STELLAR COLLAPSE

HAL Id: jpa-00219810

https://hal.archives-ouvertes.fr/jpa-00219810

Submitted on 1 Jan 1980

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire

HAL, est

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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�

STELLAR COLLAPSE R . Canal

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

Stellar collapse is a physical process that is expected to account for :

-Neutron star formation, which comprises the coming into being of radio pulsars

(single neutron stars, mainly) and of X-ray pulsars and bursters (neutron stars in clo- se binary systems) .

-Supernovae .

-The bulk of the nucleosynthesis in the Ga- laxy .

-The origin of the galactic cosmic rays.

Stellar collapse might also produce black holes, gravitational waves, and neutrino,

•y-ray, X-ray, UV and IR "supernovae" . In most cases mass ejection is needed, in addition to the collapse, to explain the observed objects and phenomena. Energy emission must always occur, since stellar collapse means forming a more gravitational ly bound object from' a less bound one . We will review the different types of stars which are collapse candidates, stressing the unsolved problems concerning their ul- timate fates . We consider first single stars . Later we will discuss the supplemen- tary possibilities related with close bina- ry evolution .

1- Single stars . - a) Very massive stars :

M>M . - 100 + 3 0 M . -

~ paxr - ©

r his means stars that form very massive he- lium cores following hydrogen burning and encounter instability due to pair formation-,

-*• +

Y *• e + e

leading to r E (-1IIL-E-) g < 4/3 just before central oxygen ignition (Barkat, Rakavy, and Sack 1967 ; Fraley 1968) . Dynamical stu- dies of this case (Arnett 1978a) give an im- plosion-explosion behaviour, both with and without remnant left, depending on the assu- med mass of the helium core . The relevance of this mass range is doubtful, however.

Dearborn (1977), extrapolating the observed main-sequence mass-loss rates, concludes that the masses of such stars, if they are formed at all, will be reduced below the li- mit for the occurrence of pair instability, already during hydrogen burning . r he dynamic process of star formation itself can also set the maximum mass of a star around 60 - 100 M@ (Larson and Starrfield 19-71) . b) Massive stars :

8 + ( 2 to 3) M. < M < M .

® ~ paxr Those stars are able to go through all the

thermonuclear burning stages, from hydrogen to silicon burning . rhey develop the classi- cal onionring structure (Arnett 1973), with succesive burning shells corresponding, from JOURNAL D E PHYSIQUE Colloque C2, supplément au n° 3, Tome 41, mars 1980, page C2-105

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 .

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, and H

.

One must have in mind, however, that most calculations stalt from helium cores, neglecting the hydrogen envelopes .The treatment of convection is doubtful, as are mass loss effects. Further uncertainties are associated with the Si burning phase (Arnett 1977a). Anyway, Fe-Kki cores developat the centers of such stars, with masses in the range 1 - 2 Mg <

-

^Mcore <

-

2 -5 Mg F hey are ne- arly isothermal, with temperatures

r

^% 5 x 10' OK, and are supported by the de- generate pressure of highly relativistic electrons, so

r

² 4 / 3 . Core contraction leads to electron captures and pressure de- crease. Rising temperature (due to compres- sion and to the captures) induces endoergic photodisintegration of the nuclei. Both pro- cesses start dynamical collapse.

At first sight, pure collapse of the massive stars would be a natural outcome of their evolution, when in their cores there is no more nuclear potential energy 1eft.rhe pro- blem is that such stars should also explode as supernovae, ejecting their mantles and envelopes and leaving condensed remnants

(neutron stars and perhaps, in some cases, black holes)

.

A few reasons for that are : -The existence of at least two associations neutron star-supernova remnant (Crab and Vela) .The Crab nebula is very helium-rich and its mass could be as high as 8

-

^{10 Ma.}

-Cas A, a supernova remnant, shows evidence for nucleosynthesis of the heavy elements.

-The onion-ring structure developed by tho- se stars appears to be the ideal site for the synthesis of the heavy elements, both explosively and non-explosively (Arnett and Schramm 1973 ; Arnett 197833)

.

-For a 1.4M Fe-IS core collapsing to a neu- 0

tron star, the gravitational energy release is % 1 0 ~ ~ e r ~ . So, only about 1 % of this energy would suffice, if transferred to the mantle and envelope, to blow them off with energies typical for supernova events.

-'Type 11 supernovae are concentrated to- wards the spiral arms in spiral galaxies (Maza and Van den Bergh 1976), where the youngest stellar population is also found"

Since Arnett, Buchler, and Livio are dis-

cussing in this same volume different as- pects of the physics of the collapse of massive stars, I will only briefly indicate the main steps leading to our present view of the situation.

Two energy sources are available for produ- cing a "mass cut" and obtaining an explo- sion : the thermonuclear energy of the man- tle and the gravitational potential of the core.The last gives rise, by core contrac- tion, to neutrino emission, infall kinetic energy, increase of rotation and of the ma- gnetic fields.

Compression and heating of the mantle was first proposed by Hoyle and Fowler (1960) :

the explosive thermonuclear burning of this material would release enough energy to eject a fraction of it and the whole enve- lope. Hydrodynamic calculations by Colgate and White (1966) showed that the compres- sed material is in fact "swallowed" by the neutronized core .The same authors sugges- ted energy transport by the neutrinos pro- duced in the accretion shock front, at the boundary of the core, to the zone corres- ponding to their last mean free path before escape -the "neutrino photospherew-, as an ejection mechanism. Later work concentrated on the problem of neutrino transport and its coupling with the hydrodynamics, both newto- nian and general-relativistic (Arnett 1968 ;

Wilson 1971)

.

Experimental results in 1973, indicating the presence of a neutral current in the weak interaction, opened up new pos- sibilities for mass ejection during collapse

(see, Freedman, Schramm, and Tubbs 1977)

.

Coherent scattering by the heavy nuclei in the outer core and in the mantle, of the neutrinos produced in the inner core, would mainly transfer momentum to those layers and perhaps reverse their motion.

In addition to this, the change of

r

^from

lower to higher than 4/3, at or above nu- clear densities, was known to cause a "boun- ce" of the inner core and then a reflected shock wave. In this way, a fraction of the kinetic energy of the collapsing core can be transferred to the overlying and less gravi- tationally bound material (Bruenn 1975)

.

Bruenn, Arnett, and Schramm (1977) have ana- lyzed the detailed calculations of Wilson

(1974, 1976), Chechetkin et a1

.

(1977), and several others, to clarify the interplay between neutrino energy and momentum deposit tion and core bounce.

Continued improvements in the calculation of neutrino opacities (Sato 1975, Nadyozhin 1977, Arnett 1977b) have led to the impor- tant conclusion that neutrinos are trapped

during collapse for densities p > lo1 2g ~ m - ~ . Adiabatic hydrodynamics thus provides a good approximation to the collapse of the inner core. Van Riper (1978, 1979), and Van Riper and Arnett (1978), find mass ejection by a reflected shock, with the appropriate ener- gies to produce a supernova, following boun- ces at greater than nuclear densities for plausible equations of state-rhe general- relativistic effects are found to be impor- tant (see Arnett 1979, this volume)

.

^Uncer-

tainties in the equation of state, both at subnuclear and supernuclear densities (see Buchler 1979, Rho 1979, both in this volume]

neutrino transport in the outer core, the effects of rotation and magnetic fields, therinonuclear reactions in the mantle, re- main to be further explored. Heating of the outer core by the reflected shock could al- so produce mass ejection (Lichtenstadt, Sack, and Bludman 1979)

.

Another mechanism is suggested by the fact, pointed out by Epstein (1978), that the strong neutronization above the neutrino photosphere produces an inversion of ye

(the electron mole number), which makes those layers convectively unstable. Colgate

(1978)

,

Bruenn, Buchler, and Livio (1979)

,

and Livio and Buchler (1979, this volume) study the RayleigWaylor growth of initial asymmetry, leading to the overturn of

Fhe

neutrino trapping core and to mass ejebtion by neutrino energy deposition.

On the other hand, Chechetkin et al. (1977, 1978), using different input physics, do not find mass ejection following core boun- ce. Ejection mechanisms as near-cr'itical rotation or magnetic pressure, either have no observational support or have been shown to be inefficient (Le Blanc and Wilson 1970;

Imshennik and Bhdyozhin 1977)

.

c) Less massive stars : 8 Ma <

-

M < 12M

a

This mass range would correspond to stars that burn their carbon in non-degenerate conditions (Barkat, Reiss, and Rakavy 1974) but where carbon burning resultsin the for-, mation of an electron-degenerate 0-*-Mg core.The evolution of such a core, sur- rounded by a carbon burning shell, has been studied by Miyaji et a1

.

⁽¹⁹⁷⁹⁾

.

^Electron

captures compete with explosive oxygen bur- ning and lead to core collapse, with possi- ble ejection of the envelope due to explo- sive carbon and helium burning.The discus- sion of this mass range is closely related to'that of the intermediate-mass stars.

d) Intermediate-mass stars : 6 f 2 M _0." < M < 8 t ( 2 t o 3) Ma

."

In mass-conservative evolutionary calcula- tions, stars of 4 Ma

<

^M

<

8 Ma develop electron-degenerate ^2~

-

160 cores with Mcore = MCh = 1.4 Ma following a common track evolution (Paczynski 1970)

.

^{Core evo-}

lution is determined by the balance between heating by gravitational contraction, 2~

+

2~ reactions and the helium-burning shell around it, and cooling by neutrino losses.

Typical conditions at carbon ignition are :

9

pC = ( 2 to 3) x 10 g cme3 andTc > 3 x

lo8 OK. Thermal runaway is initiated by the 2~ + 2~ reactions when E

CC > EL,.

Here we have a situation which can be regar- ded as the reverse of that for massive stars those cores, in the verge of dynamical ins- tability (so verylooselybound), have enough nuclear potential energy to blow the star completely apart. In order to have a collap- se, one must increase the gravitational bin- ding energy fast enough to compensate for the sudden release of energy due to thermo- nuclear runaway. Removing pressure and in- ternal energy by electron captures appears to be the only efficient mechanism. How fast the release of thermonuclear energy is depends on how the burning initiated by the thermal runaway at the center of the star propagates through the degenerate cores .The speed of the electron 'captures depends on the density at which the process takes place Afirstpossibility is the formation of a de- tonation wave (Arnett 1969 ; Wheeler and

8

C2-108 JOURNAL DE PHYSIQUE

Hansen 1971 ; Wheeler, Buchler, and Barkat 1973). We have then supersonic burning pro- pagated by a shock wave.T.he detonation wave if initiated, would self-consistently propa- gate and completely disrupt the core. Peak temperatures% lolo OX would be attained and

the material, therefore, would be processed to nuclear statistical equilibrium ("incine- ration")

.

If all the stars born in this mass range were to go through this process, large overabundances of iron-peak elements in the Galaxy would result. There are several pos- sible ways out of this problem.rhe most drastical one is to assume that the mass '

loss in the red giant stage removes enough matter for most of these stars to die as white dwarfs.2he presence of a white dwarf

in the Pleiades cluster, implying that stars dthinitialmasses

2

^{6 M} are able to do so,

0

gives support to this hypothesis.

Another way would be to stabilize the carbon burning, or at least to delay (in density) its explosive regime, trough neutrino ener- gy losses. Convection initiated by the bur- ning itself should enhance the efectiveness of the URCA losses by pairs as 21k

-

^{2 1 ~ 1}

23 Fa

-

^{23 Fe}

.

That convectively driven URCA process (Paczynski 1972;Couch and and Arnett

1975)

,

^{if really} removing the thermal energy of the core, would allow it to "fizzle" until the electron captures on the products of the carbon burning would initiate the colli~pse

.

Besides, for p

_>

^{( 2 to 3) x 10} 10 ^g

electron captures on incinerated ma- terial (especially on free protons) would be fast enough to remove pressure and ener- gy on a dynamical time scale, then produ- cing an implosion of the core even if a de- tonation had finally been formed.r'ne net thermal effect of the convective URCA pro- cess has been a matfer of discussion

(Bruenn 1973 ; Lazareff 1975 ; Shaviv and Regeu 1977)

.

It appears that it would be unable of either stabilizing the burning or of delaying its explosive regime for about one order of magnitude, as should be requi- red. The reason is that electron captures and decays cannot be mantained in equili- brimthrough the process.

The other alternative for propagating the burning is deflagration. Then, the over- pressure produced by the shock wave induced by the thermal runaway at the star's center is not enough to ignite the surrounding ma- terial.rhis has been considered by Mazurek, Truran, and Cameron (1974)

,

and by Buchler

and Mazurek (1975) .rhe burning propagates by transport processes (convection, conduc- tion) rather than by shock heating. Mazurek, Meier, and Wheeler (1977) have shown that

for pc > lo7 g cmm3, the carbon flash gives

not enough overpressure to get the detona- tion started (see also Buchler, Colgate, and Mazurek 1979, this volume)

.

^Spherical

damping, as discussed by Ono (19601, adds to the same effect.The burning front pro- pagqtes mainly by convection. Fornoto,

~uglmoto, and W o (1976) have skudied the carqon deflagration supernova model by pa- ramdtrizing the speed of propagation of the burning front.They found always final disruption of the star, but for "slow" de- flagrations ( vdefl = 0.2 v sound) there was no overproduction of the iron-peak elements.

The outcome depends on the central density at ignition, which determines the rates of electron captures and neutrino losses. Iva- nova et a1

.

(1977) obtain collapse and neu- tronization from pc 1 4 x 10 g 9 (in good agreement with the estimates of Buchler Colgate, and Mazurek 1979, this volume)

.

Energy transfer by the neutrinos produced in the inner core to the still unburnt carbon layers (neutrino "ignitacia", see Gershtein et al. 1976) can induce their detonation.

The critical density is then increased to 9

pc = 9 x 10 g cm-3 (Chechetkin et al. 19781 e) Low-mass stars : M < 6

+

^{2 M}

-2

-

0 '

rhese stars end their lives as white dwarfs.

In the case of single stars, they will re- main stable and cool down until becoming unobservable. So, they are not candidates to

collapse

.

2- Close binaries.- Close binary evolution opens up new possibilities for stellar col- lapse. In close binaries, electron-degenera- te boresmay form, their evolution being so- mewhere stopped by mass 1oss.They cool down, then, and can be activated again in a second

stage of mass exchange. Lower temperatures and higher densities are thus involved in the ignition problems .There are several reasons for looking at these new possibili- ties of collapse and/or explosion. Among others :

-The pulsar birthrate is currently estimated to be = 1 pulsar birth every 10 years

gaylor 1979) .This would imply (if conside- ring only single stars) that all stars with M

2

5 Ma should form pulsars.

-There are low-mass (Mtot <

-

5 M

^a

) compact X-ray sources where the compact object is a neutron star that cannot have formed from the collapse and explosion of a massive star.

drhe rate of death of massive stars, neces- sary to explain galactic nucleosynthesis, is only a small fraction of the current estima- tes of the supernovarates (Arnett 1978).

Reactivation of the remnant cores of "less massive stars" by mass accretion has been considered by mmoto et a1

.

⁽¹⁹⁷⁹⁾

.

^Close

binary evolution results in the formation of a 1 .2 Me core, composed of 160

,

^{20~e, and}

2 4 ~ g . Subsequent accretion leads to col- lapse triggered by the electron captures on 2 4 ~ g and Heating by the captures produces 160 ignition. Further electron captures onthe incinerated material insure the collapse to nuclear densities.

Reactivation of C'

-

160 cores produced in the binary evolution of intermediate and perhaps even some low-mass stars, has been studied by Canal and Schatzman (1976) and Canal and Isern (1 978, 1979)

.

^{A pure 2~}

white dwarf would become dynamically uns- - 3

table at pc = 2.495 x lolo g cm , due to general-relativistic effect, while a

"C

-

160 white dwarf will begin to collap- se at pc = 1 .920 g ~ m - ~ , by effect of the electron captures on 160. The maximum cen- tral density for thermal stability is pc ' ^{6 x} 10 g cm-3 (9 'C' white dwarf)

.

Collapse is favoured by fast accretion (provisionally identified with the increa- se in mass of the degenerate core), low initial tempera%ures (Tc R. lo7 OK) and low

'

C abundance (see also Mochkovitch 197 9, this volume)

.

Accretion at the Eddington

Limit leads to carbon ignition at

1 0 PC ' 10 9 white dwarf

cm-3 in the case of a pure 12c and at higher densities for faster accretion rates and/or lower carbon contents-Thermal runaway due to the hea- ting by compression, electron captures, and 12c

+

l2cl 1 2 c + 160, and 160

+

¹⁶⁰

reactions, leads to deflagration and final- ly to collapse induced by the electron cap- tures. At low initial temperatures the de- flagration is necessarily slow, since so- lidification of the central layers of the star does not allow the burning to propa- gate but by conduction (almost negligibly) and by progressive compression of the ma- terial. Solidification also broadens the range of initial central densities and of accretion rates leading to collapse, due to the demixion of carbon and oxygen when freezing : the central layers of the star will likely be almost pure oxygen (see Stevenson 197 9, this volume)

.

Possible mass ejection cannot yet be ascer- tained (see, however, Chechotkin et a1.1978);

and neutronization must be carefully compu- ted (the process reminds of silicon burning) rhe effects of accretion must be properly dealt with, in order to find the really pos- sible rates of mass increase of the cores

(whose structure might be modified by the process)

.

The infall of matter on helium white dwarfs leads to shell flash in the outer regions when accretion is fast, and to central flash followed by disruption of the star for slow accretion (Mmoto and Sugimoto 1977 ; Ergma, Rahunen, and Vilhu 1979)

.

As a very schematic conclusion, we can say that massive stars on one side (either sin- gle or in close binary systems), and less massive, intermediate or even some low-mass

stars (mainly in close binary systems), on the other side, appear as likely candidates to collapse at the end of their 1ives.Mass ejection should not necessarily occur, ex- cept for massive stars. Further improvements in our knowledge of the equations of state, neutrlno transport, nuclear reaction rates, burning regimes, phase separation, single and double star evolution, will certainly be steps towards a more clear picture of this important process.

JOURNAL DE PHYSIQUE

References

.-

Arnett, W 9. 1968, Ap

.

^J

., ^153,

^341.

Arnett, W.D

.

^{1969, Ap}

.

and Space Sci

.,

^2,18C

Arnett, W D

.

^{1973, Ap}

.

^J

., ^9,

^249.

Arnett, W 9. 1977a, Ap. J

.

^SuppJ

., 35,

^145.

Arnett, W.D. 197733, Ap. J

., ^G,

^S15.

Arnett, W D . 1978a, Varenna Lectures.

Arnett, W .D

.

^{1978b, Ap}

.

^J

.,

21 9, 1008

.

Arnett, W 9

.,

and Schramm, D .N. 1973, Ap.

J

.

^Lett

., ^184,

^L47.

Barkat, Z

.,

^{Rakavy, G}

.,

^{and Sack, N. 1967,}

Phys

.

^{Rev. Lett}

., ^19,

^379.

Barkat, Z

.,

^{Reiss, Y}

.,

and Rakavy, G. 1974, Ap

.

^J

.

^Lett

., ^193,

^{L1 21}

.

Bruenn, S .W. 1973, Ap. J

.

^Lett

., 183,

^L125.

Bruenn, S .W

.

^{1975, Ann}

.

^{NY Acad}

.

^Sci

.,

^262,

80

.

Bruenn, S .W. Arnett, W.D

.,

and Schramm, D.N 1977, Ap. J

., 213,

213.

Bruenn, S .W

.,

Buchler, J .R , and Livio, M

.

1979, preprint

.

Buchler, J .R

.,

and Mazurek, ,P .J

.

1975, Mem.

Soc

.

^Roy

^.

^Sci

^.

^LiGge,

^{8 ,}

³⁴⁵

.

Canal, R

.,

and Schatzman, E

.

1976, Astron

.

and Astrophys

., 5,

^229.

Canal, R

.,

and Isern, J. 1978, 4th

.

^Euro-

pean Regional Meeting in Astron., Uppsala Obs

.

^Astron

.

^Rep

^.

^{@b 52, B18}

^.

Canal, R

.,

and Isern, J.1979, proceedings IAU Coll. M 53, University of Roches- ter (in press)

.

Chechetkin, V M

.,

Imshennik, V .S

.,

^Ivanova,

L .N., and Nadyozhin, D.K. 1977, in Supernovae, (ed

.

D .R. Schramm)

,

^p

.

^159.

Chechetkin, V M

.,

Gershtein, V .S

.,

^Imshen-

nik, V.S

.,

Ivanova, L .N., and Khlopov, M .Y

.

1978, Inst

.

High-Energy Phys

.,

preprint

.

Colgate, S A. 1978, Erice School.

Colgate, S A. and White, R .h. 1966, Ap

.

J

., ^143,

^626.

Couch, R .G

.,

and Arnett, W.D

.

^{1975, Ap}

.

^J.,

196, 791.

-

Dearborn, D .S 9

.

1977, Astrophys

.

^Lett

.,

19, 15.

-

Epstein, R .I

.

1978, M .N .R.A .S

.,

^preprint

.

Ergma, E .V

.,

^{Rahunen, E}

.,

and Vilhu, 0.

1979, Proceedings IAU Coll. lb University of Rochester (in press)

.

Fraley, G

.

^{1968, Ap}

.

and Space Sci

., ^2,

⁹⁶

Freedman, D Z

.,

Schramm, D .N

.,

and Tubbs, D . 1977, Ann. Rev. mclear Sci

., ^27,

¹⁶⁷

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

.

Imshennik, V S

.,

and Mdyozhin, D X . 1977, Pisma Astron

.

^{Z h}

., ^3,

³⁵³

.

Ivanova, L .N., Imshennik, V .S

.,

Chechetkirq V M

.

1977, Astron

.

^{Z h}

., ^4,

³⁵⁴

.

Larson, R B

.,

and Starrfield, S. 1971, Astron

.

and Astrophys

., ^13,

¹⁹⁰

.

Lazareff, L. 1975, Astron. and Astrophys., 45, 141

.

-

Le Blanc, J .M

.,

and Wilson, J 3 . 1970, Ap.

J

., ^161,

^541.

Lichtenstadt, I

.,

Sack, N., and Bludman, S .A. 1979, preprint.

Maza, J

.,

and Van den Bergh, S

.

^{1976, Ap}

.

J.,

204,

519.

Mazurek, T J

., r

^{ruran, J .W}

.,

and Cameron, A .G .W

.

^{1974, Ap}

.

and Space Sci

.,

^2,261,

Mazurek, T J

.,

^{Meier, D L}

.,

and Wheeler, J .C. 1977, Ap. J

., 213,

^518.

Miyaji, S

.,

^{Wmoto, K}

.,

^{Yokoi, K}

.,

and Sugimoto, D

.

1979, Proceedings 16th In- tern. Cosmic Ray Conf

.,

Kyoto (in press) hadyozhin, D .K. 1977, Ap. and Space Sci

.,

49, 399.

-

Ibmoto, K

.,

Sugimoto, D

.,

and N o , S

.

^1976,

Ap

.

and Space Sci

., ^{2 ,}

^L37

.

kmoto, K

.,

and Sugimoto, D

.

1977, Pub1

.

^As-

tron. Soc. Japan,

3,

^765.

bmoto, K

.,

^{Miyaji, S}

.,

Sugimoto, D

.,

^and

Yokoi, K. 1979, Proceedings IAU Coll.

Fu

s,

University of Rochester (in press) Ono, Y. 1960, Progr .Theor. Phys

., ^2,

^825.

Paczynski, B.E. 1970, Acta Astronomica,

2 ,

47.

Paczynski, B .E. 1972, Astrophys

.

^Lett

., ^11,

53.

Sato, K

.

1975, Progr

.

^{T heor}

.

^Pktys

., 54,

^1325.

Shaviv, G

.,

and Regev, 0

.

1977, Astron

.

^and

Astrophys

., ^{2 ,}

⁵⁸¹

.

Taylor, J .H

.

1979, Highlights of Astronomy (in press)

.

Van Riper, K A . 1978, Ap. J

., 221,

304.

Van Riper, K A. 1979, Ap

.

^J

.,

^{232, 558}

.

Van Riper, K A. and Arnett, W 9 . 1978, Ap.

J

.

^Lett

., 225,

^L129.

Wheeler, J .C

.,

and Hansen, C J

.

^{1971, Ap}

.

and Space Sci

., ^11,

³⁷³

.

Wheeler, J .C

.,

^{Buchler, J .R}

^.,

and Barkat, Z

.

1973, Ap. J

., ^184,

^897.

Wilson, J R .. 1971, Ap

.

^J.,

^163,

^'239.

Wilson, J R

.

1974, Phys

.

^Rev

^.

^Lett

.,

^{32, 849.}

Wilson, J 3 . 1978, Varenna Lectures

.