Supernovae and their Progenitors

F.-K. Thielemann, Garching *

(Max - Planck - Institut für Astrophysik)

Supernovae are explosive stellar 10 events per year. One can divide SN- Fig. 1 — Radio continuum image of Kepler's events which release typically of the events into two major classes, called supernova remnant taken with the VLA (Very order 1051 erg in kinetic energy and elec­ type I and type II. SN of type II are obser­ Large Array) at a wavelength of 21 cm (Matsui tromagnetic radiation. Their visual lumi­ ved in spiral arms of spiral galaxies (ac­ et ai. Ap.J. (1984) 287, 295. The diameter of nosity is comparable to the light emis­ tive regions of ongoing star formation) the remnant is 4.4 pc and the distance sion of an entire galaxy, containing 1011 approximately 5 kpc (1.3 x1014km and which can be understood if the progeni­ 1.5 x 1017km, respectively). stars. This brightness decreases by an tors are massive fast evolving stars. order of magnitude within the first two Their optical spectra are characterized months. In the explosion, matter is ejec­ by hydrogen lines. The light curve (opti­ Stellar Evolution ted with velocities of the order of 10000 cal luminosity as a function of elapsed The reader might be referred to Iben km/s, expanding into interstellar space time after the outburst) shows a plateau and Renzini (1984) and references and forming a so-called supernova rem­ for several months after an initial peak therein. The driving force of stellar evo­ nant. The interaction of the supernova and decline. Those features are explain­ lution is gravitational contraction, which with its environment, into which it is ex­ ed in terms of an extended envelope of is halted only by internal pressure which panding leads to a variety of phenomena solar composition, which has not been can counterbalance the gravitational observable in radio, optical, ultraviolet, processed by nuclear reactions. forces. Normally this pressure (radiation and X-ray wavelengths. The remnants The distribution of SN of type I is not pressure, pressure of the electron gas created by the historically known super­ limited to spiral arms within spiral ga­ and the atomic nuclei) is a function of novae in our Galaxy, e.g. Supernova laxies. Elliptical galaxies, many of which temperature. Energy losses by radiation 1006, SN 1054 (Crab Nebula), SN 1572 have no ongoing star formation, show can be balanced by contraction (gain of (Tycho's SN), and SN 1604 (Kepler's also and only SN I events. This favours potential energy) or by the fusion energy SN), where the number indicates the old stellar populations (white dwarfs) as of atomic nuclei. A star goes through a year of appearance, can still be observ­ possible progenitors which are triggered sequence of stable burning phases ed. Fig. 1 shows a radio image of SN by a delayed mechanism to undergo a where thermal pressure is provided by 1604 at a wavelength of 21 cm. supernova explosion. The optical spec­ the energy gain due to fusion reactions, Matter, ejected by supernovae into tra of these SN are rich in lines of heavy with intermediate contraction periods, the interstellar medium was processed elements, the light curves show an ex­ leading to higher central temperatures. by nuclear reactions during stellar evolu­ ponential decay. The latter can be explai­ Increasing average velocities or the tion and is the main source of interme­ ned if unstable radioactive nuclei, produ­ kinetic energy of atomic nuclei, obeying diate and heavy atomic nuclei in galactic ced in the explosion, decay over several Boltzmann statistics, enable fusion evolution. Stars which formed later will months. Then decay energy is still relea­ reactions to take place between heavier incorporate this material and will have a sed in the expansion phase. There is a nuclei with larger electric charge. larger enrichment in metals (the astro­ strong indication for the decay chain of The burning stages are : nomical term for elements heavier than 56Ni (56Ni →56Co → 56Fe) with a produc­ (1) Hydrogen burning (1-4 x 107K) helium). This recycling process explains tion of roughly 0.5 Mo (solar masses) (2) Helium burning (1-3 x 108 K) a continuous increase in metallicities to­ per event. (3) Carbon burning (6-10 x 108 K) wards the present value. During the birth SN I remnants show no central neu­ (4) Neon burning (1.2-1.3 x 109K) of the Universe (the Big Bang) only iso­ tron stars, i.e. objects of the order of 1.4 (5) Oxygen burning (1.5-2.0 x 109 K) topes of hydrogen, helium, and lithium Mo with densities of nuclear matter, (6) Silicon burning: photodisintegra­ were produced. Whilst a first generation supporting the fact that SN I cause a tions of 28Si above 3 x 109 K produce α- of very massive stars might have pro­ complete disruption of the progenitor particles, protons and neutrons. Gene­ duced 10-3 of the present metallicities, star. Some remnants of SN II, the most rally all reaction links by both strong and from then on, supernovae have been res­ prominent one being the Crab nebula, electromagnetic reactions are now open ponsible for the metal enrichment. contain pulsars. These are point-like and a thermodynamic equilibrium of nu­ Present observational techniques sources of pulsed radio, optical on X-ray clear abundances is approached. Nuclei make it possible to observe supernova emission. They are interpreted as with the highest binding energies per outbursts in distant galaxies, typically rotating neutron stars with high magne­ nucleon (iron group) are produced. tic fields (1012 Gauss). A more detailed Each of these burning stages pro­ study of the mechanisms, responsible ceeds first in the central core; subse­ * for SN I and SN II events, requires a quently it moves outward to form a shell Presently at the Department of Astronomy, detour through the theory of stellar evo­ burning source and the star eventually University of Illinois, Urbana lution. forms an onion skin structure. After Si 5 burning, the nuclear abundances are in a rise of pressure. Such a situation leads to radius which can be described as the thermodynamic equilibrium (nuclear a thermal runaway until the temperature "neutrinosphere", similar to the photo­ statistical equilibrium = NSE) and fur­ is high enough partially to lift the dege­ sphere in a star. Weak interactions come ther temperature increase cannot cause neracy. This fixes the evolution, and a into an equilibrium, as the reverse reac­ another sequence of fusion reactions. combined oxygen and silicon burning tions (i.e. neutrino captures) also be­ The result is that the iron core of such an gives again a contracting iron core as come possible. The collapse is only hal­ evolved star contracts and collapses. final result. ted when nuclear densities are reached The events that follow will be discussed For M ≤ 8 Mo evolution calculations at 2 to 3 x 1014 g/cm3. A transition oc­ later. show that after core helium burning, the curs to a giant nucleus of the size of the In the hydrogen and helium burning outward moving hydrogen and helium homologously collapsed core. Nuclear stages cooling is done very inefficiently burning shells come very close together. matter is highly incompressible, i.e. addi­ through radiation transport. Photons This proximity causes instabilities which tional compression leads to a strong rise emitted in the burning core undergo a lead to thermal pulses and drive strong in pressure. The inner core stops collaps­ large number of scattering events until stellar winds. These wind losses involve ing, becomes firm like a hard golf ball, in­ they are emitted from the photosphere the entire material outside the carbon- falling material rebounds, and an out­ of the star. This leads to large burning oxygen core and leave a bare core with a ward moving shock wave is initiated. cores and long durations of their burning mass below the Chandrasekhar limit. The traditional picture is that this shock stages (tHB ≡ 1010 (M/Mo)-3 y is the ave­ This core turns into a white dwarf star wave lifts off the mantle, reaches the rage time scale for hydrogen burning). which undergoes no further nuclear evo­ outer envelope within days and causes After helium burning, at higher densi­ lution. an observable SN II event, with the inner ties, a much more powerful mechanism core left behind in the form of a neutron for energy loss becomes available. Neu­ Type II Supernovae star. trino-antineutrino pairs are produced by The final evolutionary states of mas­ The difficulty with this scheme is that electron-positron pair anihilation, by sive stars (M ≥ 8 Mo) have an inner core the final size of the homologously col­ electron-photon scattering processes of iron and iron group nuclei (Fe, Mn, Co, lapsing core is substantially smaller than and by electron plasma oscillations Ni). The transformation of Si to Fe at the original iron core when the contrac­ (plasmon neutrinos). As those neutrinos temperatures of 3 to 3.5 x 109 K and tion started. This is due to the quadratic can escape freely, burning cores are densities of the order 108 g/cm3 lasts dependence of MCh on Ye which decrea­ smaller and the energy loss mechanism about one day. The time scales for burn­ ses during the collapse phase. The out­ is most efficient. ing stages from hydrogen to silicon burn­ ward shock wave originates at the edge With increasing densities in late burn­ ing are logarithmically decreasing ! of the homologous core, travels through ing stages, the electron gas shows signs When the iron core size passes the matter consisting of iron nuclei, heats up of partial degeneracy, and its pressure Chandrasekhar mass MCh an additional this material, causes dissociation of iron becomes the most important part of the contraction phase starts: during con­ nuclei into nucleons, and thus looses total pressure. The pressure of a degene­ traction the Fermi energy of the electron kinetic energy. If the difference between rate gas is a function of density only and gas grows and at ρ = 109 g/cm3 it rea­ the original iron core and the homolo­ Chandrasekhar showed that an object is ches 5 MeV. At such electron energies gous core is too large, the shock dies and then stable against contraction when its the endoergic reaction of electron cap­ no ejection of the mantle occurs. The mass is less than 1.46 (2Ye)2 M0. Ye is tures on stable nuclei (inverse β--de­ critical mass of the initial iron core for the electron abundance or number of cay) is allowed. A result is the reduction a successful core-bounce mechanism electrons per nucleon, being 0.5 for nu­ of the electron abundance Ye and the seems to lie between 1.25 and 1.35 M0. clei with an equal number of neutrons pressure of the degenerate electron gas. These are only found for stars with rela­ and protons. This speeds up the contraction which tively low masses. Hillebrandt (1984), Applying this to stellar evolution we develops into a collapse. Another effect however reports a successful explosion see that the sequence of contraction is that increasing temperatures towards for a 9 and a 10 M star. and ignition phases set out above holds 1010 K also force a partial break-up of The collapse phase of the central core true only if the core masses exceed the iron nuclei into free particles — neu­ is of the order of seconds. The propaga­ Chandrasekhar limit. Evolution calcula­ trons, protons and α-particles. This is tion of the shock wave through the iron tions show that this is true only for stars again an endoergic process which mantle lasts about 0.03 s. If the shock with initial masses larger than 10 Mo. reduces the internal energy, resulting in wave is stalled there is hope for other They go through all the central burning a further speed up of the collapse. The mechanisms which work on longer time stages until an iron core develops. Very production of free protons makes elec­ scales. Bethe and Wilson (1985) conti­ massive ones undergo so strong a mass tron capture on protons dominant. The nued calculations over one second after loss by stellar winds that they loose their reduction of the electron abundance Ye the core bounce. They found that after extended envelopes of unburned hydro­ causes a decrease of the Chandrasekhar time scales related to neutrino diffusion gen and have a helium composition at mass MCh, which sets the size of the out of the inner core (0.2-0.5 s), neutrino their surface (Wolf-Rayet stars). homologously collapsing central core. absorption and emission processes on Stars with initial masses in the range 8 While Ye has a value of 0.50 in the early nuclei in the shock region heat up mate­ ≤ M/Mo ≤ 10 develop a highly (elec­ burning phases, electron captures in rial, increase the pressure and revive the tron) degenerate core before oxygen silicon burning change it already to 0.46. stalled shock wave. Although the ignition. Then the equation of state At densities of 4 x 1011 g/cm3 it is down energies found are somewhat too small [pressure as a function of temperature, to 0.35-0.39. for typical SN II events, it sheds light on density, and composition; p = p(T,ρ,Yi)] At these densities, neutrinos (formed the subject. The region close to the becomes independent of temperature. by the mechanisms discussed above neutrino sphere is unstable against tur­ Oxygen ignition, energy release, and and electron captures) can no longer bulent convection which would deposit temperature increase do not result in a escape freely. They are trapped inside a material with trapped neutrinos at loca- 6 tions outside the neutrino sphere. At the present, no calculations have included NATO Advanced Study Institute on this effect, but it is expected to be more efficient than neutrino diffusion (Arnett Physically-Based Modelling and Simulation of 1985). Climate and Climatic Change Both the neutrino diffusion and con­ vection mechanisms, however, work on 11-23 May 1986 in Erice, Sicily similar time scales. These are longer The primary objective of the course is to develop understanding of than in the pure core bounce and infall­ the design, validation and application of physically-based climate models in the simulation and understanding of past, present and ing matter increases the central "proto” potential future climates. neutron star by roughly 0.3 M0. With The lecturers will be A. Arakawa, E. Barron, L. Bengtsson, W. present uncertainties of the equation of Bourke, K. Bryan, Y. Fouquart, L. Gates, K. Hasselmann, K. Laval, state, the limiting mass of a degenerate M. MacCracken, Y. Mintz, J. Mitchell, G. North, A. Oort, G. nucleon gas which is stable against con­ Philander, V. Ramanathan, B. Saltzman, A. Semtner, G. Sommeria, traction, varies between 1.5 and 2.0 M H. Sundqvist, M. Tiedtke and T. Wigley. (MCh for nucleons). This leaves the pos­ Persons with an interest in climate modelling and simulation, in­ sibility that massive stars can undergo a cluding advanced graduate students, recent Ph.D.s, and research successful SN II event, according to the assistants, who wish to attend the ASI as a student should send a delayed explosion mechanism, and end curriculum vitae and two references to the Director of the ASI with a central object which eventually Professor Michael E. Schlesinger turns into a black hole, rather than a neu­ Department of Atmospheric Sciences tron star. Oregon State University The outward moving shock wave tra­ Corvallis, Oregon 97331 USA vels through the adjacent zones and ini­ by December 1985. Limited travel money is available to support tiates phases of explosive silicon, oxy­ students. Applicants should indicate their requirements. gen, and neon burning. The stellar zones of carbon, helium, and hydrogen burning are essentially unaltered. The final com­ position in the inner part of a 25 Mo star turns into a red giant and the size of its cretion onto the white dwarf. This enlar­ can be seen in Fig. 2, where the com­ envelope expands tremendously. If both ges the C-O core until MCh is approach­ position is shown as a function of radial stars form a close system, the common ed and a contraction and central ignition mass (rather than radius). Outer zones gravitational potential can favour mass of carbon sets in under degenerate con­ would include products of helium and overflow from the outer zones of the ex­ ditions. Such an event leads to the com­ hydrogen burning. The unprocessed tended envelope (the red giant fills its plete disruption of the white dwarf and hydrogen-rich envelope starts at M(r) = "Roche-lobe"). can explain a SN I explosion. But in gene­ 9 Mo. This result was obtained when a Mass transfer rates in excess of 4 x ral a whole set of scenarios is possible, SN II explosion was simulated by in­ 10-8 Mo Y-1 result in almost steady hydro­ including direct accretion of helium or troducing an outward velocity of mass gen and helium burning during the ac- even carbon and oxygen in a close dou- zones at ≡ 1.48 M0 with a total kinetic energy of 1.1 x 1051 erg. The uncertain­ Fig. 2 — Composition of the inner 2.5 M0 of 25 M0 star (Woosley and Weaver 1982) after explo­ ty in the mass cut between the ejected sive nuclear processing in the supernova shock front. In a SN II event the outer part will be ejec­ mantle and the inner core affects ted into the interstellar medium, the inner (dashed) part can form a neutron star. The original He especially the amount of iron in the and H-burning zones are located at 6.5 M0 and M0, respectively. ejecta. Type I Supernovae The lack of hydrogen (and also helium) in SN I spectra indicates that bare car­ bon-oxygen cores are involved in those explosions. Bare C-O cores are the final stages of intermediate mass stars (M ≤ 8 Mo) which loose their outer hydrogen and helium shells by strong stellar winds and form a "planetary nebula" and a white dwarf, consisting of helium burn­ ing products, i.e. carbon and oxygen. What mechanism can lead to the ex­ plosive ignition of white dwarfs ? About 50% of all stars are members of binary stellar systems. If the two stars have dif­ ferent masses, their evolutionary times will be different. While the more massive star might already be in its final stage and have become a white dwarf, the other member can still be in the stage of core hydrogen burning. Undergoing shell hydrogen and core helium burning it 7 mechanism or nucleosynthesis in the deeper layers. Such formation could on­ ly be obtained from SN II events, if the neutrino pulse, resulting from the col­ lapse and core bounce, could be detected and compared with model predictions. So far information only comes from supernova remnants which expose all of their ejected matter and (if existing) also a central pulsar (neutron star). The best known one is the Crab pulsar but it should be noted that, at pre­ sent, only five of 30 supernova rem­ nants in an X-ray survey show point sources (Helfand and Becker 1984). This sample includes SN I and SN II rem­ Fig. 3 — Composition for a carbon deflagration model of a type I supernova. The inner 1.23 M0 nants. Thus, there is only evidence for a of the original C-O white dwarf underwent nuclear processing in the explosion. The star is com­ neutron star in 1/3 of the SN II events if pletely disrupted and 0.58 MO of 56Ni are produced (Nomoto, Thielemann, Yokoi 1984). SN I and SN II are equally present in the given sample. Whether this indicates a ble white dwarf system. For a complete peak temperatures to ignite the fuel and specific value of rotation and intrinsic review see Iben and Tutukov (1985). the burning front propagates via mixing magnetic field, which would not allow High accretion rates of C and 0 in close of burning and unburned material behind us to see these neutron stars, or if it double white dwarf systems (≥ 2 x the compresssion wave. Thus, the burn­ gives evidence for black hole formation 10-6 M0 Y-1) can, however, ignite carbon ing front moves subsonically and allows is still in question. off-centre, burn non-explosively, and fol­ for the expansion of matter before the low the evolution of originally more mas­ approaching burning front. The Crab nebula, containing a pulsar sive stars. Central carbon ignition in a C-0 white and no strong enhancements of ele­ If the helium accretion rate is less than dwarf results in a deflagration wave. The ments heavier than sulphur, is in accor­ 4 x 10-8 Mo Y-1, a helium layer is formed expansion of matter before the burning dance with a SN II explosion of a relati­ on top of the C-O white dwarf. With in­ front leads to a weakening of the burning vely low mass (≡ 10 Mo) progenitor. creasing size it will reach the point front. While high temperatures are ob­ Those are expected to eject only minor where helium ignites in a flash under the tained at the centre of the white dwarf amounts of heavy elements. Strangely given degenerate conditions. Depending and nuclear reactions allow the build up enough, however, a Ni (and no Fe) over­ upon the strength of the flash, either of iron group nuclei, the outer regions abundance is observed. a single outward detonation wave where the burning front is already Cassiopeia A is a supernova remnant (through the He-layer) or a double deto­ weakened considerably, produce inter­ with an age of approximately 340 y. No nation wave (also proceeding into the C- mediate nuclei like Si, S, Ar, and Ca. A historical reports recorded that event, O core) forms. Such waves will trans­ detonation wave would incinerate the supporting the fact that it was optically form the fuel into nuclear statistical whole white dwarf into iron group nu­ subluminous. This indicates the equilibrium (NSE), leaving only iron clei, contrary to what is observed in the absence of an extended hydrogen group nuclei. spectra of SN I : Fig. 3 shows the radial envelope, supporting the interpretation As discussed before, ignition under composition of the products of explo­ of a massive progenitor, which lost its degenerate conditions always leads to a sive processing in a deflagration model. envelope during prior evolution. The thermal runaway, because the pressure In the inner core 0.58 Mo of 56Ni is form­ enhanced O, Si, S, Ar, and Ca abun­ is only a function of density. The ed ; the energy of the explosion is 1.3 x dances and the absence of a pulsar strength of the runaway determines if it 1051 erg. The outer zones show pro­ (neutron star) are also in favour of this in­ ends in an explosion or a controllable ducts of incomplete silicon, and explo­ terpretation. Small amounts of Fe sug­ event. The strong temperature depen­ sive oxygen, neon, and carbon burning. gest that the mass cut between the dence of the triple-alpha rate in He- SN I are the dominant iron contributors ejected mantle and the remaining core burning (transformation of helium into to galactic evolution. At present it was at a relatively large radius (black carbon via unstable 8Be) and the energy should be noted that carbon deflagra­ hole?). This is an interpretation, relying release cause a very strong runaway and tion supernovae are in accordance with on a massive progenitor and that a cen­ a detonation wave. Degenerate carbon roughly 90% of the observed SN I tral black hole will not be observed. Fur­ ignition gives rise to a weaker runaway events ; another class called peculiar SN ther investigations are needed, however, and a deflagration wave. The main cha­ I still awaits explanation. The general especially constraints on the mass of racteristics of deflagration and detona­ evolution of binary systems certainly the remnant. tion are the following : deserves further study. The absence of overlying hydrogen (a) in a detonation, a strong shock wave and helium shells exposes the products is formed and peak temperatures in the Observations of explosive nucleosynthesis shortly shock are sufficient for explosive igni­ Optical observations of SN II events after a SN I event. Fig. 4 shows the op­ tion of the fuel. A detonation wave mo­ give information mainly about the pro­ tical spectrum of SN 1981b with lines of ves supersonically when compared with genitor star. The plateau in the light O, Mg, Si, S, Ca, and Co. For comparison the sound speed in matter in front of the curve and the presence of hydrogen a "synthetic" spectrum is shown, calcu­ approaching shock wave. lines indicate an extended unprocessed lated with the abundances of Fig. 3 and (b) in the deflagration, the compression envelope. Unfortunately those observa­ the hydrodynamic behaviour of the cor­ is not sufficient to cause high enough tions give no clue to the explosion responding model (Branch et al. 1985). 8 Fig. 4 — Observational spectrum of SN 1981b (upper curve). Features UNIVERSITY OF identified with a sign are MANCHESTER due to terrestrial absorp­ tion. The lower curve Department of Physics shows a « synthetic » Postdoctoral Research spectrum calculated with Associate in Experimental the abundances and the Nuclear Structure Physics hydrodynamical input Applications are invited for from a carbon deflagra­ tion model (Branch et al. the above SERC-funded post, 1985), shifted for ease of tenable for the period Oc­ comparison. tober 1st, 1985 to January 31st, 1988. (Post may possi­ bly be extended for a further period.) The successful can­ didate will be expected to ini­ tiate and assist with research at the Nuclear Structure Faci­ lity, a 20 MV tandem van de Graaff which is now opera­ tional at the Daresbury Labo­ ratory. Applicants are expec­ ted to hold a Ph.D. degree in The spectrum was taken 32 days after (ESA, Europe). Two of the best studied Nuclear Structure Physics the explosion. At later times (≡ 100 objects are the historical remnants and should have an aptitude days), the interior, which originally con­ Tycho (SN 1572) and Kepler (SN 1604). for pursuing research in ex­ tained large amounts of 56Ni, becomes No pulsar was observed, supporting mo­ perimental physics. Salary visible. SN 1972e shows a feature at late dels which predict the complete disrup­ will be on the Research Asso­ times, decaying with the half-life of tion of the progenitor. Strong emission ciate (IA) scale, with place­ 56Co, which can be identified with a lines of Si, S, Ar, and Ca are observed. ment depending on age (e.g. Colli line (Woosley, Axelrod, Weaver The most recent analysis of Tenma data 27 year old with Ph.D. = 1984). This also supports the produc­ for the Tycho remnant results in ratios point 4 on scale = £ 8,920 tion of radioactive 56Ni, which decays to between the Si, S, Ar, and Ca abun­ p.a.). Superannuation. Appli­ 56Co (6.1 d) and 56Fe (78.76 d). The ex­ dances which are roughly solar, while Fe cations, with full C.V. and na­ ponential decay of the supernova light is about a factor of two overabundant. mes of two referees to: curve requires an amount of roughly 0.5 The abundances shown in Fig. 3 give Dr. R. Chapman, M of 56Ni. solar ratios for Si to Ca and an Fe over­ Department of Physics, Extensive studies of supernova rem­ abundance slightly in excess of two. The University, nants have been undertaken with the X- This seems to give additional support to Manchester, M13 9PL ray satellites HEAO 2 (Einstein Obser­ an interpretation based on the carbon from whom further details vatory), Tenma (Japan) and EXOSAT deflagration model of SN I. may be obtained.

REFERENCES Arnett W.D., Proceedings of the Fifth Moriond Astrophysics Meeting, eds. J. THE PENNSYLVANIA STATE UNIVERSITY Audouze and J. Tran Thanh Van (Reidel, Dordrecht), 1985. Theoretical Condensed Matter Physics and Bethe H.A. and Wilson J.R., Ap. J. (1985) 295, in press. Statistical Mechanics Branch D., Doggett J., Nomoto K. and Thielemann F.-K., Ap. J. (1985) in press. The Department of Physics is seeking candidates for a tenure-track Helfand D.J. and Becker R.H., Nature 307 position of Assistant or Associate Professor of theoretical con­ (1984) 215. densed matter physics and statistical mechanics starting in the Hillebrandt W., Ann. New York Acad. Sci. 1985-86 or 1986-87 academic year. Candidates should have an 422, (1984) 197 (11th Texas Symposium established record of research accomplishments and may expect on Relativistic Astrophysics). to work in conjunction with the ongoing research effort at Universi­ Iben I.Jr. and Renzini A., Phys. Rep. 105 ty Park. Minimal requirements include a Ph.D. degree in this field (1984) 329. and some postdoctoral experience. A desire and aptitude for the Iben I.Jr. and Tutukov A.V., Ap. J. Suppl. teaching of undergraduate and graduate students is essential. (1985) 58. Nomoto K., Thielemann F.-K. and Yokoi K., Send application, including a curriculum vitae and names of at least Ap. J. (1984)286,644. four referees, to: Woosley S.E., Axelrod T.S. and Weaver T.A., Gerald A. Smith, Head, Department of Physics, Stellar Nucleosynthesis, eds. C. Chiosi Box Z, 104 Davey Laboratory, and A. Renzini (Reidel, Dordrecht) 1984. University Park, PA 16802 USA, Woosley S.E., and Weaver T.A., Essays in Nuclear Astrophysics, eds. C.A. Barnes, by October 15, 1985 or until a suitable pool of applicants is iden­ D.D. Clayton and D.N. Schramm (Cam­ tified. An affirmative action/equal opportunity employer. bridge University Press) 1982, p.377. 9