Energy Spectral Index Research Articles

Cosmic Ray Acceleration at Ultrarelativistic Subshocks

We present the model of cosmic rays acceleration at ultrarelativistic subshocks and confront it with the observations of gamma-ray bursts and blazars. We investigate cosmic rays acceleration in shocks with Lorentz factors in the range 3 - 40. We show that fluctuations of the magnetic field downstream of the shock do not play an important role in the acceleration process. Results of numerical simulations for shocks with considered Lorentz factors and perpendicular magnetic field inclinations are presented. We fit the derived particle energy spectral index dependence on fluctuations of the magnetic field upstream and Lorentz factor of the shock with a function.

First observation of a solar X-class flare in the submillimeter range with KOSMA

We present the first solar flare observations with the KOSMA submillimeter telescope at 230 and 345 GHz. The GOES X2.0 flare on April 12, 2001 was also observed at millimeter and centimeter wavelengths, as well as in soft and hard X-rays. It exhibits both an impulsive phase of nonthermal gyrosynchrotron radiation and an extended phase of strong thermal free-free emission in the millimeter and submillimeter range. As in previous observations, a mismatch between the electron energy spectral indices, inferred from the millimeter and hard X-ray data, exists and is interpreted as a flattening of the energy spectrum above a break energy of several hundred keV. The observed thermal emission closely follows the shape of the mm/submm flux density time profile predicted from soft X-ray observations. As the observed absolute flux densities exceed the predicted ones by a factor of ~1.5–3.4, both the mm/submm emission and the soft X-rays must be thermal bremsstrahlung with a common energy source, but from locations with different plasma parameters. KOSMA observations allowed an estimate of source locations and sizes for the nonthermal and thermal sources. All of them coincide within 0.2 arcmin and with those seen in soft and hard X-rays. Surprisingly, the thermal submillimeter source diameters at 230 and 345 GHz (42 and 70 arcsec respectively) increase with frequency.

The X-ray jet and central structure of the active galaxy NGC 315

We report the Chandra detection of resolved X-ray emission of luminosity 3.5 × 1040 erg s−1 (0.4–4.5 keV) and power-law energy spectral index α= 1.5 ± 0.7 from a roughly 10 arcsec length of the north-west radio jet in NGC 315. The X-ray emission is brightest at the base of the radio-bright region about 3 arcsec from the nucleus, and is consistent with a synchrotron origin. At a projected distance of 10 arcsec from the core, the jet is in approximate pressure balance with an external medium which is also detected through its X-ray emission and which has kT≈ 0.6 ± 0.1 keV, consistent with earlier ROSAT results. The high spatial resolution and sensitivity of Chandra separates nuclear unresolved emission from the extended thermal emission of the galaxy atmosphere with higher precision than possible with previous telescopes. We measure an X-ray luminosity of 5.3 × 1041 erg s−1 (0.4–4.5 keV) and a power-law energy index of α= 0.4 ± 0.4 for the nuclear component.

Statistical properties of sep event flux declines

The interplanetary space is not a passive medium, which merely constitutes a scene for the propagation of previously accelerated energetic particles, but influences the distribution of particles by changing their energies as well due to interactions with magnetic field inhomogeneities. Such processes manifest themselves in the energy spectra of solar energetic particle (SEP) events. In this paper the fluxes of protons with energies of 4–60 MeV are investigated on the basis of two data sets. Both sets are homogeneous, obtained by the CPME instrument aboard the IMP 8 satellite between 1974 and 2001. The first includes all SEP events where the integral fluxes of >4 MeV protons exceeded 2 particle/cm 2 s sr. The other set consists of fluxes recorded in differential energy windows between 0.5 and 48 MeV. Important characteristics of SEP events include the rates of decrease of particle flux, which, as well as peak flux time, is an integral feature of the interplanetary medium within a considerable region, surrounding the observation point. The time intervals selected cover the decay phases of SEP events following flares, CMEs and interplanetary shocks of different origin. Only those parts of declines were selected, that could reasonably be described by exponential dependence, irrespective of the gradual/impulsive character of the events. It is shown that the average values of characteristic decay time, τ , and energy spectral index, γ , are all changing with the solar activity phase. Distributions of τ and γ values are obtained in SEPs with and without shocks and during different phases of events: just after peak flux and late after maximum.

Statistical properties of SEP event flux declines

Abstract The interplanetary space is not a passive medium, which merely constitutes a scene for the propagation of previously accelerated energetic particles, but influences the distribution of particles by changing their energies as well due to interactions with magnetic field inhomogeneities. Such processes manifest themselves in the energy spectra of solar energetic particle (SEP) events. In this paper the fluxes of protons with energies of 4–60 MeV are investigated on the basis of two data sets. Both sets are homogeneous, obtained by the CPME instrument aboard the IMP 8 satellite between 1974 and 2001. The first includes all SEP events where the integral fluxes of >4 MeV protons exceeded 2 particle/cm 2 s sr. The other set consists of fluxes recorded in differential energy windows between 0.5 and 48 MeV. Important characteristics of SEP events include the rates of decrease of particle flux, which, as well as peak flux time, is an integral feature of the interplanetary medium within a considerable region, surrounding the observation point. The time intervals selected cover the decay phases of SEP events following flares, CMEs and interplanetary shocks of different origin. Only those parts of declines were selected, that could reasonably be described by exponential dependence, irrespective of the gradual/impulsive character of the events. It is shown that the average values of characteristic decay time, τ , and energy spectral index, γ , are all changing with the solar activity phase. Distributions of τ and γ values are obtained in SEPs with and without shocks and during different phases of events: just after peak flux and late after maximum.

Filling factors and magnetic field strengths of nanoflare-heated coronal active regions: Yohkoh and MDI observations

The scaling laws describing the relationship between thermal and magnetic properties of active regions are derived using the concept that solar coronal active regions are heated by numerous small flare-like events (nanoflares). Thus, a coro- nal active region is viewed as an ensemble of hot elementary filaments created within the coronal magnetic field by random impulsive heating events. The scaling laws obtained are governed by the global energy balance of the active regions and are independent of the details of any heating process (such as the energy of individual heating event or energy spectral index of nanoflares). We examined 61 coronal active regions observed with the soft X-ray telescope aboard Yohkoh and found that such a model yields filling factors (defined as the ratio of the volume of hot plasma to the total volume) in the range 0.002 to 0.015 and magnetic field strengths of 20 G to 40 G. The analysis determining the mean magnetic field strength and filling factors of a large number of coronal active regions, observed by Yohkoh, based on nanoflare-heating concept is the first such analysis. We also examine 24 active regions observed with the Michelson Doppler Imager aboard Solar and Heliospheric Observatory and find that the total thermal energy content Eth is related to the total magnetic flux by a power-law index of 1.24 i.e. Eth/ 1:24 . The thermal pressure pth of the active regions is related to the magnetic flux density Bp obtained from MDI measurement as: pth/ B 0:5 p .

Approximate Expression of Ellipse Polarization Degree for Gyrosynchrotron Radiation

We study the elliptical polarization degree (EPD) of gyrosynchrotronradiation for the case of transverse propagation. The EPD decreaseswith increasing ellipticity R (i.e. ratio of the major and minoraxial lengths) and with decreasing electron energy spectral indexδ. The EPD value varies from 0.55 to 0.15 in the whole rangeof 3⩽R⩽10 and 2⩽δ⩽7. An approximateexpression for the EPD is proposed, in which we assume that theemitting electrons have an isotropic pitch angle distribution and apower-law distribution in energy. The expression is designed for theelectron energy spectral index δ from 2 to 7, as well as theharmonic numbers s from 2 to 70 with a statistical error of ±6%. The expression can be applied to the polarization analysis andmagnetic field strength diagnostic for solar limb events.

A Multiwavelength Study of Three Solar Flares

In this paper we seek a self-consistent model for three strong limb flares observed at 17 and 34 GHz by the Nobeyama radioheliograph and also in soft X-rays and hard X-rays by the Yohkoh SXT (Soft X-Ray Telescope) and HXT (Hard X-Ray Telescope) instruments. Additional radio spectral data were provided by the Nobeyama polarimeter. The flare geometry is simple, with one well-defined flaring loop in each event. The 17 and 34 GHz emissions are optically thin gyrosynchrotron radiation from energetic electrons that outlines the flaring loops and peaks close to the loop tops. We infer that the variation of magnetic field along the loops is very small. We try to reproduce the observed radio morphologies and fluxes using a model gyrosynchrotron loop. The results of our modeling rely on the model magnetic field geometry that we choose. Although the exact loop geometry cannot be constrained from a two-dimensional snapshot, we choose for simplicity a line-dipole magnetic field, and the model field lines are circular. The SXT/HXT images are used to provide the physical parameters of the model loops. The high-frequency polarimeter data give the energy spectral index of the radio-emitting electrons. We could not reconcile the observed radio morphologies and fluxes using classic dipole magnetic field models. The best-fit model that uses the same input parameters for both frequencies and partly reconciles the observed 17 and 34 GHz morphologies and fluxes is produced when we invoke a magnetic field with constant strength along the model loop. These model loops have uniform thickness. The derived densities of the radio-emitting electrons are (1-6) × 104 cm-3 with energy limits between 60 and 5000 keV. These models are the best fits we can get under the best assumptions we can justify, but they do not in fact match the radio morphologies very well; their problems and limitations are discussed.

Harmonic Structures of Gyrosynchrotron Radiation and Cyclotron Maser Instability

The harmonic structures of the gyrosynchrotron radiation are studied and compared with the results of the electron cyclotron maser instability. The structures only appear at lower harmonics (s < 10), and their peaks deviate by a small amount from integer harmonic numbers. The amplitudes of harmonic structures of the extraordinary modes are usually larger than that of the ordinary modes. The numbers and amplitudes of harmonic structures increase with increasing electron energy spectral index δ and propagation angle θ. All the properties of harmonic structures are consistent with the predictions of the electron cyclotron maser instability in an extremely magnetized plasma on the basis of Maxwell and Vlasov equations. The physical relations between gyrosynchrotron radiation and cyclotron maser instability and a possible application of the properties of the harmonic structures are discussed.

TheBeppoSAXView of the X‐Ray Active Nucleus of NGC 4258

BeppoSAX observed the Seyfert 1.9 galaxy NGC 4258 in 1998 December, when its 2-10 keV luminosity was about 1041 ergs s-1. Large amplitude (100%) variability is observed in the 3-10 keV band on timescales of a few tens of thousands of seconds, while variability of ~20% is observed on timescales as short as 1 hr. The nuclear component is visible above 2 keV only, being obscured by a column density of (9.5 ± 1.2) × 1022 cm-2; this component is detected at up to 70 keV with a signal-to-noise ratio of 3 and with a steep power-law energy spectral index of αE = 1.11 ± 0.14. Bremsstrahlung emission for the 2-70 keV X-ray luminosity, as expected in advection-dominated accretion flow models with strong winds, is ruled out by the data. The ratio between the nuclear radio (22 GHz) luminosity and the X-ray (5 keV) luminosity is consistent with that of radio-quiet quasars and Seyfert galaxies. X-ray variability, spectral shape, and radio/X-ray and near-IR/X-ray luminosity ratios suggest that the nucleus of NGC 4258 could be a scaled down version of a Seyfert nucleus and that the X-ray nuclear luminosity can be explained in terms of Comptonization in a hot corona. The soft (E 2 keV) X-ray emission is complex. There are at least two thermal-like components with temperatures of 0.6 ± 0.1 keV and 1.3 keV. The cooler (L0.1-2.4 keV~ 1040 ergs s-1) component is probably associated with the jet, resolved in X-rays by the ROSAT HRI (Cecil et al. 1994). The luminosity of the second component, which can be modeled equally well by an unobscured power-law model with αE = 0.2, is L0.1-2.4 keV~ 7 × 1039 ergs s-1, consistent with that expected from discrete X-ray sources (binaries and supernova remnants) in the host galaxy. Observations of NGC 4258 and other maser active galactic nuclei (AGNs) show strong nuclear X-ray absorption. We propose that this large column of gas might be responsible for shielding the regions of water maser emission from X-ray illumination. So a large column density absorbing gas may be a necessary property of masing AGNs.

Two-parametric representation of the solar and heliospheric protons

Abstract The dynamics of the interplanetary proton spectra in the energy range 1–40 MeV have been investigated using the data obtained on board the IMP-8 (1973–1992) and Meteor (1970–1996) satellites. Phase diagrams of the proton events are constructed in the two-parametric space { Y,g }, where Y=g −1 lg( I p ), g is the differential energy spectral index, I p represents the >1 MeV proton intensity. The results show that the phase trajectories allow separation of the background proton fluxes, proton populations accelerated mainly in the solar flares, at the propagating interplanetary shocks associated with coronal mass ejections and also in the corotating interaction regions between fast and slow solar wind streams. The estimations of the maximal and minimal >1 MeV proton fluxes in the near Earth heliosphere are obtained.

Synchrotron Radiation as the Source of Gamma‐Ray Burst Spectra

We investigate synchrotron emission models as the source of gamma-ray burst spectra. We show that including the possibility for synchrotron self-absorption, a ``smooth cutoff'' to the electron energy distribution, and an anisotropic distribution for the electron pitch angles produces a whole range of low energy spectral behavior. In addition, we show that the procedure of spectral fitting to GRB data over a finite bandwidth can introduce a spurious correlation between spectral parameters - in particular, the value of the peak of the nu F_nu spectrum, E_p, and the low energy photon spectral index alpha (the lower E_p is, the lower (softer) the fitted value of alpha will be). From this correlation and knowledge of the E_p distribution, we show how to derive the expected distribution of alpha. We show that optically thin synchrotron models with an isotropic electron pitch angle distribution can explain the distribution of alpha below alpha=-2/3. This agreement is achieved if we relax the unrealistic assumption of the presence of a sharp low energy cutoff in the spectrum of accelerated electrons, and allow for a more gradual break. We show that this low energy portion of the electron spectrum can be at most flat. We also show that optically thin synchrotron models with an anisotropic electron pitch angle distribution can explain all bursts with -2/3 < alpha <= 0$. The very few bursts with low energy spectral indices that fall above alpha=0 may be due the presence of a the synchrotron self-absorption frequency entering the lower end of the BATSE window. Our results also predict a particular relationship between alpha and E_p during the temporal evolution of a GRB. We give examples of spectral evolution in GRBs and discuss how the behavior are consistent with the above models.

Observations and Models of a Flaring Loop

Simultaneous images of a flaring loop at two frequencies are used to model the magnetic structure of the loop and the energy distribution of the radiating electrons. The imaging data were obtained with the VLA at 5 and 15 GHz. Additional spectral data were provided by the Owens Valley Radio Observatory (OVRO) solar array at several frequencies between 2 and 15 GHz. At 15 GHz, the flare emission was optically thin and came from the footpoints of the flaring loop, while at 5 GHz the loop itself was outlined. Most of the 5 GHz emission was optically thick, and its spatial maximum was close to the loop top. A striking feature of the observations is that the 5 GHz emission does not reach down to the 15 GHz footpoints. We compare the observations with calculations of gyrosynchrotron emission from an inhomogeneous magnetic loop in order to determine the conditions in the flaring loop. The best fit to the OVRO fluxes was reached with a model flaring loop with photospheric footpoint magnetic field strength of 870 G. The thickness of the model loop was small compared with its footpoint separation. The energy spectral index of the energetic electrons was 3.7, and their number density was 7.9 × 107 cm-3. The low- and high-energy cutoffs of the nonthermal electrons were 8 and 210 keV, respectively. The 5 GHz emission in this model is at low harmonics (3-7), and harmonic effects are responsible for the weak 5 GHz emission at the footpoints. The absence of electrons above 210 keV is necessary in this model to explain why no emission is observed from the loop top at 15 GHz. That model reproduced well the high-frequency part of the OVRO flux spectrum as well as the VLA spatial structure. Thus, comparisons between the spatially resolved observations and models reveal the three-dimensional structure of the loop geometry.

A Medium Survey of the Hard X‐Ray Sky withASCA. II. The Source’s Broadband X‐Ray Spectral Properties

A complete sample of 60 serendipitous hard X-ray sources with flux in the range ~1 × 10-13 ergs cm-2 s-1 to ~4 × 10-12 ergs cm-2 s-1 (2-10 keV), detected in 87 ASCA GIS2 images, was recently presented in the literature. Using this sample it was possible to extend the description of the 2-10 keV log N(> S)- log S down to a flux limit of ~6 × 10-14 ergs cm-2 s-1 (the faintest detectable flux), resolving about a quarter of the cosmic X-ray background (CXB). In this paper we have combined the ASCA GIS2 and GIS3 data of these sources to investigate their X-ray spectral properties using the hardness ratios and the stacked-spectra method. Because of the sample statistical representativeness, the results presented here, which refer to the faintest hard X-ray sources that can be studied with the current instrumentation, are relevant to the understanding of the CXB and of the active galactic nucleus (AGN) unification scheme. The stacked spectra show that the average source's spectrum hardens toward fainter fluxes; it changes from an energy spectral index = 0.87 ± 0.08 for the 20 brightest sources (2-10 keV count rate ≥3.9 × 10-3 counts s-1, the sample) to = 0.36 ± 0.14 for the remaining 40 fainter sources (the sample). The dividing line of 3.9 × 10-3 counts s-1 corresponds to unabsorbed 2-10 keV fluxes in the range ~5.4 × 10-13 to ~3.1 × 10-13 ergs cm-2 s-1 for a source described by a power-law model with energy spectral index between 0.0 and 2.0. It thus seems that we are now beginning to detect those sources that have the correct spectral shape to be responsible for the 2-10 keV CXB. The hardness-ratio analyses indicate that this flattening is due to a population of sources with very hard spectra showing up in the faint sample; about half of the sources in this sample require αE 0.5, while only ~10% of the sources in the bright sample are consistent with an energy spectral index so flat. A number of sources (~30%) in the faint sample seem to be characterized by an apparently inverted X-ray spectrum (i.e., αE 0.0). These objects are probably extremely absorbed sources, as expected from the CXB synthesis models based on the AGN unification scheme, if not a new population of very hard serendipitous sources. The broadband (0.7-10 keV) spectral properties of the selected sources, as inferred from the hardness-ratios diagram, seem to be more complex than is expected from a simple absorbed power-law model. We have thus investigated more complex models, in line with the AGN unification scheme, and we find that these models seem to be able to explain the overall spectral properties of the present sample; this result also seems to be suggested by a comparison of the hardness-ratio diagram of the serendipitous ASCA sources with that obtained using a sample of nearby and well-known Seyfert 1 and Seyfert 2 galaxies observed with ASCA.

Multiple Components in the Millimeter Emission of a Solar Flare

We analyze a small flare using imaging data at millimeter, microwave, and soft X-ray wavelengths and microwave and hard X-ray spectral observations. The remarkable aspect of this flare is evidence for the presence of MeV-energy electrons, which are responsible for the nonthermal millimeter emission, at a time when no hard X-rays from lower energy electrons are detected. This occurs during a smoothly varying phase, which is seen at radio wavelengths to last several minutes and is the brightest phase at millimeter wavelengths but is undetected in hard X-rays: it follows a brief spike of emission at flare onset, which has the more usual properties of impulsive events and features nonthermal microwave, millimeter, and hard X-ray emission. We interpret the phase that is brightest at millimeter wavelengths as being due to efficient trapping of a relatively small number of nonthermal electrons, whereas during the hard X-ray emission, trapping is much less efficient, and the decay time is much shorter at all energies, which leads to a larger ratio of hard X-ray flux to radio flux. As in many previous events studied at millimeter wavelengths, there is a discrepancy between the electron energy spectral indices inferred from the milllimeter and hard X-ray data during the impulsive phase when both are detected: again it appears that the energy spectrum at 1 MeV must be significantly flatter than at several hundred keV and below. However, there are problems in reconciling quantitatively the energy spectra for the hard X-ray-emitting and radio-emitting components: based on the most plausible parameters, the radio-emitting electrons should produce most of the hard X-rays. One solution to this contradiction is to invoke a coronal magnetic field stronger than seems likely based on the photospheric magnetic field.

Approximate expressions for gyrosynchrotron radiation in transverse propagation

Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity eta(nu)-/BN and absorptivity kappa(nu)-B/N for e-mode, effective temperature T-eff and frequency of peak brightness nu(p). The expressions are designed for the range 2 to 7 of electron energy spectral index delta and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=nu/nu(B)). Their statistical error is, respectively, +/- 18% and +/- 29% for eta(nu)-/BN and kappa(nu)-B/N for 10 less than or equal to nu/nu(B)less than or equal to 100, +/- 128% and and +/- 170% for 2 less than or equal to nu/nu(B)less than or equal to 10.

BeppoSAX observations of 3C 279

We report on BeppoSAX AO1 Core Program observations of 3C 279, performed in January 1997. 3C 279 was found in a low state, with constant X-ray flux in the 5 observations. The spectra obtained with the LECS and MECS instruments combining the 5 observations are well fitted by a single power law with energy spectral index α = 0.64 ± 0.03 and Galactic absorption. The source is weakly detected by the PDS instrument. Comparison with simultaneous γ-ray data obtained by EGRET and with previous multifrequency measurements shows that the X-ray emission is well correlated with the γ-ray emission over long timescales.

BeppoSAX observations of PKS 0528+134

We report on the BeppoSAX observations of the γ-ray blazar PKS 0528+134 performed in Feb and Mar 1997, during a multiwavelength campaign involving EGRET and ground based telescopes. The source was in a faint and hard state, with energy spectral index α = 0.48 ± 0.04 between 0.1 and 10 keV, and [2–10] keV flux of 2.7 × 10 −12 erg cm −2 s −1. No significant variability was observed. The source was detected in the 20–120 keV band by the PDS, with a flux lying slightly above the extrapolation from lower X-ray energies. Comparing this low state with previous higher states of the source, there is an indication that the X-ray spectrum hardens and the γ-ray spectrum steepens when the source is fainter.

The broad band spectrum and variability of NGC 4151 observed by BeppoSAX

We present broad band timing and spectral analysis of Beppo-SAX data of the Seyfert galaxy NGC 4151, and propose multi-component models to explain the complex spectrum of this source and the observed, energy dependent, spectral variability. Many different components are needed to model SAX NGC 4151 spectra. The intrinsic continuum is well described by a simple power law with energy spectral index slightly correlated with intensity (α ∼ 0.4–0.5) up to ∼ 15 keV. At higher energies an exponential cutoff is clearly detected in the PDS spectra ( c = 50 ± 5 keV). There is also an evidence for a flattening of the spectrum above ∼ 15 keV which is well described by a reflection model. A non-variable, complex soft component becomes dominant below ∼ 1 keV. Between 1 keV and ∼ 5 keV, a complicate absorption structure reveals the presence of either a cold absorber partially covering the nuclear continuum or a very thick warm absorber, or both. Finally, a strong Iron line at 6.4 keV is clearly detected, with varying equivalent width, becoming stronger as continuum intensity drops.

Diagnostics of magnetic field strength for gyrosynchrotron radiation regions of the lower harmonics

A diagnostic formula of magnetic field strength of gyrosynchrotron radiation regions of the tower harmonics (5 less than or equal to S less than or equal to 10) is presented based on their emissivity eta(nu)/BN, absorptivity kappa(nu)B/N, and the turnover frequency of radio spectra nu(P). Their diagnostic error is estimated. And an accurate relation between electron energy spectral index delta and brightness temperature spectral index beta is also given.