Juri Toomre

Galactic bridges and tails.

This paper argues that the bridges and tails seen in some multiple galaxies are just tidal relics of close encounters. These consequences of the brief but violent tidal forces are here studied in a deliberately simple-minded fashion. Each encounter is considered to involve only two galaxies and to be roughly parabolic; each galaxy is idealized as just a disk of noninteracting test particles which initially orbit a central mass point. As shown here, the two-sided distortions provoked by gravity alone in such circumstances can indeed evolve kinematically into some remarkably narrow and elongated features. Besides extensive pictorial survey of tidal damage, this paper offers reconstructions of the orbits and outer shapes of four specific interacting pairs: Arp 295, M51 + NGC 5195, NGC 4676, and NGC 4038/9.

Helioseismic Studies of Differential Rotation in the Solar Envelope by the Solar Oscillations Investigation Using the Michelson Doppler Imager

The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.

Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope

The operation of the solar global dynamo appears to involve many dynamical elements, including the generation of fields by the intense turbulence of the deep convection zone, the transport of these fields into the tachocline region near the base of the convection zone, the storage and amplification of toroidal fields in the tachocline by differential rotation, and the destabilization and emergence of such fields due to magnetic buoyancy. Self-consistent magnetohydrodynamic (MHD) simulations that realistically incorporate all of these processes are not yet computationally feasible, although some elements can now be studied with reasonable fidelity. Here we consider the manner in which turbulent compressible convection within the bulk of the solar convection zone can generate large-scale magnetic fields through dynamo action. We accomplish this through a series of three-dimensional numerical simulations of MHD convection within rotating spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. Since differential rotation is a key ingredient in all dynamo models, we also examine here the nature of the rotation profiles that can be sustained within the deep convection zone as strong magnetic fields are built and maintained. We find that the convection is able to maintain a solar-like angular velocity profile despite the influence of Maxwell stresses, which tend to oppose Reynolds stresses and thus reduce the latitudinal angular velocity contrast throughout the convection zone. The dynamo-generated magnetic fields exhibit a complex structure and evolution, with radial fields concentrated in downflow lanes and toroidal fields organized into twisted ribbons that are extended in longitude and achieve field strengths of up to 5000 G. The flows and fields exhibit substantial kinetic and magnetic helicity although systematic hemispherical patterns are only apparent in the former. Fluctuating fields dominate the magnetic energy and account for most of the back-reaction on the flow via Lorentz forces. Mean fields are relatively weak and do not exhibit systematic latitudinal propagation or periodic polarity reversals as in the Sun. This may be attributed to the absence of a tachocline, i.e., a penetrative boundary layer between the convection zone and the deeper radiative interior possessing strong rotational shear. The influence of such a layer will await subsequent studies.

Evolving Submerged Meridional Circulation Cells within the Upper Convection Zone Revealed by Ring-Diagram Analysis

Using the local helioseismic technique of ring-diagram analysis applied to Michelson Doppler Imager (MDI) Dynamics Program data from the Solar and Heliospheric Observatory, we have discovered that the meridional flow within the upper convection zone can develop additional circulation cells whose boundaries wander in latitude and depth as the solar cycle progresses. We report on the large-scale meridional and zonal flows that we observe from 1996 to 2001. In particular, we discuss the appearance and evolution of a submerged meridional cell during the years 1998-2001, which arose in the northern hemisphere and disrupted the orderly poleward flow and symmetry about the equator that is typically observed. The meridional flows in the southern and northern hemispheres exhibit striking asymmetry during the past four years of the advancing solar cycle. Such asymmetry and additional circulation cells should have profound impact on the transport of angular momentum and magnetic field within the surface layers. These flows may have a significant role in the establishment and maintenance of the near-surface rotational shear layer.

THREE-DIMENSIONAL SPHERICAL SIMULATIONS OF SOLAR CONVECTION. I. DIFFERENTIAL ROTATION AND PATTERN EVOLUTION ACHIEVED WITH LAMINAR AND TURBULENT STATES

Rotationally constrained convection possesses velocity correlations that transport momentum and drive mean —ows such as diUerential rotation. The nature of this transport can be very complex in turbu- lent —ow regimes, where large-scale, coherent vorticity structures and mean —ows can be established by smaller scale turbulence through inverse cascades. The dynamics of the highly turbulent solar convection zone therefore may be quite diUerent than in early global-scale numerical models, which were limited by computational resources to nearly laminar —ows. Recent progress in high-performance computing tech- nology and ongoing helioseismic investigations of the dynamics of the solar interior have motivated us to develop more sophisticated numerical models of global-scale solar convection. Here we report three- dimensional simulations of compressible, penetrative convection in rotating spherical shells in both laminar and turbulent parameter regimes. The convective structure in the laminar case is dominated by ii banana cells,ˇˇ but the turbulent case is much more complex, with an intricate, rapidly evolving down- —ow network in the upper convection zone and an intermittent, plume-dominated structure in the lower convection zone and overshoot region. Convective patterns generally propagate prograde at low lati- tudes and retrograde at high latitudes relative to the local rotation. The diUerential rotation pro—les show some similarity with helioseismic determinations of the solar rotation but still exhibit signi—cantly more cylindrical alignment. Strong, intermittent, vortical down—ow lanes and plumes play an important dynamical role in turbulent —ow regimes and are responsible for signi—cant diUerences relative to laminar —ows with regard to momentum and energy transport and to the structure of the overshoot region at the base of the convection zone. Subject headings: convectionhydrodynamicsstars: interiorsSun: interiorSun: rotation ¨ turbulence

The Global Oscillation Network Group (GONG) Project

Helioseismology requires nearly continuous observations of the oscillations of the solar surface for long periods of time in order to obtain precise measurements of the suns normal modes of oscillation. The GONG project acquires velocity images from a network of six identical instruments distributed around the world. The GONG network began full operation in October 1995. It has achieved a duty cycle of 89 percent and reduced the magnitude of spectral artifacts by a factor of 280 in power, compared with single-site observations. The instrumental noise is less than the observed solar background.

Turbulent Convection under the Influence of Rotation: Sustaining a Strong Differential Rotation

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 three-dimensional numerical simulations of turbulent convection within deep spherical shells using our anelastic spherical harmonic (ASH) code on massively parallel supercomputers. These studies of the global dynamics of the solar convection zone concentrate on how the differential rotation and meridional circulation are established. We have addressed two issues raised by previous simulations with ASH. First, can solutions be obtained that possess the apparent solar property that the angular velocity Ω continues to decrease significantly with latitude as the pole is approached? Prior simulations had most of their rotational slowing with latitude confined to the interval from the equator to about 45°. Second, can a strong latitudinal angular velocity contrast ΔΩ be sustained as the convection becomes increasingly more complex and turbulent? There was a tendency for ΔΩ to diminish in some of the turbulent solutions that also required the emerging energy flux to be invariant with latitude. In responding to these questions, five cases of increasingly turbulent convection coupled with rotation have been studied along two paths in parameter space. We have achieved in one case the slow pole behavior comparable to that deduced from helioseismology and have retained in our more turbulent simulations a consistently strong ΔΩ. We have analyzed the transport of angular momentum in establishing such differential rotation and clarified the roles played by Reynolds stresses and the meridional circulation in this process. We have found that the Reynolds stresses are crucial in transporting angular momentum toward the equator. The effects of baroclinicity (thermal wind) have been found to have a modest role in the resulting mean zonal flows. The simulations have produced differential rotation profiles within the bulk of the convection zone that make reasonable contact with ones inferred from helioseismic inversions, namely, possessing a fast equator, an angular velocity difference of about 30% from equator to pole, and some constancy along radial lines at midlatitudes. Future studies must address the implications of the tachocline at the base of the convection zone, and the near-surface shear layer, on that differential rotation.

Differential rotation and dynamics of the solar interior

Splitting of the suns global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes.

Solar Differential Rotation Influenced by Latitudinal Entropy Variations in the Tachocline

Three-dimensional simulations of solar convection in spherical shells are used to evaluate the differential rotation that results as thermal boundary conditions are varied. In some simulations a latitudinal entropy variation is imposed at the lower boundary in order to take into account the coupling between the convective envelope and the radiative interior through thermal wind balance in the tachocline. The issue is whether the baroclinic forcing arising from tachocline-induced entropy variations can break the tendency for numerical simulations of convection to yield cylindrical rotation profiles, unlike the conical profiles deduced from helioseismology. As the amplitude of the imposed variation is increased, cylindrical rotation profiles do give way to more conical profiles that exhibit nearly radial angular velocity contours at midlatitudes. Conical rotation profiles are maintained primarily by the resolved convective heat flux, which transmits entropy variations from the lower boundary into the convective envelope, giving rise to baroclinic forcing. The relative amplitude of the imposed entropy variations is of order 10 � 5 , corresponding to a latitudinal temperature variation of about 10 K. The role of thermal wind balance and tachoclineinduced entropy variations in maintaining the solar differential rotation is discussed. Subject headingg convection — Sun: interior — Sun: rotation

Transport and Storage of Magnetic Field by Overshooting Turbulent Compressible Convection

We present the results of a series of numerical experiments that investigate the transport of magnetic —elds by turbulent penetrative compressible convection. We —nd that magnetic —ux is preferentially transported downward out of a turbulent convecting region and stored in a stably strati—ed region below. This pumping mechanism is believed to be a crucial component for the operation of a large-scale solar interface dynamo since it may be responsible for the transport of —ux from the solar convection zone to the stable overshoot region. The high-resolution three-dimensional simulations show that efficient pumping occurs as a result of the action of strong coherent down—owing plumes. The properties of the transport are evaluated as a function of magnetic —eld strength, rotation rate, supercriticality, stiUness of the interface, and con—guration. The turbulent pumping of magnetic —ux is remarkably robust and more efficient than its laminar counterpart. The turbulent convection naturally ampli—es magnetic energy from any existing mean —eld. The transport of —ux from the convection zone removes the source for this local ampli—cation there, and thus the peak magnetic energy also comes to reside in the stable region. This is important for an eUective interface dynamo.