Witnessing the gradual slow-down of powerful extragalactic jets: The X-ray -- optical -- radio connection

A puzzling feature of the {\it Chandra}--detected quasar jets is that their X-ray emission decreases faster along the jet than their radio emission, resulting to an outward increasing radio to X-ray ratio. In some sources this behavior is so extreme that the radio emission peak is located clearly downstream of that of the X-rays. This is a rather unanticipated behavior given that the inverse Compton nature of the X-rays and the synchrotron radio emission are attributed to roughly the same electrons of the jet's non-thermal electron distribution. In this note we show that this morphological behavior can result from the gradual deceleration of a relativistic flow and that the offsets in peak emission at different wavelengths carry the imprint of this deceleration. This notion is consistent with another recent finding, namely that the jets feeding the terminal hot spots of powerful radio galaxies and quasars are still relativistic with Lorentz factors $\Gamma \sim 2-3$. The picture of the kinematics of powerful jets emerging from these considerations is that they remain relativistic as they gradually decelerate from Kpc scales to the hot spots, where, in a final collision with the intergalactic medium, they slow-down rapidly to the subrelativistic velocities of the hot spot advance speed.Comment: Submitted in ApJ Letters on Jan. 14, 200

Modelling the spectral evolution of classical double radio sources

The spectral evolution of powerful double radio galaxies (FR II's) is thought to be determined by the acceleration of electrons at the termination shock of the jet, their transport through the bright head region into the lobes and the production of the radio emission by synchrotron radiation in the lobes. Models presented to date incorporate some of these processes in prescribing the electron distribution which enters the lobes. We have extended these models to include a description of electron acceleration at the relativistic termination shock and a selection of transport models for the head region. These are coupled to the evolution of the electron spectrum in the lobes under the influence of losses due to adiabatic expansion, by inverse Compton scattering on the cosmic background radiation and by synchrotron radiation. The evolutionary tracks predicted by this model are compared to observation using the power/source-size (P-D) diagram. We find that the simplest scenario, in which accelerated particles suffer adiabatic losses in the head region which become more severe as the source expands produces P-D-tracks which conflict with observation, because the power is predicted to decline too steeply with increasing size. Agreement with observation can be found by assuming that adiabatic losses are compensated during transport between the termination shock and the lobe by a re-acceleration process distributed throughout the head region.Comment: 14 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

Acceleration of energetic particles by large-scale compressible magnetohydrodynamic turbulence

Fast particles diffusing along magnetic field lines in a turbulent plasma can diffuse through and then return to the same eddy many times before the eddy is randomized in the turbulent flow. This leads to an enhancement of particle acceleration by large-scale compressible turbulence relative to previous estimates in which isotropic particle diffusion is assumed.Comment: 13 pages, 3 figures, accepted for publication in Ap

Minimal Stochastic Model for Fermi's Acceleration

We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions (PDF) for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents $\nu_x$ and $\nu_v$. The diffusion process is anomalous (non Gaussian) but with a defined scaling properties i.e. $P(|{\bf x}|,t) = 1/t^{\nu_x}F_x(|{\bf x}|/t^{\nu_x})$ and similarly for velocity.Comment: RevTeX4, 4 pages, 2 eps-figures (minor revision

Particle acceleration in rotating and shearing jets from AGN

We model the acceleration of energetic particles due to shear and centrifugal effects in rotating astrophysical jets. The appropriate equation describing the diffusive transport of energetic particles in a collisionless, rotating background flow is derived and analytical steady state solutions are discussed. In particular, by considering velocity profiles from rigid, over flat to Keplerian rotation, the effects of centrifugal and shear acceleration of particles scattered by magnetic inhomogeneities are distinguished. In the case where shear acceleration dominates, it is confirmed that power law particle momentum solutions $f(p) \propto p^{-(3+\alpha)}$ exist, if the mean scattering time $\tau_c \propto p^{\alpha}$ is an increasing function of momentum. We show that for a more complex interplay between shear and centrifugal acceleration, the recovered power law momentum spectra might be significantly steeper but flatten with increasing azimuthal velocity due to the increasing centrifugal effects. The possible relevance of shear and centrifugal acceleration for the observed extended emission in AGN is demonstrated for the case of the jet in the quasar 3C273.Comment: 15 pages (including 8 pages Appendix), 4 figures; accepted for publication in A&

Spectral evolution of non-thermal electron distributions in intense radiation fields

(abridged) Models of many astrophysical gamma-ray sources assume they contain a homogeneous distribution of electrons that are injected as a power-law in energy and evolve by interacting with radiation fields, magnetic fields and particles in the source and by escaping. This problem is particularly complicated if the radiation fields have higher energy density than the magnetic field and are sufficiently energetic that inverse Compton scattering is not limited to the Thomson regime. We present a simple, time-dependent, semi-analytical solution of the electron kinetic equation that treats both continuous and impulsive injection, cooling via synchrotron and inverse Compton radiation, (taking into account Klein-Nishina effects) and energy dependent particle escape. The kinetic equation for an arbitrary, time-dependent source function is solved by the method of Laplace transformations. Using an approximate expression for the energy loss rate that takes into account synchrotron and inverse Compton losses including Klein-Nishina effects for scattering off an isotropic photon field with either a power-law or black-body distribution, we find explicit expressions for the cooling time and escape probability of individual electrons. This enables the full, time-dependent solution to be reduced to a single quadrature. From the electron distribution, we then construct the time-dependent, multi-wavelength emission spectrum. We compare our solutions with several limiting cases and discuss the general appearance and temporal behaviour of spectral features (i.e., cooling breaks, bumps etc.). As a specific example, we model the broad-band energy spectrum of the open stellar association Westerlund-2 at different times of its evolution, and compare it with observations.Comment: 14 pages, 8 figures, acccepted for publication in A&

HST optical spectral index map of the jet of 3C 273

We present HST images at 622 nm and 300 nm of the jet in 3C273 and determine the run of the optical spectral index at 0.2" along the jet. The smoothness of spectral index changes shows that the physical conditions are varying smoothly across the jet. There is no correlation between the optical flux and spectral index, as would be expected for relativistic electrons suffering strong cooling due to synchrotron emission. We find no evidence for localized acceleration or loss sites. This suggests that the spectral shape is not changing much throughout the jet. We show that relativistic beaming and/or sub-equipartition magnetic fields cannot remove the discrepancy between light-travel time along the jet and the lifetime of electrons emitting optical synchrotron radiation. We consider this further evidence in favour of a distributed electron acceleration process.Comment: Accepted for publication by Astronomy and Astrophysics (13 pages, 8 figures

Canonical Particle Acceleration in FRI Radio Galaxies

Matched resolution multi-frequency VLA observations of four radio galaxies are used to derive the asymptotic low energy slope of the relativistic electron distribution. Where available, low energy slopes are also determined for other sources in the literature. They provide information on the acceleration physics independent of radiative and other losses, which confuse measurements of the synchrotron spectra in most radio, optical and X-ray studies. We find a narrow range of inferred low energy electron energy slopes, n(E)=const*E^-2.1 for the currently small sample of lower luminosity sources classified as FRI (not classical doubles). This distribution is close to, but apparently inconsistent with, the test particle limit of n(E)=const*E^-2.0 expected from strong diffusive shock acceleration in the non-relativistic limit. Relativistic shocks or those modified by the back-pressure of efficiently accelerated cosmic rays are two alternatives to produce somewhat steeper spectra. We note for further study the possiblity of acceleration through shocks, turbulence or shear in the flaring/brightening regions in FRI jets as they move away from the nucleus. Jets on pc scales and the collimated jets and hot spots of FRII (classical double) sources would be governed by different acceleration sites and mechanisms; they appear to show a much wider range of spectra than for FRI sources.Comment: 16 figures, including 5 color. Accepted to Astrophysical Journa

On the Momentum Diffusion of Radiating Ultrarelativistic Electrons in a Turbulent Magnetic Field

Here we investigate some aspects of stochastic acceleration of ultrarelativistic electrons by magnetic turbulence. In particular, we discuss the steady-state energy spectra of particles undergoing momentum diffusion due to resonant interactions with turbulent MHD modes, taking rigorously into account direct energy losses connected with different radiative cooling processes. For the magnetic turbulence we assume a given power spectrum of the type $W(k) \propto k^{-q}$. In contrast to the previous approaches, however, we assume a finite range of turbulent wavevectors $k$, consider a variety of turbulence spectral indexes $1 =< q =< 2$, and concentrate on the case of a very inefficient particle escape from the acceleration site. We find that for different cooling and injection conditions, stochastic acceleration processes tend to establish a modified ultrarelativistic Maxwellian distribution of radiating particles, with the high-energy exponential cut-off shaped by the interplay between cooling and acceleration rates. For example, if the timescale for the dominant radiative process scales with the electron momentum as $\propto p^r$, the resulting electron energy distribution is of the form $n_e(p) \propto p^2 exp[ - (1 / a) (p / p_eq)^a]$, where $a = 2-q-r$, and $p_eq$ is the equilibrium momentum defined by the balance between stochastic acceleration and energy losses timescales. We also discuss in more detail the synchrotron and inverse-Compton emission spectra produced by such an electron energy distribution, taking into account Klein-Nishina effects. We point out that the curvature of the high frequency segments of these spectra, even though being produced by the same population of electrons, may be substantially different between the synchrotron and inverse-Compton components.Comment: 42 pages, 14 figures included. Slightly modified version, accepted for publication in Ap

A method of estimation of the dynamical age of FR II-type radio sources from multifrequency data

We propose a new approach in determining ages of FR II type radio sources. We apply the assumed dynamical model of Kaiser et al. (1997) to a number of FR II type radio galaxies observed at different radio frequencies, and fit - for each frequency separately - the model free parameters to the observed sources' quantities. Such a procedure, using enlarged in fact a number of observables, enables us to determine relatively precise ages and other crucial characteristics of the analyzed sources. The resulting age estimates agree very well with those obtained by means of `classical' spectral ageing method for objects not older than 10 Myr, for which good-quality spectral data are available. The presented method is however also applicable in the case of the sources older than this, and/or the ones for which the only available low-resolution radio data do not allow for detailed spectral ageing studies. Our analysis indicates that the main factor precluding precise age determination for FR II type radio galaxies regards the poorly known shape of the initial electron energy distribution injected by the jet terminal shocks to the expanding lobes/cocoons. We briefly consider this issue, and conclude that the broad-band single power-law form assumed here may be accurate enough for the presented estimates, although most likely it does not strictly correspond to some well-defined realistic particle acceleration process. Instead, it should be considered as a simplest model approximation of the initial electron continuum, averaged over a very broad energy range and over the age of the source, with the effective spectral index which may be different for different sources.Comment: 15 pages, 9 figures included. Accepted for publication in A&