The frequencies of solar oscillations are known to change with solar activity. We use Principal Component Analysis to examine these changes with high precision. In addition to the well-documented changes in solar normal mode oscillations with activity as a function of frequency, which originate in the surface layers of the Sun, we find a small but statistically significant change in frequencies with an origin at and below the base of the convection zone. We find that at r=(0.712^{+0.0097}_{-0.0029})R_sun, the change in sound speed is δc^2 / c^2 = (7.23 +/- 2.08) x 10^{-5} between high and low activity. This change is very tightly correlated with solar activity. In addition, we use the splitting coefficients to examine the latitudinal structure of these changes. We find changes in sound speed correlated with surface activity for r >~ 0.9R_sun.
Using data from the Global Oscillations Network Group (GONG) that covers the period from 1995 to 1998 we study the change in frequencies of solar oscillations with solar activity. From these frequencies we attempt to determine any possible variation in solar structure with solar activity. We do not find any evidence of a change in the convection zone depth or extent of overshoot below the convection zone during the solar cycle.
Helioseismology has provided very detailed inferences about rotation of the solar interior. Within the convection zone the rotation rate roughly shares the latitudinal variation seen in the surface differential rotation. The transition to the nearly uniformly rotating radiative interior takes place in a narrow tachocline, which is likely important to the operation of the solar magnetic cycle.The convection-zone rotation displays zonal flows, regions of slightly more rapid and slow rotation, extending over much of the depth of the convection zone and converging towards the equator as the solar …
The development of 2D and 3D simulations of solar convection has lead to a picture of convection quite unlike the usually assumed Kolmogorov spectrum turbulent flow. We investigate the impact of this changed structure on the dissipation properties of the convection zone, parametrized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh 1997, applied to a numerical model of solar convection (Robinson et al. 2003) to calculate an effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of…
A-type stars have a complex internal structure with the possibility of multiple convection zones. If not sufficiently separated, such zones will interact through the convectively stable regions that lie between them. It is therefore of interest to ask whether the typical conditions that exist within such stars are such that these convections zones can ever be considered as disjoint. In this paper we present results from numerical simulations that help in understanding how increasing the distance between the convectively unstable regions are likely to interact through the stable region that sep…
We consider the radial structure of radiatively inefficient hydrodynamic accretion flows around black holes. We show that low-viscosity flows consist of two zones: an outer convection-dominated zone and an inner advection-dominated zone. The transition between these two zones occurs at ~50 Schwarzschild radii.
All numerical simulations of compressible convection reveal the presence of strong downwards directed flows. Thanks to helioseismology, such plumes have now been detected also at the top of the solar convection zone, on super- granular scales. Their properties may be crudely described by adopting Taylor's turbulent entrainment hypothesis, whose validity is well established under various conditions. Using this model, one finds that the strong density stratification does not prevent the plumes from traversing the whole convection zone, and that they carry upwards a net energy flux (Rieutord & Za…
The convection code of Nordlund & Stein has been used to evaluate the 3D, radiation-coupled convection in a stellar atmosphere with Teff=7300K, logg=4.3 and [Fe/H]=0.0, corresponding to a main-sequence A9-star. I will present preliminary comparisons between the 3D-simulation and a conventional 1D stellar structure calculation, and elaborate on the consequences of the differences.
We present results from simulations to examine how the separation between two convectively unstable layers affect their interaction. We show that two convectively unstable layers remain connected via the overshooting plumes even when they are separated by several pressure scale heights.
The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a $\Lam$-effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations ($\partial\Om/\partial r<0$ and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significa…
Meridional flows with velocities of a few meters per second are observed in the uppermost regions of the solar convection zone. The amplitude and pattern of the flows deeper in the solar interior, in particular near the top of the radiative region, are of crucial importance to a wide range of solar magnetohydrodynamical processes. In this paper, we provide a systematic study of the penetration of large-scale meridional flows from the convection zone into the radiative zone. In particular, we study the effects of the assumed boundary conditions applied at the convective-radiative interface on t…
The property of inhomogeneous turbulence in conducting fluids to expel large-scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity of the convection zone to the (microscopic or turbul…
The latitudinal sound-speed structure of the Sun's convection zone gives insight into the physical processes occurring there, specifically the cellular convection and possibly the presence of magnetic fields. Using helioseismic data from the GONG network and MDI instrument on SOHO, we map the latitudinal acoustic structure of the convection zone from 1995 to 2002. The temporally averaged structure confirms previous findings of an excess in sound speed at the $10^{-4}$ level at 60 degrees latitude. There also appear to be some variations with time, with the peak in sound-speed asphericity at 60…
We study the solar-cycle variations of solar p-mode travel time for different wave packets to probe the magnetic fields at the base of the solar convection zone. We select the wave packets which return to the same spatial point after traveling around the Sun with integral number of bounces. The change in one-bounce travel time at solar maximum relative to minimum is approximately the same for all wave packets studied except a wave packet whose lower turning point is located at the base of the convection zone. This particular wave packet has an additional decrease in travel time at solar maximu…
We perform Large eddy simulations of turbulent compressible convection in stellar-type convection zones by solving the Naviér-Stokes equations in three dimensions. We estimate the extent of penetration into the stable layer above a stellar-type convection zone by varying the rotation rate ({\boldmath$\rmΩ$}), the inclination of the rotation vector ($θ$) and the relative stability ($S$) of the upper stable layer. The computational domain is a rectangular box in an f-plane configuration and is divided into two regions of unstable and stable stratification with the stable layer placed above the c…
One of the key questions in solar physics that remains to be answered concerns the strength and the distribution of the magnetic fields at the base of the convection zone. The flux tube dynamics requires that toroidal fields of strength as large as 100 kilogauss be present at the base of the convection zone. The kinetic-magnetic equipartition argument leads to smaller field strengths. For possible detection of these relatively small (compared to pressure effects) fields by helioseismic methods it is important to know the range of the field strengths and their distribution. We estimate a range …
We present results on variation in rotation rate in the upper convection zone using data from GONG and MDI/SOHO covering a period of more than four years. We find that the first few odd-order splitting coefficients vary systematically with the solar cycle. The rotation rate near the solar surface calculated from analytical methods agrees well with that of inversion techniques. The residual rotation rate in the outer layers seem to be correlated with the solar activity.
We present results of two simulations of the convection zone, obtained by solving the full hydrodynamic equations in a section of a spherical shell. The first simulation has cylindrical rotation contours (parallel to the rotation axis) and a strong meridional circulation, which traverses the entire depth. The second simulation has isorotation contours about mid-way between cylinders and cones, and a weak meridional circulation, concentrated in the uppermost part of the shell. We show that the solar differential rotation is directly related to a latitudinal entropy gradient, which pervades into…
Recent analysis of the helioseismic observations indicate that the previously observed surface torsional oscillations extend significantly downwards into the solar convection zone. In an attempt to understand these oscillations, we study the nonlinear coupling between the magnetic field and the solar differential rotation in the context of a mean field dynamo model, in which the nonlinearity is due to the action of the azimuthal component of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. The underlying zero order angular velocity is chosen to be consist…
Under nonlocal convection theory, convection extends without limit therefore no apparent boundary can be defined clearly as in the local theory. From the requirement of a similar structure for both local and non-local models having the same depth of convection zone, and taking into account the driving mechanism of turbulent convection, we argue that a proper definition of the boundary of a convective zone should be the place where the convective energy flux (i.e. the correlation of turbulent velocity and temperature) changes its sign. Therefore, it is convectively unstable region when the flux…
We present the first results from three-dimensional spherical shell simulations of magnetic dynamo action realized by turbulent convection penetrating downward into a tachocline of rotational shear. This permits us to assess several dynamical elements believed to be crucial to the operation of the solar global dynamo, variously involving differential rotation resulting from convection, magnetic pumping, and amplification of fields by stretching within the tachocline. The simulations reveal that strong axisymmetric toroidal magnetic fields (about 3000 G in strength) are realized within the lowe…
In this paper we report on the nonresonant conversion of convectively unstable linear gravity modes into acoustic oscillation modes in shear flows. The convectively unstable linear gravity modes can excite acoustic modes with similar wave-numbers. The frequencies of the excited oscillations may be qualitatively higher than the temporal variation scales of the source flow, while the frequency spectra of the generated oscillations should be intrinsically correlated to the velocity field of the source flow. We anticipate that this nonresonant phenomenon can significantly contribute to the product…
This is the fourth in a series of papers that deal with angular momentum transport by internal gravity waves in stellar interiors. Here, we want to examine the potential role of waves in other evolutionary phases than the main sequence. We study the evolution of a 3Msun Population I model from the pre-main sequence to the early-AGB phase and examine whether waves can lead to angular momentum redistribution and/or element diffusion at the external convection zone boundary. We find that, although waves produced by the surface convection zone can be ignored safely for such a star during the main …
Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface corresponding to the so-called `torsional oscillations' known from Doppler measurements of the surface. These appear as bands of slower and faster than average rotation moving equatorward. Here we establish, using complementary helioseismic observations over four years from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather they extend downward at least 60 Mm (some 8% of the total solar radius) and thus ar…
Recent analyses of the helioseismic data have produced evidence for a variety of interesting dynamical behaviour associated with torsional oscillations. What is not so far clear is whether these oscillations extend all the way to the bottom of the convection zone and, if so, whether the oscillatory behaviour at the top and the bottom of the convection zone is different. Attempts have been made to understand such modes of behaviour within the framework of nonlinear dynamo models which include the nonlinear action of the Lorentz force of the dynamo generated magnetic field on the solar angular v…
We obtain global solutions of radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self-consistently determined with the mixing-length theory. The solutions can be divided into three types according to the strength of normal viscosity. Type I solution corresponds to large viscosity parameter $α\ga 0.1$, which is purely advection-dominated and with no convection, and has been extensively studied in the literature. Type II solution is for moderate $α\sim 0.01$, which has a three-zone structure. The inner zone is advection-dominated, th…
Abundance analyses of stars with planets have revealed that their metallicities are enhanced relative to field stars. Such a trend was originally suggested to be due to accretion of iron-rich planetary material. Based on this assumption, we have developed a stellar evolution code to model stars with non-uniform metallicity distributions. We have calculated ``polluted'' stellar evolution tracks for stars with M=0.9-1.2 M_sun. Our models encompass a range of initial metal content from Z=0.01 to 0.03, and include metallicity enhancements within the stellar convection zone corresponding to Delta-Z…
The observed splittings of solar oscillation frequencies can be employed to separate the effects of internal solar rotation and to estimate the contribution from a large-scale magnetic field or any latitude-dependent thermal perturbation inside the Sun. The surface distortion estimated from the rotation rate in the solar interior is found to be in good agreement with the observed oblateness at solar surface. After subtracting out the estimated contribution from rotation, there is some residual signal in the even splitting coefficients, which may be explained by a magnetic field of approximatel…
In this paper we discuss the transport of toroidal magnetic field by a weak meridional flow at the base of the convection zone. We utilize the differential rotation and meridional flow model developed by Rempel and incorporate feedback of a purely toroidal magnetic field in two ways: directly through the Lorentz force (magnetic tension) and indirectly through quenching of the turbulent viscosity, which affects the parametrized turbulent angular momentum transport in the model. In the case of direct Lorentz force feedback we find that a meridional flow with an amplitude of around 2 m/s can tran…
Recent analyses of the helioseismic observations indicate that the previously observed surface torsional oscillations with periods of about 11 years extend significantly downwards into the solar convective zone. Furthermore, there are indications that the dynamical regimes at the base of the convection zone are different from those observed at the top, having either significantly shorter periods or non-periodic behaviour. We propose that this behaviour can be explained by the occurrence of {\it spatiotemporal fragmentation}, a crucial feature of which is that such behaviour can be explained so…
Recent analyses of helioseismological observations seem to suggest the presence of two new phenomena connected with the dynamics of the solar convective zone. Firstly, there are present torsional oscillations with periods of about 11 years, which penetrate significantly into the solar convection zone and secondly, oscillatory regimes exist near the base of the convection which are markedly different from those observed near the top, having either significantly reduced periods or being non-periodic. Recently spatiotemporal fragmentation/bifurcation has been proposed as a possible dynamical mech…
Ring diagram analysis of solar oscillation power spectra obtained from MDI data is performed to study the velocity fields within the solar convection zone. The three dimensional power spectra are fitted to a model with a Lorentzian profile in frequency and includes the advection of the wave front by horizontal flows to obtain the two horizontal components of flows as a function of the horizontal wave number and radial order of the oscillation modes. This information is then inverted using the OLA and RLS techniques to infer the variation in flow velocity with depth. The resulting velocity fiel…
In an attempt to understand the properties of convective energy transport in the solar convection zone, a numerical model has been constructed for turbulent flows in a compressible, radiation-coupled, non-magnetic, gravitationally stratified medium using a realistic equation of state and realistic opacities. The time-dependent, three-dimensional hydrodynamic equations are solved with minimal simplifications. The statistical information obtained from the present simulation provides an improved understanding of solar photospheric convection. The characteristics of solar convection in shallow reg…
Recent downward revision of solar heavy-element abundances using three-dimensional atmospheric model has introduced serious discrepancies between standard solar models and helioseismic inferences about solar structure. In this paper, we investigate the possibility of determining the heavy-element abundances using helioseismic inversion techniques with the hope of providing an independent estimate. We use the adiabatic index, Gamma_1 (logarithmic partial derivative of pressure with respect to density at constant entropy) as a probe to examine the effects of the total heavy-element abundance, as…
We present three-dimensional MHD simulations of buoyant magnetic flux tubes that rise through a stratified model convection zone in the presence of solar rotation. The equations of MHD are solved in the anelastic approximation, and the results are used to determine the effects of solar rotation on the dynamic evolution an Omega-loop. We find that the Coriolis force significantly suppresses the degree of fragmentation at the apex of the loop during its ascent toward the photosphere. If the initial axial field strength of the tube is reduced, then, in the absence of forces due to convective moti…
We use the three-dimensional hydrodynamic code of Stein and Nordlund to realistically simulate the upper layers of the solar convection zone in order to study physical characteristics of solar oscillations. Our first result is that the properties of oscillation modes in the simulation closely match the observed properties. Recent observations from SOHO/MDI and GONG have confirmed the asymmetry of solar oscillation line profiles, initially discovered by Duvall et al. In this paper we compare the line profiles in the power spectra of the Doppler velocity and continuum intensity oscillations from…
The chromosphere in internetwork regions of the quiet Sun was regarded as a static and homogeneous layer for a long time. Thanks to advances in observations and numerical modelling, the wave nature of these atmospheric regions received increasing attention during the last decade. Recent three-dimensional radiation magnetohydrodynamic simulations with CO5BOLD feature the chromosphere of internetwork regions as a dynamic and intermittent phenomenon. It is a direct product of interacting waves that form a mesh-like pattern of hot shock fronts and cool post-shock regions. The waves are excited sel…
The predictability, or lack thereof, of the solar cycle is governed by numerous separate physical processes that act in unison in the interior of the Sun. Magnetic flux transport and the finite time delay it introduces, specifically in the so-called Babcock-Leighton models of the solar cycle with spatially segregated source regions for the alpha and omega effects, play a crucial rule in this predictability. Through dynamo simulations with such a model, we study the physical basis of solar cycle predictions by examining two contrasting regimes, one dominated by diffusive magnetic flux transport…
A magnetic flux tube may be considered both as a separate body and as a confined field. As a field, it is affected both by the cyclonic convection ($α$-effect) and differential rotation ($Ω$-effect). As a body, the tube experiences not only a buoyant force, but also a dynamic pressure due to downflows above the tube. When these two dynamic effects are incorporated into the $αΩ$ dynamo equations, we obtain a dynamo operating in the convection zone. We analyze and solve the extended dynamo equations in the linear approximation by using observed solar internal rotation and assuming a downflow sug…
We have derived the mean broadening profile of the star V102 in the region of the open cluster IC4665 from high resolution spectroscopy. At a projected equatorial rotation velocity of vsini = (105 +- 12)km/s we find strong deviation from classical rotation. We discuss several scenarios, the most plausible being strong differential rotation in latitudinal direction. For this scenario we find a difference in angular velocity of DeltaOmega = 3.6 +- 0.8 rad/d (DeltaOmega/Omega = 0.42 +- 0.09). From the Halpha line we derive a spectral type of A9 and support photometric measurements classifying IC4…
We present three-dimensional numerical simulations of the rise and fragmentation of twisted, initially horizontal magnetic flux tubes which evolve into emerging Omega-loops. The flux tubes rise buoyantly through an adiabatically stratified plasma that represents the solar convection zone. The MHD equations are solved in the anelastic approximation, and the results are compared with studies of flux tube fragmentation in two dimensions. We find that if the initial amount of field line twist is below a critical value, the degree of fragmentation at the apex of a rising Omega-loop depends on its t…
Magneto-convection simulations on meso-granule and granule scales near the solar surface are used to study small scale dynamo activity, the emergence and disappearance of magnetic flux tubes, and the formation and evolution of micropores. From weak seed fields, convective motions produce highly intermittent magnetic fields in the intergranular lanes which collect over the boundaries of the underlying meso-granular scale cells. Instances of both emerging magnetic flux loops and magnetic flux disappearing from the surface occur in the simulations. We show an example of a flux tube collapsing to …
The overall framework for the study of solar convection and oscillations is the spherically symmetric component of solar structure. I discuss those properties of the solar interior which depend on convection and other possible hydrodynamical motion and the increasingly detailed information about the structure which is provided by helioseismic data. The most basic dependence of solar models on convection is the calibration to fix the solar radius. The dominant causes for differences in oscillation frequencies between the Sun and solar models seem to be located near the top of the convection zon…
We present numerical simulations of penetrative convection and gravity wave excitation in the Sun. Gravity waves are self-consistently generated by a convective zone overlying a radiative interior. We produce power spectra for gravity waves in the radiative region as well as estimates for the energy flux of gravity waves below the convection zone. We calculate a peak energy flux in waves below the convection zone to be three orders of magnitude smaller than previous estimates for m=1. The simulations show that the linear dispersion relation is a good approximation only deep below the convectiv…
We perform helioseismic holography to assess the noise in p-mode travel-time shifts which would form the basis of inferences of large-scale flows throughout the solar convection zone. We also derive the expected travel times from a parameterized return (equatorward) flow component of the meridional circulation at the base of the convection zone from forward models under the assumption of the ray and Born approximations. From estimates of the signal-to-noise ratio for measurements focused near the base of the convection zone, we conclude that the helioseismic detection of the deep meridional fl…
We present recent 3-D MHD numerical simulations of the non-linear dynamical evolution of magnetic flux tubes in an adiabatically stratified convection zone in spherical geometry, using the anelastic spherical harmonic (ASH) code. We seek to understand the mechanism of emergence of strong toroidal fields from the base of the solar convection zone to the solar surface as active regions. We confirm the results obtained in cartesian geometry that flux tubes that are not twisted split into two counter vortices before reaching the top of the convection zone. Moreover, we find that twisted tubes unde…
This paper is a ``Habilitationsschrift'', a second thesis required until recently by universities in Germany and in a few other countries to obtain the right to lecture. It was accepted by the University of Goettingen in 1990 after review by a number of german and international experts. Although the introduction and the references represent the state of research in 1990, most of the remaining content is still relevant and has never been published elsewhere. The most important part is the derivation of a linear stability formalism for thin magnetic flux tubes following an arbitrary path in a gr…
We present first realistic numerical simulations of 3D radiative convection in the surface layers of main sequence A-type stars with Teff = 8000 K and 8500 K, log g = 4.4 and 4.0, recently performed with the CO5BOLD radiation hydrodynamics code. The resulting models are used to investigate the structure of the H+HeI and the HeII convection zones in comparison with the predictions of local and non-local convection theories, and to determine the amount of "overshoot" into the stable layers below the HeII convection zone. The simulations also predict how the topology of the photospheric granulati…
We performed high-resolution simulations of two stellar collisions relevant for stars in globular clusters. We considered one head-on collision and one off-axis collision between two 0.6 M_sun main sequence stars. We show that a resolution of about 100 000 particles is sufficient for most studies of the structure and evolution of blue stragglers. We demonstrate conclusively that collision products between main-sequence stars in globular clusters do not have surface convection zones larger than 0.004 M_sun after the collision, nor do they develop convection zones during the `pre-main-sequence' …
Results of numerical 3D simulations of propagation of acoustic waves inside the Sun are presented. A linear 3D code which utilizes realistic OPAL equation of state was developed by authors. Modified convectively stable standard solar model with smoothly joined chromosphere was used as a background model. High order dispersion relation preserving numerical scheme was used to calculate spatial derivatives. The top non-reflecting boundary condition established in the chromosphere absorbs waves with frequencies greater than the acoustic cut-off frequency which pass to the chromosphere, simulating …
3D numerical simulations of a horizontal magnetic flux tube emergence with different twist are carried out in a computational domain spanning the upper layers of the convection zone to the lower corona. We use the Oslo Staggered Code to solve the full MHD equations with non-grey and non-LTE radiative transfer and thermal conduction along the magnetic field lines. The emergence of the magnetic flux tube input at the bottom boundary into a weakly magnetized atmosphere is presented. The photospheric and chromospheric response is described with magnetograms, synthetic images and velocity field dis…
The intense turbulence present in the solar convection zone is a major challenge to both theory and simulation as one tries to understand the origins of the striking differential rotation profile with radius and latitude that has been revealed by helioseismology. The differential rotation must be an essential element in the operation of the solar magnetic dynamo and its cycles of activity, yet there are many aspects of the interplay between convection, rotation and magnetic fields that are still unclear. We have here carried out a series of 3--D numerical simulations of turbulent convection wi…
Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear layer is likely to play an important role in this scenario.
