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NASA NTRS1998

Multiwavelength Observations of a Dramatic High-Energy Flare in the Blazar 3C 279

The blazar 3C 279, one of the brightest identified extragalactic objects in the gamma-ray sky, underwent a large (factor of approximately 10 in amplitude) flare in gamma-rays toward the end of a 3 week pointing by Compton Gamma Ray Observatory (CGRO), in 1996 January-February. The flare peak represents the highest gamma-ray intensity ever recorded for this object. During the high state, extremely rapid gamma-ray variability was seen, including an increase of a factor of 2.6 in approximately 8 hr, which strengthens the case for relativistic beaming. Coordinated multifrequency observations were carried out with Rossi X-Ray Timing Explorer (RXTE), Advanced Satellite for Cosmology and Astrophysics (ASCA; or, Astro-D), Roentgen Satellite (ROSAT), and International Ultraviolet Explorer (IUE) and from many ground-based observatories, covering most accessible wavelengths. The well-sampled, simultaneous RXTE light curve shows an outburst of lower amplitude (factor of approximately = 3) well correlated with the gamma-ray flare without any lag larger than the temporal resolution of approximately 1 day. The optical-UV light curves, which are not well sampled during the high-energy flare, exhibit more modest variations (factor of approximately 2) and a lower degree of correlation. The flux at millimetric wavelengths was near a historical maximum during the gamma-ray flare peak, and there is a suggestion of a correlated decay. We present simultaneous spectral energy distributions of 3C 279 prior to and near to the flare peak. The gamma-rays vary by more than the square of the observed IR-optical flux change, which poses some problems for specific blazar emission models. The synchrotron self-Compton (SSC) model would require that the largest synchrotron variability occurred in the mostly unobserved submillimeter/far-infrared region. Alternatively, a large variation in the external photon field could occur over a time-scale of a few days. This occurs naturally in the "mirror" model wherein the flaring region in the jet photoionizes nearby broad emission line clouds, which, in turn, provide soft external photons that are Comptonized to gamma-ray energies.

Wehrle, A. E.↗
NASA NTRS1998

Multiwavelength Observations of a Dramatic High-Energy Flare in the Blazar 3C 279

The blazar 3C 279, one of the brightest identified extragalactic objects in the gamma-ray sky, underwent a large (factor of approx. 10 in amplitude) flare in gamma-rays toward the end of a 3 week pointing by Compton Gamma Ray Observatory (CGRO), in 1996 January-February. The flare peak represents the highest gamma-ray intensity ever recorded for this object. During the high state, extremely rapid gamma-ray variability was seen, including an increase of a factor of 2.6 in approx. 8 hrs., which strengthens the case for relativistic beaming. Coordinated multifrequency observations were carried out with Rossi X-Ray Timing Explorer (RXTE), Advanced Satellite for Cosmology and Astrophysics (ASCA; or, Astro-D), Roentgen Satellite (ROSAT), and International Ultraviolet Explorer (IUE) and from many ground-based observatories, covering most accessible wavelengths. The well-sampled, simultaneous RXTE light curve shows an outburst of lower amplitude (factor of approx. or equal to 3) well correlated with the gamma-ray flare without any lag larger than the temporal resolution of approx. 1 day. The optical-UV light curves, which are not well sampled during the high-energy flare, exhibit more modest variations (factor of approx. 2) and a lower degree of correlation. The flux at millimetric wavelengths was near a historical maximum during the gamma-ray flare peak, and there is a suggestion of a correlated decay. We present simultaneous spectral energy distributions of 3C 279 prior to and near to the flare peak. The gamma-rays vary by more than the square of the observed IR-optical flux change, which poses some problems for specific blazar emission models. The synchrotron self-Compton (SSC) model would require that the largest synchrotron variability occurred in the mostly unobserved submillimeter/far-infrared region. Alternatively, a large variation in the external photon field could occur over a time scale of a few days. This occurs naturally in the "mirror" model wherein the flaring region in the jet photoionizes nearby broad emission line clouds, which, in turn, provide soft external photons that are Comptonized to gamma-ray energies.

Wehrle, A. E.↗
NASA NTRS1996

Ion Acceleration in Solar Flares

Solar flares are among the most energetic and interesting phenomena in the Solar system, releasing up to 1032 ergs of energy on timescales of several tens of seconds to several tens of minutes. Much of this energy is in the form of suprathermal electrons and ions, which remain trapped at the Sun and produce a wide variety of radiations, as well as escape into interplanetary space, where they can be directly observed. The radiation from trapped particles consists in general of (1) continuum emission; (2) narrow gamma-ray nuclear deexcitation lines; and (3) high-energy neutrons observed in space or by ground-based neutron monitors. The particles that escape into space consist of both electrons and ions, which often have compositions quite different than that of the ambient solar atmosphere. Flares thus present many diagnostics of the particle acceleration mechanism(s), the identification of which is the ultimate goal of flare research. Moreover, flares in fact offer the only opportunity in astrophysics to study the simultaneous energization of both electrons and ions. Hopefully, an understanding of flares with their wealth of diagnostic data will lead to a better understanding of particle acceleration at other sites in the Universe. It is now generally accepted that flares are roughly divided into two classes: impulsive and gradual. Gradual events are large, occur high in the corona, have long-duration soft and hard X-rays and gamma rays, are electron poor, are associated with Type II radio emission and coronal mass ejections (CMEs), and produce energetic ions with coronal abundance ratios. Impulsive events are more compact, occur lower in the corona, produce short-duration radiation, and exhibit dramatic abundance enhancements in the energetic ions. Their He-3/He-4 ratio is - 1, which is a huge increase over the coronal value of about 5 x 10(exp -4), and they also posses smaller but still significant enhancements of Ne, Mg, Si, and Fe relative to He-4, C, N, and O. Specifically, above about 1 MeV nucleon(exp -1), the ratio of Fe to O is about 8 times larger than in the corona or in gradual flares, while the ratio of Ne, Mg, and Si to O is about 3 times higher; He-4, C, N, and 0 are not enchanced with respect to each other. In addition to these elemental enhancements, Ne and Mg have isotopic enhancements as well. The general scenario that has emerged from these (and other) observations is that energetic particles in gradual events are accelerated by a CME-driven shock, while those particles in impulsive events are accelerated by another mechanism(s).

Miller, James A.↗
NASA NTRS2004

Thermal and Nonthermal Contributions to the Solar Flare X-Ray Flux

The relative thermal and nonthermal contributions to the total energy budget of a solar flare are being determined through analysis of RHESSI X-ray imaging and spectral observations in the energy range from approx. 5 to approx. 50 keV. The classic ways of differentiating between the thermal and nonthermal components - exponential vs. sources - can now be combined for individual flares. In addition, RHESSI's sensitivity down to approx. 4 keV and energy resolution of approx. 1 keV FWHM allow the intensities and equivalent widths of the complex of highly ionized iron lines at approx. 6.7 keV and the complex of highly ionized iron and nickel lines at approx. 8 keV to be measured as a function of time. Using the spectral line and continuum intensities from the Chianti (version 4.2) atomic code, the thermal component of the total flare emission can be more reliably separated from the nonthermal component in the measured X-ray spectrum. The abundance of iron can also be determined from RHESSI line-to-continuum measurements as a function of time during larger flares. Results will be shown of the intensity and equivalent widths of these line complexes for several flares and the temperatures, emission measures, and iron abundances derived from them. Comparisons will be made with 6.7-keV Fe-line fluxes measured with the RESIK bent crystal spectrometer on the Coronas-F spacecraft operating in third order during the peak times of three flares (2002 May 31 at 00:12 UT, 2002 December 2 at 19:26 UT, and 2003 April 26 at 03:OO UT). During the rise and decay of these flares, RESIK was operating in first order allowing the continuum flux to be measured between 2.9 and 3.7 keV for comparison with RHESSI fluxes at its low-energy end.

Dennis, Brian R.↗
NASA NTRS2004

The Solar Flare 4: 10 keV X-ray Spectrum

The 4-10 keV solar flare spectrum includes highly excited lines of stripped Ca, Fe, and Ni ions as well as a continuum steeply falling with energy. Groups of lines at approximately 7 keV and approximately 8 keV, observed during flares by the broad-band RHESSI spectrometer and called here the Fe-line and Fe/Ni-line features, are formed mostly of Fe lines but with Ni lines contributing to the approximately 8 keV feature. Possible temperature indicators of these line features are discussed - the peak or centroid energies of the Fe-line feature, the line ratio of the Fe-line to the Fe/Ni-line features, and the equivalent width of the Fe-line feature. The equivalent width is by far the most sensitive to temperature. However, results will be confused if, as is commonly believed, the abundance of Fe varies from flare to flare, even during the course of a single flare. With temperature determined from the thermal continuum, the Fe-line feature becomes a diagnostic of the Fe abundance in flare plasmas. These results are of interest for other hot plasmas in coronal ionization equilibrium such as stellar flare plasmas, hot gas in galaxies, and older supernova remnants.

Phillips, K. J. H.↗
NASA NTRS2004

Evidence for Magnetic Reconnection in Three Homologous Solar Flares Observed by RHESSI

We present RHESSI observF5oss of three homologous flares, which occurred between April 14 and 16, 2002. We find that the RHESSI images of all three flares at energies between 6 and 25 keV had some common features: (1) A. separate coronal source up to approx. 30 deg. above the flare loop appeared in the early impulsive phase and stayed stationary for several minutes. (2) Before the flare loop moved upward; previously reported by others, the flare loop-top centroid moved downward for 2-4 minutes during the early impulsive phase of the Ears: falling by 13 - 30% of its initial height with a speed between 8 and 23 km/s. We conclude that these features are associated with the formation and development of a current sheet between the loop-top and the coronal source. In the April 14-15 flare, we find that the hard X-ray flux (greater than 25 keV) is correlated with the rate at which the flare loop moves upward, indicating that the faster the loop grows, the faster the reconnection rate, and therefore, the greater the flux of accelerated electrons. Subject headings: Sun: L'iaies-Sun: X-1-ay-s -

Sui, Lin-Hui↗
NASA NTRS2004

Compact Flares and CMEs

From a search of the SOHO/LASCO CME Catalog, we found several flares that were strong but short-lived in GOES X-ray flux (peak flux > C5, duration <approx.2 hr), and produced no CME. We also found several equally strong and short-lived flares that did initiate CMEs. All of the flares were located in strong magnetic fields near sunspots and were spatially compact (brightened only a small part of the active region). From the magnetic location and magnetic surroundings determined from MDI magnetograms, it appears that the non-CME flares were confined deep within surrounding strong closed magnetic fields, while the CME-producing flares either triggered neighboring sheared fields to erupt into a CME, or were able to erupt out of the active region and directly drive a CME. Compact ejective flares of this last type may produce a large CME by driving the eruption of a large coronal loop such as a trans-equatorial loop. We present an example of such a flare and CME.

Moore, Ronald↗
NASA NTRS2005

Transition Region Emission and the Energy Input to Thermal Plasma in Solar Flares

Understanding the energetics of solar flares depends on obtaining reliable determinations of the energy input to flare plasma. X-ray observations of the thermal bremsstrahlung from hot flare plasma provide temperatures and emission measures which, along with estimates of the plasma volume, allow the energy content of this hot plasma to be computed. However, if thermal energy losses are significant or if significant energy goes directly into cooler plasma, this is only a lower limit on the total energy injected into thermal plasma during the flare. We use SOHO UVCS observations of O VI flare emission scattered by coronal O VI ions to deduce the flare emission at transition region temperatures between 100,000 K and 1 MK for the 2002 July 23 and other flares. We find that the radiated energy at these temperatures significantly increases the deduced energy input to the thermal plasma, but by an amount that is less than the uncertainty in the computed energies. Comparisons of computed thermal and nonthermal electron energies deduced from RHESSI, GOES, and UVCS are shown.

Holman, Gordon D.↗
NASA NTRS2005

Energetics of RHESSI X-Class Flares

The thermal and nonthermal energies of several X-class flares seen with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) will be presented. The same techniques described by Emslie et al. (JGR, 109, A10104, 2004) are used to take the RHESSI imaging spectroscopic observations and compute the energies in the thermal plasma and in the nonthermal electrons as a function of time throughout the flares. Radiative and conductive cooling rates are estimated and total thermal and nonthermal energies are computed for each flare. Typically, the energy in nonthermal electrons integrated up to the time of peak soft X-ray emission is equal to or exceeds the energy in the thermal plasma at that time. This suggests that energy must have been converted into a form not visible with RHESSI and that the total energy released by the flares may be significantly greater than the sum of energies calculated from the RHESSI observations alone. This conclusion is supported by the high radiative energy seen with SORCE during the impulsive phase of the 28 October 2003 flare. The peak increase in total solar irradiance of 270 mW per square meters measured with SORCE was over two orders of magnitude higher than the peak soft X-ray flux seen with GOES or RHESSI. The implications of this new observation as compared to the energetics derived from the X-ray observations of that flare will be discussed along with the energetics analysis of most of the other X- class flares in October/November 2003.

Dennis, Brian R.↗
NASA NTRS2005

Studies of Particle Acceleration, Transport and Radiation in Impulsive Phase of Solar Flares

Solar activity and its most prominent aspect, the solar flares, have considerable influence on terrestrial and space weather. Solar flares also provide a suitable laboratory for the investigation of many plasma and high energy processes important in the magnetosphere of the Earth and many other space and astrophysical situations. Hence, progress in understanding of flares will have considerable scientific and societal impact. The primary goal of this grant is the understanding of two of the most important problems of solar flare physics, namely the determination of the energy release mechanism and how this energy accelerates particles. This is done through comparison of the observations with theoretical models, starting from observations and gradually proceeding to theoretically more complex situations as the lower foundations of our understanding are secured. It is generally agreed that the source of the flare energy is the annihilation of magnetic fields by the reconnection process. Exactly how this energy is released or how it is dissipated remains controversial. Moreover, the exact mechanism of the acceleration of the particles is still a matter of debate. Data from many spacecrafts and ground based instruments obtained over the past decades have given us some clues. Theoretical analyses of these data have led to the standard thick target model (STT) where most of the released energy goes into an (assumed) power law spectrum of accelerated particles, and where all the observed radiations are the consequence of the interaction of these particles with the flare plasma. However, some theoretical arguments, and more importantly some new observations, have led us to believe that the above picture is not complete. It appears that plasma turbulence plays a more prominent role than suspected previously, and that it is the most likely agent for accelerating particles. The model we have developed is based on production of a high level of plasma waves and turbulence in the reconnection region above a flare loop. This turbulence accelerates particles stochastically which radiate some of their energy in this region but carry most of their energy to the footpoints of the loop, where they lose all their energy and radiate bulk of the observed radiation as in the traditional thick target model. In the past we have worked on various aspects of this model. We have evaluated the interaction rates of the plasma waves with electrons and ions, developed theoretical frameworks for the acceleration, transport and radiative processes, and produced numerical codes for the investigation of these processes. The goal of this grant has been further development and testing of this new paradigm, with emphases on the relative acceleration of electrons and ions and on a comprehensive investigation of the turbulence generation, cascade, and damping processes. We review several pieces of important evidence that we have uncovered indicating the crucial roles of turbulence, in and we describe accomplishments during the past two years of this grant.

Petrosian, Vahe↗
NASA NTRS2006

Implications of RHESSI Observations for Solar Flare Models and Energetics

Observations of solar flares in X-rays and gamma-rays provide the most direct information about the hottest plasma and energetic electrons and ions accelerated in flares. The Ramaty High Energy Solar Spectroscopic Imager (RHESSI) has observed over 18000 solar flares in X-rays and gamma-rays since its launch in February of 2002. RHESSI observes the full Sun at photon energies from as low as 3 keV to as high as 17 MeV with a spectral resolution on the order of 1 keV. It also provides images in arbitrary bands within this energy range with spatial resolution as good as 3 seconds of arc. Full images are typically produced every 4 seconds, although higher time resolution is possible. This unprecedented combination of spatial, spectral, and temporal resolution, spectral range and flexibility has led to fundamental advances in our understanding of flares. I will show RHESSI and coordinated observations that confirm coronal magnetic reconnection models for eruptive flares and coronal mass ejections, but also present new puzzles for these models. I will demonstrate how the analysis of RHESSI spectra has led to a better determination of the energy flux and total energy in accelerated electrons, and of the energy in the hot, thermal flare plasma. I will discuss how these energies compare with each other and with the energy contained in other flare-related phenomena such as interplanetary particles and coronal mass ejections.

Holman, Gordon D.↗
NASA NTRS2006

Understanding X-Ray Source Motions in a Solar Flare Loop

RHESSI images of a solar flare on 2002 November 28 showed a 3-6 keV hard X-ray source that was initially located at the flare loop top, split and propagated to the foot points of the loop during the flare rise phase, and then propagated back up to the loop top during the declining phase of the flare (Sai, Holman, & Dennis 2006). Higher energy X-ray sources were located lower in the legs of the loop during this period of source evolution, with X-rays above 25 keV seen only at the foot points. Sui, Holman, & Dennis suggested that this spatial evolution reflected the evolution of the spectral index and low-energy cutoff to the distribution of accelerated electrons in the flare. We construct a model flare loop and electron distribution injected at the top of this loop to reproduce the source evolution of the November 28 flare. We determine the constraints on the loop model and the evolution of the accelerated electron distribution. We also study the implications of the model for energy deposition into the loop plasma, and the integrated and imaged X-ray spectra. This work is supported in part by the RHESSI Project and the NASA Guest Investigator Program.

Holman, Gordon D.↗
NASA NTRS2008

High Variability in Vela X-1: Giant Flares and Off States

Aims. We investigate the spectral and temporal behavior of the high mass X-ray binary Vela X-1 during a phase of high activity, with special focus on the observed giant flares and off states. Methods. INTEGRAL observed Vela X-1 in a long almost uninterrupted observation for two weeks in 2003 Nov/Dec. The data were analyzed with OSA 7.0 and FTOOLS 6.2. We derive the pulse period, light curves, spectra, hardness ratios, hardness intensity diagrams, and study the eclipse. Results. In addition to an already high activity level, Vela X-1 exhibited several very intense flares, the brightest ones reaching a maximum intensity of more than 5 Crab in the 20-40 keV band and several off states where the source is no longer detected by INTEGRAL. We determine the pulse period to be 283.5320 +/- 0.0002 s which is stable throughout the whole observation. Analyzing the eclipses resulted in an improvement of the ephemeris. Spectral analysis of the flares shows that there seem to be two types of flares: relatively brief flares which can be extremely intense, and show spectral softening, contrary to high intensity states which are longer and show no softening. Conclusions. Both flares and off states are interpreted as being due to a strongly structured wind of the optical companion. When Vela X-1 encounters a cavity with strongly reduced density, the flux will drop triggering the onset of the propeller effect which inhibits further accretion, thus giving rise to off states. The required drop of the density of the material to trigger the propeller effect in Vela X-1 is of the same order as predicted by theoretical papers on the densities in the OB star winds. The same structured wind can give rise to the giant flares when Vela X-1 encounters a dense blob in the wind.

Kreykenbohm, Ingo↗
NASA NTRS2011

Variability of Thermosphere and Ionosphere Responses to Solar Flares

We investigated how the rise rate and decay rate of solar flares affect the thermosphere and ionosphere responses to them. Model simulations and data analysis were conducted for two flares of similar magnitude (X6.2 and X5.4) that had the same location on the solar limb, but the X6.2 flare had longer rise and decay times. Simulated total electron content (TEC) enhancements from the X6.2 and X5.4 flares were 6 total electron content units (TECU) and approximately 2 TECU, and the simulated neutral density enhancements were approximately 15% -20% and approximately 5%, respectively, in reasonable agreement with observations. Additional model simulations showed that for idealized flares with the same magnitude and location, the thermosphere and ionosphere responses changed significantly as a function of rise and decay rates. The Neupert Effect, which predicts that a faster flare rise rate leads to a larger EUV enhancement during the impulsive phase, caused a larger maximum ion production enhancement. In addition, model simulations showed that increased E x B plasma transport due to conductivity increases during the flares caused a significant equatorial anomaly feature in the electron density enhancement in the F region but a relatively weaker equatorial anomaly feature in TEC enhancement, owing to dominant contributions by photochemical production and loss processes. The latitude dependence of the thermosphere response correlated well with the solar zenith angle effect, whereas the latitude dependence of the ionosphere response was more complex, owing to plasma transport and the winter anomaly.

Qian, Liying↗
NASA NTRS2012

The Origin of the EUV Late Phase: A Case Study of the C8.8 Flare on 2010 May 5

Since the launch of NASA's Solar Dynamics Observatory on 2010 February 11, the Extreme ultraviolet Variability Experiment (EVE) has observed numerous flares. One interesting feature observed by EVE is that a subset of flares exhibit an additional enhancement of the 2-3 million K emission several hours after the flares soft X-ray emission. From the Atmospheric Imaging Assembly (AIA) images, we observe that this secondary emission, dubbed the EUV late phase, occurs in the same active region as the flare but not in the same coronal loops. Here, we examine the C8.8 flare that occurred on 2010 May 5 as a case study of EUV late phase flares. In addition to presenting detailed observations from both AIA and EVE, we develop a physical model of this flare and test it using the Enthalpy Based Thermal Evolution of Loops (EBTEL) model.

Hock, R. A.↗
NASA NTRS2012

Thermal Evolution and Radiative Output of Solar Flares Observed by the EUV Variability Experiment (EVE)

This paper describes the methods used to obtain the thermal evolution and radiative output during solar flares as observed by the Extreme u ltraviolet Variability Experiment (EVE) onboard the Solar Dynamics Ob servatory (SDO). Presented and discussed in detail are how EVE measur ements, due to its temporal cadence, spectral resolution and spectral range, can be used to determine how the thermal plasma radiates at v arious temperatures throughout the impulsive and gradual phase of fla res. EVE can very accurately determine the radiative output of flares due to pre- and in-flight calibrations. Events are presented that sh ow the total radiated output of flares depends more on the flare duration than the typical GOES X-ray peak magnitude classification. With S DO observing every flare throughout its entire duration and over a la rge temperature range, new insights into flare heating and cooling as well as the radiative energy release in EUV wavelengths support exis ting research into understanding the evolution of solar flares.

Chamberlin, P. C.↗
NASA NTRS2016

The Variable Crab Nebula: Evidence for a Connection Between GeV Flares and Hard X-ray Variations

In 2010, hard X-ray variations (Wilson-Hodge et al. 2011) and GeV flares (Tavani et al 2011, Abdo et al. 2011) from the Crab Nebula were discovered. Connections between these two phenomena were unclear, in part because the timescales were quite different, with yearly variations in hard X-rays and hourly to daily variations in the GeV flares. The hard X-ray flux from the Crab Nebula has again declined since 2014, much like it did in 2008-2010. During both hard X-ray decline periods, the Fermi LAT detected no GeV flares, suggesting that injection of particles from the GeV flares produces the much slower and weaker hard X-ray variations. The timescale for the particles emitting the GeV flares to lose enough energy to emit synchrotron photons in hard X-rays is consistent with the yearly variations observed in hard X-rays and with the expectation that the timescale for variations slowly increases with decreasing energy. This hypothesis also predicts even slower and weaker variations below 10 keV, consistent with the non-detection of counterparts to the GeV flares by Chandra (Weisskopf et al 2013). We will present a comparison of the observed hard X-ray variations and a simple model of the decay of particles from the GeV flares to test our hypothesis.

Variable Crab Nebula↗
NASA NTRS2016

Photospheric Current Spikes as Possible Predictors of Flares

Flares involve generation of the largest current densities in the solar atmosphere. This suggests the hypothesis that prior to a large (M,X) flare there are related time dependent changes in the photospheric current distribution, and hence in the resistive heating rate in neutral line regions (NLRs). If this is true, these changes might be useful predictors of flares. Evidence supporting this hypothesis is presented. Results from a data driven, near photospheric, 3D magnetohydrodynamic type model suggest the model might be useful for predicting M and X flares several hours to several days in advance. The model takes as input the photospheric magnetic field observed by the Helioseismic & Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) satellite. The model computes quantities in every active region (AR) pixel for 14 ARs, with spurious Doppler periods due to SDO orbital motion filtered out of the time series of the magnetic field for each pixel. Spikes in the NLR resistive heating rate Q, appearing as increases by orders of magnitude above background values in the time series of Q are found to occur, and appear to be correlated with the occurrence of M or X flares a few hours to a few days later. The subset of spikes analyzed at the pixel level are found to occur on HMI and granulation scales of 1 arcsec and 12 minutes. Spikes are found in NLRs with and without M or X flares, and outside as well as inside NLRs, but the largest spikes are localized in the NLRs of ARs with M or X flares, and associated with horizontal magnetic field strengths several hG, and vertical magnetic field strengths several orders of magnitude smaller, suggesting that the spikes are associated with current sheets.

Goodman, Michael L.↗