Energy Distribution Of Relativistic Electrons Research Articles

A new analytical model of the cosmic-ray energy flux for Galactic diffuse radio emission

Low-frequency radio observations of diffuse synchrotron radiation offer a unique vantage point from which to investigate the intricate relationship between gas and magnetic fields in the formation of structures within the Galaxy, spanning from the diffuse interstellar medium (ISM) to star-forming regions. Achieving this pivotal objective hinges on a comprehensive understanding of cosmic-ray properties; these dictate the effective energy distribution of relativistic electrons, which are primarily responsible for the observable synchrotron radiation. Notably, cosmic-ray electrons (CRe) with energies of between 100 MeV and 10 GeV play a crucial role in determining the majority of the sky brightness below the GHz range. However, their energy flux (je) remains elusive because of solar modulation. We propose a way to derive observational constraints on this energy gap of interstellar CRe through the brightness temperature spectral index of low-frequency radio emission, here denoted βobs. We introduce a new parametric analytical model that fits available data for je in accordance with the βobs values measured in the literature between 50 MHz and 1 GHz for diffuse emission in the Milky Way. Our model accounts for multiple observations considering magnetic-field strengths consistent with existing measurements below 10 μG. We present a first all-sky map of the average component of the magnetic field perpendicular to the line of sight and validate our methodology against state-of-the art numerical simulations of the diffuse ISM. This research makes headway in modeling Galactic diffuse emission with a practical, parametric form. It provides essential insights that will help preparations for the imminent arrival of the Square Kilometre Array.

Magnetic field properties inside the jet of Mrk 421

Aims. We aim to probe the magnetic field geometry and particle acceleration mechanism in the relativistic jets of supermassive black holes. Methods. We conducted a polarimetry campaign from radio to X-ray wavelengths of the high-synchrotron-peak (HSP) blazar Mrk 421, including Imaging X-ray Polarimetry Explorer (IXPE) measurements from 2022 December 6–8. During the IXPE observation, we also monitored Mrk 421 using Swift-XRT and obtained a single observation with XMM-Newton to improve the X-ray spectral analysis. The time-averaged X-ray polarization was determined consistently using the event-by-event Stokes parameter analysis, spectropolarimetric fit, and maximum likelihood methods. We examined the polarization variability over both time and energy, the former via analysis of IXPE data obtained over a time span of 7 months. Results. We detected X-ray polarization of Mrk 421 with a degree of ΠX = 14 ± 1% and an electric-vector position angle ψX = 107 ± 3° in the 2–8 keV band. From the time variability analysis, we find a significant episodic variation in ψX. During the 7 months from the first IXPE pointing of Mrk 421 in 2022 May, ψX varied in the range 0° to 180°, while ΠX remained relatively constant within ∼10–15%. Furthermore, a swing in ψX in 2022 June was accompanied by simultaneous spectral variations. The results of the multiwavelength polarimetry show that ΠX was generally ∼2–3 times greater than Π at longer wavelengths, while ψ fluctuated. Additionally, based on radio, infrared, and optical polarimetry, we find that the rotation of ψ occurred in the opposite direction with respect to the rotation of ψX and over longer timescales at similar epochs. Conclusions. The polarization behavior observed across multiple wavelengths is consistent with previous IXPE findings for HSP blazars. This result favors the energy-stratified shock model developed to explain variable emission in relativistic jets. We considered two versions of the model, one with linear and the other with radial stratification geometry, to explain the rotation of ψX. The accompanying spectral variation during the ψX rotation can be explained by a fluctuation in the physical conditions, for example in the energy distribution of relativistic electrons. The opposite rotation direction of ψ between the X-ray and longer wavelength polarization accentuates the conclusion that the X-ray emitting region is spatially separated from that at longer wavelengths. Moreover, we identify a highly polarized knot of radio emission moving down the parsec-scale jet during the episode of ψX rotation, although it is unclear whether there is any connection between the two events.

Energy Distribution of Relativistic Electrons Moderating in Matter

Energy Distribution of Relativistic Electrons Moderating in Matter

First results from the IllustrisTNG simulations: radio haloes and magnetic fields

We introduce the IllustrisTNG project, a new suite of cosmological magnetohydrodynamical simulations performed with the moving-mesh code AREPO employing an updated Illustris galaxy formation model. Here we focus on the general properties of magnetic fields and the diffuse radio emission in galaxy clusters. Magnetic fields are prevalent in galaxies, and their build-up is closely linked to structure formation. We find that structure formation amplifies the initial seed fields ($10^{-14}$ comoving Gauss) to the values observed in low-redshift galaxies ($1-10\,\mu{\rm G}$). The magnetic field topology is closely connected to galaxy morphology such that irregular fields are hosted by early-type galaxies, while large-scale, ordered fields are present in disc galaxies. Using two simple models for the energy distribution of relativistic electrons we predict the diffuse radio emission of $280$ clusters with a baryonic mass resolution of $1.1\times 10^{7}\,{\rm M_{\odot}}$, and generate mock observations for VLA, LOFAR, ASKAP and SKA. Our simulated clusters show extended radio emission, whose detectability correlates with their virial mass. We reproduce the observed scaling relations between total radio power and X-ray emission, $M_{500}$, and the Sunyaev-Zel'dovich $Y_{\rm 500}$ parameter. The radio emission surface brightness profiles of our most massive clusters are in reasonable agreement with VLA measurements of Coma and Perseus. Finally, we discuss the fraction of detected extended radio haloes as a function of virial mass and source count functions for different instruments. Overall our results agree encouragingly well with observations, but a refined analysis requires a more sophisticated treatment of relativistic particles in large-scale galaxy formation simulations.

Energy distribution of relativistic electrons in the kiloparsec scale jet of M 87 with Chandra

The X-ray emission from the jets in active galactic nuclei (AGN) carries important information on the distributions of relativistic electrons and magnetic fields on large scales. We reanalysed archival Chandra observations on the jet of M 87 from 2000 to 2016 with a total exposure of 1460 kiloseconds to explore the X-ray emission characteristics along the jet. We investigated the variability behaviours of the nucleus and the inner jet component HST-1, and confirm indications for day-scale X-ray variability in the nucleus contemporaneous to the 2010 high TeV γ-ray state. HST-1 shows a general decline in X-ray flux over the last few years consistent with its synchrotron interpretation. We extracted the X-ray spectra for the nucleus and all knots in the jet, showing that they are compatible with a single power law within the X-ray band. There are indications that the resultant X-ray photon index exhibit a trend, with slight but significant index variations ranging from ≃ 2.2 (e.g. in knot D) to ≃ 2.4−2.6 (in the outer knots F, A, and B). When viewed in a multiwavelength context, a more complex situation can be seen. Fitting the radio to X-ray spectral energy distributions (SEDs) assuming a synchrotron origin, we show that a broken power-law electron spectrum with break energy Eb around 1 (300 μG/B)1/2 TeV allows a satisfactory description of the multiband SEDs for most of the knots. However, in the case of knots B, C, and D we find indications that an additional high-energy component is needed to adequately reproduce the broad-band SEDs. We discuss the implications and suggest that a stratified jet model may account for the differences.

Sky-distribution of intensity of synchrotron radio emission of relativistic electrons trapped in Earth’s magnetic field

This paper presents the calculations of synchrotron radio emission intensity from Van Allen belts with Gaussian space distribution of electron density across L-shells of a dipole magnetic field, and with Maxwell’s relativistic electron energy distribution. The results of these calculations come to a good agreement with measurements of the synchrotron emission intensity of the artificial radiation belt’s electrons during the Starfish nuclear test. We have obtained two-dimensional distributions of radio brightness in azimuth — zenith angle coordinates for an observer on Earth’s surface. The westside and eastside intensity maxima exceed several times the maximum level of emission in the meridian plane. We have also constructed two-dimensional distributions of the radio emission intensity in decibels related to the background galactic radio noise level. Isotropic fluxes of relativistic electrons (E ~ 1 MeV) should be more than 107 cm–2s–1 for the synchrotron emission intensity in the meridian plane to exceed the cosmic noise level by 0.1 dB (riometer sensitivity threshold).

О распределении по небесной сфере интенсивности синхротронного радиоизлучения релятивистских электронов, захваченных в магнитном поле Земли

This paper presents the calculations of synchrotron radio emission intensity from Van Allen belts with Gaussian space distribution of electron density across L-shells of a dipole magnetic field, and with Maxwell’s relativistic electron energy distribution. The results of these calculations come to a good agreement with measurements of the synchrotron emission intensity of the artificial radiation belt’s electrons during the Starfish nuclear test. We have obtained two-dimensional distributions of radio brightness in azimuth — zenith angle coordinates for an observer on Earth’s surface. The westside and eastside intensity maxima exceed several times the maximum level of emission in the meridian plane. We have also constructed two-dimensional distributions of the radio emission intensity in decibels related to the background galactic radio noise level. Isotropic fluxes of relativistic electrons (E ~ 1 MeV) should be more than 107 cm–2s–1 for the synchrotron emission intensity in the meridian plane to exceed the cosmic noise level by 0.1 dB (riometer sensitivity threshold).

Energy distribution of relativistic electrons in the young supernova remnant G1.9+0.3

The broad-band X-ray observations of the youngest known galactic supernova remnant, G1.9+0.3, provide unique information about the particle acceleration at the early stages of evolution of supernova remnants. Based on the publicly available X-ray data obtained with the Chandra and NuSTAR satellites over two decades in energy, we derived the energy distribution of relativistic electrons under the assumption that detected X-rays are of entirely synchrotron origin. The acceleration of electrons was found to be an order of magnitude slower than the maximum rate provided by the shock acceleration in the nominal Bohm diffusion regime. We discuss the implications of this result in the context of contribution of SNRs to the Galactic Cosmic Rays at PeV energies.

A magnetohydrodynamic model for multiwavelength flares from Sagittarius A⋆ (I): model and the near-infrared and X-ray flares

Flares from the supermassive black hole in our Galaxy, Sagittarius A⋆ (Sgr A⋆), are routinely observed over the last decade or so. Despite numerous observational and theoretical efforts, the nature of such flares still remains poorly understood, although a few phenomenological scenarios have been proposed. In this work, we develop the Yuan et al. scenario into a magnetohydrodynamic model for Sgr A⋆ flares. This model is analogous with the theory of solar flares and coronal mass ejection in solar physics. In the model, magnetic field loops emerge from the accretion flow on to Sgr A⋆ and are twisted to form flux ropes because of shear and turbulence. The magnetic energy is also accumulated in this process until a threshold is reached. This then results in a catastrophic evolution of a flux rope with the help of magnetic reconnection in the current sheet. In this catastrophic process, the magnetic energy is partially converted into the energy of non-thermal electrons. We have quantitatively calculated the dynamical evolution of the height, size and velocity of the flux rope, as well as the magnetic field in the flare regions, and the energy distribution of relativistic electrons in this process. We further calculate the synchrotron radiation from these electrons and compare the obtained light curves with the observed ones. We find that the model can reasonably explain the main observations of near-infrared and X-ray flares including their light curves and spectra. It can also potentially explain the frequency-dependent time delay seen in radio flare light curves.

The WEBT campaign on the BL Lac object PG 1553+113 in 2013. An analysis of the enigmatic synchrotron emission

A multifrequency campaign on the BL Lac object PG 1553+113 was organized by the Whole Earth Blazar Telescope (WEBT) in 2013 April-August, involving 19 optical, two near-IR, and three radio telescopes. The aim was to study the source behaviour at low energies during and around the high-energy observations by the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes in April-July. We also analyse the UV and X-ray data acquired by the Swift and XMM-Newton satellites in the same period. The WEBT and satellite observations allow us to detail the synchrotron emission bump in the source spectral energy distribution (SED). In the optical we found a general bluer-when-brighter trend. The X-ray spectrum remained stable during 2013, but a comparison with previous observations suggests that it becomes harder when the X-ray flux increases. The long XMM-Newton exposure reveals a curved X-ray spectrum. In the SED, the XMM-Newton data show a hard near-UV spectrum, while Swift data display a softer shape that is confirmed by previous HST-COS and IUE observations. Polynomial fits to the optical-X-ray SED show that the synchrotron peak likely lies in the 4-30 eV energy range, with a general shift towards higher frequencies for increasing X-ray brightness. However, the UV and X-ray spectra do not connect smoothly. Possible interpretations include: i) orientation effects, ii) additional absorption, iii) multiple emission components, and iv) a peculiar energy distribution of relativistic electrons. We discuss the first possibility in terms of an inhomogeneous helical jet model.

Extragalactic radio sources with sharply inverted spectrum at metre wavelengths

We present the first results of a systematic search for the rare extragalactic radio sources showing an inverted (integrated) spectrum, with spectral index $\alpha \ge +2.0$, a previously unexplored spectral domain. The search is expected to yield strong candidates for $\alpha \ge +2.5$, for which the standard synchrotron self-absorption (characterized by a single power-law energy distribution of relativistic electron population) would not be a plausible explanation, even in an ideal case of a perfectly homogeneous source of incoherent synchrotron radiation. Such sharply inverted spectra, if found, would require alternative explanations, e.g., free-free absorption, or non-standard energy distribution of relativistic electrons which differs from a power-law (e.g., Maxwellian). The search was carried out by comparing two sensitive low-frequency radio surveys made with sub-arcminute resolution, namely, the WISH survey at 352 MHz and TGSS/DR5 at 150 MHz. The overlap region between these two surveys contains 7056 WISH sources classified as `single' and brighter than 100 mJy at 352 MHz. We focus here on the seven of these sources for which we find $\alpha > +2.0$. Two of these are undetected at 150 MHz and are particularly good candidates for $\alpha > +2.5$. Five of the seven sources exhibit a `Gigahertz-Peaked-Spectrum' (GPS).

INJECTION AND ACCELERATION OF ELECTRONS AT A STRONG SHOCK: RADIO AND X-RAY STUDY OF YOUNG SUPERNOVA 2011dh

In this paper, we develop a model for the radio and X-ray emissions from Type IIb Supernova (SN IIb) 2011dh in the first 100 days after the explosion, and investigate a spectrum of relativistic electrons accelerated at a strong shock wave. The widely-accepted theory of the particle acceleration, so-called diffusive shock acceleration (DSA) or Fermi mechanism, requires seed electrons with modest energy with gamma ~ 1 - 100, and little is known about this pre-acceleration mechanism: We derive the energy distribution of relativistic electrons in this pre-accelerated energy regime. We find that the efficiency of the electron acceleration must be low, i.e., epsilon_e <~ 0.01 as compared to the conventionally assumed value of epsilon_e ~ 0.1. Furthermore, independently from the low value of epsilon_e, we find that the X-ray luminosity cannot be attributed to any emission mechanisms suggested so far as long as these electrons follow the conventionally-assumed single power-law distribution. A consistent view between the radio and X-ray can only be obtained if the pre-acceleration injection spectrum peaks at gamma ~ 20-30 and then only a fraction of these electrons eventually experience the DSA-like acceleration toward the higher energy -- then the radio and X-ray properties are explained through the synchrotron and inverse Compton mechanisms, respectively. Our findings support the idea that the pre-acceleration of the electrons is coupled with the generation/amplification of the magnetic field.

Direct, Absolute, andIn SituMeasurement of Fast Electron Transport via Cherenkov Emission

We present direct measurements of the absolute energy distribution of relativistic electrons generated in intense, femtosecond laser interaction with a solid. Cherenkov emission radiated by these electrons in a novel prism target is spectrally dispersed to obtain yield and energy distribution of electrons simultaneously. A crucial advance is the observation of high density electron current as predicted by particle simulations and its transport as it happens inside the target. In addition, the strong sheath potential present at the rear side of the target is inferred from a comparison of the electron spectra derived from Cherenkov light observation with that from a magnet spectrometer.

The radio to TeV orbital variability of the microquasar LS I +61 303

Context. The microquasar LS I +61 303 has recently been detected at TeV energies by the Cherenkov telescope MAGIC, presenting variability on timescales similar to its orbital period. This system has been intensively observed at different wavelengths during the last three decades, showing a very complex behavior along the orbit. Aims. We aim to explain, using a leptonic model in the accretion scenario, the observed orbital variability and spectrum from radio to TeV energies of LS I +61 303. Methods. We apply a leptonic model based on accretion of matter from the slow inhomogeneous equatorial wind of the primary star, assuming particle injection proportional to the accretion rate. The relativistic electron energy distribution within the binary system is computed taking into account convective/adiabatic and radiative losses. The spectral energy distribution (SED) has been calculated accounting for synchrotron and (Thomson/Klein Nishina -KN-) inverse Compton (IC) processes and the photon-photon absorption in the ambient photon fields. The angle dependence of the photon-photon and IC cross sections has been considered in the calculations. Results. We reproduce the main features of the observed light curves from LS I +61 303 at radio, X-rays, high-energy (HE), and very high-energy (VHE) gamma-rays, and the whole spectral energy distribution. Conclusions. Our model is able to explain the radio to TeV orbital variability taking into account that radiation along the orbit is strongly affected by the variable accretion rate, the magnetic field strength, and by the ambient photon field via dominant IC losses and photon-photon absorption at periastron.

Radio emission models of colliding-wind binary systems. Inclusion of IC cooling

Radio emission models of colliding wind binaries (CWBs) have been discussed by Dougherty et al. (2003). We extend these models by considering the temporal and spatial evolution of the energy distribution of relativistic electrons as they advect downstream from their shock acceleration site. The energy spectrum evolves significantly due to the strength of inverse-Compton (IC) cooling in these systems, and a full numerical evaluation of the synchrotron emission and absorption coefficients is made. We have demonstrated that the geometry of the WCR and the streamlines of the flow within it lead to a spatially dependent break frequency in the synchrotron emission. We therefore do not observe a single, sharp break in the synchrotron spectrum integrated over the WCR, but rather a steepening of the synchrotron spectrum towards higher frequencies. We also observe that emission from the wind-collision region (WCR) may appear brightest near the shocks, since the impact of IC cooling on the non-thermal electron distribution is greatest near the contact discontinuity (CD), and demonstrate that the impact of IC cooling on the observed radio emission increases significantly with decreasing binary separation. We study how the synchrotron emission changes in response to departures from equipartition, and investigate how the thermal flux from the WCR varies with binary separation. Since the emission from the WCR is optically thin, we see a substantial fraction of this emission at certain viewing angles, and we show that the thermal emission from a CWB can mimic a thermal plus non-thermal composite spectrum if the thermal emission from the WCR becomes comparable to that from the unshocked winds. We demonstrate that the observed synchrotron emission depends upon the viewing angle and the wind-momentum ratio, and find that the observed synchrotron emission decreases as the viewing angle moves through the WCR from the WR shock to the O shock. We obtain a number of insights relevant to models of closer systems such as WR 140. Finally, we apply our new models to the very wide system WR 147. The acceleration of non-thermal electrons appears to be very efficient in our models of WR 147, and we suggest that the shock structure may be modified by feedback from the accelerated particles.

Radio synchrotron spectra for a leaky box approximation

The synchrotron emission observed from many astrophysical objects is commonly modelled to arise from relativistic electrons in an emission region occupied by a spatially homogeneous, but tangled magnetic field. However, we know that magnetic fields embedded in ionised gases tend to form flux ropes interspersed with regions of much lower magnetic field strengths. Here we develop a full description of the evolution of the energy distribution of relativistic electrons in a plasma divided into two distinct regions with different strengths of the magnetic field. Electrons are able to continuously leak from the low-field region into the high-field region. The model becomes fully analytic for physically reasonable assumptions. We show that such a leaky box model produces two distinct breaks in the electron energy distributions which give rise to three breaks in the resulting synchrotron spectrum. The spectral slopes in between the breaks are in general not constant and thus allow for significant curvature of the spectrum. These spectra are consistent with spatially resolved observations of the radio spectra of the lobes of radio galaxies. The exact form of the spectra depends on the adopted diffusion rate. The leaky box model significantly extends the time over which synchrotron emission can be detected at a given frequency compared to the usually assumed case of homogeneous magnetic fields. The spectral ages inferred for the electron population from standard techniques for the leaky box model are considerably younger than their real age.

X-ray and γ-ray emission from the PSR B1259-63/Be star system

PSR B1259-63 is a radio pulsar orbiting a Be star in a highly eccentric orbit. Soft and hard X-rays are observed from this unique system. We apply the shock powered emission model to this system. The collision of the pulsar and Be star winds forms a shock, which accelerates electrons and positrons to the relativistic energies. We derive the energy distribution of relativistic electrons and positrons as a function of the distance from the shock in the pulsar nebula. We calculate the X-rays and γ-rays emitted from the relativistic electrons and positrons in the nebula at various orbital phases, taking into account the Klein–Nishina effect fully. The shock powered emission model can explain the observed X-ray properties approximately. We obtain from the comparison with observations that a fraction of ∼0.1 of the pulsar spin-down luminosity should be transformed into the final energy of relativistic electrons and positrons. We find that the magnetization parameter of the pulsar wind, the ratio of the Poynting flux to the kinetic energy flux, is ∼0.1 and may decrease with distance from the pulsar. We predict the flux of 10 MeV–100 GeV γ-rays which may be nearly equal to the detection threshold in the future projects.

X-Ray and Gamma-Ray Emissions from the PSR 1259$-$63/Be Star System

Abstract PSR1259$-$63 is a radio pulsar orbiting a Be star in a highly eccentric orbit. Soft and hard X-rays are observed from this binary system. We applied a shock-powered emission model to this system. The collision of the pulsar and Be star winds forms a shock, which accelerates electrons and positrons to relativistic energies. We derived the energy distribution of relativistic electrons and positrons as a function of the distance from the shock in the pulsar nebula. We calculated the X-rays and $\gamma$-rays emitted from the relativistic electrons and positrons in the nebula at various orbital phases, while fully taking into account the Klein–Nishina effect. The shock-powered emission model can explain the observed X-ray properties approximately. We obtained from comparisons with observations that a fraction of $\sim 0.1$ of the pulsar spin-down luminosity should be transformed into the relativistic electrons and positrons. We found that the magnetization parameter of the pulsar wind, the ratio of the Poynting flux to the kinetic energy flux, is $\sim 0.1$ immediately upstream of the termination shock of the pulsar wind, and may decrease with the distance from the pulsar. We predict a flux of 10 MeV–100 GeV $\gamma$–rays, which may be nearly equal to the detection threshold in the future projects.

Maximum Energies of Shock‐accelerated Electrons in Large Magellanic Cloud Supernova Remnants

Some supernova remnant X-ray spectra show evidence for synchrotron emission from the extension of the electron spectrum that produces radio synchrotron emission. For any remnant, if the extrapolated radio flux exceeds the observed X-ray flux, thermal or nonthermal, a roll-off of the relativistic electron energy distribution must occur below X-ray-emitting energies. We have studied the X-ray emission from 11 remnants in the Large Magellanic Cloud to constrain this roll-off energy. We assume that the electron distribution is a power law with an exponential cutoff at some Emax and radiates in a uniform magnetic field. If the radio flux and spectral index are known, this simple model for the synchrotron contribution depends on only one parameter that relates directly to Emax. Here we have modeled the X-ray spectra by adding a component for thermal radiation of a Sedov blast wave to the synchrotron model. For all 11 supernova remnants in this sample, the limits for Emax range between 10 and 80 TeV (for a mean magnetic field of 10 μG). This result is similar to a study of Galactic remnants in which 13 out of 14 objects had limits between 20 and 80 TeV. We interpret Emax in the context of shock acceleration theories. Better data and models should allow either firm detections of nonthermal components or more restrictive limits on Emax.

Anisotropic inverse Compton scattering in powerful radio galaxies: The case of 3C 295

Inverse Compton (IC) scattering of nuclear photons with relativistic electrons in the lobes of powerful radio galaxies and quasars can give detectable extended X-ray emission from the radio lobes if relativistic electrons with a Lorentz factor are present (Brunetti et al. [CITE]). In general these electrons are not detected since they emit synchrotron radiation at frequencies below the radio band, so that the study of this effect provides a unique tool to measure the energy distribution of the electron population in the radio lobes at energies. In this paper we reanalyze the Chandra observation of the powerful and compact radio galaxy 3C 295 for which the IC scattering of nuclear photons is expected to be an important mechanism. We find strong evidence for extended and asymmetrical X-ray emission associated with the radio lobes in the energy band 0.1-2 keV. We show that both the luminosity and morphology of the extended X-ray emission associated with the radio lobes, not compatible with other X-ray mechanisms, can be best interpreted by the IC scattering with nuclear photons. We also show that the relativistic electron energy distribution obtained from the synchrotron radio emission can be extrapolated down to thus providing a first direct evidence on the electron spectrum in the lobes down to lower energies.