The generation of relativistic jets in active sources such as blazars is a complex problem with many aspects, most of them still not fully understood. Relativistic jets are likely produced by the accretion of matter and magnetic fields onto spinning black holes. Ergospheric dragging effects launch a Poynting-dominated outflow in the polar directions of these systems. Observations with very high resolution of the jet in the nearby radio galaxy M87 and evidence of extremely fast variability in the non-thermal radiation of several other objects indicate that charged particles produce synchrotron emission and gamma rays very close to the base of the jet. How these particles are injected into the magnetically shielded outflow is a mystery. Here we explore the effects of various processes in the hot accretion inflow close to the black hole that might result in the copious production of neutral particles which, through annihilation and decay in the jet's funnel, might load the outflow with mass and charged particles on scales of a few Schwarzschild radii.
Deceleration of relativistic jets from active galactic nuclei (AGNs) detected recently by MOJAVE team is discussed in connection with the interaction of the jet material with the external photon field. Appropriate energy density of the isotropic photon field which is necessary to decelerate jets is determined. It is shown that the disturbances of the electric potential and magnetic surfaces play important role in general dynamics of particle deceleration.
The nuclei of most normal galaxies contain supermassive black holes, which can accrete gas through a disk and become active. These Active Galactic Nuclei, AGN, can form jets which are observed on scales from AU to Mpc and from meter wavelengths to TeV gamma ray energies. High resolution radio imaging and multi-wavelength/messenger campaigns are elucidating the conditions under which this happens. Evidence is presented that: AGN jets are formed when the black hole spins and the accretion disk is strongly magnetized, perhaps on account of gas accretingat high latitude beyond the black hole spher…
Jets powered by active galactic nuclei appear impressively stable compared with their terrestrial and laboratory counterparts-they can be traced from their origin to distances exceeding their injection radius by up to a billion times. However, some less energetic jets get disrupted and lose their coherence on the scale of their host galaxy. Quite remarkably, on the same scale, these jets are expected to become confined by the thermal pressure of the intra-galactic gas. Motivated by these observations, we have started a systematic study of active galactic nuclei jets undergoing reconfinement vi…
The jets of active galactic nuclei can carry a large fraction of the accreted power of the black-hole system into interstellar and even extragalactic space. They radiate profusely from radio to X-ray and gamma-ray frequencies. In the most extreme cases, the outward flow speeds correspond to high Lorentz factors that can reach 40 or more. This chapter displays images at various wavebands as well as light curves and continuum spectra that illustrate the variability with location, time, and frequency of the emission from compact, parsec- and subparsec-scale jets. It presents a physical framework …
This is a White Paper in support of the mission concept of the Large Observatory for X-ray Timing (LOFT), proposed as a medium-sized ESA mission. We discuss the potential of LOFT for the study of radio-loud Active Galactic Nuclei. For a summary, we refer to the paper.
We investigate the consequences of acceleration of nuclei in jets of active galaxies not far from the surface of an accretion disk. The nuclei can be accelerated in the re-connection regions in the jet and/or at the jet boundary, between the relativistic jet and its cocoon. It is shown that the relativistic nuclei can efficiently fragment onto specific nucleons in collisions with the disk radiation. Neutrons, directed towards the accretion disk, take a significant part of energy from the relativistic nuclei. These neutrons develop a cascade in the dense accretion disk. We calculate the neutrin…
Collimated outflows (jets) appear to be a ubiquitous phenomenon associated with the accretion of material onto a compact object. Despite this ubiquity, many fundamental physics aspects of jets are still poorly understood and constrained. These include the mechanism of launching and accelerating jets, the connection between these processes and the nature of the accretion flow, and the role of magnetic fields; the physics responsible for the collimation of jets over tens of thousands to even millions of gravitational radii of the central accreting object; the matter content of jets; the location…
We report on our Chandra Cycle 9 program to observe half of the 60 (unobserved by Chandra) 3C radio sources at z<0.3 for 8 ksec each. Here we give the basic data: the X-ray intensity of the nuclei and any features associated with radio structures such as hot spots and knots in jets. We have measured fluxes in soft, medium and hard bands and are thus able to isolate sources with significant intrinsic column density. For the stronger nuclei, we have applied the standard spectral analysis which provides the best fit values of X-ray spectral index and column density. We find evidence for intrinsic…
The analysis of the frequency dependence of the observed shift of the cores of relativistic jets in active galactic nuclei (AGN) allows us to evaluate the number density of the outflowing plasma n and, hence, the multiplicity parameter, which is a ratio of particle number density to Goldreich-Julian number density. We have obtained the median value for the multiplicity parameter to be 3x10^13 and the median value for the Michel magnetization parameter is 8 from an analysis of 97 sources. Since the magnetization parameter can be interpreted as the maximum possible Lorentz factor of the bulk mot…
Axions or more generally axion-like particles (ALPs) are pseudo-scalar particles predicted by many extensions of the Standard Model of particle physics (SM) and considered as highly viable candidates for dark matter (DM) in the universe. If they exist in nature, they are expected to couple with photons in the presence of an external magnetic field through a form of the Primakoff effect. In this work, we examine the detectability of signals produced by ALP-photon coupling in the highly magnetized environment of the relativistic jets produced by active galactic nuclei (AGNs). Furthermore, we tes…
Ultra-high energy cosmic rays (UHECRs) may be produced in active galactic nuclei (AGN) or gamma-ray burst (GRB) jets. I argue that magnetic reconnection in jets can accelerate UHECRs rather independently of physical processes in the magnetic dissipation region. First order Fermi acceleration can efficiently take place in the region where the unreconnected (upstream) magnetized fluid converges into the reconnection layer. I find that protons can reach energies up to E~10^{20} eV in GRB and powerful AGN jets while iron nuclei can reach similar energies in AGN jets of more moderate luminosity.
We investigate the fraction of metal nuclei in the relativistic jets of gamma-ray bursts associated with core-collapse supernovae. We simulate the fallback in jet-induced explosions with two-dimensional relativistic hydrodynamics calculations and the jet acceleration with steady, radial, relativistic magnetohydrodynamics calculations, and derive detail nuclear composition of the jet by postprocessing calculation. We found that if the temperature at the jet launch site is above $4.7\times 10^9$K, quasi-statistical equilibrium (QSE) is established and heavy nuclei are dissociated to light partic…
According to the currently favored picture, relativistic jets in active galactic nuclei (AGN) are launched in the vicinity of the black hole by magnetic fields extracting energy from the spinning black hole or the accretion disk. In the past decades, various models from shocks to magnetic reconnection have been proposed as the energy dissipation mechanism in the jets. This paper presents a short review on how linear polarization observations can be used to constrain the magnetic field structure in the jets of AGN, and how the observations can be used to constrain the various emission models.
Heavy nuclei such as nickel-56 are synthesized in a wide range of core-collapse supernovae (CCSN), including energetic supernovae associated with gamma-ray bursts (GRBs). Recent studies suggest that jet-like outflows are a common feature of CCSN. These outflows may entrain synthesized nuclei at launch or during propagation, and provide interesting multi-messenger signals including heavy ultra-high energy cosmic rays. Here, we investigate the destruction processes of nuclei during crossing from the stellar material into the jet material via a cocoon, and during propagation after being successfu…
This is the fourth in a series of companion papers showing that, when an efficient dynamo can be maintained by accretion disks around supermassive black holes in Active Galactic Nuclei (AGNs), it will lead to the formation of a powerful, magnetically-collimated helix that could explain both the observed jet/radiolobe structures on very large scales and ultimately the enormous power inferred from the observed ultra high energy cosmic rays (UHECRs) with energies > 10^19 eV. Many timescales are involved in this process. Our hyper-resistive magnetohydrodynamic (MHD) model provides a bridge between…
We present a bottom-up calculation of the flux of ultra-high energy cosmic rays (UHECRs) and high-energy neutrinos produced by powerful jets of active galactic nuclei (AGNs). By propagating test particles in 3D relativistic magnetohydrodynamic jet simulations, including a Monte Carlo treatment of sub-grid pitch-angle scattering and attenuation losses due to realistic photon fields, we study the spectrum and composition of the accelerated UHECRs and estimate the amount of neutrinos produced in such sources. We find that UHECRs may not be significantly affected by photodisintegration in AGN jets…
We perform polarimetry analysis of 20 active galactic nuclei (AGN) jets using the Very Long Baseline Array (VLBA) at 1.4, 1.6, 2.2, 2.4, 4.6, 5.0, 8.1, 8.4, and 15.4 GHz. The study allowed us to investigate linearly polarized properties of the jets at parsec-scales: distribution of the Faraday rotation measure (RM) and fractional polarization along the jets, Faraday effects and structure of Faraday-corrected polarization images. Wavelength-dependence of the fractional polarization and polarization angle is consistent with external Faraday rotation, while some sources show internal rotation. Th…
Very high energy gamma-ray observations of distant active galactic nuclei (AGN) generally result in higher fluxes and harder spectra than expected, resulting in some tension with the level of the extragalactic background light (EBL). If hypothetical axions or axion-like particles (ALPs) were to exist, this tension could be relieved since the oscillation of photons to ALPs would mitigate the effects of EBL absorption and lead to softer inferred intrinsic AGN spectra. In this paper we consider the effect of photon-ALP mixing on observed spectra, including the photon-ALP mixing that would occur w…
In Mbarek & Caprioli (2019), we laid the groundwork for studying the espresso paradigm Caprioli (2015), a reacceleration mechanism to boost galactic CRs to UHECR levels. Our bottom-up approach uses realistic 3D MHD simulations of relativistic AGN jets and accounts for all of the crucial ingredients of a universal acceleration theory: injection, acceleration, and escape in realistic environments. Our results are consistent with the main features of UHECR spectra, i.e., power-law slopes, chemical composition, and anisotropy. In Mbarek & Caprioli (2021), we refine our model by including sub-grid …
The correlation between the kinetic power $P_{\rm jet}$ and intrinsic bolometric luminosity $L_{\rm jet}$ of jets may reveal the underlying jet physics in various black hole systems. Based on the recent work by Nemmen et al. (2012), we re-investigate this correlation with additional sources of black-hole X-ray binaries (BXBs) in hard/quiescent states and low-luminosity active galactic nuclei (LLAGNs). The new sample includes 29 sets of data from 7 BXBs and 20 LLAGNs, with $P_{\rm jet}$ and $L_{\rm jet}$ being derived from spectral modeling of the quasi-simultaneous multi-band spectra under the…
For the first time it has become possible to compare global 3D general relativistic magnetohydrodynamic (GRMHD) jet formation simulations directly to very-long baseline interferometric multi-frequency polarization observations of the pc-scale structure of active galactic nucleus (AGN) jets. Unlike the jet emission, which requires post hoc modeling of the non-thermal electrons, the Faraday rotation measures (RMs) depend primarily upon simulated quantities and thus provide a robust way in which to confront simulations with observations. We compute RM distributions of 3D global GRMHD jet formatio…
Magnetic reconnection is often invoked to explain the non-thermal radiation of relativistic outflows, including jets of active galactic nuclei (AGN). Motivated by the largely unknown plasma composition of AGN jets, we study reconnection in the unexplored regime of electron-positron-proton (pair-proton) plasmas with large-scale two-dimensional particle-in-cell simulations. We cover a wide range of pair multiplicities (lepton-to-proton number ratio $κ=1-199$) for different values of the all-species plasma magnetization ($σ=1,3$ and 10) and electron temperature ($Θ_e\equiv kT_e/m_ec^2=0.1-100$). …
Energy deposition by active galactic nuclei jets into the ambient medium can affect galaxy formation and evolution, the cooling of gas flows at the centres of galaxy clusters, and the growth of the supermassive black holes. However, the processes that couple jet power to the ambient medium and determine jet morphology are poorly understood. For instance, there is no agreement on the cause of the well-known Fanaroff-Riley (FR) morphological dichotomy of jets, with FRI jets being shorter and less stable than FRII jets. We carry out global 3D magnetohydrodynamic simulations of relativistic jets p…
Simulations of active galactic nuclei (AGN) jets have thus far been performed almost exclusively using grid-based codes. We present the first results from hydrodynamical tests of AGN jets, and their interaction with the intracluster medium (ICM), using smoothed particle hydrodynamics (SPH) as implemented in the SWIFT code. We launch these jets into a constant-density ICM, as well as ones with a power-law density profile. We also vary the jet power, velocity, opening angle and numerical resolution. In all cases we find broad agreement between our jets and theoretical predictions for the lengths…
The direction of parsec-scale jets in active galactic nuclei (AGNs) is essential information for many astrophysical and astrometric studies, including linear polarization and magnetic field structure, frequency-dependent synchrotron opacity, proper motion, and reference frame alignment. We developed a rigorous, simple, and completely automated method to measure the directions from calibrated interferometric visibility data at frequencies ranging from 1.4 GHz to 86 GHz. We publish the results for 9220 AGNs with the typical accuracy below 10 degrees. An internal check of the method comparing the…
In this work we discuss the recent criticism by Zdziarski of the maximal jet model derived in Falcke & Biermann (1995). We agree with Zdziarski that in general a jet's internal energy is not bounded by its rest-mass energy density. We describe the effects of the mistake on conclusions that have been made using the maximal jet model and show when a maximal jet is an appropriate assumption. The maximal jet model was used to derive a 1-D hydrodynamical model of jets in agnjet, a model that does multiwavelength fitting of quiescent/hard state X-ray binaries and low-luminosity active galactic nucle…
The recent detection of high-energy gamma rays from Narrow-Line Seyfert 1 Galaxies has confirmed that also this type of active galactic nuclei can generate powerful relativistic jets. I outline the evolution of the knowledge in this research field and the implications on the unification of relativistic jets at all scales.
Dense populations of stars surround the nuclear regions of galaxies. In active galactic nuclei, these stars can interact with the relativistic jets launched by the supermasive black hole. In this work, we study the interaction of early-type stars with relativistic jets in active galactic nuclei. A bow-shaped double-shock structure is formed as a consequence of the interaction of the jet and the stellar wind of each early-type star. Particles can be accelerated up to relativistic energies in these shocks and emit high-energy radiation. We compute, considering different stellar densities of the …
It has been proposed that Ultra-High-Energy Cosmic Rays (UHECRs) up to $10^{20}$eV could be produced in the relativistic jets of powerful Active Galactic Nuclei (AGNs) via a one-shot reacceleration of lower-energy CRs produced in supernova remnants (the $\textit{espresso}$ mechanism). We test this theory by propagating particles in realistic 3D magneto-hydrodynamic simulations of ultra-relativistic jets and find that about $10\%$ of the CRs entering the jet are boosted by at least a factor of $\simΓ^2$ in energy, where $Γ$ is the jet's effective Lorentz factor, in agreement with the analytical…
Active Galactic Nuclei (AGNs) and their relativistic jets belong to the most promising class of ultra-high-energy cosmic ray (UHECR) accelerators. This compact review summarises basic experimental findings by recent instruments, and discusses possible interpretations and astrophysical constraints on source energetics. Particular attention is given to potential sites and mechanisms of UHECR acceleration in AGNs, including gap-type particle acceleration close to the black hole, as well as first-order Fermi acceleration at trans-relativistic shocks and stochastic shear particle acceleration in la…
As part of our program to build a complete radio and X-ray database of all the 3CR extragalactic radio sources, we present an analysis of 93 sources for which Chandra archival data are available. Most of these sources have been already published. Here we provide a uniform re-analysis and present nuclear X-ray fluxes and X-ray emission associated with radio jet knots and hotspots using both publicly available radio images and new radio images that have been constructed from data available in the VLA archive. For about 1/3 of the sources in the selected sample a comparison between the Chandra an…
Jets, collimated outflows of particles and fields, are observed in a wide variety of astrophysical systems, including Active Galactic Nuclei of various types, microquasars, gamma-ray bursts, and young stellar objects. Despite intensive efforts along several decades of observational and theoretical research, there are still many uncertainties and open questions related to how jets are produced and what is their composition. In this review I offer an outline of some current views on the content and basic properties of astrophysical jets.
The reionization of the Universe ends the dark ages that started after the recombination era. In the case of H, reionization finishes around $z\sim 6$. Faint star-forming galaxies are the best candidate sources of the H-ionizing radiation, although active galactic nuclei may have also contributed. We have explored whether the termination regions of the jets from active galactic nuclei may have contributed significantly to the ionization of H in the late reionization epoch, around $z\sim 6-7$. We assumed that, as it has been proposed, active galactic nuclei at $z\sim 6$ may have presented a hig…
Jets are found in a variety of astrophysical sources, from young stellar objects to active galactic nuclei. In all the cases the jet propagates with a supersonic velocity through the external medium, which can be inhomogeneous, and inhomogeneities could penetrate into the jet. The interaction of the jet material with an obstacle produces a bow shock in the jet in which particles can be accelerated up to relativistic energies and emit high-energy photons. In this work, we explore the active galactic nuclei scenario, focusing on the dynamical and radiative consequences of the interaction at diff…
The effect of a mass-loading of the magnetohydrodynamic (MHD) flow in a relativistic jet from active galactic nuclei (AGN) due to $γγ\rightarrow e^+e^-$ conversion is considered analytically. We argue that the effects of charge average separation due to specific initial pairs' motion lead to partial magnetic and electric fields screening or enhancement. The effect of the fields screening has not been considered earlier. The pairs with the center-of-mass moving faster or slower than the bulk plasma flow create a surface charge and a current which either screen or enhance both electric and magne…
Relativistic jets are observed only in the low/hard and intermediate states of X-ray binaries (XRBs), and are switched off in the thermal state, but they appear to be present in both low-luminosity and luminous active galactic nuclei (AGNs). It is widely believed that strong large-scale magnetic fields is a crucial ingredient in jet production; such fields can be attained only through efficient advection from the outer disc. We suggest that geometrically thin accretion discs with magnetic outflows are present in luminous radio-loud AGNs; this is likely because the interstellar medium provides …
Low luminosity active galactic nuclei are more abundant and closer to us than the luminous ones but harder to explore as they are faint. We have selected the four sources NGC 315, NGC 4261, NGC 1275, and NGC 4486, which have been detected in gamma rays byFermi-LAT. We have compiled their long-term radio, optical, X-ray data from different telescopes, analysed XMM-Newton data for NGC 4486, XMM-Newton and Swift data for NGC 315. We have analysed the Fermi-LAT data collected over the period of 2008 to 2020 for all of them. Electrons are assumed to be accelerated to relativistic energies in sub-pa…
We present a numerical model developed to calculate observed fluxes of relativistic jets in active galactic nuclei. The observed flux of each turbulent eddy is dependent upon its variable Doppler boosting factor, computed as a function of the relativistic sum of the individual eddy and bulk jet velocities and our viewing angle to the jet. The total observed flux is found by integrating the radiation from the eddies over the turbulent spectrum. We consider jets that contain turbulent eddies that have either standard Kolmogorov or recently derived relativistic turbulence spectra. We also account…
One possible origin for polarization structures across jets of Active Galactic Nuclei (AGNs) with a central "spine" of orthogonal magnetic field and a "sheath" of longitudinal magnetic field along one or both edges of the jet is the presence of a helical jet magnetic field. Simultaneous Very Long Baseline Array (VLBA) polarization observations of AGN displaying partial or full spine--sheath polarization structures were obtained at 4.6, 5.0, 7.9, 8.9, 12.9 and 15.4 GHz, in order to search for additional evidence for helical jet magnetic fields, such as transverse Faraday rotation gradients (due…
We perform Monte Carlo simulations of transrelativistic shear acceleration dedicated to a jet-cocoon system of active galactic nuclei. A certain fraction of galactic cosmic rays in a halo is entrained, and sufficiently high-energy particles can be injected to the reacceleration process and further accelerated up to 100 EeV. We show that the shear reacceleration mechanism leads to a hard spectrum of escaping cosmic rays, $dL_E/dE\propto E^{-1}-E^0$, distinct from a conventional $E^{-2}$ spectrum. The supersolar abundance of ultrahigh-energy nuclei is achieved due to injections at TeV-PeV energi…
The evolution of powerful extragalactic jets is not only interesting by itself, but also for its impact on the evolution of the host galaxy and its surroundings. We have performed long-term axisymmetric numerical simulations of relativistic jets with different powers to study their evolution through an environment with a pressure and density gradient. Our results show key differences in the evolution of jets with different powers in terms of the spatial and temporal scales of energy deposition. According to our results, the observed morphology in X-ray cavities requires that an important fract…
Jets associated with Active Galactic Nuclei (AGN) have been observed for almost a century, initially at optical and radio wavelengths. They are now widely accepted as "exhausts" produced electromagnetically by the central, spinning, massive black hole and its orbiting, accreting gas. Observations at X-ray and, especially, gamma-ray energies have transformed our understanding of how these jets evolve dynamically, accelerate electrons (and positrons) and radiate throughout the entire electromagnetic spectrum. Some new approaches to modeling the powerful and rapidly variable TeV emission observed…
In this first paper from forthcoming series of works devoted to radio image of relativistic jets from active galactic nuclei the role of internal structure of a flow is discussed. We determine the radial profiles of all physical values for reasonable Michel magnetization parameter $σ_{\rm M}$ and ambient pressure $P_{\rm ext}$. Maps of Doppler boosting factor $δ$ and observed directions of linear polarization of synchrotron emission are also constructed.
In this paper we give a brief review of the astrophysics of active galactic nuclei (AGN). After a general introduction motivating the study of AGNs, we discuss our present understanding of the inner workings of the central engines, most likely accreting black holes with masses between a million and ten billion solar masses. We highlight recent results concerning the jets (collimated outflows) of AGNs derived from X-ray observations (Chandra) of kpc-scale jets and gamma-ray observations of AGNs (Fermi, Cherenkov telescopes) with jets closely aligned with the lines of sight (blazars), and discus…
We report the systematic analysis of knots, hotspots, and lobes in 57 active galactic nuclei (AGNs) to investigate the variation of the magnetic field along with the jet from the sub-pc base to the terminus in kpc-to-Mpc scales. Expanding the number of radio/X-ray samples in Kataoka & Stawarz (2005), we analyzed the data in 12 FR I and 30 FR II radio galaxies, 12 quasars, and 3 BL Lacs that contained 76 knots, 42 hotspots, and 29 radio lobes. We first derived the equipartition magnetic fields in the cores and then estimated those in various jet components by assuming $B_{\rm est}$ $\propto$ $d…
Relativistic jets of active galactic nuclei have been known to exist for 100 years. Blazars with their jet pointing close to our line of sight are some of the most variable and extreme objects in the universe, showing emission from radio to very-high-energy gamma rays. In this review, we cover relativistic jets of blazars from an observational perspective with the main goal of discussing how observations can be used to constrain theoretical models. We cover a range of topics from multiwavelength observations to imaging of jets with a special emphasis on current open questions in the field.
The classical diagrams of radio loudness and jet power as a function of mass and accretion rate of the central spacetime singularity in active galactic nuclei are reanalyzed by including the data of the recently discovered powerful relativistic jets in Narrow-Line Seyfert 1 Galaxies. The results are studied in the light of the known theories on the relativistic jets, indicating that while the Blandford-Znajek mechanism is sufficient to explain the power radiated by BL Lac Objects, it fails to completely account the power from quasars and Narrow-Line Seyfert 1. This favors the scenario outlined…
VLBI Detections of Compact Nuclei in Spiral-hosted Double-lobed Radio-loud Active Galactic Nuclei (DRAGNs): Evidence for Weak Parsec-Scale Jet Activity
Ulsan National Institute of Science and Technology (UNIST)（蔚山科学技术院）
The presence of a helical magnetic field threading the jet of an Active Galactic Nucleus (AGN) should give rise to a gradient in the observed Faraday rotation measure (RM) across the jet, due to the associated systematic change in the line-of-sight magnetic field. Reports of observations of transverse RM gradients across AGN jets have appeared in the literature starting from 2002, but concerns were raised about the resolution required for these gradients to be reliable, and there was a lack of a full understanding of the best approach to accurate estimation of the uncertainties of local RM val…
Extragalactic jets launched from the immediate vicinity of supermassive black holes in radio-loud active galactic nuclei (AGN) are key objects in modern astronomy and astroparticle physics. AGN jets carry a fraction of the total gravitational energy released during the accretion of matter onto supermassive black holes and are prime suspects as possible sources of ultrahigh-energy cosmic rays and the recently detected extraterrestrial neutrinos at PeV energies. TANAMI (Tracking Active galactic Nuclei with Austral Milliarcsecond Interferometry) is a multiwavelength program monitoring AGN jets of…
In the current paradigm, it is believed that the compact VLBI radio core of radio-loud active galactic nuclei (AGNi) represents the innermost upstream regions of relativistic outflows. These regions of AGN jets have generally been modeled by a conical outflow with a roughly constant opening angle and flow speed. Nonetheless, some works suggest that a parabolic geometry would be more appropriate to fit the high energy spectral distribution properties and it has been recently found that, at least in some nearby radio galaxies, the geometry of the innermost regions of the jet is parabolic. We com…
