International Journal of Modern Physics D

The main characteristics of relativistic, steady, ideal magnetohydrodynamic (MHD) outflows are discussed, focusing on their bulk acceleration and collimation. It is shown that the Bernoulli equation relates the bulk Lorentz factor with the shape of the flow, permitting an analytic estimation of the acceleration efficiency, while the transfield force-balance equation gives a simple relation of the bulk Lorentz factor to the distance.

We present numerical simulations of cold, axisymmetric, magnetically driven relativistic outflows. The outflows are initially sub-Alfvénic and Poynting-flux dominated, with total–to–rest-mass energy flux ratio up to μ ~ 620. To study the magnetic acceleration of jets we simulate flows confined within a funnel with a rigid wall of prescribed shape, which we take to be z ∝ r^a (in cylindrical coordinates, with a ranging from 1 to 2). This allows us to eliminate the numerical dissipative effects induced by a free boundary with an ambient medium. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. For the jet solutions the acceleration process is very efficient — on the outermost scale of the simulation more than half of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approached its maximum possible value (Γ_∞ ≃ μ). The acceleration is accompanied by the collimation of magnetic field lines in excess of that dictated by the funnel shape. The numerical solutions are generally consistent with the semi-analytic self-similar jets solutions and the spatially extended acceleration observed in some astrophysical relativistic jets. In agreement with previous studies, we also find that the acceleration is significantly less effective for wind solutions suggesting that pulsar winds may remain Poynting dominated when they reach the termination shock.

We discuss numerical results of relativistic magnetohydrodynamic (MHD) jet formation models. We first review some examples of stationary state solutions treating the collimation and acceleration process of relativistic MHD jets. We provide an a posteriori check for the MHD condition in highly magnetized flows, namely the comparison of particle density to Goldreich–Julian density. Using the jet dynamical parameters calculated from the MHD model, we show the rest-frame thermal X-ray spectra of the jet, from which we derive the overall spectrum taking into account a variation of Doppler boosting and Doppler shift of emission lines along the outflow. Finally, we present preliminary results of relativistic MHD simulations of jet formation demonstrating the acceleration of a low velocity (0.01 c) disk wind to a collimated high velocity (0.8 c).

We present a self-consistent MHD model for the jet of M87. The model consist of two distinct zones: an inner relativistic outflow, which we identify with the observed jet, and an outer cold disk wind. While the former does not self-collimate efficiently due to its high effective inertia, the latter fulfills all the conditions for efficient collimation by the magneto-centrifugal mechanism. Given the right balance between the effective inertia of the inner flow and the collimation efficiency of the outer disk wind, the relativistic flow is magnetically confined into a well collimated beam for a wide range of parameters and matches the measurements of the opening angle of M87 over several orders of magnitude in spatial extent.

In the second part of this work, we present synthetic synchrotron emission maps for our MHD models. In principle, the two-zone model can reproduce the morphological structure seen in radio observations, as central-peaked profiles across the jet close the the source, limb-bright further down the jet, and a bright knot close to the position of HST-1. However it is difficult to reconcile all features with a single set of parameters.

Many quasars and active galactic nuclei are connected with long, thin jets. When observed with high angular resolution, these jets show a structure with bright knots separated by relatively dark regions. We consider magnetic collimation, connected with torsional oscillations of a cylinder with elongated magnetic field, and periodically distributed initial rotation around the cylinder axis. The stabilizing azimuthal magnetic field is created here by torsional oscillations. An approximate, simplified model is developed. The parameters for which jets may be stabilized by torsional oscillations are estimated quantitatively.

We investigate the launching and stability of extragalactic jets through magnetohydrodynamic simulations of jet evolution. In these simulations, a small scale equilibrium magnetic corona is twisted by a differentially rotating accretion disk. Two-dimensional calculations show the formation of a collimated outflow. This outflow is divided into two regions by the Alfvén surface: a magnetically dominated Poynting region, and a kinetically dominated region. Three-dimensional calculations show that the outflow is unstable to the m = 1 kink instability, and that the growth rate of the kink instability decreases as the rotation rate of the accretion disk increases.

Magnetic reconnection plays a critical role in many astrophysical processes where high energy emission is observed, e.g. particle acceleration, relativistic accretion powered outflows, pulsar winds and probably in dissipation of Poynting flux in GRBs. The magnetic field acts as a reservoir of energy and can dissipate its energy to thermal and kinetic energy via the tearing mode instability. We have performed 3D nonlinear MHD simulations of the tearing mode instability in a current sheet. Results from a temporal stability analysis in both the linear regime and weakly nonlinear (Rutherford) regime are compared to the numerical simulations. We observe magnetic island formation, island merging and oscillation once the instability has saturated. The growth in the linear regime is exponential in agreement with linear theory. In the second, Rutherford regime the island width grows linearly with time. We find that thermal energy produced in the current sheet strongly dominates the kinetic energy. Finally preliminary analysis indicates a P(k) 4.8 power law for the power spectral density which suggests that the tearing mode vortices play a role in setting up an energy cascade.

We use axisymmetric magnetohydrodynamic simulations to investigate the spinning-down of magnetars rotating in the propeller regime and moving supersonically through the interstellar medium. The simulations indicate that magnetars spin down rapidly due to this interaction, and faster than for the case of a non-moving star. We discuss this model with respect to soft gamma repeaters (SGRs) and the isolated neutron star candidates.

The goal of this paper is to pay attention to the 1D cylindrical version of the Grad-Shafranov (GS) equation. In our opinion, this approach is more rich than classical self-similar ones, and more suitable for the astrophysical jets we observe. In particular, it allows us to describe the central (and, hence, the most energetic) part of the flow.

Spectral line profiles produced in an outflow near a neutron star or a black hole can be strongly influenced by gravitational redshifting and by Doppler shifting due to a global motion of plasma. We consider a scenario in which a resonant absorption in a spectral line takes place in the outflowing plasma within several tens of Schwarzschild radii from a compact object. The main goal of this work is to show that under certain conditions a combination of the gravitational redshifting and Doppler blue/redshifting may produce line profiles which can be considered as "fingerprints" of the gravitational field of the compact object, much as P-Cygni profiles are "fingerprints" of stellar winds.

Difficulties arise in the process of Fermi acceleration at relativistic shocks because they are generically in the superluminal regime and they strongly compress turbulence downstream. Under reasonable conditions usually considered for the turbulent spectrum upstream, cosmic rays do not undergo the scattering that would allow them to make several Fermi cycles. An intense short scale turbulence must be excited in order that the Fermi process can be operative. In this paper, we show the requirement for the turbulence spectrum and give a solution to this issue in the form of the generation of intense compressive waves at short scale upstream. We indicate how the magnetic turbulence compression downstream should not be an obstacle for getting a significant return probability. Thus we conclude that, despite the necessity of some further analysis, the Fermi process at relativistic shock is still promising.

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations using injected relativistic electron-ion (electron-positron) jets show that acceleration occurs within the downstream jet. Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, other two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electrons' transverse deflection behind the jet head. The "jitter" radiation from deflected electrons has different properties to synchrotron radiation which assumes a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.

We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic e⁺e^- shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, non-propagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Our theory predicts that the overall magnetic energy decays as (ω_p t)^-q with q ~ 1, which compares favorably with simulations, but predicts overly rapid damping of short-wavelength modes. The magnetic trapping of particles within the magnetic structures may be the origin of this discrepancy. We conclude that initially unmagnetized relativistic shocks in electron-positron plasmas are unable to form persistent downstream magnetic fields. These results put interesting constraints on synchrotron models for the prompt and afterglow emission from GRBs.

Thermally emitting, radiative, Newtonian shocks exhibit a global oscillatory instability. The luminosity variations that accompany such oscillations raise the possibility that, if relativistic shocks that emit nonthermal (synchrotron and inverse-Compton) radiation are also subject to such an instability, this could be relevant to the interpretation of certain flares observed in relativistic jet sources associated with AGNs and GRBs. A linear stability analysis, using the equations of special-relativistic MHD and accounting for both the energy and the momentum carried by the radiation, has, however, revealed no unstable modes for physically plausible parameter values. The likely explanation is that, even though synchrotron cooling gives rise to a local radiative instability, the dependence on the magnetic field amplitude is not strong enough to counter the stabilizing effect of enhanced magnetic pressure, due to cooling-induced compression, on the global behavior of the shock. Numerical simulations are under way to ascertain that this conclusion continues to hold also in the nonlinear regime.

Cosmic ray acceleration may occur at a supernova shock expanding into a circumstellar wind. Self-similar solutions for the cosmic ray distribution are derived firstly when diffusion is isotropic and secondly when the wind sustains a magnetic field in the form of a Parker spiral.

We investigate the so-called nonresonant cosmic-ray streaming instability, first discussed by Bell (2004). The extent to which thermal damping and ion-neutral collisions reduce the growth of this instability is calculated. Limits on the growth of the nonresonant mode in SN1006 and RX J1713.7-3946 are presented.

We study the current-driven instability predicted by Bell (2004) using particle-in-cell simulations. We use one-dimensional simulations to test the dispersion relation and the nonlinear properties of the instability for the case of a relativistic shock front under idealized conditions. We find that if the cosmic rays (CR) are energetic enough to not get deflected by the generated magnetic field, the instability can grow exponentially until the Alfvén velocity of the plasma becomes comparable to the speed of light. We also use one- and two-dimensional simulations to study the effect of the back reaction of the instability on CR. We find that the deflection and filamentation of CR and background plasma play an important role in the saturation of the instability. The current-driven instability is a viable mechanism for the amplification of magnetic fields in both non-relativistic and relativistic shock environments.

I review recent results concerning the effects that relativistic parallel shocks can have on the particle-scattering turbulence, and how these effects, in turn, can change the shock's particle acceleration properties. I discuss the possibility of increased compression ratio due to this kind of turbulence transmission, and consider the effects of additional compression on the energy spectrum of the accelerated particles. Emphasis is put on the possibility of producing spectral indices that are significantly harder than what is usually expected from the first-order Fermi mechanism, but required by some observations. Finally, I discuss the physical requirements — and their plausibility in real astronomical objects — of this mechanism to have notable effects.

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. Using a semi-analytic approach we find that the cut-off energy differs greatly from the nonrelativistic approximation. Our results also show that, while low energy particles remain nearly isotropic, high energy particles downstream of the shock have a large degree of anisotropy which increases with the Lorentz factor of the shock. The implications for the synchrotron emission of relativistic jets, such as those in microquasars and blazars, are discussed.

We review the theoretical progress in the field of cosmic-ray first-order Fermi acceleration at relativistic shock fronts, showing that recent results change our knowledge about these processes substantially. In particular, relativistic shocks are unlikely to form particle distributions extending to very high energies. Instead, recent simulations give particle distributions where a shock-compressed injected component is followed by a more or less extended high energy tail. An increase of the Lorentz factor of the shock usually leads to steepening and a decrease of the energetic tail, so that fitted spectral indices to the high energy part can substantially deviate from the "universal power law index" σ ≈ 2.2.

We report on observational findings from the hot spots in Cygnus A, showing that the derived electron spectra (with a very flat, σ ≈ 1.5, low energy part up to ~ 1 GeV, followed by a much steeper, σ > 3, part at higher energies) indeed deviate from the standard expectation for relativistic shocks.

We conclude with a short discussion of some qualitative features of shear and second-order Fermi acceleration in turbulent relativistic plasmas.

We compare different acceleration mechanisms in application to relativistic jets and show that the converter mechanism, suggested recently, is the least sensitive to the geometry of the magnetic field in accelerators, and can routinely operate up to cosmic-ray energies close to the fundamental limit. The converter mechanism utilizes multiple conversions of charged particles into neutral ones (protons to neutrons and electrons/positrons to photons) and back by means of photon-induced reactions or inelastic nucleon-nucleon collisions. It works efficiently both in relativistic shocks and in shear flows under the conditions typical for active galactic nuclei, gamma-ray bursts, and microquasars, where it often outperforms the standard diffusive shock acceleration. The main advantages of the converter mechanism in such environments are that it greatly diminishes particle losses downstream and avoids the reduction in the energy gain factor, which normally takes place due to the highly collimated distribution of accelerated particles. We also discuss the properties of gamma-ray radiation, which accompanies acceleration of cosmic rays via the converter mechanism and can provide evidence for the latter. In particular, we point out that the opening angle of the radiation beam-pattern is different at different photon energies, which is relevant to the observability of gamma-ray sources as well as to their timing properties.

The detection of TeV gamma-rays from LS 5039 and the binary pulsar PSR B1259–63 by HESS, and from LS I +61 303 and the stellar-mass black hole Cygnus X-1 by MAGIC, provides clear evidence of very efficient acceleration of particles to multi-TeV energies in X-ray binaries. These observations demonstrate the richness of nonthermal phenomena in compact galactic objects containing relativistic outflows or winds produced near black holes and neutron stars. I review here some of the main observational results on very high energy (VHE) γ-ray emission from X-ray binaries, as well as some of the proposed scenarios to explain the production of VHE γ-rays. I put special emphasis on the flare TeV emission, suggesting that the flaring activity might be a common phenomena in X-ray binaries.

We report on the results from the observations in very high energy band (VHE, E_γ ≥ 100 GeV) of the γ-ray binary LS I +61 303 and the black hole X-ray binary (BHXB) Cygnus X-1. LS I +61 303 was recently discovered at VHE by MAGIC¹ and here we present the preliminary results from an extensive observation campaign, comprising 112 observation hours covering 4 orbital cycles, aiming at determining the time-dependent features of the VHE emission. Cygnus X-1 was observed for a total of 40 hours during 26 nights, spanning the period between June and November 2006. We report on the results of the searches for steady and variable γ-ray signals from Cygnus X-1, including the first experimental evidence for an intense flare, of duration between 1.5 and 24 hours.

We present an analysis of two Chandra observations of LS 5039 performed in 2004 in two different orbital phases during the same orbital cycle. Our results show a clear flux variability, confirming a trend of increasing flux with orbital phase in the range 0.05 ≲ ϕ ≲ 0.7 as has been found in XMM observations carried out in 2005 during the same orbital cycle. We suggest that the X-ray variations are linked to orbital changes of the intrinsic properties of the emitter, which should have implications for possible emission models to explain the present multiwavelength knowledge of the source.

LS I +61 303 is a puzzling object detected from radio up to very high-energy gamma-rays. Variability has recently been observed in its high-energy emission. The object is a binary system, with a compact object and a Be star as primary. The nature of the secondary and the origin of the gamma-ray emission are not clearly established at present. Recent VLBA radio data have been used to claim that the system is a Be/neutron star colliding wind binary, instead of a microquasar. We review the main views on the nature of LS I +61 303 and present results of 3D SPH simulations that can shed some light on the nature of the system. Our results support an accretion powered source, compatible with a microquasar interpretation.

There are three Galactic jet sources from which TeV emission has been detected: LS 5039, LS I +61 303 and Cygnus X-1. These three sources show power-law tails in X-rays and soft gamma-rays that could indicate a nonthermal origin of this radiation. In addition, all three sources apparently show correlated and complex behavior at X-ray and TeV energies. In some cases, this complex behavior is related to the orbital motion (e.g. LS 5039, LS I +61 303), and in some others it is related to some transient events occurring in the system (e.g. Cygnus X-1, and likely also LS I +61 303 and LS 5039). Based on modeling results or on energetic grounds, it seems difficult to explain the emission in the X-/soft gamma-ray and the TeV bands as coming from the same (i.e. one-zone) region. We also stress the importance of the pair creation phenomena in these systems, which harbor a massive and hot star, for the radio and the X-ray emission, as a secondary pair radiation component may be significant in these energy ranges. Finally, we point out that the presence of the star can indeed have a strong impact on both the nonthermal radiation production and the jet dynamics.

Recent radio observations support a picture for star formation where there is accretion of matter onto a central protostar with the ejection of molecular outflows that can affect the surrounding medium. The impact of a supersonic outflow on the ambient gas can produce a strong shock that could accelerate particles up to relativistic energies. Strong evidence for this has been the detection of nonthermal radio emission coming from the jet termination region of some young massive stars. In the present contribution, we study the possible high-energy emission due to the interaction of relativistic particles, electrons and protons, with the magnetic, photon and matter fields inside a giant molecular cloud. Electrons lose energy via relativistic Bremsstrahlung, synchrotron radiation and inverse Compton interactions, and protons cool mainly through inelastic collisions with atoms in the cloud. We conclude that some massive young stellar objects (YSOs) might be detectable at gamma-rays by next generation instruments, both satellite-borne and ground based.

Microquasars (MQs) are X-ray binary systems that display relativistic radio jets. These objects constitute a suitable laboratory for testing high energy astrophysical processes still not well understood, such as those present when jets interact with the interstellar medium (ISM). Focusing on the study of the nonthermal contribution from cocoon and bow-shock regions, we explore, under different ISM densities and ages of the jet source, the possibility to detect MQ jet termination regions. We conclude that emission from these regions may be faint, but still detectable in the radio, X-ray, and gamma-ray bands.

Unlike high-mass gamma-ray binaries, low-mass microquasars lack external sources of radiation and matter that could produce high-energy emission through interactions with relativistic particles. In this work, we consider the synchrotron emission of protons and leptons that populate the jet of a low-mass microquasar. In our model photohadronic and inverse Compton (IC) interactions with synchrotron photons produced by both protons and leptons result in a high-energy tail of the spectrum. We also estimate the contribution from secondary pairs injected through photopair production. The high-energy emission is dominated by radiation of hadronic origin, so we can call these objects "proton microquasars".

The hydrodynamics of the interaction of pulsar and stellar winds in binary systems harboring a pulsar and its impact on the nonthermal radiation of the binary pulsar PSR B1259-63/SS2883 is discussed. The collision of an ultrarelativistic pulsar wind with a nonrelativistic stellar outflow results in significant bulk acceleration of the shocked material from the pulsar wind. Already at distances comparable to the size of the binary system, the Lorentz factor of the shocked flow can be as large as γ ~ 4. This results in significant anisotropy of the inverse Compton radiation of accelerated electrons. Because of the Doppler boosting of the produced radiation, one should expect a variable gamma-ray signal from the system. In particular, this effect may naturally explain the reported tendency of a decrease of TeV gamma-ray flux close to the periastron. The modeling of the interaction of pulsar and stellar winds allows self-consistent calculations of adiabatic losses. Our results show that adiabatic losses dominate over the radiative losses. These results have direct impact on the orbital variability of radio, X-ray and gamma-ray signals detected from the binary pulsar PSR B1259-63/SS2883.

Gamma-ray-loud binary systems are a newly identified class of X-ray binaries detected up to TeV energies. Three such systems — PSR B1259–63, LS 5039 and LSI +61 303 — have been firmly detected as persistent or regularly variable TeV γ-ray emitters. The origin of the high-energy activity of these sources is not clear. In this paper we review the multiwavelength properties of these systems and discuss their similarities and peculiarities.

We fit Chandra HETGS data obtained for the unusual X-ray binary SS 433. While line strengths and continuum levels hardly change, the jet Doppler shifts show aperiodic variations that probably result from shocks in interactions with the local environment. The X-ray and optical emission line regions are found to be related but not coincident as the optical line emission persists for days while the X-ray emission lines fade in less than 5000 s. The X-ray spectrum of the blueshifted jet shows over two dozen emission lines from plasma at a variety of temperatures. The emission measure distribution derived from the spectrum can be used to test jet cooling models.

We introduce the use of a well-known parameter, the Alfvén Radius, R_A, as a new tool to discern whether an X-ray binary system may undergo a microquasar phase, i.e. ejecting relativistic particles orthogonal to the accretion disk. We study what we call the basic condition, R_A/R_* = 1 in its dependency on the magnetic field strength and the mass accretion rate. With this basic condition we establish under which combination of parameters any class of accreting neutron stars could become a microquasar instead of confining disk-material down to the magnetic poles and creating the two emitting caps typical for an X-ray pulsar. In the case of black-hole accreting binaries we equate the magnetic field pressure to the plasma pressure in the last stable orbit (i.e. R_A/R_LSO = 1) and we get upper limits for the magnetic field strength as a function of the mass accretion rate and the black hole mass.

In high-mass microquasars (HMMQ), strong interactions between jets and stellar winds at binary system scales could occur. In order to explore this possibility, we have performed numerical two-dimensional hydrodynamical simulations of jets crossing the dense stellar material to study how the jet will be affected by these interactions. We find that the jet head generates strong shocks in the wind. These shocks reduce the jet advance speed, and compress and heat up the jet and wind material. In addition, strong recollimation shocks can occur where pressure balance between the jet side and the surrounding medium is reached. All this, together with jet bending, could lead to the destruction of jets with power < 10³⁶erg/s. The conditions around the outflow shocks would be convenient for accelerating particles up to ~ TeV energies. These accelerated particles could emit via synchrotron and inverse Compton (IC) scattering if they were leptons, and via hadronic processes if they were hadrons.

We discuss the evidence for proton loading in relativistic jets from microquasars in light of recent constraints on the jet power. We argue that, both in the case of the Cygnus X-1 jet and the entire ensemble of Galactic microquasars, the evidence points towards a significant contribution to the total kinetic energy flux from cold protons. However, as with all other methods of constraining jet composition (except for the singular case of SS 433), a number of alternative, though maybe less plausible, explanations exist. In light of this continued elusiveness of a single slam-dunk argument for proton loading, the best we can hope for is a continuing accumulation of bits of evidence such as these which will, on the whole, form a preponderance of evidence against pure pair jets.

We consider the effect of thermal conduction along with AGN jet feedback on the intracluster medium (ICM) in cooling flow clusters. A series of three-dimensional AMR hydrodynamic simulations has been carried out to analyze the dynamic of such interaction. We show the limit of applicability of the Spitzer thermal conduction during jet/ICM interaction.

Most of the rotational luminosity of a pulsar is carried away by a relativistic magnetized wind in which the matter energy flux is negligible compared to the Poynting flux. However, observations indicate that most of the Poynting flux is eventually converted into ultrarelativistic particles. The mechanism responsible for this transformation remains poorly understood. Near the equatorial plane of an obliquely rotating pulsar magnetosphere, the magnetic field reverses polarity with the pulsar period, forming a wind with oppositely directed field lines, called a striped wind.

We study the conditions required for magnetic energy release at the termination shock of the striped pulsar wind. Magnetic reconnection is considered via analytical methods and 1D relativistic PIC simulations. An analytical condition on the upstream parameters for partial and full magnetic reconnection is derived from the conservation laws of energy, momentum and particle number density across the relativistic shock. Furthermore, by using a 1D relativistic PIC code, we study in detail the reconnection process at the termination shock for different upstream Lorentz factors and magnetizations, and find good agreement with our analytical criterion. Thus, alternating magnetic fields annihilate easily at relativistic highly magnetized shocks. We apply our criterion for dissipation to deduce bounds on the pair multiplicity, κ, in the pulsar wind.

To date, seven gamma-ray pulsars are known, showing pulsed emission up to tens of GeV and associated light-curves with a double-pulse structure. We study this pulsed high-energy emission in the framework of the striped wind model. By numerical integration of the time-dependent emissivity in the current sheets, we compute the phase-dependent spectral variability of the inverse Compton radiation. Several light curves and spectra are presented. The pulses are a direct consequence of relativistic beaming. Our model is able to explain some of the high-energy (10 MeV–10 GeV) spectral features and behavior of several gamma-ray pulsars, such as Geminga and Vela.