Observations of magnetic flux compression in jet impact experiments

The astrophysical jet experiment at Caltech generates a T=2–5 eV, n=10²¹–10²² m⁻³ plasma jet using coplanar disk electrodes linked by a poloidal magnetic field. A 100 kA current generates a toroidal magnetic field; the toroidal field pressure inflates the poloidal flux surface, magnetically driving the jet. The jet travels at up to 50 km/s for ∼20–25 cm before colliding with a cloud of initially neutral gas. We study the interaction of the jet and the cloud in analogy to an astrophysical jet impacting a molecular cloud. Diagnostics include magnetic probe arrays, a 12-channel spectroscopic system and a fast camera with optical filters. When a hydrogen plasma jet collides with an argon target cloud, magnetic measurements show the magnetic flux compressing as the plasma jet deforms. As the plasma jet front slows and the plasma piles up, the density of the frozen-in magnetic flux increases.     

On the local magnetorotational instability of astrophysical jets

We present the local linear stability analysis of rotating jets confined by a toroidal magnetic field. Under the thin flux tube approximation, we derive the equation of motion for slender magnetic flux tubes. In addition to the terms responsible for the conventional instability of the toroidal magnetic field, a term related to the magnetic buoyancy and a term corresponding to the differential rotation become relevant for the stability properties. We find that the rigid rotation stabilizes while the differential rotational destabilizes the jet in a way similar to the Balbus–Hawley instability. Within the frame of our local analysis, we find that if the azimuthal velocity is of the order of or higher than the Alfvén azimuthal speed, the rigidly rotating part of the jet interior can be completely stabilized, while the strong shearing instability operates in the transition layer between the rotating jet interior and the external medium. This can explain the limb-brightening effect observed in several jets. However, it is still possible to find jet equilibria that are stable all across the jet, even in the presence of differential rotation. We discuss observational consequences of these results.     

The physics of E × B-drifting jets

E × B-drifting jets have been generally ignored for the past 25 years even though they may well describe all the astrophysical jet sources, both on galactic and stellar scales. Here we present closed-form solutions for their joint field-and-particle distribution, argue that the observed jets are near equipartition, with extremely relativistic, monoenergetic e^±-pairs of bulk Lorentz factor γ ≲ 10⁴, and are first-order stable. We describe plausible mechanisms for the jets’ (i) formation, (ii) propagation, and (iii) termination. Wherever a beam meets with resistance, its frozen-in Poynting flux transforms the delta-shaped energy distribution of the pairs into an almost white power law,E ² N _E ∼E ^−∫ with ∫ ≳ 0, via single-step falls through the huge convected potential.     

On the MHD Acceleration of Astrophysical Jets

We present a 2.5D magnetohydrodynamic (MHD) simulation of the acceleration of a collimated jet from a magnetized accretion disk. We employ a MHD Adaptive Mesh Refinement (AMR) code (FLASH—University of Chicago). Thanks to this tool we can follow the evolution of the system for many dynamical timescales with a high-spatial resolution. Assuming an initial condition in which a Keplerian disk, thus with no accretion motions, is threaded by a uniform poloidal magnetic field, we show how both the accretion flow and the acceleration of the outflow occur, and we present in detail which are the forces responsible for the jet launching and collimation. Our simulation also shows how the collimating forces due to the self-generated toroidal magnetic field can produce some peculiar knotty features.     

Doppler boosting, superluminal motion, and the kinematics of AGN jets

We discuss results from a decade long program to study the fine-scale structure and the kinematics of relativistic AGN jets with the aim of better understanding the acceleration and collimation of the relativistic plasma forming AGN jets. From the observed distribution of brightness temperature, apparent velocity, flux density, time variability, and apparent luminosity, the intrinsic properties of the jets including Lorentz factor, luminosity, orientation, and brightness temperature are discussed. Special attention is given to the jet in M87, which has been studied over a wide range of wavelengths and which, due to its proximity, is observed with excellent spatial resolution. Most radio jets appear quite linear, but we also observe curved non-linear jets and non-radial motions. Sometimes, different features in a given jet appear to follow the same curved path but there is evidence for ballistic trajectories as well. The data are best fit with a distribution of Lorentz factors extending up to γ∼30 and intrinsic luminosity up to ∼10²⁶ W Hz⁻¹. In general, gamma-ray quasars may have somewhat larger Lorentz factors than non gamma-ray quasars. Initially the observed brightness temperature near the base of the jet extend up to ∼5×10¹³ K which is well in excess of the inverse Compton limit and corresponds to a large excess of particle energy over magnetic energy. However, more typically, the observed brightness temperatures are ∼2×10¹¹ K, i.e., closer to equipartition.     

Constraints on the Solar Internal Magnetic Field from a Buoyancy Driven Solar Dynamo

We report here results from a dynamo model developed on the lines of the Babcock-Leighton idea that the poloidal field is generated at the surface of the Sun from the decay of active regions. In this model magnetic buoyancy is handled with a realistic recipe – wherein toroidal flux is made to erupt from the overshoot layer wherever it exceeds a specified critical field B _c (10⁵ G). The erupted toroidal field is then acted upon by the α-effect near the surface to give rise to the poloidal field. In this paper we study the effect of buoyancy on the dynamo generated magnetic fields. Specifically, we show that the mechanism of buoyant eruption and the subsequent depletion of the toroidal field inside the overshoot layer, is capable of constraining the magnitude and distribution of the magnetic field there. We also believe that a critical study of this mechanism may give us new information regarding the solar interior and end with an example, where we propose a method for estimating an upper limit of the difusivity within the overshoot layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes

A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 10⁵ G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 10⁵-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the “Ω effect” in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 10⁵-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of “convective collapse” for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed.     

黑洞双星的B型QPO频率与幂律通量的相关性的解释

观测表明, 黑洞双星的B型准周期振荡(Quasi-Periodic Oscillation, QPO)频率与幂律通量之间存在正相关性. 试图基于阿尔文波振荡模型定量解释该相关性. 标准薄吸积盘辐射通量极大值处的阿尔文波振荡产生QPO. 标准薄盘上的软光子与冕或喷流基部的热电子介质发生逆康普顿散射产生幂律通量. 通过吸积率的连续变化, 得到QPO频率与幂律通量关系的分析解和数值解. 模拟得到的相关性在合理的参数范围内与观测值相吻合. QPO频率与幂律通量的正相关性可以理解为, 较强的磁场导致较高的阿尔文波频率和较高的电子温度从而得到较高的幂律通量. 结果表明B型QPO可能与吸积盘或喷流中的环向磁场的活动有关.     

Experimental Studies of Magnetically Driven Plasma Jets

We present experimental results on the formation of supersonic, radiatively cooled jets driven by pressure due to the toroidal magnetic field generated by the 1.5 MA, 250 ns current from the MAGPIE generator. The morphology of the jet produced in the experiments is relevant to astrophysical jet scenarios in which a jet on the axis of a magnetic cavity is collimated by a toroidal magnetic field as it expands into the ambient medium. The jets in the experiments have similar Mach number, plasma beta and cooling parameter to those in protostellar jets. Additionally the Reynolds, magnetic Reynolds and Peclet numbers are much larger than unity, allowing the experiments to be scaled to astrophysical flows. The experimental configuration allows for the generation of episodic magnetic cavities, suggesting that periodic fluctuations near the source may be responsible for some of the variability observed in astrophysical jets. Preliminary measurements of kinetic, magnetic and Poynting energy of the jets in our experiments are presented and discussed, together with estimates of their temperature and trapped toroidal magnetic field.     

Ejector and bipolar outflow of the radio galaxy M87

The superfine structure of the jet formation region in the radio galaxy M87 has been investigated. An accretion disk and high- and low-velocity jet and counterjet components have been identified. The high-velocity bipolar outflow is ejected from the central disk region, a nozzle 4 mpc in diameter, while the low-velocity one is ejected from a ring 60 mpc in diameter and 14 mpc in width. The low-velocity plasma flow is a hollow tube with a built-in helix. The observed helical structure of the high-velocity jet is determined by precession. The components of the structure, its disk and bipolar outflow, suggest solid-body rotation. Ring currents and aligned magnetic fields are generated in them under the action of an external magnetic field. The bipolar outflows are ejected coaxially but in opposite directions—along and opposite to the disk field. As a result, the jet flow accelerates, while the counterjet one decelerates. This causes the extent of the region of radiative cooling of the ejected relativistic electrons in the counterjet to decrease and maintains their “afterglow” at large distances in the jet. The high collimation of the rotating flows is determined by their interaction with the environment.     

A 2D numerical study of explosive events in the solar atmosphere

Two-dimensional (2D) compressible magnetohydrodynamic simulations are performed to explore the idea that the asymmetric reconnection between newly emerging intranetwork magnetic field flux and pre-existing network flux causes the explosive events in the solar atmosphere. The dependence of the reconnection rate as a function of time on the density and temperature of the emerging flux are investigated. For a Lundquist number of L _u= 5000 we find that the tearing mode instability can lead to the formation and growth of small magnetic islands. Depending on the temperature and density ratio of the emerging plasma, the magnetic island can be lifted upward and convected out of the top boundary, or is suppressed downward and convected out of the top boundary, or is suppressed downward nad submerged below the bottom boundary. The motions of the magnetic islands with different direction are accompanied respectively with upward or downward high velocity flow which might be associated with the red- and blue-shifted components detected in the explosive events.     

Frequency spectrum of toroidal Alfvén mode in a neutron star with Ferraro’s form of nonhomogeneous poloidal magnetic field

Using the energy variational method of magneto-solid-mechanical theory of a perfectly conducting elastic medium threaded by magnetic field, the frequency spectrum of Lorentz-force-driven global torsional nodeless vibrations of a neutron star with Ferraro’s form of axisymmetric poloidal nonhomogeneous internal and dipole-like external magnetic field is obtained and compared with that for this toroidal Alfvén mode in a neutron star with homogeneous internal and dipolar external magnetic field. The relevance of considered asteroseismic models to quasi-periodic oscillations of the X-ray flux during the ultra powerful outbursts of SGR 1806−20 and SGR 1900+14 is discussed.     

The Pressure Limitations on Flux Pile-up Reconnection

The problem of the plasma pressure limitations on the rapidity of flux pile-up magnetic reconnection is re-examined, following the claim made by Jardine and Allen (1998) that the limitations can be removed by relaxing the assumption of zero-vorticity two-dimensional plasma flows. It is shown that for a two-dimensional stagnation point flow with nonzero vorticity the magnetic merging rate cannot exceed the Sweet–Parker scaling in a low-beta plasma. The pressure limitation appears to be much less restrictive for weak three-dimensional flux pile-up, provided the perturbation length scale in the third dimension is much less than the global length scale. The actual reconnection rate in the latter case, however, is much lower than this upper estimate unless the current sheet width is also much less than the global scale.     

Robust Scalings in Compressible Flux Pile-Up Reconnection

Flux pile-up magnetic reconnection is traditionally considered only for incompressible plasmas. The question addressed in this paper is whether the pile-up scalings with resistivity are robust when plasma compressibility is taken into account. A simple analytical argument makes it possible to understand why the transition from a highly compressible limit to the incompressible one is difficult to discern in typical simulations spanning a few decades in resistivity. From a practical standpoint, however, flux pile-up reconnection in a compressible plasma can lead to anomalous electric resistivity in the current sheet and flare-like energy release of magnetic energy in the solar corona.     

The equilibrium of coronal flux tubes under toroidal forces

The properties of slender isolated flux tubes, taking into account curvature effects, were investigated by Parker (1975, 1979) and Spruit (1981), and many studies have been made concerning the equilibrium of slender flux tubes in the solar corona. In this paper we use a different approach considering the coronal loop as a part of a circular torus and studying the position of its top when the loop is in equilibrium under toroidal forces. Toroidal forces were considered by Shafranov (1966) for toroidal pinches and the equilibrium can be studied for different values of the toroidal current intensity and external magnetic field. The results show that it is possible to have a coronal flux tube in equilibrium without considering gravity and external magnetic field. Furthermore, the total twist of the flux tube and its variation with the toroidal intensity has been studied.     

The rate of flux pile-up magnetic reconnection in reduced MHD

The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 10²⁵– 10²⁶ erg s^–1and heating of quiet coronal loops are within the compass of the model.     

Flare-like energy release by flux pile-up reconnection

Flux pile-up magnetic merging solutions are discussed using the simple robust arguments of traditional steady-state reconnection theory. These arguments determine a unique scaling for the field strength and thickness of the current layer, namely B _s^–1/3, l^2/3, which are consistent with a variety of plasma inflow conditions. Next we demonstrate that flux pile-up merging can also be understood in terms of exact magnetic annihilation solutions. Although simple annihilation models cannot provide unique reconnection scalings, we show that the previous current sheet scalings derive from an optimized solution in which the peak dynamic and magnetic pressures balance in the reconnection region. The build-up of magnetic field in the current sheet implicit in flux pile-up solutions naturally leads to the idea of saturation. Hydromagnetic pressure effects limit the magnetic field in the sheet, yielding an upper limit on the reconnection rate for such solutions. This rate is still far superior to the Sweet–Parker merging rate, which can be derived by seeking solutions that avoid all forms of saturation. Finally we compare time dependent numerical simulations of the coalescence instability with the optimized flux pile-up models. This comparison suggests that merging driven by the relatively slow approach of large flux systems may be favored in practice.     

New ideas on jets and outflows interactions

We propose an alternative global model for the flows surrounding both low and high mass YSOs. In addition to a central accretion-ejection engine driving the jet, the molecular outflow is powered by the infalling matter and follows a circulation pattern around the central object without necessarily being entrained by the jet. The model produces a heated pressure-driven outflow with magneto-centrifugal acceleration and collimation. We will try to clarify the relation between the fast jet and its surrounding molecular outflow, which does not primarily rely on entrainment (prompt or turbulent) in the model. Hence, there is no need to transfer a large momentum from the jet to the molecular outflow through the entrainment processes. The model suggests that radiative heating and the Poynting flux may ultimately be the main energy sources driving molecular outflow in addition to the entrainment processes by the fast jet.     

Simulations of jet formation from a magnetized accretion disk

Axisymmetric magnetohydrodynamic (MHD) simulations have been made of the formation of jets from a Keplerian disk threaded by a magnetic field. The disk is treated as a boundary condition, where matter with high specific entropy is ejected with a Keplerian azimuthal speed and a poloidal speed less than the slow magnetosonic velocity, and where boundary conditions on the magnetic fields correspond to a highly conducting disk. Initially, the space above the disk, the corona, is filled with high specific entropy plasma in the thermal equilibrium in the gravitational field of the central object. The initial magnetic field is poloidal and is represented by the superposition of the fields of monopoles located below the plane of the disk.The rotation of the disk twists the initial poloidal magnetic field lines, and this twist propagates into the corona pushing matter into jet-like outflow in a cylindrical region. After the first switch-on wave, which originates during the first rotation period of the inner radius of the disk, the matter outflowing from the disk starts to flow and accelerate in thez-direction owing to both the magnetic and pressure gradient forces. The flow accelerates through the slow magnetosonic and Alfvén surfaces and at larger distances through the fast magnetosonic surface. The flow velocity of the jet is approximately parallel to thez-axis, with the collimation mainly a result of the pinching force of the toroidal magnetic field. The energy flux of the flow increases with increasing magnetic field strength on the disk. Some of the cases studied have been run for long times, 60 rotation periods of the inner radius of the disk, and show indications of approaching a stationary state.     

Optimized magnetic reconnection solutions in three dimensions

It has recently been shown that there is a well defined upper limit to the rate of magnetic merging for two-dimensional flux pile-up solutions. This rate, derived by equalizing the dynamic and magnetic pressures in the reconnection region and saturating the magnetic field in the current layer, leads to a significant enhancement of the classical Sweet–Parker merging limit. In this study we explore optimal merging rates in the case of three-dimensional fan and spine reconnection solutions. The ideas of optimization and saturation are first illustrated using an exact fan solution. We go on to show that while spine solutions seem ineffective as flare release mechanisms, optimized fan solutions have energy release characteristics typical of modest events.