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COMPTEL solar flare observations

COMPTEL as part of a solar target of opportunity campaign observed the sun during the period of high solar activity from 7-15 Jun. 1991. Major flares were observed on 9 and 11 Jun. Although both flares were large GOES events (greater than or = X10), they were not extraordinary in terms of gamma-ray emission. Only the decay phase of the 15 Jun. flare was observed by COMPTEL. We report the preliminary analysis of data from these flares, including the first spectroscopic measurement of solar flare neutrons. The deuterium formation line at 2.223 MeV was present in both events and for at least the 9 Jun. event, was comparable to the flux in the nuclear line region of 4-8 MeV, consistent with Solar-Maximum Mission (SSM) Observations. A clear neutron signal was present in the flare of 9 Jun. with the spectrum extending up to 80 MeV and consistent in time with the emission of gamma-rays, confirming the utility of COMPTEL in measuring the solar neutron flux at low energies. The neutron flux below 100 MeV appears to be lower than that of the 3 Jun. 1982 flare by more than an order of magnitude. The neutron signal of the 11 Jun. event is under study. Severe dead time effects resulting from the intense thermal x-rays require significant corrections to the measured flux which increase the magnitude of the associated systematic uncertainties.

Ryan, J. M.↗

X-rays from stellar flares

A summary of X-ray observations of flares on dMe, active spectroscopic binaries and young stars is presented. Consideration is given to the energy associated with the X-ray emission and its relation to other components of the flare energy budget, the time behavior of the flaring plasma as seen by the X-ray emission, and comparisons of stellar flare parameters with solar compact and two ribbon flares. Flares are easily detected when the contrast in the emission from the flaring plasma relative to the stellar photosphere is large as in the X-ray, microwave, and UV regions of the spectrum.

Linsky, Jeffrey L.↗

The effects of flaring in H1 on the observed velocity field of spirals

This work is part of a larger project in which we want to determine the shapes of dark halos around spiral galaxies. Rotation curves 'probe' the halos in the radial direction. The derived halo mass distributions are badly constrained. The local halo densities fully determine the width of the gas distribution once the gaseous velocity dispersion is known. There where the dark halo dominates, the Full Width at Half Maximum (FWHM) of the gas layer is proportional to (rho(sub halo))(exp -0.5). Therefore, measuring the width of the gas layer probes the halo density directly. In a dark halo dominated potential, the FWHM of the gas layer increases linearly with radius. This increase of the thickness of the gas layer is known as 'flaring'. Flaring has been found inside the stellar disk. Beyond the edge of the stellar disk, the analysis is hampered by the onset of the warp. Since the galaxy we are studying, NGC 4244, has no significant warp we hope to extend Rupen's analysis into the halo dominated regime. The usual method to derive a rotation curve from an observed 2-dimensional velocity field is to assume that the hydrogen is distributed in infinitely thin rings. For a flaring disk, any line of sight samples many different parts of the galaxy, all having different densities and projected velocities. In order to fully exploit the information contained in the gas distribution, we have to understand the effects of flaring on the observables (the spectrum for each point of the galaxy). We have investigated the effects of a flaring disk on the observed velocity field. It is obvious that the largest (kinematical) effects are to be expected for low density dark halos at large inclinations. For low mass galaxies we expect that the flaring of the H1 layer will have a major effect on the observed kinematics. For galaxy with intermediate V(sub max,halo) seen at intermediate inclinations, one overestimates Vsin(i) typically by a few percent. For more massive galaxies, any effects arising from the flaring H1 layer are minuscule unless the inclination is not too far from 90 deg.

Olling, Rob↗

Diagnostics of electron-heated solar flare models. III - Effects of tapered loop geometry and preheating

A series of hydrodynamic numerical simulations of nonthermal electron-heated solar flare atmospheres and their corresponding soft X-ray Ca XIX emission-line profiles, under the conditions of tapered flare loop geometry and/or a preheated atmosphere, is presented. The degree of tapering is parameterized by the magnetic mirror ratio, while the preheated atmosphere is parameterized by the initial upper chromospheric pressure. In a tapered flare loop, it is found that the upward motion of evaporated material is faster compared with the case where the flare loop is uniform. This is due to the diverging nozzle seen by the upflowing material. In the case where the flare atmosphere is preheated and the flare geometry is uniform, the response of the atmosphere to the electron collisional heating is slow. The upward velocity of the hydrodynamic gas is reduced due not only to the large coronal column depth, but also to the increased inertia of the overlying material. It is concluded that the only possible electron-heated scenario in which the predicted Ca XIX line profiles agree with the BCS observations is when the impulsive flare starts in a preheated dense corona.

Emslie, A. G.↗

The morphology of flare phenomena, magnetic fields, and electric currents in active regions. III - NOAA active region 6233 (1990 August)

We investigate the spatial relationship between vertical electric currents and flare phenomena in NOAA Active Region 6233, which was observed 1990, August 28-31 at Mees Solar Observatory. The two flares studied are the 1N/M1.8 flare on August 28, 22:30 UT and the 1N/M1.6 flare on August 29, 20:35 UT. Using Stokes polarimetry we make magnetograms of the region and compute the vertical current density. Using H-alpha imaging spectroscopy we identify sites of intense nonthermal electron precipitation or of high coronal pressure. The precipitation in these flares is barely strong enough to be detectable. We find that both precipitation and high pressure tend to occur near vertical currents, but that neither phenomenon is cospatial with current maxima. In contrast with the conclusion of other authors, we argue that these observations do not support a current-interruption model for flares, unless the relevant currents are primarily horizontal. The magnetic morphology and temporal evolution of these flares suggest that an erupting filament model may be relevant, but this model does not explicitly predict the relationship between precipitation, high pressure, and vertical currents.

De La Beaujardiere, J.-F.↗

Extreme Ultraviolet Explorer deep survey observations of a large flare on AU Microscopii

We have made the first extended observation of a stellar flare in the EUV with 100 s time resolution. The flare was detected on AU Mic by the Extreme Ultraviolet Explorer satellite at 12:38 UT on 1992 July 15 during a 4 d observation from 1992 July 14 to 18. This was a large flare detected in the Lexan/boron (65-190 A) band with an observed peak count rate of 7.0 +/- 0.5 counts/s, corresponding to a peak luminosity of 10 exp 30 erg/s in the Lexan/boron bandpass. This is significantly above the measured quiescent level of 0.4 +/- 0.2 counts/s. The flare consisted of a sharp peak lasting about 2 hr, followed by a decaying tail that lasted more than a day. The total EUV energy of the event is estimated to be 3 x 10 exp 34 ergs. A second, smaller flare was also observed and is described. We conclude that the large emission measures on order of 6 x 10 exp 53/cu cm are due to large volumes with characteristic length scales of order the stellar radius. We compare these EUV observations with stellar flare observations in other bandpasses and estimate the likelihood of seeing similar flares in future observations.

Cully, Scott L.↗

The 1991 November 9 flare at 03.2 UT: Observations from Yohkoh

We discuss X-ray spectra and soft X-ray images of an M1.9 flare that occurred on 1991 November 9 near 03.2 UT. These data were obtained with instrumentation on the Japanese Yohkoh spacecraft. They cover the entire rise phase and peak flare emission, and the beginning of the decay phase. We determine the dynamics, temperature, and emission measure of the flare as inferred from the X-ray line profiles of resonance lines of Fe XXV, Ca XIX, and S XV. We discuss the morphology of the flare as inferred from the soft X-ray images. The November 9 flare is atypical in that a stronger than usual blueshifted emission component (relative to the stationary component) is observed for the resonance lines at flare onset. We discuss several methods for deconvolving the blueshifted component from the stationary component. The X-ray line profiles are consistent with predictions of numerical simulations of chromospheric evaporation. The X-ray images reveal a flare with a complicated loop geometry that is not fully understood. Many of the features in the images are moving upwards at speeds ranging from a few km/s to about 800 km/s. The blueshifted emission begins near the onset of hard X-ray emission, implying that particle acceleration and upflowing plasma have a common energy source.

Doschek, G. A.↗

Searching for hard X-ray directivity during the rise, peak, and decay phases of solar flares

We have identified 72 large solar flares (peak counting rates more than 1000 counts/s) observed by Hard X-ray Burst Spectroscopy (HXRBS) on-board the Solar Maximum Mission (SMM). Using a database of these flares, we have studied hard X-ray (50-850 keV) spectral center-to-limb variation and its evolution with time. The major results are the following: (1) During the rise phase, the center-to-limb spectral variation is small, with a hardness of delta delta = 0.02 +/- 0.25, and a statistical significance of 0.1 sigma. (2) During the peak phase, the center-to-limb variation is delta delta = 0.13 +/- 0.13, with a statistical significance of 1 sigma. (3) During the decay phase, the center-to-limb variation changes to softening. The softness is relatively large with delta delta = -0.25 +/- 0.21, and a statistical significance of 1.2 sigma. (4) The linear least-squares fits to the spectral center-to-limb variations do not have slopes significantly different from zero during all those three phases. (5) The center events and limb events spectral distributions are shown to be not different by using Kolmogorov-Smirnov two-samples test. (6) The fraction of events detected near the limb is marginally consistent with that expected from isotropically emitting flares. (7) On average, flares evolve as soft-hard-soft. These results suggest that there is no statistically significant evidence for hard X-ray directivity during the rise, peak, and decay phases of solar flares. The hard X-ray radiation pattern at those energies is almost isotropic during all those phases. This lack of directivity (or anisotropy) found in this study is not in agreement with the results discovered by Vestrand et al. (1987) in which they found energetic photon source is anisotropic, using SMM Gamma-Ray Spectrometer (GRS) data at a much higher energy band of 0.3-1 MeV. If we want to interpret the results of Vestrand et al. (1987) and our present results in a self-consistent way, we must conclude that at energies of greater than 50 keV, the Compton backscattering suppresses the hard X-ray anisotropy sufficiently so that no significant directivity can be measured during the rise, peak, and decay phases of solar flares. during the rise, peak, and decay phases of solar flares.

Li, Peng↗

Metric type III bursts from a flaring X-ray bright point near an active region

X-ray bright points (XBPs) are known to show variability on a number of timescales, including impulsive X-ray brightenings. The relationship between these XBP 'flares' and normal flares is poorly known. A fundamental question is whether nonthermal acceleration of particles takes place in XBP flares. We address this issue by seravhing for nonthermal radio emission at metric wavelengths from flaring XBPs identified in Yohkoh/SXT data. Unequivocal evidence for type III-like radio bursts usually attributed to beams of nonthermal electrons on open field lines was found recently by Kundu et al. This suggests that XBP flares are similar to normal flares and can indeed accelerate nonthermal populations of energetic particles. Here we provide further evidence of metric type III bursts from flaring XBPs located near active regions.

Kundu, M. R.↗

New observational facts about particle acceleration and transport during solar flares

Extensive hard X-ray (HXR)/gamma-ray (GR) observations of solar flares, performed during solar cycles 21 and 22 have led to important new discoveries. These data, combined with observations obtained in other parts of the electromagnetic spectrum (soft X-ray, Hard X-ray, optical, and radio) largley contributed to get a better understanding and to develop new ideas on particle acceleration and transport during solar flares. This review presents new observational facts relevant to hard X-ray/gamma-ray producing flares. Among these are the frequent presence of sub-second time structure in the hard X-ray emission, the variability in hard X-ray and radio spatial distributions during a flare and from flare to flare, the evidence for strong gamma-ray line emission from the Corona and the existence of extended phases of the gamma-ray emission lasting for several hours after the flare onset. This ensemble of observations indicates that particle acceleration takes place at different sites in a complex and dynamic magnetic field environment.

Trottel, G.↗

A Mechanism for Bulk Energization in the Impulsive Phase of Solar Flares: MHD Turbulent Cascade

We propose that the large production rate (approximately 10(exp 36)/s) of energetic electrons (greater than or approximately equal to 25 keV) required to account for the impulsive-phase hard X-ray burst in large flares is achieved through MHD turbulent cascade of the bulk kinetic energy of the outflows from many separate reconnection events. Focusing on large two- ribbon eruptive flares as representative of most large flares, we envision the reconnection events to be the driven reconnection of oppositely directed elementary flux tubes pressing into the flare-length current-sheet interface that forms in the wake of the eruption of the sheared core of the preflare bipolar field configuration. We point out that, because the outflows from these driven reconnection events have speeds of order the Alfven speed and because the magnetic field reduces the shear viscosity of the plasma, it is reasonable that the outflows are unstable and turbulent, so that the kinetic energy of an outflow is rapidly dissipated through turbulent cascade. If the largest eddies in the turbulence have diameters of order the expected widths of the outflows (10(exp 7)-10(exp 8)cm), then the cascade dissipation of each of these eddies could produce approximately 10(exp 26) erg burst of energized electrons (approximately 3 x (10(exp 33) 25 keV electrons) in approximately 0.3 s, which agrees well with hard X-ray and radio sub-bursts commonly observed during the impulsive phase. Of order 10(exp 2) simultaneous reconnection events with turbulent outflow would produce the observed rate of impulsive-phase plasma energization in the most powerful flares (approximately 10(exp 36) 25 keV electrons/ s); this number of reconnection sites can easily fit within the estimated 3 x 10(exp 9) cm span of the overall current-sheet dissipation region formed in these large flares. We therefore conclude that MHD turbulent cascade is a promising mechanism for the plasma energization observed in the impulsive phase of solar flares.

LaRosa, T. N.↗

Electron Densities in Solar Flare Loops, Chromospheric Evaporation Upflows, and Acceleration Sites

We compare electron densities measured at three different locations in solar flares: (1) in Soft X-Ray (SXR) loops, determined from SXR emission measures and loop diameters from Yohkoh Soft X-Ray Telescope maps (n(sub e, sup SXR) = (0.2-2.5) x 10(exp 11)/ cu cm); (2) in chromospheric evaporation upflows, inferred from plasma frequency cutoffs of decimetric radio bursts detected with the 0.1-3 GHz spectrometer Phoenix of ETH Zuerich (n(sub e, sup upflow) = (0.3-11) x 10(exp 10)/cu cm; and (3) in acceleration sites, inferred from the plasma frequency at the separatrix between upward-accelerated (type III bursts) and downward-accelerated (reverse-drift bursts) electron beams [n(sub e, sup acc) = (0.6-10) x 10(exp 9)/cu cm]. The comparison of these density measurements, obtained from 44 flare episodes (during 14 different flares), demonstrates the compatibility of flare plasma density diagnostics with SXR and radio methods. The density in the upflowing plasma is found to be somewhat lower than in the filled loops, having ratios in a range n(sub e, sup upflow)/n(sub e, sup SXR) = 0.02-1.3, and a factor of 3.6 higher behind the upflow front. The acceleration sites are found to have a much lower density than the SXR-bright flare loops, i.e., n(sub e, sup acc)/n(sub e, sup SXR) = 0.005- 0.13, and thus must be physically displaced from the SXR-bright flare loops. The scaling law between electron time-of-flight distances l' and loop half-lengths s, l'/s = 1.4 +/- 0.3, recently established by Aschwanden et al. suggests that the centroid of the acceleration region is located above the SXR-bright flare loop, as envisioned in cusp geometries (e.g., in magnetic reconnection models).

Aschwanden, Markus J.↗

Quantifying the Complexity of Flaring Active Regions

While solar physicists have a better understanding of the importance magnetic fields play in the solar heating mechanism, it is still not possible to predict whether or when an active region will flare. In recent decades, qualitative studies of the changes in active region morphology have shown that there is generally an increase in the complexity of the spatial configuration of a solar active region leading up to a flare event. In this study, we quantify the spatial structure of the region using the differential Box-Counting Method (DBC) of fractal analysis. We analyze data from NASA/Marshall Space Flight Centr's vector magnetograph from two flaring active regions: AR 6089 from June 10, 1990, which produced one M1.7 flare, and AR 6659 from June 8, 9 and 10, 1991, this data set including one C5.7 and two M(6.4 and 3.2) flare. (AR 6659 produced several other flares). Several magnetic parameters are studied, including the transverse and longitudinal magnetic field components (Bt and B1), the total field (Bmag), and the magnetic shear, which describes the non-potentiality of the field. Results are presented for the time series of magnetograms in relation to the timing of flare events.

Stark, B.↗

The Stabilizing Effectiveness of Conical Flares on Bodies with Conical Noses

An analysis is presented of published results of force tests on 80 cone-cylinder-flare configurations at Mach numbers of 2.18, 2.81, and 4.04. The contributions, excluding interference effects, of the cone-cylinder bodies to the over-all normal force derivatives have been removed by means of the second-order shock-expansion method, and the normal force derivatives at zero angle of attack due to the flares alone are shown. The results from a wide variety of configurations are correlated by plotting ratios of the normal force derivatives of the flares to the normal force derivatives of cones having the same included angle. Comparisons are made of the experimental normal force results with the normal force derivatives obtained by assuming conical flow over the flares and with those obtained by use of the second-order shock-expansion method. The comparisons show that use of the second-order shock-expansion method is generally the superior of the two, and in most cases gives values of the normal force derivatives of the flares which agree very well with the experimental results. Centers of pressure of the flares are presented and comparisons are made with results obtained from the theories mentioned. In general, the comparisons show that the assumption of conical flow over the flares is comparable to use of the second-order shock-expansion method in determining the centers of pressure, and in many cases both methods give values which agree closely with the experimental results.

Kirk, Donn B.↗

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.↗

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.↗

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.↗

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.↗