Modeling the Subsurface Evolution of Active Region Flux Tubes
Y. Fan
备注：
6 pages, 3 figures, in Proceedings of the GONG 2008 / SOHO XXI conference on "Solar-stellar dynamos as revealed by helio- and asteroseismology", in press
I present results from a set of 3D spherical-shell MHD simulations of the buoyant rise of active region flux tubes in the solar interior which put new constraints on the initial twist of the subsurface tubes in order for them to emerge with tilt angles consistent with the observed Joy's law for the mean tilt of solar active regions. Due to the asymmetric stretching of the $Ω$-shaped tube by the Coriolis force, a field strength asymmetry develops with the leading side having a greater field strength and thus being more cohesive compared to the following side. Furthermore, the magnetic flux in the leading leg shows more coherent values of local twist $α\equiv {\bf J} \cdot {\bf B} / B^2$, whereas the values in the following leg show large fluctuations and are of mixed signs.
We use the SPARC code for MHD simulations with monolithic flux tubes of varying subsurface topology. Our studies involve the interactions of waves caused by a single source with subsurface magnetic fields. Mode conversion causing acoustic power to trickle downwards along the flux tube has been described before and can be visualized in our simulations. We show that this downward propagation causes the flux tube to act as an isolated source, creating a characteristic surface wavefield. Measuring this wavefield at the surface reveals subsurface properties of the magnetic field topology. Using tim…
Magnetic field emerges at the surface of the Sun as sunspots and active regions. This process generates a poloidal magnetic field from a rising toroidal flux tube, it is a crucial but poorly understood aspect of the solar dynamo. The emergence of magnetic field is also important because it is a key driver of solar activity. We show that measurements of horizontal flows at the solar surface around emerging active regions, in combination with numerical simulations of solar magnetoconvection, can constrain the subsurface rise speed of emerging magnetic flux. The observed flows imply that the rise…
The 1-D mean-field equation describing the evolution of the subsurface toroidal field can be used together with the observed surface radial field to model the subsurface toroidal flux density. We aim to test this model and determine the relationship between the observationally inferred surface toroidal field (as a proxy for flux emergence), and the modelled subsurface toroidal flux density. We use a combination of sunspot area observations, the surface toroidal field inferred from WSO line-of-sight magnetic field observations, and compare with the results of a 1-D mean-field evolution equation…
The fluting instability has been suggested as the driver of the subsurface structure of sunspot flux tubes. We conducted a series of numerical experiments where we used flux tubes with different initial curvatures to study the effect of the fluting instability on the subsurface structure of spots. We used the MURaM code, which has previously been used to simulate complete sunspots, to first compute four sunspots in the slab geometry and then two complete circular spots of opposite polarities. We find that the curvature of a flux tube indeed determines the degree of fluting the flux tube will u…
A solar active region (AR) is a three-dimensional magnetic structure formed in the convection zone, whose property is fundamentally important for determining the coronal structure and solar activity when emerged. However, our knowledge on the detailed 3-D structure prior to its emergence is rather poor, largely limited by the low cadence and sensitivity of previous instruments. Here, using the 45-second high-cadence observations from the Helioseismic and Magnetic Imager (\emph{HMI}) onboard the Solar Dynamics Observatory (\emph{SDO}), we are able for the first time to reconstruct a 3-D datacub…
Strong solar flares occur in $δ$-spots characterized by the opposite-polarity magnetic fluxes in a single penumbra. Sunspot formation via flux emergence from the convection zone to the photosphere can be strongly affected by convective turbulent flows. It has not yet been shown how crucial convective flows are for the formation of $δ$-spots. The aim of this study is to reveal the impact of convective flows in the convection zone on the formation and evolution of sunspot magnetic fields. We simulated the emergence and transport of magnetic flux tubes in the convection zone using radiative magne…
The solar surface is covered by high-speed jets transporting mass and energy into the solar corona and feeding the solar wind. The most prominent of these jets have been known as spicules. However, the mechanism initiating these eruptions events is still unknown. Using realistic numerical simulations we find that small-scale eruptions are produced by ubiquitous magnetized vortex tubes generated by the Sun's turbulent convection in subsurface layers. The swirling vortex tubes (resembling tornadoes) penetrate into the solar atmosphere, capture and stretch background magnetic field, and push surr…
Magnetic flux tubes reaching from the solar convective zone into the chromosphere have to pass through the relatively cool, and therefore non-ideal (i.e. resistive) photospheric region enclosed between the highly ideal sub-photospheric and chromospheric plasma. It is shown that stationary MHD equilibria of magnetic flux tubes which pass through this region require an inflow of photospheric material into the flux tube and a deviation from iso-rotation along the tube axis. This means that there is a difference in angular velocity of the plasma flow inside the tube below and above the non-ideal r…
We study the combined effects of convection and radiative diffusion on the evolution of thin magnetic flux tubes in the solar interior. Radiative diffusion is the primary supplier of heat to convective motions in the lower convection zone, and it results in a heat input per unit volume of magnetic flux tubes that has been ignored by many previous thin flux tube studies. We use a thin flux tube model subject to convection taken from a rotating spherical shell of turbulent, solar-like convection as described by Weber, Fan, and Miesch (2011, Astrophys. J., 741, 11; 2013, Solar Phys., 287, 239), n…
We numerically study the evolution of magnetic fields and fluid flows in a thin spherical shell. We take the initial field to be a latitudinally confined, predominantly toroidal flux tube. For purely toroidal, untwisted flux tubes, we recover previously known radial-shredding instabilities, and show further that in the nonlinear regime these instabilities can very effectively destroy the original field. For twisted flux tubes, including also a poloidal component, there are several possibilities, including the suppression of the radial-shredding instability, but also a more directly induced evo…
We use numerial simulations to study the absorption and phase shift of surface-gravity waves caused by groups of magnetic flux tubes. The dependence of the scattering coefficients with the distance between the tubes and their positions is analyzed for several cases with two or three flux tubes embedded in a quiet Sun atmosphere. The results are compared with those obtained neglecting completely or partially multiple scattering effects. We show that multiple scattering has a significant impact on the absorption measurements and tends to reduce the phase shift. We also consider more general case…
Active-region Modulation of Subsurface Meridional Flows and Magnetic Flux Transport on the Sun
Indian Institute of Astrophysics（印度天体物理研究所）；Pondicherry University（本地治里大学）；W. W. Hansen Experimental Physics Laboratory, Stanford University（斯坦福大学W.W.汉森实验物理实验室）；National Solar Observatory（国家太阳天文台）
We present a series of numerical sunspot models addressing the subsurface field and flow structure in up to 16 Mm deep domains covering up to 2 days of temporal evolution. Changes in the photospheric appearance of the sunspots are driven by subsurface flows in several Mm depth. Most of magnetic field is pushed into a downflow vertex of the subsurface convection pattern, while some fraction of the flux separates from the main trunk of the spot. Flux separation in deeper layers is accompanied in the photosphere with light bridge formation in the early stages and formation of pores separating fro…
Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisy…
We investigate least-squares fitting methods for estimating the winding rate of field lines about the axis of twisted magnetic-flux tubes. These methods estimate the winding rate by finding the values for a set of parameters that correspond to the minimum of the discrepancy between magnetic-field measurements and predictions from a twisted flux-tube model. For the flux-tube model used in the fitting, we assume that the magnetic field is static, axisymmetric, and does not vary in the vertical direction. Using error-free, synthetic vector magnetic-field data constructed with models for twisted m…
Three-dimensional numerical simulations have been used to study the scattering of a surface-gravity wave packet by vertical magnetic flux tubes, with radii from 200 km to 3 Mm, embedded in stratified polytropic atmosphere. The scattered wave was found to consist primarily of m=0 (axisymmetric) and m=1 modes. It was found that the ratio of the amplitude of these two modes is strongly dependant on the radius of the flux tube: The kink mode is the dominant mode excited in tubes with a small radius while the sausage mode is dominant for large tubes. Simulations of this type provide a simple, effic…
We carried out a magnetohydrodynamics simulation where a subsurface twisted kink-unstable flux tube emerges from the solar interior to the corona. Unlike the previous expectations based on the bodily emergence of a knotted tube, we found that the kinked tube can spontaneously form a complex quadrupole structure at the photosphere. Due to the development of the kink instability before the emergence, the magnetic twist at the kinked apex of the tube is greatly reduced, although the other parts of the tube is still strongly twisted. This leads to the formation of a complex quadrupole structure: a…
The aim of this paper is to model the propagation of slow magnetohydrodynamic (MHD) sausage waves in a thick expanding magnetic flux tube in the context of the quiescent (VAL C) solar atmosphere. The propagation of these waves is found to be described by the Klein-Gordon equation. Using the governing MHD equations and the VAL C atmosphere model we study the variation of the cut-off frequency along and across the magnetic tube guiding the waves. Due to the radial variation of the cut-off frequency the flux tubes act as low frequency filters for waves.
We present the results of three-dimensional numerical simulations to investigate the excitation of waves in the magnetic network of the Sun due to footpoint motions of a magnetic flux tube. We consider motions that typically mimic granular buffeting and vortex flows and implement them as driving motions at the base of the flux tube. The driving motions generates various MHD modes within the flux tube and acoustic waves in the ambient medium. The response of the upper atmosphere to the underlying photospheric motion and the role of the flux tube in channeling the waves is investigated. We compu…
A system of multiple open magnetic flux tubes spanning the solar photosphere and lower corona is modelled analytically, within a realistic stratified atmosphere subject to solar gravity. This extends results for a single magnetic flux tube in magnetohydrostatic equilibrium, described in Gent et al. (MNRAS, 435, 689, 2013). Self-similar magnetic flux tubes are combined to form magnetic structures, which are consistent with high-resolution observations. The observational evidence supports the existence of strands of open flux tubes and loops persisting in a relatively steady state. Self-similar …
In this paper we study the dynamics of toroidal flux tubes emerging from the solar interior, through the photosphere and into the corona. Many previous theoretical studies of flux emergence use a twisted cylindrical tube in the solar interior as the initial condition. Important insights can be gained from this model, however, it does have shortcomings. The axis of the tube never fully emerges as dense plasma becomes trapped in magnetic dips and restrains its ascent. Also, since the entire tube is buoyant, the main photospheric footpoints (sunspots) continually drift apart. These problems make …
In this Letter we present a seismological detection of a rising motion of magnetic flux in the shallow convection zone of the Sun, and show estimates of the emerging speed and its decelerating nature. In order to evaluate the speed of subsurface flux that creates an active region, we apply six Fourier filters to the Doppler data of NOAA AR 10488, observed with SOHO/MDI, to detect the reduction of acoustic power at six different depths from -15 to -2 Mm. All the filtered acoustic powers show reductions, up to 2 hours before the magnetic flux first appears at the visible surface. The start times…
We study how active-region-scale flux tubes rise buoyantly from the base of the convection zone to near the solar surface by embedding a thin flux tube model in a rotating spherical shell of solar-like turbulent convection. These toroidal flux tubes that we simulate range in magnetic field strength from 15 kG to 100 kG at initial latitudes of 1 degree to 40 degrees in both hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J., 741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of 10^20 Mx and 10^21 Mx, and more simulations of the previously investi…
We investigate the rising flux tube and the formation of sunspots in an unprecedentedly deep computational domain that covers the whole convection zone with a radiative magnetohydrodynamics simulation. Previous calculations had shallow computational boxes (< 30 Mm) and convection zones at a depth of 200 Mm. By using our new numerical code R2D2, we succeed in covering the whole convection zone and reproduce the formation of the sunspot from a simple horizontal flux tube because of the turbulent thermal convection. The main findings are (1) The rising speed of the flux tube is larger than the up…
This work is to study the dynamics of coronal mass ejections and to investigate possible correlation between CME productivity and subsurface structure. Two CMEs and six active regions are selected for the study. The CMEs are examined by comparing observations and theoretical models, and the subsurface structures are probed by local helioseismic inversions. The analysis of the CMEs shows that the eruptive flux-rope model is in good agreement with both events. However, some discrepancies with the observation are also found, indicating that the model can be further improved. The helioseismic inve…
Two approaches are used for description of linear transverse (kink) modes excited in a vertical thin magnetic flux tube. First one is based on the elastic thread model (Spruit, 1981). The second one follows from the the Taylor and Laurent series expansions of wave variables with respect to the tube radius inside and outside of the magnetic flux tube (Lopin and Nagorny, 2013). It has been shown that the main reason of the discrepancy of these approaches is related to the phenomenological equation of plasma motion used in the former case. This suggests that results obtained on the basis of this …
Using two-dimensional magnetohydrodynamics calculations, we investigate a twist gen- eration mechanism on a magnetic flux tube at the base of the solar convection zone based on the idea of Choudhuri, 2003, Sol. Phys., 215, 31 in which a toroidal mag- netic field is wrapped by a surrounding mean poloidal field. During generation of the twist, the flux tube follows four phases. (1) It quickly splits into two parts with vortex motions rolling up the poloidal magnetic field. (2) Owing to the physical mechanism similar to that of the magneto-rotational instability, the rolled-up poloidal field is b…
Observations suggest that twisted magnetic flux tubes are ubiquitous in the Sun's atmosphere. The main aim of this work is to advance the study of axisymmetric modes of magnetic flux tubes by modeling both twisted internal and external magnetic field, when the magnetic twist is weak. In this work, we solve the derived wave equations numerically assuming twist outside the tube is inversely proportional to the distance from its boundary. We also study the case of constant magnetic twist outside the tube and solve these equations analytically. We show that the solution for a constant twist outsid…
In this study, the properties of wavefunctions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero-βapproximation. A single three-dimensional wave equation (eigen value problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method (FEM). Wavefunctions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink and fluting modes. Concerning the amplit…
The buoyant transport of magnetic fields from the solar interior towards the surface plays an important role in the emergence of active regions, the formation of sunspots and the overall solar dynamo. Observations suggest that toroidal flux concentrations often referred to as "flux tubes", rise from their region of initiation likely in the solar tachocline towards the solar surface due to magnetic buoyancy. Many studies have assumed the existence of such magnetic structures and studied the buoyant rise of an isolated flux tube in a quiescent, field-free environment. Here, motivated by their fo…
The temporal variation of the horizontal velocity in subsurface layers beneath three different types of active regions is studied using the technique of ring diagrams. In this study, we select active regions (ARs) 10923, 10930, 10935 from three consecutive Carrington rotations: AR 10930 contains a fast-rotating sunspot in a strong emerging active region while other two have non-rotating sunspots with emerging flux in AR 10923 and decaying flux in AR 10935. The depth range covered is from the surface to about 12 Mm. In order to minimize the influence of systematic effects, the selection of acti…
We model the evolution of buoyant magnetic flux tubes in the Sun's convection zone. A flux tube is assumed to lie initially near the top of the stably stratified radiative core below the convection zone, but a segment of it is perturbed into the convection zone by gradual heating and convective overshoot motions. The ends ("footpoints") of the segment remain anchored at the base of the convection zone, and if the segment is sufficiently long, it may be buoyantly unstable, rising through the convection zone in a short time. The length of the flux tube determines the ratio of buoyancy to magneti…
Magnetic flux tubes in the solar wind can be twisted as they are transported from the solar surface, where the tubes are twisted owing to photospheric motions. It is suggested that the twisted magnetic tubes can be detected as the variation of total (thermal+magnetic) pressure during their passage through observing satellite. We show that the total pressure of several observed twisted tubes resembles the theoretically expected profile. The twist of isolated magnetic tube may explain the observed abrupt changes of magnetic field direction at tube walls. We have also found some evidence that the…
We argue that if color-superconducting quark matter exists in the core of a neutron star, it may contain a high density of flux tubes, carrying flux that is mostly color-magnetic, with a small admixture of ordinary magnetic flux. We focus on the two-flavor color-superconducting ("2SC") phase, and assume that the flux tubes are energetically stable, although this has not yet been demonstrated. The density of flux tubes depends on the nature of the transition to the color-superconducting phase, and could be within an order of magnitude of the density of magnetic flux tubes that would be found if…
Current sheets are ubiquitous in the solar wind.They are a major source of the solar wind MHD turbulence intermittency. They may result from non-linear interactions of the solar wind MHD turbulence or are the boundaries of flux tubes that originate from the solar surface. Some current sheets appear in pairs and are the boundaries of transient structures such as magnetic holes and reconnection exhausts, or the edges of pulsed Alfvén waves. For an individual current sheet, discerning whether it is a flux tube boundary or due to non-linear interactions, or the boundary of a transient structure is…
