Jet Acceleration Research Articles

Shocks in Radiatively Driven Time-dependent, Relativistic Jets around Black Holes

We study time-dependent relativistic jets under the influence of the radiation field of the accretion disk. The accretion disk consists of an inner compact corona and an outer sub-Keplerian disk. The thermodynamics of the fluid is governed by a relativistic equation of state (EOS) for multispecies fluid that enables us to study the effect of composition on jet dynamics. Jets originate from the vicinity of the central black hole, where the effect of gravity is significant and traverses large distances where only special relativistic treatment is sufficient. So we have modified the flat metric to include the effect of gravity. In this modified relativistic framework we have developed a new total variation diminishing routine along with a multispecies EOS for the purpose. We show that the acceleration of jets crucially depends on flow composition. All the results presented are transonic in nature; starting from very low injection velocities, the jets can achieve high Lorentz factors. For sub-Eddington luminosities, lepton-dominated jets can be accelerated to Lorentz factors >50. The change in radiation field due to variation in the accretion disk dynamics will be propagated to the jet in a finite amount of time. Hence, any change in radiation field due to a change in disk configuration will affect the lower part of the jet before it affects the outer part. This can drive shock transition in the jet flow. Depending on the disk oscillation frequency, amplitude, and jet parameters, these shocks can collide with each other and may trigger shock cascades.

A simple analytical model of magnetic jets

ABSTRACT We propose a simple analytical jet model of magnetic jets, in which radially averaged profiles of main physical quantities are obtained based on conservation laws and some results of published general relativistic magnetohydrodynamic jet simulations. We take into account conversion of the magnetic energy flux to bulk acceleration in jets formed around rotating black holes assuming the mass continuity equation and constant jet power, which leads to the Bernoulli equation. For assumed profiles of the bulk Lorentz factor and the radius, this gives us the profile of the toroidal magnetic field component along the jet. We then consider the case where the poloidal field component is connected to a rotating black hole surrounded by an accretion disc. Our formalism then recovers the standard formula for the power extracted from a rotating black hole. We find that the poloidal field strength dominates over the toroidal one in the comoving frame up to large distances, which means that jets should be more stable to current-driven kink modes. The resulting magnetic field profiles can then be used to calculate the jet synchrotron emission.

Testing particle acceleration models for BL Lac jets with the Imaging X-ray Polarimetry Explorer

Mechanisms such as shock acceleration, magnetic reconnection in a kink unstable jet, and extreme turbulence in the jet flow are all expected to produce a distinctive time variability pattern of the X-ray polarization properties of high synchrotron peak blazars (HSP). To determine whether the recently launched Imaging X-ray Polarimetry Explorer (IXPE) can follow the polarization variations induced by different particle acceleration mechanisms in blazar jets, we simulated observations of an HSP blazar variable in terms of the polarization degree and angle according to theoretical predictions. We used the Monte Carlo tool ixpeobssim to create realistic IXPE data products for each model and for three values of flux (i.e., 1, 5, and 10 × 10−10 erg s−1 cm−2). We generated simulated light curves of the polarization degree and angle by time-slicing the simulated data into arbitrary short time bins. We used an χ2 test to assess the performance of the observations in detecting the time variability of the polarization properties. In all cases, even when the light curves are diluted in an individual time bin, some degree of polarization is still measurable with IXPE. A series of ~10 ks long observations permits IXPE to follow the time variability of the polarization degree in the case of the shock acceleration model. In the case of the magnetic reconnection model, the nominal injected model provides the best fit of the simulated IXPE data for time bins of ~5–10 ks, depending on the tested flux level. For the TEMZ model, shorter time slices of ~0.5 ks are needed for obtaining a formally good fit of the simulated IXPE data with the injected model. On the other hand, we find that a fit with a constant model provides a χ2 lower than the fit with the nominal injected model when using time slices of ~20 ks, ~60/70 ks, and ~5 ks for the case of the shock acceleration, magnetic reconnection, and TEMZ model, respectively. In conclusion, provided that the statistics of the observation allows for the slicing of the data in adequately short time bins, IXPE observations of an HSP blazar at a typical flux level can detect the time variability predicted by popular models for particle acceleration in jets. IXPE observations of HSP blazars are a useful tool for addressing the issue of particle acceleration in blazar jets.

Experimental investigation of flow control of a curved-surface jet at Mach 5 hypersonic flow

Jet flow-control technology is a promising area of fluid research. In this work, the flow-control effect of a curved-surface jet in an incoming flow of Mach = 5 and its underlying control mechanism are experimentally studied using high-speed photography and dynamic force measurement. From the establishment of complete stability of the flow field, the evolutionary process can be roughly divided into five stages: two equilibrium stages (short and long term), jet acceleration stage, bow shock formation stage, interference removal stage, and stable state. By defining the pressure ratio (PR) as an independent variable, it is found that the flow control of the jet occurs through different wave-system structures. The interaction between the jet and the incoming flow produces an oblique shockwave and expansion waves. The shockwave generates thrust and forms a virtual rudder surface; the expansion waves interact with the backflow region and the separated shear layer to generate lift. Moreover, PR has an optimal solution of PRopt. When PR < PRopt, the effect of flow control is related to α, Ve, and ρe, and the greater the PR, the stronger the flow-control effect. When PR > PRopt, the flow-control effect is related to α and ρe, and the larger the PR, the weaker the effect of the shockwave and the stronger the effect of the expansion waves but the slower the growth. In experiments, the thrust, pitching moment, and lift increased by 17.43%, 17.75%, and 9.45%, respectively, because of the appearance of wave-system structure when PRopt = 201.32.

Modeling the Spectral Energy Distributions and Spectropolarimetry of Blazars—Application to 4C+01.02 in 2016–2017*

Abstract The optical radiation emitted by blazars contains contributions from synchrotron radiation by relativistic electrons in the jets, as well as thermal radiation emitted mainly by the accretion disk (AD), the broad-line region (BLR), and the host galaxy. The unpolarized radiation components from the AD, BLR, and host galaxy present themselves by decreasing the total polarization in the optical/ultraviolet (UV) spectrum. A combined model for the spectral energy distribution (SED) and degree of optical/UV polarization is constructed, enabling the disentanglement of the synchrotron and AD components. Our model is applied to the multiwavelength SED and spectropolarimetry observations of the flat-spectrum radio quasar 4C+01.02 (z = 2.1) in its 2016 July–August flaring state and 2017 July–August quiescent state, using data from the Fermi Large Area Telescope, the Southern African Large Telescope, and the Las Cumbres Observatory network of telescopes. By constraining the AD component, the mass of the supermassive black hole is obtained as ∼3 × 109 M ⊙. Furthermore, the model retrieves the characteristics of the relativistic electron distribution in the jet and the degree of ordering of the magnetic field. Our results highlight the potential of spectropolarimetry observations for disentangling thermal from nonthermal (jet) emission components, thus revealing the physics of particle acceleration and high-energy emission in active galactic nucleus jets.

GRMHD Simulations and Modeling for Jet Formation and Acceleration Region in AGNs

Relativistic jets are collimated plasma outflows with relativistic speeds. Astrophysical objects involving relativistic jets are a system comprising a compact object such as a black hole, surrounded by rotating accretion flows, with the relativistic jets produced near the central compact object. The most accepted models explaining the origin of relativistic jets involve magnetohydrodynamic (MHD) processes. Over the past few decades, many general relativistic MHD (GRMHD) codes have been developed and applied to model relativistic jet formation in various conditions. This short review provides an overview of the recent progress of GRMHD simulations in generating relativistic jets and their modeling for observations.

Effect of Inverse Compton Cooling on Relativistic Particles Accelerated at Shear Boundary Layers in Relativistic Jets

AbstractRecent theoretical considerations and observational evidence evince the spine-sheath morphology of relativistic jets emitted from active galactic nuclei (AGNs) or gamma-ray bursts (GRBs). The resulting shear boundary layers (SBLs) are likely to be an avenue for particle acceleration in relativistic jets. The effect of radiation drag on radiating particles has yet to be addressed in most studies of particle acceleration at shear boundary layers, even though radiative cooling may considerably affect particle dynamics. By using particle-in-cell simulations, we study the effects of inverse Compton cooling on particle dynamics and emerging particle spectra.

Acceleration of ultrahigh-energy cosmic rays in the early afterglows of gamma-ray bursts: Concurrence of jet dynamics and wave-particle interactions

The origin of ultra-high energy cosmic rays $($UHECRs$)$ remains a mystery. It has been suggested that UHECRs can be produced by the stochastic acceleration in relativistic jets of gamma-ray bursts $($GRBs$)$ at the early afterglow phase. Here, we develop a time-dependent model for proton energization by cascading compressible waves in GRB jets considering the concurrent effect of the jet's dynamics and the mutual interactions between turbulent waves and particles. Considering fast mode of magnetosonic wave as the dominant particle scatterer and assuming interstellar medium $($ISM$)$ for the circumburst environment, our numerical results suggest that protons can be accelerated up to $\textrm{10}^{\textrm{19}}\,$eV during the early afterglow. An estimation shows ultra-high energy nuclei can easily survive photodisintegration in the external shocks in most cases, thus allowing the acceleration of $\textrm{10}^{\textrm{20}}\,$eV cosmic-ray nuclei in the proposed frame. The spectral slope can be as hard as $\textrm{d}\textit{N}/\textrm{d}\textit{E} \propto \textit{E}^\textrm{0}$, which is consistent with the requirement for the interpretation of intermediate-mass composition of UHECR as measured by the Pierre Auger Observatory.

Laser-driven collisionless shock acceleration of protons from gas jets tailored by one or two nanosecond beams

It was proposed recently that laser-ion acceleration in gas jets may be significantly improved if each side of a gas jet target is tailored by an auxiliary nanosecond laser pulse [Marquès et al., Phys. Plasmas 28, 023103 (2021)]. In the present study, the proton acceleration by electrostatic shock in these one- or two-side tailored plasmas is investigated using particle-in-cell simulations. It is demonstrated that the formation of a thin plasma layer with a steep density profile and a maximum density of the order of the critical density strongly improves the proton acceleration in the forward direction with a maximum ion energy of tens of MeV with mildly relativistic laser pulses. Proton acceleration up to tens of MeV is predicted using realistic plasma density profiles obtained from tailored gas jet targets compared to a few MeV reported in other publications.

Identifying changing jets through their radio variability

Context. Supermassive black holes can launch highly relativistic jets with velocities reaching Lorentz factors of as high as Γ > 50. How the jets accelerate to such high velocities and where along the jet they reach terminal velocity are open questions that are tightly linked to their structure as well as their launching and dissipation mechanisms. Aims. Changes in the beaming factor along the jets could potentially reveal jet acceleration, deceleration, or bending. We aim to (1) quantify the relativistic effects in multiple radio frequencies and (2) study possible jet velocity–viewing angle variations at parsec scales. Methods. We used the state-of-the-art code Magnetron to model light curves from the University of Michigan Radio Observatory and the Metsähovi Radio Observatory’s monitoring programs in five frequencies covering about 25 years of observations in the 4.8 to 37 GHz range for 61 sources. We supplement our data set with high-frequency radio observations in the 100–340 GHz range from ALMA, CARMA, and SMA. For each frequency we estimate the Doppler factor which we use to quantify possible changes in the relativistic effects along the jets. Results. The majority of our sources do not show any statistically significant difference in their Doppler factor across frequencies. This is consistent with constant velocity in a conical jet structure, as expected at parsec scales. However, our analysis reveals 17 sources where relativistic beaming changes as a function of frequency. In the majority of cases, the Doppler factor increases towards lower frequencies. Only 1253–053 shows the opposite behavior. By exploring their jet properties we find that the jet of 0420–014 is likely bent across the 4.8–340 GHz range. For 0212+735, the jet is likely parabolic, and still accelerating in the 4.8–37 GHz range. We discuss possible interpretations for the trends found in the remaining sources.

The Bulk Flow Velocity and Acceleration of the Inner Jet in M87

Abstract A high sensitivity, 7 mm Very Long Baseline Array image of M87 is analyzed in order to estimate the jet velocity within 0.65 mas of the point of origin. The image captured a high signal-to-noise, double-ridged, counter-jet extending ∼1 mas from the nucleus. After defining conditions and requirements that justify approximate time averaged bilateral symmetry, a continuous set of Lorentz transformations are found that map the double-ridged counter-jet intensity profile into the double-ridged jet intensity profile. The mapping is realized by a uniformly accelerating flow with intrinsic velocity of ∼0.27c at 0.4 mas (a de-projected distance of 0.38 lt-yr) to 0.38c at 0.65 mas (a de-projected distance of 0.61 lt-yr) from the nucleus. Since the velocity field is derived from the global surface brightness profile and does not depend on the motion of enhanced features, it is most likely a bulk flow velocity as opposed to a pattern velocity. This interpretation is corroborated by the fact that the distribution of the apparent velocities of previously identified individual features (from the literature) within 0.65 mas of the nucleus are consistent with local hydrodynamic shocks being advected with the local bulk flow velocity. The bulk flow velocity of the visible inner jet is a constraint that can potentially break degeneracies between numerical simulations that are designed to replicate both the annulus that was imaged by the Event Horizon Telescope as well as the base of the inner jet.

Simulating the dynamics and synchrotron emission from relativistic jets – II. Evolution of non-thermal electrons

ABSTRACT We have simulated the evolution of non-thermal cosmic ray electrons (CREs) in 3D relativistic magneto hydrodynamic (MHD) jets evolved up to a height of 9 kpc. The CREs have been evolved in space and in energy concurrently with the relativistic jet fluid, duly accounting for radiative losses and acceleration at shocks. We show that jets stable to MHD instabilities show expected trends of regular flow of CREs in the jet spine and acceleration at a hotspot followed by a settling backflow. However, unstable jets create complex shock structures at the jet head (kink instability), the jet spine-cocoon interface, and the cocoon itself (Kelvin–Helmholtz modes). CREs after exiting jet head undergo further shock crossings in such scenarios and are re-accelerated in the cocoon. CREs with different trajectories in turbulent cocoons have different evolutionary history with different spectral parameters. Thus, at the same spatial location, there is mixing of different CRE populations, resulting in a complex total CRE spectrum when averaged over a given area. Cocoons of unstable jets can have an excess build up of energetic electrons due to re-acceleration at turbulence driven shocks and slowed expansion of the decelerated jet. This will add to the non-thermal energy budget of the cocoon.

The jet collimation profile at high resolution in BL Lacertae

Context. Controversial studies on the jet collimation profile of BL Lacertae (BL Lac), the eponymous blazar of the BL Lac objects class, complicate the scenario in this already puzzling class of objects. Understanding the jet geometry in connection with the jet kinematics and the physical conditions in the surrounding medium is fundamental for better constraining the formation, acceleration, and collimation mechanisms in extragalactic jets. Aims. With the aim of investigating the jet geometry in the innermost regions of the BL Lac jet, and resolving the controversy, we explore the radio jet in this source using high-resolution millimeter-wave VLBI data. Methods. We collect 86 GHz GMVA and 43 GHz VLBA data to obtain stacked images that we use to infer the jet collimation profile by means of two comparable methods. We analyze the kinematics at 86 GHz, and we discuss it in the context of the jet expansion. Finally, we consider a possible implication of the Bondi sphere in shaping the jet of BL Lac. Results. The jet in BL Lac expands with an overall conical geometry. A higher expanding rate region is observed between ∼5 and 10 pc (de-projected) from the black hole. Such a region is associated with the decrease in brightness usually observed in high-frequency VLBI images of BL Lac. The jet retrieves the original jet expansion around 17 pc, where the presence of a recollimation shock is supported by both the jet profile and the 15 GHz kinematics (MOJAVE survey). The change in the jet expansion profile occurring at ∼5 pc could be associated with a change in the external pressure at the location of the Bondi radius (∼3.3 × 105RS).

Chromospheric and coronal heating and jet acceleration due to reconnection driven by flux cancellation

Context. Recent observations have shown that magnetic flux cancellation occurs at the photosphere more frequently than previously thought. Aims. In order to understand the energy release by reconnection driven by flux cancellation, we previously studied a simple model of two cancelling polarities of equal flux. Here, we further develop our analysis to achieve a more general setup where the two cancelling polarities have unequal magnetic fluxes and where many new features are revealed. Methods. We carried out an analytical study of the cancellation of two magnetic fragments of unequal and opposite flux that approach one another and are located in an overlying horizontal magnetic field. Results. The energy release as microflares and nanoflares occurs in two main phases. During phase 1a, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating plasma jets in the process. During phase 1b, once the separator moves back to the photosphere, it bifurcates into two null points. Reconnection is no longer driven at the separator and an isolated magnetic domain connecting the two polarities is formed. During phase 2, the polarities cancel out at the photosphere as magnetic flux submerges below the photosphere and as reconnection occurs at and above the photosphere and plasma jets and a mini-filament eruption can be produced.

An adaptive mesh, GPU-accelerated, and error minimized special relativistic hydrodynamics code

ABSTRACT We present a new special relativistic hydrodynamics (SRHD) code capable of handling coexisting ultra-relativistically hot and non-relativistically cold gases. We achieve this by designing a new algorithm for conversion between primitive and conserved variables in the SRHD solver, which incorporates a realistic ideal-gas equation of state covering both the relativistic and non-relativistic regimes. The code can handle problems involving a Lorentz factor as high as 106 and optimally avoid the catastrophic cancellation. In addition, we have integrated this new SRHD solver into the code gamer (https://github.com/gamer-project/gamer) to support adaptive mesh refinement and hybrid OpenMP/MPI/GPU parallelization. It achieves a peak performance of 7 × 107 cell updates per second on a single Tesla P100 GPU and scales well to 2048 GPUs. We apply this code to two interesting astrophysical applications: (a) an asymmetric explosion source on the relativistic blast wave and (b) the flow acceleration and limb brightening of relativistic jets.

Particle acceleration and magnetic field amplification in massive young stellar object jets

ABSTRACT Synchrotron radio emission from non-relativistic jets powered by massive protostars has been reported, indicating the presence of relativistic electrons and magnetic fields of strength ∼0.3–5 mG. We study diffusive shock acceleration and magnetic field amplification in protostellar jets with speeds between 300 and 1500 km s−1. We show that the magnetic field in the synchrotron emitter can be amplified by the non-resonant hybrid (Bell) instability excited by the cosmic ray streaming. By combining the synchrotron data with basic theory of Bell instability we estimate the magnetic field in the synchrotron emitter and the maximum energy of protons. Protons can achieve maximum energies in the range 0.04–0.65 TeV and emit γ rays in their interaction with matter fields. We predict detectable levels of γ rays in IRAS 16547−5247 and IRAS 16848−4603. The γ ray flux can be significantly enhanced by the gas mixing due to Rayleigh–Taylor instability. The detection of this radiation by the Fermi satellite in the GeV domain and the forthcoming Cherenkov Telescope Array at higher energies may open a new window to study the formation of massive stars, as well as diffusive acceleration and magnetic field amplification in shocks with velocities of about 1000 km s−1.

Jet Collimation and Acceleration in the Giant Radio Galaxy NGC 315

Abstract We study the collimation and acceleration of jets in the nearby giant radio galaxy NGC 315, using multifrequency Very Long Baseline Array observations and archival High Sensitivity Array and Very Large Array data. We find that the jet geometry transitions from a semi-parabolic shape into a conical/hyperbolic shape at a distance of ≈105 gravitational radii. We constrain the frequency-dependent position of the core, from which we locate the jet base. The jet collimation profile in the parabolic region is in good agreement with the steady axisymmetric force-free electrodynamic solution for the outermost poloidal magnetic field line anchored to the black hole event horizon on the equatorial plane, similar to the nearby radio galaxies M87 and NGC 6251. The velocity field derived from the asymmetry in brightness between the jet and counterjet shows gradual acceleration up to the bulk Lorentz factor of Γ ∼ 3 in the region where the jet collimation occurs, confirming the presence of the jet acceleration and collimation zone. These results suggest that the jets are collimated by the pressure of the surrounding medium and accelerated by converting Poynting flux to kinetic energy flux. We discover limb brightening of the jet in a limited distance range where the angular resolution of our data is sufficient to resolve the jet transverse structure. This indicates that either the jet has a stratified velocity field of fast-inner and slow-outer layers or the particle acceleration process is more efficient in the outer layer owing to the interaction with the surroundings on parsec scales.

Chromospheric and coronal heating and jet acceleration due to reconnection driven by flux cancellation

Context.The recent discovery of much greater magnetic flux cancellation taking place at the photosphere than previously realised has led us in our previous works to suggest magnetic reconnection driven by flux cancellation as the cause of a wide range of dynamic phenomena, including jets of various kinds and solar atmospheric heating.Aims.Previously, the theory considered energy release at a two-dimensional current sheet. Here we develop the theory further by extending it to an axisymmetric current sheet in three dimensions without resorting to complex variable theory.Methods.We analytically study reconnection and treat the current sheet as a three-dimensional structure. We apply the theory to the cancellation of two fragments of equal but opposite flux that approach each another and are located in an overlying horizontal magnetic field.Results.The energy release occurs in two phases. During Phase 1, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating a plasma jet as it does so. During Phase 2 the fluxes cancel in the photosphere and accelerate a mixture of cool and hot plasma upwards.

Understanding the Puzzling Acceleration of Jets of Active Galactic Nuclei

Abstract As relativistic plasma launches from a compact object at the center of a galaxy, the corresponding outflow should slow down with the increase of separation from the core due to energy dissipation along the path. However, some long-baseline observations of active galactic nucleus (AGN) jets show that the velocity of jets increases rather than decreases at a larger and larger separation from the core. The mechanism of such an acceleration of astrophysical jets has not been well understood so far, although much progress has been achieved on theoretical and observational perspectives. This paper illustrates the phenomenon of jet acceleration that emerged in some AGNs by the nonballistic model in which some nonconsecutive knots are produced by a continuous outflow at different distances from the central black hole; such knots appear to rotate along different radii at the same precession cone in the case of a precessing jet. The projection of the trajectories of such knots on the plane of the sky leads us to expect that jet components further from the core move at larger apparent velocities. The investigation provides a very simple scenario to the puzzling phenomena of astrophysical jets.

Particle Acceleration by Relativistic Magnetic Reconnection Driven by Kink Instability Turbulence in Poynting Flux–Dominated Jets

Abstract Particle acceleration in magnetized relativistic jets still puzzles theorists. In this work, we investigate the acceleration of particles injected into a three-dimensional relativistic magnetohydrodynamical jet subject to current-driven kink (CDK) instability. We find that, once turbulence driven by CDK fully develops, achieving a nearly stationary state, the amplitude of excited wiggles along the jet spine attains maximum growth, causing disruption of the magnetic field lines and the formation of several sites of fast reconnection. Low-energy protons injected into the jet at this state experience exponential acceleration, mostly in directions parallel to the local magnetic field, up to maximum energies eV for G and eV for G. The Larmor radius of the particles attaining these energies corresponds to the size of the acceleration region (∼the diameter of the perturbed jet). There is a clear association of the accelerated particles with regions of fast reconnection. In the early nonlinear growth stage of the CDK, when there are no sites of fast reconnection yet, injected particles with initially much larger energy are accelerated by magnetic curvature drift. We have also obtained the acceleration time due to reconnection with a dependence on the particles’ energy, . The energy spectrum of the accelerated particles develops a power-law index ∼ −1.2 in the beginning, in agreement with earlier works. Our results provide a multidimensional framework for exploring this process in real systems and explain their emission patterns, especially at very high energies, and associated neutrino emission recently detected in some blazars.