Stellar Collapse R

STELLAR COLLAPSE R. Canal

To cite this version:

R. Canal. STELLAR COLLAPSE. Journal de Physique Colloques, 1980, 41 (C2), pp.C2-105-C2-110. 10.1051/jphyscol:1980218. jpa-00219810

HAL Id: jpa-00219810 https://hal.archives-ouvertes.fr/jpa-00219810 Submitted on 1 Jan 1980

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C2, supplément au n° 3, Tome 41, mars 1980, page C2-105

STELLAR COLLAPSE

R . Canal

Depar-tamento de Fisica de la Tierra y del Cosmos Univevsidad de Barcelona Spain

Résumé .- On considère le problème de l'effondrement des étoiles à la fin de leur évolution . Las étoiles à grande masse (M ~ 10 M„) vont vers leur effondrement ayant épuisé (dans leurs couches centrales au moins) leurs combustibles thermonu cléaires . L'explosion de leurs couches extérieures doit se produire par transfert de 1'énergie gravitationnelle du noyau . On examine les différents mécanismes qui ont été proposés, ainsi que les incertitudes qui s'y rattachent. Les étoiles aux masses plus petites (sauf celles qui finissent comme naines blanches) rencontrent des instabilités explosives par suite de la formation, dans leur intérieur, de noyauKdont la composante électronique est fortement dégénérée. Là, l'issue dépend de la compétition des captures électroniques avec les. réactions thermonucléaires . Les conditions les plus favorables à l'effondrement ont lieu dans les systèmes doubles. La solution du problème posé par l'effondrement des étoiles passe par une meilleure connaissance de l'équation d'état aux grandes densités, des taux des réactions nucléaires, de l'opacité de la matière aux neutrinos, des régimes de combustion, des séparations de phase, de l'évolution des étoiles isolées et de celle des systèmes doubles rapprochés .

Stellar collapse is a physical process that r his means stars that form very massive he is expected to account for : lium cores following hydrogen burning and -Neutron star formation, which comprises encounter instability due to pair formation-, the coming into being of radio pulsars -*• + (single neutron stars, mainly) and of X-ray Y *• e + e pulsars and bursters (neutron stars in clo

se binary systems) . leading to r E (-1IIL-E-) g < 4/3 just before -Supernovae . central oxygen ignition (Barkat, Rakavy, -The bulk of the nucleosynthesis in the Ga and Sack 1967 ; Fraley 1968) . Dynamical stu laxy . dies of this case (Arnett 1978a) give an im -The origin of the galactic cosmic rays. plosion-explosion behaviour, both with and Stellar collapse might also produce black without remnant left, depending on the assu holes, gravitational waves, and neutrino, med mass of the helium core . The relevance •y-ray, X-ray, UV and IR "supernovae" . In of this mass range is doubtful, however. most cases mass ejection is needed, in Dearborn (1977), extrapolating the observed addition to the collapse, to explain the main-sequence mass-loss rates, concludes observed objects and phenomena. Energy that the masses of such stars, if they are emission must always occur, since stellar formed at all, will be reduced below the li collapse means forming a more gravitational mit for the occurrence of pair instability, ly bound object from' a less bound one . already during hydrogen burning . r he dynamic We will review the different types of stars process of star formation itself can also which are collapse candidates, stressing set the maximum mass of a star around the unsolved problems concerning their ul 60 - 100 M@ (Larson and Starrfield 19-71) . timate fates . We consider first single b) Massive stars : stars . Later we will discuss the supplemen 8 + ( 2 to 3) M. < M< M . tary possibilities related with close bina ® ~ paxr ry evolution . Those stars are able to go through all the 1- Single stars . - thermonuclear burning stages, from hydrogen a) Very massive stars : to silicon burning . rhey develop the classi cal onionring structure (Arnett 1973), with M>M . - 100 + 30M.- ~ paxr - © succesive burning shells corresponding, from

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980218 JOURNAL DE PHYSIQUE the center outwards, to Si, 0, Ne, C, He, cussing in this same volume different as- and H . One must have in mind, however, that pects of the physics of the collapse of most calculations stalt from helium cores, massive stars, I will only briefly indicate neglecting the hydrogen envelopes .The the main steps leading to our present view treatment of convection is doubtful, as are of the situation. mass loss effects. Further uncertainties are Two energy sources are available for produ- associated with the Si burning phase (Arnett cing a "mass cut" and obtaining an explo- 1977a). Anyway, Fe-Kki cores developat the sion : the thermonuclear energy of the man- centers of such stars, with masses in the tle and the gravitational potential of the 2 Mg F hey are ne- core.The last gives rise, by core contrac- range 1 -2 Mg <- Mcore -< -5 arly isothermal, with temperatures tion, to neutrino emission, infall kinetic r % 5 x 10' OK, and are supported by the de- energy, increase of rotation and of the ma- generate pressure of highly relativistic gnetic fields. electrons, so r 2 4/3. Core contraction Compression and heating of the mantle was leads to electron captures and pressure de- first proposed by Hoyle and Fowler (1960) : crease. Rising temperature (due to compres- the explosive thermonuclear burning of this sion and to the captures) induces endoergic material would release enough energy to photodisintegration of the nuclei. Both pro- eject a fraction of it and the whole enve- cesses start dynamical collapse. lope. Hydrodynamic calculations by Colgate At first sight, pure collapse of the massive and White (1966) showed that the compres- stars would be a natural outcome of their sed material is in fact "swallowed" by the evolution, when in their cores there is no neutronized core .The same authors sugges- more nuclear potential energy 1eft.rhe pro- ted energy transport by the neutrinos problem is that such stars should also explode duced in the accretion shock front, at the as supernovae, ejecting their mantles and boundary of the core, to the zone corres- envelopes and leaving condensed remnants ponding to their last mean free path before (neutron stars and perhaps, in some cases, escape -the "neutrino photospherew-, as an ejection mechanism. Later work concentrated black holes) . A few reasons for that are : -The existence of at least two associations on the problem of neutrino transport and its neutron star-supernova remnant (Crab and coupling with the hydrodynamics, both newto- Vela) .The Crab nebula is very helium-rich nian and general-relativistic (Arnett 1968 ; and its mass could be as high as 8 - 10 Ma. Wilson 1971) . Experimental results in 1973, -Cas A, a supernova remnant, shows evidence indicating the presence of a neutral current for nucleosynthesis of the heavy elements. in the weak interaction, opened up new pos- -The onion-ring structure developed by tho- sibilities for mass ejection during collapse se stars appears to be the ideal site for (see, Freedman, Schramm, and Tubbs 1977) . the synthesis of the heavy elements, both Coherent scattering by the heavy nuclei in explosively and non-explosively (Arnett and the outer core and in the mantle, of the neutrinos produced in the inner core, would Schramm 1973 ; Arnett 197833) . -For a 1.4M Fe-IS core collapsing to a neu- mainly transfer momentum to those layers and 0 tron star, the gravitational energy release perhaps reverse their motion. In addition to this, the change of r from is % 10~~er~.So, only about 1 % of this energy would suffice, if transferred to the lower to higher than 4/3, at or above nu- mantle and envelope, to blow them off with clear densities, was known to cause a "boun- energies typical for supernova events. ce" of the inner core and then a reflected -'Type 11 supernovae are concentrated to- shock wave. In this way, a fraction of the wards the spiral arms in spiral galaxies kinetic energy of the collapsing core can be (Maza and Van den Bergh 1976), where the transferred to the overlying and less gravi- youngest stellar population is also found" tationally bound material (Bruenn 1975) . Since Arnett, Buchler, and Livio are dis- Bruenn, Arnett, and Schramm (1977) have ana- lyzed the detailed calculations of Wilson (1974, 1976), Chechetkin et a1 . (1977), and This mass range would correspond to stars several others, to clarify the interplay that burn their carbon in non-degenerate between neutrino energy and momentum deposit conditions (Barkat, Reiss, and Rakavy 1974) tion and core bounce. but where carbon burning resultsin the for-, Continued improvements in the calculation of mation of an electron-degenerate 0-*-Mg neutrino opacities (Sato 1975, Nadyozhin core.The evolution of such a core, sur- 1977, Arnett 1977b) have led to the impor- rounded by a carbon burning shell, has been tant conclusion that neutrinos are trapped studied by Miyaji et a1 . (1979) . Electron during collapse for densities p > lo1 2g ~m-~.captures compete with explosive oxygen bur- Adiabatic hydrodynamics thus provides a good ning and lead to core collapse, with possi- approximation to the collapse of the inner ble ejection of the envelope due to explo- core. Van Riper (1978, 1979), and Van Riper sive carbon and helium burning.The discus- and Arnett (1978), find mass ejection by a sion of this mass range is closely related reflected shock, with the appropriate ener- to'that of the intermediate-mass stars. gies to produce a supernova, following boun- d) Intermediate-mass stars : ces at greater than nuclear densities for 6f 2M < M < 8t (2to 3) Ma 0." ." plausible equations of state-rhe general- relativistic effects are found to be impor- In mass-conservative evolutionary calcula- tant (see Arnett 1979, this volume) . Uncer- tions, stars of 4 Ma < M < 8 Ma develop tainties in the equation of state, both at electron-degenerate 2~ - 160 cores with subnuclear and supernuclear densities (see Mcore = MCh = 1.4 Ma following a common Buchler 1979, Rho 1979, both in this volume] neutrino transport in the outer core, the track evolution (Paczynski 1970) . Core evolution is determined by the balance between effects of rotation and magnetic fields, therinonuclear reactions in the mantle, re- heating by gravitational contraction, 2~ + 2~ reactions and the helium-burning shell main to be further explored. Heating of the around it, and cooling by neutrino losses. outer core by the reflected shock could al- Typical conditions at carbon ignition are so produce mass ejection (Lichtenstadt, : to 3) 109 Sack, and Bludman 1979) . pC = (2 x g cme3 andTc > 3 x Another mechanism is suggested by the fact, lo8 OK. Thermal runaway is initiated by the pointed out by Epstein (1978), that the 2~ + 2~ reactions when E EL,. CC > strong neutronization above the neutrino Here we have a situation which can be regar- photosphere produces an inversion of ye ded as the reverse of that for massive stars (the electron mole number), which makes those cores, in the verge of dynamical ins- those layers convectively unstable. Colgate tability (so verylooselybound), have enough (1978), Bruenn, Buchler, and Livio (1979), nuclear potential energy to blow the star and Livio and Buchler (1979, this volume) completely apart. In order to have a collap- study the RayleigWaylor growth of initial se, one must increase the gravitational bin- asymmetry, leading to the overturn of Fhe ding energy fast enough to compensate for neutrino trapping core and to mass ejebtion the sudden release of energy due to thermo- by neutrino energy deposition. nuclear runaway. Removing pressure and in- On the other hand, Chechetkin et al. (1977, ternal energy by electron captures appears 1978), using different input physics, do to be the only efficient mechanism. How not find mass ejection following core boun- fast the release of thermonuclear energy is ce. Ejection mechanisms as near-cr'itical depends on how the burning initiated by the rotation or magnetic pressure, either have thermal runaway at the center of the star no observational support or have been shown propagates through the degenerate cores .The to be inefficient (Le Blanc and Wilson 1970; speed of the electron 'captures depends on Imshennik and Bhdyozhin 1977) . the density at which the process takes place c) Less massive stars : 8 Ma -< M < 12M a Afirstpossibility is the formation of a detonation wave (Arnett 1969 ; Wheeler and 8 C2-108 JOURNAL DE PHYSIQUE

Hansen 1971 ; Wheeler, Buchler, and Barkat The other alternative for propagating the 1973). We have then supersonic burning pro- burning is deflagration. Then, the over- pagated by a shock wave.T.he detonation wave pressure produced by the shock wave induced if initiated, would self-consistently propa- by the thermal runaway at the star's center gate and completely disrupt the core. Peak is not enough to ignite the surrounding ma- temperatures% lolo OX would be attained and terial.rhis has been considered by Mazurek, the material, therefore, would be processed Truran, and Cameron (1974), and by Buchler to nuclear statistical equilibrium ("incine- and Mazurek (1975) .rhe burning propagates ration") . If all the stars born in this mass by transport processes (convection, conduc- range were to go through this process, large tion) rather than by shock heating. Mazurek, overabundances of iron-peak elements in the Meier, and Wheeler (1977) have shown that Galaxy would result. There are several pos- for pc > lo7 g cmm3, the carbon flash gives sible ways out of this problem.rhe most not enough overpressure to get the detona-

drastical one is to assume that the mass ' tion started (see also Buchler, Colgate, loss in the red giant stage removes enough and Mazurek 1979, this volume) . Spherical matter for most of these stars to die as damping, as discussed by Ono (19601, adds white dwarfs.2he presence of a white dwarf to the same effect.The burning front pro- in the Pleiades cluster, implying that stars pagqtes mainly by convection. Fornoto, ~uglmoto,and Wo (1976) have skudied the dthinitialmasses 2 6 M0 are able to do so, gives support to this hypothesis. carqon deflagration supernova model by pa- Another way would be to stabilize the carbon ramdtrizing the speed of propagation of burning, or at least to delay (in density) the burning front.They found always final its explosive regime, trough neutrino ener- disruption of the star, but for "slow" de- gy losses. Convection initiated by the bur- flagrations ( vdefl = 0.2 v sound) there was ning itself should enhance the efectiveness no overproduction of the iron-peak elements. of the URCA losses by pairs as 21k- 21~1 The outcome depends on the central density 23 Fa - 23 Fe . That convectively driven URCA at ignition, which determines the rates of process (Paczynski 1972;Couch and and Arnett electron captures and neutrino losses. Iva- 1975) , if really removing the thermal energy of nova et a1 . (1977) obtain collapse and neu- 9 the core, would allow it to "fizzle" until tronization from pc 1 4 x 10 g (in the electron captures on the products of good agreement with the estimates of Buchler the carbon burning would initiate the Colgate, and Mazurek 1979, this volume) . 10 colli~pse. Besides, for p _> ( 2 to 3) x 10 g Energy transfer by the neutrinos produced in electron captures on incinerated ma- the inner core to the still unburnt carbon terial (especially on free protons) would layers (neutrino "ignitacia", see Gershtein be fast enough to remove pressure and ener- et al. 1976) can induce their detonation. gy on a dynamical time scale, then produ- The critical density is then increased to 9 cing an implosion of the core even if a de- pc = 9 x 10 g cm-3 (Chechetkin et al. 19781 tonation had finally been formed.r'ne net e) Low-mass stars : M < 6 + 2 M -2 - 0 ' thermal effect of the convective URCA pro- rhese stars end their lives as white dwarfs. cess has been a matfer of discussion In the case of single stars, they will re- (Bruenn 1973 ; Lazareff 1975 ; Shaviv and main stable and cool down until becoming Regeu 1977) . It appears that it would be unobservable. So, they are not candidates to unable of either stabilizing the burning or collapse . of delaying its explosive regime for about 2- Close binaries.- Close binary evolution one order of magnitude, as should be requi- opens up new possibilities for stellar col- red. The reason is that electron captures lapse. In close binaries, electron-degenera- and decays cannot be mantained in equili- te boresmay form, their evolution being so- brimthrough the process. mewhere stopped by mass 1oss.They cool down, then, and can be activated again in a second 10 stage of mass exchange. Lower temperatures PC ' 10 9 cm-3 in the case of a pure 12c and higher densities are thus involved in white dwarf and at higher densities for the ignition problems .There are several faster accretion rates and/or lower carbon reasons for looking at these new possibili- contents-Thermal runaway due to the hea- ties of collapse and/or explosion. Among ting by compression, electron captures, others : and 12c + l2cl 12c+ 160, and 160 + 160 -The pulsar birthrate is currently estimated reactions, leads to deflagration and final- to be = 1 pulsar birth every 10 years ly to collapse induced by the electron cap- gaylor 1979) .This would imply (if conside- tures. At low initial temperatures the de- ring only single stars) that all stars with flagration is necessarily slow, since so- M 2 5 Ma should form pulsars. lidification of the central layers of the -There are low-mass (Mtot -< 5 M a ) compact star does not allow the burning to propa- X-ray sources where the compact object is a gate but by conduction (almost negligibly) neutron star that cannot have formed from and by progressive compression of the ma- the collapse and explosion of a massive star. terial. Solidification also broadens the drhe rate of death of massive stars, neces- range of initial central densities and of sary to explain galactic nucleosynthesis, is accretion rates leading to collapse, due only a small fraction of the current estima- to the demixion of carbon and oxygen when tes of the supernovarates (Arnett 1978). freezing : the central layers of the star Reactivation of the remnant cores of "less will likely be almost pure oxygen (see massive stars" by mass accretion has been Stevenson 197 9, this volume) . considered by mmoto et a1 . (1979) . Close Possible mass ejection cannot yet be ascer- binary evolution results in the formation tained (see, however, Chechotkin et a1.1978); of a 1 .2 Me core, composed of 160, 20~e, and and neutronization must be carefully compu- 24~g.Subsequent accretion leads to col- ted (the process reminds of silicon burning) lapse triggered by the electron captures rhe effects of accretion must be properly on 24~gand Heating by the captures dealt with, in order to find the really pos- produces 160 ignition. Further electron sible rates of mass increase of the cores captures onthe incinerated material insure (whose structure might be modified by the the collapse to nuclear densities. process) . Reactivation of 'C - 160 cores produced in The infall of matter on helium white dwarfs the binary evolution of intermediate and leads to shell flash in the outer regions perhaps even some low-mass stars, has been when accretion is fast, and to central flash studied by Canal and Schatzman (1976) and followed by disruption of the star for slow Canal and Isern (1978, 1979) . A pure 2~ accretion (Mmoto and Sugimoto 1977 ; Ergma, white dwarf would become dynamically uns- Rahunen, and Vilhu 1979) . -3 table at pc = 2.495 x lolo g cm , due to As a very schematic conclusion, we can say general-relativistic effect, while a that massive stars on one side (either sin- "C - 160 white dwarf will begin to collap- gle or in close binary systems), and less se at pc = 1 .920 g ~m-~,by effect of the massive, intermediate or even some low-mass electron captures on 160. The maximum cen- stars (mainly in close binary systems), on tral density for thermal stability is the other side, appear as likely candidates 9 pc ' 6 x 10 g cm-3 (' 'C white dwarf) . to collapse at the end of their 1ives.Mass Collapse is favoured by fast accretion ejection should not necessarily occur, ex- (provisionally identified with the increa- cept for massive stars. Further improvements se in mass of the degenerate core), low in our knowledge of the equations of state, initial tempera%ures (Tc R. lo7 OK) and low neutrlno transport, nuclear reaction rates, 'C 'C abundance (see also Mochkovitch 197 9, burning regimes, phase separation, single this volume) . Accretion at the Eddington and double star evolution, will certainly be Limit leads to carbon ignition at steps towards a more clear picture of this important process. JOURNAL DE PHYSIQUE

References .- Arnett, W 9.1968, Ap .J ., 153, 341. Imshennik, V S ., and Mdyozhin, D X. 1977, Pisma Astron . Z h ., 3, 353 . Arnett, W.D . 1969, Ap . and Space Sci ., 2,18C Ivanova, L .N., Imshennik, V .S ., Chechetkirq Arnett, W D . 1973, Ap .J ., 9,249. V M . 1977, Astron . Z h ., 4,354 . Arnett, W 9.1977a, Ap. J . SuppJ ., 35, 145. Larson, RB., and Starrfield, S. 1971, Arnett, W.D. 197733, Ap. J ., G, S15. Astron . and Astrophys ., 13, 190 . Arnett, WD. 1978a, Varenna Lectures. Lazareff, L. 1975, Astron. and Astrophys., -45, 141 . Arnett, W .D . 1978b, Ap . J ., 21 9, 1008 . Le Blanc, J .M ., and Wilson, J 3. 1970, Ap. Arnett, W 9 ., and Schramm, D .N. 1973, Ap. J ., 161, 541. J . Lett ., 184, L47. Lichtenstadt, I ., Sack, N., and Bludman, Barkat, Z ., Rakavy, G ., and Sack, N. 1967, S .A. 1979, preprint. Phys . Rev. Lett ., 19, 379. Maza, J ., and Van den Bergh, S . 1976, Ap . Barkat, Z ., Reiss, Y ., and Rakavy, G. 1974, J., 204, 519. Ap . J . Lett ., 193, L1 21 . Mazurek, T J ., r ruran, J .W ., and Cameron, Bruenn, S .W. 1973, Ap. J . Lett ., 183, L125. A .G .W . 1974, Ap . and Space Sci ., 2,261, Bruenn, S .W . 1975, Ann .NY Acad . Sci ., 262, Mazurek, T J ., Meier, D L ., and Wheeler, 80 . J .C. 1977, Ap. J ., 213, 518. Bruenn, S .W. Arnett, W.D ., and Schramm, D.N Miyaji, S ., Wmoto, K ., Yokoi, K ., and 1977, Ap. J ., 213, 213. Sugimoto, D . 1979, Proceedings 16th In- tern. Cosmic Ray Conf ., Kyoto (in press) Bruenn, S .W ., Buchler, J .R , and Livio, M . 1979, preprint . hadyozhin, D .K. 1977, Ap. and Space Sci ., Buchler, J .R ., and Mazurek, ,P .J . 1975, Mem. -49, 399. Soc . Roy . Sci . LiGge, 8, 345 . Ibmoto, K ., Sugimoto, D ., and No, S . 1976, Canal, R ., and Schatzman, E . 1976, Astron . Ap . and Space Sci ., 2, L37 . and Astrophys ., 5,229. kmoto, K ., and Sugimoto, D . 1977, Pub1 . As- Canal, R ., and Isern, J. 1978, 4th . Euro- tron. Soc. Japan, 3, 765. pean Regional Meeting in Astron., bmoto, K ., Miyaji, S ., Sugimoto, D ., and Uppsala Obs . Astron . Rep . @b52, B18 . Yokoi, K. 1979, Proceedings IAU Coll. Canal, R ., and Isern, J.1979, proceedings Fu s, University of Rochester (in press) IAU Coll. M 53, University of Roches- Ono, Y. 1960, Progr .Theor. Phys ., 2,825. ter (in press) . Paczynski, B.E. 1970, Acta Astronomica, 2, Chechetkin, V M ., Imshennik, V .S ., Ivanova, 47. L .N., and Nadyozhin, D.K. 1977, in Supernovae, (ed . D .R. Schramm) , p . 159. Paczynski, B .E. 1972, Astrophys . Lett ., 11, 53. Chechetkin, V M ., Gershtein, V .S ., Imshen- nik, V.S ., Ivanova, L .N., and Khlopov, Sato, K . 1975, Progr .T heor . Pktys ., 54, 1325. M .Y . 1978, Inst . High-Energy Phys ., Shaviv, G ., and Regev, 0 . 1977, Astron . and preprint . Astrophys ., 2, 581 . Colgate, S A. 1978, Erice School. Taylor, J .H . 1979, Highlights of Astronomy Colgate, S A. and White, R .h. 1966, Ap . (in press) . J ., 143, 626. Van Riper, KA. 1978, Ap. J ., 221, 304. Couch, R .G ., and Arnett, W.D . 1975, Ap .J., Van Riper, K A. 1979, Ap J 232, 558 196, 791. . ., . - Van Riper, K A. and Arnett, W 9. 1978, Ap. Dearborn, D .S 9 . 1977, Astrophys . Lett ., J Lett 225, L129. 19, 15. . ., - Wheeler, J .C ., and Hansen, C J . 1971, Ap . Epstein, R .I . 1978, M .N .R.A .S ., preprint . and Space Sci ., 11, 373 . Ergma, E .V ., Rahunen, E ., and Vilhu, 0. Wheeler, J .C ., Buchler, J .R ., and Barkat, 1979, Proceedings IAU Coll. lb Z . 1973, Ap. J ., 184, 897. University of Rochester (in press) . Wilson, J R .. 1971, Ap .J., 163, '239. Fraley, G . 1968, Ap . and Space Sci ., 2, 96 Wilson, J R . 1974, Phys . Rev . Lett ., 32, 849. Freedman, D Z ., Schramm, D .N ., and Tubbs, D. 1977, Ann. Rev. mclear Sci ., 27, 167 Wilson, J 3. 1978, Varenna Lectures . Gershtein, S .S ., Imshennik, V .S .,Nadyozhin, D X ., Folomeshkin, .N., Khlopov, M .Y ., Chechetkin, V M ., Eramzhyan, R A . 1976, Phys; Lett ., 628, 100. Hoyle, F ., and Fowler, W A. 1960, Ap. J ., 13 2, 565 .