An Improved Method to Derive the Lower Energy Cutoff of non-Thermal Electrons From Hard x-Rays of Solar Flares

By changing a dimensionless calculation to a dimensional one, introducing a more accurate bremsstrahlung cross section, and using a more reasonable fitting energy range, we have recalculated the hard X-ray bremsstrahlung produced by a beam of power-law electrons with a lower energy cutoff (E _c). The method to deduce E _c from the hard X-ray spectral observations has therefore been refined in comparison with our previous one. The universality of this method has been clarified and discussed. We have applied this improved method to the 54 BATSE/Compton Gamma Ray Observatory (CGRO) hard X-ray events. It was found that about 44% of sample hard X-ray spectra can be directly explained by a beam of power-law electrons with a lower energy cutoff. The value of E _c, varying from 45 keV to 97 keV, is on average 60 keV. Another 44% of sample hard X-ray spectra might be explained by a beam of power-law electrons with the energy cutoff lower than 45 keV, which is however beyond the availability of BATSE/CGRO. Still another 11% sample hard X-ray spectra cannot be explained by a beam of power-law electrons with a lower energy cutoff. These results, based on the lower energy resolution data, however, should be compared in the future with that based on a higher energy resolution data, like the data from HESSI.     

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.     

Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey

The Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) X-ray data base (February 2002 – May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularized inversion technique, we determine the mean electron flux distribution from count spectra for a selection of events with flat photon spectra in the 15 – 20 keV energy range. Such spectral behavior is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range (e.g., a low-energy cutoff in the mean electron spectra of nonthemal particles). We have found 18 cases that exhibit a statistically significant local minimum (a dip) in the range of 13 – 19 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction is applied, all low-energy cutoffs in the mean electron spectrum are removed, and hence the low-energy cutoffs in the mean electron spectrum of solar flares above ∼ 12 keV cannot be viewed as real features. If low-energy cutoffs exist in the mean electron spectra, their energies should be less than ∼ 12 keV.     

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.

     

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.     

Observations of solar gamma ray continuum between 360 keV and 7 MeV on August 4, 1972

Measurements were made of the time-averaged gamma ray energy loss spectrum in the energy range 360 keV to 7 MeV by the gamma ray detector on the OSO-7 satellite during the 3B flare on August 4, 1972. The differential photon spectrum unfolded from this spectrum after subtracting the background spectrum and contributions from gamma ray lines is best described by a power law with spectral index of 3.4±0.3 between 360–700 keV and by an exponential law of the form exp (-E/E ₀) with E ₀ = 1.0±0.1 MeV above 700 keV. It is suggested that this spectrum is due to nonthermal electron bremsstrahlung from a population of electrons, with a strong break in the spectrum at 2 MeV. Since the observational data indicates that the matter number density must be n _H ? 5 × 10¹⁰ cm^-3 in the production region, the number of electrons above 100 keV required to explain the results is ?2 × 10³⁴.     

Multi-Wavelength Analysis of High-Energy Electrons in Solar Flares: A Case Study of the August 20, 2002 Flare

A multi-wavelength spatial and temporal analysis of solar high-energy electrons is conducted using the August 20, 2002 flare of an unusually flat (γ₁ = 1.8) hard X-ray spectrum. The flare is studied using RHESSI, Hα, radio, TRACE, and MDI observations with advanced methods and techniques never previously applied in the solar flare context. A new method to account for X-ray Compton backscattering in the photosphere (photospheric albedo) has been used to deduce the primary X-ray flare spectra. The mean electron flux distribution has been analysed using both forward fitting and model-independent inversion methods of spectral analysis. We show that the contribution of the photospheric albedo to the photon spectrum modifies the calculated mean electron flux distribution, mainly at energies below ∼100 keV. The positions of the Hα emission and hard X-ray sources with respect to the current-free extrapolation of the MDI photospheric magnetic field and the characteristics of the radio emission provide evidence of the closed geometry of the magnetic field structure and the flare process in low altitude magnetic loops. In agreement with the predictions of some solar flare models, the hard X-ray sources are located on the external edges of the Hα emission and show chromospheric plasma heated by the non-thermal electrons. The fast changes of Hα intensities are located not only inside the hard X-ray sources, as expected if they are the signatures of the chromospheric response to the electron bombardment, but also away from them.     

Observation of the energy spectrum of cosmic diffuse X-rays in the energy range 20 keV-4 MeV

Balloon observations of the cosmic diffuse component of hard X-rays were conducted with two independent directional counters in two energy bands, from 20 keV to 120 keV and from 90 keV to 4 MeV. The build-up effect of primary X-rays and the altitude dependence of atmospheric X-rays were properly taken into account in the analysis of the growth curves. These two experiments gave consistent results in the overlapping energy region. If the differential energy spectrum of the photon flux is represented by a power lawE ^?α, the value of α is 2.3 up to 100 keV, gradually increases to 2.8 at about 500 keV, and decreases to 2.0 thereabove. The spectrum above 300 keV is in parallel to the Apollo-15 spectrum, whereas the absolute intensity is somewhat smaller. The shape of the spectrum suggests the necessity of a multi-component theory on the origin of cosmic diffuse X-rays.     

Evidence for an ionized disc in the narrow-line Seyfert 1 galaxy Ark 564

We present simultaneous ASCA and RXTE observations of Ark 564, the brightest known 'narrow-line' Seyfert 1 in the 2–10 keV band. The measured X-ray spectrum is dominated by a steep (Γ≈2.7) power-law continuum extending to at least 20 keV, with imprinted Fe K-line and edge features and an additional 'soft excess' below ∼1.5 keV. The energy of the iron K-edge indicates the presence of highly ionized material, which we identify in terms of reflection from a strongly irradiated accretion disc. The high reflectivity of this putative disc, together with its strong intrinsic O  viii Ly α and O  viii recombination emission, can also explain much of the observed soft excess flux. Furthermore, the same spectral model also provides a reasonable match to the very steep 0.1–2 keV spectrum deduced from ROSAT data. The source is much more rapidly variable than 'normal' Seyfert 1s of comparable luminosity, increasing by a factor of ∼50 per cent in 1.6 h, with no measurable lag between the 0.5–2 keV and 3–12 keV bands, consistent with much of the soft excess flux arising from reprocessing of the primary power-law component in the inner region of the accretion disc. We note, finally, that if the unusually steep power-law component is a result of Compton cooling of a disc corona by an intense soft photon flux, then the implication is that the bulk of these soft photons lie in the unobserved extreme ultraviolet.     

Fourier-resolved energy spectra of the Narrow-Line Seyfert 1 Mkn 766

We compute Fourier-resolved X-ray spectra of the Seyfert 1 Markarian 766 to study the shape of the variable components contributing to the 0.3–10 keV energy spectrum and their time-scale dependence. The fractional variability spectra peak at 1–3 keV, as in other Seyfert 1 galaxies, consistent with either a constant contribution from a soft excess component below 1 keV and Compton reflection component above 2 keV or variable warm absorption enhancing the variability in the 1–3 keV range. The rms spectra, which show the shape of the variable components only, are well described by a single power law with an absorption feature around 0.7 keV, which gives it an apparent soft excess. This spectral shape can be produced by a power law varying in normalization, affected by an approximately constant (within each orbit) warm absorber, with parameters similar to those found by Turner et al. for the warm-absorber layer covering all spectral components in their scattering scenario  [ N _H∼ 3 × 10²¹ cm⁻², log(ξ) ∼ 1]  . The total soft excess in the average spectrum can therefore be produced by a combination of constant warm absorption on the power-law plus an additional less variable component. On shorter time-scales, the rms spectrum hardens and this evolution is well described by a change in power-law slope, while the absorption parameters remain the same. The frequency dependence of the rms spectra can be interpreted as variability arising from propagating fluctuations through an extended emitting region, whose emitted spectrum is a power law that hardens towards the centre. This scenario reduces the short time-scale variability of lower energy bands making the variable spectrum harder on shorter time-scales and at the same time explains the hard lags found in these data by Markowitz et al.     

Hard X-ray spectrum of Mkn 421 during the active phase

Spectral measurement of Mkn 421 were made in the hard X-ray energy band of 20–200 keV using a high sensitivity, large area scintillation counter telescope on November 21, 2000 and these coincided with the onset of an active X-ray phase as seen in the ASM counting rates on board RXTE. The observed spectrum can not be fitted to a single power law similar to the PDS data of BeppoSAX. The data can be fitted both by a two component power-law function or a combination of an exponential function with a power law component at the high energies above 80 keV. We identify these components with those arising from the synchrotron self compton and the high energy power-law tail arising from the upgrading of the thermal photons due to multiple Compton scattering a la Cyg X-1. A comparison with the earlier data clearly suggests a spectral variability in the hard X-ray spectrum of the source. We propose a continuously flaring geometry for the source as the underlying mechanism for energy release.     

Variations of the X-ray INTEGRAL spectrum of the active galactic nucleus of NGC 4945

Results of 11-year-long X-ray INTEGRAL observations of the nucleus of Seyfert galaxy NGC 4945 in the 3–500 keV range were processed. A two-component spectrum model, which includes strong radiation absorption in the Compton-thick torus around the AGN “central engine” and secondary radiation reflected from the torus walls, was used in the analysis. The following primary spectrum parameters were determined based on the data accumulated throughout the entire exposure period: photon index Γ = 1.60 ± 0.07, exponential cutoff energy E _c =157 _-22 ⁺²⁹ keV, and column density of the medium that absorbs primary radiation N _H,1 =5.0 _-0.9 ^+1.0 × 10²⁴ cm^–2. The column density of the medium absorbing reflected radiation is two orders of magnitude lower. Both the X-ray flux in the ranges of 20–40, 40–60, and 60–100 keV and the shape of the X-ray spectrum of NGC 4945 vary. The spectrum shape variations may be induced by inhomogeneities of the absorbing medium surrounding the AGN. At the same time, there is some evidence for moderate spectrum variations in the highenergy region, which may be associated with changes in the “central engine.”     

Spectral measurements of Cyg X-3: A thermal source embedded in hot plasma within a cold shell

The attempts at unified model fitting to explain the spectral variations in Cyg X-3 suggest equally probable fits with a combination of an absorbed blackbody and a separately absorbed power law with an exponential cut-off or a composite of absorbed free-free emission with a power law hard X-ray component apart from the iron emission line. These seemingly ordinary but ad hoc mixtures of simple X-ray emission mechanisms have a profound implication about the geometry of the X-ray source. While the first set suggests a black-hole nature of the compact object, the second combination is consistent with a neutron star binary picture. The spectral variability at hard X-ray energies above 30 keV can provide crucial input for the unified picture. In this paper, we present spectral observations of Cyg X-3, made in our on-going survey of galactic and extragalactic X-ray sources in the 20–200 keV energy region, using Large Area Scintillation counter Experiment. The data show a clear power-law photon spectrum of the form dN/dE ∼ E^−2.8 in the 20 to 130 keV energy range. A comparison with earlier data suggests that the total number of X-ray photons in the entire 2–500 keV energy band is conserved at all time for a given luminosity level irrespective of the state. We propose that this behaviour can be explained by a simple geometry in which a thermal X-ray source is embedded in a hot plasma formed by winds from the accretion disk within a cold shell. The high/soft and low/hard X-ray states of the source are simply the manifestation of the extent of the surrounding scattering medium in which the seed photons are Comptonized and hot plasma can be maintained by either the X-ray driven winds or the magneto-centrifugal winds.     

The spectrum of diffuse cosmic X-rays in the 20–125 keV range

Diffuse cosmic X-rays in the energy range 20–125 keV were measured in four balloon flights from Hyderabad, India during 1968–70 using almost identical X-ray telescopes mounted on oriented platforms. The results from these flights show that the spectrum of the diffuse cosmic X-rays can be represented by the form dN/dE=29E ^–2.1±0.3 photons/(cm² sr s keV) in 20–125 keV interval after corrections for photoelectric absorption and Compton scattering effects in the atmosphere. The best fit spectrum of all published results in the energy interval 20–200 keV can be represented by the form dN/dE=36E ^–2.1±0.1 photons/(cm² sr s keV) after similar corrections are effected, and there is no need for a change of spectral index in this energy interval. The intensity at 20 keV obtained from the above spectrum agrees well with that given by the spectral form dN/dE=10E ^–1.7±0.1 photons/(cm² sr s keV) in the energy interval 1–20 keV in several rocket experiments. Therefore it is concluded that if there is a break in the spectrum, it occurs between 10 and 20 keV with a change of spectral index by about 0.5, or the index is continuously changing from 1.7±0.1 to 2.1±0.1 in 10–20 keV interval. The implications of the results are briefly discussed.     

Models of the iron Kα fluorescent line and the Compton Shoulder in irradiated accretion disc spectra

We present a full set of model atmosphere equations for the accretion disc around a supermassive black hole irradiated by a hard X-ray lamp of power-law spectral distribution. Model equations allow for multiple Compton scattering of radiation on free electrons, and for large relative photon–electron energy exchange at the time of scattering. We present spectra in specific intensities integrated over the disc surface. Theoretical outgoing intensity spectra show soft X-ray excess below 1 keV, and distinct Kα and Kβ fluorescent lines of iron. We demonstrate the existence of the Compton Shoulder and claim that it can contribute to the asymmetry and equivalent widths of some observed Fe Kα lines in active galactic nuclei. Our models exhibit the effect of limb-brightening in reflected X-rays.     

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…     

Multiple compton scattering of electrons in a photon field

Consideration is given to the motion of electrons in a photon field of the monoenergetic or power-law spectrum under the conditions when the main mechanism of energy loss is the inverse Compton scattering by field photons. This process changes the primary spectrum of electrons and converts low-energy field photons to high-energy gamma-quanta for which the electron confinement region is assumed to be optically thin. The electron and gamma-ray spectra have been obtained in a wide energy interval including the Klein-Nishina and Thomson regions. A simple qualitative dependence of the solutions found on the field parameters and the primary spectrum of electrons has been established.The electron and gamma-ray spectra have been obtained by numerically solving the kinetic equation dependent on two variables: the energy of electrons and their path (or the time of motion) in a photon field. The results dramatically differ from the solution of the steady-state kinetic equation which depends only on the electron energy and is frequently used in the given problem.     

The first multi-wavelength campaign of AXP 4U 0142+61 from radio to hard X-rays

For the first time a quasi-simultaneous multi-wavelength campaign has been performed on an Anomalous X-ray Pulsar from the radio to the hard X-ray band. 4U 0142+61 was an INTEGRAL target for 1 Ms in July 2005. During these observations it was also observed in the X-ray band with Swift and RXTE, in the optical and NIR with Gemini North and in the radio with the WSRT. In this paper we present the source-energy distribution. The spectral results obtained in the individual wave bands do not connect smoothly; apparently components of different origin contribute to the total spectrum. Remarkable is that the INTEGRAL hard X-ray spectrum (power-law index 0.79±0.10) is now measured up to an energy of ～230 keV with no indication of a spectral break. Extrapolation of the INTEGRAL power-law spectrum to lower energies passes orders of magnitude underneath the NIR and optical fluxes, as well as the low ～30 μJy (2σ) upper limit in the radio band.     

Dynamics and energetics of the thermal and nonthermal components in the solar flare of January 20, 2005, based on data from hard electromagnetic radiation detectors onboard the CORONAS-F satellite

Based on data from the SONG and SPR-N multichannel hard electromagnetic radiation detectors onboard the CORONAS-F space observatory and the X-ray monitors onboard GOES satellites, we have distinguished the thermal and nonthermal components in the X-ray spectrum of an extreme solar flare on January 20, 2005. In the impulsive flare phase determined from the time of the most efficient electron and proton acceleration, we have obtained parameters of the spectra for both components and their variations in the time interval 06:43–06:54 UT. The spectral index in the energy range 0.2–2 MeV for a single-power-law spectrum of accelerated electrons is shown to have been close to 3.4 for most of the time interval under consideration. We have determined the time dependence of the lower energy cutoff in the energy spectrum of nonthermal photons E _γ0(t) at which the spectral flux densities of the thermal and nonthermal components become equal. The power deposited by accelerated electrons into the flare volume has been estimated using the thick-target model under two assumptions about the boundary energy E ₀ of the electron spectrum: (i) E ₀ is determined by E _γ0(t) and (ii) E ₀ is determined by the characteristic heated plasma energy (≈5kT (t)). The reality of the first assumption is proven by the fact that plasma cooling sets in at a time when the radiative losses begin to prevail over the power deposited by electrons only in this case. Comparison of the total energy deposited by electrons with a boundary energy E _γ0(t) with the thermal energy of the emitting plasma in the time interval under consideration has shown that the total energy deposited by accelerated electrons at the beginning of the impulsive flare phase before 06:47 UT exceeds the thermal plasma energy by a factor of 1.5–2; subsequently, these energies become approximately equal and are ～(4–5) × 10³⁰ erg under the assumption that the filling factor is 0.5–0.6.