Vibrational stability of stars in thermal imbalance: A solution in terms of asymptotic expansions

The solution of the partial differential equation describing the ‘non-isentropic’ oscillations of a star in thermal imbalance has been obtained in terms of asymptotic expansions up to the first order in the parameterII/t _s, whereII is the adiabatic pulsation period for the fundamental mode andt _s , a secular time scale of the order of the Kelvin-Helmholtz time. Use has been made of the zeroth order ‘isentopic’ solution derived in I. The solution obtained allows one to derive unambiguously a general integral expression for the coefficient of vibrational stability for arbitrary stellar models in thermal imbalance. The physical interpretation of this stability coefficient is discussed and its generality and its simplicity are stressed. Application to some simple analytic stellar models in homologous and nonhomologous contraction enables one to recover, in a more straightforward manner, results obtained by Coxet al. (1973). Aizenman and Cox (1974) and Davey (1974). Finally, we emphasize that the inclusion of the effects of thermal imbalance in the stability calculations of realistic evolutionary sequences of stellar models, not considered up to now by the other authors, is quite easy and straightforward with the simple formula derived here.     

Large-scale ionization fronts and the nature and distribution of light scattering particles in the orion nebula

Image-tube filter photographs calibrated against photoelectric filter photometry have been used to give maps of M42 in absolute flux units over the central 15 arc min of the nebula in Hα, [Nii] (λ 6584 Å), Hβ and continuum at λ 4700 Å. Maps of the ratios Hα/[Nii] and (for the first time) of continuum/Hβ have been produced with unprecedented spatial resolution. These show that the gas to dust ratio is high near the exciting stars and falls strongly in the vicinity of large scale ionization fronts marked by minima in the Hα/[Nii] ratio. These results are interpreted in terms of detailed shell models containing either ice or graphite or silicate scattering particles. In all models there must be a central hole in the distribution of scattering particles. The effect of neutral globules and intrusions is investigated. It is found that all types of grain are trapped inside neutral intrusions near the centre of the nebula by the pressure of the Lα light surrounding the globule, but in the early evolution of the nebula particles can escape into the ionized medium when fronts are R-type. Ice grains escaping at this time will be destroyed for distances to the exciting stars less than 1 pc. These results can explain both the central hole in dust and the underabundance of oxygen in the ionized gas observed earlier. Arguments depending on colour index of the scattered light indicate that mixtures of scattered light from ice in the globules and from ice in the ionized medium can explain the observations, but that the graphite and silicate particles fail. A schematic model of the Orion Nebula is presented to attempt to explain the large scale phenomena observed here. It demonstrates that simple shell models for this nebula are dubious.     

The spectral reflectivity of select areas on Europa

The July 12, 1973, occultation of Europa by Io was observed in 30 wavelength channels in the spectral region λλ3200-11, 000 Å with the 200-inch Hale telescope and a multichannel spectrometer. The data are presented in absolute units above the Earth's atmosphere. The data are analyzed to obtain the spectral reflectivity of seven localized areas on the disk of Europa centered on 324°W longitude. The equatorial material is confirmed to be darker than the eastward-skewed bright north polar cap and a hint is evident that the darker material as well may be somewhat redder than the cap material.     

Observations of Venus water vapor over the disk of Venus: The 1972–1974 data using the H2O lines at 8197 Å and 8176 Å

The Venus water vapor line at 8197.71 Å has been monitored at several positions on the disk of Venus and at phase angles between 21° and 162°. Variations in the abundance have been found with spatial location, phase angle and time. During the 1972–1974 period, the total two-way absorption has varied from less than 1 to 77 μm of water vapor. The dependence on phase angle indicates 20 to 50 μm over the disk between 30° and 110° and small, but detectable amounts present during the rest of the observations. The spatial distribution with respect to the intensity equator is uniform with no location on the disk having systematically a higher or lower abundance. Comparisons made between the water vapor abundandances and the CO₂ abundances determined from near-simultaneous observations of CO₂ bands at the same positions on the disk of Venus show no correlation for the majority of the samples.     

The atmosphere of Io from Pioneer 10 radio occultation measurements

The occultation of the Pioneer 10 spacecraft by Io (JI) provided an opportunity to obtain two S-band radio occultation measurements of its atmosphere. The dayside entry measurements revealed an ionosphere having a peak density of about 6 × 10⁴ elcm^?3 at an altitude of about 100 km. The topside scale height indicates a plasma temperature of about 406 K if it is composed of Na⁺ and 495 K if N₂⁺ is principal ion. A thinner and less dense ionosphere was observed on the exit (night side), having a peak density of 9 × 10³ elcm^?3 at an altitude of 50 km. The topside plasma temperature is 160 K for N₂^? and 131 K for Na⁺. If the ionosphere is produced by photoionization in a manner analogous to the ionospheres of the terrestrial planets, the density of neutral particles at the surface of Io is less than 10¹¹?10¹² cm³, corresponding to a surface pressure of less than 10^?8 to 10^?9 bars. Two measurements of its radius were also obtained yielding a value of 1830 km for the entry and 192 km for the exit. The discrepancy between these values may indicate an ephemeris uncertainty of about 45 km. The two measurements yield an average radius of 1875 km, which is not in agreement with the results of the Beta Scorpii stellar occultation.     

Galactic magnetic fields and their interactions with the gas and cosmic rays

(i) The controversy of dynamo or primordial origin of galactic magnetic fields is summarized and extended to show that the dynamo theory appears to fail. However, much more important than their origin are the characteristics of the fields and their interactions with the gas and cosmic rays. (ii) A passive magnetic field frozen into a turbulent plasma is not dissipated like a cloud of smoke (turbulent or eddy diffusion) as believed previously. On the contrary it is amplified exponentially until, within a few eddy periods, either the growing magnetic stresses halt the turbulence or the field becomes chaotic. Even if the Petschek reconnection mechanism operates, the field is always disordered to a scale <0.1L, whereL is the eddy dimension. The investigation may at last provide a semi-quantitative deductive theory of hydromagnetic eddies. (iii) It is concluded that the gas motions observed in our Galaxy are not convective but are mainly hydromagnetic waves or oscillations, with the magnetic field in control. The significance of this result is discussed in connection with the overall gas velocity field, the creation of stars and stellar systems, and with the origin and distribution of cosmic rays.     

On the origin of the metagalaxy

An attempt is made to explain two properties of the metagalaxy: its expansion and the absence of causal connection of its distant regions during a large part of its initial history. It is postulated that the gravitating matter was born from the cosmological field, i.e., a medium with equation of statep=–.It is shown that such a postulate explains the expansion of metagalaxy and leads to a correct estimate of the entropy per baryon. The problem of causal connection can also be solved on this basis.     

The absorption of soft X-rays from the Crab nebula

The X-ray spectrum of the Crab nebula has been determined in the energy range 0.5 10 keV using thin window proportional counters carried aboard a Centaur IIA rocket launched from TERLS, India. The spectrum can be well represented by a power law with an exponent?2.1 beyond 2 keV. The absorption of the soft X-ray component below 2 keV is clearly seen in the experiment. Attempts to understand quantitatively the spectral features in terms of interstellar absorption lead to a column density of hydrogen in the iirection of the Crab nebula of 3.5×10²¹ H atoms cm^?2, if we adopt a revised version of the interstellar absorption coefficients of Brown and Gould to include the contributions of heavier elements, especially of iron. This value of density is a factor of 2 higher than the density obtained from 21 cm radio observations, but falls well within the range of values for atomic and total hydrogen deducible from UV measurements with satellites and the measured visual extinction coefficients for the Crab nebula. It is concluded that it is not necessary to consider anomalous abundance of elements like carbon or neon either in the source or in the interstellar medium as suggested by some authors. The absorption of X-rays in the interstellar dust in the light of current dust models is presented.     

The quadratic Zeeman effect in the Caii H and K lines

The effects of a large magnetic field on the H and K lines of Caii are investigated incorporating both the linear and quadratic Zeeman effects for fields in the range 10⁶–10⁸ G. For these fields the linear term is the dominant one, resulting in a Paschen-Back effect with a smaller quadratic Zeeman shift superimposed on all components. Due to the partial cancellation of the quadratic effect between the upper and lower states of the lines, a much smaller quadratic Zeeman shift occurs than in the lines of other atoms previously studied at similar fields.