Author name code: emonet ADS astronomy entries on 2022-09-14 author:"Emonet, Thierry" ------------------------------------------------------------------------ Title: Simulations of magneto-convection in the solar photosphere. Equations, methods, and results of the MURaM code Authors: Vögler, A.; Shelyag, S.; Schüssler, M.; Cattaneo, F.; Emonet, T.; Linde, T. Bibcode: 2005A&A...429..335V Altcode: We have developed a 3D magnetohydrodynamics simulation code for applications in the solar convection zone and photosphere. The code includes a non-local and non-grey radiative transfer module and takes into account the effects of partial ionization. Its parallel design is based on domain decomposition, which makes it suited for use on parallel computers with distributed memory architecture. We give a description of the equations and numerical methods and present the results of the simulation of a solar plage region. Starting with a uniform vertical field of 200 G, the processes of flux expulsion and convective field amplification lead to a dichotomy of strong, mainly vertical fields embedded in the granular downflow network and weak, randomly oriented fields filling the hot granular upflows. The strong fields form a magnetic network with thin, sheet-like structures extending along downflow lanes and micropores with diameters of up to 1000 km which form occasionally at vertices where several downflow lanes merge. At the visible surface around optical depth unity, the strong field concentrations are in pressure balance with their weakly magnetized surroundings and reach field strengths of up to 2 kG, strongly exceeding the values corresponding to equipartition with the kinetic energy density of the convective motions. As a result of the channelling of radiation, small flux concentrations stand out as bright features, while the larger micropores appear dark in brightness maps owing to the suppression of the convective energy transport. The overall shape of the magnetic network changes slowly on a timescale much larger than the convective turnover time, while the magnetic flux is constantly redistributed within the network leading to continuous formation and dissolution of flux concentrations.

Appendices A-D are only available in electronic form at http://www.edpsciences.org Title: The Generation of Surface Magnetic Fields Authors: Cattaneo, F.; Emonet, T. Bibcode: 2004cosp...35.4443C Altcode: 2004cosp.meet.4443C The most readily observable manifestation of convection at the solar surface is the granulation. Granules with a characteristic size of 1,000 km and a lifetime of 5 min are too small and too short-lived to be significantly affected by the solar rotation. Thus, the upper layers of the convective zone are in a state of strongly turbulent, non-helical convection. Because of the high electrical conductivity of the solar plasma, the magnetic Reynmolds number of the granulation is large (> 10^5). These considerations, suggest that the granular flows can act as local small-scale dynamos, generating disordered small-scale magnetic fields with lifetimes comparable to that of the granulation. Numerical simulations support this conclusion showing that intense highly intermittent fields can readily be generated provided the magnetic Reynolds number is large enough. One interesting aspect of the solar small-scale dynamo problem is related to the extremely small value of the plasma viscosity; much smaller than the magnetic diffusivity. In this regime (small magnetic Prandtl number) the velocity has strong fluctuations at the magnetic diffusion scale with profound consequences for the operation of the dynamo. In this talk I will address how our ideas of dynamo action, mostly based on smooth velocity fields, must be modified to account for this fact Title: On the Interaction between Convection and Magnetic Fields Authors: Cattaneo, Fausto; Emonet, Thierry; Weiss, Nigel Bibcode: 2003ApJ...588.1183C Altcode: Turbulent convection in the solar photosphere can act as a small-scale dynamo, maintaining a disordered magnetic field that is locally intense. On the other hand, convection is inhibited in the presence of a strong, externally imposed magnetic field, as for instance, in a sunspot. Large-scale, three-dimensional, numerical experiments on highly nonlinear magnetoconvection in a Boussinesq fluid show that there is a continuous transition from a dynamo regime through a convective regime to an oscillatory regime as the strength of the imposed magnetic field is progressively increased. The patterns found in these different regimes are described and analyzed. Title: Polarization of Photospheric Lines from Turbulent Dynamo Simulations Authors: Sánchez Almeida, J.; Emonet, T.; Cattaneo, F. Bibcode: 2003ApJ...585..536S Altcode: 2002astro.ph.11175S; 2002astro.ph.11175A We employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line. The synthetic Stokes profiles have properties in common with those observed in the quiet Sun. The simulated magnetograms present a level of signal similar to that of the Inter-Network regions. Asymmetric Stokes V profiles with two, three, and more lobes appear in a natural way. The intensity profiles are broadened by the magnetic fields in fair agreement with observational limits. Furthermore, the Hanle depolarization signals of the Sr I λ4607 Å line turn out to be within the solar values. Differences between synthetic and observed polarized spectra can also be found. There is a shortage of Stokes V asymmetries, which we attribute to a deficit of structuring in the magnetic and velocity fields from the simulations as compared to the Sun. This deficit may reflect the fact that the Reynolds numbers of the numerical data are still far from solar values. We consider the possibility that intense and tangled magnetic fields, like those in the simulations, exist in the Sun. This scenario has several important consequences. For example, less than 10% of the existing unsigned magnetic flux would be detected in present magnetograms. The existing flux would exceed by far that carried by active regions during the maximum of the solar cycle. Detecting these magnetic fields would involve improving the angular resolution, the techniques to interpret the polarization signals, and to a lesser extent, the polarimetric sensitivity. Title: The Polarized Spectrum Emerging from Fast Dynamo Simulations Authors: Sánchez Almeida, J.; Emonet, T.; Cattaneo, F. Bibcode: 2003ASPC..307..293S Altcode: No abstract at ADS Title: Simulation of Solar Magnetoconvection Authors: Vögler, A.; Shelyag, S.; Schüssler, M.; Cattaneo, F.; Emonet, T.; Linde, T. Bibcode: 2003IAUS..210..157V Altcode: No abstract at ADS Title: Theories and observations of surface dynamos Authors: Emonet, Thierry Bibcode: 2002ocnd.confE...7E Altcode: No abstract at ADS Title: Small-Scale Photospheric Fields: Observational Evidence and Numerical Simulations Authors: Emonet, Thierry; Cattaneo, Fausto Bibcode: 2001ApJ...560L.197E Altcode: Observations suggest that magnetic fields at the solar photosphere may be structured below the limit of the present resolution. We argue that numerical simulations could be used in a complementary way to observations in order to study the small-scale structure of photospheric fields. We present a number of illustrative examples. Title: The Zigzag Path of Buoyant Magnetic Tubes and the Generation of Vorticity along Their Periphery Authors: Emonet, T.; Moreno-Insertis, F.; Rast, M. P. Bibcode: 2001ApJ...549.1212E Altcode: We study the generation of vorticity in the magnetic boundary layer of buoyant magnetic tubes and its consequences for the trajectory of magnetic structures rising in the solar convection zone. When the Reynolds number is well above 1, the wake trailing the tube sheds vortex rolls, producing a von Kármán vortex street, similar to the case of flows around rigid cylinders. The shedding of a vortex roll causes an imbalance of vorticity in the tube. The ensuing vortex force excites a transverse oscillation of the flux tube as a whole so that it follows a zigzag upward path instead of rising along a straight vertical line. In this paper, the physics of vorticity generation in the boundary layer is discussed and scaling laws for the relevant terms are presented. We then solve the two-dimensional magnetohydrodynamic equations numerically, measure the vorticity production, and show the formation of a vortex street and the consequent sinusoidal path of the magnetic flux tube. For high values of the plasma beta, the trajectory of the tubes is found to be independent of β but varying with the Reynolds number. The Strouhal number, which measures the frequency of vortex shedding, shows in our rising tubes only a weak dependence with the Reynolds numbers, a result also obtained in the rigid-tube laboratory experiments. In fact, the actual values measured in the latter are also close to those of our numerical calculations. As the Reynolds numbers are increased, the amplitude of the lift force grows and the trajectory becomes increasingly complicated. It is shown how a simple analytical equation (which includes buoyancy, drag, and vortex forces) can satisfactorily reproduce the computed trajectories. The different regimes of rise can be best understood in terms of a dimensionless parameter, χ, which measures the importance of the vortex force as compared with the buoyancy and drag forces. For χ2<<1, the rise is drag dominated and the trajectory is mainly vertical with a small lateral oscillation superposed. When χ becomes larger than 1, there is a transition toward a drag-free regime and epicycles are added to the trajectory. Title: Effects of Limited Resolution on the Inferred Structure of Photospheric Magnetic Fields Authors: Emonet, T.; Cattaneo, F. Bibcode: 2001ASPC..236..355E Altcode: 2001aspt.conf..355E No abstract at ADS Title: The Dynamics of Buoyant Magnetic Ropes and the Generation of Vorticity in their Periphery Authors: Emonet, T.; Moreno-Insertis, F.; Rast, M. P. Bibcode: 2000SPD....31.0133E Altcode: 2000BAAS...32..807E When the Reynolds number is not small, the wake trailing a buoyant magnetic flux tube sheds vortex rolls therefore producing a Von Karman vortex street and an imbalance of vorticity in the tube which results in a transverse oscillation of the tube as a whole. The actual path followed by the magnetic structure is therefore directly affected by the amount of vorticity being produced in its boundary. Analytical expressions for the magnetic generation and viscous dissipation of vorticity in the boundary layer of buoyant magnetic flux tubes are obtained. Corresponding scaling laws are deduced and checked using a full compressible 2D MHD code. Interestingly, the observed trajectories can be satisfactorily reproduced by a simple analytical equation (which includes buoyancy, drag and vortex forces). I will conclude with some comparisons with classical results from the hydrodynamical literature (Strouhal number), and some comments about the rise time of buoyant magnetic structures through the solar convection zone. Title: The Physics of Twisted Magnetic Tubes Rising in a Stratified Medium: Two-dimensional Results Authors: Emonet, T.; Moreno-Insertis, F. Bibcode: 1998ApJ...492..804E Altcode: 1997astro.ph.11043E The physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical magnetohydrodynamic (MHD) code. The problem considered is fully compressible (has no Boussinesq approximation), includes ohmic resistivity, and is two-dimensional, i.e., there is no variation of the variables in the direction of the tube axis. We study a high-plasma β-case with a small ratio of radius to external pressure scale height. The results obtained will therefore be of relevance to understanding the transport of magnetic flux across the solar convection zone.

We confirm that a sufficient twist of the field lines around the tube axis can suppress the conversion of the tube into two vortex rolls. For a tube with a relative density deficit on the order of 1/β (the classical Parker buoyancy) and a radius smaller than the pressure scale height (R2<<H2p), the minimum amount of twist necessary corresponds to an average pitch angle on the order of sin-1 [(R/Hp)1/2]. The evolution of a tube with this degree of twist is studied in detail, including the initial transient phase, the internal torsional oscillations, and the asymptotic, quasi-stationary phase. During the initial phase, the outermost, weakly magnetized layers of the tube are torn off its main body and endowed with vorticity. They yield a trailing magnetized wake with two vortex rolls. The fraction of the total magnetic flux that is brought to the wake is a function of the initial degree of twist. In the weakly twisted case, most of the initial tube is turned into vortex rolls. With a strong initial twist, the tube rises with only a small deformation and no substantial loss of magnetic flux. The formation of the wake and the loss of flux from the main body of the tube are basically complete after the initial transient phase.

A sharp interface between the tube interior and the external flows is formed at the tube front and sides; this area has the characteristic features of a magnetic boundary layer. Its structure is determined as an equilibrium between ohmic diffusion and field advection through the external flows. It is the site of vorticity generation via the magnetic field during the whole tube evolution.

From the hydrodynamical point of view, this problem constitutes an intermediate case between the rise of air bubbles in water and the motion of a rigid cylinder in an external medium. As with bubbles, the tube is deformable and the outcome of the experiment (the shape of the rising object and the wake) depends on the value of the Weber number. Several structural features obtained in the present simulation are also observed in rising air bubbles, such as a central tail, and a skirt enveloping the wake. As in rigid cylinders, the boundary layer satisfies a no-slip condition (provided for in the tube by the magnetic field), and secondary rolls are formed at the lateral edges of the moving object. Title: The internal structure of rising twisted magnetic tubes and the emergence of magnetic flux in the Sun Authors: Emonet, T. Bibcode: 1997PhDT.........8E Altcode: No abstract at ADS Title: The Rise of Magnetic Flux Tubes across a Stratified Medium: Effects of the Twist Authors: Emonet, T.; Moreno-Insertis, F. Bibcode: 1997ASPC..118...71E Altcode: 1997fasp.conf...71E The results of a 2D numerical simulation of the rise of twisted magnetic flux tubes are sketched. The theoretical criterion for the minimum twist necessary to prevent the conversion of the tube into a pair of strong vortices is shown to be correct. The transition from a low-twist to a high-twist regime is exemplified. There is a sharp transition between the tube interior and the outside medium. A well-developed wake is formed, which however contains only a fraction of the original magnetic flux of the tube. Title: The Rise of Twisted Magnetic Tubes in a Stratified Medium Authors: Moreno-Insertis, F.; Emonet, T. Bibcode: 1996ApJ...472L..53M Altcode: First results from a two-dimensional numerical study of the buoyant rise of twisted magnetic flux tubes in the solar convection zone are presented. We show in detail the process by which the transverse component of the field can suppress the splitting of the rising tube into two vortex filaments. For the suppression to be effective, the pitch angle of the twisted field lines has to be above a threshold given by the condition that the magnetic equivalent of the Weber number (see § 2.2) be below 1. The shape obtained for the tube and wake is strongly reminiscent of laboratory experiments with air bubbles rising in liquids. The magnetized region outside an equipartition boundary is peeled away from the tube: two sidelobes are formed, which lag behind the tube and contain only a fraction of the initial magnetic flux. This is similar to the formation of a skirt in the fluid dynamical case. The velocities of rise predicted by the thin flux tube approximation are compared with those obtained here. Title: Equilibrium of Twisted Horizontal Magnetic Flux Tubes Authors: Emonet, T.; Moreno-Insertis, F. Bibcode: 1996ApJ...458..783E Altcode: The equilibrium of non-force-free twisted horizontal magnetic flux tubes is studied including gravity and an arbitrary pressure perturbation on the tube boundary. To solve this free-boundary problem, we use general nonorthogonal flux coordinates and consider the two-dimensional case in which there is no variation of the physical quantities along the tube axis. For the applications in the convection zone and corona, we consider the case of weak external stratification by assuming that the radius of the tube is smaller than the external pressure scale height. This allows us to introduce a perturbation scheme which is much less restrictive than the customary slender flux-tube approximation. In particular, it has the advantage of not imposing any limitation on the strength of the azimuthal field as compared to the longitudinal field. Within this scheme, one retains to zero order all the functional degrees of freedom of a general axisymmetric magnetostatic equilibrium; the geometry of the perturbed azimuthal field lines is then obtained from the equilibrium equations as a consequence of the zero-order density (or rather buoyancy) distribution in the tube and of the circular wavenumber of the external pressure perturbation. We show that, as a result of the presence of gravity, the field lines are no longer concentric, although they continue being circular. The resulting changes in magnetic pressure and tension of the azimuthal field exactly counteract the differences in buoyancy in the tube cross section. On the other hand, external pressure fluctuations of circular wavenumber higher than one can only be countered by bending the azimuthal field lines. In general terms, the present scheme allows one to study in detail the mutual dependence of the (differential) buoyancy in the tube, the intensity and field line geometry of the azimuthal magnetic field, and the gas pressure and longitudinal magnetic field distributions.

The main application of the equations and results of this paper is to study the transverse structure of magnetic flux rings embedded in a stratified medium with a flow around the tube that causes pressure fluctuations on its surface. This includes tubes in the deep convection zone, e.g., in its subadiabatic lower part, or those kept in place by a meridional flow. It also applies to flux rings moving in a quasi-static regime in which the drag force of the relative motion with respect to the external medium exactly compensates the total buoyancy of the tube. In this way, this study can complement the numerical simulations of the rise of magnetized tubes and bubbles toward the surface. Title: MHS-Equilibrium of Twisted Magnetic Tubes Authors: Emonet, T.; Moreno-Insertis, F. Bibcode: 1996ApL&C..34....9E Altcode: No abstract at ADS