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A multifrequency study of sub-parsec jets with the Event Horizon Telescope

Context. The 2017 observing campaign of the Event Horizon Telescope (EHT) delivered the first very long baseline interferometry (VLBI) images at the observing frequency of 230 GHz, leading to a number of unique studies on black holes and relativistic jets from active galactic nuclei (AGN). In total, eighteen sources were observed, including the main science targets, Sgr A* and M 87, and various calibrators. Sixteen sources were AGN.Aims. We investigated the morphology of the sixteen AGN in the EHT 2017 data set, focusing on the properties of the VLBI cores: size, flux density, and brightness temperature. We studied their dependence on the observing frequency in order to compare it with the Blandford-Königl (BK) jet model. In particular, we aimed to study the signatures of jet acceleration and magnetic energy conversion.Methods. We modeled the source structure of seven AGN in the EHT 2017 data set using linearly polarized circular Gaussian components (1749+096, 1055+018, BL Lac, J0132–1654, J0006–0623, CTA 102, and 3C 454.3) and collected results for the other nine AGN from dedicated EHT publications, complemented by lower frequency data in the 2–86 GHz range. Combining these data into a multifrequency EHT+ data set, we studied the dependences of the VLBI core component flux density, size, and brightness temperature on the frequency measured in the AGN host frame (and hence on the distance from the central black hole), characterizing them with power law fits. We compared the observations with the BK jet model and estimated the magnetic field strength dependence on the distance from the central black hole.Results. Our observations spanning event horizon to parsec scales indicate a deviation from the standard BK model, particularly in the decrease of the brightness temperature with the observing frequency. Only some of the discrepancies may be alleviated by tweaking the model parameters or the jet collimation profile. Either bulk acceleration of the jet material, energy transfer from the magnetic field to the particles, or both are required to explain the observations. For our sample, we estimate a general radial dependence of the Doppler factor δ ∝ r≤0.5. This interpretation is consistent with a magnetically accelerated sub-parsec jet. We also estimate a steep decrease of the magnetic field strength with radius B ∝ r−3, hinting at jet acceleration or efficient magnetic energy dissipation.Key words: techniques: interferometric / galaxies: active / galaxies: jets / galaxies: nuclei / quasars: general / quasars: supermassive black holes⋆⋆ Deceased.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

COLLIMATION AND CONFINEMENT OF MAGNETIC JETS BY EXTERNAL MEDIA

We study the collimation of a highly magnetized jet by a surrounding cocoon that forms as a result of the interaction of the jet with the external medium. We show that in regions where the jet is well confined by the cocoon, current-driven instabilities should develop over timescales shorter than the expansion time of the jet's head. We speculate that these instabilities would give rise to complete magnetic field destruction, whereby the jet undergoes a transition from high to low sigma above the collimation zone. Using this assumption, we construct a self-consistent model for the evolution of the jet-cocoon system in an ambient medium of arbitrary density profile. We apply the model to jet breakout in long gamma-ray bursts (GRBs) and show that the jet is highly collimated inside the envelope of the progenitor star and is likely to remain confined well after breakout. We speculate that this strong confinement may provide a channel for magnetic field conversion in GRB outflows, whereby the hot, low-sigma jet section thereby produced is the source of the photospheric emission observed in many bursts.

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HYPERACCRETING BLACK HOLE AS GAMMA-RAY BURST CENTRAL ENGINE. I. BARYON LOADING IN GAMMA-RAY BURST JETS

A hyperaccreting stellar-mass black hole has been long speculated as the best candidate for the central engine of gamma-ray bursts (GRBs). Recent rich observations of GRBs by space missions such as Swift and Fermi pose new constraints on GRB central engine models. In this paper, we study the baryon-loading processes of a GRB jet launched from a black hole central engine. We consider a relativistic jet powered by {nu} {nu}-bar -annihilation or by the Blandford-Znajek (BZ) mechanism. We consider baryon loading from a neutrino-driven wind launched from a neutrino-cooling-dominated accretion flow. For a magnetically dominated BZ jet, we consider neutron drifting from the magnetic wall surrounding the jet and subsequent positron capture and proton-neutron inelastic collisions. The minimum baryon loads in both types of jet are calculated. We find that in both cases a more luminous jet tends to be more baryon poor. A neutrino-driven ''fireball'' is typically ''dirtier'' than a magnetically dominated jet, while a magnetically dominated jet can be much cleaner. Both models have the right scaling to interpret the empirical {Gamma}-L{sub iso} relation discovered recently. Since some neutrino-driven jets have too much baryon loading as compared with the data, we suggest that at least a good fraction of GRBs should have a magnetically dominated central engine.

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THE PARABOLIC JET STRUCTURE IN M87 AS A MAGNETOHYDRODYNAMIC NOZZLE

The structure and dynamics of the M87 jet from sub-milliarcsec to arcsecond scales are continuously examined. We analyzed the Very Long Baseline Array archival data taken at 43 and 86 GHz to measure the size of very long baseline interferometry (VLBI) cores. Millimeter/sub-millimeter VLBI cores are considered as innermost jet emissions, which has been originally suggested by Blandford and Königl. Those components fairly follow an extrapolated parabolic streamline in our previous study so that the jet has a single power-law structure with nearly 5 orders of magnitude in the distance starting from the vicinity of the supermassive black hole (SMBH), less than 10 Schwarzschild radius (r{sub s}). We further inspect the jet parabolic structure as a counterpart of the magnetohydrodynamic (MHD) nozzle in order to identify the property of a bulk acceleration. We interpret that the parabolic jet consists of Poynting-flux dominated flows, powered by large-amplitude, nonlinear torsional Alfvén waves. We examine the non-relativistic MHD nozzle equation in a parabolic shape. The nature of trans-fast magnetosonic flow is similar to the one of transonic solution of Parker's hydrodynamic solar wind; the jet becomes super-escape as well as super-fast magnetosonic at around ∼10{sup 3} r{sub s}, while the upstream trans-Alfvénic flow speed increases linearly as a function of the distance at ∼10{sup 2}-10{sup 3} r{sub s}. We here point out that this is the first evidence to identify these features in astrophysical jets. We propose that the M87 jet is magnetically accelerated, but thermally confined by the stratified interstellar medium inside the sphere of gravitational influence of the SMBH potential, which may be a norm in active galactic nucleus jets.

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PHYSICAL PARAMETERS OF STANDARD AND BLOWOUT JETS

The X-ray Telescope on board the Hinode mission revealed the occurrence, in polar coronal holes, of much more numerous jets than previously indicated by the Yohkoh/Soft X-ray Telescope. These plasma ejections can be of two types, depending on whether they fit the standard reconnection scenario for coronal jets or if they include a blowout-like eruption. In this work, we analyze two jets, one standard and one blowout, that have been observed by the Hinode and STEREO experiments. We aim to infer differences in the physical parameters that correspond to the different morphologies of the events. To this end, we adopt spectroscopic techniques and determine the profiles of the plasma temperature, density, and outflow speed versus time and position along the jets. The blowout jet has a higher outflow speed, a marginally higher temperature, and is rooted in a stronger magnetic field region than the standard event. Our data provide evidence for recursively occurring reconnection episodes within both the standard and the blowout jet, pointing either to bursty reconnection or to reconnection occurring at different locations over the jet lifetimes. We make a crude estimate of the energy budget of the two jets and show how energy is partitioned among different forms. Also, we show that the magnetic energy that feeds the blowout jet is a factor of 10 higher than the magnetic energy that fuels the standard event.

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NUMERICAL SIMULATIONS OF CHROMOSPHERIC ANEMONE JETS ASSOCIATED WITH MOVING MAGNETIC FEATURES

Observations with the space-based solar observatory Hinode show that small-scale magnetic structures in the photosphere are found to be associated with a particular class of jets of plasma in the chromosphere called anemone jets. The goal of our study is to conduct a numerical experiment of such chromospheric anemone jets related to the moving magnetic features (MMFs). We construct a 2.5 dimensional numerical MHD model to describe the process of magnetic reconnection between the MMFs and the pre-existing ambient magnetic field, which is driven by the horizontal motion of the magnetic structure in the photosphere. We include thermal conduction parallel to the magnetic field and optically thin radiative losses in the corona to account for a self-consistent description of the evaporation process during the heating of the plasma due to the reconnection process. The motion of the MMFs leads to the expected jet and our numerical results can reproduce many observed characteristics of chromospheric anemone jets, topologically and quantitatively. As a result of the tearing instability, plasmoids are generated in the reconnection process that are consistent with the observed bright moving blobs in the anemone jets. An increase in the thermal pressure at the base of the jet is also driven by the reconnection, which induces a train of slow-mode shocks propagating upward. These shocks are a secondary effect, and only modulate the outflow of the anemone jet. The jet itself is driven by the energy input due to the reconnection of the MMFs and the ambient magnetic field.

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MOJAVE. XII. ACCELERATION AND COLLIMATION OF BLAZAR JETS ON PARSEC SCALES

We report on the acceleration properties of 329 features in 95 blazar jets from the MOJAVE Very Long Baseline Array program. Nearly half the features and three-quarters of the jets show significant changes in speed and/or direction. In general, apparent speed changes are distinctly larger than changes in direction, indicating that changes in the Lorentz factors of jet features dominate the observed speed changes rather than bends along the line of sight. Observed accelerations tend to increase the speed of features near the jet base, ≲ 10-20 pc projected, and decrease their speed at longer distances. The range of apparent speeds at a fixed distance in an individual jet can span a factor of a few, indicating that shock properties and geometry may influence the apparent motions; however, we suggest that the broad trend of jet features increasing their speed near the origin is due to an overall acceleration of the jet flow out to deprojected distances of the order of 10{sup 2} pc, beyond which the flow begins to decelerate or remains nearly constant in speed. We estimate intrinsic rates of change of the Lorentz factors in the galaxy frame of the order of Γ-dot /Γ≃10{sup −3} to 10{sup –2} yr{sup –1}, which can lead to total Lorentz factor changes of a factor of a few on the length scales observed here. Finally, we also find evidence for jet collimation at projected distances of ≲ 10 pc in the form of the non-radial motion and bending accelerations that tend to better align features with the inner jet.

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STABILITY OF ROTATING MAGNETIZED JETS IN THE SOLAR ATMOSPHERE. I. KELVIN–HELMHOLTZ INSTABILITY

Observations show various jets in the solar atmosphere with significant rotational motions, which may undergo instabilities leading to heat ambient plasma. We study the Kelvin–Helmholtz instability (KHI) of twisted and rotating jets caused by the velocity jumps near the jet surface. We derive a dispersion equation with appropriate boundary conditions for total pressure (including centrifugal force of tube rotation), which governs the dynamics of incompressible jets. Then, we obtain analytical instability criteria of KHI in various cases, which were verified by numerical solutions to the dispersion equation. We find that twisted and rotating jets are unstable to KHI when the kinetic energy of rotation is more than the magnetic energy of the twist. Our analysis shows that the azimuthal magnetic field of 1–5 G can stabilize observed rotations in spicule/macrospicules and X-ray/extreme-ultraviolet (EUV) jets. On the other hand, nontwisted jets are always unstable to KHI. In this case, the instability growth time is several seconds for spicule/macrospicules and a few minutes (or less) for EUV/X-ray jets. We also find that standing kink and torsional Alfvén waves are always unstable near the antinodes, owing to the jump of azimuthal velocity at the surface, while the propagating waves are generally stable. Kelvin–Helmholtz (KH) vortices may lead to enhanced turbulence development and heating of surrounding plasma; therefore, rotating jets may provide energy for chromospheric and coronal heating.

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MAGNETIZED JETS DRIVEN BY THE SUN: THE STRUCTURE OF THE HELIOSPHERE REVISITED

The classic accepted view of the heliosphere is a quiescent, comet-like shape aligned in the direction of the Sun’s travel through the interstellar medium (ISM) extending for thousands of astronomical units (AUs). Here, we show, based on magnetohydrodynamic (MHD) simulations, that the tension (hoop) force of the twisted magnetic field of the Sun confines the solar wind plasma beyond the termination shock and drives jets to the north and south very much like astrophysical jets. These jets are deflected into the tail region by the motion of the Sun through the ISM similar to bent galactic jets moving through the intergalactic medium. The interstellar wind blows the two jets into the tail but is not strong enough to force the lobes into a single comet-like tail, as happens to some astrophysical jets. Instead, the interstellar wind flows around the heliosphere and into the equatorial region between the two jets. As in some astrophysical jets that are kink unstable, we show here that the heliospheric jets are turbulent (due to large-scale MHD instabilities and reconnection) and strongly mix the solar wind with the ISM beyond 400 AU. The resulting turbulence has important implications for particle acceleration in the heliosphere. The two-lobe structure is consistent with the energetic neutral atom (ENA) images of the heliotail from IBEX where two lobes are visible in the north and south and the suggestion from the Cassini ENAs that the heliosphere is “tailless.”.

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HH 1158: THE LOWEST LUMINOSITY EXTERNALLY IRRADIATED HERBIG–HARO JET

We have identified a new externally irradiated Herbig–Haro (HH) jet, HH 1158, within ∼2 pc of the massive OB type stars in the σ Orionis cluster. At an L{sub bol} ∼ 0.1 L{sub ⊙}, HH 1158 is the lowest luminosity irradiated HH jet identified to date in any cluster. Results from the analysis of high-resolution optical spectra indicate asymmetries in the brightness, morphology, electron density, velocity, and the mass outflow rates for the blue and redshifted lobes. We constrain the position angle of the HH 1158 jet at 102° ± 5°. The mass outflow rate and the mean accretion rate for HH 1158 using multiple diagnostics are estimated to be (5.2 ± 2.6) × 10{sup −10} M{sub ⊙} yr{sup −1} and (3.0 ± 1.0) × 10{sup −10} M{sub ⊙} yr{sup −1}, respectively. The properties for HH 1158 are notably similar to the externally irradiated HH 444–HH 447 jets previously identified in σ Orionis. In particular, the morphology is such that the weaker jet beam is tilted toward the massive stars, indicating a higher extent of photo-evaporation. The high value for the Hα/[S ii] ratio is also consistent with the ratios measured in other irradiated jets, including HH 444–HH 447. The presence of an extended collimated jet that is bipolar and the evidence of shocked emission knots make HH 1158 the first unique case of irradiated HH jets at the very low-luminosity end, and provides an opportunity to learn the physical properties of very faint HH jet sources.

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Enhanced Deuteron Coalescence Probability in Jets

The transverse-momentum ($p_T$) spectra and coalescence parameters $B_2$ of (anti)deuterons are measured in p-p collisions at $\sqrt{s}=13$ $\text{TeV}$ for the first time in and out of jets. In this measurement, the direction of the leading particle with the highest $p_T$ in the event ($p^{lead}_T > 5 GeV/c$) is used as an approximation for the jet axis. The event is consequently divided into three azimuthal regions, and the jet signal is obtained as the difference between the toward region, that contains jet fragmentation products in addition to the underlying event (UE), and the transverse region, which is dominated by the UE. The coalescence parameter in the jet is found to be approximately a factor of 10 larger than that in the underlying event. This experimental observation is consistent with the coalescence picture and can be attributed to the smaller average phase-space distance between nucleons in the jet cone as compared with the underlying event. The results presented in this Letter are compared to predictions from a simple nucleon coalescence model, where the phase-space distributions of nucleons are generated using pythia8 with the Monash 2013 tuning, and to predictions from a deuteron production model based on ordinary nuclear reactions with parametrized energy-dependent cross sections tuned on data. The latter model is implemented in pythia8.3. Both models reproduce the observed large difference between in-jet and out-of-jet coalescence parameters, although the almost flat trend of the $B^{Jet}_2$ is not reproduced by the models, which instead give a decreasing trend.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Observation of Enhanced Long-Range Elliptic Anisotropies Inside High-Multiplicity Jets in p p Collisions at s = 13 TeV

A search for collective effects inside jets produced in proton-proton collisions is performed via correlation measurements of charged particles using the CMS detector at the CERN LHC. The analysis uses data collected at a center-of-mass energy of s = 13 TeV , corresponding to an integrated luminosity of 138 fb − 1 . Jets are reconstructed with the anti- k T algorithm with a distance parameter of 0.8 and are required to have transverse momentum greater than 550 GeV and pseudorapidity | η jet | < 1.6 . Two-particle correlations among the charged particles within the jets are studied as functions of the particles’ azimuthal angle and pseudorapidity separations ( Δ ϕ * and Δ η * ) in a jet coordinate basis, where particles’ η * , ϕ * are defined relative to the direction of the jet. The correlation functions are studied in classes of in-jet charged-particle multiplicity up to N ch j ≈ 100 . Fourier harmonics are extracted from long-range azimuthal correlation functions to characterize azimuthal anisotropy for | Δ η * | > 2 . For low- N ch j jets, the long-range elliptic anisotropic harmonic, v 2 * , is observed to decrease with N ch j . This trend is well described by Monte Carlo event generators. However, a rising trend for v 2 * emerges at N ch j ≳ 80 , hinting at a possible onset of collective behavior, which is not reproduced by the models tested. This observation yields new insights into the dynamics of jet evolution in the vacuum. © 2024 CERN, for the CMS Collaboration 2024 CERN

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Hard-photon-triggered jets in 𝑝−𝑝 and 𝐴−𝐴 collisions

An investigation of high-transverse-momentum (high-𝑝 𝑇 ) photon-triggered jets in proton-proton (𝑝−𝑝) and ion-ion (𝐴−𝐴) collisions at $\sqrt{s_{NN}}$=0.2 and 5.02TeV is carried out, using the multistage description of in-medium jet evolution. Monte Carlo simulations of hard scattering and energy loss in heavy-ion collisions are performed using parameters tuned in a previous study of the nuclear modification factor (𝑅 𝐴⁢𝐴 ) for inclusive jets and high-𝑝𝑇 hadrons. We obtain a good reproduction of the experimental data for photon-triggered jet 𝑅 𝐴⁢𝐴 , as measured by the ATLAS detector, the distribution of the ratio of jet to photon 𝑝 𝑇 (𝑋 𝐽⁢𝛾 ), measured by both CMS and ATLAS, and the photon-jet azimuthal correlation as measured by CMS. We obtain a moderate description of the photon-triggered jet 𝐼 𝐴⁢𝐴 , as measured by STAR. A noticeable improvement in the comparison is observed when one goes beyond prompt photons and includes bremsstrahlung and decay photons, revealing their significance in certain kinematic regions, particularly at 𝑋 𝐽⁢𝛾 >1. Moreover, azimuthal angle correlations demonstrate a notable impact of bremsstrahlung photons on the distribution, emphasizing their role in accurately describing experimental results. This work highlights the success of the multistage model of jet modification to straightforwardly predict (this set of) photon-triggered jet observables. This comparison, along with the role played by bremsstrahlung photons, has important consequences on the inclusion of such observables in a future Bayesian analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ESTIMATING LONG GRB JET OPENING ANGLES AND REST-FRAME ENERGETICS

We present a method to estimate the jet opening angles of long duration gamma-ray bursts (GRBs) using the prompt gamma-ray energetics and an inversion of the Ghirlanda relation, which is a correlation between the time-integrated peak energy of the GRB prompt spectrum and the collimation-corrected energy in gamma-rays. The derived jet opening angles using this method and detailed assumptions match well with the corresponding inferred jet opening angles obtained when a break in the afterglow is observed. Furthermore, using a model of the predicted long GRB redshift probability distribution observable by the Fermi Gamma-ray Burst Monitor (GBM), we estimate the probability distributions for the jet opening angle and rest-frame energetics for a large sample of GBM GRBs for which the redshifts have not been observed. Previous studies have only used a handful of GRBs to estimate these properties due to the paucity of observed afterglow jet breaks, spectroscopic redshifts, and comprehensive prompt gamma-ray observations, and we potentially expand the number of GRBs that can be used in this analysis by more than an order of magnitude. In this analysis, we also present an inferred distribution of jet breaks which indicates that a large fraction of jet breaks are not observable with current instrumentation and observing strategies. We present simple parameterizations for the jet angle, energetics, and jet break distributions so that they may be used in future studies.

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THE INTERNAL STRUCTURE OF OVERPRESSURED, MAGNETIZED, RELATIVISTIC JETS

This work presents the first characterization of the internal structure of overpressured, steady superfast-magnetosonic relativistic jets in connection with their dominant type of energy. To this aim, relativistic magnetohydrodynamic simulations of different jet models threaded by a helical magnetic field have been analyzed covering a wide region in the magnetosonic Mach number–specific internal energy plane. The merit of this plane is that models dominated by different types of energy (internal energy: hot jets; rest-mass energy: kinetically dominated jets; magnetic energy: Poynting-flux-dominated jets) occupy well-separated regions. The analyzed models also cover a wide range of magnetizations. Models dominated by the internal energy (i.e., hot models, or Poynting-flux-dominated jets with magnetizations larger than but close to one) have a rich internal structure characterized by a series of recollimation shocks and present the largest variations in the flow Lorentz factor (and internal energy density). Conversely, in kinetically dominated models, there is not much internal or magnetic energy to be converted into kinetic, and the jets are featureless with small variations in the flow Lorentz factor. The presence of a significant toroidal magnetic field threading the jet produces large gradients in the transversal profile of the internal energy density. Poynting-flux-dominated models with high magnetization (≈10 or larger) are prone to be unstable against magnetic pinch modes, which sets limits on the expected magnetization in parsec-scale active galactic nucleus jets or constrains their magnetic field configuration.

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DETECTING RELATIVISTIC X-RAY JETS IN HIGH-REDSHIFT QUASARS

We analyze Chandra X-ray images of a sample of 11 quasars that are known to contain kiloparsec scale radio jets. The sample consists of five high-redshift ( z ≥ 3.6) flat-spectrum radio quasars, and six intermediate redshift (2.1 < z < 2.9) quasars. The data set includes four sources with integrated steep radio spectra and seven with flat radio spectra. A total of 25 radio jet features are present in this sample. We apply a Bayesian multi-scale image reconstruction method to detect and measure the X-ray emission from the jets. We compute deviations from a baseline model that does not include the jet, and compare observed X-ray images with those computed with simulated images where no jet features exist. This allows us to compute p -value upper bounds on the significance that an X-ray jet is detected in a pre-determined region of interest. We detected 12 of the features unambiguously, and an additional six marginally. We also find residual emission in the cores of three quasars and in the background of one quasar that suggest the existence of unresolved X-ray jets. The dependence of the X-ray to radio luminosity ratio on redshift is a potential diagnostic of the emission mechanism, since the inverse Compton scattering of cosmic microwave background photons (IC/CMB) is thought to be redshift dependent, whereas in synchrotron models no clear redshift dependence is expected. We find that the high-redshift jets have X-ray to radio flux ratios that are marginally inconsistent with those from lower redshifts, suggesting that either the X-ray emissions are due to the IC/CMB rather than the synchrotron process, or that high-redshift jets are qualitatively different.

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ON THE MAGNETIC AND ENERGY CHARACTERISTICS OF RECURRENT HOMOLOGOUS JETS FROM AN EMERGING FLUX

In this paper, we present the detailed analysis of recurrent homologous jets originating from an emerging negative magnetic flux at the edge of an active region. The observed jets show multithermal features. Their evolution shows high consistence with the characteristic parameters of the emerging flux, suggesting that with more free magnetic energy, the eruptions tend to be more violent, frequent, and blowout-like. The average temperature, average electron number density, and axial speed are found to be similar for different jets, indicating that they should have been formed by plasmas from similar origins. Statistical analysis of the jets and their footpoint region conditions reveals a strong positive relationship between the footpoint region total 131 Å intensity enhancement and jets’ length/width. Stronger linearly positive relationships also exist between the total intensity enhancement/thermal energy of the footpoint regions and jets’ mass/kinetic/thermal energy, with higher cross-correlation coefficients. All the above results together confirm the direct relationship between the magnetic reconnection and the jets and validate the important role of magnetic reconnection in transporting large amounts of free magnetic energy into jets. It is also suggested that there should be more free energy released during the magnetic reconnection of blowout than of standard jet events.

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Disk–Jet Connection in Active Supermassive Black Holes in the Standard Accretion Disk Regime

We study the disk–jet connection in supermassive black holes by investigating the properties of their optical and radio emissions utilizing the SDSS DR7 and the NVSS catalogs. Our sample contains 7017 radio-loud quasars with detection both at 1.4 GHz and SDSS optical spectra. Using this radio-loud quasar sample, we investigate the correlation among the jet power (${P}_{\mathrm{jet}}$), the bolometric disk luminosity (${L}_{\mathrm{disk}}$), and the black hole mass (${M}_{\mathrm{BH}}$) in the standard accretion disk regime. We find that the jet powers correlate with the bolometric disk luminosities as $\mathrm{log}{P}_{\mathrm{jet}}=(0.96\pm 0.012)\mathrm{log}{L}_{\mathrm{disk}}+(0.79\pm 0.55)$. This suggests the jet production efficiency of ${\eta }_{\mathrm{jet}}\simeq {1.1}_{-0.76}^{+2.6}\,\times {10}^{-2}$ assuming the disk radiative efficiency of 0.1, implying low black hole spin parameters and/or low magnetic flux for radio-loud quasars. But it can be also due to the dependence of this efficiency on the geometrical thickness of the accretion flow, which is expected to be small for quasars accreting at the disk Eddington ratios $0.01\lesssim \lambda \lesssim 0.3$. This low jet production efficiency does not significantly increase even if we set the disk radiative efficiency to be 0.3. We also investigate the fundamental plane in our samples among ${P}_{\mathrm{jet}}$, ${L}_{\mathrm{disk}}$, and ${M}_{\mathrm{BH}}$. In conclusion, we could not find a statistically significant fundamental plane for radio-loud quasars in the standard accretion regime.

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