The East-West arm of the ‘Northern Cross’ radio telescope of the Bologna University has been used to observe 14 planetary nebulae at the frequency of 408 MHz.

I am to report on a rather extensive series of observations of planetary nebulae, using the Mark-II radio telescope at Jodrell Bank. The method of observation adopted involves comparing the signal received from a beam centered on the nebula with two beam areas horizontally displaced to either side of it. If the source is not too far South, the confusion effects can be reduced by making observations at different hour angles. A second source of error, particularly in the earlier results, arises from the fact that the positions adopted for some nebulae were not as accurate as had been assumed. The anomalously low 6 cm flux for IC418 in particular is now believed to be due to this cause, and can be disregarded.

Observations have been made of 5 planetary nebulae at 1407 and 408 MHz with beam widths of 23′′ of arc and 80′′ of arc respectively. Measurements of positions, fluxes and angular structure have been obtained; some results are presented in the form of contour maps.

Sixty-eight planetary nebulae have been investigated in a series of observations at 10-cm wavelength using the two 90-ft diameter antennas of the Owens Valley Radio Observatory. Of these, 52 were found to have flux densities greater than a minimum detectable level of approximately 10–27 Wm–2 Hz–1. To indicate cases of possible confusion in the radio observations, the measured radio position of each nebula was compared with an accurate optical position. For a number of the stronger nebulae angular widths in the East–West direction and flux densities at 21 cm were also measured. The results lead to the conclusion that the radio emission is thermal, and on this basis the expected flux densities in Hβ have been calculated. A comparison with optical data shows values of the Hβ extinction Δ log FHβ, ranging from zero to approximately 2·0 for NGC 6537 and NGC 6369.

A small number of nebulae show prominently the effects of self-absorption in their radio spectra. For two of these, IC 418 and NGC 6572, an attempt has been made to derive accurate optical depths and electron temperatures using models based on Balmer-line isophotes. The temperature values have large uncertainties, but appear to be less than the values derived from forbidden-line ratios by a factor of at least 1·5. A possible explanation of this difference in terms of temperature variations within the nebulae is discussed.

Preliminary results of observations to detect absorption features at the wavelength of the 21-cm hydrogen line are described for 6 nebulae with high radio-flux densities. Two nebulae, NGC 6369 and NGC 6857 show absorption which is probably attributable to hydrogen clouds within the galaxy. No definite evidence of absorption at frequencies near the radial velocities of the nebulae was found, and an upper limit on the mass of neutral hydrogen in two nebulae is briefly discussed.

The following processes have to be considered.

1. (a) Radiative capture,

   The number of captures on the level i of the atom X, per unit volume per unit time, is NeN(X+)αi(Te), where the recombination coefficient αi (cm3 sec−1) may be expressed in terms of the cross-section for photo-ionization from level i.

2. (b) Cascade,

   The coefficients α(c)i and αi′i are defined to be such that NeN(X+) α(c)i is the number of atoms entering i due to capture and cascade, and that NeN(X+) αi′i is the number of photons emitted in the i′→ i line.

3. (c) Collisional transitions between excited states, including: collisional redistribution of angular momentum; collisional redistribution of energy between highly excited states; and collision processes which depopulate metastable states.

4. (d) Effects of radiative transfer. The following limiting cases have been considered:

   • Case A: Nebulae optically thin in all spectrum lines.

   • Case B: Nebulae optically thick for transitions to the ground state.

   • Case C: As Case B, but with absorption of stellar quanta in transitions from the ground state, assuming the central star to radiate as a black body.

New calculations of collision strengths are being made for ions in configurations npq, n = 2 and 3 and q = 1–5. Wave functions for the entire system are represented by sums over anti-symmetrized products of ion functions and orbitals for the colliding electron, and sets of coupled integro-differential equations are obtained for the colliding electron radial functions. The main approximation is neglect of coupling to configurations other than npq. Calculations are made using improved forms of the exact resonance and distorted wave approximations. For the 2pq ions it is found that the dominant contributions come from the p-waves; the exact resonance approximation is used for the p-waves and the distorted wave approximation is used for all other partial waves. It is considered that the results obtained should approximate closely to those which would be obtained from full solutions of the coupled equations. For the 3pq ions the dominant contributions come from the p-waves; for these ions the distorted wave approximation is used for all partial waves.

A compilation is given of transition probabilities of forbidden lines which occur in the spectra of gaseous nebulae.

Depuis peu, on témoigne un grand intérêt aux régions nébulaires, suscité par la découverte des raies d'émission de radiofréquence dues aux transitions entre niveaux atomiques fortement excités. Etant donné que la fréquence v de ces raies est telle que hv/kT ≪1, il est évident qu'il faut tenir compte de l'émission stimulée. Mais, comme a remarqué Goldberg (1966), ceci s'avère difficile en raison de la grande sensibilité de l'émission stimulée aux écarts à l'équilibre thermodynamique. Par exemple, considérons le facteur de correction pour l'émission stimulée oò bn est l'écart à l'équilibre thermodynamique du niveau n, v est la fréquence de la raie émise par la transition n → n'. Dans les conditions typiques d'une région nébulaire, l'hypothèse que l'on puisse remplacer bn/bn' par l'unité est loin d'être justifiée. Il nous a donc semblé intéressant d'étudier la variation de la quantité dbn/dn avec la densité et avec n.

From theoretical treatments of the physical processes in planetary nebulae, the average physical conditions in these objects are known with some certainty. However, the physical parameters of the individual nebulae have not been determined exactly. This may be due to the different methods used for determining these quantities, and to the inhomogeneous data available. Therefore, it seems to be of great importance to obtain individual physical parameters for a large number of planetaries in a homogeneous system.

Knowledge of the interstellar extinction is of great importance for the study of the properties of planetary nebulae. An estimate of the interstellar reddening for an individual nebula may be obtained by means of three independent methods. In the first method the observed Balmer decrement is compared with the theoretical decrement (case B of Baker and Menzel). The second method consists of a comparison of the observed ratio of Balmer and Paschen intensities of lines, arising from a common upper level, with the theoretically predicted ratio. Finally, for thermal planetary nebulae with well-determined radio spectra, the optically thin part of their spectra can be used for a determination of interstellar reddening. Comparison of the radio flux from an optically thin nebula with the observed Hβ flux (in absolute units) allows us to evaluate the amount of extinction. Radio observations may thus give the interstellar extinction with high accuracy. It may especially be noted that the Balmer-decrement method, which is widely applied, gives satisfactory accuracy only if highly accurate H-line intensities are used. In all other cases it gives the most uncertain results, since its wavelength base-line is small. One must also take into account the fact that the Hα-line intensity is often not measured.

Following the well-known physical theory of recombination and forbidden-line emission, we have carried out calculations which may be useful for a quantitative analysis of the observations of planetary nebulae and other emission objects (diffuse nebulae, emission details in extragalactic nebulae, symbiotic and flare stars). As the result, we have a set of four types of graphs.

The physical aspects of radiative transfer processes that may be of importance in planetary nebulae are discussed, and recent work on these problems is summarized.

The average Ly-α radiation densities are calculated for 9 planetary nebulae from the observed λ 10830/λ5876 line-intensity ratios under the assumption that the 23S state of He I is depopulated via photo-ionization by Ly-α radiation. Three of the nebulae are probably optically thick in their respective hydrogen Lyman continua. For these objects, the Ly-α radiation densities as determined from the λ10830/λ5876 line-intensity ratios may represent the actual Ly-α radiation densities. If they do, then the Ly-α radiation pressures exceed the respective gas pressures in these objects. For the remaining nebulae, it seems that the observationally determined Ly-α radiation densities are representative only if either one or both of the following conditions is fulfilled in each case:

1. (1) The object is essentially optically thick in the hydrogen Lyman continuum when other properties show it to be optically thin in the hydrogen Lyman continuum.

2. (2) We are viewing the object during a specific 100-year time span during the course of its evolution.

The ionization of the most abundant elements in planetary nebulae has been determined for a number of models of nebulae at different epochs in their expansion. The values used for the temperatures and radii of the central stars and the sizes and densities of the shells have come from Seaton's evolutionary sequence. The ionizing radiation field has been taken from model atmosphere calculations of the central stars by Gebbie and Seaton, and Böhm and Deinzer. Emission-line fluxes have been calculated for the models and compared with observations of planetary nebulae by O'Dell, Osterbrock's group, and Aller and his collaborators. Results indicate that the central stars have strong He+ Lyman continuum excesses, similar to those predicted by Gebbie and Seaton. The mean abundance determinations for the nebulae made by Aller are confirmed, with the exception of nitrogen, which appears to be 3 or 4 times more abundant than his value. It is also seen that the electron temperatures of the nebulae are higher than previous theoretical determinations, providing better agreement with empirically derived values.

Calculations are being made of the distribution of the ions of heavy elements in planetary nebulae. Initial work has been concentrated on the central or He2+ zone of planetaries. The optical depths of ions of C, N, O, and Ne have been computed using ground state ionisation cross-sections and using approximations which should be substantially better than hydrogenic. A comparison has been made between the combined optical depth of the heavy elements and the optical depth of He+ in the far ultraviolet. The optical depths of the heavy elements in this spectral region may become significant, but a reasonable first approximation to the radiation field may be obtained by neglecting the absorption of all ions except He+. The distribution of the ions of the heavy elements has been calculated on this assumption.

The problem of the determination of the chemical compositions of planetary and other gaseous nebulae constitutes one of the most exasperating problems in astrophysics. On the one hand, the problem appears to be conceptually simple – the mechanisms of excitation of the various lines appear to be well understood and the necessary physical parameters can be obtained by quantum mechanical theory. Yet the task is a difficult one and we want to explore some of the significant features.

There are two approaches to the problem of the dynamics of planetary nebulae. The first is based on the investigation of the velocity fields in the nebulae. The second can be carried out by studying the spatial distribution of the matter in these objects. In an ideal case both approaches can be united. However, data on the velocity fields in planetary nebulae still are very scarce and fragmentary and their rate of accumulation is rather slow.

The expansion of a typical planetary nebula is studied by means of a simple model, with spherical symmetry. It is shown that there is a build-up of radiation pressure, due to Lyman-α photons trapped in the nebula, and that this causes the initial acceleration outwards. After some 1·5 × 1011 sec the nebula will have a radius of the order of 1017 cm, and an expansion velocity of about 2 × 106 cm/sec. At roughly this time the dynamical effects of radiation pressure begin to be superseded by those of the recoil pressure at the ionization front, which continues to dominate until the nebula is fully ionized.

Finally some reasons are considered why most nebulae do not have spherically symmetrical shapes, but why so often they appear to be ring-like or butterfly-shaped.