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 upward convection velocity because of the low density caused by the magnetic pressure and the suppression of the mixing. (2) The rising speed of the flux tube exceeds 250 m/s at a depth of 18 Mm, while we do not see any clear evidence of the divergent flow 3 hr before the emergence at the solar surface. (3) Initially, the root of the flux tube is filled with the downflows and then the upflow fills the center of the flux tube during the formation of the sunspot. (4) The essential mechanisms for the formation of the sunspot are the coherent inflow and the turbulent transport. (5) The low-temperature region is extended to a depth of at least 40 Mm in the matured sunspot, with the high-temperature region in the center of the flux tube. Some of the findings indicate the importance of the deep computational domain for the flux emergence simulations.
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…
The rise of flux-tubes with intense magnetic fields from the base of the convection zone to the solar surface has been substantiated as a probable mechanism for sunspot formation. The origin of flux-tubes of sufficient strength (~10^5 G) is however uncertain. This paper considers the instability of a large-scale toroidal magnetic field caused by the magnetic suppression of convective heat transport as a candidate for the flux tube forming mechanism. The consideration employs the analytical dependence of the eddy diffusion on the magnetic field supplied by mean-field magnetohydrodynamics. The i…
Data analysis of sunspot oscillation based on 6-hr SDO run of observation showed that low frequency (0.2 < ! < 1 mHz) oscillations are local similar to three and five minute oscillations. The oscillations in the sunspot are concentrated in cells of a few arcsec, each of which has its own oscillation spectrum. The analysis of two scenario for sunspot oscillations leads to conclusion that local sunspot oscillations occur due to subphotospheric resonator for slow mhd waves. Empirical models of sunspot atmosphere and the theory of slow waves in thin magnetic flux tubes is applied to the modeling o…
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on sub-photospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging sub-photospheric magnetic flux tube on the rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a sub-photospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is …
Some preliminary processing results are presented for a dataset obtained with the Solar Optical Telescope on the Hinode satellite. The idea of the project is to record, nearly simultaneously, the full velocity and magnetic-field vectors in growing active regions and sunspot groups at a photospheric level. Our ultimate aim is to elaborate observational criteria to distinguish between the manifestations of two mechanisms of sunspot-group formation --- the rising of an Omega-shaped flux tube of a strong magnetic field and the in situ amplification and structuring of magnetic field by convection (…
We use numerical simulations to investigate the interaction of an $f$-mode wave packet with small and large models of a sunspot in a stratified atmosphere. While a loose cluster model has been largely studied before, we focus in this study on the scattering from an ensemble of tightly compact tubes. We showed that the small compact cluster produces a slight distorted scattered wave field in the transverse direction, which can be attributed to the simultaneous oscillations of the pairs of tubes within the cluster aligned in a perpendicular direction to the incoming wave. However, no signature o…
The stability of sunspots is one of the long-standing unsolved puzzles in the field of solar magnetism. We study the effects that destabilise and stabilise the flux tube of a simulated sunspot in the upper convection zone. The depth-varying effects of fluting instability, buoyancy forces, and timescales on the flux tube are analysed. The simulation was calculated with the MURaM code. The domain has a lateral extension of 98 Mm x 98 Mm and extends almost 18 Mm below the solar surface. The analysed data set of 30 hours shows a stable sunspot at the solar surface. We studied the evolution of the …
We present a 3D simulation of the dynamic emergence of a twisted magnetic flux tube from the top layer of the solar convection zone into the solar atmosphere and corona. It is found that after a brief initial stage of flux emergence during which the two polarities of the bipolar region become separated and the tubes intersecting the photosphere become vertical, significant rotational motion sets in within each polarity. The rotational motions of the two polarities are found to twist up the inner field lines of the emerged fields such that they change their orientation into an inverse configura…
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 …
It is generally believed that sunspots are the emergent part of magnetic flux tubes in the solar interior. These tubes are created at the base of the convection zone and rise to the surface due to their magnetic buoyancy. The motion of plasma in the convection zone being highly turbulent, the surface manifestation of sunspots may retain the signature of this turbulence, including its intermittency. From direct observations of sunspots, and indirect observations of the concentration of cosmogenic isotopes $^{14}$C in tree rings or $^{10}$Be in polar ice, power spectral densities in frequency ar…
Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected i…
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…
The aim of this work is the determination of the twist, writhe, and self magnetic helicity of penumbral filaments located in an inner Sunspot penumbra. To this extent, we inverted data taken with the spectropolarimeter (SP) aboard Hinode with the SIR (Stokes Inversion based on Response function) code. For the construction of a 3D geometrical model we applied a genetic algorithm minimizing the divergence of the magnetic field vector and the net magnetohydrodynamic force, consequently a force-free solution would be reached if possible. We estimated two proxies to the magnetic helicity frequently…
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…
We analyse the multiwavelength observations of an M2.9/1N flare that occurred in the active region (AR) NOAA 11112 in the vicinity of a huge filament system on 16 October 2010. SDO/HMI magnetograms reveal the emergence of a bipole (within the existing AR) 50 hours prior to the flare event. During the emergence, both the positive and negative sunspots in the bipole show translational as well as rotational motion. The positive polarity sunspot shows the significant motion/rotation in the south-westward/clockwise direction and continuously pushing/sliding the surrounding opposite polarity field r…
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…
Motivated by the question of how to distinguish seismically between monolithic and cluster models of sunspots, we have simulated the propagation of an $f$-mode wave packet through two identical small magnetic flux tubes (R=200 km), embedded in a stratified atmosphere. We want to study the effect of separation $d$ and incidence angle $χ$ on the scattered wave. We have demonstrated that the horizontal compact pair of tubes ($d/R=2$, $χ=0$) oscillate as a single tube when the incident wave is propagating, which gives a scattered wave amplitude of about twice that from a single tube. The scattered…
We present the new results of the two-dimensional numerical experiments on the cross-sectional evolution of a twisted magnetic flux tube rising from the deeper solar convection zone (-20,000 km) to the corona through the surface. The initial depth is ten times deeper than most of previous calculations focusing on the flux emergence from the uppermost convection zone. We find that the evolution is illustrated by the two-step process described below: the initial tube rises due to its buoyancy, subject to aerodynamic drag due to the external flow. Because of the azimuthal component of the magneti…
Observations reveal that strong solar flares and coronal mass ejections tend to occur in complex active regions characterized by delta-sunspots, spot rotation, sheared polarity inversion lines (PILs), and magnetic flux ropes. Here we report on the first modeling of spontaneous delta-spot generation as a result of flux emergence from the turbulent convection zone. Utilizing state-of-the-art radiative magnetohydrodynamics code R2D2, we simulate the emergence of a force-free flux tube in the convection zone that stretches down to -140 Mm. Elevated by large-scale convective upflows, the tube appea…
In this paper, we present a study on persistent and gradual penumbral decay and correlated decline of the photospheric transverse field component during 10-20 hours before a major flare (X1.8) eruption on 2011 September 7. This long-term pre-eruption behavior is corroborated with the well-imaged pre-flare filament rising, the consistent expansion of coronal arcades overlying the filament, as well as the NLFFF modelling results in the literature. We suggest that both the long-term pre-flare penumbral decay and the transverse field decline are the photospheric manifestation of the gradual rise o…
Penumbrae are known to be area of mainly horizontal magnetic field surrounding umbrae of relatively large and mature sunspots. In this paper, we observationally studied the formation of penumbrae in NOAA10978, where several penumbral formations were observed in G-band images of SOT/Hinode. Thanks to the continuous observation by Hinode, we could morphologically follow the evolution of sunspots and found that there are several paths to the penumbral formation: (1) Active accumulation of magnetic flux, (2) Rapid emergence of magnetic field, and (3) Appearance of twisted or rotating magnetic tube…
We study the buoyant rise of magnetic flux tubes embedded in an adiabatic stratification using two-and three-dimensional, MHD simulations. We analyze the dependence of the tube evolution on the field line twist and on the curvature of the tube axis in different diffusion regimes. To be able to achieve a comparatively high spatial resolution we use the FLASH code, which has a built-in Adaptive Mesh Refinement (AMR) capability. Our 3D experiments reach Reynolds numbers that permit a reasonable comparison of the results with those of previous 2D simulations. When the experiments are run without A…
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 average tilt angle of sunspot groups emerging throughout the solar cycle determines the net magnetic flux crossing the equator, which is correlated with the strength of the subsequent cycle. I suggest that a deep-seated, non-local process can account for the observed cycle-dependent changes in the average tilt angle. Motivated by helioseismic observations indicating cycle-scale variations in the sound speed near the base of the convection zone, I determined the effect of a thermally perturbed overshoot region on the stability of flux tubes and on the tilt angles of emerging flux loops. I f…
Active regions (AR) appearing on the surface of the Sun are classified into $α$, $β$, $γ$, and $δ$ by the rules of the Mount Wilson Observatory, California on the basis of their topological complexity. Amongst these, the $δ$-sunspots are known to be super-active and produce the most X-ray flares. Here, we present results from a simulation of the Sun by mimicking the upper layers and the corona, but starting at a more primitive stage than any earlier treatment. We find that this initial state consisting of only a thin sub-photospheric magnetic sheet breaks into multiple flux-tubes which evolve …
Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the disintegration of a magnetic flux tube by nonlinear diffusion. Previous theoretical studies are extended by considering two physically motivated functional forms for the nonlinear diffusion coefficient $D$: an inverse power-law dependence $D \propto B^{-ν}$ and a step-function dependence of $D$ on the magnetic field magnitude $B$. Analytical self-similar solutions ar…
Observations of cool stars reveal dark spot-like features on their surfaces. Compared to sunspots, starspots can be bigger or cover a larger fraction of the stellar surface. While sunspots appear only at low latitudes, starspots are also found in polar regions, in particular on rapidly rotating stars. Sunspots are believed to result from the eruption of magnetic flux-tubes rising from the deep interior of the Sun. The strong magnetic field locally reduces convective heat transport to the solar surface. Such flux-tube models have also been invoked to explain starspot properties. However, these …
We present the observation of a major solar eruption that is associated with fast sunspot rotation. The event includes a sigmoidal filament eruption, a coronal mass ejection, and a GOES X2.1 flare from NOAA active region 11283. The filament and some overlying arcades were partially rooted in a sunspot. The sunspot rotated at $\sim$10$^\circ$ per hour rate during a period of 6 hours prior to the eruption. In this period, the filament was found to rise gradually along with the sunspot rotation. Based on the HMI observation, for an area along the polarity inversion line underneath the filament, w…
We analyzed the size, intensity, and magnetic field strength of sunspot umbrae to compare the present cycle 24 with the previous one. We used data of the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory and selected all sunspots between May 2010 and October 2012, using one image per day. We created two subsets of this data with a manual tracking algorithm, both without duplication. One is containing each sunspot (910 umbrae within 488 spots) and was used to analyze the distribution of umbral areas, selected with an automated thresholding method. The other one contains 20…
A moderate C1.1 class confined flare is investigated here, which occurred on 2013 September 24 at 22:56~UT, in an arch filament system close to a regular, unipolar sunspot. Spectro-polarimetric observations from the Tenerife Infrared Polarimeter at the 70 cm German Vacuum Tower Telescope were combined with data from the Helioseismic Magnetic Imager and the Atmospheric Imaging Assembly to identify the processes that triggered the flare. The legs of this arch filament were anchored in the leading sunspot and the network flux region of opposite polarity. The flare was driven by small-scale, flux …
We study a filament eruption, two-ribbon flare, and coronal mass ejection (CME) that occurred in Active Region NOAA 10898 on 6 July 2006. The filament was located South of a strong sunspot that dominated the region. In the evolution leading up to the eruption, and for some time after it, a counter-clockwise rotation of the sunspot of about 30 degrees was observed. We suggest that the rotation triggered the eruption by progressively expanding the magnetic field above the filament. To test this scenario, we study the effect of twisting the initially potential field overlying a pre-existing flux-…
Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observations utilize just 2D surface information near the spot, but it is debatable how to infer deep structures and properties from local helioseismology. For a long time, it was believed that flux tubes rising from the bottom of the convection zone are th…
A qualitative analysis is given to the data on the full magnetic and velocity vector fields in a growing sunspot group, recorded nearly simultaneously with the Solar Optical Telescope on the Hinode satellite. Observations of a young bipolar subregion developing within AR 11313 were carried out on 9-10 October 2011. Our aim was to form am idea about the consistency of the observed pattern with the well-known rising-tube model of the formation of bipolar acrive regions and sunspot groups. We find from our magnetograms that the distributions of the vertical [B_v] and the horizontal [B_h] componen…
Oscillation properties in two sunspots and two facular regions are studied using Solar Dynamics Observatory (SDO) data and ground-based observations in the SiI 10827 and HeI 10830 lines. The aim is to study different-frequency spatial distribution characteristics above sunspots and faculae and their dependence on magnetic-field features and to detect the oscillations that reach the corona from the deep photosphere most effectively. We used Fast-Fourier-Transform and frequency filtration of the intensity and Doppler-velocity variations with Morlet wavelet to trace the wave propagating from the …
We use a thin flux tube model in a rotating spherical shell of turbulent convective flows to study how active region scale flux tubes rise buoyantly from the bottom of the convection zone to near the solar surface. We investigate toroidal flux tubes at the base of the convection zone with field strengths ranging from 15 kG to 100 kG at initial latitudes ranging from 1 degree to 40 degrees with a total flux of 10^22 Mx. We find that the dynamic evolution of the flux tube changes from convection dominated to magnetic buoyancy dominated as the initial field strength increases from 15 kG to 100 kG…
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…
Combining the Solar Dynamics Observatory and the New Vacuum Solar Telescope observations, we study a confined flare triggered by a rising flux rope within the trailing sunspots of active region 12733. The flux rope lying above the sheared polarity inversion line can be constructed through magnetic extrapolation but could not be detected in multi-wavelength images at the pre-flare stage. The conspicuous shearing motions between the opposite-polarity fields in the photosphere are considered to be responsible for the flux rope formation. The maximum twist of the flux rope is as high as -1.76, and…
We study the observational signature of flux emergence in the photosphere using synthetic data from a 3D MHD simulation of the emergence of a twisted flux tube. Several stages in the emergence process are considered. At every stage we compute synthetic Stokes spectra of the two iron lines Fe I 6301.5 Å and Fe I 6302.5 Å and degrade the data to the spatial and spectral resolution of Hinode's SOT/SP. Then, following observational practice, we apply Milne-Eddington-type inversions to the synthetic spectra in order to retrieve various atmospheric parameters and compare the results with recent Hino…
The sunspot-associated sources at the frequency of 17 GHz give information on plasma parameters in the regions of magnetic field about B=2000 G at the level of the chromosphere-corona transition region. The observations of short period (from 1 to 10 minutes) oscillations in sunspots reflect propagation of magnetohydrodynamic (MHD) waves in the magnetic flux tubes of the sunspots. We investigate the oscillation parameters in active regions in connection with their flare activity. We confirm the existence of a link between the oscillation spectrum and flare activity. We find differences in the o…
Many fully convective stars exhibit a wide variety of surface magnetism, including starspots and chromospheric activity. The manner by which bundles of magnetic field traverse portions of the convection zone to emerge at the stellar surface is not especially well understood. In the Solar context, some insight into this process has been gleaned by regarding the magnetism as consisting partly of idealized thin flux tubes (TFT). Here, we present the results of a large set of TFT simulations in a rotating spherical domain of convective flows representative of a 0.3 solar-mass, main-sequence star. …
We present a study of wave processes in the sunspot region NOAA 12670 on 2017 August 10 observed by the Goode Solar Telescope in the TiO 7057 A and Ha 6563 A spectral lines. To study the distribution of power oscillations and their dynamics, we applied the pixelized wavelet filtering (PWF) technique. For the first time, the spatial structure of oscillation sources as a footpoints of fine magnetic tubes, anchored in the sunspot umbra was obtained. We found that at the chromosphere level, emission variation is a combination of numerous independent oscillations located in the sources with small a…
We quantify the emergence and decay rates of preceder (p) and follower (f) sunspots within ten active regions from 2010-2014 using Space-weather Helioseismic Magnetic Imager Active Region Patch data. The sunspots are small- to mid-sized regions and contain a signed flux within a single polarity sunspot of $(1.1-6.5)\times 10^{21}$ Mx. The net unsigned flux within the regions, including plage, ranges from $(5.1-20)\times 10^{21}$ Mx. Rates are calculated with and without intensity contours to differentiate between sunspot formation and flux emergence. Signed flux emergence rates, calculated wit…
At present, many works about magneto-hydrodynamics wave diagnostics in magnetic flux tubes are based on some pioneer works not considering the contributions of magnetic twist. Other works considered the effect on magneto-hydrodynamics waves, but the dispersion relationship they presented only gave the wave modes of m=0,1,2. The kink mode of m=-1 was absent. Therefore, in this work we would like to present a complete dispersion relationship that includes both magnetic twist and the wave mode of m=-1. Analogous to the m=+1 wave mode, the mode of m=-1 also exhibits the mode change at finite kr0, …
Motivated by the problem of local solar subsurface magnetic structure, we have used numerical simulation to investigate the propagation of waves through monolithic magnetic flux tubes of different size. A cluster model can be a good approximation to simulate sunspots as well as solar plage regions which are composed of an ensemble of compactly packed thin flux tubes. Simulations of this type is a powerful tool to probe the structure and the dynamic of various solar features which are related directly to solar magnetic field activity.
The emergence and magnetic evolution of solar active regions (ARs) of beta-gamma-delta type, which are known to be highly flare-productive, were studied with the SOHO/MDI data in Cycle 23. We selected 31 ARs that can be observed from their birth phase, as unbiased samples for our study. From the analysis of the magnetic topology (twist and writhe), we obtained the following results. i) Emerging beta-gamma-delta ARs can be classified into three topological types as "quasi-beta", "writhed" and "top-to-top". ii) Among them, the "writhed" and "top-to-top" types tend to show high flare activity. ii…
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…
After summarizing the relevant observational data, we discuss how a study of flux tube dynamics in the solar convection zone helps us to understand the formation of sunspots. Then we introduce the flux transport dynamo model and assess its success in modelling both the solar cycle and its departures from strictly periodic behaviour.
Research results from solar-dynamo models show the northern and southern hemispheres may evolve separately throughout the solar cycle. The observed phase lag between the hemispheres provides information regarding the strength of hemispheric coupling. Using hemispheric sunspot-area and sunspot-number data from Cycles 12 - 23, we determine how out of phase the separate hemispheres are during the rising, maximum, and declining period of each solar cycle. Hemispheric phase differences range from 0 - 11, 0 - 14, and 2 - 19 months for the rising, maximum, and declining periods, respectively. The pha…
We analyse a sequence of high-resolution spectropolarimetric observations of a sunspot taken at the 1-m SST, to determine the nature of flux emergence in a light bridge and the processes related to its evolution in the photosphere and chromosphere. Blueshifts of about 2 km/s are seen near the entrance of a granular light bridge on the limbward side of the spot. They lie next to a strongly redshifted patch that appeared 6 mins earlier. Both patches are seen for 25 mins until the end of the sequence. The blueshifts coincide with an elongated emerging granule, while the redshifts appear at the en…
We present a series of numerical experiments that model the evolution of magnetic flux tubes with a different amount of initial twist. As a result of calculations, tightly twisted tubes reveal a rapid two-step emergence to the atmosphere with a slight slowdown at the surface, while weakly twisted tubes show a slow two-step emergence waiting longer the secondary instability to be triggered. This picture of the two-step emergence is highly consistent with recent observations. These tubes show multiple magnetic domes above the surface, indicating that the secondary emergence is caused by intercha…
