Thermal cyclotron radiation from hot coronal loops and peculiarities of the polarization structure of solar microwave emission sources: II. Integrated characteristics

We present our calculations of the expected characteristics of the integrated spectrum of thermal cyclotron radiation from a solar active region with a coronal magnetic loop. A hot torus is considered as a three-dimensional loop model. We show that the hot-loop emission can change appreciably the emission characteristics of the active region at centimeter and decimeter wavelengths. At certain loop parameters, the emission frequency spectrum can have a nonmonotonic and complex pattern with several peaks or contain narrow-band cyclotron lines. The polarization structure of the source with a hot loop is also complex and the polarization is repeatedly reversed over the observed frequency range under certain conditions. The revealed spectral-polarization peculiarities are considered from the standpoint of whether some atypical observed properties of the emission sources associated with solar active regions can be explained.     

Diagnosis of coronal magnetic field with data of Nobeyama Radio Heliograph

The expression is derived for the coronal magnetic field strength from the observations of brightness, temperature, peak frequency, spectral index, and polarization degree of solar microwave bursts. One example of solar burst on November 28, 1998 is given for the calculation of coronal magnetic field from the data of Nobeyama Radio Heliograph (NoRH). The results are comparable with the SOHO/MDI magnetogram and the calculation from the Nobeyama Radio Polarimeters (NoRP), as well as the coronal loops in SOHO/EIT and YOHKOH/SXT images. Therefore, it may be the first time that the two-dimensional diagnosis of coronal magnetic field in a microwave burst source from the radio observations has been made.     

Reversal of the polarization of cyclotron radiation in a hot coronal loop

Spectropolarimetric features of thermal cyclotron radiation of solar coronal loops and the possibility of interpretation of the observed reversal of the sense of polarization of centimeter and decimeter waves are discussed. To this end, thermal cyclotron radiation is computed in terms of the simplest model of a three-dimensional hot loop (a half-torus). Such a loop is shown to be capable of changing appreciably the properties of the radiation of a solar active region at centimeter and decimeter wavelengths. A detailed analysis is performed to determine the conditions under which the radiation spectrum of an active region containing a coronal loop may have a complex pattern with several maxima or relatively narrow-band cyclotron lines, and the sense of polarization may change several times in the wavelength interval considered. These conditions are modelled by such parameters as the structure of the magnetic field, electron density, and size of the loop. The results of the computations of two-dimensional brightness temperature distributions at different wavelengths for ordinary and extraordinary waves at fixed points of the loop and the integrated parameters of the flux and polarization of radiation in terms of the model discussed are reported. Cases are considered where the line of sight is crossed by one or two loops. The expected distribution of polarization across the source in the model considered is compared to the results of RATAN-600 observations of the solar active region AR 7962 made on May 12–14, 1996.     

Joint radio and soft x-ray imaging of an ‘anemone’ active region

The Very Large Array and the Soft X-ray Telescope (SXT) aboard the Yohkoh satellite jointly observed the rapid growth and decay of a so-called anemone active region on 3–6 April, 1992 (AR 7124). The VLA obtained maps of the AR 7124 at 1.5, 4.7, and 8.4 GHz. In general, discrete coronal loop systems are rarely resolved at 1.5 GHz wavelengths because of limited brightness contrast due to optical depth effects and wave scattering. Due to its unusual anemone-like morphology, however, several discrete loops or loop systems are resolved by both the VLA at 1.5 GHz and the SXT in AR 7124.Using extrapolations of the photospheric field and the radio observations at 4.7 and 8.4 GHz, we find that the microwave emission is the result of gyroresonance emission from a hot, rarefied plasma, at the second and/or third harmonic. The decimetric source is complex -1.5 GHz emission from the leading part of AR 7124 is due to free-free emission, while that in the trailing part of the active region is dominated by gyroresonance emission. We also examine an interesting case of a discrete radio loop with no soft X-ray (SXR) emission adjacent to a hot SXR loop. This observation clearly shows the multithermal nature of the solar corona.     

Evolvement of microwave spike bursts in a solar flare on 2006 December 13

Solar radio spikes are one of the most intriguing spectral types of radio bursts. Their very short lifetimes, small source size and super-high brightness temperature indicate that they should be involved in some strong energy release, particle acceleration and coherent emission processes closely related to solar flares. In particular, for the microwave spike bursts, their source regions are much close to the related flaring source region which may provide the fundamental information of the flaring process. In this work,we identify more than 600 millisecond microwave spikes which recorded by the Solar Broadband Radio Spectrometer in Huairou(SBRS/Huairou) during an X3.4 solar flare on 2006 December 13 and present a statistical analysis about their parametric evolution characteristic. We find that the spikes have nearly the same probability of positive and negative frequency drifting rates not only in the flare rising phase, but also in the peak and decay phases. So we suppose that the microwave spike bursts should be generated by shockaccelerated energetic electrons, just like the terminational shock(TS) wave produced by the reconnection outflows near the loop top. The spike bursts occurred around the peak phase have the highest central frequency and obviously weak emission intensity, which imply that their source region should have the lowest position with higher plasma density due to the weakened magnetic reconnection and the relaxation of TS during the peak phase. The right-handed polarization of the most spike bursts may be due to the TS lying on the top region of some very asymmetrical flare loops.     

Steady models for the hard X-ray loops in the solar corona

In some gradual hard X-ray bursts with high intensity, hard X-ray source (15–40 keV) is steadily located in the corona along with softer X-ray source (5–10 keV).Two stationary models, high density and high temperature models, are proposed to solve the difficult problem of confinement of hot (or nonthermal) plasma in the direction of the magnetic field along the loops in the corona. In both models, an essential point is that the effective X-ray source is composed of fine dense filamentary loops imbeded in a larger rarefied coronal loop, and the electron number density in the filaments is so high as 10¹¹–10¹² cm^-3. If the density is so high heat conduction can be as reasonably small as of the order of 10²⁷ erg s ^-1 for the given emission measures of observed X-rays, since the required cross-sectional area is small and also classical conduction is valid. Collisional confinement of thermal tail, and nonthermal electrons if any, up to 50–60 keV in the filaments is also possible, so that the hard X-ray images can be loop like structure instead of double source (foot points).High density model is applicable to the coronal filamentary loops with temperature T _m < 5 × 10⁷ K at the loop summit. The heat flow from the summit downwards is lost almost completely by the radiation from the loop during the conduction to the foot points. A continuous energy release is assumed near the summit to maintain the stationary temperature T _m, and pressure balance is maintained along the loop. In this model, the number density at the summit is given by n _m - 10⁶ T _m ² /s_m, where s _m is the length of the loop from the summit to the foot point, and the distribution of temperature and density along the loop are given by T = T _m(s/s_m)^1/3 and n = n _m(s/s_m)^-1/3, respectively.High temperature model is applicable to the filamentary loops with higher temperature up to about 10^8.5 K and comparatively lower number density as 10¹¹ cm^-3 for the requirement of magnetic confinement of the hot plasma in radial direction. The radiation from the loop is negligibly small in this model so that the heat flux is nearly conserved down to the foot points. In this case, temperature gradient is smaller than that of the high density model, depending on the tapering of the magnetic bottle.In both models, the differential emission measure is maximum at the highest temperature T _m and the brightness distribution along the loop shows a maximum around the summit of the loop if some magnetic tapering is taken into account.     

The Effect of Mass Motions Inside the Coronal Loops on Emission Line Profiles

The observed green coronal emission line profiles have been often found to have multi-components. Further examinations reveal that the occurrence of multi-components in line profiles is related to the solar cycle variations as well as the activity of the coronal region. The spatial correspondence between the intense loops in active regions and strong multi-components in line profiles suggests that the presence of loops affects the line shapes. The emission line profiles have been found to be fitted well with single or multi-Gaussians with line-of-sight velocities up to 70 km s–1. A simple radiative transfer model of coronal emission line profiles is developed which shows that coronal loops with mass motions inside may give rise to multi-components in line profiles. The effects of loop parameters such as electron density, flow velocity and kinetic temperature and the line-of-sight variations are studied. It is found that line profiles strongly reflect the physical conditions inside the loop.     

Similarities and Differences between Coronal Holes and the Quiet Sun: Are Loop Statistics the Key?

Coronal holes (CH) emit significantly less at coronal temperatures than quiet-Sun regions (QS), but can hardly be distinguished in most chromospheric and lower transition region lines. A key quantity for the understanding of this phenomenon is the magnetic field. We use data from SOHO/MDI to reconstruct the magnetic field in coronal holes and the quiet Sun with the help of a potential magnetic model. Starting from a regular grid on the solar surface we then trace field lines, which provide the overall geometry of the 3D magnetic field structure. We distinguish between open and closed field lines, with the closed field lines being assumed to represent magnetic loops. We then try to compute some properties of coronal loops. The loops in the coronal holes (CH) are found to be on average flatter than in the QS. High and long closed loops are extremely rare, whereas short and low-lying loops are almost as abundant in coronal holes as in the quiet Sun. When interpreted in the light of loop scaling laws this result suggests an explanation for the relatively strong chromospheric and transition region emission (many low-lying, short loops), but the weak coronal emission (few high and long loops) in coronal holes. In spite of this contrast our calculations also suggest that a significant fraction of the cool emission in CHs comes from the open flux regions. Despite these insights provided by the magnetic field line statistics further work is needed to obtain a definite answer to the question if loop statistics explain the differences between coronal holes and the quiet Sun.     

Very Large Array and SOHO Observations of Type I Noise Storms,Large-Scale Loops and Magnetic Restructuring in the Corona

Very Large Array (VLA) observations at 91-cm wavelength are combined with data from the SOHO EIT, MDI and LASCO and used to study the evolving coronal magnetic environment in which Type I noise storms and large-scale coronal loops occur. On one day, we have shown the early evolution of a coronal mass ejection (CME) in projection in the disk by tracing its decimetric continuum emission. The passage of the CME and an associated EUV ejection event coincided with an increase in the 91-cm brightness temperature of an extended coronal loop located a significant distance away and with the displacement of the 91-cm source during the early stage of the CME. We suggest that the energy deposited into the corona by the CME may have caused a local increase in the thermal or nonthermal electron density or in the electron temperature in the middle corona resulting in a transient increase in the brightness of the 91-cm loop. On a second observing day, we have consolidated the known association between magnetic changes in the photosphere and low corona with noise storm enhancements in an overlying radio source well in advance of a flare event in the same region. We find anti-correlated changes in the brightness of a bipolar 91-cm Type I noise storm that appear to be associated with the cancellation and emergence of magnetic flux in the underlying photosphere. In this case, the evolving fields may have led to magnetic instabilities and reconnection in the corona and the acceleration of nonthermal particles that initiated and sustained the Type I noise storm.     

The efficiency of electron acceleration in solar type-IV radio pulsations with a zebra pattern

Based on a comprehensive analysis of the October 25, 1994 event, we consider the balance of energetic particles in a type-IV solar radio emission source with a zebra-type fine structure (in a coronal magnetic loop). The zebra pattern is formed through the injection of fast electrons into a trap and the formation of a ring-type nonequilibrium electron distribution function. We estimated the characteristic zebra-pattern lifetime, which is determined by the escape of fast particles from the trap into the loss cone. In addition, we determined the number of fast particles that must be injected into the trap to provide the observed radio brightness temperature in zebra-pattern stripes by analyzing the plasma emission mechanism responsible for the zebra-pattern generation. As a result, we estimated the efficiency of the electron acceleration mechanism in coronal magnetic loops at the post-flare evolutionary phase of an active region.     

The XUV structure of solar active regions

XUV spectroheliograms of 2 active regions are studied. The images are due to lines emitted at temperatures between 8 x 10⁴ K and 2 x 10⁶ K and thus are indicative of transition region and coronal structures. The hot coronal lines are formed solely in loop structures which connect regions of opposite photospheric magnetic polarity but are not observed over sunspots. Transition region lines are emitted in plages overlying regions of intense photospheric magnetic field and in loops or loop-segments connecting such regions. The hot coronal loops are supported hydrostatically while only some of the transition zone loops are. The coronal and transition zone loops are distinctly separated and are not coaxial. A comparison of direct measurements of electron densities using density sensitive line ratios with indirect measurements using emission measures and path lengths shows the existence of fine structures of less than a second of arc in transition region loops. From a similar analysis, hot coronal loops do not have any fine structure below about 2 seconds of arc.     

Calculations of Coronal Magnetic Field Parallel and Perpendicular to Line-of-Sight in Microwave Bursts

Based on the approximations of the non-thermal gyro-synchrotron radiation used by G.A. Dulk, and K.A. Marsh, Astrophs. J. 259, 350, 1982, the author analyses calculations of the propagation angle and coronal magnetic field self-consistently with brightness temperature, spectral index, frequency, turnover frequency, and polarization degree in solar microwave bursts. Hence, the coronal magnetic fields parallel and perpendicular to the line-of-sight in the sources of microwave bursts are calculated theoretically, and discussed in an event observed by the Nobeyama Radio Polarimeters (NoRP).     

Microwave and Soft X-ray Study of Solar Active Region Evolution

We have studied the properties and evolution of several active regions observed at multiple wavelengths over a period of about 10 days. We have used simultaneous microwave (1.5 and 17 GHz) and soft X-ray measurements made with the Very Large Array (VLA), the Nobeyama Radio Heliograph (NRH) and the Soft X-ray Telescope (SXT) on board the Yohkoh spacecraft, as well as photospheric magnetograms from KPNO. This is the first detailed comparison between observations at radio wavelengths differing by one order of magnitude. We have performed morphological and quantitative studies of active region properties by making inter-comparison between observations at different wavelengths and tracking the day-to-day variations. We have found good general agreement between the 1.5 and 17 GHz radio maps and the soft X-rays images. The 17 GHz emission is consistent with thermal bremsstrahlung (free-free) emission from electrons at coronal temperatures plus a small component coming from plasma at lower temperatures. We did not find any systematic limb darkening of the microwave emission from active regions. We discuss the difference between the observed microwave brightness temperature and the one expected from X-ray data and in terms of emission of a low temperature plasma at the transition region level. We found a coronal optical thickness of 10^-3 and 1 for radiation at 17 and 1.5 GHz, respectively. We have also estimated the typical coronal values of emission measure ( 5 × 10²⁸ cm^-5), electron temperature ( 4.5 × 10⁶6 K) and density ( 1.2 × 10⁹ cm₃). Assuming that the emission mechanism at 17 GHz is due to thermal free-free emission, we calculated the magnetic field in the source region using the observed degree of polarization. From the degree of polarization, we infer that the 17 GHz radiation is confined to the low-lying inner loop system of the active region. We also extrapolated the photospheric magnetic field distribution to the coronal level and found it to be in good agreement with the coronal magnetic field distribution obtained from microwave observations.     

Energetic Electrons in Loop Top and Footpoint Microwave Sources

We have studied two microwave events with one-loop top (LT) and two-footpoint (FP) sources observed at 17 and 34 GHz by the Nobeyama Radioheliograph (NoRH). The microwave brightness peak is located near the FPs of the flare loop for one event, but near the LT for the other event. The microwave spectra of the FP sources are considerably softer (by 2.0) than that of the LTs for both events. We assume that the microwave emission is gyro-synchrotron radiation from energetic electrons trapped in a magnetic dipole field and the energetic electron distribution is isotropic in pitch angle and power law. In the gyro-synchrotron calculations, the self-absorption and gyro-resonance absorption are taken into account simultaneously. The numerical calculations based on the general equation of radiative transfer show that the distributions of energetic electrons along a flare loop are highly inhomogeneous: accelerated electrons are concentrated in the FPs for both events. Even for the event with brightness maximum near the LT the electron number density of the LT source is still an order of magnitude lower than that of the FP sources. The emission peak near LT results mainly from the much harder spectral index of the energetic electrons in the LT source.     

Thermal equilibria of coronal magnetic loops with non-constant cross-sectional area

Equations of thermal equilibrium along coronal loops are solved in the absence of gravity but where the cross-sectional area changes along the loop. The footpoint temperature is assumed to be 2 × 10⁴ K. Several fundamental types of solution are found, namely hot loops, cool loops, hot-cool loops (where the footpoints and summits are cool but the intermediate parts are hotter) and warm loops (cool along most of their lengths except the summits). On increasing the cross-sectional area the summit temperature generally increases slightly except for warm loops where no increase in temperature is recorded and hot-cool loops where a dramatic increase in summit temperature may occur. The cool and hot-cool loops may model elementary fibril structures within prominences.     

A model of hot loops associated with solar flares

A dynamical model is proposed for the formation of soft X-ray emitting hot loops in solar flares. It is examined by numerical simulations how a solar model atmosphere in a magnetic loop changes its state and forms a hot loop when the flare energy is released in the form of heat liberation either at the top part or around the transition region in the loop.When the heat liberation takes place at the top part of the loop which arches in the corona, the plasma temperature around the loop apex rises rapidly and, as the result, the downward thermal conductive flux is increased along the magnetic tube of force. Soon after the thermal conduction front rushes into the upper chromosphere, a local peak of pressure is produced near the conduction front and the chromospheric material begins to expand into the corona to form a high-temperature (10⁷ K-3 × 10⁷ K at the loop apex) and high-density (10¹⁰ cm^–3-10¹¹ cm^–3 at the loop apex) loop. The velocity of the expanding material can reach a few hundred kilometres per second in the coronal part. The thermal conduction front also plays a role of piston pushing the chromospheric material downward and gives birth to a shock wave which propagates through the minimum temperature region into the photosphere. If, on the other hand, the heat source is placed around the transition region in the loop, the expansion of the material into the corona occurs from the beginning of the flare and the formation process of the hot loop differs somewhat from the case with the heat source at the top part of the loop.Thermal components of radiations emitted from flare regions, ranging from soft X-rays to radio wavelengths, are interpreted in a unified way by using physical quantities obtained as functions of time and position in our flare loop model as will be discussed in detail in a following paper.     

Coronal Temperature Profiles Obtained from Kinetic Models and from Coronal Brightness Measurements Obtained During Solar Eclipses

Coronal density, temperature, and heat-flux distributions for the equatorial and polar corona have been deduced from Saito’s model of averaged coronal white-light (WL) brightness and polarization observations. These distributions are compared with those determined from a kinetic collisionless/exospheric model of the solar corona. This comparison indicates similar distributions at large radial distances (>?7 R_⊙) in the collisionless region. However, rather important differences are found close to the Sun in the acceleration region of the solar wind. The exospheric heat flux is directed away from the Sun, while that inferred from all WL coronal observations is in the opposite direction, i.e. conducting heat from the inner corona toward the chromosphere. This could indicate that the source of coronal heating extends up into the inner corona, where it maximizes at r>1.5 R_⊙, well above the transition region.     

The Prominence-Corona Transition Region in transverse magnetic fields

An emission measure analysis is performed for the Prominence-Corona Transition Region (PCTR) under the assumption that the cool matter of quiescent filaments is contained in long, thin magnetic flux loops imbedded in hot coronal cavity gas. Consequently, there is a transition region around each thread.Comparison of the model and observations implies that the temperature gradient is perpendicular to the magnetic lines of force in the lower part of the PCTR (T < 10⁵ K). It is shown that in this layer the heating given by the divergence of the transverse conduction fails to account for the observed UV and EUV emission by several orders of magnitude. It is, therefore, suggested that the heating of these layers could be due to dissipation of Alfvén waves.In the high-temperature layers (T 10⁵ K), where the plasma 1, the temperature gradient is governed by radiative cooling balancing conductive heating from the surrounding hot coronal gas. Also in these outer layers the presence of magnetic fields reduces notably the thermal conduction relative to the ideal field-free case. Numerical modelling gives good agreement with observed DEM; the inferred value of the flux carried by Alfvén waves, as well as that of the damping length, greatly support the suggested form of heating. The model assumes that about 1/3 of the volume is occupied by threads and the rest by hot coronal cavity matter.The brightness of the EUV emission will depend on the angle between the thread structure and the line of sight, which may lead to a difference in brightness from observations at the limb and on the disk.     

Radioheliograph Observations of Microwave Bursts with Zebra Structures

The so-called zebra structures in radio dynamic spectra, specifically their frequencies and frequency drifts of emission stripes, contain information on the plasma parameters in the coronal part of flare loops. This paper presents observations of zebra structures in a microwave range. Dynamic spectra were recorded by Chinese spectro-polarimeters in the frequency band close to the working frequencies of the Siberian Solar Radio Telescope. The emission sources are localized in the flare regions, and we are able to estimate the plasma parameters in the generation sites using X-ray data. The interpretation of the zebra structures in terms of existing theories is discussed. The conclusion has been arrived at that the preferred generation mechanism of zebra structures in the microwave range is the conversion of plasma waves to electromagnetic emission on the double plasma resonance surfaces distributed across a flare loop.     

Effect of Variable Background on an Oscillating Hot Coronal Loop

We investigate the effect of a variable, i.e. time-dependent, background on the standing acoustic (i.e. longitudinal) modes generated in a hot coronal loop. A theoretical model of 1D geometry describing the coronal loop is applied. The background temperature is allowed to change as a function of time and undergoes an exponential decay with characteristic cooling times typical for coronal loops. The magnetic field is assumed to be uniform. Thermal conduction is assumed to be the dominant mechanism for damping hot coronal oscillations in the presence of a physically unspecified thermodynamic source that maintains the initial equilibrium. The influence of the rapidly cooling background plasma on the behaviour of standing acoustic (longitudinal) waves is investigated analytically. The temporally evolving dispersion relation and wave amplitude are derived by using the Wenzel–Kramers–Brillouin theory. An analytic solution for the time-dependent amplitude that describes the influence of thermal conduction on the standing longitudinal (acoustic) wave is obtained by exploiting the properties of Sturm–Liouville problems. Next, numerical evaluations further illustrate the behaviour of the standing acoustic waves in a system with a variable, time-dependent background. The results are applied to a number of detected loop oscillations. We find a remarkable agreement between the theoretical predictions and the observations. Despite the emergence of the cooling background plasma in the medium, thermal conduction is found to cause a strong damping for the slow standing magneto–acoustic waves in hot coronal loops in general. In addition to this, the increase in the value of thermal conductivity leads to a strong decay in the amplitude of the longitudinal standing slow MHD waves.