Implications of liouville's theorem on the apparent brightness temperatures of solar radio bursts

Liouville's theorem for radiation, of which the generalized étendue is a consequence, implies ² d² d² A = constant along the ray path, where is the refractive index and d² and d² A are the ranges, respectively, of solid angle and of area that define a ray (actually a bundle of rays). Implications of this concept on the propagation of radio waves from the actual to the apparent source in the solar corona (i.e., the scatter image of the true source) are discussed. The implications for sources of fundamental plasma radiation include: (1)The observed solid angle (defining the directivity) and apparent area A of the source are compatible with Liouville's theorem only if the apparent source (the scatter image of the true source) corresponds to the envelope of subsources with a small filling factor f. (2) The brightness temperature T _Bof the actual source is greater than that of the apparent source by f ^-1. (3) For sources of fundamental plasma radiation the factor f is very small ( 10^-2). (4) A long-standing discrepancy between the observed low value of T _B at meter/decameter wavelengths for the quiet Sun and the known coronal temperature may be resolved by noting that the implied coronal temperature is given by T _B f and that the factor f must be significantly less than unity.A brief discussion is included of the relation between Liouville's theorem, the generalized étendue, Milne's laws, occupation numbers, extension in phase, and suppression of emission by a medium with refractive index unequal to unity.     

Tracing the Electron Density from the Corona to 1 au

We derive the electron density distribution in the ecliptic plane, from the corona to 1 AU, using observations from 13.8 MHz to a few kHz by the radio experiment WAVES aboard the spacecraft Wind. We concentrate on type III bursts whose trajectories intersect the spacecraft, as determined by the presence of burst-associated Langmuir waves, or by energetic electrons observed by the 3-D Plasma experiment. For these bursts we are able to determine the mode of emission, fundamental or harmonic, the electron density at 1 AU, the distance of emission regions along the spiral, and the time spent by the beams as they proceed from the low corona to 1 AU. For all of the bursts considered, the emission mode at burst onset was the fundamental; by contrast, in deriving many previous models, harmonic emission was assumed.By measuring the onset time of the burst at each frequency we are able to derive an electron density model all along the trajectory of the burst. Our density model, after normalizing the density at 1 AU to be ne(215 R0)=7.2 cm–3 (the average value at the minimum of solar activity when our measurements were made), is ne=3.3×105 r–2+4.1×106 r–4+8.0×107 r–6 cm–3, with r in units of R0. For other densities at 1 AU our result implies that the coefficients in the equation need to be multiplied by n _e (1 AU)/7.2.We compare this with existing models and those derived from direct, in-situ measurements (normalized to the same density at 1 AU) and find that it agrees very well with in-situ measurements and poorly with radio models based on apparent source positions or assumptions of the emission mode. One implication of our results is that isolated type III bursts do not usually propagate in dense regions of the corona and solar wind, as it is still sometimes assumed.     

Propagation and absorption of electron-cyclotron maser radiation during solar flares

The electron-cyclotron maser is believed to be the source of microwave spike bursts often observed during solar and stellar flares. Partial absorption of this radiation as it propagates through the corona can produce plasma heating and soft X-ray emission over an extended region. In this paper, the propagation and absorption of the maser radiation during solar flares are examined through linear theory and electro-magnetic particle simulations. It is shown using linear theory that strong absorption of the radiation should occur as it propagates towards the second harmonic layer where the magnetic field is half as strong as in the emission region. Only radiation propagating nearly parallel to the magnetic field in a low-temperature plasma may be able to escape under certain, limited conditions. Finite temperature effects can cause radiation propagating nearly perpendicular to the magnetic field to refract, causing enhanced absorption. Particle simulations are then used to evaluate the nonlinear response of the plasma as the maser radiation propagates through the absorption layer. It is shown that some of the maser radiation is able to escape through a process of absorption below the second harmonic of the local gyrofrequency and re-emission above it. The fraction able to escape is much higher than that predicted by linear theory, although the amount of escaping energy is only a small fraction of the incident energy. The bulk of incident energy goes into the perpendicular heating of the ambient electrons, with the rate of energy absorption showing no signs of leveling off during the simulations. This indicates that the absorption layer does not become optically thin after continuous heating by the maser radiation. A few electrons are accelerated to several tens of keVs as a result of the heating.     

Evidence for cyclotron maser emission from the Sun and stars

In recent years radiation has been observed from planets, Sun and stars that is best explained by the cyclotron maser instability; in fact, all celestial bodies that might feasibly emit and be detected by their cyclotron maser radiation have been detected. Here we review those observations, the developments in the theory, the recent work on the effiency of energy transfer by cyclotron maser radiation, and some recent and future observations that might demonstrate whether the mechanism is energetically important in solar and stellar flares.This work was supported in part by NASA's Solar Heliospheric Physics and Solar Terrestrial Theory Programs under grants NSG-7287 and NAGW-91 to the University of Colorado. The numerical simulations were performed on the Cray XMP at the San Diego Supercomputer Center which is funded by the National Science Foundation.     

Stellar dynamic spectroscopy

The dynamic spectrum, a three dimensional record of the radio intensity as a function both of time and frequency, has long been used as a probe of plasma processes in the solar corona. Beginning with the work of Wild and McCready (1950) dynamic spectroscopy has been used to distinguish between the multitude of radio wave emitting phenomena which occur in the solar corona and to infer the physical mechanisms responsible.

Stellar dynamic spectroscopy has always been a tantalizing prospect. The vast body of experience with solar dynamic spectroscopy would prove invaluable in interpreting stellar dynamic spectra. Further, the new parameter regimes presented by stellar coronas would allow further insight to be gained in the physical processes at work in stellar coronas.

Recently, Bastian and Bookbinder (1987) used the Very Large Array in spectral line mode at 1.4 GHz with a bandwidth of 50 MHz to obtain the first dynamic spectra of nearby flare stars. The spectral resolution was 3.125 MHz and the temporal resolution was 5 s. While the relative bandwidth was less than ideal (δν/ν ∼ 5%), the spectra so obtained were sufficient to show the presence of narrowband structure in a radio outburst from the well-known dMe flare star UV Ceti.

Several efforts are now underway to obtain stellar dynamic spectra, of both RS CVn binaries and dMe flare stars, with higher degrees of spectral and temporal resolution. Among these are use of a 1024 channel correlator with the 1000' telescope at Arecibo and use of the Berkeley Fast Pulsar Search Machine (Kulkarni et al. 1984) with the Green Bank 140' telescope.

     

VLA and Trieste observations of type I storms,type IV and pulsations

A prime objective of this experiment was to determine whether type I or IV sources at 333 MHz contain features of small (arc sec) scale. With the VLA, our resolution was better than 4. However, we never observed any structure of size smaller than about 30, with the typical source sizes being between about 40 and 90.Many observations were simultaneous with the Trieste Astronomical Observatory records at 327 MHz. The observations were made on two days in November 1988. On 8 November the observations were of a type I storm about two hours after a major flare. On 14 November they were mostly of the main phase of a type IV event, including pulsations of a kind rarely seen, strongly circularly polarized, and having a well-defined period of about 12 s. The size of the pulsating source was about 40 by 60, and the brightness temperature was about 10⁹ K. We compare these pulsations with those observed earlier.     

Coronal magnetic fields

The observational evidence on the strength of the coronal magnetic field above active regions is reviewed. Recent advances in observations and plasma theory are used to determine which data are the more reliable and to revise some earlier estimates of field strength. The results from the different techniques are found to be in general agreement, and the relation 279-01, 1.02 R/R 10 is consistent with all the data to within a factor of about 3.The National Center for Atmospheric Research is supported by the National Science Foundation.     

Observations of coronal disturbances from 1 to 9 R ⊙

Solar Physics - Hα, white-light and radio observations of a coronal disturbance on 1973 January 11 commencing at about 00h36m UT show that a piston-driven shock wave propagated outwards...     

White light and radio studies of the coronal transient of 14–15 September 1973

Observations of a coronal transient event were obtained in white light by the Skylab coronagraph and at metric wavelengths by the radioheliograph and spectrograph at Culgoora and the spectrograph-interferometer at Boulder. The continuum radio burst was found to originate above the outward-moving white light loop - a region of compressed material headed by a bow wave. The computed density in the region of radio emission, based on either gyro-synchrotron or harmonic plasma radiation mechanisms, was approximately 10 times the ambient coronal density; this is compatible with the density deduced from the white light observations. The magnetic energy density derived from the radio observations was greater than 10 times the thermal energy density, marginally larger than the kinetic energy density in the fastest moving portion of the transient, and considerably larger in most other regions. The ambient medium, the white light front, the compression region, the loop, and the slower, massive flow of material behind are each examined. It is found that the plasma was magnetically controlled throughout, and that magnetic forces provided the principal mechanism for acceleration of the transient material from the Sun.Also, High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado.Now at Los Alamos Scientific Laboratory, Los Alamos, New Mexico.The National Center for Atmospheric Research is sponsored by the National Science Foundation.On leave from Institute of Applied Physics, University of Berne, Switzerland.Also, Division of Radiophysics, CSIRO, Sydney, Australia.     

Interplanetary particle beams

The purpose of this paper is to review the observations of particle beams of the kind that are frequently observed in the interplanetary medium, usually but not always accompanying a solar flare. Most frequent are beams of electrons. They are generally associated with radio bursts of type III and only sometimes with flares and X-ray bursts. The properties of these electron beams have been well studied using quasi-linear and nonlinear theory, in situ observations of electrons and of plasma waves, and remote observations of radio waves Thanks to the interaction between theory and observation, the decade of the 1980s has been one of great progress in understanding the main features of these beams and their associated plasma waves and radio bursts. However, uncertainties remain in terms of (1) whether fine scale features, filamentary structures or wave condensations, occur together with the beams, (2) whether quasi-linear or nonlinear wave emission is the dominant process, and (3) if wave condensations are important, what is the mechanism of conversion of some Langmuir wave energy into radio emission.Other particle beams are composed of protons, of neutrons, of helium ions (sometimes with a large excess of ³He), and of heavy ions with varying concentrations. Sometimes the observations seem to require the fractionation of certain ions, followed by resonant acceleration of certain species.Objects other than the Sun that are the source of interplanetary particle beams include comets and planets, especially the Earth and Jupiter.