to a predicted age of the sun of 4.563 – 4.576 billions of years (Wasserburg 1995)). Guenther & Demarque (1997) find 4.5± 0.1 billions of years for the age of the sun, whereas Brun & Turck-Chieze & Morel (1998) favor an age closer to 4.6 billions of years, as do Dziembowski et al (1998). All three results are nicely consistent with the predictions from standard theories of solar system formation. For other stars the results are less precise, which is natural given our limited knowledge of them; a few examples, together with a description of the dating process, can be found in Ford & Rasio (1998).
The standard solar model calculations are described in detail in various works by John Bahcall and associates (Bahcall 1989; Bahcall & Pinsonneault 1995; Bahcall & Basu & Pinsonneault 1998). Bahcall & Pinsonneault (1995) is the standard review paper to which most other people refer. For another nice review, with a detailed presentation of the assumptions and complications, as well as a critical perspective on Bahcall et al, see Dar & Shaviv (1996; also Dar 1998). Two crucial issues in solar physics are nuclear reaction rates under solar conditions (Adelberger et al 1998; Junker 1998), and the opacity of the solar material (Iglesias & Rogers 1996).
The solar-model calculations give only indirect knowledge of the solar interior, leaving some room for questioning and doubt. The fact that the models do converge on a consistent picture of the sun, and are able to reproduce the current surface conditions using known physics and reasonable initial conditions, is of course a strong sign that the models aren't completely off. Nevertheless, an independent check would be nice. Helioseismology provides precisely such an independent double-check of the model.
Seismology here on earth is the science of earthquakes, so helioseismology is about sunquakes. And sunquakes can be used to probe the solar interior, in just the same way as earth-seismologists have been able to map the earth's interior using earthquakes. The way in which shockwaves propagate through matter depends to begin with on whether it's a solid or a fluid. Shockwaves from earthquakes can be either pressure waves (P-waves) or shear waves (S-waves). P-waves propagate through anything (except vacuum), but S-waves can only travel in a solid. The fact that S-waves do not penetrate through some parts of the earth's core, has led to the conclusion that those parts are liquid. Likewise, the fact that we observe no S-waves in the sun demonstrates that the sun isn't solid, but fluid all the way through. P-waves are observed in plenty, at many different frequencies.
The sun is quivering and pulsating all the time, at various frequencies, causing surface vibrations that can be observed from earth. From the pattern of surface vibrations, the speed of P-waves at different depths can be derived through a mathematically somewhat arduous procedure that I shall not go into here. Gough et al (1996a) give an introduction, as does Bahcall (1989). For more detail, see e.g. Christensen-Dalsgaard (1997) or Guenther & Demarque (1997), and references therein, as well as a whole range of articles in Science 31 May 1996: (Hathaway et al, 1996; Thompson et al, 1996; Gough et al, 1996b; Hill et al, 1996; Christensen-Dalsgaard et al, 1996; Harvey et al, 1996; Hellemans, 1996). Non-technical introductions at all levels (from kindergarten to college) can be found at http://solar-center.stanford.edu/heliopage.html .
The speed of P-waves is the speed of sound in the material, which for a gas depends on the temperature and mean molecular weight. The speed of sound at different depths in the sun can thus be predicted from the standard solar model calculations, and compared with helioseismological measurements. Brun & Turck-Chieze & Morel (1998) give comparisons between the solar model and helioseismological measurements, both for the sound speed, and for the actual vibrational frequencies that helioseismologists measure. The frequencies agree to better than a microHertz, and the sound speeds to better than a percent throughout the sun (much better than a percent for the most part, with a full percent deviation only right at the convective-radiative boundary). Similar comparisons can be found in numerous other recent papers, such as Bahcall & Basu & Pinsonneault (1998), or Christensen-Dalsgaard (1997). The agreement between model and data was good to begin with (Christensen-Dalsgaard et al 1996), but various refinements in the solar model (not adjusting it to fit the data, but taking into account processes that previously had been neglected, notably diffusion) has further improved the fit (Bahcall 1998).
In summary, helioseismological measurements strongly confirm the predictions from the standard solar model, and severely constrain unorthodox theories of the sun.
Neutrinos are elusive particles, that are emitted in a variety of nuclear reactions and decays. They are relevant for the sun, because they are an unavoidable by-product of nuclear fusion, and because they are the only known type of particle that can escape from the sun's core without interacting, bringing direct information about the solar interior. This possibility had been noted early on, but experimental difficulties delayed a search for solar neutrinos until the 1960s, when John Bahcall (1964) calculated a specific prediction for the neutrino flux, and Raymond Davis (1964) proposed to test the prediction. Unfortunately, when the results from Davis et al (1968) subsequently came in, they disagreed with the prediction. That was the root of what was known as the solar neutrino problem.
Interestingly enough, the neutrino was first invented as an ad hoc hypothesis, in order to save the laws of conservation of energy and momentum from falsification. Around 1930, in the first detailed studies of radioactive beta-decays, it was found that some energy and momentum went missing in each decay. Beta decay involves the conversion of a neutron into a proton, accompanied by the emission of an electron, and nothing else visible. The energy carried away by the electron ought to match the energy released by the atom in the process – but it didn't! Wolfgang Pauli proposed to explain this discrepancy by postulating that an additional, invisible particle was emitted along with the electron, carrying away the missing energy and momentum. This "ghost particle" was named neutrino. (For some of Pauli's original musings about the neutrino, see Mössbauer (1998).)
Now, ad hoc hypotheses, invented purely to save our favorite theories, are generally frowned upon in science, and for good reason. But the neutrino hypothesis was ultimately vindicated, when the ghost particle was finally demonstrated to have a real existence, more than twenty years later. Today, the neutrino is well established as partner to the electron in our standard theory of elementary particles. It has the same basic properties as the electron, and participates in the same interactions, except that it lacks an electric charge, and has a nearly zero mass.
Furthermore, there exists three families of elementary particles, each family consisting of two quarks, and two leptons. Quarks are constituents of protons and neutrons, and need not worry us further in this context. Lepton is the collective term for electrons and neutrinos and their relatives in the other families. The electron and the (electron-)neutrino make up the lepton pair of the first family. In the other two families, the electron-equivalents are called muon and tau, each with their neutrino partner, called mu-neutrino and tau-neutrino. So we have three different charged leptons: electron, muon, and tau; and three neutrinos, one associated with each of the three charged leptons (though it wasn't until recently that the tau neutrino was actually observed (Antia 1998)). The corresponding particles in different families are identical apart from having different masses.
It appears established beyond reasonable doubt, through the success of the standard solar model, that the sun shines from nuclear fusion in its core. A fusion reaction involves the merging of two atomic nuclei into one. In the sun, a chain of several different fusion reactions along any of about four different pathways, leads from four hydrogen nuclei (single protons) to one helium nucleus (two protons and two neutrons). In this process, two protons have to be converted into neutrons through beta decays. In each beta decay, a neutrino is emitted (an electron-flavored neutrino, that is). So it is straightforward to calculate that, if the sun shines through hydrogen fusion, it ought to emit two neutrinos per fusion chain. And in our standard theory of particle physics, the neutrinos will zip straight out from the sun, without interacting with the intervening material. The total flux of neutrinos from the sun ought to be some 200 000 000 000 000 000 000 000 000 000 000 000 000 per second, corresponding to a flux of about 6.5 × 1010 neutrinos per square centimeter per second hitting the earth.
Most of those neutrinos come from the main energy-producing reaction chain in the sun: proton-proton fusion. Unfortunately, the neutrinos from proton-proton (pp) fusion have a very low energy. Energy in this context in measured in electron-volts (1 eV = 1.6 × 10-19 Joule), or millions of electron-volts (MeV), and the energy of the pp neutrinos is less than 0.42 MeV, making them difficult to detect.
Smaller (but still enormous) numbers of higher-energy neutrinos are expected from various side reactions, notably boron and beryllium decays. There is also an alternative energy-producing chain, CNO-fusion, where the fusion of hydrogen to helium is catalyzed by carbon. This CNO-chain is expected to be the main energy source in larger, hotter stars, but it should only give a modest contribution in the sun. The CNO neutrinos are otherwise easier to detect than pp-neutrinos, having three to four times more energy each.
The details of the solar fusion reaction web can be found in many works, both on astrophysics and on neutrino physics, such as Karttunen et al (1994) or Bahcall (1989). Less advanced astronomy textbooks, such as Pasachoff (1995) or Zeilik (1994), however, often omit the side reactions that are highly relevant to solar neutrino studies. A nice diagram of the solar neutrino flux from the standard solar model, as a function of neutrino energy, can be found on John Bahcall's homepage, http://www.sns.ias.edu/~jnb/ , together with tons of information, data and software pertaining to solar neutrinos. If you are serious about solar neutrinos, his page is a goldmine!
The problem with solar neutrino experiments is that neutrinos are notoriously difficult to detect and measure. (After all, they were invented for the purpose of sneaking away unnoticed... ) The only way to detect them is through their occasional interactions with matter as they pass through. But the probability of such an interaction is extremely low; the vast majority of the neutrinos will pass straight through the earth without interacting at all. The few that do interact can do so in a couple of different ways:
The first solar neutrino experiment (Davis 1964) was based on the "reverse beta decay" of chlorine atoms. It consists of a large tank placed deep in a mine in South Dakota, USA. The tank is filled with some 600 tons of cleaning fluid, perchloroethylene, containing more than 1030 atoms of chlorine. Every few days, one of these atoms is reverse-beta-converted into argon. According to the standard solar model, an atom should have been converted every day, but the rate actually measured was no more than half of this. In 2002, Davis received the Nobel Prize for his pioneering work on solar neutrinos.
Chlorine is experimentally convenient – it is reasonably cheap (important when you need hundreds of tons!), and the resulting argon is chemically nice, making it feasible to find the needles in the haystack, and count the atoms one by one. Unfortunately, chlorine has too high an energy threshold for the neutrinos from the sun's primary proton-proton reaction. It only detects the higher-energy neutrinos from beryllium and boron decays, and from the CNO chain. Now, beryllium and boron are produced in minor side reactions in the sun that are highly sensitive to the exact temperature in the solar core; it is possible to tweak the standard solar model enough to significantly reduce their production rate (Bahcall 1989; Dar & Shaviv 1996), without any major disruption of our understanding of how the sun works, and how neutrinos work. Nevertheless, the discrepancy was disturbing.
Gallium is better from a physics point of view, in that it is sensitive also to the primary solar neutrinos from proton-proton fusion. The rate at which these are produced is fixed by the luminosity of the sun, and cannot be changed by any minor tweaking of the model. In gallium, the standard model predicts some 70-odd SNUs from pp fusion, and another 60 or so from the other stuff (mostly beryllium) (Bahcall 1997b). Gallium is, however, a rare and expensive element; the amount required for a neutrino experiment is a large fraction of the world's annual production of the stuff. So gallium experiments weren't built until around 1990, when two of them, called GALLEX and SAGE, started taking data. Both experiments have been running for some years now, and have produced essentially the same result: a flux of 70-odd SNUs detected (Altmann 1998; Hampel et al 1999). Within the errors, this is equal to the number expected from proton-proton fusion alone, leaving no room at all for neutrinos from beryllium and other sources. Furthermore, both experiments have been calibrated with a known flux of neutrinos from a terrestrial neutrino source, which pretty much excludes experimental error as an explanation for the solar neutrino discrepancy.
In parallel with the gallium experiments, a completely different neutrino experiment was running: Kamiokande (recently enlarged and upgraded, and renamed to Super-Kamiokande). Originally built to search for proton decays (Kamiokande = Kamioka Nucleon Decay Experiment), it was found to be eminently suited for neutrino astronomy as well. Solar neutrinos are detected when they bounce off electrons – or rather, the light-shower from the electron is detected. This has the disadvantage that low-energy neutrinos can't be detected, so Kamiokande is sensitive only to neutrinos from boron decays (and some even more minor side chains; see e.g. Bahcall & Krastev 1998). But there are considerable advantages as well:
These four solar neutrino experiments (one chlorine, two
gallium, and Super-K) were until recently the only ones.
All show a significant deficit of neutrinos, measuring on
the order of one third to one half the expected flux. Their
measurements thus implied that either the standard solar
model was wrong, or the standard model of particle physics
(and thus neutrino behavior) was wrong. The data were solid
enough that the standard models could be excluded even if
it were assumed that one of the experiments was worthless;
any three of them were enough (Hata & Langacker 1997),
(or any two, if the two weren't both gallium).
The solar neutrino problem existed for three decades, during which numerous possible solutions were proposed. The problem was never regarded as an unsolvable mystery – it was more a matter of deciding between different possibilities. But with the new data available during the past year, both from the new solar neutrino experiments, and from helioseismology, most of the proposed solutions can be excluded, and only a few possibilities remain, all of which involve modified neutrino physics. The evidence for non-standard neutrino behavior was strong already a few years ago, and is now conclusive.
Conceivable solutions to the solar neutrino problem can be divided into two broad classes: solar solutions, based on modifications of the standard model of the sun, and neutrino solutions, based on modifications of the standard model of particle physics. Experimental error is of course always a possibility as well, but with several different experiments, thoroughly calibrated, and working on two entirely different principles, all giving similar results, that possibility has become remote.
The possibility of finding errors in the standard solar model has been investigated at length (see e.g. Bahcall & Basu & Pinsonneault (1998)), with the conclusion that, considering the excellent fit to all other data, including helioseismology, such errors are highly improbable. Furthermore, many different people have implemented their own version of the model, with their own computer code and minor differences in the details of the physics, without significant differences in the outcome (see compilation in fig 1 of Bahcall (1998)). Likewise, concocting an alternative model which fits the neutrino measurements, and simultaneously fits helioseismological and other data, appears very difficult. The models of Dar & Shaviv (1996) and Cumming & Haxton (1996) come closest, but a sizeable neutrino discrepancy remains.
An even stronger argument against a solar solution, is the analysis of Hata & Langacker (1997). They show that even if one totally disregards the solar model, and allows the relative fluxes of neutrinos from different sources to vary freely, the neutrino discrepancies are not eliminated. It doesn't even help to assume that the sun is not fully fusion-powered! Hata & Langacker conclude that "... [solar] solutions in general have difficulties unless all experiments are wrong,..." (1997, p 9). Other authors have made similar calculations, with similar conclusions, e.g. Fiorentini & Ricci (1998), Ricci & Villante & Lissia (1999), or Bahcall & Krastev & Smirnov (1998) and references therein (but see also Dar & Shaviv (1999) who disagree).
A solar solution having been effectively excluded, to the satisfaction of most people in the field, we are left with a quest for a neutrino solution. Concerning solutions in the realm of neutrino physics, there are three possibilities:
Neutrino travel across astronomical distances is obviously inaccessible to laboratory studies, and has for a long time been regarded as the most promising area to search for anomalies, that can explain the missing solar neutrinos. The conclusion that the solution to the solar neutrino problem is most likely the disappearance of neutrinos en route received further support from the recent reports of anomalies in neutrino travel across terrestrial distances (Fukuda et al 1998a; Athanassopoulos et al 1997; Oyama 2001; further discussed below), and the matter was finally settled by SNO (Ahmad et al 2002a).
To have neutrinos disappear into thin air would be highly problematical, violating among other things the conservation of energy and momentum (the preservation of which was the main motive for inventing the neutrino in the first place). Converting the neutrinos into something else is a much more palatable solution. Luckily, there is ample precedent for such conversions among other elementary particles, and speculation about the possibility of similar behavior among neutrinos long predates the solar neutrino problem (Pontecorvo 1957). This conversion process is known as neutrino oscillations.
[Now, explaining how neutrino oscillations work is a bit tricky, since it depends on subtle quantum effects, and I cannot assume here that all readers are familiar with quantum theory. The explanation below is of necessity highly simplified; if any purists object, they are welcome to propose a better one.]
An indispensable, but counterintuitive, concept in quantum mechanics is that of superposition. Suppose a certain particle has a property that can have several different values; the classic example is that of Schrödinger's cat (e.g. http://www.upscale.utoronto.ca/PVB/Harrison/SchrodCat/SchrodCat.html), but I'll take a different one: ordinary playing cards have the property 'suit', with the four possible values ´spades', 'hearts', 'diamonds', and 'clubs'. In ordinary non-quantum life, each individual card has a well-defined suit. Not so in quantum mechanics! A quantum card may be in a mixed state, a so-called 'superposition' of say 30% spades, 60% hearts, and 10% clubs. When you check which suit that card belongs to, you have a 30% chance of finding that it's a spade, 60% chance of finding it's a heart, and so on. Note that this is not just a matter of your ignorance of the card's "true" suit – it doesn't have a single well-defined suit until you check it (there are some philosophical loose ends here, but never mind those for the moment).
In particle physics, the equivalent of the suits are the three families, discussed above in the section 'What are neutrinos?'. A neutrino may belong to any one of the three families, making it an electron-neutrino, or a mu-neutrino, or a tau-neutrino. Or, it may be a superposition of the three family flavors, mixed in some proportions. Now, the standard model assumes that the neutrinos emitted from the sun are in a pure electron-neutrino state, with no mixing. If this assumption is wrong, however, interesting things may happen en route.
A similar case, which has been extensively studied at particle accelerators, is that of the neutral K meson (a meson is a combination of two quarks (or to be precise, one quark and one anti-quark), in the case of the K meson it's one 'down' (d) quark from the first family, and one 'strange' (s) quark from the second family). The neutral K meson (K0) brings us to the next funny concept that we need, that of an eigenstate. To put it simply, an eigenstate is a state that is recognized as pure, non-mixed, without superposition, in a certain context. For example, in the context of poker, the normal four suits are eigenstates of the cards in that game; an unmixed spade is recognized as a spade, and nothing else. But in a different game, the eigenstates may be different! If you play whist, the suits recognized in that game as pure suits may (in a quantum world) be different from those recognized as pure suits in poker. A whist-spade may be a mix of 80% poker-spade and 20% poker-clubs, and similarly for the other suits. A pure poker-spade would in whist be regarded as a mixture, with only an 80% probability of being recognized as a whist-spade. In card games, this sounds preposterous – but in particle physics, this is exactly what happens. Different 'games' – different interactions – recognize and interact each with a different set of eigenstates for the particles.
The relevant 'games' played in the subatomic world
For most particles and most interactions this is not a problem; the different eigenstates are identical, as far as we can tell. But weak interactions do not always conform. The weak eigenstates of quarks are different from their strong/electromagnetic eigenstates. This is well established experimentally; see e.g. Halzen & Martin (1984) or Parodi & Roudeau & Stocchi (1999). The K0 mesons are produced in strong interactions of quarks, but decay through weak interactions of their constituent quarks. There are further subtleties involved, but to make a long story short, the end result is that the production eigenstates are different from the travel/decay eigenstates of the K0. The travel/decay eigenstates are called K0_long and K0_short, due to their longer and shorter lifetimes. So a K0 is produced as a pure strong-interaction eigenstate, but this is not a travel/decay eigenstate. As soon as it travels away from the production point, it travels as a mix of K0_long and K0_short, the travelling eigenstates.
Now, if K0_long and K0_short traveled at exactly the same speed, they would remain "in step" with each other, and the mix wouldn't be noticeable. However, their mass is slightly different, causing a difference in speed, making them fall out of sync as they travel. Experimentally, this is observable as a change in the mixing ratio depending on the distance traveled, oscillating between two extremes. Numerous experiments have been performed on K0-mesons, confirming the existence of these oscillations. (See e.g. Perkins (1982) for further details). Similar oscillations were theoretically predicted for B0-mesons (the third-family equivalent of the second-family K0 meson), and have now been observed experimentally (Schröder 1987; Abe et al 1999, and references therein).
As far as the weak interaction is concerned, leptons are expected to behave in the same manner as quarks. It would therefore be natural to expect similar mixing effects among leptons. Specifically, neutrinos occupy the corresponding place in the lepton families as the K0 and B0 constituent quarks do in the quark families, so mixing would primarily be expected among neutrinos. However, as with the K0 mesons, the mixing would be unobservable if the neutrinos all had the same mass. And as far as we can tell through direct measurements, all three neutrinos do have the same mass, namely zero (Klapdor-Kleingrothaus & Staudt 1995; Ackerstaff et al 1998). So in the standard model of particle physics, it was simply assumed that the neutrinos had zero mass, but it is a straightforward modification of the model to insert a suitable mass.
If neutrinos do have a tiny mass, and different neutrinos have different masses, they will behave in the same way as K0 mesons. They will be produced in a weak-interaction eigenstate, but travel in a mass eigenstate, which may be different from the weak eigenstate. (The weak-interaction eigenstates are the three neutrino flavors discussed earlier: electron-neutrino, mu-neutrino, tau-neutrino.) When they arrive and interact in our detectors, they do not arrive as the original weak eigenstate in which they were produced, but as a mixture of two or more flavors. This was always a potential solution to the solar neutrino problem, since the original solar neutrino experiments measured an apparent disappearance of electron-neutrinos, without measuring the other flavors. If the neutrinos oscillate from the 100% electron-neutrino that they are produced as in the sun, to a mixture with around 40% electron-neutrino and 60% some other neutrinos, we get a fairly good fit to the experimental data. And now that SNO has confirmed that the other 60% do indeed exist as other flavors of neutrinos, the problem is effectively solved.
Remember also that this re-mixing is an oscillating process, going back and forth. At a certain distance (and twice, three times, four times that distance, etc) from the production point, the neutrinos will have gone through a full oscillation cycle, and be back in the state they started with. At half that distance (and 1.5, and 2.5, etc, times that distance, the mixing will be at a maximum. This oscillation distance scale depends on the mass difference between the neutrinos, and on the energy of the neutrinos. A small mass difference and a high energy means a very long oscillation distance.
With solar neutrinos, the distance is known, 150 million kilometers, and the energy is known. But the fact that solar neutrinos from different fusion chains have different energy, may cause them to arrive at the earth at different points in their oscillation cycles. This may explain the apparently larger discrepancy for neutrinos from beryllium than from either boron or proton-proton fusion. Also, the distance varies along the earth's elliptical orbit around the sun, causing a seasonal effect, that would be a 'smoking-gun' signature for neutrino oscillations. No such effect has been seen to date, but the statistics are still too poor to exclude it.
Apart from the oscillation effects from the travel distance alone, there is another oscillation mechanism that may be relevant for solar neutrinos (as it is for K0 mesons). Different neutrino flavors have different interaction probabilities on their way out from the sun. In the case of a mixed neutrino, the different components of the mix will undergo different interactions, removing different fractions of them from the mix. The result is a modified mixture, which will then travel through space to the earth, possibly arriving as a different flavor from the one that was originally produced.
This neutrino conversion in matter is called the Mikheyev-Smirnov-Wolfenstein (MSW) effect, named for the people who figured it out (Wolfenstein 1978; Mikheyev & Smirnov 1985). A thorough, if somewhat technical, account of the MSW effect (as well as ordinary (vacuum) neutrino oscillations) can be found in Klapdor-Kleingrothaus & Staudt (1995). A clear signature of the MSW effect would be a difference in the measured neutrino flux between day and night, because at night the neutrinos have to pass through the earth, and undergo additional MSW conversion.
Neutrino oscillations is today the most promising of the proposed solutions to the solar neutrino problem. But until recently, the sun had provided no direct evidence that oscillations were indeed taking place. The SNO measurement of solar neutrinos of other flavors than electron-neutrinos is, however, a smoking gun. Mu- or tau-neutrinos from the sun have to be oscillation-converted electron-neutrinos, since no such neutrinos are produced in the sun.
Apart from the solar neutrino experiments, there is a plethora of other neutrino experiments in progress, several of which search for neutrino oscillations and related phenomena. During the past two years, positive results have been reported from some of them, lending support to the concept of neutrino oscillations.
The most solid non-solar neutrino-oscillation result to date comes from Super-Kamiokande. Super-K is a highly versatile experiment, capable of detecting neutrinos from many different sources apart from the sun. One prominent neutrino source here on earth is the interactions of cosmic rays with the earth's atmosphere. The relevant cosmic rays consist mainly of high-energy protons, which interact with nuclei in the air, producing showers of subatomic particles, some of which beta-decay on their way to the ground. These beta decays give a flux of medium to high energy neutrinos that hit the surface of the earth, pass through the planet, and exit on the other side. If neutrinos do not oscillate, one would expect the same number of neutrinos coming up through the ground as went down on the other side. Super-K, however, observes a significant difference. A substantial fraction of the mu-neutrinos apparently disappear on their way through the earth. For the Super-K group's own presentations, see (Fukuda et al 1998a, b, d; Learned et al 1998; Super-Kamiokande 1998); for perspectives, see (Normile 1998b; Wilczek 1998).
Similar results have been reported also from the MACRO experiment in Italy (Ambrosio et al 1998; Spurio 1998), and from Soudan2 and IMB (Gonzalez-Garcia et al 1998), though all have poorer statistics and worse systematics than Super-K. The earlier negative results of Frejus and NUSEX (Gonzalez-Garcia et al 1998) have so large statistical uncertainties that they are compatible within the errors with the Super-K results.
The atmospheric-neutrino oscillation searches complement the solar neutrinos in that they have higher-energy neutrinos and a shorter travel distance, thus investigating a different range of possible neutrino mass differences. Yet another range is probed in accelerator experiments, where high-energy neutrinos are created at particle accelerators, and allowed to travel for some distance. Many such experiments have been performed, most with negative results (see e.g. Klapdor-Kleingrothaus & Staudt (1995) and references therein, or Altegoer et al (1998), CHORUS (1998), Armbruster et al (1998)). There was, however, one claim last year that neutrino oscillations had been observed, by the LSND experiment (Athanassopoulos et al 1997; Glanz 1996). The LSND result is not universally accepted, though, and it indicates a neutrino mass difference much larger than that found by Super-K or implied by solar neutrinos. Another positive result, more consistent with the rest than LSND, can be found in the preliminary reports from the K2K experiment (Oyama 2001), in which a neutrino beam from an accelerator is directed at Super-K from a distance of a few hundred km.
Nuclear reactors are yet another source of neutrinos, and several experiments have been searching for neutrino oscillations near reactors. The most recent one, CHOOZ (Apollonio et al 1997), excludes a large fraction of the possible explanations for the Super-K results. A larger experiment, KAMLAND (Dazeley 2002), yet another descendant of Kamiokande, has just started taking data.
Neutrino physics is in general a "hot" experimental topic today, with much work in progress, not only on neutrino oscillations, but also on other aspects of neutrino physics, as well as on neutrino astronomy. Just to mention a few examples: Lake Baikal (Balkanov et al 1997), ANTARES (Moorhead 1998b), and last but not least my own modest contributions in the PAN (Johansson 1991) and AMANDA (Askebjer et al 1995; Halzen 1997) groups. Reviews can also be found in e.g. Petrera (1998) or Klapdor-Kleingrothaus & Staudt (1995). For a review of open theoretical issues, see Haxton (1998).
The solar neutrino results can be explained either through straightforward oscillations, or through the MSW effect. The neutrino mass differences and mixing parameters implied by the solar neutrino deficit are discussed in various works, e.g. Bahcall (1997a). With the new compelling evidence of neutrino oscillations presented by Super-Kamiokande (Fukuda et al 1998a), a large number of people have presented a variety of proposals for modifying the standard model of particle physics, in order to incorporate neutrino oscillations. Three categories of proposed solutions emerge:
All the proposed solutions claim to be consistent with the available data (or, in some cases, claim that some of the data, most often LSND, should be disregarded as insufficiently established), and many of them are quite similar, at least as far as experimentally accessible aspects are concerned. Further experiments are needed to distinguish between the models. For now, though, the conclusion must be that there is no shortage of neutrino solutions to the solar neutrino problem.
With the arrival of the SNO results, we reached a solid consensus: neutrino oscillations are happening. The solar neutrino problem alone was suggestive but not compelling evidence; the atmospheric-neutrino results clinched the case for non-standard neutrino behavior, and SNO confirmed that this solved the solar neutrino problem. This also means that we can be quite confident that the standard solar model is a close approximation of what goes on in the sun, since its prediction for total neutrino flux is confirmed with good precision by the SNO result. The details of the new neutrino physics are not fully worked out yet, and several different oscillation scenarios are still tenable, but new experimental data are on the way, and are expected to resolve minor outstanding issues within a few years from now.
Much of what has been written about the sun in creationist sources focuses on its age. The standard 4.5 billion years is of course anathema for a young-earth creationist. So various attempts are made to argue for a younger age, correctly noting that a young sun implies a recent origin for life on earth (but glossing over the fact that the converse also is true; evidence of a long history of life on earth implies an old sun).
There are two different lines of argument concerning a shrinking sun. The first one refers directly to the classical Kelvin-Helmholtz theory of the sun shining through gravitational contraction. The second line is based on a supposed change in the measured diameter of the sun.
The gravitational-contraction theory was perfectly
respectable mainstream science, in the 19th century. As
described in the
historical section above, it was abandoned
in the early part of the 20th century, for good scientific
reasons that had nothing to do with creationism. Some
creationists, notably Barnes (1974), appear to be unaware of
developments in science beyond 1895 or so, and continue to
invoke Kelvin's arguments as if they were still valid. But
even if we didn't know anything about nuclear fusion (or if
fusion for some reason didn't work in the sun), Eddington's
(1920; 1924) refutation of the
gravitational-contraction theory would still remain solid.
This directly contradicts the claims of Akridge (1980), that the theory was
abandoned solely because evolution required more time: "
have not always attributed the energy source of the sun to
thermonuclear fusion. Prior to the discovery of
thermonuclear fusion, Helmholtz predicted that the energy
of the sun was supplied by the gravitational collapse of
the sun. This model was accepted until the theory of
evolution began to dominate the scientific scene. Then
Helmholtz's explanation was discarded because it did not
provide the vast time span demanded by the theory of
organic evolution on the earth. The substitute theory was
introduced by Bethe in the 1930's precisely because
thermonuclear fusion was the only known energy source that
would last over the vast times required by evolution.
Science may now be on the verge of disproving the
substitute evolutionary model of the sun." (ibid, p 3). Akridge's last sentence
is also misleading, in that the standard model of the sun
isn't "evolutionary" in any sense connected with the
Darwinian evolution that he's referring to elsewhere in the
quote (and of course also misleading in that science is
nowhere near disproving it).
Akridge (1980) is also the primary source for the other line of argument, claiming that the shrinking of the sun has been measured. He bases this claim entirely on the results of Eddy & Boornazian (1979). Remarkably enough, it nevertheless appears as if he hasn't even read their paper – he does not refer directly to it, but only to a popularization (Lubkin 1980, see ref in Akridge 1980). It is also interesting to note that Akridge implies that E&B observed 400 years of shrinking, whereas the title of the E&B paper is 'Secular decrease in the solar diameter, 1863-1953', with only a 90-year period. Despite these (and other) obvious flaws, Akridge's claim has nevertheless become standard creationist fare, repeated in numerous creationist publications, from Brown (1995) to Molén (1991).
Strahler (1987) reviews the data available at the time of Akridge's writing, and contrasts it with Akridge's (1980) presentation. He notes that
A recent measurement of the solar diameter is that of Brown & Christensen-Dalsgaard (1998). From data taken over the period 1981-1988, they report a radius of 695,508 ± 26 km, with no evidence of change over time. The issue of surface definition is discussed at some length, leading to the conclusion that their definition is about 500 km smaller than that used in most previous estimates. Even over such a short period of time, their time series is sufficient to exclude an ongoing shrinking at the Akridge rate of five feet per hour, albeit at a modest statistical confidence level. I extracted the data from figure 2 in Brown & Christensen-Dalsgaard (1998) and did some line fitting, finding that the best fit to the data is a slight, statistically insignificant, growth of the diameter of the sun. No support whatsoever for shrinkage.
For a slightly longer time base, I'll use the value from Allen (1973), cited by both Brown & Christensen-Dalsgaard (1998) and Castellani & Degl'Innocenti & Fiorentini (1998) as the standard reference value before the 1990s. Working from Brown & Christensen-Dalsgaard (1998), I have re-calculated both their measurement, and that of Allen (1973) to what I believe is the same surface definition, obtaining a value for the angular diameter of the sun of 1919.31 ± 0.19 arcseconds in 1973, and 1919.359 ± 0.018 arcseconds on average 1981-1988. Akridge's alleged shrinkage corresponds to about 0.25 arcseconds over the same length of time, no trace of which is visible. It appears that the sun has stopped shrinking.
Fusion is the only known source of energy that can keep
the sun going for billions of years. The shortage of
neutrinos from the sun has been invoked by several
creationists as evidence that there is something wrong with
the standard solar model and as proof that the sun cannot
be billions of years old. This argument is closely tied to
the shrinkage discussed in the previous section; Davies (1996) concludes that, because of the
lack of neutrinos, the sun must still be getting most of
its energy from gravitational contraction, thus being
young. Still, Davies admits that some fusion is taking
place, producing those neutrinos that we do see. Walter
Brown (1995) likewise invoked the
shortage of neutrinos as evidence against the standard
solar model (along with a plethora of other astrophysical
fallacies), and it is also repeated (along with a similar
set of astrophysical fallacies) in the Creation-Evolution
Encyclopedia from Harvestime Books (http://www.pathlights.com/ce_encyclopedia/Index.htm).
Akridge (1980) also attributes
most solar energy to gravitational contraction, but he has
the opposite problem – his shrinking-sun model
provides two orders of magnitude too much gravitational
energy! On fusion, he says only that "
not all of
this [the sun's] energy comes from thermonuclear
fusion." (ibid, p 3),
leaving open the issue of what to do with the surplus, and
how to fit it in with the solar neutrino results.
Concerning the lack of solar neutrinos as "proof" that there is no (or too little) fusion in the sun (e.g. Snelling 1997, Oard 1995), I believe that this argument has been amply rebutted in the previous sections of this faq. There is strong evidence that the apparent solar neutrino deficit is due to neutrino oscillations, and not to any shortcomings of the solar fusion model. This has received independent support from both solar and terrestrial neutrino oscillation results, and there are also several independent lines of evidence in favor of the standard solar model, with fusion. A model of the sun as a young star, with a large fraction of its energy coming from gravitational contraction, is inconsistent with its current color and luminosity, and grossly inconsistent with helioseismological results. That the sun cannot still be in the contracting phase was established already in the 1920s, well before the discovery of fusion.
Sarfati (2000/2002) is
another creationist who in the original 2000 version of his
paper invoked the solar neutrino problem as evidence
against fusion in the sun. However, in the online version
of his paper at http://www.answersingenesis.org/docs/4180.asp
there is a note added in May 2002, after the SNO results
came out: "
is consistent with other lines of evidence that fusion is
the primary source of energy, e.g. the core temperature.
This means that neutrinos must have a very tiny rest mass
after all—experimental data must take precedence over
the theories of particle physicists that neutrinos have
zero rest mass. Therefore creationists should no longer
invoke the missing neutrino problem to deny that fusion is
the primary source of energy for the sun." This is
commendable honesty -- but then he ruins the good
impression by inserting a totally obsolete second-hand
quote (from Eddy 1978) in the same note as if it still had
As a side note, creationist Unruh (1995) appears to accept the standard
solar model, and explicitly acknowledges that fusion is the
main energy source. But he commits other astrophysical
blunders instead, like claiming that "
It is a
known fact that most stars produce visible light in only
small proportions and are most intense in their output of
lethal radiations like X-rays and gamma rays." (ibid, p 3) All main sequence stars
emit a large fraction of their radiation as visible light.
The proof is available on every starry night – if the
stars didn't shine with a lot of visible light, we wouldn't
see them in the sky! He also notes, correctly, that the
majority of stars are smaller than the sun – but then
goes on to claim that the sun is unique, ignoring the fact
that even the minority of G-type stars (to which the sun
belongs) numbers billions of stars in the Milky Way
Apart from the solar neutrino deficit discussed above, Davies (1996) presents two more arguments for a young sun:
Davies (1996) claims that the evidence points towards a homogeneous sun, with a thoroughly mixed core. The possibility of a mixed core was indeed considered and discussed in the early seventies, but when the predictions from mixed-core models are compared with recent helioseismological measurements, it is found that all models with large-scale mixing can be firmly excluded (Degl'Innocenti & Ricci 1998; Richard & Vauclair 1997; Stix 1998). This is implicit also in the recent measurements of the age of the sun (discussed above), which likewise exclude the possibility of a young homogeneous sun (Guenther & Demarque 1997; Brun & Turck-Chieze & Morel 1998).
Nevertheless, minor amounts of mixing are indicated by helioseismological data (Brun & Turck-Chieze & Zahn 1998), not deep in the core, but at the boundary between the radiative and the convective zones in the sun. This shallow mixing, however, does nothing to help Davies' (1996) case for a young sun. Instead it serves to weaken his other argument, the one concerning beryllium and lithium in the sun.
Lithium and beryllium are two light elements, that are both estimated to have been part of the sun's original chemical composition at certain (low) concentrations. Both elements are easily consumed by fusion, lithium somewhat more so than beryllium – it takes a temperature of around 2.5 million degrees to "burn" lithium, whereas beryllium requires 4 million degrees (to be compared with the sun's present core temperature of some 15 million degrees).
Oddly enough, as Davies (1996) correctly points out, the sun's surface material still has all its original beryllium (Balachandran & Bell 1998), whereas the lithium is severely depleted. From this one may conclude that the surface material has been exposed to a temperature of 2.5 million degrees, but not 4 million degrees. Davies proceeds then to claim this as evidence that the core temperature of the sun has not yet reached 4 million degrees, implying, of course, that the sun is till young and hasn't got its fusion going properly yet.
Careful calculations of the amount of mixing of surface and core material in young stars result, however, in the prediction that no significant amount of either lithium or beryllium should be lost in stars of the sun's size during their early contraction phase, in which Davies wishes to place the sun. This prediction is borne out by observations of newborn stars, which still retain their original lithium. The lithium is lost later, during the stars' main sequence life (Bahcall & Pinsonneault 1995).
A slight amount of mixing along the boundary between the surface convective zone and the core radiative zone, similar to that found by Brun & Turck-Chieze & Zahn (1998), can explain this slow lithium depletion. Calculations by Blöcker et al (1998) give the exact amount of mixing needed to reproduce the current surface abundance of lithium (while retaining the beryllium), finding a consistent solution with the sun 4.5 billion years old. Other proposed solutions to the lithium deficit also exist; see references in Blöcker et al (1998).
In conclusion, one of the arguments of Davies is simply obsolete, and the other serves to confirm the old age of the sun, rather than proving its youth.
The so-called '"faint young sun paradox" refers to the fact that the sun, according to the standard solar model, slowly increases in luminosity, as the giga-years go by. During the tenure of life on earth, close to 4 billion years, the sun's output has increased by something like 25% (Sagan & Chyba 1997). Despite this increase in solar heating, the climate here has been stable enough to permit life to go on.
Faulkner (1998) invokes the faint young sun paradox as evidence that the sun is young. Orthodox explanations of the paradox (to which we shall return below) are dismissed as too improbable, unless there is a guiding intelligence behind them. If the earth were recently created (presumably with an artificially aged sun, to match its current luminosity, which indeed is not that of a 6000-year-old star ), the paradox is trivially resolved, since there has been no time for any appreciable change in luminosity.
However, Faulkner's argument is less than perfectly compelling, for several reasons. The connection between solar output and Earthly climate is far from straightforward. There are also minor misleading details in his reasoning, like his quoting a 40% change in luminosity since 4.6 billion years ago, rather than the more interesting 25% change since life got started a while later. The climate before life got started is quite irrelevant, and so are any luminosity changes before that time. Selecting the right starting point allows you to pick any change you like — the luminosity of the sun was 100% less 6 billion years ago, when it wasn't shining at all...
It should also be noted that a 25% (or 40%) change in solar output, does not translate into a corresponding change in the temperature on earth. To begin with, the temperature is determined by the balance between heat inflow and outflow. The inflow is directly proportional to the solar luminosity -- but the outflow is to first order proportional to the fourth power of the earth's temperature ( Stefan-Boltzmann's law; check any physics textbook). In the absence of any feedback effects, a 25% change in solar luminosity translates into a 7% change in surface temperature here, which need not be lethal -- it is the same order of magnitude as the difference between tropical and arctic climates today, which is survivable.
There is, however, plenty of feedback in the earth's climate system, both positive and negative. Faulkner notes, quite correctly, that unchecked positive feedback will be fatal, as has happened on both Mars and Venus (in opposite directions). He asserts also that any negative feedback has to be carefully "tuned" to handle the large change in insolation, and pronounces such fine-tuning in a naturalistic framework to be less plausible than recent divine creation.
The feedback system of the earth is highly complex, but two major factors can be discerned:
There are two major points to cover, in order to assess how seriously to take the arguments of Faulkner (1998):
While life may conceivably have formed underneath a thick ice cover, the fossil record indicates the presence of an ice-free surface within a few hundred million years from the beginning. Stromatolites (common early fossils) are shallow-water formations, and photosynthesis appears to be an early development as well (Cowen 1995). There is also isotopic evidence of a warm climate at early times (Weisstein 1996). So we nevertheless need a decent climate at a time when the sun was 20% dimmer than today. The most reasonable way to achieve this, is by invoking a larger greenhouse effect.
There is a fair body of evidence that the atmosphere of the early earth was quite different from the nitrogen-oxygen mix that we're breathing today. The oxygen is almost exclusively the product of photosynthetic organisms, which weren't around in the beginning. There is also evidence from ancient minerals that the atmosphere was free from oxygen at the time when they formed, and evidence from later minerals (notably the so-called "banded iron formations") of a transition to an oxygen-rich atmosphere after perhaps two billion years (Cowen 1995; Kerr 1999).
At present, huge amounts of carbon have been locked away by organisms, both in living biomass and in carbonate sediments; it is very likely that much of this carbon used to be in the form of carbon dioxide (Sagan & Chyba 1997). The present carbon reservoirs, if totally converted to carbon dioxide, would give an atmosphere similar to that of Venus, with more than enough greenhouse effect to compensate for a fainter sun. It is not clear just how much of the carbon actually was in the atmosphere (Kasting 1993; Sagan & Chyba 1997), but even if it were only a small fraction of that available, a sizeable greenhouse effect would result. Some measurements of ancient carbon dioxide have been done (Mora & Driese & Colarusso 1996), but not in the relevant time periods.
Furthermore, there are other gases that are potentially large greenhouse contributors on the early earth, notably methane and ammonia (Kerr 1999). Sagan & Chyba (1997) propose an ammonia-dominated model, in which enough greenhouse warming is generated to achieve above-zero temperatures despite a faint sun.
Carbon dioxide, methane, and ammonia are all common gases in the atmospheres of other planets, and are reasonable (nearly unavoidable) components of the original atmosphere of the earth, given our current theories of planetary formation. It is thus highly plausible that a substantial greenhouse effect at least partially compensated for the faint early sun.
Conditions on the very early earth that permit the appearance and early evolution of life seem to be achievable without invoking too many improbabilities. As the sun then became hotter, however, we have a problem; if the greenhouse atmosphere is maintained for too long, as the sun brightens, a runaway greenhouse effect may result from positive feedback, creating a Venus-like situation and rendering the earth uninhabitable. A compensating negative feedback is required.
Some geochemical feedback may be possible, but it appears unlikely to be sufficient (Lenton 1998). Living organisms, too, started converting carbon dioxide into oxygen and organic matter, substantially decreasing the greenhouse effect as soon as photosynthesis got going. There is, however, no obvious reason for this process to keep exactly in step with the sun's increasing luminosity. It may be that we have simply been lucky, but as an explanation that is not entirely satisfactory. If the tuning did need to be very precise, Faulkner (1998) would have a point in calling it "miraculous".
It appears, however, that the earth can tolerate substantial climatic swings, alleviating the need for high-precision lucky/miraculous fine-tuning. There is evidence of extensive glaciations in Precambrian times (Kaufman & Knoll & Narbonne 1997; Jenkins & Frakes 1998), interleaved with much warmer periods. At least one of the glaciations may well have covered the entire planet, resulting in a deep-frozen "snowball earth" (Hoffman & Kaufman & Halverson 1998; Kerr 1998; Hoffman et al 1998). Life under several kilometers of ice can survive for a reasonable period of time, using e.g. geochemical energy (Gaidos & Nealson & Kirschvink 1999), even though massive extinctions of less hardy life forms can be expected.. The Precambrian fossil record is spotty enough that one (or even more than one) mass extinction of the magnitude expected from such a deep-freeze may well have passed unnoticed, even if only a few organisms survived, and then re-diversified.
If life could survive such an unstable climate, the implausibility argument of Faulkner (1998) is severely weakened.
A different solution to the faint young sun problem is offered by adherents of the Gaia hypothesis (Lenton 1998, and references therein). The basic idea is that the climate is kept stable by active biological feedback; either through some mystical Gaian planetary consciousness, or through more naturalistic means, as argued by Lenton (1998; but see also Robertson & Robinson (1998)). It would be instructive for creationists to study Gaian publications, because here we have another unorthodox hypothesis with scientific aspirations and religious affiliations. Nevertheless, unlike creationists, Gaians manage to get published in highly respected peer-reviewed journals (Lenton (1998) is in Nature), that wouldn't touch a paper like Faulkner's with a ten-foot pole. The difference can hardly be explained by an anti-religious bias, since there is just as much religion in the Gaia hypothesis, nor by a specific anti-Christian bias -- I'm willing to bet that there are more Christians than religious Gaians among the editors of Nature. For anybody who is actually familiar with how science works, a comparison of Lenton (1998) and Faulkner (1998) makes the answer obvious: Lenton is a competent scientists, who knows the rules, and who is capable of separating his science and his religion. He avoids elementary blunders, and avoids falling into shrill rhetoric. Creationists do none of these things, (though Faulkner's paper is far above average quality among creationist writings). If creationists could write like Lenton, they, too, could get published in real journals and earn some scientific respect.
Among the odder claims concerning the nature of the sun is that of Leontiev (1998). According to him, the sun is a giant crystal, with no ugly Chernobyl-like fusion going on; energy is instead supplied through some kind of unspecified, eternal, clean, non-nuclear magic.
The bulk of the sun, according to Leontiev, consists of crystalline matter, of a nature distinct from normal matter. A thin layer of normal matter covers the surface, producing the observed spectral lines, and fooling spectroscopists into believing that the whole sun is composed of atoms. Sunspots are supposed to be gaps in the surface layer, where the crystal is directly visible; it is unfortunate for Leontiev's theory that spectral lines from normal atoms (including purely atomic phenomena like the Zeeman effect) can be observed also within sunspots (Karttunen et al 1994).
Now, if the sun is one huge crystal, it ought to rotate like a solid body. It doesn't. The sun's equatorial regions rotate much more rapidly than at higher latitudes (Pasachoff 1995). Helioseismological studies have confirmed that the differential rotation continues much deeper than the bottom of the sunspots (Thompson et al 1996). Helioseismology has also confirmed, beyond reasonable doubt, that the sun's interior is fluid all the way through; a crystalline interior would be glaringly obvious in their data. Not that it needed confirming; the notion that the sun is solid was abandoned shortly after the discovery of sunspots, from which followed the observation of differential rotation.
In conclusion, the crystalline sun is an unadulterated crackpot notion, without even the deceptive verisimilitude of standard creationist fare.
NOTE: For your convenience, many of the references point to websites, sometimes in addition to the formal reference to publication in peer-reviewed journals. The Los Alamos preprint repository ( http://xxx.lanl.gov ) is heavily used, since a large fraction of all relevant physics and astronomy articles turn up there, before being formally published. It's an excellent site for anyone who wishes to keep up with new developments in the field.
Less convenient may be the frequent references to actual research papers, which can be non-trivial reading for the layperson. Particularly the theoretical papers with new neutrino oscillation hypotheses are often rather opaque for anybody not a theoretical physicist.
For quotes from Internet-available documents (notably the ICR publications), I give page numbers from Netscape printouts.
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