Radio emission from solar flares offers a number of unique diagnostic tools to address long-standing questions about energy release, plasma heating, particle acceleration, and particle transport in magnetized plasmas. At millimeter and centimeter wavelengths, incoherent gyrosynchrotron emission from electrons with energies of tens of kilo electron volts to several mega electron volts plays a dominant role. These electrons carry a significant fraction of the energy released during the impulsive phase of flares. At decimeter and meter wavelengths, coherent plasma radiation can play a dominant role. Particularly important are type III and type III‐like radio bursts, which are due to upward- and downwarddirected beams of nonthermal electrons, presumed to originate in the energy release site. With the launch of Yohkohand the Compton Gamma-Ray Observatory , the relationship between radio emission and energetic photon emissions has been clarified. In this review, recent progress on our understanding of radio emission from impulsive flares and its relation to X-ray emission is discussed, as well as energy release in flare-like phenomena (microflares, nanoflares) and their bearing on coronal heating.

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Radio emission from solar flares

An overview is given of the observational and the theoretical methods used to investigate solar magnetic fields. It includes an introduction to the Stokes parameters, their radiative transfer in the presence of a magnetic field, and empirical techniques used to measure various properties of solar magnetic features, such as the strength and direction of the magnetic field, magnetic flux, temperature, velocity, size and lifetime. The MHD equations are introduced and some of the most common simplifications used to describe solar magnetic features are outlined. The application of these techniques to small-scale magnetic features is surveyed. The results of empirical and theoretical investigations of small-scale solar magnetic features are reviewed. Current views on their magnetic structure, thermal stratification, velocity field, size, distribution and evolution are presented. Finally, some open questions concerning small-scale solar magnetic fields are listed.

Small-scale solar magnetic fields: An overview

The magnetic field in the solar photosphere evolves as flux concentrations fragment in response to sheared flows, merge when they collide with others of equal polarity, or (partially) cancel against concentrations of opposite polarity. Newly emerging flux replaces the canceled flux. We present a quantitative statistical model that is consistent with the histogram of fluxes contained in concentrations of magnetic flux in the quiet network for fluxes exceeding ≈ 2 × 1018 Mx, as well as with estimated collision frequencies and fragmentation rates. This model holds for any region with weak gradients in the magnetic flux density at scales of more than a few supergranules. We discuss the role of this dynamic flux balance (i) in the dispersal of flux in the photosphere, (ii) in sustaining the network-like pattern and mixed-polarity character of the network, (iii) in the formation of unipolar areas covering the polar caps, and (iv) on the potential formation of large numbers of very small concentrations by incomplete cancellation. Based on the model, we estimate that as much flux is cancelled as is present in quiet-network elements with fluxes exceeding ≈ 2 × 1018 Mx in 1.5 to 3 days, which is compatible with earlier observational estimates. This timescale is close to the timescale for flux replacement by emergence in ephemeral regions, so that this appears to be the most important source of flux for the quiet-Sun network; based on the model, we cannot put significant constraints on the amount of flux that is injected on scales that are substantially smaller than that of the ephemeral regions. We establish that ephemeral regions originate in the convection zone and are not merely the result of the reemergence of previously cancelled network flux. We also point out that the quiet, mixed-polarity network is generated locally and that only any relatively small polarity excess is the result of flux dispersal from active regions.

https://iopscience.iop.org/article/10.1086/304581/pdf

Sustaining the Quiet Photospheric Network: The Balance of Flux Emergence, Fragmentation, Merging, and Cancellation

We present an ab initio approach to the solar coronal heating problem by modelling a small part of the solar corona in a computational box using a 3D MHD code including realistic physics. The observed solar granular velocity pattern and its amplitude and vorticity power spectra, as reproduced by a weighted Voronoi tessellation method, are used as a boundary condition that generates a Poynting flux in the presence of a magnetic field. The initial magnetic field is a potential extrapolation of a SOHO/MDI high resolution magnetogram, and a standard stratified atmosphere is used as a thermal initial condition. Except for the chromospheric temperature structure, which is kept fixed, the initial conditions are quickly forgotten because the included Spitzer conductivity and radiative cooling function have typical timescales much shorter than the time span of the simulation. After a short initial start up period, the magnetic field is able to dissipate 3 − 4 × 10 6 ergscm 2 s 1 in a highly intermittent corona, maintaining an average temperature of ∼ 10 6 K, at coronal density values for which emulated images of the Transition Region And Coronal Explorer(TRACE) 171 and 195 u pass bands reproduce observed photon count rates. Subject headings: Sun: corona – Sun: magnetic fields – MHD

An Ab Initio Approach to the Solar Coronal Heating Problem

The magnetic field of the Sun is the underlying cause of the many diverse phenomena combined under the heading of solar activity. Here we describe the magnetic field as it threads its way from the bottom of the convection zone, where it is built up by the solar dynamo, to the solar surface, where it manifests itself in the form of sunspots and faculae, and beyond into the outer solar atmosphere and, finally, into the heliosphere. On the way it transports energy from the surface and the subsurface layers into the solar corona, where it heats the gas and accelerates the solar wind.

https://iopscience.iop.org/article/10.1088/0034-4885/69/3/R02/pdf

The solar magnetic field

Big Bear deep magnetograms of June 4, 1992 provide unprecedented observations for direct measurements of solar intranetwork (IN) magnetic fields. More than 2500 individual IN elements and 500 network elements are identified and their magnetic flux measured in a quiet region of 300 × 235 arc sec. The analysis reveals the following results:

(1)

IN element flux ranges from 1016 Mx (detection limit) to 2 × 1018 Mx, with a peak flux distribution of 6 × 1016 Mx.




(2)

More than 20% of the total flux in this quiet region is in the form of IN elements at any given time.




(3)

Most IN elements appear as a cluster of mixed polarities from an emergence center (or centers) somewhere within the network interior.




(4)

The IN flux is smaller than the network flux by more than an order of magnitude. It has a uniform spatial distribution with equal amount of both polarities.

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Flux distribution of solar intranetwork magnetic fields

We report peculiar spectral activity of four large microwave bursts as obtained from the Solar Arrays at the Owens Valley Radio Observatory during observations of X-class flares on 1990 May 24 and 1991 March 7, 8, and 22. Main observational points that we newly uncovered are: (1) flat flux spectra over 1–18 GHz in large amounts of flux ranging from 102 to 104 s.f.u. at the maximum phase, (2) a common evolutionary pattern in which the spectral region of dominant flux shifts from high frequencies at the initial rise to low frequencies at the decaying phase, and (3) unusual time profiles that are impulsive at high frequencies but more extended at lower frequencies.

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Flat microwave spectra seen at X-class flares

In this paper, we are primarily concerened with the solar neutron emission during the 1990 May 24 flare, utilizing the counting rate of the Climax neutron monitor and the time profiles of hard X-rays and gamma-rays obtained with the GRANAT satellite (Pelaez et al., 1992; Talon et al., 1993; Terekhov et al., 1993). We compare the derived neutron injection function with macroscopic parameters of the flare region as obtained from the H-alpha and microwave observations made at the Big Bear Solar Observatory (BBSO) and the Owens Valley Radio Observatory (OVRO) respectively. Our results are summarized as folows: (1) to explain the neutron monitor counting rate and 57.5-110 MeV and 2.2 MeV gamma-ray time profiles, we consider a two-component neutron injection function, Q(E, t). (2) From the H-alpha observations, we find a relatively small loop of length approximattely equal to 2 x 10(exp 4) km, which may be regarded as the source for the fast-decaying component of gamma-rays (57.5-110 MeV) and for the first component of neutron emission. From microwave visibility and the microwave total power spectrum we postulate the presence of a rather big loop (approximately equal to 2 x 10(exp 5) km), which we regard as being responsible for the slow-decaying component of the high-energy emission. We show how the neutron and gamma-ray emission data can be explained in terms of the macroscopic parameters derived from the H-alpha and microwave observations. (3) The H-alpha observations also reveal the presence of a fast mode MHD shock (the Moreton wave) which precedes the microwave peak by 20-30 s and the peak of gamma-ray intensity by 40-50 s. From this relative timing and the single-pulsed time profiles of both radiations, we can attribute the whole event as due to a prompt acceleration of both electrons and protons by the shock and subsequent deceleration of the trapped particles while they propagate inside the magnetic loops.

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Neutron and electromagnetic emissions during the 1990 May 24 solar flare

From the gyroresonance brightness temperature spectrum of a sunspot, one can determine the magnetic field strength by using the property that microwave brightness is limited above a frequency given by an integer-multiple of the gyrofrequency. In this paper, we use this idea to find the radial distribution of magnetic field at the coronal base of a sunspot in the active region, NOAA 4741. The gyroresonance brightness temperature spectra of this sunspot are obtained from multi-frequency interferometric observations made at the Owens Valley Radio Observatory at 24 frequencies in the range of 4.0–12.4 GHz with spatial resolution 2.2″–6.8″. The main results of present study are summarized as follows: first, by comparison of the coronal magnetic flux deduced from our microwave observation with the photospheric magnetic flux measured by KPNO magnetograms, we show that theo-mode emission must arise predominantly from the second harmonic of the gyrofrequency, while thex-mode arises from the third harmonic. Second, the radial distribution of magnetic fieldsB(r) at the coronal base of this spot (say, 2000–4000 km above the photosphere) can be adequately fitted by

$$B(r) = 1420(1 \pm 0.080)\exp \left[ { - \left( {\frac{r}{{11.05''(1 \pm 0.014)}}} \right)^2 } \right]G,$$

wherer is the radial distance from the spot center at coronal base. Third, it is found that coronal magnetic fields originate mostly from the photospheric umbral region. Fourth, although the derived vertical variation of magnetic fields can be approximated roughly by a dipole model with dipole moment 1.6 × 1030 erg G−1 buried at 11000 km below the photosphere, the radial field distribution at coronal heights is found to be more confined than predicted by the dipole model.

Microwave emission from a sunspot - I. Implications for the sunspot magnetic structure

New measurements of Moving Magnetic Features (MMFs) based on the observations of the active region NOAA 5612 made at Big Bear Solar Observatory (BBSO) on August 2, 1989 are presented. The existing theoretical models are checked against the new observations, and the origin of MMFs conjectured from the deduced observational constraints is discussed.

Jeongwoo W. Lee

Papers

Flux distribution of solar intranetwork magnetic fields

Flat microwave spectra seen at X-class flares

Neutron and electromagnetic emissions during the 1990 May 24 solar flare

Microwave emission from a sunspot - I. Implications for the sunspot magnetic structure

Observational evidence for various models of Moving Magnetic Features