13 pages, 7 figures. To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 2009
Numerical simulations have by now revealed that the fine scale structure of the penumbra in general and the Evershed effect in particular is due to overturning convection, mainly confined to gaps with strongly reduced magnetic field strength. The Evershed flow is the radial component of the overturning convective flow visible at the surface. It is directed outwards -- away from the umbra -- because of the broken symmetry due to the inclined magnetic field. The dark penumbral filament cores visible at high resolution are caused by the 'cusps' in the magnetic field that form above the gaps. Still remaining to be established are the details of what determines the average luminosity of penumbrae, the widths, lengths, and filling factors of penumbral filaments, and the amplitudes and filling factors of the Evershed flow. These are likely to depend at least partially also on numerical aspects such as limited resolution and model size, but mainly on physical properties that have not yet been adequately determined or calibrated, such as the plasma beta profile inside sunspots at depth and its horizontal profile, the entropy of ascending flows in the penumbra, etc.
There have been a few reports in the literature of counter-Evershed flows observed in well developed sunspot penumbrae, i.e. flows directed towards the umbra along penumbral filaments. Here we investigate the driving forces of such counter-Evershed flows in a radiative magnetohydrodynamic simulation of a sunspot and compare them with the forces acting on the normal Evershed flow. The simulation covers a timespan of 100 solar hours and generates an Evershed outflow exceeding 8 km s$^{-1}$ in the penumbra along radially aligned filaments where the magnetic field is almost horizontal. Additionall…
We investigate the temporal relation between the Evershed flow, dot-like bright features (penumbral grain), the complex magnetic field structure, and dark lanes (dark core) along bright filaments in a sunspot penumbra. We use a time series of high spatial resolution photospheric intensity, vector magnetic field maps, and Doppler velocity maps obtained with the Solar Optical Telescope aboard the \textit{Hinode} spacecraft. We conclude that the appearance and disappearance of the Evershed flow and penumbra grains occur at nearly the same time and are associated with changes of the inclination an…
Discovered in 1909 the Evershed effect represents strong mass outflows in sunspot penumbra, where the magnetic field of sunspots is filamentary and almost horizontal. These flows play important role in sunspots and have been studied in detail using large ground-based and space telescopes, but the basic understanding of its mechanism is still missing. We present results of realistic numerical simulations of the Sun's subsurface dynamics, and argue that the key mechanism of this effect is in non-linear magnetoconvection that has properties of traveling waves in the presence of strong, highly inc…
The Evershed flow is a systematic motion of gas that occurs in the penumbra of all sunspots. Discovered in 1909, it still lacks a satisfactory explanation. We know that the flow is magnetized, often supersonic, and that it shows conspicuous fine structure on spatial scales of 0.2"-0.3", but its origin remains unclear. The hope is that a good observational understanding of the relation between the flow and the penumbral magnetic field will help us determine its nature. Here I review advances in the characterization of the Evershed flow and sunspot magnetic fields from high-resolution spectrosco…
The amplitudes of the Evershed flow are measured using pairs of carefully selected FeI and FeII spectral lines located close in wavelength and registered simultaneously. A sunspot belonging to the NOAA 11582 group was scanned using the spectrograph of the German Vacuum Tower Telescope (Observatorio del Teide, Tenerife). Velocities were extracted from intensity profiles using the lambda-meter technique. The formation heights of the observed spectral lines were calculated using semi-empirical models of a bright and dark penumbral filament taking into account the sunspot location at the limb. Our…
We present G-band and Ca II H observations of NOAA AR 10930 obtained by Hinode/SOT on 2006 December 6 covering an X6.5 flare. Local Correlation Tracking (LCT) technique was applied to the foreshortening-corrected G-band image series to acquire horizontal proper motions in this complex beta-gamma-delta active region. With the continuous high quality, spatial and temporal resolution G-band data, we not only confirm the rapid decay of outer penumbrae and darkening of the central structure near the flaring neutral line, but also unambiguously detect for the first time the enhancement of the sheare…
Sunspot fine structure has been modeled in the past by a combination of idealized magneto-convection simulations and simplified models that prescribe the magnetic field and flow structure to a large degree. Advancement in numerical methods and computing power has enabled recently 3D radiative MHD simulations of entire sunspots with sufficient resolution to address details of umbral dots and penumbral filaments. After a brief review of recent developments we focus on the magneto-convective processes responsible for the complicated magnetic structure of the penumbra and the mechanisms leading to…
Numerical simulations indicate that the filamentation of sunspot penumbrae and the associated systematic outflow (the Evershed effect) are due to convectively driven fluid motions constrained by the inclined magnetic field. We investigate whether these motions, in particular the upflows in the bright filaments and the downflows at their edges can be reliably observed with existing instrumentation. We use a snapshot from a sunspot simulation to calculate 2D maps of synthetic line profiles for the spectral lines Fe\sci 7090.4 Å~ and C\sci 5380.34 Å. The maps are spatially and spectrally degraded…
Observations with the 1-m Swedish Solar Telescope of the flows seen in penumbral filaments are presented. Time sequences of bright filaments show overturning motions strikingly similar to those seen along the walls of small isolated structures in the active regions. The filaments show outward propagating striations with inclination angles suggesting that they are aligned with the local magnetic field. We interpret it as the equivalent of the striations seen in the walls of small isolated magnetic structures. Their origin is then a corrugation of the boundary between an overturning convective f…
MHD simulations of sunspots have successfully reproduced many aspects of sunspot fine structure as consequence of magneto convection in inclined magnetic field. We study how global sunspot properties and penumbral fine structure depend on the magnetic top boundary condition as well as on grid spacing. The overall radial extent of the penumbra is subject to the magnetic top boundary condition. All other aspects of sunspot structure and penumbral fine structure are resolved at an acceptable level starting from a grid resolution of 48 [24] km (horizontal [vertical]). We find that the amount of in…
Recent advances in helioseismology, numerical simulations and mean-field theory of solar differential rotation have shown that the meridional circulation pattern may consist of two or more cells in each hemisphere of the convection zone. According to the mean-field theory the double-cell circulation pattern can result from the sign inversion of a nondiffusive part of the radial angular momentum transport (the so-called $Λ$-effect) in the lower part of the solar convection zone. Here, we show that this phenomenon {can result} from the radial inhomogeneity of the Coriolis number, which depends o…
Context. Recent discoveries of intensity correlated downflows in the interior of a sunspot penumbra provide direct evidence for overturning convection, adding to earlier strong indications of convection from filament dynamics observed far from solar disk center, and supporting recent simulations of sunspots. Aims. Using spectropolarimetric observations obtained at a spatial resolution approaching 0'.'1 with the Swedish 1-m Solar Telescope (SST) and its spectropolarimeter CRISP, we investigate whether the convective downflows recently discovered in the C i line at 538.03 nm can also be detected…
Helioseismology shows that the regions occupied by convection and differential rotation inside the sun almost coincide. This supports the leading theoretical concept for the origin of differential rotation as a result of interaction between convection and rotation. This talk outlines the current state of the differential rotation theory. Numerical models based on the theory reproduce the observed solar rotation quite closely. The models also compute meridional flow and predict that the flow at the bottom of the convection zone is not small compared to the surface. Theoretical predictions for s…
High-precision photometric observations have revealed ubiquitous stochastic low-frequency photometric variability in early type stars. It has been suggested that this variability arises due to either subsurface convection or internal gravity waves launched by the convective core. Here we show that relevant properties of convection in subsurface convective layers correlate very well with the timescale and amplitude of stochastic low-frequency photometric variability, as well as with the amplitude of macroturbulence. We suggest that low-frequency, stochastic photometric variability and surface t…
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…
We analyse a sunspot simulation in an effort to understand the origin of the convective instabilities giving rise to the penumbral and umbral distinct regimes. We applied the criterion from Gough \& Tayler (1966), accounting for the stabilising effect of the vertical magnetic field to investigate the convective instabilities in a MURaM sunspot simulation. We find: (1) a highly unstable shallow layer right beneath the surface extending all over the simulation box in which convection is triggered by radiative cooling in the photosphere; (2) a deep umbral core (beneath -5 Mm) stabilised against o…
The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this paper, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The resul…
We present a realistic numerical model of sunspot and active region formation based on the emergence of flux bundles generated in a solar convective dynamo. To this end we use the magnetic and velocity fields in a horizontal layer near the top boundary of the solar convective dynamo simulation to drive realistic radiative-magnetohydrodynamic simulations of the upper most layers of the convection zone. The main results are: (1) The emerging flux bundles rise with the mean speed of convective upflows, and fragment into small-scale magnetic elements that further rise to the photosphere, where bip…
A quite remarkable aspect of non-interacting O-stars with detected surface magnetic fields is that they all are very slow rotators. This paper uses this unique property to first demonstrate that the projected rotational speeds of massive, hot stars, as derived using current standard spectroscopic techniques, can be severely overestimated when significant "macroturbulent" line-broadening is present. This may, for example, have consequences for deriving the statistical distribution of rotation rates in massive-star populations, and for the use of these rates in stellar evolution models. It is ne…
Convective motions in the deep layers of the solar convection zone are affected by rotation, making the convective heat transport latitude-dependent, but this is not the case in the top layers near the surface. We use the thermal wind balance condition in the deeper layers to estimate the pole-equator temperature difference. Surface observations of this temperature difference can be used for estimating the depth of the near-surface layer within which convection is not affected by rotation. If we require that the thermal wind balance holds in this layer also, then we have to conclude that this …
Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore,…
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…
We study the generation of large-scale vortices in rotating turbulent convection by means of Cartesian direct numerical simulations. We find that for sufficiently rapid rotation, cyclonic structures on a scale large in comparison to that of the convective eddies, emerge, provided that the fluid Reynolds number exceeds a critical value. For slower rotation, cool cyclonic vortices are preferred, whereas for rapid rotation, warm anti-cyclonic vortices are favored. In some runs in the intermediate regime both types of cyclones co-exist for thousands of convective turnover times. The temperature co…
Pulsation harmonics reveal the origin of the century-old Blazhko effect
Institute of Theoretical Physics, Shanxi University（山西大学理论物理研究所）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
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.
In early-type stars a fossil magnetic field may be generated during the star formation process or be the result of a stellar merger event. Surface magnetic fields are thought to be erased by (sub)surface convection layers, which typically leave behind weak disordered fields. However, if the fossil field is strong enough it can prevent the onset of (sub)surface convection and so be preserved onto the main sequence. We calculate the critical field strength at which this occurs, and find that it corresponds well with the lower limit amplitude of observed fields in strongly magnetised Ap/Bp stars …
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…
Mean-field hydrodynamics advanced to clear explanations for the origin and properties of the global meridional flow in stellar convection zones. Qualitative arguments and analysis of basic equations both show that the meridional circulation is driven by non-conservative centrifugal and buoyancy forces and results from a slight disbalance between these two drivers. The deviations from the thermal wind balance are relatively large near the boundaries of convection zones. Accordingly, the meridional flow attains its largest velocities in the boundary layers and decreases inside the convection zon…
Examination of the temporal variability properties of several strong optical recombination lines in a large sample of Galactic Wolf-Rayet (WR) stars reveals possible trends, especially in the more homogeneous WC than the diverse WN subtypes, of increasing wind variability with cooler subtypes. This could imply that a serious contender for the driver of the variations is stochastic, magnetic subsurface convection associated with the 170 kK partial-ionization zone of iron, which should occupy a deeper and larger zone of greater mass in cooler WR subtypes. This empirical evidence suggests that th…
We investigated the vertical penumbral plasma flow on small spatial scales using data recorded by the spectropolarimeter of the solar optical telescope onboard Hinode. To this end we computed maps of apparent Doppler velocities by comparing the spectral position of the Fe I 630.15 nm & Fe I 630.25 nm lines with the averaged line profiles of the quiet Sun. To visualize the flow pattern in the low photosphere, we used a bisector of the wing of the absorption lines. Due to the small heliocentric angle (3 < Theta < 9) of our data sets, the horizontal component of the Evershed flow (EF) does not co…
We amend Babcock's original scenario for the global dynamo process that sustains the Sun's 22-year magnetic cycle. The amended scenario fits post-Babcock observed features of the magnetic activity cycle and convection zone, and is based on ideas of Spruit and Roberts (1983) about magnetic flux tubes in the convection zone. A sequence of four schematic cartoons lays out the proposed evolution of the global configuration of the magnetic field above, in, and at the bottom of the convection zone through sunspot Cycle 23 and into Cycle 24. Three key elements of the amended scenario are: (1) as the …
We revisit a phenomenological description of turbulent thermal convection along the lines proposed originally by Gough (1965) in which eddies grow solely by extracting energy from the unstably stratified mean state and are subsequently destroyed by internal shear instability. This work is part of an ongoing investigation for finding a procedure to calculate the turbulent fluxes of heat and momentum in the presence of a shearing background flow in stars.
I review our current knowledge of magnetic fields in stars more massive than around 1.5 Msun, in particular their nature and origin. This includes the strong magnetic fields found in a subset of the population and the fossil field theory invoked to explain them; the subgauss fields detected in Vega and Sirius and their possible origin; and what we can infer about magnetic activity in massive stars and how it might be linked to subsurface convection.
As they keep cooling and contracting, Solar System giant planets radiate more energy than they receive from the Sun. Applying the first and second principles of thermodynamics, one can determine their cooling rate, luminosity, and temperature at a given age. Measurements of Saturn's infrared intrinsic luminosity, however, reveal that this planet is significantly brighter than predicted for its age. This excess luminosity is usually attributed to the immiscibility of helium in the hydrogen-rich envelope, leading to "rains" of helium-rich droplets. Existing evolution calculations, however, sugge…
We report the first successful simulation of spontaneous formation of surface magnetic structures from a large-scale dynamo by strongly-stratified thermal convection in Cartesian geometry. The large-scale dynamo observed in our strongly-stratified model has physical properties similar to those in earlier weakly-stratified convective dynamo simulations, indicating that the $α^2$-type mechanism is responsible for it. Additionally to the large-scale dynamo, we find that large-scale structures of the vertical magnetic field are spontaneously formed in the convection zone surface only for the case …
Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it becomes clear that the key to understanding the enigma of sunspots is a synergy between models…
The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric f…
