.o. s O.
3
Joel Selbin S~ote-n ners IY
Baton Rouge, 70803
I
I
The Origin of the Chemical Elements, 2
In order to discuss the role that stars play in nucleosynthesis, we shall have to deal in a t least a very general (and superficial) way with the formation, structure and evolution of stars. It is generally accepted that stars form out of gravitationally condensing and then collapsing interstellar gas and dust. Several stars may he produced about the same time and in the same region of space from the fragmentation of very large clouds of gas and dust into smaller globules regarded in the early stage as "proto-stars." Even today, new stars appear to he forming, for example, in the bright cloud called the Orion Nebula, perhaps the most studied of such regions. Let's now follow the formation of a hypothetical Population Il star ("first generation," i.e., formed in the early years of our galaxy), assuming first that it is condensing out of a region of pure hydrogen (plus perhaps the cosmological proportions of D, 3He, 4He and 'Li). We shall keep the model as simple as possible, introducing additional complexing features only as required. A great diffuse mass of gas agglomerates a t a n accelerating pace, becoming progressively smaller, denser, and hotter as the atoms (and particles, if dust were present) fall freely inward as their gravitational potential energy converts to kinetic energy. A stage will be reached perhaps after many thousands or even millions of years, when the center of the now spherical proto-star becomes optically opaque to radiation. The density and the temperature are still relativelv. verv- low. hut then. thermal eauilibrium develops and the star hdgins a more rapid condensation; and it begins to radiate more or less like a hlack-body a t the temperature of its opaque core. Most or all of its radiation is emitted in the infrared region.8 The evolving star may he pictured as describing a n evolutionary track in the temperature-luminosity (i.e., H-R) diagram which takes it eventually on to the main sequence when it has finally h.nnmo
ltah:l:".a
9
energy, any molecular hydrogen that might be present he 99% into atoms at -6000"K; at -lo4 "K the hydrogen atoms would he ionized; a t -lo6 "K any deuterium present in the gas would he destroyed via 1H + ZD 3He + y 5.49 MeV; a t 2-3 X 106°K any Li and Be would he destroyed via BLib, 3He)'He, ' ~ i ( p , a)4He and 9Be(2p, 2a)aHe; and just below 5 X 106 "K the boron isotopes would he destroyed via 10B(2p, 2a)hHe and '1B(p, 2a)'He. These nuclear reactions are important in accounting for the low ahundances of D, Li, Be, and B in the sun and other stars. Clearly, the only light nucleus (Z < 6 ) other than the proton itself, which can exist any appreciable time inside a star is 4He, and any original deuterium, lithium, beryllium, and boron that might have been present in the pre-stellar material will be burned up in the core of the star before the star even begins its stable thermonuclear burning stage.
-
+
Hydrogen Burning
Now, let us assume that pavitational contraction has heated the core to a temperature a t which hydrogenburning can begin. This is a t least 5 x 106 "K or Ts = 5,1° hut may more often he Ts = 10-30. The density may he 380 / Journal of Chemical Education
-100 g/cma a t this time. Contraction of the star ceases when the main nuclear reactions begin, with a delicate balance resulting from the inwardly directed gravitational forces and the outwardly directed thermal pressure, and the rate of energy release from the core reactions just compensates for the radiation loss. The star is now relatively stable for the longest stretch of time of its active life. Stars in the hydrogen-burning stage are identified with those on the main sequence of the H-R diagram. There are basically four sets af hydrogen-to-helium burning reactions which are accomplished through two important mechanisms:" the proton-proton chain (responsible for three sets of reactions called P P I, P P II, and P P III chains), and the carhon-nitrogen cycle (one set called P P IV or CN cycle) which is now recognized to include another set of reactions involving oxygen, so that it is called the carhon-nitrogen-oxygen bi-cycle (CNO hi-cycle). Since this last mechanism presumes the initial presence of C, N, and 0 nuclei (only C is required), only stars which have condensed out of a n interstellar medium already containing these elements (therefore, second or later generation Population I stars) can utilize this energy producing cycle.12 The reactions involved in the proton-proton chains, some combinations of which are believed to power stars residing on the lower half of the main sequence (temperatures up to Te = -17) are given in Table 2.13 The reactions involved in the CNO bi-cycle, which is helieved to This is the second of a two-part series on nucleasynthesis. Part I appeared in the May issue [SO. 306 (1973)l. All figures, tables, footnotes, and references are numbered consecutively throughout the series. 8For example, by Wien's Law, if the temperature were T = 1000'K. the maximum emission would be at y, = 2900/1000 = 2.9 g. Large numbers of such "infrared stars." almost or comSThe particular pathway on the H-R diagram towards the main sequence, how long the process takes, and where on the main sequence the star will settle (i.e., its evolutionary track) is determined primarily by the total mass. Thus, a very large mass of pas will take . perhaps 105 vr and end up at the hot upper left end of the main sequence, hkause the larger gravitationaifield of a larger mass causes it to contract relatively quickly. A star closer to the mass of our sun will contract to its lower right position an the main sequence in perhaps lo8-lo7 yr. Stars are believed to go through a stage called the variable T Tauri stage in which they have not yet contracted down to a stable radius or heated up to a stable temperature. 10 We shall adopt a papular shorthand way of expressing the magnitude of stellar temperatures, which is to use the exponent of 10 as a subscript on T and set this equal to the number which ivauld otherwise multiply the power of ten. "Hans Bethe won the 1967 Nobel Prize in Physics for his pioneering 1938-39 papers on these means of hydrogen fusion. '*However, it may also he possible far a first generation star to produce some 12C and then start burning on the carbownitrogen cycle. 13The first step in the p-p chain is the slowest, and therefore it determines the overall rate. The crass section for the first step is so small that it has never been observed in the laboratory and it must be calculated quantum mechanically. Ur'rCLrU'"'SLSL'L'Sa'"
Table 2. Nuclear Reactions Involved in the Proton-Proton Chains Energy Liberated (Me")
Reaction
Mean Lifetimen
-
Net: 4'H 'He 2e+ + 2v + 27 26.73 3He + 4He 'Be + y 1.587 -106yr 0.861 (0.80)b 53 da TBe e- = TLi u TLi+lH-sBe+yd 1 -10 min 8Be 2 'He ' 117.35 TBe+'H-sB+y 0.133 '66 yr 8B SBe* + & + 17.98 (7.2)b spontaneous 0.10 -10-'6sec sBe* 2 4He
+
+
i
--
-
--
+
,
@ Ameasure of the speed at whieh the reaction proceeds under conditions like those of our sun's core; depends upon temperature and usually the concentrations of reacting particles. b This is the average neutrino energy loss in Mev; anenergy which the ...-lnrnrticallv) ~ -.-. ,, zero cross section neutrino carries out of the star w ~ t hd,and is therefore not available to the star. c There is presumably a free electron gas in the stellar core, d The main energy reaction of a fusion or "H-bomb"? ~~~~
Table 3. Nuclear Reactions Involved in the CNO Bi-cycle
Reaction W+lH-lSN+y 13N-13C + e+ + u lSC+'H-"N+y 'LN+1H-150+y Cycle lsO-'5N + e+ + v 1W+1H-W+4He cN 4lH-'He + 2e+ or < ~ e t . 37 15N + 'H 160+ y 2000 times 160+ 1H- I7F + y lessfrequently 17F- 1 7 0 + e+ + u 1 7 0 + lH l4N + 4He
i
Energy Liberated (Me4
Mean Lifetime 108yr 10 min 2x1O5yr 108 yr 2 min 10' yr
-
-
, ' back to the
4th reaction of CN cycle a A measure of the speed at whieh the reaction proceeds under conditions like those of our sun's core: depends upon temperature and usually the concentrations of reacting particle;. 0 Thrsrs the average neutrmwencrg).loss in Me": anenergy which the (practically, zero cross section neutrino ramen out of the star with i t , and is therefore not avadahl~to the star.
he the important power source for the more massive, hence hotter and more dense, main-sequence stars (Tg = -30), which have condensed from earlier material processed a t least through the C, N, 0 elements, are given in Table 3. It is seen that all of the four mechanisms convert hydrogen into helium; that is, four protons into one helium nucleus, with a mass loss of 0.0287 mass units or an energy release of 26.73 Mev (6.682 Mev/nucleon). Most of the stars in the sky, for most of their stable lifetimes, are believed to he running on one or a combination of these energy sources. Solar Neutrino Experiment The very energetic neutrinos (7.2 Mev) from the disintegration of the unstable *B (formed from ?Be + lH) have been the object of a long and elaborate search. R. Davis, who had studied the reaction14 of neutrinos with 37CI as early a s 1955, set up the "Brookhaven Solar Neutrino Observatory" in 1967 about one mile deep in the old Homestake Gold Mine of South Dakota. Using a 100,000gal tank of Cl&=CC12 he hoped to detect the solar neu-
trinos, the only source of direct information able to come from the center of the sun. After five years of running, . the very important solar neutrino experiment is in even worse agreement with theoretical predictions than i t was earlier. While the theoretvalues of solar neutrino flux (which deically pend upon the exact solar evolution model used) have risen slightly, the experimental limit (an upper limit) has continually dropped and is now nearly consistent with zero! Fowler (10) has recently proposed two possible (he calls them "desperate") solutions to the solar neutrino puzzle, but we shall leave those for the interested reader to explore on his own. One result from the efforts a t solar neutrino astronomy, appears to he the demonstration that no more than about 5% of the sun's power is provided by the carbon-nitrogen cycle.15 Before we continue with the story of element build-up in stars, we need to point out the necessity that the transmuted material he returned to interstellar space. For it is there that general mixing of the stellar synthesized nuclei with uncondensed galactic hydrogen (and perhaps other interstellar gas and dust) occurs and becomes available for later condensation into second- and later-generation stars. Mechanisms by which stars eject material range from the rather mundane continuous process of blowing away their most tenuous outer layers (creating stellar winds, which in the case of our sun is called the solar wind), to minor internal instabilities which cause surface eruptions a t irregular periods, (such as was recently witnessed in our sun on August 2, 4 and 7, 1972) to such catastrophic events as nova explosions and the far more spectacular supernova explosions. In a nova explosion, the mass loss is only of the order of 0.1-1.0% and the star, in most cases, returns to approximately its original luminosity. Such an event may apparently reoccur with the same star. However, in a supernova explosion, nearly all or a substantial fraction of the stellar mass is ejected into space with high velocity; and the ejected material contains not only elements synthesized over the stellar lifetime, hut (more importantly, as we shall see) elements synthesized a t the time of the explosion. Helium Burning Getting hack to our hypothetical star, we next assume it has exhausted its core hydrogen fuel and that the core is mainly helium. Nuclear reactions now cease in the central region, but may of course still be occurring in the 3 with p 10 g/cm3) hot shell (having perhaps T7 around the core which still has unhurnt hydrogen.16 But since no nuclear reactions are yet occurring in the core, gravitational contraction again sets in and the star now runs mainly on this energy source as the core temperature
-
-
-
"The reaction is 37Cl(u,e-)3'Ar, followed by 3'Ar
D 36da
+ 37C1*
W1
+ e-
(Auger) of 2.8 kev
15There are many problems which affect the counting of solar neutrinos, same theoretical and others experimental, and until these are resolved, we shall probably not get much more of the critical information anticipated earlier. '6For example, if the star formed with C, 0, etc. already present (a Population I star), then such reactions as 'SO(p,y)'T(etv)l70 followed by 170(p,a)14N and the cyc!e ~ONe(p,y)21Na(e+v)21Ne(p,y)22Na(e+~)22(p,a)0Ne can occur in
the hydrogen burning shell probably after helium burning in the core has begun. '?Red giants result when the core temperatures and densities are very high and the star's diameter has grown by a factor of 102 or so. The greater increased surface area permits energy to be radiated at a lower surface temperature then when it was a smaller main sequence star, hence its "redder" color. However, because of its much greater surface area, its luminosity is much higher. Volume 50, Number 6. June 1973 / 381
and density continue to rise. The star moves off the main sequence and traces out a path leading toward the region of the H-R diagram where the red giantsl7 reside. Eventually the helium in the core reaches temperatures (-108°K) and densities (-105 g/cm3) at which Coulomb repulsions can no longer critically inhibit nuclear reactions between helium nuclei (11). I t is then that the socalled "triple-a" reaction of helium burning can provide the necessary nuclear energy to counteract further gravitational contraction and to nower the star in its red aiant staee of evolution. Even at these incredible temperatures and densities. true ternaw collisions (of three He nuclei, are not frequent enough t; be important; but they are not required. What is necessary is that when unstable 8Be nuclides form from binary collisions of 'He nuclides, a certain number exist long enough to capture a third 4He to form stahle 1ZC. What is believed to occur is that an equilibrium concentration of 8Be (lifetime -10-l6 see) builds up (to perhaps 1 part in 101° at lo8 "K) and then a very rapid a-capture process can take place to produce an excited state of lZC*(7.656 MeV above the ground state), which then drops to the stable ground state with y emission. The 12C may then capture another helium nucleus to form 160.In fact, results of recent studies of the rates of helium-hurnine reactions are now accurate enough to confidently p e d i c t t h a t helium fusion in s t a n should result in comoarahle yields of 12Candl=O. I t was originally helievkd that further additions of alpha particles would produce 2ONe and even 24Mg. This is now clearly led out for helium burning by detailed knowledge of the appropriate nuclear reactions. Because only a relatively small fraction (-0.07%) of mass is converted into energy during the helium hurning process, the star is not stabilized for nearly as long in the red giant stage as it is during hydrogen burning.I1 So we see that even after most of the lifetime of a star has passed, not very much nucleosynthesis has transpired: basically, hydrogen has been converted into 'He, and the 4He into W , and '60, and very little else. However, recall that if our hypothetical evolving star had originally contained 'ZC i t very likely also produced small quantities of '4N (compared to 1% and 160) via the CN cycle, as well as minor amounts of other nuclides. If the "N is not ejected into space prior to helium burning, it may be transformed into neon during this stage in the following or more likely, manner: 14N(a,y)18F(e+v)180(a,n)2*Ne, 180(a,y)22Ne. This is extremely important since it appears that the positron decay (of the 'SF) is the way nature has chosen to s u ~ n l vthe very slight neutron excess is required f i r ohtaining agreewhich, we shall see I& ment between calculated and observed abundance data. When the helium fuel is exhausted in the core, leaving essentially a carbon-oxygen "ash," gravitational contraction will again set in and serve not only to power the star through its next brief evolutionary stage, hut to heat the core from about Ts = 3 to Ts = 8-11 and to raise the density, The several major nuclear reaction processes which we now discuss as occurring in successive time periods in the stellar core actually may all be occurring a t the same time in a given evolved star. The process taking place in the core would alwavs (each stage of the wav) he the one requiring the greatest density aGd temperat"re, and then in successive shells radiating from the core the reactions requiring successively lower temperatures and densities might also he proceeding. Carbon Burning Carbon hurning is the next major thermonuclear epoch and it is the first of several nuclear reaction sequences believed responsible for most of the element synthesis in normal stars. The pertinent primary reactions of carbon burning are: 382
/ Journal of Chemical Education
IZC
--
+ 'y:
+
+ cr + 4.62 MeV (-50%) 13Na + p + 2.24 MeV (-50%) 20Ne
23Mgf n Z4Mg
- 2.60 MeV (few %, T
dependent)
+ y + 13.93 MeV (very rare,
