Alexander L. MacKinnon

Local re-acceleration and a modified thick target model of solar flare electrons

Context. The collisional thick target model (CTTM) of solar hard X-ray (HXR) bursts has become an almost “standard model” of flare impulsive phase energy transport and radiation. However, it faces various problems in the light of recent data, particularly the high electron beam density and anisotropy it involves. Aims. We consider how photon yield per electron can be increased, and hence fast electron beam intensity requirements reduced, by local re-acceleration of fast electrons throughout the HXR source itself, after injection. Methods. We show parametrically that, if net re-acceleration rates due to e.g. waves or local current sheet electric (E) fields are a significant fraction of collisional loss rates, electron lifetimes, and hence the net radiative HXR output per electron can be substantially increased over the CTTM values. In this local re-acceleration thick target model (LRTTM) fast electron number requirements and anisotropy are thus reduced. One specific possible scenario involving such re-acceleration is discussed, viz, a current sheet cascade (CSC) in a randomly stressed magnetic loop. Results. Combined MHD and test particle simulations show that local E fields in CSCs can efficiently accelerate electrons in the corona and and re-accelerate them after injection into the chromosphere. In this HXR source scenario, rapid synchronisation and variability of impulsive footpoint emissions can still occur since primary electron acceleration is in the high Alfven speed corona with fast re-acceleration in chromospheric CSCs. It is also consistent with the energy-dependent time-of-flight delays in HXR features. Conclusions. Including electron re-acceleration in the HXR source allows an LRTTM modification of the CTTM in which beam density and anisotropy are much reduced, and alleviates theoretical problems with the CTTM, while making it more compatible with radio and interplanetary electron numbers. The LRTTM is, however, different in some respects such as spatial distribution of atmospheric heating by fast electrons.

Chromospheric magnetic field and density structure measurements using hard X-rays in a flaring coronal loop

Aims. A novel method of using hard X-rays as a diagnostic for chromospheric density and magnetic structures is developed to inf er sub-arcsecond vertical variation of magnetic flux tube size and neutral gas density. Methods. Using Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed X-ray visibilities forward fitting technique we find the FWHM and ce ntroid positions of hard X-ray sources with sub-arcsecond r esolution (∼ 0.2 ′′ ) for a solar limb flare. We show that the height variations of t he chromospheric density and the magnetic flux densities can be found with unprecedented vertical resolution of∼ 150 km by mapping 18-250 keV X-ray emission of energetic electrons propagating in the loop at chromospheric heights of 400-1500 km. Results. Our observations suggest that the density of the neutral gas is in good agreement with hydrostatic models with a scale height of around 140± 30 km. FWHM sizes of the X-ray sources decrease with energy suggesting the expansion (fanning out) of magnetic flux tube in the chromosphere with height. The magnetic scale height B(z) (dB/dz) −1 is found to be of the order of 300 km and strong horizontal magnetic field is associated with noticeable flux tube expansion at a height of∼ 900 km.

LOFAR tied-array imaging of Type III solar radio bursts

The Sun is an active source of radio emission which is often associated with energetic phenomena such as solar flares and coronal mass ejections (CMEs). At low radio frequencies (<100 MHz), the Sun has not been imaged extensively because of the instrumental limitations of previous radio telescopes. Here, the combined high spatial, spectral and temporal resolution of the Low Frequency Array (LOFAR) was used to study solar Type III radio bursts at 30-90 MHz and their association with CMEs. The Sun was imaged with 126 simultaneous tied-array beams within 5 solar radii of the solar centre. This method offers benefits over standard interferometric imaging since each beam produces high temporal (83 ms) and spectral resolution (12.5 kHz) dynamic spectra at an array of spatial locations centred on the Sun. LOFARs standard interferometric output is currently limited to one image per second. Over a period of 30 minutes, multiple Type III radio bursts were observed, a number of which were found to be located at high altitudes (4 solar radii from the solar center at 30 MHz) and to have non-radial trajectories. These bursts occurred at altitudes in excess of values predicted by 1D radial electron density models. The non-radial high altitude Type III bursts were found to be associated with the expanding flank of a CME. The CME may have compressed neighbouring streamer plasma producing larger electron densities at high altitudes, while the non-radial burst trajectories can be explained by the deflection of radial magnetic fields as the CME expanded in the low corona.

High energy particles accelerated during the large solar flare of 1990 May 24: X/γ-ray observations

The PHEBUS experiment aboard GRANAT observed γ-ray line emission and γ-ray continuum above 10 MeV from the 24 May, 1990 solar flare. Observations and interpretation of the high-energy continuum have been discussed previously. Here we re-examine these, combining the PHEBUS observations above 10 MeV with calculations of the pion decay continuum to quantitatively constrain the accelerated ion energy distribution at energies above 300 MeV. The uncertainty in the determination of the level of the primary electron bremsstrahlung as well as the lack of measurements on the γ-ray emission above ≃100 MeV combine to allow rather a wide range of energy distribution parameters (in terms of the number of protons above 30 MeV, the spectral index of the proton distribution and the high energy cut-off of the energetic protons). Nevertheless we are able to rule out some combinations of these parameters. Using the additional information provided by the γ-ray line observations we discuss whether it is possible to construct a consistent picture of the ions which are accelerated in a wide energy range during this flare. Our findings are discussed with respect to previous works on the spectrum of energetic protons in the 10 MeV to GeV energy range.

The high energy solar corona: waves, eruptions, particles

Introduction: The High-energy Corona - Waves, Eruptions, Particles.- Introduction: The High-energy Corona - Waves, Eruptions, Particles.- Particle Acceleration During Flares.- Magnetic Complexity, Fragmentation, Particle Acceleration and Radio Emission from the Sun.- Review of Selected RHESSI Solar Results.- RHESSI Results - Time for a Rethink?.- Small Scale Energy Release and the Acceleration and Transport of Energetic Particles.- Large-scale Disturbances.- Large-scale Waves and Shocks in the Solar Corona.- Energetic Particles Related with Coronal and Interplanetary Shocks.- Particle Acceleration at the Earths Bow Shock.- On the Existence of Non-maxwellian Velocity Distribution Functions in the Corona and their Consequences for the Solar Wind Acceleration.- Recent Research: Large-scale Disturbances, their Origin and Consequences.- Plasma of the Solar Corona.- Quasi-periodic Pulsations as a Diagnostic Tool for Coronal Plasma Parameters.- Pulsating Solar Radio Emission.

Cross-field diffusion of electrons in tangled magnetic fields and implications for coronal fine structure

High-resolution images of the solar corona suggest that some degree of tangling exists in the coronal magnetic structure. We show that a very low level of such magnetic tangling is sufficient for Rechester-Rosenbluth diffusion to be the dominant cross-field plasma transport mechanism. This diffusive process, which moves particles rapidly across the field on tangled field lines, is thus likely to be a governing mechanism in controlling plasma structure in the direction perpendicular to the magnetic field. We generate model coronal loops with cross-field dimensions governed by Rechester-Rosenbluth diffusion and show that the cross-field transport is consistent with the observed widths of coronal magnetic loops. Together with observed loop morphology, these calculations allow us to constrain the degree of magnetic field disorder likely to be present in the corona, and in particular the degree of tangling as invoked in discussions of coronal heating.

High energy particles during the large solar flare of 1990 May 24: X/γ ray observations.

The PHEBUS experiment aboard GRANAT observed γ-ray line emission and γ-ray continuum above 10 MeV from the 24 May, 1990 solar flare. Observations and interpretation of the high-energy continuum have been discussed previously. Here we re-examine these, combining the PHEBUS observations above 10 MeV with calculations of the pion decay continuum to quantitatively constrain the accelerated ion energy distribution at energies above 300 MeV. The uncertainty in the determination of the level of the primary electron bremsstrahlung as well as the lack of measurements on the γ-ray emission above ≃100 MeV combine to allow rather a wide range of energy distribution parameters (in terms of the number of protons above 30 MeV, the spectral index of the proton distribution and the high energy cut-off of the energetic protons). Nevertheless we are able to rule out some combinations of these parameters. Using the additional information provided by the γ-ray line observations we discuss whether it is possible to construct a consistent picture of the ions which are accelerated in a wide energy range during this flare. Our findings are discussed with respect to previous works on the spectrum of energetic protons in the 10 MeV to GeV energy range.

LOFAR tied-array imaging and spectroscopy of solar S bursts

Context. The Sun is an active source of radio emission that is often associated with energetic phenomena ranging from nanoflares to coronal mass ejections (CMEs). At low radio frequencies (<100 MHz), numerous millisecond duration radio bursts have been reported, such as radio spikes or solar S bursts (where S stands for short). To date, these have neither been studied extensively nor imaged because of the instrumental limitations of previous radio telescopes. Aims. Here, Low Frequency Array (LOFAR) observations were used to study the spectral and spatial characteristics of a multitude of S bursts, as well as their origin and possible emission mechanisms. Methods. We used 170 simultaneous tied-array beams for spectroscopy and imaging of S bursts. Since S bursts have short timescales and fine frequency structures, high cadence (~50 ms) tied-array images were used instead of standard interferometric imaging, that is currently limited to one image per second. Results. On 9 July 2013, over 3000 S bursts were observed over a time period of ~8 hours. S bursts were found to appear as groups of short-lived (<1 s) and narrow-bandwidth (~2.5 MHz) features, the majority drifting at ~3.5 MHz/s and a wide range of circular polarisation degrees (2-8 times more polarised than the accompanying Type III bursts). Extrapolation of the photospheric magnetic field using the potential field source surface (PFSS) model suggests that S bursts are associated with a trans-equatorial loop system that connects an active region in the southern hemisphere to a bipolar region of plage in the northern hemisphere. Conclusions. We have identified polarised, short-lived solar radio bursts that have never been imaged before. They are observed at a height and frequency range where plasma emission is the dominant emission mechanism, however they possess some of the characteristics of electron-cyclotron maser emission.

Quantitative analysis of hard X-ray 'footpoint' flares observed by the solar maximum mission

AbstractWe describe the instrumental corrections which have to be incorporated for reliable correction and deconvolution of images obtained in the 16–22 keV and 22–30 keV energy bands of the Hard X-Ray Imaging Spectrometer (HXIS) aboard the Solar Maximum Mission (SMM). These corrections include amplifier gain and collimator hole size variations across the field of view, amplifier/filter efficiency, variation in effective collimator hole size and angular response with photon energy, dead-time, and hard X-ray plate transmission. We also emphasise the substantial Poisson noise in these energy bands, and describe the maximum entropy deconvolution/correction routine we have developed to establish the spatial structure which can be reliably inferred from HXIS data.Next we discuss the results of application of our routine to the three impulsive flare phases reported by Duijveman et al. (1982) as exhibiting hard X-ray ‘footpoints’, namely 1980, April 10, May 21, and November 5. Our main conclusions are: (1)Maximum entropy smoothing and Poisson noise data perturbations do not remove the main footpoint features in 16–30 keV nor change their basic morphology. However the results emphasise the asymmetry in footpoint size in the May 21 flare and confirm its possible presence in April 10. They also reveal the 3rd weak distant footpoint in the May 21 flare at an earlier time than found by Duijveman et al. When the 16–22 and 22–30 keV bands are analysed separately, however, it is found that the footpoints are much less visible above noise in the harder band - i.e. the footpoint spectra are steep. In the April 10 and November 5 flares they are steeper than either the spectrum of intervening pixels or the spectrum at higher energies measured for the whole flare by the SMM Hard X-Ray Burst Spectrometer (HXRBS). (2)The footpoint contrast with surroundings is less than found by Duijveman et al., despite image deconvolution, because of the maximum entropy smoothing of noise.(3)The 16–30keV HXIS footpoint fluxes in the three flares are respectively 28%, 17%, and 15% of the simultaneous HXRBS flare power-law spectrum extrapolated into this energy range.(4)Where Poisson noise is taken into account we find, by cross-correlating pixel count rates, that footpoint synchronism was either not provable at all, or substantially less close than reported by Duijveman et al. Next we considered the implications of these results for models of the footpoint emission. Contrary to Duijveman et al. we do not consider the HXIS ‘footpoint’ data as supporting a conventional thick target beam interpretation since: (A)The footpoint photon (and electron) fluxes are much less than expected from HXRBS extrapolation. This result casts doubt on recent models of chromospheric heating by electron beams which usually assume all of the HXRBS emission to come from HXIS footpoints.(B)The footpoint spectra for the April 10 and November 5 flares are much softer than the HXRBS spectrum and than the spectrum of intervening pixels, contrary to thick target predictions.(C)Contrary to Duijveman et al. footpoint synchronism does not demand an unreasonable Alfvén speed and so does not require non-thermal particles. In spite of these objections we also re-considered the constraints placed on the acceleration site conditions in a beam interpretation by return current stability and footpoint contrast in the summed 16–30 keV range. Using the smoothed maximum entropy contrast and taking explicit account of coronal thermal emission, we find maximum densities somewhat larger than Duijveman et al. estimated, and much higher maximum values of Te/Ti.Regarding thermal interpretations we found: (a)Models involving continuous production of short-lived hot kernels in the arch top with Maxwellian tail electrons escaping to the footpoints could explain the 16–30 keV contrast with a rather higher energetic efficiency than a pure beam model. However, whatever the temperature distribution of hot kernel production, the model predicts footpoints harder than the arch summit, contrary to HXIS data.(b)A model with hot kernels produced in one limb of an arch can explain the asymmetry in footpoint size observed in May 21, and probably April 10, and is energetically even more efficient than (a) but is also inconsistent with the spectral data.(c)Finally we point out that HXIS footpoint data may be consistent with a purely geometric interpretation in an almost uniform arch filled with hot plasma.

Modelling the radio pulses of an ultracool dwarf

Context. Recently, unanticipated magnetic activity in ultracool dwarfs (UCDs, spectral classes later than M7) has emerged from a number of radio observations. The highly (up to 100%) circularly polarized nature and high brightness temperature of the emission have been interpreted as requiring an effective amplification mechanism of the high-frequency electromagnetic waves − the electron cyclotron maser instability (ECMI). Aims. We aim to understand the magnetic topology and the properties of the radio emitting region and associated plasmas in these ultracool dwarfs, interpreting the origin of radio pulses and their radiation mechanism. Methods. An active region model was built, based on the rotation of the UCD and the ECMI mechanism. Results. The high degree of variability in the brightness and the diverse profile of pulses can be interpreted in terms of a large-scale hot active region with extended magnetic structure existing in the magnetosphere of TVLM 513-46546. We suggest the time profile of the radio light curve is in the form of power law in the model. Combining the analysis of the data and our simulation, we can determine the loss-cone electrons have a density in the range of 1.25 ×10 5 −5 ×10 5 cm −3 and temperature between 10 7 and 5 ×10 7 K. The active region has a size <1 RJup, while the pulses produced by the ECMI mechanism are from a much more compact region (e.g. ∼0.007 RJup). A surface magnetic field strength of ≈7000 G is predicted. Conclusions. The active region model is applied to the radio emission from TVLM 513-46546, in which the ECMI mechanism is responsible for the radio bursts from the magnetic tubes and the rotation of the dwarf can modulate the integral of flux with respect to time. The radio emitting region consists of complicated substructures. With this model, we can determine the nature (e.g. size, temperature, density) of the radio emitting region and plasma. The magnetic topology can also be constrained. We compare our predicted X-ray flux with Chandra X-ray observation of TVLM 513-46546. Although the X-ray detection is only marginally significant, our predicted flux is significantly lower than the observed flux. Further multi-wavelength observations will help us better understand the magnetic field structure and plasma behavior on the ultracool dwarf.