Joint Effects of Compton Backscattering and Low-Energy Cutoff on the Flattening of Solar Hard X-Ray Spectra at Lower Energies

Theoretical calculation has shown that the spectrum of the Compton backscattering component in solar hard X-ray flares has a peak around 30 keV for a primary power-law source. Thus the superposition of the Compton backscattering component could cause a photon spectrum received at the Earth to be flattened below the peak energy and steeper above the peak energy. On the other hand, because a thick-target bremsstrahlung photon with a given energy E only could be produced by a nonthermal electron with an energy larger than E, thus if a power-law electron spectrum is cutoff below an energy E _c, then the produced photon spectrum will become flattened below E _c. In this work we present a calculation of the joint effects of the Compton backscattering and the low-energy cutoff on the spectral characteristics of the received solar hard X-ray in the energy range 10–100 keV. The results show that the flattening caused purely by the Compton backscattering could be comparable with that by the low-energy cutoff for hard spectra. So, it is obvious that the joint effects of the low-energy cutoff and the Compton backscattering could result in the received photon spectra to be much more flattened at lower energies. On the other hand, compared to the primary photon spectrum, the received photon spectral index will increase about 0.15 due to the Compton backscattering at higher energy, which seems independent of the primary spectral index.     

On the Lower Energy Cutoff of Nonthermal Electrons in Solar Flares

1 INTRODUCTIONThe lower energy cutoff of nonthermal electron beams is an important quantity. Not only isit related to the acceleration mechanism, but it also determines the total number of acceleratedelectrons and the energy they carry. The power-law of electron beams cannot extend to lowerenergies indefinitely for if it did, it would imply an indeflnite1y large nuInber of electrons.A lower energy cutoff (E.), therefore, must exist, to keep the number of electrons within areasonable rang…     

Interpreting Yohkoh hard and soft X-ray flare observations

A simple model is presented to account for theYohkoh flare observations of Feldmanet al. (1994), and Masuda (1994). Electrons accelerated by the flare are assumed to encounter the dense, small regions observed by Feldmanet al. at the tops of impulsively flaring coronal magnetic loops. The values of electron density and volume inferred by Feldmanet al. imply that these dense regions present an intermediate thick-thin target to the energised electrons. Specifically, they present a thick (thin) target to electrons with energy much less (greater) thanE _c , where 15 keV <E _c < 40 keV. The electrons are either stopped at the loop top or precipitate down the field lines of the loop to the footpoints. Collisional losses of the electrons at the loop top produce the heating observed by Feldmanet al. and also some hard X-rays. It is argued that this is the mechanism for the loop-top hard X-ray sources observed in limb flares by Masuda. Adopting a simple model for the energy losses of electrons traversing the dense region and the ambient loop plasma, hard X-ray spectra are derived for the loop-top source, the footpoint sources and the region between the loop top and footpoints. These spectra are compared with the observations of Masuda. The model spectra are found to qualitatively agree with the data, and in particular account for the observed steepening of the loop-top and footpoint spectra between 14 and 53 keV and the relative brightnesses of the loop-top and footpoint sources.     

Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy (E _c ). The growth rate of LWs increases with the steepness index (δ) and decreases with the power-law index (α). The wave number of the fastest growing LWs (kλ _D ), decreases with the characteristic velocity of the power-law electrons ( \(v_{c}=\sqrt{2E_{c}/m_{e}}\) ) and increases with the thermal velocity of ambient electrons (v _T ). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.     

Energy Cutoff,Energy Index,and Density of Nonthermal Electrons Responsible for Solar Microwave and HXR Bursts

The purpose of this paper is to investigate the crossing point of the power-law distribution lines calculated during different times of microwave and hard X-ray bursts. A linear correlation between the logarithm of the total density and the energy index of nonthermal electrons described by a power-law is proven to be a necessary condition for the crossing of a group of power-law distribution lines corresponding to the time evolution of the nonthermal electrons during a solar microwave and HXR burst. The common crossing point of these lines may be considered as evidence of a common cutoff energy of the nonthermal electrons responsible for gyrosynchrotron or bremsstrahlung radiation. When the common crossing point is close to the low-energy cutoff, the correlation coefficient is negative, and vice versa. The result may be useful for estimating the cutoff energy as well as the particle acceleration mechanism.     

On the Evolution of the Lower Energy Cutoff of Nonthermal Electrons in Solar Flares

1 INTRODUCTION Gan, Li and Chang (2001a) proposed a quantitative method to obtain the lower energycutoff (Er) of power-law electrons from the observed broken-down double power-law hard Xray spectrum. Most recently Can et al. (2002) improved the method and let it be moreself-consistent. They applied their improved method to the 54 hard X-ray events observed withBATSE/CGRO and acquired more general results in comparison with those obtained by Canet al. (2001b). Despite the data is rel…     

A Study of the Low Energy Cutoff of Nonthermal Electrons in RHESSI Flares

The flattening at the low energy end of the hard X-ray (HXR) photon spectrum of solar flares was generally thought to be due to a cutoff of nonthermal electrons in flares. However, some authors have suggested that inverse Compton scattering (i.e., the albedo effect) or certain other reaction of flare photons with the lower atmosphere can also lead to the flattening. This paper adopts the method of deriving the cutoff proposed by Gan et al. ^[12–14], and makes a statistical analysis on 100 flares observed by the satellite Ramaty High Energy Solar Spectroscopy Imager (RHESSI) in 2002–2005. We found that after the albedo correction, the HXR photon spectra of 18 flares can be fitted with single powerlaw spectra, and those of 80 flares, with double power-law spectra. Besides, 21 flares can be directly interpreted with a single power-law electron spectrum plus a low energy cutoff. The range of the low energy cutoff is 20–50 keV and the mean value is approximately 30 keV. Some other possible interpretations are also investigated.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (≲1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting ∼3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to ≳100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically ∼10² kV compared to ∼10 kV for auroral substorms.

     

On the origin of subsecond pulses at 17 GHz

We have analyzed three flare events with subsecond structures in hard X-rays (CGRO/ BATSE) and 17 GHz data (Nobeyama radioheliograph). It was shown that microwave subsecond brightenings (SSB) were generated by directly precipitating electrons with energy of 100–200 keV from tiny regions close to footpoints. In two events, when high correlation between microwaves and X-rays was observed, the SSB can be interpreted in terms of gyrosynchrotron emission. Plasma emission seems to be a more credible explanation of the spontaneous pulses in the event when poor correlation with X-rays was observed.     

Temporal correlation of solar hard X-ray bursts with chromospheric evaporation

During the impulsive phase of many solar flares, blueshifted emission wings are observed on the soft X-ray spectral lines of highly excited ions that are produced in the flare plasma. This emission has been commonly interpreted as chromospheric evaporation of material from the footpoints of coronal loops by non-thermal particle beams, although the question of whether the bulk of the energy is carried by electrons or ions (protons) has been the subject of much debate. The precise temporal relationship between the onsets of the blueshifted emission and the hard X-ray bursts is particularly important in resolving the mechanism of energy transfer to the hot plasma in the impulsive phase. A sample of flares observed with the Bragg Crystal Spectrometer (BCS) onYohkoh has been analysed for blueshifted emission and the results compared with hard X-ray light turves obtained with the Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO). In some flares, the blueshifted emission precedes the onset of the hard X-rays by up to 100 s. There is no evidence for a temporal correlation between the maximum energy input to the hard X-ray bursts and the maximum blueshifted intensity. These results lend support to those models favouring protons as the dominant energy carrier in the impulsive phase of flares and are inconsistent with the hypothesis that the bulk of the energy resides in electron beatos, although some other energy input, while unlikely, cannot be completely eliminated.     

Compttonization-softening and the hard X-ray spectrum of CYG X-1

The Comptonization-softening of very hard X-ray photons withEm ₀ c ² in the cold electron gas is discussed. The frequency diffusion equation for Comptonization of hard X-rays has been derived to the zero-temperature approximation. By use of this equation, and under the assumption of pair-annihilation origin of hard X-rays, we calculated the energy spectrum withE>80 keV, for Cyg X-1, which is in good fit with the observation. The high-energy edge 400 keV of the observed spectrum and the small bump in the range 100–200 keV also can be explained by this way.     

Observations of soft gamma-ray or hard X-ray bursts in the GRIF experiment on the <Emphasis Type="Italic">Mir</Emphasis> orbiting station

During the GRIF experiment onboard the Mir orbiting station, the sky was monitored with a PX-2 wide-field (～1 sr) scintillation X-ray spectrometer to detect bursts in the photon energy range 10–300 keV. Because of the comprehensive instrumentation, which, apart from the X-ray and gamma-ray instruments, also included charged-particle detectors, the imitations of astrophysical bursts by magnetospheric electron precipitations and strongly ionizing nuclei were effectively filtered out. It was also possible to separate solar and atmospheric events. Several tens of bursts interpreted as being astrophysical were detected in the experiment at sensitivity levels S～10^?7 erg cm^?2 (for bursts whose spectra were characterized by effective temperatures kT～100 keV) and S～3×10^?8 erg cm^?2 (for bursts with kT～25 keV). Some of the soft gamma-ray or hard X-ray bursts with kT～10–50 keV were identified with the bursting pulsar GRO J1744-28. Our estimate of the detection rate for cosmological soft gamma-ray or hard X-ray bursts from the entire sky suggests that the distributions of long-duration (>1 s) gamma-ray bursts (GRBs) in characteristic energy kT and duration are inconsistent with the steady-state cosmological model in which the evolution of burst sources is disregarded. Based on GRIF and BATSE/CGRO data, we conclude that most of the GRB sources originate at redshifts 1<z<5.     

A Clarification on the invariable point in the power-law energy spectra of non-thermal electrons of solar flares

The invariable point of non-thermal electrons was proposed two years ago, based on analyzing the two intense gamma-ray line flares observed with the X2 detector on GRS/SMM. Due to too strong hard X-ray flux in those two flares, the influence of pile-up effect might not be fully excluded. In this paper, we check the invariable point by using some medium hard X-ray events observed with HXRBS/SMM and BATSE/CGRO. It is found that the invariable point could indeed appear in some weaker hard X-ray events, in which the pile-up effect cannot play a role. Further refinement should be based on the observations with a high energy resolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectral development of a solar X-ray burst observed on OSO-7

The UCSD solar X-ray instrument on the OSO-7 satellite observes X-ray bursts in the 2–300 keV range with 10.24 s time resolution. Spectra obtained from the proportional counter and scintillation counter are analyzed for the event of November 16, 1971, at 0519 UT in terms of thermal (exponential spectrum) and non-thermal (power law) components. The energy content of the approximately 20 × 10⁶K thermal plasma increased with the 60 s duration hard X-ray burst which entirely preceded the 5 keV soft X-ray maximum. If the hard X-rays arise by thick target bremsstrahlung, the nonthermal electrons above 10 keV have sufficient energy to heat the thermally emitting plasma. In the thin target case the collisional energy transfer from non-thermal electrons suffices if the power law electron spectrum is extrapolated below 10 keV, or if the ambient plasma density exceeds 4 × 10¹⁰ cm^–3.Formerly at UCSD.     

INTEGRAL serendipitous detection of the gamma-ray microquasar LS 5039

LS 5039 is the only X-ray binary persistently detected at TeV energies by the Cherenkov HESS telescope. It is moreover a γ-ray emitter in the GeV and possibly MeV energy ranges. To understand important aspects of jet physics, like the magnetic field content or particle acceleration, and emission processes, such as synchrotron and inverse Compton (IC), a complete modeling of the multiwavelength data is necessary. LS 5039 has been detected along almost all the electromagnetic spectrum thanks to several radio, infrared, optical and soft X-ray detections. However, hard X-ray detections above 20 keV have been so far elusive and/or doubtful, partly due to source confusion for the poor spatial resolution of hard X-ray instruments. We report here on deep (∼300 ks) serendipitous INTEGRAL hard X-ray observations of LS 5039, coupled with simultaneous VLA radio observations. We obtain a 20–40 keV flux of 1.1±0.3 mCrab (5.9 (±1.6) ×10⁻¹² erg cm⁻² s⁻¹), a 40–100 keV upper limit of 1.5 mCrab (9.5×10⁻¹² erg cm⁻² s⁻¹), and typical radio flux densities of ∼25 mJy at 5 GHz. These hard X-ray fluxes are significantly lower than previous estimates obtained with BATSE in the same energy range but, in the lower interval, agree with extrapolation of previous RXTE measurements. The INTEGRAL observations also hint to a break in the spectral behavior at hard X-rays. A more sensitive characterization of the hard X-ray spectrum of LS 5039 from 20 to 100 keV could therefore constrain key aspects of the jet physics, like the relativistic particle spectrum and the magnetic field strength. Future multiwavelength observations would allow to establish whether such hard X-ray synchrotron emission is produced by the same population of relativistic electrons as those presumably producing TeV emission through IC.     

Comment on the X-ray event of July 7, 1966

According to Snijders (1968) the decay profile of an X-ray burst determines the effective temperature describing the distribution of fast electrons in the emitting source. In this paper it is concluded that the observations of the hard X-ray burst of 7 July, 1966; 0038 UT are not in disagreement with the concept of thermal bremsstrahlung from electrons with a Maxwellian distribution of about 10⁸ K. Some physical parameters of the source are determined. The magnetic field strength is found to be about 1200 gauss. The initial temperature kT ₀ is approximately 40 keV.     

Interpretation of time characteristics of solar X-ray bursts referring to associated microwave bursts

It has been controversial whether the flare-associated hard X-ray bursts are thermal emission or non-thermal emission. Another controversial point is whether or not the associated microwave impulsive burst originates from the common electrons emitting the hard X-ray burst.It is shown in this paper that both the thermal and non-thermal bremsstrahlung should be taken into account in the quantitative explanation of the time characteristics of the hard X-ray bursts observed so far in the photon energy range of 10–150 keV. It is emphasized that the non-thermal electrons emitting the hard X-rays and those emitting the microwave impulsive burst are not common. The model is as follows, which is also consistent with the radio observations.At the explosive phase of the flare a hot coronal condensation is made, its temperature is generally 10⁷ to 10⁸K, the number density is about 10¹⁰ cm^–3 and the total volume is of the order of 10²⁹ cm³. A small fraction, 10^–3–10^–4, of the thermal electrons is accelerated to have power law distribution. Both the non-thermal and thermal electrons in the sporadic condensation contribute to the X-ray bursts above 10 keV as the bremsstrahlung. Fast decay of the harder X-rays (say, above 20 keV) for a few minutes is attributed to the decay of non-thermal electrons due to collisions with thermal electrons in the hot condensation. Slower decay of the softer X-rays including around 10 keV is attributed to the contribution of thermal component.The summary of this paper was presented at the Symposium on Solar Flares and Space Research, COSPAR, Tokyo, May, 1968.     

Chromospheric Height and Density Measurements in a Solar Flare Observed with RHESSI – II. Data Analysis

We present an analysis of hard X-ray imaging observations from one of the first solar flares observed with the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft, launched on 5 February 2002. The data were obtained from the 22 February 2002, 11:06 UT flare, which occurred close to the northwest limb. Thanks to the high energy resolution of the germanium-cooled hard X-ray detectors on RHESSI we can measure the flare source positions with a high accuracy as a function of energy. Using a forward-fitting algorithm for image reconstruction, we find a systematic decrease in the altitudes of the source centroids z(ε) as a function of increasing hard X-ray energy ε, as expected in the thick-target bremsstrahlung model of Brown. The altitude of hard X-ray emission as a function of photon energy ε can be characterized by a power-law function in the ε=15–50 keV energy range, viz., z(ε)≈2.3(ε/20 keV)^−1.3 Mm. Based on a purely collisional 1-D thick-target model, this height dependence can be inverted into a chromospheric density model n(z), as derived in Paper I, which follows the power-law function n _e(z)=1.25×10¹³(z/1 Mm)^−2.5 cm⁻³. This density is comparable with models based on optical/UV spectrometry in the chromospheric height range of h≲1000 km, suggesting that the collisional thick-target model is a reasonable first approximation to hard X-ray footpoint sources. At h≈1000–2500 km, the hard X-ray based density model, however, is more consistent with the `spicular extended-chromosphere model' inferred from radio sub-mm observations, than with standard models based on hydrostatic equilibrium. At coronal heights, h≈2.5–12.4 Mm, the average flare loop density inferred from RHESSI is comparable with values from hydrodynamic simulations of flare chromospheric evaporation, soft X-ray, and radio-based measurements, but below the upper limits set by filling-factor insensitive iron line pairs.     

Observation of ultra low hard X-ray flux from Cyg X-1 —A possible partial occulation of the X-ray source

The black hole candidate Cyg X-1 was observed in ultra low state on march 30, 1997 using Large Area Scintillation counter Experiment (LASE) in the hard X-ray energy region of 20–180 keV. During the 30 minute exposure a combined signal of 68 sigma was obtained, however, the measured flux at 50 keV was lower by a factor of 2 than the minimum flux reported so far. Using the recent orbital ephemeris of the source, our snap-shot observations were made at ϕ_5.6 = 0.915, which corresponds to the binary minimum revealed by the ASM light curves. The daily average data from the BATSE detectors give the source intensity level to be higher by a factor of 5. Very low flux values measured in the present experiment suggest that the hard X-ray source may have been partially occulted by the primary companion during its transit near the X-ray minimum.