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The tachocline may be subject to a variety of instabilities leading to turbulent motion and angular momentum transport. This chapter reviews some approaches that have been found useful in the study of astrophysical accretion discs and discusses their possible application to the tachocline.
Introduction
The solar tachocline is a thin structure characterized by strong differential rotation, presumably in the presence of a magnetic field. It forms the interface between the radiative interior and the convective envelope of the Sun, which differ greatly in their dynamical properties, states of rotation and mechanisms of angular momentum transport. While the tachocline might have the character of a laminar boundary layer between these regions, it is more likely to be turbulent, at least in part, as a result of intrinsic instabilities or possibly because of forcing by the convective motions above.
Instabilities of the tachocline could derive from kinetic, gravitational or magnetic sources of free energy. Shear instabilities depend on the free kinetic energy in differential rotation, and may, as in the case of the magnetorotational instability, require the assistance of a magnetic field. Gravitational energy may be liberated through magnetic buoyancy (Parker) instabilities, while magnetic energy in non-potential configurations may be released in purely magnetic (Tayler) instabilities. To understand the existence and dynamics of the tachocline requires an appreciation of such instabilities and the transport effects, especially angular momentum transport, to which they give rise in a nonlinear regime.
The region near and just below the solar convection zone is characterized by a strong shear in rotation rate, between the latitudinally differential rotation in the convection zone and the nearly uniform rotation of the radiative interior. This so-called tachocline is also a region of substantial uncertainty in the modelling of solar structure, where convective overshoot and rotationally induced mixing may affect the thermal and compositional structure. Helioseismology led to the identification of the rotational shear and has provided fairly detailed information about the properties, structure and rotation of the tachocline, although unavoidably at somewhat limited resolution. Here we briefly discuss the techniques used in the helioseismic analyses and review the results of such analyses, as a background for the modelling of the properties of the tachocline and its effects on the generation of the solar magnetic field.
Introduction
As will be abundantly evident from other articles in this volume, knowledge of the solar internal rotation is essential for understanding solar magnetic activity, as it is for understanding important aspects of solar structure and evolution. Before the advent of helioseismology little was known about solar rotation below the surface, beyond the indication, from the surface latitudinal differential rotation, that it was non-uniform.
The physical processes causing the turbulent dissipation and mixing of momentum and magnetic fields in the solar tachocline are discussed in the context of a simple model of two-dimensional MHD turbulence on a β-plane. The mean turbulent resistivity and viscosity for this model are calculated. Special attention is given to the enhanced dynamical memory induced by small scale magnetic fields and to the effects of magnetic fluctuations on nonlinear energy transfer. The analogue of the Rhines scale for β-plane MHD is identified. The implications of the results for models of the solar tachocline structure are discussed.
Introduction
The tachocline is a thin, stably stratified layer of the solar interior situated in the radiative zone, immediately below the convection zone (Miesch 2005;Tobias 2005). This layer connects the latitudinal differential rotation of the solar convection zone to the expected solid body rotation of the solar interior (Schou et al. 1998; see also Chapter 3 in this book by Christensen-Dalsgaard & Thompson). Thus, flows in the tachocline are sheared (both poloidally and radially), with the predominant structure being that of a radially sheared toroidal flow. The stratification of the tachocline is strongly stable (with Richardson number Ri ≫ 1), and the magnetic field strength is significant, though magnetic pressure is still much smaller than thermal pressure, consistent with hydrostatic equilibrium, i.e. B2/8π ≪ p.
Star-disk interaction is thought to drive the angular momentum evolution of young stars. In this review, I present the latest results obtained on the rotational properties of low mass and very low mass pre-main sequence stars. I discuss the evidence for extremely efficient angular momentum removal over the first few Myr of pre-main sequence evolution and describe recent results that support an accretion-driven braking mechanism. Angular momentum evolution models are presented and their implication for accretion disk lifetimes discussed.
We present results of 3D simulations of MHD instabilities at the accretion disk-magnetosphere boundary. The instability is Rayleigh-Taylor, and develops for a large range of parameter values. It manifests itself in the form of tall, thin tongues of plasma that reach the star by penetrating through the magnetosphere in the equatorial plane. The tongues rotate around the star in the equatorial plane, and their shape and number changes with time on inner-disk dynamical timescales. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator.
Accretion and magnetic fields play major roles in several of the many models put forward to explain the properties of T Tauri stars since their discovery by Alfred Joy in the 1940s. Early investigators already recognized in the 1950s that a source of energy external to the star was needed to account for the emission properties of these stars in the optical range.
The opening of new spectral windows from the infrared to the ultraviolet in the 1970s and 1980s showed that the excess emission of T Tauri stars and related objects extends into all wavelength domains, while evidence of outflow and/or infall in their circumstellar medium was accumulating.
Although the disk hypothesis had been put forward by Merle Walker as early as 1972 to explain properties of YY Orionis stars and although Lynden-Bell and Pringle worked out the accretion disk model and applied it specifically to T Tauri stars in 1974, the prevailing model for young stellar objects until the mid-1980s assumed that they experienced extreme solar-type activity. It then took until the late 1980s before the indirect evidence of disks presented by several teams of researchers became so compelling that a paradigm shift occurred, leading to the current consensual picture.
I briefly review the various models proposed for explaining the properties of young stellar objects, from their discovery to the direct observations of circumstellar disks that have so elegantly confirmed the nature of young stars. I will go on to discuss more modern issues concerning their accretion disk properties and conclude with some results obtained in a recent attempt to better understand the evolution of Taurus-Auriga young stellar objects.
Stellar magnetic fields including a strong dipole component are believed to play a critical role in the early evolution of newly formed stars and their circumstellar accretion disks. It is currently believed that the stellar magnetic field truncates the accretion disk several stellar radii above the star. This action forces accreting material to flow along the field lines and accrete onto the star preferentially at high stellar latitudes. It is also thought that the stellar rotation rate becomes locked to the Keplerian velocity near the radius where the disk is truncated. This paper reviews recent efforts to measure the magnetic field properties of low mass pre-main sequence stars, focussing on how the observations compare with the theoretical expectations. A picture is emerging indicating that quite strong fields do indeed cover the majority of the surface on these stars; however, the dipole component of the field appears to be alarmingly small. On the other hand, at least one accretion model which takes into account the non-dipole nature of the magnetic field provides predictions relating various stellar and accretion parameters which are present in the current data.
This is a selective historical overview of the progess in understanding T Tauri spectra. Originally they were understood to be very young, but the physical conditions (or even geometry) of the material on the star and in its surroundings were mysterious. The origin and meaning of the emission lines was largely unknown. Today we have a detailed consensus of what is happening near and on these newly forming stars. They are very magnetically active, and the stellar field is strong and extensive enough to control both the final accretion onto the star and the launching of outflows which solve the angular momentum problem during formation. Much of this consensus has emerged from spectral information, but much remains to be learned. I highlight some of the seminal breakthroughs that have led to the current picture. There are very complex and time-variable components to the entire physical system that constitutes a T Tauri star, and spectral information at various wavelengths and resolutions is crucial to making further progress.
We studied the structure of the H2O super maser region in Orion with VLBI angular resolution of 0.1 mas or 0.05 AU. The maser emission (F ∼ 8 MJy) was determined by highly organized structure: accretion disk, bipolar outflow, torus and surrounding shell. The accretion disk, divided into protoplanetary rings, is viewed edge-on. The disk rotates as a rigid body with velocities V ∼ ΩR and the rotation period is ∼ 170 yrs. The highly collimated bipolar outflow has a size of 9×0.7 AU, a velocity of ∼ 10 km/s. In the center a bright compact (≤0.05 AU) source – ejector is located, surrounded by a torus 0.6 AU in diameter. The outflow has a helix structure, which is determined by precession with a period of T ∼ 10 yrs. Comet-like bullets were observed on distances up to 80 AU.
Until recently, X-rays from low-mass young stars (105–106 yr) were thought to be a universal proxy for magnetic activity, enhanced by 3-4 orders of magnitude with respect to the Sun, but otherwise similar in nature to all low-mass, late-type convective stars (including the Sun itself). However, there is now evidence that other X-ray emission mechanisms are at work in young stars. The most frequently invoked mechanism is accretion shocks along magnetic field lines (“magnetic accretion”). In the case of the more massive A- and B-type stars, and their progenitors the Herbig AeBe stars, other, possibly more exotic mechanisms can operate: star-disk magnetic reconnection, magnetically channeled shocked winds, etc. In any case, magnetic fields, both on small scale (surface activity) and on large scale (dipolar magnetospheres), play a distinctive role in the emission of X-rays by young stars, probably throughout the IMF.
Accreting T Tauri stars are observed to be less luminous in X-rays than non-accretors, an effect that has been detected in various star forming regions. To explain this we have combined, for the first time, a radiative transfer code with an accretion model that considers magnetic fields extrapolated from surface magnetograms obtained from Zeeman-Doppler imaging. Such fields consist of compact magnetic regions close to the stellar surface, with extended field lines interacting with the disk. We study the propagation of coronal X-rays through the magnetosphere and demonstrate that they are strongly absorbed by the dense gas in accretion columns.
In this contribution we first briefly review our current knowledge on the physics of accretion discs driving self-confined jets. It will be shown that a large scale magnetic field is expected to thread the innermost disc regions, giving rise to a transition from an outer standard accretion disc to an inner jet emitting disc. We then report new progresses on the theory of star-disc interaction, allowing to explain the formation of accretion funnel flows with stellar dipole fields consistent with observational constraints. Such a connection is now not only probed by modern observations but it is also requested for spinning down protostars, which are known to be both actively accreting and contracting. This spin down most probably relies on the angular momentum removal by ejection. Two such scenarios will be addressed here, namely “accretion-powered stellar winds” (Matt & Pudritz 2005) and “Reconnection X-winds” (Ferreira, Pelletier & Appl 2000). The latter can slow down a protostar on time scales shorter or comparable to the embedded phase. It will be shown that these two scenarios are not incompatible and that transitions from one to another may even occur as they mainly depend on the stellar dynamo.
Emission line profiles from pre-main-sequence objects accreting via magnetically-controlled funnel flows encode information on the geometry and kinematics of the material on stellar radius scales. In order to extract this information it is necessary to perform radiative-transfer modelling of the gas to produce synthetic line profiles. In this review I discuss the physics that needs to be included in such models, and the numerical methods and assumptions that are used to render the problem tractable. I review the progress made in the field over the last decade, and summarize the main successes and failures of the modelling work.
Our present understanding of the coronal structure of T Tauri stars is fragmentary and observations in different wavelength regimes often appear to give contradictory results. X-ray data suggest the presence of magnetic loops on a variety of scales, from compact loops of size less than a stellar radius, up to very large loops of up to 10 stellar radii which may connect to the disk. While some stars show a clear rotational modulation in X-rays, implying distinct bright and dark regions, many do not. This picture is complicated by the accretion process itself, which also contributes to the X-ray emission. The location of the inner edge of the accretion disk and the nature of the magnetic field there are still hotly-contested issues. Accretion indicators often suggest the presence of discrete accretion funnels. This has implications for the structure of the corona, as does the presence of an outflowing wind. All of these factors are linked to the structure of the magnetic field, which we are now beginning to unravel through Zeeman-Doppler imaging. In this review I will describe the present state of our understanding of the magnetic structure of T Tauri coronae and the impact this has during such an early evolutionary stage.
We apply results from FUV and X-ray spectroscopy to evaluate the role of photoevaporation in dispersing the disk around TW Hya. Accretion produces bright EUV emission that may be smothered by the accretion column. Solar-like magnetic activity produces fewer ionizing photons, which may be absorbed by an accretion-powered neutral wind. We estimate a photoevaporation rate of ∼ 5 × 10−11M⊙ yr−1 for the disk around TW Hya. These models can be tested by detecting gas in the ionized disk surface, including emission in the [Ne II] 12.8μm line. Photoevaporation is likely a minor process in disk dispersal during the accretion phase, but could remove ∼ 1 MJ of remnant gas around a solar-mass star after accretion ceases.
The presence of close (≲ 0.1 AU) stellar companions must greatly alter the circumstellar environment of classical T Tauri stars, including severe truncation if not elimination of circumstellar disks. It is thus remarkable how little impact the presence of a close companion has on our observable diagnostics for accretion and outflow. Emission line shapes, degrees of continuum veiling, and spectral energy distributions are all indistinguishable between single classical T Tauri stars and classical T Tauri close binaries. Some of the most classical T Tauri stars that laid the foundation for our single-star accretion-disk paradigm have turned out to have close companions. Periodicities in spectral signatures are suggestive of the presence of accretion flows from circumbinary disks to the circumstellar regions; the subsequent flow of material through the circumstellar region to the stellar surface in the presence of a stellar magnetosphere is unstudied. Observations of stellar rotation distributions in close binaries suggest that inner disk regions may act to regulate stellar angular momentum.
The evolution of angular momentum is a key to our understanding of star formation and stellar evolution. The rotational evolution of solar-mass stars is mostly controlled by magnetic interaction with the circumstellar disc and angular momentum loss through stellar winds. Major differences in the internal structure of very low-mass stars and brown dwarfs – they are believed to be fully convective throughout their lives, and thus should not operate a solar-type dynamo – may lead to major differences in the rotation and activity of these objects. Here, we report on observational studies to understand the rotational evolution of the very low-mass stars and brown dwarfs.