DOCSLIB.ORG

Magnetic Buoyancy and Rotational Instabilities in the Tachocline

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Magnetic Buoyancy and Rotational Instabilities in the Tachocline The Astrophysical Journal, 853:65 (18pp), 2018 January 20 https://doi.org/10.3847/1538-4357/aaa4f4 © 2018. The American Astronomical Society. All rights reserved. Magnetic Buoyancy and Rotational Instabilities in the Tachocline Peter A. Gilman High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green, Boulder, CO 80307-3000, USA; [email protected] Received 2017 September 7; revised 2017 November 27; accepted 2018 January 1; published 2018 January 24 Abstract We present results from an analytical model for magnetic buoyancy and rotational instabilities in a full spherical shell tachocline that includes rotation, differential rotation close to that observed helioseismically, and toroidal field. Perturbation solutions are found for the limit of large latitudinal wave number, a limit commonly used to maximize instability due to magnetic buoyancy. We find that at all middle and high latitudes vigorous rotational instability is induced by weak toroidal fields, particularly for high longitudinal wave number, even when the vertical rotation gradient is marginally stable without toroidal field. We infer that this instability will prevent much storage of toroidal fields in the tachocline at these latitudes, but could be responsible for the appearance of ephemeral active regions there. By contrast, the low-latitude vertical rotation gradient, opposite in sign to that at high latitudes, is not only stable itself but also prevents magnetic buoyancy instability until the peak toroidal field is raised above a threshold of about 9 kG at the equator, declining to zero where the vertical rotation gradient changes sign, at 32.3 in our model. Thus this rotation gradient provides a previously unnoticed mechanism for storage of toroidal fields until they amplify by dynamo action to order 10 kG, whereupon they can overcome the rotation gradient to emerge as sunspots. These results provide a new explanation for why sunspots are seen only at low latitudes. The purely rotational instability at latitudes above 50°, even without toroidal fields, also suggests that the high-latitude tachocline should be much thicker, due to HD turbulence, than has been inferred for lower latitudes from helioseismic measurements. Key words: stars: activity – stars: rotation – Sun: interior – Sun: magnetic fields – Sun: rotation – sunspots 1. Introduction dynamo models and simulations (Parker 1975, 1977; Cline et al. 2003). Limits to magnetic buoyancy instability in dynamos Parker (1955) introduced the concept of magnetic buoyancy because of j×B feedbacks on shear flow, representing to explain how magnetic flux generated by the solar dynamo differential rotation, have also been simulated (Vasil & can come to the photosphere and be seen as sunspots. Magnetic Brummell 2008, 2009). Hughes (2007) has recently reviewed buoyancy occurs in a flux tube when the tube is in total (gas ) the status of buoyancy instabilities in the tachocline. plus magnetic pressure equilibrium with its surroundings, One feature common to almost all the work cited above is coupled with the tendency for the temperature inside and that it was done in Cartesian geometry, in order to focus outside the tube to equilibrate due to radiative diffusion. This more on the physical processes involved. Furthermore, all condition is always met if the cross-section of the tube is small the early studies were done before the existence of the solar enough in at least one dimension perpendicular to the local axis tachocline was discovered, so differential rotation in radius of the tube. ’ similar to the tachocline was not considered. Our results for Since Parker s original work, magnetic buoyancy has been instability of combinations of magnetic fields and differential invoked in many contexts. It has been applied both to tubes rotation are done in spherical geometry, and for tachocline fi embedded in a plasma with much weaker magnetic elds differential rotation that is set by helioseismic observations. exterior to it, and to magnetic layers from which tubes might But to get solutions we return to the traditional eigenvalue arise. The study of magnetic buoyancy as a mechanism for instability problem, approximations for which are discussed fi producing instability of a magnetic layer was rst done in Gilman (1970) and more recently in Mizerski et al. (2013). ( ) systematically by Gilman 1970 . The study of magnetic One study that was done including spherical geometry buoyancy instability of magnetic layers has continued ever and differential rotation was that of Acheson (1978), since (Acheson 1978; Acheson & Gibbons 1978; Hughes which did use local analysis in latitude and radius as we 1985a, 1985b;Cattaneoetal.1990;Thelen2000; Tobias & do, but it contains very few numerical results and did not Hughes 2004; Kersale et al. 2007; Davies & Hughes 2011; have the benefit of knowledge of the existence of the Barker et al. 2012;Mizerskietal.2013), as has the study of tachocline. It also placed heavy emphasis on results with magnetic buoyancy instability of isolated toroidal flux tubes finite diffusion. Therefore, unfortunately there are few or rings (Schüssler 1979, 1980; Spruit & van Ballegooijen 1982; detailed points of comparison that can be made with the van Ballegooijen 1982; Moreno Insertis et al. 1992; Ferriz-Mas results presented here. & Schüssler 1993). Magnetic buoyancy has been modeled as a There is also a relevant literature on the destabilization of component of 3D magnetohydrodynamic (MHD) simulations of solar and stellar tachocline rotation gradients, particularly in magneto-convection applied to the solar convection zone the vertical, by weak toroidal magnetic fields (Balbus 1995; (Fan 2001, 2008; Nelson et al. 2014;Weber&Fan2015) and Menou et al. 2004; Parfrey & Menou 2007; Kagan & studied as a form of double-diffusive instability (Schmitt & Wheeler 2014), sometimes referred to as magneto-rotational Rosner 1983; Hughes & Weiss 1995; Skinner & Silvers 2013). instability. It appears that magnetic buoyancy effects are not Magnetic buoyancy effects have been modeled explicitly in solar included in any of these studies, so it is not possible to 1 The Astrophysical Journal, 853:65 (18pp), 2018 January 20 Gilman examine the interplay between magnetic buoyancy and the instability, so the difference might not be easily detected rotational instabilities in these results. We can see the in observations, but it can have profound implications for the absence of magnetic buoyancy effects in the eigenvalue solar dynamo and for the location of emergence of magnetic equations for unstable modes in these studies; they contain flux to the surface (Dikpati & Gilman 2005). no terms involving the vertical gradient of toroidal fields, The same rationale can be used to justify local instability which is essential for magnetic buoyancy instability to exist studies of the radial gradient of rotation, as we do below. In this (Gilman 1970). In addition, only Kagan & Wheeler (2014) case, the starting point for instability analysis is the observation allow for non-axisymmetric instability modes, which are of the radial rotation gradient via helioseismic methods. But known to be important for magnetic buoyancy instability this is difficult to do at high latitudes; in fact we do not (Gilman 1970), particularly when rotation is present. currently know very well what the tachcocline thickness is The approach taken in Kagan & Wheeler (2014) was to there. We only have an estimate of the total change in rotation include full diffusive effects in the stability analysis and across the tachocline, not the radial rotation gradient itself. We differentiate domains in latitude and radius according to the will see that whether the high latitude local radial rotation type of instability found there; we will take the opposite gradient inferred from helioseismic measurements is unstable approach, keeping our model as simple as possible and to local perturbations is crucially dependent on this thickness. building up results first from physically meaningful special Therefore, in this case the instability calculation acquires a cases and limits, which form a basis for interpreting our full different role, namely leading to questioning assumptions made results for magnetic buoyancy and rotational instabilities in a about tachocline thickness at high latitudes. In addition, the differentially rotating spherical shell that represents the timescale for growth of rotational instability may not be very tachocline. different from the timescale to re-establish the radial rotation — Before presenting the details of our analysis of magnetic gradient by angular momentum transport from above unlike buoyancy and rotational instability, some more general the case of coronal mass ejections in the solar atmosphere. discussion is appropriate. Instability calculations can have Only turbulence calculations beyond the scope of this paper different purposes and goals, depending on the physics thought may be able to address the nonlinear competition between to be relevant and the observations that are available. For the rotational instability and restoration of the radial rotation Sun, there are examples of instability in action and observed, gradient. such as the sudden change in magnetic field in the photosphere, By contrast, no reliable direct observations of toroidal magnetic fields inside the Sun have ever been possible, but chromosphere, and corona that quickly leads to eruption of the existence of erupting solar activity and Hale’s magnetic flares and coronal mass ejections.
Load more

Recommended publications
  • Principles of Instability and Stability in Digital PID Control Strategies and Analysis for a Continuous Alcoholic Fermentation Tank Process Start-Up
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 July 2019 doi:10.20944/preprints201809.0332.v2 Principles of Instability and Stability in Digital PID Control Strategies and Analysis for a Continuous Alcoholic Fermentation Tank Process Start-up Alexandre C. B. B. Filhoa a Faculty of Chemical Engineering, Federal University of Uberlândia (UFU), Av. João Naves de Ávila 2121 Bloco 1K, Uberlândia, MG, Brazil. [email protected] Abstract The art work of this present paper is to show properly conditions and aspects to reach stability in the process control, as also to avoid instability, by using digital PID controllers, with the intention of help the industrial community. The discussed control strategy used to reach stability is to manipulate variables that are directly proportional to their controlled variables. To validate and to put the exposed principles into practice, it was done two simulations of a continuous fermentation tank process start-up with the yeast strain S. Cerevisiae NRRL-Y-132, in which the substrate feed stream contains different types of sugar derived from cane bagasse hydrolysate. These tests were carried out through the resolution of conservation laws, more specifically mass and energy balances, in which the fluid temperature and level inside the tank were the controlled variables. The results showed the facility in stabilize the system by following the exposed proceedings. Keywords: Digital PID; PID controller; Instability; Stability; Alcoholic fermentation; Process start-up. © 2019 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 July 2019 doi:10.20944/preprints201809.0332.v2 1.
    [Show full text]
  • Helioseismology of the Tachocline
    HISTORY OF SOLAR ACTIVITY RECORDED IN POLAR ICE Helioseismology of the Tachocline arkus Roth $iepenheuer-Institut für Sonnen%hysi" History of Solar Acti(ity Reco!)e) in Polar Ice Düben)orf, ,-.,,./0,1 HISTORY OF Theoretical Kno2ledge abo#t SOLAR ACTIVITY RECORDED IN the Solar Interio! POLAR ICE What is the structure of the Sun? Theo!y of the inte!nal st!#ct#!e of the sta!s is *ase) on the f#n)amental %!inci%les of %hysics: Energy conservation, Mass conservation, Momentum conservation P!essu!e an) gra(ity a!e in *alance4 hy)!ostatic e5#ili*!i#m 6 the Sun is stable A theo!etical mo)el of the S#n can *e *#ilt on these %hysical la2s. Is there a possibility to „look inside“ the Sun? HISTORY OF SOLAR ACTIVITY RECORDED IN Oscillations in the Sun and the Sta!s POLAR ICE The Sun and the stars exhibit resonance oscillations! Excitation Mechanism: Small perturbations of the equilibrium lead to oscillations Origin: Granulation (turbulences) that generate sound waves, i.e. pressure perturbations (430.5 nm; courtesy to KIS -) 5 Mm HISTORY OF SOLAR ACTIVITY RECORDED IN Oscillations in the Sun and the Sta!s POLAR ICE The Sun and the stars exhibit resonance oscillations! Excitation Mechanism: Small perturbations of the equilibrium lead to oscillations Origin: Granulation (turbulences) that generate sound waves, i.e. pressure perturbations The superposition of sound waves lead to interferences: amplifications or annihilations. Sun and stars act as resonators ? Fundamental mode and higher harmonics are possible Roth, 2004, SuW 8, 24 10 million10 oscillations,
    [Show full text]
  • Control Theory
    Control theory S. Simrock DESY, Hamburg, Germany Abstract In engineering and mathematics, control theory deals with the behaviour of dynamical systems. The desired output of a system is called the reference. When one or more output variables of a system need to follow a certain ref- erence over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. Rapid advances in digital system technology have radically altered the control design options. It has become routinely practicable to design very complicated digital controllers and to carry out the extensive calculations required for their design. These advances in im- plementation and design capability can be obtained at low cost because of the widespread availability of inexpensive and powerful digital processing plat- forms and high-speed analog IO devices. 1 Introduction The emphasis of this tutorial on control theory is on the design of digital controls to achieve good dy- namic response and small errors while using signals that are sampled in time and quantized in amplitude. Both transform (classical control) and state-space (modern control) methods are described and applied to illustrative examples. The transform methods emphasized are the root-locus method of Evans and fre- quency response. The state-space methods developed are the technique of pole assignment augmented by an estimator (observer) and optimal quadratic-loss control. The optimal control problems use the steady-state constant gain solution. Other topics covered are system identification and non-linear control. System identification is a general term to describe mathematical tools and algorithms that build dynamical models from measured data.
    [Show full text]
  • On a Transition from Solar-Like Coronae to Rotation-Dominated Jovian-Like
    On a transition from solar-like coronae to rotation-dominated jovian-like magnetospheres in ultracool main-sequence stars Carolus J. Schrijver Lockheed Martin Advanced Technology Center, 3251 Hanover Street, Palo Alto, CA 94304 [email protected] ABSTRACT For main-sequence stars beyond spectral type M5 the characteristics of magnetic activity common to warmer solar-like stars change into the brown-dwarf domain: the surface magnetic field becomes more dipolar and the evolution of the field patterns slows, the photospheric plasma is increasingly neutral and decoupled from the magnetic field, chromospheric and coronal emissions weaken markedly, and the efficiency of rotational braking rapidly decreases. Yet, radio emission persists, and has been argued to be dominated by electron-cyclotron maser emission instead of the gyrosynchrotron emission from warmer stars. These properties may signal a transition in the stellar extended atmosphere. Stars warmer than about M5 have a solar-like corona and wind-sustained heliosphere in which the atmospheric activity is powered by convective motions that move the magnetic field. Stars cooler than early-L, in contrast, may have a jovian- like rotation-dominated magnetosphere powered by the star’s rotation in a scaled-up analog of the magnetospheres of Jupiter and Saturn. A dimensional scaling relationship for rotation-dominated magnetospheres by Fan et al. (1982) is consistent with this hypothesis. Subject headings: stars: magnetic fields — stars: low-mass, brown dwarfs — stars: late-type — planets and satellites: general arXiv:0905.1354v1 [astro-ph.SR] 8 May 2009 1. Introduction Main sequence stars have a convective envelope around a radiative core from about spectral type A2 (with an effective temperature of Teff ≈ 9000 K) to about M3 (Teff ≈ 3200 K).
    [Show full text]
  • Perspective Helioseismology
    Proc. Natl. Acad. Sci. USA Vol. 96, pp. 5356–5359, May 1999 Perspective Helioseismology: Probing the interior of a star P. Demarque* and D. B. Guenther† *Department of Astronomy, Yale University, New Haven, CT 06520-8101; and †Department of Astronomy and Physics, Saint Mary’s University, Halifax, Nova Scotia, Canada B3H 3C3 Helioseismology offers, for the first time, an opportunity to probe in detail the deep interior of a star (our Sun). The results will have a profound impact on our understanding not only of the solar interior, but also neutrino physics, stellar evolution theory, and stellar population studies in astrophysics. In 1962, Leighton, Noyes and Simon (1) discovered patches of in the radial eigenfunction. In general low-l modes penetrate the Sun’s surface moving up and down, with a velocity of the more deeply inside the Sun: that is, have deeper inner turning order of 15 cmzs21 (in a background noise of 330 mzs21!), with radii than higher l-valued p-modes. It is this property that gives periods near 5 minutes. Termed the ‘‘5-minute oscillation,’’ the p-modes remarkable diagnostic power for probing layers of motions were originally believed to be local in character and different depth in the solar interior. somehow related to turbulent convection in the solar atmo- The cut-away illustration of the solar interior (Fig. 2 Left) sphere. A few years later, Ulrich (2) and, independently, shows the region in which p-modes propagate. Linearized Leibacher and Stein (3) suggested that the phenomenon is theory predicts (2, 4) a characteristic pattern of the depen- global and that the observed oscillations are the manifestation dence of the eigenfrequencies on horizontal wavelength.
    [Show full text]
  • Multi-Spacecraft Analysis of the Solar Coronal Plasma
    Multi-spacecraft analysis of the solar coronal plasma Von der Fakultät für Elektrotechnik, Informationstechnik, Physik der Technischen Universität Carolo-Wilhelmina zu Braunschweig zur Erlangung des Grades einer Doktorin der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation von Iulia Ana Maria Chifu aus Bukarest, Rumänien eingereicht am: 11.02.2015 Disputation am: 07.05.2015 1. Referent: Prof. Dr. Sami K. Solanki 2. Referent: Prof. Dr. Karl-Heinz Glassmeier Druckjahr: 2016 Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. Dissertation an der Technischen Universität Braunschweig, Fakultät für Elektrotechnik, Informationstechnik, Physik ISBN uni-edition GmbH 2016 http://www.uni-edition.de © Iulia Ana Maria Chifu This work is distributed under a Creative Commons Attribution 3.0 License Printed in Germany Vorveröffentlichung der Dissertation Teilergebnisse aus dieser Arbeit wurden mit Genehmigung der Fakultät für Elektrotech- nik, Informationstechnik, Physik, vertreten durch den Mentor der Arbeit, in folgenden Beiträgen vorab veröffentlicht: Publikationen • Mierla, M., Chifu, I., Inhester, B., Rodriguez, L., Zhukov, A., 2011, Low polarised emission from the core of coronal mass ejections, Astronomy and Astrophysics, 530, L1 • Chifu, I., Inhester, B., Mierla, M., Chifu, V., Wiegelmann, T., 2012, First 4D Recon- struction of an Eruptive Prominence
    [Show full text]
  • The Sun and the Solar Corona
    SPACE PHYSICS ADVANCED STUDY OPTION HANDOUT The sun and the solar corona Introduction The Sun of our solar system is a typical star of intermediate size and luminosity. Its radius is about 696000 km, and it rotates with a period that increases with latitude from 25 days at the equator to 36 days at poles. For practical reasons, the period is often taken to be 27 days. Its mass is about 2 x 1030 kg, consisting mainly of hydrogen (90%) and helium (10%). The Sun emits radio waves, X-rays, and energetic particles in addition to visible light. The total energy output, solar constant, is about 3.8 x 1033 ergs/sec. For further details (and more accurate figures), see the table below. THE SOLAR INTERIOR VISIBLE SURFACE OF SUN: PHOTOSPHERE CORE: THERMONUCLEAR ENGINE RADIATIVE ZONE CONVECTIVE ZONE SCHEMATIC CONVECTION CELLS Figure 1: Schematic representation of the regions in the interior of the Sun. Physical characteristics Photospheric composition Property Value Element % mass % number Diameter 1,392,530 km Hydrogen 73.46 92.1 Radius 696,265 km Helium 24.85 7.8 Volume 1.41 x 1018 m3 Oxygen 0.77 Mass 1.9891 x 1030 kg Carbon 0.29 Solar radiation (entire Sun) 3.83 x 1023 kW Iron 0.16 Solar radiation per unit area 6.29 x 104 kW m-2 Neon 0.12 0.1 on the photosphere Solar radiation at the top of 1,368 W m-2 Nitrogen 0.09 the Earth's atmosphere Mean distance from Earth 149.60 x 106 km Silicon 0.07 Mean distance from Earth (in 214.86 Magnesium 0.05 units of solar radii) In the interior of the Sun, at the centre, nuclear reactions provide the Sun's energy.
    [Show full text]
  • Local and Global Instability of Buoyant Jets and Plumes
    XXIV ICTAM, 21-26 August 2016, Montreal, Canada LOCAL AND GLOBAL INSTABILITY OF BUOYANT JETS AND PLUMES Patrick Huerre1a), R.V.K. Chakravarthy1 & Lutz Lesshafft 1 1Laboratoire d’Hydrodynamique (LadHyX), Ecole Polytechnique, Paris, France Summary The local and global linear stability of buoyant jets and plumes has been studied as a function of the Richardson number Ri and density ratio S in the low Mach number approximation. Only the m = 0 axisymmetric mode is shown to become globally unstable, provided that the local absolute instability is strong enough. The helical mode of azimuthal wavenumber m = 1 is always globally stable. A sensitivity analysis indicates that in buoyant jets (low Ri), shear is the dominant contributor to the growth rate, while, for plumes (large Ri), it is the buoyancy. A theoretical prediction of the Strouhal number of the self-sustained oscillations in helium jets is obtained that is in good agreement with experimental observations over seven decades of Richardson numbers. INTRODUCTION Buoyant jets and plumes occur in a wide variety of environmental and industrial contexts, for instance fires, accidental gas releases, ventilation flows, geothermal vents, and volcanic eruptions. Understanding the onset of instabilities leading to turbulence is a research challenge of great practical and fundamental interest. Somewhat surprisingly, there have been relatively few studies of the linear stability properties of buoyant jets and plumes, in contrast to the related purely momentum driven classical jet. In the present study, local and global stability analyses are conducted to account for the self-sustained oscillations experimentally observed in buoyant jets of helium and helium-air mixtures [1].
    [Show full text]
  • Dynamics of the Fast Solar Tachocline
    A&A 389, 629–640 (2002) Astronomy DOI: 10.1051/0004-6361:20020586 & c ESO 2002 Astrophysics Dynamics of the fast solar tachocline I. Dipolar field E. Forg´acs-Dajka1 and K. Petrovay1,2 1 E¨otv¨os University, Department of Astronomy, Budapest, Pf. 32, 1518 Hungary 2 Instute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA Received 15 January 2002 / Accepted 16 April 2002 Abstract. One possible scenario for the origin of the solar tachocline, known as the “fast tachocline”, assumes that the turbulent diffusivity exceeds η ∼> 109 cm2 s−1. In this case the dynamics will be governed by the dynamo- generated oscillatory magnetic field on relatively short timescales. Here, for the first time, we present detailed numerical models for the fast solar tachocline with all components of the magnetic field calculated explicitly, assuming axial symmetry and a constant turbulent diffusivity η and viscosity ν. We find that a sufficiently strong oscillatory poloidal field with dipolar latitude dependence at the tachocline–convective zone boundary is able to confine the tachocline. Exploring the three-dimensional parameter space defined by the viscosity in the range log ν = 9–11, the magnetic Prandtl number in the range Prm =0.1−10, and the meridional flow amplitude −1 (−3to+3cms ), we also find that the confining field strength Bconf, necessary to reproduce the observed thickness of the tachocline, increases with viscosity ν, with magnetic Prandtl number ν/η, and with equatorward 3 4 meridional flow speed. Nevertheless, the resulting Bconf values remain quite reasonable, in the range 10 −10 G, for all parameter combinations considered here.
    [Show full text]
  • Astrophysical Fluid Dynamics: II. Magnetohydrodynamics
    Winter School on Computational Astrophysics, Shanghai, 2018/01/30 Astrophysical Fluid Dynamics: II. Magnetohydrodynamics Xuening Bai (白雪宁) Institute for Advanced Study (IASTU) & Tsinghua Center for Astrophysics (THCA) source: J. Stone Outline n Astrophysical fluids as plasmas n The MHD formulation n Conservation laws and physical interpretation n Generalized Ohm’s law, and limitations of MHD n MHD waves n MHD shocks and discontinuities n MHD instabilities (examples) 2 Outline n Astrophysical fluids as plasmas n The MHD formulation n Conservation laws and physical interpretation n Generalized Ohm’s law, and limitations of MHD n MHD waves n MHD shocks and discontinuities n MHD instabilities (examples) 3 What is a plasma? Plasma is a state of matter comprising of fully/partially ionized gas. Lightening The restless Sun Crab nebula A plasma is generally quasi-neutral and exhibits collective behavior. Net charge density averages particles interact with each other to zero on relevant scales at long-range through electro- (i.e., Debye length). magnetic fields (plasma waves). 4 Why plasma astrophysics? n More than 99.9% of observable matter in the universe is plasma. n Magnetic fields play vital roles in many astrophysical processes. n Plasma astrophysics allows the study of plasma phenomena at extreme regions of parameter space that are in general inaccessible in the laboratory. 5 Heliophysics and space weather l Solar physics (including flares, coronal mass ejection) l Interaction between the solar wind and Earth’s magnetosphere l Heliospheric
    [Show full text]
  • Symmetric Stability/00176
    Encyclopedia of Atmospheric Sciences (2nd Edition) - CONTRIBUTORS’ INSTRUCTIONS PROOFREADING The text content for your contribution is in its final form when you receive your proofs. Read the proofs for accuracy and clarity, as well as for typographical errors, but please DO NOT REWRITE. Titles and headings should be checked carefully for spelling and capitalization. Please be sure that the correct typeface and size have been used to indicate the proper level of heading. Review numbered items for proper order – e.g., tables, figures, footnotes, and lists. Proofread the captions and credit lines of illustrations and tables. Ensure that any material requiring permissions has the required credit line and that we have the relevant permission letters. Your name and affiliation will appear at the beginning of the article and also in a List of Contributors. Your full postal address appears on the non-print items page and will be used to keep our records up-to-date (it will not appear in the published work). Please check that they are both correct. Keywords are shown for indexing purposes ONLY and will not appear in the published work. Any copy editor questions are presented in an accompanying Author Query list at the beginning of the proof document. Please address these questions as necessary. While it is appreciated that some articles will require updating/revising, please try to keep any alterations to a minimum. Excessive alterations may be charged to the contributors. Note that these proofs may not resemble the image quality of the final printed version of the work, and are for content checking only.
    [Show full text]
  • Radio Emission from Ultra-Cool Dwarfs P
    Radio Emission from Ultra-Cool Dwarfs P. K. G. Williams Abstract This is an expanded version of a chapter submitted to the Handbook of Exoplanets, eds. Hans J. Deeg and Juan Antonio Belmonte, to be published by Springer Verlag. The 2001 discovery of radio emission from ultra-cool dwarfs (UCDs), the very low- mass stars and brown dwarfs with spectral types of ∼M7 and later, revealed that these objects can generate and dissipate powerful magnetic fields. Radio observations pro- vide unparalleled insight into UCD magnetism: detections extend to brown dwarfs with temperatures .1000 K, where no other observational probes are effective. The data reveal that UCDs can generate strong (kG) fields, sometimes with a stable dipolar structure; that they can produce and retain nonthermal plasmas with electron accel- eration extending to MeV energies; and that they can drive auroral current systems resulting in significant atmospheric energy deposition and powerful, coherent radio bursts. Still to be understood are the underlying dynamo processes, the precise means by which particles are accelerated around these objects, the observed diversity of mag- netic phenomenologies, and how all of these factors change as the mass of the central object approaches that of Jupiter. The answers to these questions are doubly impor- tant because UCDs are both potential exoplanet hosts, as in the TRAPPIST-1 system, and analogues of extrasolar giant planets themselves. 1. Introduction The process that generates the solar magnetic field is called the dynamo. It is widely believed to depend on the tachocline, the shearing layer between the Sun's radiative inner core and its convective outer envelope (e.g., Charbonneau 2014).
    [Show full text]