Small-scale Magnetic Flux Tubes Research Articles

Black hole magnetosphere with small-scale flux tubes – II. Stability and dynamics

ABSTRACT In some Seyfert galaxies, the hard X-rays that produce fluorescent emission lines are thought to be generated in a hot corona that is compact and located at only a few gravitational radii above the supermassive black hole. We consider the possibility that this X-ray source may be powered by small-scale magnetic flux tubes attached to the accretion disc near the black hole. We use three-dimensional, time-dependent, special relativistic, force-free simulations in a simplified setting to study the dynamics of such flux tubes as they get continuously twisted by the central compact star/black hole. We find that the dynamical evolution of the flux tubes connecting the central compact object and the accretion disc is strongly influenced by the confinement of the surrounding field. Although differential rotation between the central object and the disc tends to inflate the flux tubes, strong confinement from surrounding field quenches the formation of a jet-like outflow, as the inflated flux tube becomes kink unstable and dissipates most of the extracted rotational energy relatively close to the central object. Such a process may be able to heat up the plasma and produce strong X-ray emission. We estimate the energy dissipation rate and discuss its astrophysical implications.

Mass and energy supply of a cool coronal loop near its apex

Context. Different models for the heating of solar corona assume or predict different locations of the energy input: concentrated at the footpoints, at the apex, or uniformly distributed. The brightening of a loop could be due to the increase in electron density ne, the temperature T, or a mixture of both.Aim. We investigate possible reasons for the brightening of a cool loop at transition region temperatures through imaging and spectral observation.Methods. We observed a loop with the Interface Region Imaging Spectrograph (IRIS) and used the slit-jaw images together with spectra taken at a fixed slit position to study the evolution of plasma properties in and below the loop. We used spectra of Si iv, which forms at around 80 000 K in equilibrium, to identify plasma motions and derive electron densities from the ratio of inter-combination lines of O IV. Additional observations from the Solar Dynamics Observatory (SDO) were employed to study the response at coronal temperatures (Atmospheric Imaging Assembly, AIA) and to investigate the surface magnetic field below the loop (Helioseismic and Magnetic Imager, HMI).Results. The loop first appears at transition region temperatures and later also at coronal temperatures, indicating a heating of the plasma in the loop. The appearance of hot plasma in the loop coincides with a possible accelerating upflow seen in Si IV, with the Doppler velocity shifting continuously from ~−70 km s−1 to ~−265 km s−1. The 3D magnetic field lines extrapolated from the HMI magnetogram indicate possible magnetic reconnection between small-scale magnetic flux tubes below or near the loop apex. At the same time, an additional intensity enhancement near the loop apex is visible in the IRIS slit-jaw images at 1400 Å. These observations suggest that the loop is probably heated by the interaction between the loop and the upflows, which are accelerated by the magnetic reconnection between small-scale magnetic flux tubes at lower altitudes. Before and after the possible heating phase, the intensity changes in the optically thin (Si IV) and optical thick line (C II) are mainly contributed by the density variation without significant heating.Conclusions. We therefore provide evidence for the heating of an envelope loop that is affected by accelerating upflows, which are probably launched by magnetic reconnection between small-scale magnetic flux tubes underneath the envelope loop. This study emphasizes that in the complex upper atmosphere of the Sun, the dynamics of the 3D coupled magnetic field and flow field plays a key role in thermalizing 1D structures such as coronal loops.

Theoretical basal Ca II fluxes for late-type stars: results from magnetic wave models with time-dependent ionization and multi-level radiation treatments

In the current study we present ab initio numerical computations of the generation and propagation of longitudinal waves in magnetic flux tubes embedded in the atmospheres of late-type stars. The interaction between convective turbulence and the magnetic structure is computed and the obtained longitudinal wave energy flux is used in a self-consistent manner to excite the small-scale magnetic flux tubes. In the current study we reduce the number of assumptions made in our previous studies by considering the full magnetic wave energy fluxes and spectra as well as time-dependent ionization (TDI) of hydrogen, employing multi-level Ca II atomic models, and taking into account departures from local thermodynamic equilibrium. Our models employ the recently confirmed value of the mixing-length parameter $\alpha=1.8$ . Regions with strong magnetic fields (magnetic filling factors of up to 50%) are also considered in the current study. The computed Ca II emission fluxes show a strong dependence on the magnetic filling factors, and the effect of time-dependent ionization (TDI) turns out to be very important in the atmospheres of late-type stars heated by acoustic and magnetic waves. The emitted Ca II fluxes with TDI included into the model are decreased by factors that range from 1.4 to 5.5 for G0V and M0V stars, respectively, compared to models that do not consider TDI. The results of our computations are compared with observations. Excellent agreement between the observed and predicted basal flux is obtained. The predicted trend of Ca II emission flux with magnetic filling factor and stellar surface temperature also agrees well with the observations but the calculated maximum fluxes for stars of different spectral types are about two times lower than observations. Though the longitudinal MHD waves considered here are important for chromosphere heating in high activity stars, additional heating mechanism(s) are apparently present.

GENERATION OF MAGNETOHYDRODYNAMIC WAVES IN LOW SOLAR ATMOSPHERIC FLUX TUBES BY PHOTOSPHERIC MOTIONS

Recent ground- and space-based observations reveal the presence of small-scale motions between convection cells in the solar photosphere. In these regions small-scale magnetic flux tubes are generated due to the interaction of granulation motion and background magnetic field. This paper studies the effects of these motions, on magnetohydrodynamic wave excitation from broadband photospheric drivers. Numerical experiments of linear magnetohydrodynamic wave propagation in a magnetic flux tube embedded in a realistic gravitationally stratified solar atmosphere between the photosphere and the low choromosphere (above $\beta=1$) are performed. Horizontal and vertical velocity field drivers mimic granular buffeting and solar global oscillations. A uniform torsional driver as well as Archimedean and logarithmic spiral drivers mimic observed torsional motions in the solar photosphere. The results are analysed using a novel method for extracting the parallel, perpendicular and azimuthal components of the perturbations, which caters for both the linear and non-linear case. Employing this method yields the identification of the wave modes excited in the numerical simulations and enables a comparison of excited modes via velocity perturbations and wave energy flux. The wave energy flux distribution is calculated, to enable the quantification of the relative strengths of excited modes. The torsional drivers excite primarily Alfv\'en modes (~60% of the total flux) with small contributions from the slow kink mode, and, for the logarithmic spiral driver, small amounts of slow sausage mode. The horizontal and vertical drivers excite primarily slow kink or fast sausage modes respectively, with small variations dependent upon flux surface radius.

A Statistical Study on the Reconnection in Boundary Layers of Small-scale Magnetic Flux Tubes in Solar Winds

With the data from WIND satellite in 1995—2005, the small-scale magnetic flux tubes determined with two methods, i.e., the artificial recognition and program selection respectively, are compared. It is found that there are magnetic reconnections in the boundary layers of 41% small-scale magnetic flux tubes determined with the program selection method, which is similar to the re- sult of small-scale magnetic flux tubes determined with the method of artificial recognition. The features of magnetic reconnections, such as the magnetic shear angle, magnetic field strength, and duration of the dissipation region of recon- nection at the small-scale flux tubes’ boundaries determined from both methods have the same statistical tendency. This shows that there is no essential differ- ence in the properties of reconnections in the boundary layers of the small-scale magnetic flux tubes determined with the two methods. Hence the data yielded by both methods can be used as the samples for statistically studying the events of reconnection in the front and back boundary layers of small-scale flux ropes. There are totally 71 magnetic reconnection events selected in this paper. Our statistical result shows that in 50 events (70%) the decrease of magnetic field strength in the dissipation region of reconnection is larger than 20%, and in 47 events (66%) the magnetic shear angle is larger than 90 degrees. These indicate that the magnetic reconnections in boundaries of the small-scale magnetic flux tubes are more likely to be anti-parallel. The statistics has been performed sep- arately in the reconnections of the front and back boundary layers of small-scale magnetic flux tubes. The results show that the features of reconnections in the front and back boundaries are similar to each other, which is different from the various properties in the front and back boundaries of the magnetic clouds, and this means that the expansion in the large-scale magnetic flux tubes, such as magnetic clouds, does not happen in the small-scale magnetic flux tubes.

To the problem of temporal changes of magnetic fields in small-scale magnetic fluxtubes during 11-years cycle of solar activity

To the problem of temporal changes of magnetic fields in small-scale magnetic fluxtubes during 11-years cycle of solar activity

Channeling 5 Minute Photospheric Oscillations into the Solar Outer Atmosphere through Small-Scale Vertical Magnetic Flux Tubes

We report two-dimensional MHD simulations which demonstrate that photospheric 5 minute oscillations can leak into the chromosphere inside small-scale vertical magnetic flux tubes. The results of our numerical experiments are compatible with those inferred from simultaneous spectropolarimetric observations of the photosphere and chromosphere obtained with the Tenerife Infrared Polarimeter (TIP) at 10830 Å. We conclude that the efficiency of energy exchange by radiation in the solar photosphere can lead to a significant reduction of the cutoff frequency and may allow for the propagation of the 5 minute waves vertically into the chromosphere.

Electron heating by large-amplitude shear Alfvén waves in the upper chromosphere with a force-free magnetic configuration

Aims. We investigate how large-amplitude shear Alfven waves (AWs) can heat the upper chromosphere with a magnetic force-free configuration. Methods. We used a 2D3V fully relativistic electromagnetic particle-in-cell simulation. Results. We found that the shear AWs with linear polarization and about one period can excite quasi-electrostatic waves driven by the modified two-stream instability, resulting in electron heating within a short time $t\simeq50{\omega_{\rm ci}}^{-1}$. The results could be applied to the electron heating in the upper chromosphere where small-scale magnetic flux tubes are interacting with each other, making shear magnetic field structures between them.

Numerical modeling of solar faculae close to the limb

A numerical simulation was performed to interpret high-resolution spectropolarimetric observations of polar faculae on the Sun. A semi-empirical three-dimensional model of facula structures, controlled by several free parameters, was constructed. It consists of two components, the atmosphere within small-scale magnetic flux tubes and the exterior atmosphere. Multi-ray 1.5D radiative transfer calculations were performed along oblique rays passing through a highly inhomogeneous atmosphere of the simulation box. By the comparison of the properties of the calculated Stokes profiles from the synthetic faculae with the observed properties, a set of free parameters of the model (such as: size, number density of flux tubes, internal temperature stratification and magnetic field strength) was deduced, which satisfies the observational constraints. The hypothesis about solar faculae as a conglomerate of small-scale magnetic flux tubes is verified. The model reproduces all observed properties: the continuum contrast and its center-to-limb variation, the Stokes I and V profiles of Fe I and Fe II lines, the apparent magnetic field strengths, and the displacement towards the limb of the continuum intensity against the line-of-sight magnetograms.

The structure of small-scale magnetic flux tubes

Three main mechanisms have been described to determine the maximum field strength and structure of a solar or stellar magnetic flux tube. This paper attempts to relate them to one another through a series of magnetoconvective calculations. The first process is the balancing of the Lorentz force by radial gradients in the buoyancy force. It was first found in the Boussinesq regime, where it was studied in the late 1970s by Galloway, Proctor & Weiss. A similar balance can occur in the fully compressible case, where we refer to it as quasi-Boussinesq (QB). The second process involves a balance between an outward-directed radial pressure gradient and radial gradients in the buoyancy force outside the tube. This is the mechanism proposed in the early 1990s by Kerswell & Childress (the KC mechanism). The third mechanism, convective collapse (CC), is a process whereby a flux tube can evolve to a high field strength because of an instability due to the superadiabaticity of the material within the tube. Until now, it has been studied using the so-called ‘thin flux tube’ approximation in which convective motions are ignored even though there is a background superadiabatic density stratification. Here we place these three mechanisms in a unified framework and explore the transitions between the solutions as various parameters are varied. In particular, we show that the QB solutions are preferred for a wide range of parameters, whereas CC solutions occur only in very specific circumstances. In particular, on the Sun, the latter are probably limited to flux tubes with radii less than approximately 10 km, the turbulent magnetic diffusivity length-scale.

Study of polar faculae by means of spectro‐polarimetric observations and radiative transfer calculations

AbstractPolar faculae are of special interest for solar physics because of their close relationship to the global magnetic field of the Sun and to solar activity, and because of the recently found kilogauss magnetic fields, which are very unusual for the structures outside active regions at high latitudes of the Sun. The idea is that polar faculae can be represented by bundles of unresolved small‐scale magnetic flux tubes, which are characterized by sizes of about 100 km and strong magnetic fields. High resolution spectro‐polarimetric observations of the considered structures were performed and complemented by the radiation transfer calculations with oblique rays passing through an inhomogeneous magnetic medium. The recent results of observations and numerical calculations are presented.

Heating of Coronal Loop Footpoints by Magnetic Reconnection Resulting from Surface Alfven Waves and Colliding Plasma Flows in Chromospheric Current Sheets

New observations with NASA's Transition Region and Coronal Explorer (TRACE) spacecraft reveal the location of the unidentified energy source, showing that the main corona heating occurs in a lower corona, at a height not greater than about 16,000 km above the photosphere. To explain these new observations, we present a model of chromospheric loop heating based on our simulation results, which reveal that surface Alfven waves and upward plasma flows excited from the footpoints of the small-scale magnetic flux tubes can be effectively dissipated through magnetic reconnection near the chromospheric current sheets that may exist near the interaction regions of several magnetic flux tubes.

Simulation of a Collision between Shock Waves and a Magnetic Flux Tube: Excitation of Surface Alfven Waves and Body Alfven Waves

To explain the observed dynamics of the small-scale magnetic flux tubes in the quiet photospheric network, Furusawa & Sakai presented simulation results on the collision of two flux tubes. They found that shock waves appear during the collision of two magnetic flux tubes, when two magnetic flux tubes with weak electric current collide with each other. The shock waves so generated can subsequently collide with another flux tube, and we investigate here the interaction process of the shock with the flux tube. It is found that during the collision of a shock wave with a magnetic flux tube with weak electric current, surface Alfven waves can be generated and propagate along the flux tube. However, when the shock wave collides with a magnetic flux tube with strong current, body Alfven waves can be generated and propagate along the flux tube. It is also shown that, when we take into account the effect of a background density inhomogeneity due to gravity, there occurs a strong upward plasma jet along the flux tube, as well as surface Alfven waves. The energy conversion rate from the shock wave energy to the upward MHD waves, as well as upward plasma flows, is about 40% and thus is very efficient. We apply our results to the problem of solar coronal heating.

Heating and Jet Formation by Hydrodynamic Cumulation in the Solar Atmosphere

The solar transition region is the site of supersonic plasma jets and sporadic radiative events, whose origin and physical nature have not been understood. Here we show that ubiquitous small-scale magnetic flux tubes, constantly emerging from subsurface layers, may cause the formation of plasma jets and a sporadic excess of temperature near the solar surface. These flux tubes collide and reconnect, creating a sling-shot effect that generates complex three-dimensional shock waves with the curved surface. Self-focusing of these shocks occurs as they propagate upward in the rarefied atmosphere. Depending on the geometry of the shock collision, highly concentrated energy may be converted entirely into either heat or strong jets, or distributed between the two.

CAN WE OBSERVE THE TEMPERATURE INHOMOGENEITIES AND MAGNETIC FLUX TUBES AS THE FINE STRUCTURE ON THE EXTREME LIMB OF THE SUN

Fine structure of brightness inhomogeneities with ΔI r.m.s. = 2.9% was discovered on the extreme limb of the Sun on the best quality white-light photographs obtained at the Soviet Stratospheric Solar Observatory. The concept is that temperature inhomogeneities are responsible for the limb structure. The real value δT r.m.s. = 109K is required to explain our observations. Another possible explanation is that small-scale magnetic flux tubes with the realistic filling factor f* = 1% are the source of the limb brightness fluctuations.

New Observations of Subarcsecond Photospheric Bright Points

We have used an interference filter centered at 4305 A within the bandhead of the CH radical (the 'G band') and real-time image selection at the Swedish Vacuum Solar Telescope on La Palma to produce very high contrast images of subarcsecond photospheric bright points at all locations on the solar disk. During the 6 day period of 1993 September 15-20 we observed active region NOAA 7581 from its appearance on the East limb to a near-disk-center position on September 20. A total of 1804 bright points were selected for analysis from the disk center image using feature extraction image processing techniques. The measured Full Width at Half Maximum (FWHM) distribution of the bright points in the image is lognormal with a modal value of 220 km (0 sec .30) and an average value of 250 km (0 sec .35). The smallest measured bright point diameter is 120 km (0 sec .17) and the largest is 600 km (O sec .69). Approximately 60% of the measured bright points are circular (eccentricity approx. 1.0), the average eccentricity is 1.5, and the maximum eccentricity corresponding to filigree in the image is 6.5. The peak contrast of the measured bright points is normally distributed. The contrast distribution variance is much greater than the measurement accuracy, indicating a large spread in intrinsic bright-point contrast. When referenced to an averaged 'quiet-Sun' area in the image, the modal contrast is 29% and the maximum value is 75%; when referenced to an average intergranular lane brightness in the image, the distribution has a modal value of 61% and a maximum of 119%. The bin-averaged contrast of G-band bright points is constant across the entire measured size range. The measured area of the bright points, corrected for pixelation and selection effects, covers about 1.8% of the total image area. Large pores and micropores occupy an additional 2% of the image area, implying a total area fraction of magnetic proxy features in the image of 3.8%. We discuss the implications of this area fraction measurement in the context of previously published measurements which show that typical active region plage has a magnetic filling factor on the order of 10% or greater. The results suggest that in the active region analyzed here, less than 50% of the small-scale magnetic flux tubes are demarcated by visible proxies such as bright points or pores.

Theoretical Models of Magnetic Flux Tubes: Structure and Dynamics

Two types of model calculations for small scale magnetic flux tubes in the solar atmosphere are reviewed. In the first kind, one follows the temporal evolution governed by the complete set of the MHD and radiative transfer equations to a (quasi) stationary solution. From such a solution the continuum contrasts of a photospheric flux tube in the visible and in the infrared continuum at 1.6 μm have been computed and are briefly discussed. The second, more empirical type of method assumes the flux tubes to be in magnetohydrostatic equilibrium. It is computationally faster and more flexible and allows us to explore a wide range of parameters. Models and insights obtained from such parameter studies are discussed in some detail. These include an explanation for the peculiar variation of the area asymmetry of Stokes V profiles across the solar disk in terms of mass motions in the surroundings of magnetic flux tubes.Furthermore, a two-dimensional model of the lower chromosphere that has been developed is presented. Emphasis is laid on the effect of thermal bifurcation of the lower chromosphere on the structure of the chromospheric magnetic field. If the cool carbon monoxide clouds, observed in the infrared, occupy the non-magnetic regions, the flux tubes expand very strongly and form a magnetic canopy with an almost horizontal base. This has consequences for the spatial distribution of the Ca II K spectral line emission.Finally, some consideration is given to the formation and destruction of intense magnetic flux tubes in the solar photosphere. The formation is described as a consequence of the flux expulsion process that leads to a convective instability. A possible observational signature of this mechanism is proposed.