One seeks the condition of spontaneous collapse of a layer of interstellar matter by the method of marginal stability. The radiation field is included in this treatment of the gas-dynamic properties of the interstellar material. The optical model used is that of Ambartsumian's, which neglects interlocking.

We examine here the problem of the gravitational instability of a medium in nonuniform rotation. We seek therefore to resolve a problem differing somewhat from that examined by Chandrasekhar and Fricke. We imagine a gaseous medium in rotation in a potential field, ɸ, and consider only the plane problem. In the unperturbed motion, the particles describe circular orbits in uniform motion. We examine the stability against perturbations.

If we suppose that at least some stars are the result of the gravitational collapse of HI clouds, it seems necessary to consider Jeans' criterion. This can be derived by a number of arguments, but for our purpose it is sufficient to consider it a result of dimensional analysis, and we get where G is the gravitational constant, M is a typical dimension, and V is a characteristic velocity comprising all velocities interior to the region of gas being considered.

In a recent paper, Mestel and Spitzer discussed the problem of star formation from cool matter in the presence of a magnetic field of energy density comparable with the thermal energy density. If the field were frozen into the gas, the magnetic pressure would put a lower limit of order 103M⊙ to the mass that could be gravitationally bound, and this limit is unaltered by contraction of the cloud. However, in a lightly ionized gas, the field moves not with the gas as a whole, but with the plasma, and the motion of the plasma through the cloud is determined by a balance between mgnetic force and friction between neutral gas and plasma. A cloud containing sufficient dust can extinguish the galactic ionizing radiation; the plasma density decays quickly enough for the plasma and neutral gas to become uncoupled during the time of gravitational contraction. In this way high densities are built up without correspondingly high magnetic energy, and the cloud can break up into stars.

The problem of turbulence in the protoplanetary cloud is of importance for planetary cosmogony. Chaotic macroscopic motions probably existed in the cloud during its formation. Further evolution of the cloud depended to a great extent upon whether these original motions damped in a short time, or turbulence supported by some source of energy existed during planet formation. According to Kuiper and Fessenkov's hypotheses, massive protoplanets formed as a result of gravitational instability and turned into planets after the dissipation of light elements. Large-scale turbulent motions with mean velocities exceeding the thermal velocities of atoms and molecules would prevent, however, gravitational instability in the cloud, even if its mass was of the order of the mass of the sun. According to Edgeworth and to Gurevitch and Lebedinsky the planets grew gradually from small condensations formed in a flattened dust disk with a mass equal to that of the present planetary system. But even small scale turbulent motions would prevent extreme flattening of the disk necessary in this case for gravitational instability. The problem of turbulence is also connected with the problem of present distribution of angular momentum between the sun and planets, as large-scale turbulence produces redistribution of matter and of angular momentum in the cloud.

A common form of planetary nebula consists of a high temperature nuclear star surrounded by an ovoid or ellipsoidal shell of gas which has originated in some manner in the nucleus. The radiation from the nebula consists of the ordinary spectral lines and continua of hydrogen and helium plus the so-called forbidden lines of atoms and ions of oxygen, nitrogen, neon, argon, etc. It has become clear that, as in other cosmic bodies, the bulk of the nebula consists of hydrogen and helium, and the remainder of the chemical elements occur only as a slight admixture of impurities. For instance, recent data by Aller and Minkowski lead to relative numbers of atoms of various chemical species in a particular nebula (NGC 7027) as follows (oxygen arbitrarily taken as 104):

We may summarize Wilson's extended study of internal motions in planetary nebulae by stating that he finds the average expansion velocity in the regions whence originate the lines of H, NeIII, OIII to be roughly 20 km/sec, with rare examples ranging as low as O and as high as 50 km/sec. We ask whether radiation pressure and/or gas pressure may give, in an elementary calculation, velocities anywhere near these values.

Densities in ionized nebulae may be estimated from the surface brightness, which essentially gives an rms density,.

In the first and second Symposia of this series von Weizsäcker and von Hoerner discussed the problem of turbulence in the Orion Nebula, while in the second Symposium Courtès has further treated the problem. Von Hoerner has presented a detailed discussion of the methodologies of the treatment. It was suggested that the observed variations in radial velocity in the nebula are consistent with the predictions of the Kolmogoroff equilibrium theory of turbulence, which is valid at sufficiently high Reynolds numbers. However, their results to some extent were inconclusive, mainly because the observations which they analyzed were not sufficiently numerous and accurate. With the purpose of reanalyzing the whole problem, Dr. O. C. Wilson and I undertook the task of determining radial velocities and profiles of selected emission lines in the spectrum of the nebula, using the largest practical resolving power in angle and frequency available with the 200-in. telescope. In order to use advantageously the efficiency of the instrument, we have photographed the brighter parts of the nebula (roughly subtending a solid angle of about 6′ aperture) with the Coudé spectrograph fitted with 31 parallel entrance slits, which are separated from each other by a distance of 1 mm in the focal plane or 1″.3 in the sky. In this manner we obtain in one exposure the spectrum of an area about 40″X40″ with a dispersion such that 1 μ = 0.27 km/sec. In each of these plates about 600 Doppler shifts of the lines [OII] λ3726, Hγ, and [OII] λ5007 have been measured, each of which represents some average value (not necessarily the same for the three lines) of the velocities of nebular matter along the line of sight. Altogether we have about 50 000 radial velocities measured. The accuracy with which a radial velocity may be determined is set by the intrinsic shape of the lines, which reflects the distribution of velocities along the line of sight. To give an idea of the orders of magnitude of the quantities involved, I may mention here that typical values of the mean widths h at half-intensity of the hydrogen, [OIII], and Fe—comparison lines are h(H) = 28.6 km/sec, h(OIII) = 20.0 km/sec, h(Fe) = 8.3 km/sec. The bisection of a line with a cross wire to an accuracy around 0.5 km/sec is thus feasible; repeated measurements have, indeed, shown such precision. On the assumption that the profiles to which the above widths correspond are Gaussian, we may easily disentangle the thermal and turbulent components of the mean square radial velocities, through the dependence on atomic weight of the former. We find from the representative values given above

The corresponding kinetic temperature is 9700°K, in close agreement with the value of the electron temperature determined by other methods.

The Crab Nebula, remnant of the supernova of 1054, may be observed today in the recombination spectrum of the filamentary component, or in the continuous spectrum of the central amorphous mass. The recent optical discovery of a high degree of polarization in the amorphous component has led to a striking confirmation and general acceptance of the hypothesis first advanced by Shklovsky, which considers the continuous spectrum as emitted by relativistic electrons moving in a magnetic field.

The emission of the Crab Nebula is perhaps connected with the internal motions of the gas. As shown by the observations, the power of the emission sources differs by some hundred times in different points of the amorphous mass (“wisps” and other details). Oort and Walraven believe the “wisps” to be condensations of relativistic electrons ejected from the central star. However, there are some other variable details elsewhere in the nebula (as described by Lampland, and Oort and Walraven).

Oort and Walraven's hypothesis met some important difficulties: (a) the direction of the magnetic lines in this region of the nebula is perpendicular to the wisp's velocity; (b) the dimension of the wisp is about three light months, while it appears during a month and faster, so that the relativistic electrons moving along the lines of force have no time to spread along the wisp; and (c) if the strength is not changing, the energy of the relativistic electrons in the wisp must be some hundred times greater than the density of the magnetic energy, consequently the field strength must grow in the wisp to keep the electrons in the volume.

The suggestion by Oort that the Cygnus loop, an object of a diameter of about 3° whose brightest parts are NGC 6960 and NGC 6992, is an expanding supernova shell slowed down by interaction with the interstellar medium has led to an increased interest in objects of this type. As better information on the Cygnus loop becomes available, it seems to become increasingly probable that Oort's suggestion provides an acceptable interpretation.

Bright rims at the edge of dark markings associated with diffuse nebulae have been noticed for more than thirty years. An example is shown in Fig. 1, a photographic negative of the diffuse nebula IC 1396. Figure 1(a) shows the entire nebula, which is excited by an O6 star (circled). Figure 1(b) is an enlargement of one of the bright rims in this nebula. A number of general characteristics can be pointed out. The bright rim is always at the edge of what appears to be dark matter and always is bright on that side of the matter closest to the exciting star. If a line of symmetry is drawn through the dark material it is found in general to pass very near to the exciting star. Sometimes isolated matter similar to Bok's globules are present, and when present also show bright rims. These globules are included in the observational study.

The boundaries between HII and HI regions often have shapes which suggest that the motion of the interstellar gas is unstable there. A characteristic shape of this kind is the so-called “elephant's trunk,” a long tongue of dark material (presumably an HI region) seen superimposed on the luminous HII region, and outlined by a thin rim brighter than the luminous background. A detailed study of these shapes has recently been made by Pottasch; earlier observations had been made by Duncan and by Struve.

The problem discussed here is that of determining the motion of a cloud of neutral atomic hydrogen gas, when it is subjected to ionizing radiation from a star embedded in it. Initially the gas is in gravitational equilibrium at a constant temperature of about 100°K. It is supposed that at time t=0 the star suddenly begins to radiate with a certain intensity, which remains constant thereafter. Part of the surrounding gas will be ionized and an ionization front (separating the ionized gas from the neutral gas) will move outwards into the neutral gas. A shock wave may also propagate ahead of the ionization front into the neutral gas. There will therefore be two regions to consider—a region of ionized gas (HII region) and a region of neutral gas (HI region) in which there may be a shock.

If two rarefied masses of gas collide at a sufficiently high speed, their relative motion will be stopped by a collective plasma instability, rather than by collisions of individual particles. This is true even if the gases are initially non-ionized. In the present note, the possible influence of magnetic fields is ignored for the most part, but a criterion is found to decide under what conditions the collective interaction remains dominant even when they cannot be ignored. It seems that the neglect of magnetic effects may be justified, for example, in the case of two galaxies in collision at a relative speed of 1000 km/sec. The magnetic energy density here is (1/8π)H2∼4X10−12 erg/cm3 (with H∼10−5 gauss), which is much less than the kinetic energy density 1/2NmU2∼8X10−9 erg/cm3 (with N∼1 particle per cm3).

At the Second Symposium, various contributors discussed the possibility that star formation might provide the energy to maintain the motion field in the interstellar medium. Although Oort and Spitzer emphasized the importance of the recoil momentum produced by the gradual ionization of the surrounding gas, the important effect appears to be the gas pressure itself when the ionized region is enclosed by the surrounding gas. Indeed, Kahn has shown (for one-dimensional flow into a vacuum) that the recoil momentum is inefficient in producing mass motion; only a limited range in photon fluxes result in acceleration of neutral hydrogen.

When two galaxies collide at extremely high velocities, Baade and Spitzer note that negligible stellar effects are anticipated but that the interstellar medium is violently affected. Recently the radio source Cygnus A has been identified with what appears to be two colliding galaxies. Baade and Minkowski describe the optical nebula as two … “late-type systems, judging by low density gradients of the two disks. Spatially they are oriented face to face, they are slightly decentered, and we look upon them at an angle not far from 45°.” “ … the two systems must be in close contact because of the strong signs of tidal distortion which the nuclei show.” The lines are noted as diffuse.

In connection with the problem of the explanation of stellar outbursts exact solutions for gas flows with spherical symmetry can be given in the following three cases.

1. Propagation of detonation waves from the interior to the surface of a star, accompanied by an output of nuclear energy on the wave front. Effects of the increase of detonation velocity depending upon the law of density decrease from the center to the outer layer (failure of Chapman-Jourguet's rule) are investigated. As a result of a sufficiently rapid density decrease one obtains a complete dispersion of the detonation products with the formation of a vacuum near the center. Similar solutions are obtained for the spherical problem of the propagation of a rarefaction jump, accompanied by an energy output (a jump of flame front type) through a gas at rest.

2. Perturbed gas motion due to an explosion caused by a sudden large output of energy inside a star. The energy is transferred to the surface together with the shock wave. Exact automodel solutions of the equations for adiabatic time-dependent gas motion, accompanied by the formation of a vacuum when γ=Cp/Cv = 4/3 and without it, are given, gravitation being taken into account. Some solutions for larger values of y are studied.

3. Examples of dynamically unstable equilibrium states disturbed by an explosion followed by the development of a shock wave, propagating through a gas at rest with density gradient. A motion without energy output develops. The energy of the disturbed motion at any time is equal to the initial energy in the equilibrium state.

This paper describes recent work on magnetohydrodynamics by M. H. Rogers and myself. It has seemed to us that the large-scale dynamics of cosmical gas clouds must take into account the fact that a gas is a compressible material, so that the hypothesis of a constant density must be avoided. Secondly, there must be present a pressure-gradient force. Thirdly, self-gravitation cannot be omitted. Fourthly, the motion should be adiabatic, in the first instance at least. To these conditions we have now also added the effects of the presence of magnetic fields, but have assumed that the conductivity of the material is infinite and that it is of constant permeability. We have neglected the effects of turbulence, of viscosity, and of heat conduction.