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.

     

On 5694 Å coronal line observations

Coronal yellow line emission was observed by the Lyot coronagraph at the Abastumani Astrophysical Observatory. Line intensity is I = 45 erg cm^?2 s^?1 sr^?1 Å^?1, its half-width Δλ = 1.3 Å, electronconcentration n _e = 7.5 × 10⁹ cm^?3.     

Radiation loss and mechanical heating in the solar chromosphere

The raditation loss of the solar chromosphere is evaluated on the basis of the Harvard Smithsonian Reference Atmosphere. The total radiative flux is found to be between 2.5 and 3.3 E6 erg cm^?2 s^?1. A discussion of possible heating mechanisms shows that the short period acoustic wave theory is the only one able to balance the chromospheric radiation loss and is consistent with observation.     

On the heat flow of a gravitationally-differentiated moon of fission origin

It is shown that the mean value for the heat flow of a gravitationally-differentiated Moon of fission origin is about 13 erg cm^?2 s^?1 and that the heat flow varies regionally from about 3 erg cm^?2s^?1 to more than 45 erg cm^?2s^?1. These regional variations in the heat flow are caused by a non-uniform distribution of K, U and Th in the KREEP zone at the crust-upper mantle boundary and the redistribution of crustal materials and K, U and Th rich KREEP materials by basin-forming impacts. The scale of these regional variations is hundreds of km. The models presented are in accord with the Apollo 15 and 17 heat flow measurements.     

Analysis of the August 7, 1972 white light flare: Light curves and correlation with hard X-rays

Cinematic, photometric observations of the 3B flare of August 7, 1972 are described in detail. The time resolution was 2 s; the spatial resolution was 1–2″. Flare continuum emissivity at 4950 Å and at 5900 Å correlated closely in time with the 60–100 keV non-thermal X-ray burst intensity. The observed peak emissivity was 1.5 × 10¹⁰ erg cm^?2 s^?1 and the total flare energy in the 3900–6900 Å range was ～10³⁰ erg. From the close temporal correspondence and from the small distance (3″) separating the layers where the visible emission and the X-rays arose, it is argued that the hard X-ray source must have had the same silhouette as the white light flare and that the emission patches had cross-sections of 3–5″. There was also a correlation between the location of the most intense visible emissions near sunspots and the intensity and polarization of the 9.4 GHz radio emission. The flare appeared to show at least three distinct particle acceleration phases: one, occurring at a stationary source and associated with proton acceleration gave a very bluish continuum and reached peak intensity at ～ 1522 UT. At 1523 UT, a faint wave spread out at 40 km s^?1 from flare center. The spectrum of the wave was nearly flat in the range 4950–5900 Å. Association of the wave with a slow drift of the microwave emission peak to lower frequencies and with a softening of the X-ray spectrum is interpreted to mean that the particle acceleration process weakened while the region of acceleration expanded. The observations are interpreted with the aid of the flare models of Brown to mean that the same beam of non-thermal electrons that was responsible for the hard X-ray bremsstrahlung also caused the heating of the lower chromosphere that produced the white light flare.     

Problems with non-thermal models for the narrow line gamma rays reported from SS 433

The jet/grain model proposed by Ramatyet al. (1984, hereafter abbreviated as RKL) for production of the narrow gamma-ray lines reported from SS433 is examined and shown to be untenable on numerous grounds. Most importantly:

1. The huge Coulomb collisional losses (W _c?2×10⁴¹ erg s^?1) from the jet, which would necessarily accompany non-thermal production of the gamma rays, demands a jet acceleration/collimation process acting over a very long range and with a power at least 10² times the Eddington limit for any stellar object.
2. There is a collisional thick target limit (irrespective of jet mass) to the gamma ray yield per interstellar proton. Consequently, the gamma-ray data demand an improbably high interstellar density (?10⁹ cm^?3).
3. For the grains to be kept cool enough (?3000 K) to survive the heating rateW _c either by radiation or jet expansion would demand a ‘jet’ wider than its length and so inconsistent with narrow lines. In the case of radiative cooling, the resultant IR flux would exceed the observed values by a factor ?10⁴.
4. Light scattered on the jet grain mass required would be highly polarized, contrary to observations, unless the jet was optically thick to grains, again precluding their radiative cooling.
5. To avoid unacceptable precessional broadening of the gamma-ray lines demands an emitting jet length ?0.5 days atv=0.26c. This increases the necessary mass loss rate by a factor ?10 over the values obtained by RKL who assumed a 4-day ‘flare’.
6. The model also predicts rest energy gamma-ray lines which are not observed.

     

A relationship between the brightness temperatures for type III bursts

Type III bursts often have brightness temperatures at the fundamental greater than 10⁹K. If the fundamental emission is due to scattering of Langmuir waves into transverse waves by thermal ions, this implies that induced scattering dominates over spontaneous scattering, which in turn requires that the energy density in Langmuir waves be greater than some minimum value, e.g. W ^l > 3 × 10^-10 erg cm^-3 for bursts at f _p = 100 MHz. Such Langmuir waves become isotropic on a time-scale shorter than the rise-time of type III bursts, e.g. < l s at f _p = 100 MHz. Consequently, their coalescence, leading to emission at the second harmonic, proceeds. The above inequalities would imply a brightness temperature at the second harmonic in excess of 10⁹K at f = 200 MHz.The predicted values of the brightness temperatures _T1 ^t and _T2 ^t (at the fundamental and second harmonic respectively) can be expressed in terms of an optical depth . After is eliminated a functional relation between _T1 ^t , _T2 ^t and the plasma frequency, f _p , remains. The form of this relation is not dependent on a quantitative theory of how the Langmuir waves are generated by the stream of electrons. Consequently, comparison with observed quantities should provide further insight into the detailed properties of the emission processes.     

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.

     

The cooling of a sunspot

This paper considers the recent criticism by Mullan (1973) of sunspot models and the cooling mechanism which I have proposed in Papers I, II and III of this series. The discussion of the cooling produced by an idealized flow cycle has been extended to include vertical temperature gradients which are consistent with a convectively unstable atmosphere. This leads to an expression for Mullan's parameter f (the ratio in which estimates of the energy flux based on an idealized Carnot cycle should be reduced) which is appropriate to this situation. It is shown that, for a cycle similar to that of Paper III, f = 0.82, while for one which has a vertical extent of order 5 Mm, f= 0.4. Hence the energy flux which, in principle, can be transported away from a sunspot by such a cycle is conservatively estimated to be 1.1 × 10²⁹ erg s^?1 compared with a typical sunspot energy deficit of 2.2 × 10²⁹ erg s^?1. Other criticisms relating to the magnetic field amplification and the ‘cool one’ model are discussed. It is concluded that the essential features of these models remain valid and that the modifications suggested by Mullan's criticism greatly increase their applicability to the sunspot problem.     

Spectral analysis of the optical continuum in the 24 April 1981 flare

Spectrograph and multiple-band polarimeter observations of the 24 April 1981 white-light flare indicate the presence of an optical continuum with intensity increasing strongly below 4000 Å. The flare emission (lines and continuum combined) is unpolarized and, at 3600 Å, exceeds the brightness of the background solar surface by 360%. Analysis of the spectrum between 3600 and 8200 Å, at a location three arc sec from the brightest point in the kernel, yields a probable temperature of 6700 K for the continuum emitting layer. The wavelength dependence of the continuum indicates emission by both negative hydrogen (H^?) and Balmer continuum, with the H^? probably originating in the upper photosphere at a height (above τ_{5000 Å} = 1) in the range 200–300 km. Analysis of the Balmer lines and continuum yields an electron density 5.3 × 10¹³ cm^?3 and a second-level hydrogen column density 1.1 × 10¹⁶ cm^?2. The peak radiative output integrated over wavelength is 6.1 × 10²⁷ erg s^?1. The observed continuum intensity, if originating at a height of 300 km, implies an energy loss rate of 10³ erg s^?1 cm^?3.     

Hot vibrating white dwarf models of pulsating X-ray sources

A number of white dwarf models have been calculated which correspond to various radial and nonradial modes of vibration with eigenfrequencies in agreement with the observed pulsation frequencies of the X-ray sources Hercules X-1 and Centaurus X-3. Most of the white dwarf models have hot interiors, but for calculational purposes these were simplified so that the bulk of the interior was isothermal, and the surface layers were designed to produce an energy generation rate of 10³⁷ erg s^?1 and to transport this energy continuously to the surface by radiative transfer. Cold white dwarfs have a fairly large spread of masses corresponding to the different overtone modes with the given eigenfrequencies, but in the hot models this spread of masses is greatly reduced, for both radial and nonradial modes. It is concluded that if the pulsating X-ray sources are hot white dwarfs, the mass of Cen X-3 probably lies in the range 0.7–1.2M _⊙, and the mass of Her X-1 probably lies in the range 1.1–1.25M _⊙ (in accord with observation).     

X-ray nova flares

In order to find out the physical nature of galactic X-ray sources, data on variability of 24 sources during 1964–1971 have been investigated. The fluxes of 9 sources are found to be increasing to the maximum value (for several months) and then slowly decreasing (for }3 yr). These 9 sources have been related by us to the class of X-ray novae. The X-ray nova synthetic light curve has been drawn from data on the fluxes of 9 discovered novae. Assumptions have been made on the physical nature of the X-ray novae. Between the flares the X-ray novae may be weak X-ray sources with luminosity about 10³⁴ erg s^?1. During the flares the luminosity increases to about 10³⁸ erg s^?1. The number of X-ray sources in the Galaxy is about 10⁴–10⁵, the average distance between them about 0.5 kpc. The object of the optical identification may be a dwarf star of no earlier spectral class than F.     

Wave zone structure of NP 0532 and infrared radiation excess of Crab Nebula

At the distancer?10¹⁵ cm from NP 0532 the plasma concentration decreases so that the intense low-frequency wave (ν=30 Hz) can propagate. The interaction of this wave with the electrons ejected from the pulsar should result in the IR radiation withF _ν～10² fu at λ～10 μ. This flux is the order of the excess IR radiation from the Crab Nebula.     

Dynamics of a cloud of fast electrons travelling through the plasma

A simulation of normal type III radio bursts has been made in a whole frequency range of about 200 MHz to 30 kHz by the usage of the semi-analytical method as developed in previous papers for the plasma waves excited by a cloud of fast electrons. Three-dimensional plasma waves are computed, though the velocities of fast electrons are assumed to be one-dimensional. Many basic problems about type III radio bursts and associated solar electrons have been solved showing the following striking or unexpected results.Induced scattering of plasma waves, by thermal ions, into the plasma waves with opposite wave vectors is efficient even for a solar electron cloud of rather low number density. Therefore, the second harmonic radio emission as attributed to the coalescence of two plasma waves predominates in a whole range from meter waves to km waves. Fundamental radio emission as ascribed to the scattering of plasma waves by thermal ions is negligibly small almost in the whole range. On the other hand, third harmonic radio emission can be strong enough to be observed in a limited frequency range.If, however, the time integral of electron flux is, for example, 2 × 10¹³ cm^–2 (>5 keV) or more at the height of 4.3 × 10¹⁰ cm ( _p = 40 MHz) above the photosphere, the fundamental may be comparable with or greater than the second harmonic, but an effective area of cross-section of the electron beam is required to be very small, 10¹⁷ cm² or less, and hence much larger sizes of the observed radio sources must be attributed to the scattering alone of radio waves.The radio flux density expected at the Earth for the second harmonic can increase with decreasing frequencies giving high flux densities at low frequencies as observed, if x-dependence of the cross-sectional area of the electron beam is x ^1.5 or less instead of x ², at least at x 2 × 10¹² cm.The second harmonic radio waves are emitted predominantly into forward direction at first, but the direction of emission may reverse a few times in a course of a single burst showing a greater backward emission at the low frequencies.In a standard low frequency model, a total number of solar electrons above 18 keV arriving at the Earth orbit reduces to 12% of the initial value due mainly to the collisional decay of plasma waves before the waves are reabsorbed by the beam electrons arriving later. However, no deceleration of the apparent velocity of exciter appears. A change in the apparent velocity, if any, results from a change in growth rate of the plasma waves instead of the deceleration of individual electrons.Near the Earth, the peak of second harmonic radio flux as emitted from the local plasma appears well after the passage of a whole solar electron cloud through this layer. This is ascribed to the secondary and the third plasma waves as caused in non-resonant regions by the induced scattering of primary plasma waves in a resonant region.     

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 10¹⁵ cm^?3. This requires chromospheric heating at heights h ? 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies ν _p ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n ₁ > 4 × 10⁹ cm^?3. The generation of emission at the plasma frequency harmonic ν ≈ 2ν _p rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.     

Seismic effects from major basin formations on the moon and mercury

Grooved and hilly terrains occur at the antipode of major basins on the Moon (Imbrium, Orientale) and Mercury (Caloris). Such terrains may represent extensive landslides and surface disruption produced by impact-generatedP-waves and antipodal convergence of surface waves. Order-of-magnitude calculations for an Imbrium-size impact (10³⁴ erg) on the Moon indicateP-wave-induced surface displacements of 10 m at the basin antipode that would arrive prior to secondary ejecta. Comparable surface waves would arrive subsequent to secondary ejecta impacts beyond 10³ km and would increase in magnitude as they converge at the antipode. Other seismically induced surface features include: subdued, furrowed crater walls produced by landslides and concomitant secondary impacts; emplacement and leveling of light plains units owing to seismically induced ‘fluidization’ of slide material; knobby, pitted terrain around old basins from enhancement of seismic waves in ancient ejecta blankets; and perhaps the production and enhancement of deep-seated fractures that led to the concentration of farside lunar maria in the Apollo-Ingenii region.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

Heating and cooling of the thermal X-ray plasma in solar flares

Characteristic times for heating and cooling of the thermal X-ray plasma in solar flares are estimated from the time profile of the thermal X-ray burst and from the temperature, emission measure and over-all length scale of the flare-heated plasma at thermal X-ray maximum. The heating is assumed to be due to magnetic field reconnection, and the cooling is assumed to be due to heat conduction and radiation. Temperatures and emission measures derived from UCSD OSO-7 X-ray flare observations are used, and length scales are obtained from Big Bear large-scale Hα filtergrams for 17 small (subflare to Class 1) flares. The empirical values obtained for the characteristic times imply (1) that flares are produced by magnetic field reconnection, (2) that conduction cooling of the thermal X-ray plasma dominates radiative cooling and (3) that reconnection heating and conduction cooling of the thermal X-ray plasma are approximately in balance at thermal X-ray maximum. This model in combination with the data gives estimates for the electron number density (10¹⁰–10¹¹ cm^?3) and the magnetic field strength (10–100 G) in the thermal X-ray plasma and for the total thermal energy generated in a subflare (≈ 10³⁰ erg for an Hα area ≈ 1 square degree) which agree with previous observational and theoretical estimates obtained by others.     

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.

     

Revivals of a coronal arch

The giant post-flare arch of 6 November 1980 revived 11 hr and 25 hr after its formation. Both these revivals were caused by two-ribbon flares with growing systems of loops. The first two brightenings of the arch were homologous events with brightness maxima moving upwards through the corona with rather constant speed; during all three brightenings the arch showed a velocity pattern with two components: a slow one (8–12 km^?1), related to the moving maxima of brightness, and a fast one (～ 35 km s^?1), the source of which is unknown. During the first revival, at an altitude of 100000 km, temperature in the arch peaked ～ 1 hr, brightness ～ 2 hr, and emission measure ～ 3.5 hr after the onset of the brightening. Thus the arch looks like a magnified flare, with the scales both in size and time increased by an order of magnitude. At ～ 100000 km altitude the maximum temperature was ?14 × 10⁶K, max.n _e? 2.5 × 10⁹cm^?3, and max. energy density ? 11.2 erg cm^?3. The volume of the whole arch can be estimated to 1.1 × 10³⁰ cm³, total energy ?1.2 × 10³¹ erg, and total mass ?4.4 × 10¹⁵g. The density decreased with the increasing altitude and remained below 7 × 10⁹ cm^?3 anywhere in the arch. The arch cooled very slowly through radiation whereas conductive cooling was inhibited. Since its onset the revived arch was subject to energy input within the whole extent of the preexisting arch while a thermal disturbance (a new arch?) propagated slowly from below. We suggest that the first heating of the revived arch was due to reconnection of some of the distended flare loops with the magnetic field of the old preexisting arch. The formation of the ‘post’-flare loop system was delayed and started only some 30–40 min later. Since that time a new arch began to be formed above the loops and the velocities we found reflect this formation.