The Energy Spectrum of Solar Energetic Electron Events

Solar energetic electron events (SEEs) are one of the most common particle acceleration phenomena occurring at the Sun, and their energy spectrum likely reflects the crucial information on the acceleration. Here we present a statistical survey of the energy spectrum of 160 SEEs measured by Wind/3DP with a clear velocity dispersion at energies of ~1-200 keV from January 1995 through December 2016, utilizing a general spectrum formula proposed by Liu et al. (2000). We find that among these 160 SEEs, 144 (90%) have a power-law (or power-law-like) spectrum bending down at high energies, including 108 (67.5%) double-power-law events, 24 (15%) Ellison-Ramaty-like events and 12 (7.5%) log-parabola events, while 16 (10%) have a power-law spectrum extending to high energies. The average power-law spectral index &#946;1&#160;is 2.1&#177;0.4 for double-power-law events, 1.7&#177;0.8 for Ellison-Ramaty-like events, and 2.8&#177;0.11 for single-power-law events. For the 108 double-power-law events, the spectral break energy E0&#160;ranges from 2 keV to 165 keV, with an average of 71&#177;79 keV, while the average spectral index &#946;2&#160;at energies above E0is 4.4&#177;2.3. E0&#160;shows a positive correlation with the electron peak flux at energies above ~40 keV, while &#946;1&#160;has a negative correlation with the electron peak flux at energies above ~15 keV. &#160;

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Variation of the Solar Flare Energy Spectrum Over the 11-Year Activity Cycle

International Astronomical Union Colloquium ◽

10.1017/s0252921100154296 ◽

1989 ◽

Vol 104 (2) ◽

pp. 255-258 ◽

Cited By ~ 1

Author(s):

V.V. Kasinsky ◽

R.T. Sotnikova

Keyword(s):

Energy Spectrum ◽

Solar Flare ◽

Spectral Index ◽

Power Law ◽

Activity Cycle ◽

Energy Spectra ◽

Cycle Phase ◽

X Ray ◽

Flux Data ◽

Flare Energy

AbstractBased on X-ray (1-8 Å) flux data for 1977-1987, the integral spectra of solar flare energy were computed. The energy spectra were approximated by a power law N(E) α; E~n, with N being the number of flares with energy in excess of E. It is shown that the spectral index (β) varies systematically with the 11-year cycle phase.

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Solar Energetic Electron Events Associated with Hard X-ray Flares

10.5194/egusphere-egu21-10734 ◽

2021 ◽

Author(s):

Wen Wang ◽

Linghua Wang ◽

Sam Krucker ◽

Glenn M. Mason ◽

Yang Su ◽

...

Keyword(s):

Spectral Index ◽

Power Law ◽

Heliocentric Distance ◽

Energetic Electron ◽

High Energy ◽

Thick Target ◽

The Other ◽

Ion Acceleration ◽

X Ray ◽

Positive Correlation

We investigate 16 solar energetic electron (SEE) events measured by WIND/3DP with a double power-law spectrum and the associated western hard X-ray (HXR) flares measured by RHESSI with good count statistics, from 2002 February to 2016 December. In all 16 cases, the presence of an SEE power-law spectrum extending down to 65 keV at 1 AU implies that the SEE source would be high in the corona, at a heliocentric distance of >1.3 solar radii, while the footpoint or footpoint-like emissions shown in HXR images suggest that the observed HXRs are likely produced mainly by thick target bremsstrahlung processes very low in the corona. We find that in 8 cases (the other 8 cases), the power-law spectral index of HXR-producing electrons, estimated under the relativistic thick-target bremsstrahlung model, is significantly larger than (similar to) the observed high-energy spectral index of SEEs, with a positive correlation. In addition, the estimated number of SEEs is only &#8764;10-4 - 10-2 of the estimated number of HXRproducing electrons at energies above 30 keV, but also with a positive correlation. These results suggest that in these cases, SEEs are likely formed by upward-traveling electrons from an acceleration source high in the corona, while their downward-traveling counterparts may undergo a secondary acceleration before producing HXRs via thick-target bremsstrahlung processes. In addition, the associated 3He=4He ratio is positively correlated with the observed high-energy spectral index of SEEs, indicating a possible relation of the 3He ion acceleration with high-energy SEEs

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General Spectrum Fitting for Energetic Particles

10.5194/egusphere-egu2020-8189 ◽

2020 ◽

Author(s):

Zixuan Liu ◽

Linghua Wang ◽

Haobo Fu ◽

Krucker Sam ◽

Wimmer-Schweingruber Robert

Keyword(s):

Energy Spectrum ◽

Power Law ◽

Energetic Particles ◽

Particle Energy ◽

X Rays ◽

Amplitude Coefficient ◽

Spectral Break ◽

Particle Intensity ◽

Spectrum Fitting ◽

Suprathermal Particles

We propose a general fitting formula of energy spectrum of suprathermal particles, J=AE-&#946;1[1+(E/E0)&#945;](&#946;1-&#946;2)/&#945;, where J is the particle flux (or intensity), E is the particle energy, A is the amplitude coefficient, E0 represents the spectral break energy, &#945; (>0) describes the sharpness of energy spectral break around E0, and the power-law index &#946;1 (&#946;2) gives the spectral shape before (after) the break. &#160;When &#945; tends to infinity (zero), this spectral formula becomes a classical double-power-law (logarithmic-parabola) spectrum. When both &#946;2 and E0 tend to infinity, this formula can be simplified to an Ellison-Ramaty-like equation. Under some other specific parameter conditions, this formula can be transformed to a Kappa or Maxwellian function. Considering &#160;the uncertainties both in particle intensity and energy, we fit this general formula well to the representative energy spectra of various suprathermal particle phenomena including solar energetic particles (electrons, protons, &#160;3He and heavier ions), shocked particles, anomalous cosmic rays, hard X-rays, solar wind suprathermal particles, etc. Therefore, this general spectrum fitting formula would help us to comparatively examine the energy spectrum of different suprathermal particle phenomena and understand their origin, acceleration and transportation.

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Synchrotron Emission from Particles Having A Truncated Power-law Energy Spectrum

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/168.2.379 ◽

1974 ◽

Vol 168 (2) ◽

pp. 379-397 ◽

Cited By ~ 3

Author(s):

L. J. Gleeson ◽

M. P. C. Legg ◽

K. C. Westfold

Keyword(s):

Energy Spectrum ◽

Power Law ◽

Synchrotron Emission

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SPECTRUM OF COSMIC RAYS WITH ENERGY ABOVE 1017 EV

International Journal of Modern Physics A ◽

10.1142/s0217751x05030375 ◽

2005 ◽

Vol 20 (29) ◽

pp. 6878-6880 ◽

Cited By ~ 3

Author(s):

V. P. EGOROVA ◽

A. V. GLUSHKOV ◽

A. A. IVANOV ◽

S. P. KNURENKO ◽

V. A. KOLOSOV ◽

...

Keyword(s):

Distribution Function ◽

Energy Spectrum ◽

Cosmic Rays ◽

Time Distribution ◽

Arrival Time ◽

Lateral Distribution ◽

Arrival Time Distribution ◽

Array Data ◽

Lateral Distribution Function ◽

High Energies

The energy spectrum of primary cosmic rays with ultra-high energies based on the Yakutsk EAS Array data is presented. For the largest events values of S600 and axis coordinates have been obtained using revised lateral distribution function. The effect of the arrival time distribution at several axis distance on estimated density for Yakutsk and AGASA is considered.

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The starburst galaxy NGC 253 revisited by H.E.S.S. and Fermi-LAT

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833202 ◽

2018 ◽

Vol 617 ◽

pp. A73 ◽

Cited By ~ 12

Author(s):

◽

H. Abdalla ◽

F. Aharonian ◽

F. Ait Benkhali ◽

E. O. Angüner ◽

...

Keyword(s):

Spectral Index ◽

Power Law ◽

Cosmic Ray ◽

High Energy ◽

Thick Target ◽

Starburst Galaxy ◽

Particle Accelerators ◽

Power Law Distribution ◽

Particle Population ◽

Measurement Uncertainties

Context. NGC 253 is one of only two starburst galaxies found to emit γ-rays from hundreds of MeV to multi-TeV energies. Accurate measurements of the very-high-energy (VHE; E > 100 GeV) and high-energy (HE; E > 60 MeV) spectra are crucial to study the underlying particle accelerators, probe the dominant emission mechanism(s) and to study cosmic-ray interaction and transport. Aims. The measurement of the VHE γ-ray emission of NGC 253 published in 2012 by H.E.S.S. was limited by large systematic uncertainties. Here, the most up to date measurement of the γ-ray spectrum of NGC 253 is investigated in both HE and VHE γ-rays. Assuming a hadronic origin of the γ-ray emission, the measurement uncertainties are propagated into the interpretation of the accelerated particle population. Methods. The data of H.E.S.S. observations are reanalysed using an updated calibration and analysis chain. The improved Fermi–LAT analysis employs more than 8 yr of data processed using pass 8. The cosmic-ray particle population is evaluated from the combined HE–VHE γ-ray spectrum using NAIMA in the optically thin case. Results. The VHE γ-ray energy spectrum is best fit by a power-law distribution with a flux normalisation of (1.34 ± 0.14stat ± 0.27sys) × 10−13 cm−2 s−1 TeV1 at 1 TeV – about 40% above, but compatible with the value obtained in Abramowski et al. (2012). The spectral index Γ = 2.39 ± 0.14stat ± 0.25sys is slightly softer than but consistent with the previous measurement within systematic errors. In the Fermi energy range an integral flux of F(E > 60 MeV) = (1.56 ± 0.28stat ± 0.15sys) × 10−8 cm−2 s−1 is obtained. At energies above ∼3 GeV the HE spectrum is consistent with a power-law ranging into the VHE part of the spectrum measured by H.E.S.S. with an overall spectral index Γ = 2.22 ± 0.06stat. Conclusions. Two scenarios for the starburst nucleus are tested, in which the gas in the starburst nucleus acts as either a thin or a thick target for hadronic cosmic rays accelerated by the individual sources in the nucleus. In these two models, the level to which NGC 253 acts as a calorimeter is estimated to a range of fcal = 0.1 to 1 while accounting for the measurement uncertainties. The presented spectrum is likely to remain the most accurate measurements until the Cherenkov Telescope Array (CTA) has collected a substantial set of data towards NGC 253.

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Spectral Index Versus Frequency and Models for the Continua of AGN and QSOs

Symposium - International Astronomical Union ◽

10.1017/s0074180900140835 ◽

1989 ◽

Vol 134 ◽

pp. 201-202

Author(s):

Wayne A. Stein

Keyword(s):

Accretion Disk ◽

Spectral Index ◽

Power Law ◽

Spectral Distribution ◽

Secondary Electron ◽

Low Frequency ◽

Spectral Indices ◽

Ultraviolet Continuum ◽

Electron Synchrotron ◽

X Ray

The observed spectral index as a function of frequency of QSO continua must be explained in models. It is generally increasing (F(ν) ∝ ν−α, α increasing) with higher frequency in the infrared (downward curvature). The visual to ultraviolet continuum has been shown to be a broken power law with F(ν) ∝ ν−0.5 at low frequency and a break to larger α at νo ∼ 3×1015 Hz. X-ray observations frequently exhibit a flat continuum with α < 1. One prominent example is 3C273 for which α1–3μm → 2, αvis ∼ 0.5 and αx ∼ 0.5. These spectral indices arise naturally in Secondary Electron Synchrotron Self-Compton (SESSC) models. Some accretion disk models approach these spectral indices for the visual-ultraviolet portion of the spectral distribution.

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Two optical emission components with different variability in V404 Cygni

Proceedings of the International Astronomical Union ◽

10.1017/s1743921317000011 ◽

2016 ◽

Vol 12 (S324) ◽

pp. 43-44

Author(s):

Yutaro Tachibana ◽

Taketoshi Yoshii ◽

Nobuyuki Kawai

Keyword(s):

Spectral Index ◽

Power Law ◽

Time Domain ◽

Optical Emission ◽

Time Domain Analysis ◽

Blackbody Radiation ◽

Light Curves ◽

Variable Component ◽

Single Temperature ◽

The Time Domain

AbstractV404 Cygni went into an outburst again on June 15, 2015 after 26 years of quietness. Soon after the notifications, we started intense optical observation campaign of this source. The spectral index between RC and IC-band was stable over the outburst, whereas that between g′ and RC-band varied violently. With the time domain analysis of the multi-color optical light curves, we successfully decomposed optical variations into three components: highly-variable component (HVC), little-variable component (LVC). The loci of the LVC in the color-color diagram is consistent with that of a single temperature blackbody radiation or a multi-color blackbody radiation from a standard accretion disk, while those of the HVC trace that of power-law spectra.

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Power-law plateau and inverse symmetric inflation

International Journal of Modern Physics D ◽

10.1142/s0218271818500876 ◽

2018 ◽

Vol 27 (08) ◽

pp. 1850087 ◽

Cited By ~ 1

Author(s):

Abdul Jawad ◽

Shahid Chaudhary

Keyword(s):

Scalar Field ◽

Power Spectrum ◽

Spectral Index ◽

Power Law ◽

Field Model ◽

Chaplygin Gas ◽

Generalized Chaplygin Gas ◽

Planck Data ◽

Inflationary Parameters ◽

Ratio Versus

Warm generalized Chaplygin gas inflation is being studied by assuming power-law plateau and inverse symmetric potentials with standard scalar field model. We consider strong dissipative regime with generalized dissipative coefficient and extract the various inflationary parameters such as scalar power spectrum, spectral index, tensor-to-scalar ratio and running of spectral index. It is found that both inflationary potentials favor the strong dissipative regime. Also, we construct the [Formula: see text]–[Formula: see text] (running of spectral index versus spectral index) and [Formula: see text]–[Formula: see text] (tensor-to-scalar ratio versus spectral index) planes and found that the trajectories of these planes favor WMAP 7 [Formula: see text] WMAP 9 and latest Planck data.

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k-essence for warm inflation on the brane

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817500931 ◽

2017 ◽

Vol 14 (06) ◽

pp. 1750093 ◽

Cited By ~ 2

Author(s):

Lorenzo Sebastiani ◽

Ratbay Myrzakulov

Keyword(s):

Spectral Index ◽

Power Law ◽

General Class ◽

Kinetic Term ◽

Warm Inflation ◽

Scalar Perturbations

In this paper, [Formula: see text]-inflation is analyzed in warm braneworld scenario. A general class of [Formula: see text]-essence models with power-law kinetic term is investigated and weak and strong dissipation regimes are studied. Scalar perturbations and spectral index are derived. The results are discussed and applied to specific examples.

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