Physics of Flow through Porous Media

Hydrodynamic and hydromagnetic stability

The Sun and other stars are magnetic: magnetism pervades their interiors and affects their evolution in a variety of ways In the Sun, both the fields themselves and their influence on other phenomena can be uncovered in exquisite detail, but these observations sample only a moment in a single star's life By turning to observations of other stars, and to theory and simulation, we may infer other aspects of the magnetism-eg, its dependence on stellar age, mass, or rotation rate-that would be invisible from close study of the Sun alone Here, we review observations and theory of magnetism in the Sun and other stars, with a partial focus on the "Solar-stellar connection": ie, ways in which studies of other stars have influenced our understanding of the Sun and vice versa We briefly review techniques by which magnetic fields can be measured (or their presence otherwise inferred) in stars, and then highlight some key observational findings uncovered by such measurements, focusing (in many cases) on those that offer particularly direct constraints on theories of how the fields are built and maintained We turn then to a discussion of how the fields arise in different objects: first, we summarize some essential elements of convection and dynamo theory, including a very brief discussion of mean-field theory and related concepts Next we turn to simulations of convection and magnetism in stellar interiors, highlighting both some peculiarities of field generation in different types of stars and some unifying physical processes that likely influence dynamo action in general We conclude with a brief summary of what we have learned, and a sampling of issues that remain uncertain or unsolved

Magnetism, dynamo action and the solar-stellar connection

By studying the oscillations of a star's surface, it is possible to extract information about stellar strata, age, and dynamics. Though one might guess that observation of surface oscillatory motions would be limited to our Sun, high-precision brightness measurements of distant stars, performed over many years, have enabled the field of asteroseismology. This comprehensive review covers the recent development of this field, the necessary blending of numerical simulation and data, and the way in which this new information enhances our understanding of stellar evolution.

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Probing the interior physics of stars through asteroseismology

The 3D MHD Anelastic Spherical Harmonic code, using slope-limited diffusion, is employed to capture convective and dynamo processes achieved in a global-scale stellar convection simulation for a model solar-mass star rotating at three times the solar rate. The dynamo-generated magnetic fields possesses many timescales, with a prominent polarity cycle occurring roughly every 6.2 years. The magnetic field forms large-scale toroidal wreaths, whose formation is tied to the low Rossby number of the convection in this simulation. The polarity reversals are linked to the weakened differential rotation and a resistive collapse of the large-scale magnetic field. An equatorial migration of the magnetic field is seen, which is due to the strong modulation of the differential rotation rather than a dynamo wave. A poleward migration of magnetic flux from the equator eventually leads to the reversal of the polarity of the high-latitude magnetic field. This simulation also enters an interval with reduced magnetic energy at low latitudes lasting roughly 16 years (about 2.5 polarity cycles), during which the polarity cycles are disrupted and after which the dynamo recovers its regular polarity cycles. An analysis of this grand minimum reveals that it likely arises through the interplay of symmetric and antisymmetric dynamo families. This intermittent dynamo state potentially results from the simulation’s relatively low magnetic Prandtl number. A mean-field-based analysis of this dynamo simulation demonstrates that it is of the α-Ω type. The timescales that appear to be relevant to the magnetic polarity reversal are also identified.

https://iopscience.iop.org/article/10.1088/0004-637X/809/2/149/pdf

Grand minima and equatorward propagation in a cycling stellar convective dynamo

Magnetic activity and differential rotation are commonly observed features on main-sequence F-type stars. We seek to make contact with such observations and to provide a self-consistent picture of how differential rotation and magnetic fields arise in the interiors of these stars. The three-dimensional magnetohydrodynamic anelastic spherical harmonic code is employed to simulate global-scale convection and dynamo processes in a 1.2 M ☉ F-type star at two rotation rates. The simulations are carried out in spherical shells that encompass most of the convection zone and a portion of the stably stratified radiative zone below it, allowing us to explore the effects a stable zone has upon the morphology of the global-scale magnetic fields. We find that dynamo action with a high degree of time variation occurs in the star rotating more rapidly at 20 Ω☉, with the polarity of the mean field reversing on a timescale of about 1600 days. Between reversals, the magnetic energy rises and falls with a fairly regular period, with three magnetic energy cycles required to complete a reversal. The magnetic energy cycles and polarity reversals arise due to a linking of the polar-slip instability in the stable region and dynamo action present in the convection zone. For the more slowly rotating case (10 Ω☉), persistent wreaths of magnetism are established and maintained by dynamo action. Compared to their hydrodynamic progenitors, the dynamo states here involve a marked reduction in the exhibited latitudinal differential rotation, which also vary during the course of a cycle.

Dynamo Action and Magnetic Cycles in F-type Stars

Velocity amplitudes in global convection simulations: The role of the Prandtl number and near-surface driving

Aims. We investigate from a theoretical perspective if space asteroseismology can be used to distinguish between different thermal structures and shapes of the near-core mixing profiles for different types of coherent oscillation modes in massive stars with convective cores; we also examine whether this capacity depends on the evolutionary stage of the models along the main sequence.Methods. We computed 1D stellar structure and evolution models for four different prescriptions of the mixing and temperature gradient in the near-core region. We investigated their effect on the frequencies of dipole prograde gravity modes in slowly pulsating B stars and in β Cep stars as well as pressure modes in β Cep stars.Results. A comparison between the mode frequencies of the different models at various stages during the main sequence evolution reveals that they are more sensitive to a change in temperature gradient than to the exact shape of the mixing profile in the near-core region. Depending on the duration of the observed light curve, we can distinguish between either just the temperature gradient, or also between the shapes of the mixing coefficient. The relative frequency differences are in general larger for more evolved models and are largest for the higher frequency pressure modes in β Cep stars.Conclusions. In order to unravel the core boundary mixing and thermal structure of the near-core region, we must have asteroseismic masses and radii with ∼1% relative precision for hundreds of stars.

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Probing the shape of the mixing profile and of the thermal structure at the convective core boundary through asteroseismology

A monomodal model for stellar and planetary convection is derived for the magnitude of the rms velocity, degree of superadiabaticity, and characteristic length scale as a function of rotation rate as well as with thermal and viscous diffusivities. The convection model is used as a boundary condition for a linearization of the equations of motion in the transition region between convectively unstable and stably-stratified regions, yielding the depth to which convection penetrates into the stable region and establishing a relationship between that depth and the local convective Rossby number, diffusivity, and pressure scale height of those flows. Upward and downward penetrative convection have a similar scaling with rotation rate and diffusivities, but they depend differently upon the pressure scale height due to the differing energetic processes occurring in convective cores of early-type stars versus convective envelopes of late-type stars.

A Model of Rotating Convection in Stellar and Planetary Interiors. I. Convective Penetration

Context. Our knowledge of the dynamics of stars has undergone a revolution through the simultaneous large amount of high-quality photometric observations collected by space-based asteroseismology and ground-based high-precision spectropolarimetry. They allowed us to probe the internal rotation of stars and their surface magnetism in the whole Hertzsprung-Russell diagram. However, new methods should still be developed to probe the deep magnetic fields in these stars.Aims. Our goal is to provide seismic diagnoses that allow us to probe the internal magnetism of stars.Methods. We focused on asymptotic low-frequency gravity modes and high-frequency acoustic modes. Using a first-order perturbative theory, we derived magnetic splittings of their frequencies as explicit functions of stellar parameters.Results. As in the case of rotation, we show that asymptotic gravity and acoustic modes can allow us to probe the different components of the magnetic field in the cavities in which they propagate. This again demonstrates the high potential of using mixed-modes when this is possible.

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Kyle Augustson

Papers

Dynamo Action and Magnetic Cycles in F-type Stars

Velocity amplitudes in global convection simulations: The role of the Prandtl number and near-surface driving

Probing the shape of the mixing profile and of the thermal structure at the convective core boundary through asteroseismology

A Model of Rotating Convection in Stellar and Planetary Interiors. I. Convective Penetration

Probing the internal magnetism of stars using asymptotic magneto-asteroseismology