Revised equipartition and minimum energy formula for magnetic field strength estimates from radio synchrotron observations

The commonly used classical equipartition or minimum‐energy estimate of total magnetic fields strengths from radio synchrotron intensities is of limited practical use because it is based on the hardly known ratio K of the total energies of cosmic ray protons and electrons and also has inherent problems. We present a revised formula, using the number density ratio K for which we give estimates. For particle acceleration in strong shocks K is about 40 and increases with decreasing shock strength. Our revised estimate for the field strength gives larger values than the classical estimate for flat radio spectra with spectral indices of about 0.5–0.6, but smaller values for steep spectra and total fields stronger than about 10 µG. In very young supernova remnants, for example, the classical estimate may be too large by up to 10×. On the other hand, if energy losses of cosmic ray electrons are important, K increases with particle energy and the equipartition field may be underestimated significantly. Our revised larger equipartition estimates in galaxy clusters and radio lobes are consistent with independent estimates from Faraday rotation measures, while estimates from the ratio between radio synchrotron and X‐ray inverse Compton intensities generally give much weaker fields. This may be explained e.g. by a concentration of the field in filaments. Our revised field strengths may also lead to major revisions of electron lifetimes in jets and radio lobes estimated from the synchrotron break frequency in the radio spectrum. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probing magnetic turbulence by synchrotron polarimetry: statistics and structure of magnetic fields from Stokes correlators

We describe a novel technique for probing the statistical properties of cosmic magnetic fields based on radio polarimetry data. Second-order magnetic field statistics like the power spectrum cannot always distinguish between magnetic fields with essentially different spatial structure. Synchrotron polarimetry naturally allows certain fourth-order magnetic field statistics to be inferred from observational data, which lifts this degeneracy and can thereby help us gain a better picture of the structure of the cosmic fields and test theoretical scenarios describing magnetic turbulence. In this work we show that a fourth-order correlator of specific physical interest, the tension force spectrum, can be recovered from the polarized synchrotron emission data. We develop an estimator for this quantity based on polarized emission observations in the Faraday rotation free frequency regime. We consider two cases: a statistically isotropic field distribution, and a statistically isotropic field superimposed on a weak mean field. In both cases the tension force power spectrum is measurable; in the latter case, the magnetic power spectrum may also be obtainable. The method is exact in the idealized case of a homogeneous relativistic electron distribution that has a power-law energy spectrum with a spectral index of   p = 3  , and assumes statistical isotropy of the turbulent field. We carry out numerical tests of our method using synthetic polarized emission data generated from numerically simulated magnetic fields. We show that the method is valid, that it is not prohibitively sensitive to the value of the electron spectral index p , and that the observed tension force spectrum allows one to distinguish between e.g. a randomly tangled magnetic field (a default assumption in many studies) and a field organized in folded flux sheets or filaments.     

Synchrotron X-ray emission from supernova remnants. Exponential cut-off in the electron spectrum

We present a model which describes the evolution of the energy spectrum of relativistic electrons in supernova remnants, with radiation losses of electrons taken into account. The model can be used to calculate the synchrotron X-ray emission from supernova remnants in the uniform interstellar medium and in the uniform interstellar magnetic field. The importance of various factors in the variations of spatial distributions of nonthermal electrons and their synchrotron emissive capacity is demonstrated. We analyze the errors which arise in the magnetic field strength when it is estimated with the use of the models which ignore the detailed pattern of the evolution of the magnetic field and the electron spectrum behind the shock front in the remnant. The evolution of synchrotron emission spectrum and the ratio between the synchrotron radio and X-ray fluxes from supernova remnants are calculated.     

Coherent synchrotron emission observed: implications for radio astronomy

Synchrotron radiation by relativistic electrons spiralling in magnetic fields is a mainstay of radio astronomy, accounting for emissions from many objects. Conventional models assume that electrons radiate singly, so power scales with number of electrons. Yet recently jets from active galactic nuclei have shown very high luminosity, inconsistent with plausible single-particle synchrotron emission. We report experiments showing that, by stimulating plasma instabilities with relativistic electron beams, one can induce increases in the synchrotron emission by factors of ∼10⁶. Enhancement presumably arises from coherent bunching of the relativistic electrons as they spiral in an ambient magnetic field. Polarization measurements suggest that electrons radiatively cooperate on scales of ∼6.6 cm. Radio telescope Stokes parameters may be able to reveal such polarization effects in high-brightness sources, a new observing diagnostic.     

Radio signature of cosmological structure formation shocks

In the course of the formation of cosmological structures, large shock waves are generated in the intracluster medium (ICM). In analogy to processes in supernova remnants, these shock waves may generate a significant population of relativistic electrons which, in turn, produce observable synchrotron emission. The extended radio relics found at the periphery of several clusters and possibly also a fraction of radio halo emission may have this origin. Here, we derive an analytic expression for (i) the total radio power in the downstream region of a cosmological shock wave, and (ii) the width of the radio-emitting region. These expressions predict a spectral slope close to −1 for strong shocks. Moderate shocks, such as those produced in mergers between clusters of galaxies, lead to a somewhat steeper spectrum. Moreover, we predict an upper limit for the radio power of cosmological shocks. Comparing our results to the radio relics in Abell 115, 2256 and 3667, we conclude that the magnetic field in these relics is typically at a level of 0.1 μG. Magnetic fields in the ICM are presumably generated by the shocks themselves; this allows us to calculate the radio emission as a function of the cluster temperature. The resulting emissions agree very well with the radio power–temperature relation found for cluster haloes. Finally, we show that cosmic accretion shocks generate less radio emission than merger shock waves. The latter may, however, be detected with upcoming radio telescopes.     

The K-band luminosity function at z = 1: a powerful constraint on galaxy formation theory

We report the first detection of an inverse Compton X-ray emission, spatially correlated with a very steep spectrum radio source (VSSRS), 0038-096, without any detected optical counterpart, in cluster Abell 85. The ROSAT PSPC data and its multiscale wavelet analysis reveal a large-scale (linear diameter of the order of 500 h ⁻¹₅₀ kpc), diffuse X-ray component, in addition to the thermal bremsstrahlung, overlapping an equally large-scale VSSRS. The primeval 3 K background photons, scattering off the relativistic electrons, can produce the X-rays at the detected level. The inverse Compton flux is estimated to be (6.5 ± 0.5) × 10⁻¹³ erg s⁻¹ cm⁻² in the 0.5–2.4 keV X-ray band. A new 327-MHz radio map is presented for the cluster field. The synchrotron emission flux is estimated to be (6.6 ± 0.90) × 10⁻¹⁴ erg s⁻¹ cm⁻² in the 10–100 MHz radio band. The positive detection of both radio and X-ray emission from a common ensemble of relativistic electrons leads to an estimate of (0.95 ± 0.10) × 10⁻⁶ G for the cluster-scale magnetic field strength. The estimated field is free of the 'equipartition' conjecture, the distance, and the emission volume. Further, the radiative fluxes and the estimated magnetic field imply the presence of 'relic' (radiative lifetime ≳ 10⁹ yr) relativistic electrons with Lorentz factors γ ≈ 700–1700; this would be a significant source of radio emission in the hitherto unexplored frequency range ν ≈ 2–10 MHz.     

The power of blazar jets

We estimate the power of relativistic, extragalactic jets by modelling the spectral energy distribution of a large number of blazars. We adopt a simple one-zone, homogeneous, leptonic synchrotron and inverse Compton model, taking into account seed photons originating both locally in the jet and externally. The blazars under study have an often dominant high-energy component which, if interpreted as due to inverse Compton radiation, limits the value of the magnetic field within the emission region. As a consequence, the corresponding Poynting flux cannot be energetically dominant. Also the bulk kinetic power in relativistic leptons is often smaller than the dissipated luminosity. This suggests that the typical jet should comprise an energetically dominant proton component. If there is one proton per relativistic electrons, jets radiate around 2–10 per cent of their power in high-power blazars and 3–30 per cent in less powerful BL Lacs.     

Synchrotron emission in the fast cooling regime: which spectra can be explained?

We consider the synchrotron emission from relativistic shocks assuming that the radiating electrons cool rapidly (either through synchrotron or any other radiation mechanism). It is shown that the theory of synchrotron emission in the fast cooling regime can account for a wide range of spectral shapes. In particular, the magnetic field, which decays behind the shock front, brings enough flexibility to the theory to explain the majority of gamma-ray burst spectra even in the parameter-free fast cooling regime. Also, we discuss whether location of the peak in observed spectral energy distributions of gamma-ray bursts and active galactic nuclei can be made consistent with predictions of diffusive shock acceleration theory, and find that the answer is negative. This result is a strong indication that a particle injection mechanism, other than the standard shock acceleration, works in relativistic shocks.     

Thermal synchrotron radiation and its Comptonization in compact X-ray sources

We investigate the process of synchrotron radiation from thermal electrons at semirelativistic and relativistic temperatures. We find an analytic expression for the emission coefficient for random magnetic fields with an accuracy significantly higher than those derived previously. We also present analytic approximations to the synchrotron turnover frequency, treat Comptonization of self-absorbed synchrotron radiation, and give simple expressions for the spectral shape and the emitted power. We also consider modifications of the above results by bremsstrahlung.
We then study the importance of Comptonization of thermal synchrotron radiation in compact X-ray sources. We first consider emission from hot accretion flows and active coronae above optically thick accretion discs in black hole binaries and active galactic nuclei (AGNs). We find that for plausible values of the magnetic field strength, this radiative process is negligible in luminous sources, except for those with hardest X-ray spectra and stellar masses. Increasing the black hole mass results in a further reduction of the maximum Eddington ratio from this process. Then, X-ray spectra of intermediate-luminosity sources, e.g. low-luminosity AGNs, can be explained by synchrotron Comptonization only if they come from hot accretion flows, and X-ray spectra of very weak sources are always dominated by bremsstrahlung. On the other hand, synchrotron Comptonization can account for power-law X-ray spectra observed in the low states of sources around weakly magnetized neutron stars.     

Gyrosynchrotron Emission from Anisotropic Pitch-Angle Distribution of Electrons in 3-D Solar Flare Sources

We present calculations, made for the first time, of the gyrosynchrotron emission by mildly relativistic electrons with anisotropic pitch-angle distribution using a realistic magnetic loop model in three dimensions. We investigated the intensity, spectral index of the optically thin region of the spectrum, the spatial morphology and the dependency on the source position on the solar disk. The method to describe a three-dimensional source and the procedure to perform the calculations are presented. We have modified the Ramaty’s gyrosynchrotron code to allow the evaluation of anisotropic pitch-angle electron distributions, as described in the complete formalism. We found that anisotropic electron distributions affect the intensity of the radiation, spatial morphology and spectrum of spatially resolved sources. However, the spatially integrated spectrum of the emission seems to be insensitive to the electron pitch-angle distribution, as the magnetic field inhomogeneity smooths out the effects of the anisotropic distribution in the produced radiation, in contrast to homogeneous sources.     

The precession of eccentric discs in close binaries

If the emission of gamma-ray bursts were as a result of the synchrotron process in the standard internal shock scenario, then the typical observed spectrum should have a slope F _ν ∝ ν ^−1/2, which strongly conflicts with the much harder spectra observed. This directly follows from the cooling time being much shorter than the dynamical time. Particle re-acceleration, deviations from equipartition, quickly changing magnetic fields and adiabatic losses are found to be inadequate to account for this discrepancy. We also find that in the internal shock scenario the relativistic inverse Compton scattering is always as important as the synchrotron process, and faces the same problems. This indicates that the burst emission is not produced by relativistic electrons emitting synchrotron and inverse Compton radiation.     

Radio and X-ray properties of relativistic beaming models for ultraluminous X-ray sources

We calculate the broad-band radio–X-ray spectra predicted by microblazar and microquasar models for ultraluminous X-ray sources (ULXs), exploring the possibility that their dominant power-law component is produced by a relativistic jet, even at near-Eddington mass accretion rates. We do this by first constructing a generalized disc–jet theoretical framework in which some fraction of the total accretion power, P _a, is efficiently removed from the accretion disc by a magnetic torque responsible for jet formation. Thus, for different black hole masses, mass accretion rates and magnetic coupling strength, we self-consistently calculate the relative importance of the modified disc spectrum, as well as the overall jet emission due to synchrotron and Compton processes. In general, transferring accretion power to a jet makes the disc fainter and cooler than a standard disc at the same mass accretion rate; this may explain why the soft spectral component appears less prominent than the dominant power-law component in most bright ULXs. We show that the apparent X-ray luminosity and spectrum predicted by the microquasar model are consistent with the observed properties of most ULXs. We predict that the radio synchrotron jet emission is too faint to be detected at the typical threshold of radio surveys to date. This is consistent with the high rate of non-detections over detections in radio counterpart searches. Conversely, we conclude that the observed radio emission found associated with a few ULXs cannot be due to beamed synchrotron emission from a relativistic jet.     

FAST Continuum Mapping of the SNR VRO 42.05.01

The relativistic electrons rotate in the enhanced magnetic field of the supernova remnants and emit the synchrotron radio emission.We aim to use the Five-hundre...     

Near-infrared/optical counterparts of hotspots in radio galaxies

We present new high spatial resolution Very Large Telescope (VLT) and Very Large Array (VLA) observations of a sample of nine low-power (   P _1.4 GHz≤ 10²⁵  W Hz⁻¹) radio hotspots. Infrared/optical emission is definitely detected in four of the nine observed objects, resulting in a detection rate of at least 45 per cent. This emission is interpreted as synchrotron radiation from the electrons accelerated in the hotspots. The integrated spectra of these hotspots reveal typical break frequencies between 10⁵ and 10⁶ GHz, two orders of magnitude higher than typically found in high-power hotspots. This supports the idea that in low-power hotspots with their relatively low magnetic field strengths, electrons emit most of their energy at higher frequencies. A simple spectral ageing analysis would imply that the emitting electrons have been injected into the hotspot volume less than  ∼10³  years ago. We discuss possible scenarios to explain the lack of older electrons in the hotspot region. In particular, the extended morphology of the near-infrared/optical emission would suggest that efficient re-acceleration mechanisms rejuvenate the electron populations.     

Magnetic field strengths in the hotspots of 3C 33 and 111

We report on ROSAT HRI observations of the nearby powerful radio galaxies 3C 33 and 111, which both have detected optical hotspots. We find nuclear X-ray sources in both objects, but no X-ray emission from the hotspots. This confirms the presence of a high-energy cut-off in the spectrum of synchrotron-emitting electrons. Since these electrons necessarily scatter the synchrotron photons by the inverse Compton process, our upper limits on the X-ray fluxes of the hotspots allow us to set lower limits of a few nanotesla on their magnetic flux density, close to or greater than the fields implied by equipartition of energy between radiating particles and magnetic field.     

Linkage between accretion disks and blazars

The magnetic field in an accretion disk is estimated assuming that all of the angular momentum within prescribed accretion disk radii is removed by a jet. The magnetic field estimated at the base of the jet is extrapolated to the blazar emission region using a model for a relativistic axisymmetric jet combined with some simplifying assumptions based on the relativistic nature of the flow. The extrapolated magnetic field is compared with estimates based upon the synchrotron and inverse Compton emission from three blazars, MKN 501, MKN 421 and PKS 2155-304. The magnetic fields evaluated from pure synchrotron self-Compton models are inconsistent with the magnetic fields extrapolated in this way. However, in two cases inverse Compton models in which a substantial part of the soft photon field is generated locally agree well, mainly because these models imply magnetic field strengths consistent with an important Poynting Flux component. This comparison is based on estimating the mass accretion rate from the jet energy flux. Further comparisons along these lines will be facilitated by independent estimates of the mass accretion rate in blazars and by more detailed models for jet propagation near the black hole.     

The nanoflare model and stellar quiescent radio emission

The concept of the nanoflare, used in interpreting the solar X-ray corona, is extended to RS CVn stars which, unlike the Sun, exhibit non-thermal quiescent radio spectra. The theoretical synchrotron-radiation radio spectrum emitted by a regular series of nanoflare-electron pulses, injected into the coronal magnetic field, is derived: for an electron energy spectrum N ( γ )∝ γ ^{− s} , the spectral power density is given by P ( ν )∝ ν ^{− s /2}. This result is valid for the observation of a series of nanoflares with total time duration ≳ the characteristic electron radiation lifetime, which is the case for electrons trapped in extensive coronal regions such as exist in RS CVn stars on the magnetic-dipole magnetospheric model. The tenuous coronal plasma allows the electrons to give a radio spectrum unaffected at high frequencies (≳5 GHz) by electron collision loss, while the emission of bremsstrahlung X-rays by the electrons also occurs with a spectrum that is related to their radio emission. The observation of individual X-ray bursts, which would provide direct evidence for microflares, is not, however, attainable with current instrumentation.     

Radiative losses and cut-offs of energetic particles at relativistic shocks

We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. Particles undergo pitch angle diffusion, gaining energy as they cross the shock by the Fermi mechanism and also emitting synchrotron radiation in the ambient magnetic field. A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. The implications for the synchrotron emission of relativistic jets, such as those in gamma-ray burst sources and blazars, are discussed.     

The flat synchrotron spectra of partially self-absorbed jets revisited

Flat radio spectra with large brightness temperatures at the core of active galactic nuclei and X-ray binaries are usually interpreted as the partially self-absorbed bases of jet flows emitting synchrotron radiation. Here we extend previous models of jets propagating at large angles to our line of sight to self-consistently include the effects of energy losses of the relativistic electrons due to the synchrotron process itself and the adiabatic expansion of the jet flow. We also take into account energy gains through self-absorption. Two model classes are presented. The ballistic jet flows, with the jet material travelling along straight trajectories, and adiabatic jets. Despite the energy losses, both scenarios can result in flat emission spectra; however, the adiabatic jets require a specific geometry. No re-acceleration process along the jet is needed for the electrons. We apply the models to observational data of the X-ray binary Cygnus X-1. Both models can be made consistent with the observations. The resulting ballistic jet is extremely narrow with a jet opening angle of only 5 arcsec. Its energy transport rate is small compared to the time-averaged jet power and therefore suggests the presence of non-radiating protons in the jet flow. The adiabatic jets require a strong departure from energy equipartition between the magnetic field and the relativistic electrons. These models also imply a jet power of two orders of magnitude higher than the Eddington limiting luminosity of a  10-M_⊙  black hole. The models put strong constraints on the physical conditions in the jet flows on scales well below achievable resolution limits.     

Source models with electron diffusion

The general solution for the energy distribution of relativistic electrons in which electrons generated within the source diffuse and decay through synchrotron or Compton radiation is given for the case in which the magnetic field and the diffusion coefficient are constant. A very simple spherically symmetric model with an electron point-source at the centre is considered and the equations are explicitly solved. It is shown that notwithstanding its great simplicity this model gives a fair representation of the continuous emission of the Crab nebula from the radio to the X-ray region, with the simple assumption that it is due only to ordinary synchrotron radiation. If the central point source is identified with the pulsar there appears to be an upper limit of about 10⁷ MeV to the energy of the electrons accelerated by the pulsar mechanism.