The theme of this Colloquium is radiation hydrodynamics in and around stars and other compact bodies. To open our discussions, I would like to offer some rather elementary remarks about the role played by radiation in astrophysics.

It is probably true that most astronomers view radiation primarily as a diagnostic tool. After all, the only access we have to astrophysical bodies (with a few exceptions inside the Solar System) is the photons we capture from them. And so an immense effort has been devoted to the development of techniques for converting raw information about the spatial, temporal, spectral, and polarization variation of the observed radiation field into knowledge about the physical structure of the object that produced the radiation. There are many difficult challenges, both observational and theoretical, to be met in this process, and the field is in a state of rapid development today, and will remain so for the forseeable future. Nevertheless, in the context of this conference it is worth emphasizing that in the diagnostic problem radiation plays an essentially passive role; it is merely the tool used to analyze the situation.

Recent optical observations have shown that many young stars are capable of generating highly-collimated bipolar flows. Such flows are evident from narrow emission-line jets extending over 0.01-1 pc and having opening angles of a few degrees. Their measured radial velocities reach values of up to 400 km/s. For most known jets the “driving stars” are T Tauri stars or IR-sources of low to moderate luminosity (1-100 L⊙) . The typical velocities, Mach numbers, particle densities, and mass fluxes of these jets are estimated to be 200-400 km/s, 10-40, 15-150 cm−3, and 10−10−10−7 M⊙/yr, respectively. The estimated mass fluxes and velocities are consistent with our present knowledge of T Tauri star wind properties.

The emission-line spectra of the jets are the same as observed in Herbig-Haro (HH) objects. Furthermore, the brightest parts of some jets (hot spots) are known as HH objects, having often been discovered many years before their associated jet. Thus, both phenomena are highly related and in both cases the emission lines are very probably formed in the cooling regions of shock waves with velocities of 50-100 km/s. There are a variety of mechanisms, which can in principal excite internal (oblique) Shockwaves in these jets. Examples of likely excitation mechanisms are fluid dynamical instabilities or pressure gradients in the ambient medium.

A model is proposed in which HH objects are representing the locations of the most strongly radiating (internal)shock waves in these jets. For those HH objects being located at the end of the jet the observational data strongly suggest that they are tracing the working surface of the jet. This idea is consistent with the observed proper motions of these HH objects, the typical densities near the edges of their associated molecular clouds, and with the jet parameter given above. For a more detailed discussion of these jets the reader is refered to the review articles listed below.

Many problems in the theory of star formation are amenable to a complementary attack in which the analytical approach is used to reduce the governing equations to a form amenable to efficient numerical solution. This strategy has proven very useful in helping to resolve several astrophysical puzzles which arise because the bulk of star formation today is observed to occur, with relatively low efficiency, in giant molecular cloud complexes. How does a cloud of 105-106M⊙ know how to form stars of mass ~ 1 M⊙? How does the interstellar medium know, to one or two orders of magnitude, that roughly hydrogen atoms of mass mH are needed to yield thermonuclear fusion in a self-gravitating ball of gas? Why have radio astronomers not detected unambiguous evidence for the collapse motions attendant to star formation? Why has a true protostar, the “holy grail” of infrared astronomy, been so hard to find? Why do young stellar objects almost universally exhibit powerful outflows? Why is the geometry for these outflows often bipolar? Why do T Tauri stars have such active chromospheres? In this review we suggest that these puzzles all have a related resolution, in the nature of how gravitational collapse is initiated and terminated in the slowly rotating cores of molecular clouds.

The topic of this review encompasses all aspects of pulsation theory, for the radiation field is never negligible in stellar stability problems, on the contrary, it is usually the primary destabilizing factor through its thermal effects, and modifies the envelope structure and stability through its dynamic effects. The impossibility of a general review of such a broad topic is apparent, and I will concentrate in this talk on the most striking aspect of pulsating stars: nonlinear effects in the outer layers. To focus the discussion, I will address primarily two problems of current interest: shock development driven by the pulsating velocity field, and time dependent turbulence in the ionization zones. The emphasis will be on methodology rather than specific problems and developments.

Solar flares are currently understood as the explosive release of energy stored in the form of stressed magnetic fields. In many cases, the released energy seems to take the form of large numbers of electrons accelerated to high energies (the nonthermal electron “thick target” model), or alternatively plasma heated to very high temperatures behind a rapidly moving conduction front (the “thermal” model). The transport of this energy into the remaining portion of the atmosphere results in violent mass motion and strong emission across the electromagnetic spectrum. Radiation processes play a crucial role in determining the ensuing plasma motion.

One important phenomenon observed during flares is the appearance in coronal magnetic loops of large amounts of upflowing, soft X-ray emitting plasma at temperatures of 1−2×107 [K]. It is believed that this is due to chromospheric evaporation, the process of heating cool (T - 104[K]) chromospheric material beyond its ability to radiate. Detailed calculations of thick target heating show that if nonthermal electrons heat the chromosphere directly, then the evaporation process can result in explosive upward motion of X-ray emitting plasma if the heating rate exceeds a threshold value. In such a case, upflow velocities approach an upper limit of roughly 2.35 cs as the heating rate is increased beyond the threshold, where cs is the sound speed in the evaporated plasma. This is known as explosive evaporation. If the flare heating rate is less than the threshold, evaporation takes place indirectly through thermal conduction of heat deposited in the corona by the energetic electrons. Upflows in this case are roughly 10 to 20% of the upper limit. Evaporation by thermal model heating always takes place through thermal conduction, and the computed upflow speeds seem to be about 10% to 20% of the upper limit, independent of the energy flux.

The pressure increase in the evaporated plasma for either the thick target or thermal model leads to a number of interesting phenomena in the flare chromosphere. The sudden pressure increase initiates a downward moving “chromospheric condensation”, an overdense region which gradually decelerates as it accretes material and propagates into the gravitationally stratified chromosphere. Solutions to an equation of motion for this condensation shows that its motion decays after about one minute of propagation into the chromosphere. When the front of this downflowing region is supersonic relative to the atmosphere ahead of it, a radiating shock will form. If the downflow is rapid enough, the shock strength should be sufficient to excite UV radiation normally associated with the transition region, and furthermore, the radiating shock will be brighter than the transition region. These results lead to a number of observationally testable relationships between the optical and ultraviolet spectra from the condensation and radiating shock.

In this review, attention will be focussed exclusively on the winds of hot stars, concentrating for the most part on spectral types 0 and B. For these stars, a clear consensus has emerged that it is the gradient of selective radiation pressure - i.e., line-driving - that explains the high terminal velocities, typically ~ 2000 km s−1, of their winds. Accordingly, few would now doubt that the supersonic zones of these winds present us with rather clean examples of line-driven flow, whose investigation therefore properly belongs under the heading “Radiation Hydrodynamics”. Moreover, in marked contrast with other astronomical environments where line-driven winds may exist, the stellar case is geometrically and parametrically well defined and is thus by far the best natural example from which to learn about such flows.

Presupernova models of massive stars are presented and their explosion by “delayed neutrino transport” examined. A new form of long duration Type II supernova model is also explored based upon repeated encounter with the electron-positron pair instability in stars heavier than about 60 M⊙. Carbon deflagration in white dwarfs is discussed as the probable explanation of Type I supernovae and special attention is paid to the physical processes whereby a nuclear flame propagates through degenerate carbon.

We discuss the full problem of neutrino transport in the context of a Type II supernova environment. We describe the “standard model” of Type II supernova, which involves the core collapse and core bounce of an 8 — 20M⊙ star. Although the shock produced in the standard model is supposed to expel the outer layers of the star, this does not happen in the best numerical collapse calculations without considerable numerical tweaking, if at all. In this model, neutrino transport plays an important role. We describe the weakness of the best transport approximation currently used in collapse calculations, the flux-limited diffusion approximation. We investigate the effect of a full transport approach by constructing two different types of model atmospheres, with conditions chosen to closely approximate conditions found in full collapse calculations. The first model is to construct equilibrium plane-parallel hydrostatic neutrino atmospheres. The second is to solve the equations of neutrino hydrodynamics for a spherical shell of matter, with a piston and a source of neutrinos at the lower boundary. We describe in detail the neutrino interactions which are important in the supernova problem. We present the equations of neutrino hydrodynamics and neutrino hydrostatics which are solved in the two models, and emphasize the differences between photon transport and neutrino transport. We describe briefly a “toy” model, the neutrino Eddington atmosphere, which highlights the differences between photon and neutrino atmospheres. We present the results of our model atmosphere calculations for a few selected cases of interest. Finally, we summarize alternatives and extensions to the standard model which are of current interest and may hold the answer to the Type II supernova problem. However, the delicate balance between competing effects suggest that a rigorous calculation of neutrino transport will be required to obtain a definitive answer.

In his review in 1972 Woltjer [1] divided the evolution of supernova remnants into three different phases, the free expansion phase, the adiabatic Sedov phase and the radiative phase, when cooling of the gas becomes important. The first of these was only briefly discussed and little connection between the supernova explosion and the remnant phase was made. The reason for this is also easy to understand in view of the difficulty of determining the type of explosion even for well-known, young remnants like Cas A, Tycho, Kepler and the Crab remnant.

This situation has changed considerably during the last five years or so, mainly due to observations with new instruments like VLA, IUE and Einstein. With these, as well as large optical and infrared telescopes, the information about the supernova explosion and the early evolution of the supernova remnant has increased dramatically, and a more or less new picture of the explosion has emerged. Instead of a free expansion into a virtual vacuum, with few observational consequences, the supernova undergoes a complex interaction with its immediate surroundings, with a wealth of observational information. In this stage both the structure of the supernova ejecta and the circumstellar medium is crucial for the observational properties. Perhaps, the most interesting aspect of it is that we in this way can bridge the gap between the supernova explosion and the remnant stage.

Most of our knowledge of supernovae comes from studies of their optical radiation. Very high quality optical spectra have been available for several years now. The new data have aided the development of theoretical models of supernova explosions, particularly Type I events, which until recently, were very poorly understood. Type II explosions, which are believed to arise from core collapse in massive stars (Woosley, this volume;, produce optical spectra which can be simply interpreted in terms of a nearly blackbody continuum with prominent lines of hydrogen superimposed. The Type II atmosphere is of near solar composition, expanding at a characteristic velocity of 5000 km/s and at least bears some resemblance to a more familiar stellar atmosphere. Type I supernovae produce a much more violent expansion and the optical spectrum cannot be so easily accounted for. The progress made in the last few years stems mostly from the work of David Branch (Branch 1980,1981; Branch et. al. 1982,1983,1985). His synthetic spectra for Type I’s showed that the spectrum can be explained in terms of the resonance lines of mostly singly ionised metals. The lines are formed in matter moving with a bulk velocity of about 11,000 km/s and at a characteristic temperature of approximately 10,000 K. Furthermore, Branch concluded that the density profile in this region should be relatively steep and that the matter was very deficient in hydrogen and helium. As we shall see, this description fits very well with the hypothesis that Type I supernovae originate in the incineration of white dwarfs. Following the focus of recent developments this discussion will be mainly limited to the early evolution of Type I models of this kind, although many of the important features of the radiation transport are directly relevant to Type II explosions.

Compact binary X-ray sources include white dwarfs, neutron stars, and black holes that are accreting matter from a companion star. The X-ray emission from these systems is produced by the accreting matter as it flows through an accretion disk and strikes the surface of the compact object. The emitting regions have opacities dominated by electron scattering, and radiation pressure is likely to play an important role in the hydrodynamics. Strong magnetic fields greatly modify the hydrodynamics and radiation transfer in the pulsating neutron star sources. Accretion disks have complex structure, including an electron scattering corona, a cool outer region, and possibly a thick torus in their inner region. The structure and stability properties of accretion disks are only partially understood. Major problems exist with the interpretation of the spectra and luminosities of the X-ray burst sources. The pulsed X-ray emission from the pulsating binary X-ray sources probably comes from “mounds” of accreting gas at the magnetic poles of neutron stars, in which the accreting matter is decelerated by radiation pressure. The physics of these systems is reviewed, with an emphasis on problems for which hydrodynamical simulations may be especially useful.

This paper reviews the present status of observations of compact X-ray sources with emphasis on the aspects related to radiation hydrodynamics, based on the recent observational results, in particular those from the Japanese X-ray astronomy satellite Tenma. The main feature of Tenma is a large-area gas scintillation proportional counters (GSPC) with energy resolution twice that of ordinary proportional counters, which can yield information on energy spectrum superior in quality to previous results. We shall deal here only with those galactic X-ray sources in which the compact object is a neutron star or possibly a black hole, and exclude white dwarf sources.

There exist more than one hundred bright X-ray sources in our galaxy in the luminosity range 1036−1038 ergs/sec. They are most probably binaries involving a neutron star or, in some cases, possibly a black hole. The high luminosities of these sources are explained in terms of the large gravitaional energy release by matter accreting from the companion star to the compact object.

In this review I will present and discuss both the nova outburst and the theoretical calculations related to its cause and evolution. I use the commonly accepted model for a nova: a close binary system with one member a white dwarf and the other member a larger, cooler star that fills its Roche lobe. Because it fills its lobe, any tendency for it to grow in size because of evolutionary processes or for the lobe to shrink because of angular momentum losses will cause a flow of gas through the inner Lagrangian point into the lobe of the white dwarf. The size of the white dwarf is small compared to the size of its lobe and the high angular momentum of the transferred material causes it to spiral into an accretion disk surrounding the white dwarf. Some viscous process, as yet unknown, acts to transfer mass inward and angular momentum outward through the disk so that a fraction of the material lost by the secondary ultimately ends up on the white dwarf. Over a long period of time, the accreted layer will grow in thickness until the bottom reaches a temperature that is high enough to initiate thermonuclear burning of hydrogen by the proton-proton reaction chain. The further evolution of thermonuclear burning on the white dwarf now depends upon the mass and luminosity of the white dwarf, the rate of mass accretion, and the chemical composition of the reacting layer.

In this article we discuss two instabilities of stationary accretion disks which lead to an understanding of observed light variations in accretion disk systems, the dwarf novae and the rapid burster MXB 17030-335. The accretion disks in these systems avoid instability at the cost of stationarity and perform stable cycles in which sudden changes of the accretion flow lead to corresponding, often dramatic, variations of their accretion luminosity.

Figure 1 shows a light curve of U Geminorum. It was discovered In 1855 by J.R. Hind and has become a prototype of the dwarf novae. In these systems an extended time of quiescence of up to several weeks Is followed by a short outburst of a few days during which the luminosity rises by a factor of 30 to 100. The dwarf novae belong to the cataclysmic variables. They are all close binaries In which a white dwarf primary is orbited by a Roche lobe-filling low mass secondary. Through the inner Lagrangian point mass flows over from the secondary and forms a luminious accretion disk around the white dwarf. In the case of the dwarf novae this disk has temperatures below about 10000K in Its outer region. It will be discussed how partial lonizatlon and convection then affect the vertical structure of the disk such that the stationary flow becomes unstable.

Fig. 1. Light curve of the dwarf nova U Geminorum. Abszissa in days С [2])

At outburst the classical nova generates an extended optically-thick wind driven by radiation pressure in the continuum. At maximum light the optical luminosity is close to the Eddington-limit. The subsequent decline illustrates the interaction between radiation and matter in a wind which gradually thins as the mass loss rate falls at an approximately constant Eddington-limit luminosity. As the wind thins so the effective photosphere shrinks back into the underlying binary, and an increasing fraction of the radiation is emitted at ultraviolet wavelengths. Model atmosphere computations show how the increasing flux of ultraviolet photons is associated with the shell becoming more and more ionized through radiative ionization. Attempts to study the internal structure of the wind confirm that the luminosity must be close to the Eddington limit and must be expelled from close to the white dwarf surface. It is generally agreed that the outbursts are caused by runaway nuclear burning of accreted material at the white dwarf surface, but it is possible that some events of the classical nova type may be caused by runaway accretion at a super-critical rate.

In dwarf novae very different behaviour is evident. The outbursts are located within the accretion disc and are generated either by mass-transfer bursts due to dynamical instability of the Roche-lobe filling star, or by an instability within the disc itself. In either case the eruption behaviour is due to an enhanced accretion flux through the accretion disc. One important aspect of the radiation hydrodynamics is the luminosity generated by impact of the mass-transfer stream with the accretion disc and penetration by the stream within the disc. Attempts at examining this penetration region are described and results compared with observed behaviour of disc evolution through the course of an outburst. The possibility that disc instabilities will not propogate in realistic discs which deviate from axial symmetry is considered.

Type I cosmic X-ray bursts are widely thought to result from thermonuclear flashes in the surface layers of accreting neutron stars. The thermonuclear-flash model is able to account for a wide variety of observed burst phenomena. However, a number of theoretical and observational problems persist. Foremost among these are related to the existence of apparent luminosities in excess of the Eddington limit in many observed bursts. Under circumstances of very high luminosity, the theoretical treatment of radiative transfer and radiatively driven mass loss at the neutron-star surface becomes complex. We discuss the current status of theoretical work in this area and the prospects for developing an understanding of the remaining phenomenological problems: (a) What is the nature of the precursor in some fast transients and of the twin-peak structure observed in some shorter bursts? (b) Do some bursts actually achieve super-Eddington luminosities, and if so, how? (c) What are the characteristics of quasi-static mass loss in the presence of such luminosities? (d) How is the color temperature related to the effective temperature? and, (e) What are the implications concerning the Galactic distance scale?

The power per logarithmic bandwidth in gamma-ray burst spectra generally increases rapidly with energy through the x-ray range and does not cut off sharply above a few MeV. This spectral form indicates that a very small fraction of the energy from a gamma-ray burst source is emitted at low energies or is reprocessed into x-rays and that the high-energy gamma rays are not destroyed by photon-photon interactions. The implications are that the emission mechanism for the gamma-ray bursts is not synchrotron radiation from electrons that lose most of their energy before being re-accelerated and that either the regions from which the gamma rays are emitted are large compared to the size of a neutron star or the emission is collimated and beamed away from the stellar surface.

Active galactic nuclei (AGNs) emit continuum radiation evenly spread over up to ten decades in frequency from the radio into the gamma-ray range. Plausible emission mechanisms and their characteristics are reviewed. In the deep potential wells around black holes the mean energy per proton can reach 100 MeV. Part or all of this energy may be channeled to all electrons equally (thermal plasma) or, preferentially, into only a small fraction of the electrons (nonthermal plasma). In the former case thermal Comptonization of soft photons may be the dominant emission mechanism, while in the latter case the synchrotron and the inverse Compton scattering process (synchro-self-Compton) are likely to dominate.

When the compactness parameter L (hν≈mc2 )/R. (power L, radius R) exceeds about 1030 ergs cm−1s−1 or L>Lc ≡ 1030R ergs s−1, then electron-positron pair production takes place due to photon-photon interactions causing the source to shroud itself with an electron-positron atmosphere. The efficiency of pair cascades in converting injected energy into electron-positron rest mass can reach levels of about 10% in static pair atmospheres. The emerging radiation is strongly modified by the pair atmosphere causing the spectrum to soften and to have characteristic breaks.

For emission coming from a region near the Schwarzschild radius, L>10-3LEdd is sufficient to cause prolific pair production. Radiation pressure then drives a mildly relativistic pair wind with Compton drag limiting the Lorentz factor to be less then 10. The pair rest mass power is at most of the order of Lc.

Most results so far on static pair atmospheres and pair winds are either qualitative or based on simple analytical models. Needed numerical treatments of both time dependent and steady radiative transfer of both the continuum and the annihilation line radiation in mildly relativistic flows are relevant not only for AGNs but also for gamma ray bursts and galactic black hole sources.

The broad line region in quasars and in the nuclei of active galaxies is the site of remarkable hydrodynamic activity unprecedented elsewhere in the universe. Considerable theoretical effort has been directed to determine how this intense radiation is related to high velocity gas motions in these small regions, which, because of their great distances, cannot be resolved by direct observation. A better theoretical understanding of the nature of the broad line-emitting gas involves many novel aspects of radiation hydrodynamics and may eventually provide insights into the nature of the mysterious quasar phenomenon itself.

Continuum and emission line properties of active galaxies and quasars are sufficiently similar that there is little doubt that both can be accounted for by a similar or closely related physical model. The main difference is one of luminosity; typical quasars are considerably brighter than Seyfert galaxies.

In the discussion below the relevant observations of quasars and active galaxies are briefly reviewed with an emphasis on the physical properties of the line-emitting gas and its immediate environment. Arguments that support the importance of radiation forces in producing the observed gas velocities are summarized. Finally, the nature of the acceleration process is described with particular attention paid to the various instabilities that may be present and which are generally characteristic of situations in which plasma velocities result directly from the deposition of radiative momentum. In fact, these troublesome instabilities suggest that radiative forces, although very strong, may provide only a partial explanation of the gasdynamical activity observed.

The “central engine” of quasars and active galactic nuclei Is most likely powered by accretion into a supermassive black hole. A menagerie of steady state accretion flows have been developed, and these are briefly reviewed. Several examples from recent numerical calculations of axisymmetric accretion flows provide disk formation scenarios from which one can calculate plasma densities, and other values of interest for a range of accretion rates and black hole masses. These results can be compared with the well studied, but physically unrealistic case of radial accretion. Although a reasonable conceptual picture of the central engine has been developed, considerable work remains to be done.