On the velocity of jets powering hot spots similar to those in Cygnus A

Hot spots similar to those in the radio galaxy Cygnus A can be explained by the strong shock produced by a supersonic but classical jet \(\left( {u_{jet}< c/\sqrt 3 } \right)\) . The high integrated radio luminosity (L?2×10⁴⁴ erg s^?1) and the strength of mean magnetic field (B?2×10^?4 G) suggest the hot spots are the downstream flow of a very strong shock which generates the ultrarelativistic electrons of energy ?≥20 MeV. The fully-developed subsonic turbulence amplifies the magnetic field of the jet up to 1.6×10^?4 G by the dynamo effect. If we assume that the post-shock pressure is dominated by relativistic particles, the ratio between the magnetic energy density to the energy density in relativistic particles is found to be ?2×10^?2, showing that the generally accepted hypothesis of equipartition is not valid for hot spots. The current analysis allows the determination of physical parameters inside hot spots. It is found that:

1. The velocity of the upstream flow in the frame of reference of the shock isu ₁?0.2c. Radio observations indicate that the velocity of separation of hot spots isu _sep?0.05c, so that the velocity of the jet isu _jet=u ₁+u _sep?0.25c.
2. The density of the thermal electrons inside the hot spot isn ₂?5×10^?3 e ^? cm^?3 and the mass ejected per year to power the hot spot is ?4M ₀yr^?1.
3. The relativistic electron density is less than 20% of the thermal electron density inside the hot spot and the spectrum is a power law which continues to energies as low as 30 MeV.
4. The energy density of relativistic protons is lower than the energy density of relativistic electrons unlike the situation for cosmic rays in the Galaxy.

     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Observations of the Orion Nebula in Hα, [NII] and Hβ lines

Monochromatic photographs of the Orion Nebula taken through narrow bandpass interference filters (Δλ=10 Å) centred on Hα, Hβ and [NII] lines are presented. Ratio contours of Hα/[NII] and Hα/Hβ are derived. They enable a detailed study of the point-to-point variation in ionization structure and temperature throughout the nebula. Dust located within the ionized gas is studied from the Hα/Hβ ratio which varies from point to point over the nebula. Its strongest concentration, apart in the obvious ‘dark bay’, occurs in a shell surrounding the exciting stars, with about 2′ of diameter. Close to Θ¹ Ori the Hα/Hβ ratio, corrected for interstellar reddening, is about 3.0 in good agreement with the predicted value (Brocklehurst, 1971). To account for these measures, the following arguments are proposed:

1. Dust grains are completely or partially destroyed in region close to the exciting stars.
2. Radiation pressure and stellar wind push the remaining dust up to some equilibrium distance outwards. The consequence of this action is obviously the formation of a ‘dust mantle’ which is seen as a ring in projection.

     

Exotic ion H 3 ++ in strong magnetic fields

1. The exotic system H ₃ ⁺⁺ (which does not exist without magnetic field) exists in strong magnetic fields:
   1. In triangular configuration for B≈10⁸–10¹¹?G (under specific external conditions)
   2. In linear configuration for B>10¹⁰?G
2. In the linear configuration the positive z-parity states 1σ _g , 1π _u , 1δ _g are bound states
3. In the linear configuration the negative z-parity states 1σ _u , 1π _g , 1δ _u are repulsive states
4. The H ₃ ⁺⁺ molecular ion is the most bound one-electron system made from protons at B>3×10¹³?G

Possible application: The H ₃ ⁺⁺ molecular ion may appear as a component of a neutron star atmosphere under a strong surface magnetic field B=10¹²–10¹³?G.     

A varying cosmological term as a link between cosmology and microphysics

The Weinberg relation (which connects the Hubble constantH to the mass of a typical elementary particle) is an empirical relation hitherto unexplained. I suggest an explanation based on the Zel'dovich energy tensor of vacuum in a Robertson-Walker universe with constant deceleration parameter,q = const. This model leads to

1. the Weinberg relation,
2. a varying cosmological term Λ scaling asH ²,
3. a varying gravitational constantG scaling asH,
4. a matter creation process throughout the universe at the rate 10^?47 g s^?1 cm³,
5. a deceleration parameter in the range -1 to 1/2, which allows a horizon-free universe and makes the lawG/H = constant, consistent with the Viking lander data on the orbit of planet Mars.

     

3C 120 and the surrounding region of sky

Image processing performed on a series of photographs of the superluminal Seyfert galaxy, 3C 120, shows the outer optical disc to consist of fragmented segments generally pointing toward the centre. One long arm of peculiar, separated knots comes off to the W and SW. A peculiar companion is seen along the line of the NW radio jet. In the interior, optical jets are detected which are aligned along the direction of the outer radio jets. A region of the sky 45 ×; 25 degrees around 3C120 is investigated. It is found that:

1. A nebulous filament about 3/4 degree in length points to 3C 120.
2. Hydrogen clouds of redshiftz = ?130 and ?210 km s^?1 are situated at 3 and 1 degrees on either side of 3C 120.
3. Eleven low-surface-brightness galaxies with 4500 <z < 5300 km s^?1 fall within a radius of 8 degrees.
4. Seven quasars withz ? 1.35 and radio fluxesS _b ? 0.3 fall within a radius of 10 degrees.

It is concluded that the concentration of these objects in the vicinity of this unique, active galaxy has a negligible chance of being accidental and that all those objects of diverse redshift are at the same nearby distance. This smaller distance reduces the supposed superluminal motions in 3C 120 to quite precedented ejection velocities.     

Problems of matter-antimatter boundary layers

This paper outlines the problems of the quasi-steady matter-antimatter boundary layers discussed in Klein-Alfvén's cosmological theory, and a crude model of the corresponding ambiplasma balance is presented:

1. At interstellar particle densities, no well-defined boundary layer can exist in presence of neutral gas, nor can such a layer be sustained in an unmagnetized fully ionized ambiplasma.
2. Within the limits of applicability of the present model, sharply defined boundary layers are under certain conditions found to exist in a magnetized ambiplasma. Thus, at beta values less than unity, a steep pressure drop of the low-energy components of matter and antimatter can be balanced by a magnetic field and the electric currents in the ambiplasma.
3. The boundary layer thickness is of the order of 2x ₀?10/BT ₀ ^1/4 metres, whereB is the magnetic field strength in MKS units andT ₀ the characteristic temperature of the low-energy components in the layer.

     

Gamma radiation and photospheric white-light flare continuum

Recent gamma-ray observations of solar flares have provided a better means for estimating the heating of the solar atmosphere by energetic protons. Such heating has been suggested as the explanation of the continuum emission of the white-light flare. We have analyzed the effects on the photosphere of high-energy particles capable of producing the intense gamma-ray emission observed in the 1978 July 11 flare. Using a simple energy-balance argument and taking into account hydrogen ionization, we have obtained the following conclusions:

1. Heating near τ₅₀₀₀ = 1 in the input HSRA model atmosphere is negligible, even for very high fluxes of energetic particles.
2. Energy deposition increases with height for the inferred proton spectra, and does not depend strongly upon the assumed angle of incidence. The computed energy inputs fall in the range 10–100 ergs (cm³ s)^?1 at the top of the photosphere.
3. H^? continuum dominates for column densities as small as 10²² cm^?3, but at greater heights hydrogen ionizes sufficiently for the higher continua to dominate the energy balance.
4. The total energy deposited in the ‘photospheric’ region of H^? dominance could be within a factor of 3 of the necessary energy deposition, by comparison with the white-light flare of 1972 August 7, but the emergent spectrum is quite red so that the intensity excess in the visible band is insufficient to explain the observations.

In summary, it remains energetically possible, within observational limits, that high-energy protons could cause sufficient heating of the upper photosphere to produce detectable excess continuum, but emission from the vicinity of τ = 1 is not significant.     

Flares and changing magnetic fields

An observational study of maps of the longitudinal component of the photospheric fields in flaring active regions leads to the following conclusions:

1. The broad-wing Hα kernels characteristic of the impulsive phase of flares occur within 10″ of neutral lines encircling features of isolated magnetic polarity (‘satellite sunspots’).
2. Photospheric field changes intimately associated with several importance 1 flares and one importance 2B flare are confined to satellite sunspots, which are small (10″ diam). They often correspond to spot pores in white-light photographs.
3. The field at these features appears to strengthen in the half hour just before the flares. During the flares the growth is reversed, the field drops and then recovers to its previous level.
4. The magnetic flux through flare-associated features changes by about 4 × 10¹⁹ Mx in a day. The features are the same as the ‘Structures Magnétiques Evolutives’ of Martres et al. (1968a).
5. An upper limit of 10²¹ Mx is set for the total flux change through McMath Regions 10381 and 10385 as the result of the 2B flare of 24 October, 1969.
6. Large spots in the regions investigated did not evince flux changes or large proper motions at flare time.
7. The results are taken to imply that the initial instability of a flare occurs at a neutral point, but the magnetic energy lost cannot yet be related to the total energy of the subsequent flare.
8. No unusual velocities are observed in the photosphere at flare time.

     

Microwave emission above steady and moving sunspots

Two-dimensional maps of radio brightness temperature and polarization, computed assuming thermal emission with free-free and gyroresonance absorption, are compared with observations of active region 2502, performed at Westerbork at λ = 6.16 cm during a period of 3 days in June 1980. The computation is done assuming a homogeneous model in the whole field of view (5′ × 5′) and a force-free extrapolation of the photospheric magnetic field observed at MSFC with a resolution of 2″.34. The mean results are the following:

1. A very good agreement is found above the large leading sunspot of the group, assuming a potential extrapolation of the magnetic field and a constant conductive flux in the transition region ranging from 2 × 10⁶ to 10⁷ erg cm^?2s^?1.
2. A strong radio source, associated with a new-born moving sunspot, cannot be ascribed to thermal emission. It is suggested that this source may be due to synchrotron radiation by mildly relativistic electrons accelerated by resistive instabilities occurring in the evolving magnetic configuration. An order-of-magnitude computation of the expected number of accelerated particles seems to confirm this hypothesis.

     

On the Hβ, [OIII] lines and continuum variability character in the nucleus of Seyfert galaxy NGC 1275

The radiation fluxes of the NGC 1275 galaxy central region are being observed on the 1.25-m telescope, using a scanning spectrophotometer with the entrance aperture 10″ in three Δλ=80 Å spectral regions: Hβ, 4959+5007 Å [OIII] and continuum. There were 35 nights of observations during 1982–1987. With the time resolution of half an hour 379 measurements were obtained in each spectral region. The analysis of these results shows:

1. The standard deviations of measurements in each spectral region 2–3 times exceed the errors of observations.
2. The radiation flux distribution resembles to normal one only for Hβ line.
3. Two-humps forms of continuum flux distribution curve is like that of radio emission in 8 mm and 2.6 cm wavelengths.
4. Various forms of fluxes distribution curves of Hβ and [OIII] lines permit us to suppose that the location of these lines emission regions near the sources of excitation are different.

     

Starbursts at space ultraviolet wavelengths

Starbursts are systems with very high star formation rate per unit area. They are the preferred place where massive stars form; the main source of thermal and mechanical heating in the interstellar medium, and the factory where the heavy elements form. Thus, starbursts play an important role in the origin and evolution of galaxies. The similarities between the physical properties of local starbursts and high-z star-forming galaxies, highlight the cosmological relevance of starbursts. On the other hand, nearby starbursts are laboratories where to study violent star formation processes and their interaction with the interstellar and intergalactic media, in detail and deeply. Starbursts are bright at ultraviolet (UV) wavelengths, as they are in the far-infrared, due to the ‘picket-fence’ interstellar dust distribution. After the pioneering IUE program, high spatial and spectral resolution UV observations of local starburst galaxies, mainly taken with HST and FUSE, have made relevant contributions to the following issues:

The determination of the initial mass function (IMF) in violent star forming systems in low and high metallicity environments, and in dense (e.g. in stellar clusters) and diffuse environments: A Salpeter IMF with high-mass stars constrains well the UV properties.

The modes of star formation: Starburst clusters are an important mode of star formation. Super-stellar clusters have properties similar to globular clusters.

The role of starbursts in AGN: Nuclear starbursts can dominate the UV light in Seyfert 2 galaxies, having bolometric luminosities similar to the estimated bolometric luminosities of the obscured AGN.

The interaction between massive stars and the interstellar and intergalactic media: Outflows in cold, warm and coronal phases leave their imprints on the UV interstellar lines. Outflows of a few hundred km s^?1 are ubiquitous phenomena in starbursts. These metal-rich outflows and the ionizing radiation can travel to the halo of galaxies and reach the intergalactic medium.

The contribution of starbursts to the reionization of the universe: In the local universe, the fraction of ionizing photons that escape from galaxies and reach the intergalactic medium is of a few percent. However, in high-z star-forming galaxies, the results are more controversial.

Despite the very significant progress over the past two decades in our understanding of the starburst phenomenon through the study of the physical processes revealed at satellite UV wavelengths, there are important problems that still need to be solved. High-spatial resolution UV observations of nearby starbursts are crucial to further progress in understanding the violent star formation processes in galaxies, the interaction between the stellar clusters and the interstellar medium, and the variation of the IMF. High-spatial resolution spectra are also needed to isolate the light from the center to the disk in UV luminous galaxies at z = 0.1–0.3 found by GALEX. Thus, a new UV mission furnished with an intermediate spectral resolution long-slit spectrograph with high spatial resolution and high UV sensitivity is required to further progress in the study of starburst galaxies and their impact on the evolution of galaxies.     

Observation of the impulsive phase of a simple flare

We present a broad range of complementary observations of the onset and impulsive phase of a fairly large (1B, M1.2) but simple two-ribbon flare. The observations consist of hard X-ray flux measured by the SMM HXRBS, high-sensitivity measurements of microwave flux at 22 GHz from Itapetinga Radio Observatory, sequences of spectroheliograms in UV emission lines from Ov (T ≈ 2 × 10⁵ K) and Fexxi (T ≈ 1 × 10⁷ K) from the SMM UVSP, Hα and Hei D₃ cine-filtergrams from Big Bear Solar Observatory, and a magnetogram of the flare region from the MSFC Solar Observatory. From these data we conclude:

1. The overall magnetic field configuration in which the flare occurred was a fairly simple, closed arch containing nonpotential substructure.
2. The flare occurred spontaneously within the arch; it was not triggered by emerging magnetic flux.
3. The impulsive energy release occurred in two major spikes. The second spike took place within the flare arch heated in the first spike, but was concentrated on a different subset of field lines. The ratio of Ov emission to hard X-ray emission decreased by at least a factor of 2 from the first spike to the second, probably because the plasma density in the flare arch had increased by chromospheric evaporation.
4. The impulsive energy release most likely occurred in the upper part of the arch; it had three immediate products:

1. An increase in the plasma pressure throughout the flare arch of at least a factor of 10. This is required because the Fexxi emission was confined to the feet of the flare arch for at least the first minute of the impulsive phase.
2. Nonthermal energetic (～ 25 keV) electrons which impacted the feet of the arch to produce the hard X-ray burst and impulsive brightening in Ov and D₃. The evidence for this is the simultaneity, within ± 2 s, of the peak Ov and hard X-ray emissions.
3. Another population of high-energy (～100keV) electrons (decoupled from the population that produced the hard X-rays) that produced the impulsive microwave emission at 22 GHz. This conclusion is drawn because the microwave peak was 6 ± 3 s later than the hard X-ray peak.

     

Large scale circulation in the convection zone and solar differential rotation

In this paper we study the dependence on depth and latitude of the solar angular velocity produced by a meridian circulation in the convection zone, assuming that the main mechanism responsible for setting up and driving the circulation is the interaction of rotation with convection. We solve the first order equations (perturbation of the spherically symmetric state) in the Boussinesq approximation and in the steady state for the axissymmetric case. The interaction of convection with rotation is modelled by a convective transport coefficient k _c = k _co + ?k _c2 P ₂(cos θ) where ? is the expansion parameter, P ₂ is the 2nd Legendre polynomial and k _c2 is taken proportional to the local Taylor number and the ratio of the convective to the total fluxes. We obtain the following results for a Rayleigh number 10³ and for a Prandtl number 1:

1. A single cell circulation extending from poles to the equator and with circulation directed toward the equator at the surface. Radial velocities are of the order of 10 cm s^?1 and meridional ones of the order of 150 cm s^?1.
2. A flux difference between pole and equator at the surface of about 5 percent, the poles being hotter.
3. An angular velocity increasing inwards.
4. Angular velocity constant surfaces of spheroidal shape. The model is consistent with the fact that the interaction of convection with rotation sets up a circulation (driven by the temperature gradient) which carries angular momentum toward the equator against the viscous friction. Unfortunately also a large flux variation at the surface is obtained. Nevertheless it seems that the model has the basic requisites for correct dynamo action.

     

Dwarf elliptical galaxies

Dwarf elliptical (dE) galaxies, with blue absolute magnitudes typically fainter than _MB =?16, are the most numerous type of galaxy in the nearby universe. Tremendous advances have been made over the past several years in delineating the properties of both Local Group satellite dE's and the large dE populations of nearby clusters. We review some of these advances, with particular attention to how well currently available data can constrain

1. models for the formation of dE's
2. the physical and evolutionary connections between different types of galaxies (nucleated and nonnucleated dE's, compact E's, irregulars, and blue compact dwarfs) that overlap in the same portion of the mass-spectrum of galaxies
3. the contribution of dE's to the galaxy luminosity functions in clusters and the field
4. the star-forming histories of dE's and their possible contribution to faint galaxy counts, and
5. the clustering properties of dE's.

In addressing these issues, we highlight the extent to which selection effects temper these constraints, and outline areas where new data would be particularly valuable.     

Orbital eccentricity study for the spherical component of our galaxy

An analysis of the data concerning high-velocity stars from Eggen's catalogue aimed at a determination of the approximate slope of the mass function for the spherical component of our Galaxy, and at estimating the local circular velocity, as well as the local rotation velocity, as by-products, has been performed. Our conclusions are that:

1. A linear dependence of the mass on the radius is very likely;
2. the value of the limiting radius is most likely equal to (40±10) kpc;
3. the two local velocities are approximately equal to each other, being both equal to (230±30) km s^?1;
4. the local escape velocity appears to be most likely equal to (520±30) km s^?1;
5. the total mass of a corona, obtained in this way, is (5±1)×10¹¹ M _⊙.

     

Magnetic field versus gas density,in different physical conditions

A search is made here for possible variations in the behavior of magnetic field valuesB at various gas density valuesn, when comparing low density gas versus high density gas, and when comparing compressed gas versus quiescent gas.

1. For thequiescent microturbulent interstellar gas (e.g., clouds, interclumps — see TableI), the statistical relationB ~n ^k yieldsk = 0.46 ± 0.07 forhigh gas densityn > 100 cm^?3, andk = 0.17 ± 0.03 forlow gas densityn < 100 cm^?3 (see Figure 1).
2. For thecompressed macroturbulent interstellar gas (e.g., masers, expanding shells — see Table II), the statistical relationB ~n ^K yieldsK = 0.61 ± 0.09 forhigh gas densityn > 100 cm^?3, andK = 0.37 ± 0.2 forlow gas densityn < 100 cm^?3 (see Figure 2).
3. The separation betweenlow density gas andhigh density gas is statistically significant. The 2 different physical behaviors (below and above the break at 100 cm^?3) are confirmed statistically (about 2 to 4 sigma away for the quiescent gas alone; about 3 to 6 sigma away for the combined quiescent plus compressed gas).
4. The separation betweencompressed gas andquiescent gas is not statistically significant now (see Figure 3). Atn > 100 cm^?3, a comparison of quiescent gas versus compressed gas shows no statistically significant differences in behavior (they are only about 1 sigma away). Atn < 100 cm^?3, a comparison of quiescent versus compressed gas also shows no statistically significant differences in behavior (less than 1 sigma away).
5. A relation between the densityn and the galactic-wide Star Formation Rate (SFR) can be made for galactic magnetic fields, i.e.: (SFR) ~n ⁿ . For galactic-wide parameters using quiescent, low densityn < 100 cm^?3, and the known relationshipsB ~n ^k/j withk = 0.17,B ~ (SFR) ^j withj = 0.13, then one gets here a lawSFR ~n ^k/j with an exponentk/j = 1.3. This is in rough accord with known data for the Milky Way and for NGC6946.

     

The Alfvén-wave theory of solar flares

Evidence is discussed showing that a representative solar flare event comprises three or more separate but related phenomena requiring separate mechanisms. In particular it is possible to separate the most energetic effect (the interplanetary blast) from the thermal flare and from the rapid acceleration of particles to high energies. The phenomena are related through the magnetic structure characteristic of a composite flare event, being a bipolar surface field with most of its field lines ‘closed’. Of primary importance are helical twists on all scales, starting with the ‘flux rope’ of the spot pair which was fully twisted before it emerged. Subsequent untwisting by the upward propagation of an Alfvén twist wave provides the main flare energy.

1. The interplanetary blast model is based on subsurface, helically twisted flux ropes which erupt to form spots and then transfer their twists and energy by Alfvén-twist waves into the atmospheric magnetic fields. The blast is triggered by the prior-commencing flash phase or by a coronal wave.
2. The thermal flare is explained in terms of Alfvén waves travelling up numerous ‘flux strands’ (Figure 3) which have frayed away from the two flux ropes. The waves originate in interaction (collisions, bending, twisting, rubbing) between subsurface flux strands; the sudden flash is caused by a collision. The classical twin-ribbon flare results from the collision of a flux rope with a tight bunch of S-shaped flux strands.
3. The impulsive acceleration of electrons (hard X-ray, EUV, Hα and radio bursts) is tentatively attributed to magnetic reconnection between fields in two parallel, helically twisted flux strands in the low corona.
4. Flare (Moreton) waves in the corona have the same origin as the interplanetary blast. Sympathetic flares represent only the start of enhanced activity in a flare event already in the slow phase. Filament activation also occurs during the slow phase as twist Alfvén waves store their energy in the atmosphere.
5. Flare ejecta are caused by Alfvén waves moving up flux strands. Surges are attributed to packets of twist Alfvén waves released into bundles of flux strands; the waves become non-linear and drive plasma upwards. Spray-type prominences result from accumulations of Alfvén wave energy in dome-shaped fields; excessive energy density eventually explodes the field.

     

On pulsar-driven isothermal blast-wave models of supernova remanants

We investigate the ‘equilibrium’ and stability of spherically-symmetric self-similar isothermal blast waves with a continuous post-shock flow velocity expanding into medium whose density varies asr ^?ω ahead of the blast wave, and which are powered by a central source (a pulsar) whose power output varies with time ast ^ω?3. We show that:

1. for ω<0, no physically acceptable self-similar solution exists;
2. for ω>3, no solution exists since the mass swept up by the blast wave is infinite;
3. ? must exceed zero in order that the blast wave expand with time, but ?<2 in order that the central source injects a finite total energy into the blast wave;
4. for 3>ω_min(?)>ω>ω_max(?)>0, where $$\begin{gathered} \omega _{\min } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} + {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} + {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \omega _{\max } (\varphi ){\text{ }} = {\text{ }}2[5{\text{ }} - {\text{ }}\varphi {\text{ }} - {\text{ }}(10{\text{ }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 )^{1/2} ]^2 [2{\text{ }} - {\text{ (10 }} + {\text{ 4}}\varphi {\text{ }} - {\text{ 2}}\varphi ^2 {\text{)}}^{{\text{1/2}}} ]^{ - 2} , \hfill \\ \end{gathered} $$ two critical points exist in the flow velocity versus position plane. The physically acceptable solution must pass through the origin with zero flow speed and through the blast wave. It must also pass throughboth critical points if \(\varphi > \tfrac{5}{3}\) , while if \(\varphi< \tfrac{5}{3}\) it must by-pass both critical points. It is shown that such a solution exists but a proper connection at the lower critical point (for ?>5/3) (through whichall solutions pass with thesame slope) has not been established;
5. for 3>ω>ω_min(?) it is shown that the two critical points of (iv) disappear. However a new pair of critical points form. The physically acceptable solution passing with zero flow velocity through the origin and also passing through the blast wave mustby-pass both of the new critical points. It is shown that the solution does indeed do so;
6. for 3>ω_min(?)>ω_max(?)>ω it is shown that the dependence of the self-similar solution on either ω or ? is non-analytic and therefore, inferences drawn from any solutions obtained in ω>ω_max(?) (where the dependence of the solutionis analytic on ω and ?) are not valid when carried over into the domain 3>ω_min(?)>ω_max(?)>ω;
7. all of the physically acceptable self-similar solutions obtained in 3>ω>0 are unstable to short wavelength, small amplitude but nonself-similar radial velocity perturbations near the origin, with a growth which is a power law in time;
8. the physical self-similar solutions are globally unstable in a fully nonlinear sense to radial time-dependent flow patterns. In the limit of long times, the nonlinear growth is a power law in time for 5<ω+2?, logarithmic in time for 5>ω+2?, and the square of the logarithm in time for 5=ω+2?.

The results of (vii) and (viii) imply that the memory of the system to initial and boundary values does not decay as time progresses and so the system does not tend to a self-similar form. These results strongly suggest that the evolution of supernova remnants is not according to the self-similar form.     

Spectral analysis of four quiescent prominences observed at the Peruvian eclipse

Two-dimensional distributions of kinetic temperature, density and turbulent velocity are obtained for four quiescent prominences observed at the Peruvian eclipse of 12 November, 1966.

1. The kinetic temperature derived from line widths is around 6000–7000 K in the central part of prominences and rises to 12000K in both edges and possibly in the top of prominences.
2. The turbulent velocity shows a similar tendency, being 7–9 km/sec in the central part and ≈ 20 km/sec in the outer part. The turbulent velocity also increases slowly towards higher heights in the prominence.
3. The electron density derived both from the Stark effect and the intensity ratio of the continuous spectra turns out to be about 10^10.2–10^10.6 cm^?3 in the central portion of two prominences.
4. From the width and the intensity, neutral helium lines are shown to originate in the same region as hydrogen and metallic lines where the kinetic temperature goes down to 6000 K. This indicates that neutral helium is emitted after the ionization due to UV radiation from the corona and the transition region.