Energy Spectral Index Research Articles

Microwave diagnostics of flare plasma by the direct fitting method based on data from the Siberian Radioheliograph

In this paper, we analyze images and the frequency spectrum of microwave emission in the maximum of brightness distribution in the January 20, 2022 and July 16, 2023 flares recorded by the Siberian Radioheliograph in the 3–6 GHz and 6–12 GHz ranges. We use the obtained spectrum data for radio diagnostics of magnetic field strength and orientation, plasma density, and parameters of accelerated particles in a radio source. The radio diagnostics is carried out by a method based on minimizing the functional containing the intensities of theoretically calculated and observed frequency spectra of left-polarized and right-polarized emission. Since the form of such a multidimensional functional is quite complex, and it is not possible to minimize it by standard approaches, we employ a genetic minimization method. The radio diagnostics allows us to determine features of the dynamics of the magnetic field intensity and orientation, as well as the density and the energy spectral index of non-thermal electrons in the region of maximum brightness of the radio source. We have found that during the growth phase of the main radiation peaks the magnetic field decreases, whereas during the decay phase, on the contrary, it increases. The rate of these changes varies from a few G/s to 11 G/s for the January 20, 2022 flare and is about 1 G/s for the July 16, 2023 flare.

Микроволновая диагностика вспышечной плазмы методом фитирования по данным Cибирского радиогелиографа

In this paper, we analyze images and the frequency spectrum of microwave emission in the maximum of brightness distribution in the January 20, 2022 and July 16, 2023 flares recorded by the Siberian Radioheliograph in the 3–6 GHz and 6–12 GHz ranges. We use the obtained spectrum data for radio diagnostics of magnetic field strength and orientation, plasma density, and parameters of accelerated particles in a radio source. The radio diagnostics is carried out by a method based on minimizing the functional containing the intensities of theoretically calculated and observed frequency spectra of left-polarized and right-polarized emission. Since the form of such a multidimensional functional is quite complex, and it is not possible to minimize it by standard approaches, we employ a genetic minimization method. The radio diagnostics allows us to determine features of the dynamics of the magnetic field intensity and orientation, as well as the density and the energy spectral index of non-thermal electrons in the region of maximum brightness of the radio source. We have found that during the growth phase of the main radiation peaks the magnetic field decreases, whereas during the decay phase, on the contrary, it increases. The rate of these changes varies from a few G/s to 11 G/s for the January 20, 2022 flare and is about 1 G/s for the July 16, 2023 flare.

Characterization of Relativistic Electron Precipitation Events Observed by the CALET Experiment Using Self‐Organizing‐Maps

AbstractRelativistic electron precipitation (REP) is a relatively high‐latitude phenomenon where high‐energy electrons trapped in the outer radiation belt are lost into the Earth’s atmosphere. REP events observed at low Earth orbit show varying temporal profiles and global distributions. While the precipitation origin has been attributed to specific wave modes or scattering sources, the sorting of REP events by type or driver remains an unsolved challenge. In this study, we analyze the temporal profile of relativistic electron precipitation events observed by the CALorimetric Electron Telescope (CALET) experiment on board the International Space Station. We use an unsupervised machine learning technique called Self‐Organizing‐Maps (SOM) to automatically detect and then classify relativistic electron events observed by the two scintillator layers at the top of the apparatus, sensitive to electrons with energies >1.5 MeV and >3.4 MeV, respectively. We calculate the power spectral density (PSD) of the count rates observed by both sensors and use them as an input for the SOM. The SOM technique groups the PSDs by their similarity, resulting in a classification of relativistic electron events by the periodicity of the observed precipitation. We investigate the L‐shell and magnetic local time distribution of the resulting classification, and energy spectral index associated with the observations. Clear precipitation patterns are observed and compared to past precipitation categorization attempts as well as known distributions of various scattering mechanisms. The classification reveals features through the sorting of the variability of the rapid precipitation, allowing the identification of different precipitation populations with varying properties.

Magnetar Central Engine Powering the Energetic GRB 210610B?

The bright GRB 210610B was discovered simultaneously by Fermi and Swift missions at redshift 1.13. We utilized broadband Fermi-GBM observations to perform a detailed prompt emission spectral analysis and to understand the radiation physics of the burst. Our analysis displayed that the low energy spectral index (αpt) exceeds boundaries expected from the typical synchrotron emission spectrum (-1.5,-0.67), suggesting additional emission signature. We added an additional thermal model with the typical Band or CPL function and found that CPL + BB function is better fitting to the data, suggesting a hybrid jet composition for the burst. Further, we found that the beaming corrected energy (Eγ,θj = 1.06 × 1051 erg) of the burst is less than the total energy budget of the magnetar. Additionally, the X-ray afterglow light curve of this burst exhibits achromatic plateaus, adding another layer of complexity to the explosion’s behavior. Interestingly, we noted that the X-ray energy release during the plateau phase (EX,iso = 1.94 × 1051 erg) is also less than the total energy budget of the magnetar. Our results indicate the possibility that a magnetar could be the central engine for this burst.

IceCat-1: The IceCube Event Catalog of Alert Tracks

We present a catalog of likely astrophysical neutrino track-like events from the IceCube Neutrino Observatory. IceCube began reporting likely astrophysical neutrinos in 2016, and this system was updated in 2019. The catalog presented here includes events that were reported in real time since 2019, as well as events identified in archival data samples starting from 2011. We report 275 neutrino events from two selection channels as the first entries in the catalog, the IceCube Event Catalog of Alert Tracks, which will see ongoing extensions with additional alerts. The Gold and Bronze alert channels respectively provide neutrino candidates with a 50% and 30% probability of being astrophysical, on average assuming an astrophysical neutrino power-law energy spectral index of 2.19. For each neutrino alert, we provide the reconstructed energy, direction, false-alarm rate, probability of being astrophysical in origin, and likelihood contours describing the spatial uncertainty in the alert's reconstructed location. We also investigate a directional correlation of these neutrino events with gamma-ray and X-ray catalogs, including 4FGL, 3HWC, TeVCat, and Swift-BAT.

Solar activity relations in energetic electron events measured by the MESSENGER mission

Aims. We perform a statistical study of the relations between the properties of solar energetic electron (SEE) events measured by the MESSENGER mission from 2010 to 2015 and the parameters of the respective parent solar activity phenomena in order to identify the potential correlations between them. During the time of analysis, the MESSENGER heliocentric distance varied between 0.31 and 0.47 au. Methods. We used a published list of 61 SEE events measured by MESSENGER, which includes information on the near-relativistic electron peak intensities, the peak-intensity energy spectral indices, and the measured X-ray peak intensity of the flares related to the SEE events. Taking advantage of multi-viewpoint remote-sensing observations, we reconstructed, whenever possible, the associated coronal mass ejections (CMEs) and shock waves; and we determined the three-dimensional (3D) properties (location, speed, and width) of the CMEs and the maximum speed of the 3D CME-driven shocks in the corona. We used different methods (Spearman, Pearson, and a Bayesian approach, namely the Kelly method to linear regression) to estimate the correlation coefficients between the flare intensity, maximum speed at the apex of the CME-driven shock, CME speed at the apex, and CME width with the electron peak intensities and with the energy spectral indices. In this statistical study, we considered and addressed the limitations of the particle instrument on board MESSENGER (elevated background intensity level, anti-Sun pointing). Results. There is an asymmetry to the east in the range of connection angles (CAs) for which the SEE events present the highest peak intensities, where the CA is the longitudinal separation between the footpoint of the magnetic field connecting to the spacecraft and the flare location. Based on this asymmetry, we define a subsample of well-connected events as when −65° ≤ CA ≤ +33°. For the well-connected sample, we find moderate to strong correlations between the near-relativistic electron peak intensity and the 3D CME-driven shock maximum speed at the apex (Spearman: cc = 0.53 ± 0.05; Pearson: cc = 0.65 ± 0.04; Kelly: cc = 0.87 ± 0.20), the flare peak intensity (Spearman: cc = 0.63 ± 0.03; Pearson: cc = 0.59 ± 0.03; Kelly: cc = 0.74 ± 0.30), and the 3D CME speed at the apex (Spearman: cc = 0.50 ± 0.04; Pearson: cc = 0.46 ± 0.03; Kelly: cc = 0.60 ± 0.39). When including poorly connected events (full sample), the relations between the peak intensities and the solar-activity phenomena are blurred, showing lower correlation coefficients. Conclusions. Based on the comparison of the correlation coefficients presented in this study using near 0.4 au data, (1) both flare and shock-related processes may contribute to the acceleration of near relativistic electrons in large SEE events, in agreement with previous studies based on near 1 au data; and (2) the maximum speed of the CME-driven shock is a better parameter to investigate particle-acceleration-related mechanisms than the average CME speed, as suggested by the stronger correlation with the SEE peak intensities.

Dipolarization Fronts in the Jovian Magnetotail: Statistical Survey of Ion Intensity Variations Using Juno Observations

AbstractEnergetic particle acceleration and energization in planetary magnetotails are often associated with dipolarization fronts characterized by a rapid increase of the meridional component of the magnetic field. Despite many studies of dipolarization events in Earth's magnetotail, Jupiter’s magnetotail provides an almost ideal environment to study high‐energetic ion acceleration by dipolarization fronts because of its large spatial scales and plasma composition of heavy and light ions. In this study, we focus on the response of different high‐energetic ion intensities (H, He, S, and O) to prominent magnetic dipolarization fronts inside the Jovian magnetotail. We investigate if ion energization and acceleration are present in the observations around the identified dipolarization fronts. Therefore, we present a statistical study of 87 dipolarization front signatures, which are identified in the magnetometer data of the Juno spacecraft from July 2016 to July 2021. For the ion intensity analysis, we use the energetic particle observations from the Jupiter Energetic Particle Detector Instrument. Our statistical study reveals that less than half of the identified events are accompanied by an increase of the ion intensities, while most of the other events show no significant change in the ion intensity dynamics. In about 40% of the events located in the dawn sector a significant decrease of the energy spectral index is detected indicating ion acceleration by the dipolarization fronts.

Antenna source of radio-frequency emission in ion-proton pulsars

ABSTRACT The growth of a longitudinal or quasi-longitudinal Langmuir mode in the outward-moving beam of ions and protons that forms the open sector of an ion-proton pulsar magnetosphere radiates as an analogue of an end-fed high-impedance horizontal straight-wire antenna an integral number of half-waves in length. The radiation has, broadly, the energy flux, linear polarization, and spectral index that are widely observed: also, the notch phenomenon seen in some integrated pulse profiles occurs naturally. The new field of pulsar observations below 100 MHz may lead to productive tests of the radio emission mechanism.

Photons’ Scattering in Relativistic Plasma with Velocity Shear: Generation of High Energy Power-law Spectra

A high energy power law is a common feature in the spectra of many astrophysical objects. We show that the photons in an unmagnetized relativistic plasma composed of electrons and protons with a variable Lorentz factor (or a velocity shear) go through repeated scattering with electrons to gain energy. The escaped population of photons naturally produces a power-law-shaped spectrum making it a photon’s analog to the conventional Fermi acceleration mechanism for charged particles. Thus, this mechanism provides a natural alternative to current explanations of high energy power-law spectra via synchrotron or thermal Comptonization. The model is applicable to any relativistic plasma beam with an arbitrary Lorentz factor profile. We implement the theory to the gamma-ray burst prompt phase and show that the obtained range of the photon indices is compatible with the observed values and the results of Monte Carlo simulations that we carry out independently. Therefore, the observed high energy spectral indices provide a unique indicator of the jet structure.

On the energy dependence of the QPO phenomenon in the black hole system MAXI J1535-571

ABSTRACT Previous analysis of AstroSat observations of the black hole system MAXI J1535-571 have revealed the presence of a strong Quasi-Periodic Oscillation (QPO) whose frequency is correlated with the high energy spectral index. Here, we fit the spectra as emitted from a truncated disc with an inner hot corona, study the QPO frequency dependence on other spectral parameters and model the energy-dependent r.m.s and time-lag of the QPO to identify the physical spectral parameters whose variation are responsible for the QPO. The QPO frequency is found to also correlate with the scattering fraction (i.e. the fraction of the soft photons Comptonized) and its dependence on the accretion rate and inner disc radii is consistent with it being the dynamical frequency. The time-lag between the hard and soft photons is negative for QPO frequency >2.2 Hz and is positive for lesser values, making this the second black hole system to show this behaviour after GRS 1915+105. Modelling the energy-dependent time-lag and r.m.s requires correlated variation of the accretion rate, inner disc radii, and the coronal heating rate, with the latter having a time-lag compared to the other two for QPO frequencies less than <2.2 Hz and which changes sign (i.e. the coronal heating variation precedes the accretion rate one) for higher values. The implications of the results are discussed.

Power-law spectrum of energetic particles in classical thermal equilibrium by pitch-angle scattering process

The Boltzmann–Gibbs thermodynamic equilibrium state of charged particles pitch-angle scattered by weak plasma waves is discussed. Degrees of freedom of these waves play a fundamental role in constructing the grand canonical ensemble. Via the gyro-resonance condition, fast particles have an inverse break power-law spectrum for ɛ−μ≪T, where ɛ is the particle energy, μ is the chemical potential, T is the temperature. The break energies are the rest energy and −μ. For ɛ≪−μ≪T, the energy spectral index α is δ/2+1 and δ+1 for non- and ultra-relativistic particles, respectively, with δ an effective fractal dimension of background magnetic field lines. The spectral index for −μ≪ɛ≪T is α+1. This thermal equilibrium scenario, combined with the leaky-box model and cosmic-ray observations, seems to suggest that the Galactic magnetic field is super-diffusive with δ≈1.4.

Energy Spectra vs. Element Abundances in Solar Energetic Particles and the Roles of Magnetic Reconnection and Shock Acceleration

We reexamine the relationship between energy spectral indices and element abundance enhancements in solar energetic particle (SEP) events at energies of a few MeV amu−1. We find a correlated behavior only in the largest gradual SEP4 events when all ions are accelerated from the ambient coronal plasma by shock waves driven by fast, wide coronal mass ejections (CMEs). This correlated abundance behavior can track complex time variations in the spectral indices during an event. In other (SEP3) events, CME-driven shock waves, days apart, sample seed particles from a single pool of suprathermal impulsive ions contributed earlier. Of the smaller, Fe-rich, impulsive SEP events, previously related to magnetic reconnection in solar jets, over half are subsequently reaccelerated by CME-driven shock waves (SEP2), causing typical ion intensities to have a 64% correlation with shock speeds. In these SEP2 events, the onset of shock acceleration is signaled by a new component in the abundances, large proton excesses. The remaining SEP1 events lack evidence of shock acceleration. However, for all these events (SEP1–SEP3) with abundances determined by magnetic reconnection, energy spectra and abundances are decoupled.

Probing into emission mechanisms of GRB 190530A using time-resolved spectra and polarization studies: Synchrotron Origin?

Abstract Multi-pulsed GRB 190530A, detected by the GBM and LAT onboard Fermi, is the sixth most fluent GBM burst detected so far. This paper presents the timing, spectral, and polarimetric analysis of the prompt emission observed using AstroSat and Fermi to provide insight into the prompt emission radiation mechanisms. The time-integrated spectrum shows conclusive proof of two breaks due to peak energy and a second lower energy break. Time-integrated (55.43 ± 21.30 %) as well as time-resolved polarization measurements, made by the Cadmium Zinc Telluride Imager (CZTI) onboard AstroSat, show a hint of high degree of polarization. The presence of a hint of high degree of polarization and the values of low energy spectral index (αpt) do not run over the synchrotron limit for the first two pulses, supporting the synchrotron origin in an ordered magnetic field. However, during the third pulse, αpt exceeds the synchrotron line of death in few bins, and a thermal signature along with the synchrotron component in the time-resolved spectra is observed. Furthermore, we also report the earliest optical observations constraining afterglow polarization using the MASTER (P < 1.3 %) and the redshift measurement (z= 0.9386) obtained with the 10.4m GTC telescopes. The broadband afterglow can be described with a forward shock model for an ISM-like medium with a wide jet opening angle. We determine a circumburst density of n0 ∼ 7.41, kinetic energy EK ∼ 7.24 × 1054 erg, and radiated γ-ray energy Eγ, iso ∼ 6.05 × 1054 erg, respectively.

Spectral Signature of Mass Outflow in the Two Component Advective Flow Paradigm

Abstract Outflows are common in many astrophysical systems. In the Two Component Advective Flow (TCAF) paradigm, which is essentially a generalized Bondi flow including rotation, viscosity, and cooling effects, the outflow originates in the hot, puffed up, post-shock region at the inner edge of the accretion disk. We consider this region to be the base of the jet carrying away matter with a high velocity. In this paper, we study the spectral properties of black holes using TCAF that includes also a jet (JeTCAF) in the vertical direction of the disk plane. Soft photons from the Keplerian disk are up-scattered by the post-shock region as well as by the base of the jet and are emitted as hard radiation. We also include the bulk motion Comptonization effect by the diverging flow of the jet. Our self-consistent accretion-ejection solution shows how the spectrum from the base of the jet varies with accretion rates, geometry of the flow, and the collimation factor of the jet. We apply the solution to a jetted candidate GS 1354-64 to estimate its mass outflow rate and the geometric configuration of the flow during the 2015 outburst observed by NuSTAR. The estimated mass outflow to mass inflow rate is 0.12 − 0.03 + 0.02 . From the model-fitted accretion rates, shock compression ratio, and the energy spectral index, we identify the presence of hard and intermediate spectral states of the outburst. Our model-fitted jet collimation factor (f col) is found to be 0.47 − 0.09 + 0.09 .

On the shear-current effect: toward understanding why theories and simulations have mutually and separately conflicted

ABSTRACT The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient β21 with a favourable negative sign for exponential mean-field growth, rather than positive for diffusion. There have been long-standing disagreements among theoretical calculations and comparisons of theory with numerical experiments as to the sign of kinetic ($\beta ^u_{21}$) and magnetic ($\beta ^b_{21}$) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike $\beta ^b_{21}$, the kinetic SCE $\beta ^u_{21}$ has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at $\mathcal {O}(10)$ Reynolds numbers if the spectrum is not too steep. Conversely, $\beta ^b_{21}$ is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive $\beta ^u_{21}$ can dominate even at energy equipartition urms ≃ brms, resulting in a positive total β21 even though $\beta ^b_{21}\lt 0$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation versus the spectral-τ closure, for which opposite signs for $\beta ^u_{21}$ have been reported, with the same sign for $\beta ^b_{21}\lt 0$. The results also offer an explanation for the simulations that find $\beta ^u_{21}\gt 0$ and an inconclusive overall sign of β21 for $\mathcal {O}(10)$ Reynolds numbers. The transient behaviour of $\beta ^u_{21}$ is demonstrated using the kinematic test-field method. We compute dynamo growth rates for cases with or without rotation, and discuss opportunities for further work.

Proton Properties in Mercury's Magnetotail: A Statistical Study

AbstractThis study investigates the properties of protons in the magnetotail plasma sheet of Mercury. By superposing 5‐year measurements from the MESSENGER spacecraft, we obtain the average energy spectrum of protons in the plasma sheet, which can be fitted nicely by the Gaussian‐Kappa model. The proton density, pressure, and energy spectral index κ are found to be higher on the dawnside than on the duskside. The proton temperature shows a clearly outward radial gradient. The field‐aligned density profile indicates that the protons in the outer plasma sheet move adiabatically. The pitch angle distribution reveals the reflected fluxes to be always less than the incident fluxes and indicates the loss of protons due to their impact on the planetary surface.

Contribution of High-energy GRB Emissions to the Spectrum of the Isotropic Diffuse γ-Ray Background

Abstract High-precision measurement of the isotropic diffuse γ-ray background (IGRB) has been extrapolated to the TeV energy region using the Fermi-LAT experiment. Various kinds of astrophysical sources are candidates for its origin. However, a consensus on the dominant source has been difficult to reach. Recent observations of the γ-ray emission of γ-ray bursts (GRBs), denoted as the synchrotron self-Compton (SSC) component in the afterglow phase, in the sub-TeV energy region by MAGIC and HESS experiments shed new light on this topic. In this work, we revisit the contribution from the SSC component of GRBs to the IGRB. First, a sample set of GRB events is obtained and examined using observations from Fermi-LAT. Second, the SSC component, described by the energy ratio R ext and spectral index β ext, is assigned to every GRB event. We can obtain the total spectrum contribution based on this GRB sample. We find that when R ext and β ext reach ∼20% and −1.6, respectively, the contribution from GRB emission dominates in the energy region of hundreds of GeV. We hope that the LHAASO and CTA experiments under construction can observe a large number of GRBs to fix those parameters in coming years. A surviving tail is expected, which can serve to check our calculations based on future satellite experiments such as HERD and GAMMA400.

Suprathermal Electron Acceleration by a Quasi-perpendicular Shock: Simulations and Observations

Abstract The acceleration of suprathermal electrons in the solar wind is mainly associated with shocks driven by interplanetary coronal mass ejections (ICMEs). It is well known that the acceleration of electrons is much more efficient at quasi-perpendicular shocks than at quasi-parallel ones. Yang et al. studied the acceleration of suprathermal electrons with observations at a quasi-perpendicular ICME-driven shock event to claim the important role of shock-drift acceleration (SDA). Here, we perform test-particle simulations to study the acceleration of electrons in this event, by calculating the downstream electron intensity distribution for all energy channels assuming an initial distribution based on the average upstream intensities. Using simulations, we obtain the results similar to the observations from Yang et al. as follows. It is shown that the ratio of downstream to upstream intensities peaks at about 90° pitch angle. In addition, in each pitch angle direction the downstream electron energy spectral index is much larger than the theoretical index of diffusive shock acceleration. Furthermore, the estimated drift length is proportional to the electron energy but the drift time is almost energy independent. Finally, we use a theoretical model based on SDA to describe the drift length and drift time especially, to explain their energy dependence. These results indicate the importance of SDA in the acceleration of electrons by quasi-perpendicular shocks.

Origin for the Prompt Spectral Evolution Characteristics and High Energy Emission during the X-Ray Flare in GRB 180720B

Abstract The gamma-ray burst GRB 180720B is very peculiar. On one hand, some interesting features have been found by performing the detailed time-resolved spectral analysis in the prompt phase. First, the “flux-tracking” pattern is exhibited both for the low energy spectral index α and the peak energy E p in the Band function. Second, some parameter relations show strong monotonous positive correlations, include E p –F, α–F, E p –α, and E p –L γ,iso for all time-resolved spectra. Lastly, it should be noted that the values of α do not exceed the synchrotron limits . On the other hand, the photons with the energy of ≳100 MeV were detected by LAT both in the prompt phase and afterglow. Notably, the 5 GeV photon was observed at 142 s after the GBM trigger. The spectrum of this burst in the LAT range can be described as F ν ∝ ν −1.3 t −1.54±0.02 in the afterglow phase. And there are six GeV photons during the X-ray flare when the lower energy emission is fading to a weaker level. We try to give reasonable interpretations of the mechanism for prompt emission and the high energy emission (100 MeV to GeV) in the afterglow. The interpretations suggesting that synchrotron origin can account for the prompt emission and synchrotron self-Compton radiation can account for both the spectrum and temporal behavior of the 100 MeV to GeV afterglow emission that have been accepted by us.

Acceleration of Ions in Jovian Plasmoids: Does Turbulence Play a Role?

AbstractThe dissipation processes which transform electromagnetic energy into kinetic particle energy in space plasmas are still not fully understood. Of particular interest is the distribution of the dissipated energy among different species of charged particles. The Jovian magnetosphere is a unique laboratory to study this question because outflowing ions from the moon Io create a high diversity in ion species. In this work, we use multispecies ion observations and magnetic field measurements by the Galileo spacecraft. We limit our study to observations of plasmoids in the Jovian magnetotail, because there is strong ion acceleration in these structures. Our model predicts that electromagnetic turbulence in plasmoids plays an essential role in the acceleration of oxygen, sulfur, and hydrogen ions. The observations show a decrease of the oxygen and sulfur energy spectral index γ at ∼30 to ∼400 keV/nuc with the wave power indicating an energy transfer from electromagnetic waves to particles, in agreement with the model. The wave power threshold for effective acceleration is of the order of 10 nT2Hz−1, as in terrestrial plasmoids. However, this is not observed for hydrogen ions, implying that processes other than wave‐particle interaction are more important for the acceleration of these ions or that the time and energy resolution of the observations is too coarse. The results are expected to be confirmed by improved plasma measurements by the Juno spacecraft.