Author name code: macgregor ADS astronomy entries on 2022-09-14 author:"MacGregor, Keith B." ------------------------------------------------------------------------ Title: Frequency regularities of acoustic modes and multi-colour mode identification in rapidly rotating stars Authors: Reese, D. R.; Lignières, F.; Ballot, J.; Dupret, M. -A.; Barban, C.; van't Veer-Menneret, C.; MacGregor, K. B. Bibcode: 2017A&A...601A.130R Altcode: 2017arXiv170109164R Context. Mode identification has remained a major obstacle in the interpretation of pulsation spectra in rapidly rotating stars. This has motivated recent work on calculating realistic multi-colour mode visibilities in this type of star.
Aims: We would like to test mode identification methods and seismic diagnostics in rapidly rotating stars, using oscillation spectra that are based on these new theoretical predictions.
Methods: We investigate the auto-correlation function and Fourier transform of theoretically calculated frequency spectra, in which modes are selected according to their visibilities. Given that intrinsic mode amplitudes are determined by non-linear saturation and cannot currently be theoretically predicted, we experimented with various ad-hoc prescriptions for setting the mode amplitudes, including using random values. Furthermore, we analyse the ratios between mode amplitudes observed in different photometric bands to see up to what extent they can identify modes.
Results: When non-random intrinsic mode amplitudes are used, our results show that it is possible to extract a mean value for the large frequency separation or half its value and, sometimes, twice the rotation rate, from the auto-correlation of the frequency spectra. Furthermore, the Fourier transforms are mostly sensitive to the large frequency separation or half its value. The combination of the two methods may therefore measure and distinguish the two types of separations. When the intrinsic mode amplitudes include random factors, which seems more representative of real stars, the results are far less favourable. It is only when the large separation or half its value coincides with twice the rotation rate, that it might be possible to detect the signature of a frequency regularity. We also find that amplitude ratios are a good way of grouping together modes with similar characteristics. By analysing the frequencies of these groups, it is possible to constrain mode identification, as well as determine the large frequency separation and the rotation rate. Title: Properties of 42 Solar-type Kepler Targets from the Asteroseismic Modeling Portal Authors: Metcalfe, T. S.; Creevey, O. L.; Doğan, G.; Mathur, S.; Xu, H.; Bedding, T. R.; Chaplin, W. J.; Christensen-Dalsgaard, J.; Karoff, C.; Trampedach, R.; Benomar, O.; Brown, B. P.; Buzasi, D. L.; Campante, T. L.; Çelik, Z.; Cunha, M. S.; Davies, G. R.; Deheuvels, S.; Derekas, A.; Di Mauro, M. P.; García, R. A.; Guzik, J. A.; Howe, R.; MacGregor, K. B.; Mazumdar, A.; Montalbán, J.; Monteiro, M. J. P. F. G.; Salabert, D.; Serenelli, A.; Stello, D.; Ste&şacute; licki, M.; Suran, M. D.; Yıldız, M.; Aksoy, C.; Elsworth, Y.; Gruberbauer, M.; Guenther, D. B.; Lebreton, Y.; Molaverdikhani, K.; Pricopi, D.; Simoniello, R.; White, T. R. Bibcode: 2014ApJS..214...27M Altcode: 2014arXiv1402.3614M Recently the number of main-sequence and subgiant stars exhibiting solar-like oscillations that are resolved into individual mode frequencies has increased dramatically. While only a few such data sets were available for detailed modeling just a decade ago, the Kepler mission has produced suitable observations for hundreds of new targets. This rapid expansion in observational capacity has been accompanied by a shift in analysis and modeling strategies to yield uniform sets of derived stellar properties more quickly and easily. We use previously published asteroseismic and spectroscopic data sets to provide a uniform analysis of 42 solar-type Kepler targets from the Asteroseismic Modeling Portal. We find that fitting the individual frequencies typically doubles the precision of the asteroseismic radius, mass, and age compared to grid-based modeling of the global oscillation properties, and improves the precision of the radius and mass by about a factor of three over empirical scaling relations. We demonstrate the utility of the derived properties with several applications. Title: Oscillations and Surface Rotation of Red Giant Stars Authors: Hedges, C.; Mathur, S.; Thompson, M. J.; MacGregor, K. B. Bibcode: 2013ASPC..479..197H Altcode: 2013arXiv1308.0644H More than 15000 red giants observed by Kepler for a duration of almost one year became public at the beginning of this year. We analysed a subsample of 416 stars to determine the global properties of acoustic modes (mean large separation and frequency of maximum power). Using the effective temperature from the Kepler Input Catalog, we derived a first estimate of the masses and radii of these stars. Finally, we applied wavelets to look for a signature of surface rotation, which relies on the presence of spots or other surface features crossing the stellar visible disk. Title: Mode Visibilities and Frequency Patterns in Rapidly Rotating Stars Authors: Reese, D. R.; Lignières, F.; Ballot, J.; Prat, V.; Barban, C.; van't Veer-Menneret, C.; MacGregor, K. B. Bibcode: 2013ASPC..479..545R Altcode: One of the main obstacles in interpreting the pulsation spectra of rapidly rotating stars is mode identification. In order to address this issue, we generalise mode visibility calculations to rapidly rotating stars. These new calculations take into account gravity and limb darkening, as well as stellar deformation resulting from both the centrifugal force and the pulsation modes. Based on these new calculations, we produce synthetic pulsation spectra and study the frequency patterns present within. We then go on to discuss multi-colour photometry and its potential for mode identification. Title: Mode visibilities in rapidly rotating stars Authors: Reese, D. R.; Prat, V.; Barban, C.; van 't Veer-Menneret, C.; MacGregor, K. B. Bibcode: 2013A&A...550A..77R Altcode: 2012arXiv1212.2384R Context. Mode identification is a crucial step to comparing observed frequencies with theoretical ones. However, it has proven to be particularly difficult in rapidly rotating stars. An important reason for this is the lack of simple frequency patterns such as those present in solar-type pulsators. This problem is further aggravated in δ Scuti stars by their particularly rich frequency spectra.
Aims: As a first step to obtaining further observational constraints towards mode identification in rapid rotators, we aim to accurately calculate mode visibilities and amplitude ratios while fully taking into account the effects of rotation.
Methods: We derive the relevant equations for calculating mode visibilities in different photometric bands while fully taking into account the geometric distortion from both the centrifugal deformation and the pulsation modes, the variations in effective gravity, and an approximate treatment of the temperature variations, given the adiabatic nature of the pulsation modes. These equations are then applied to 2D oscillation modes, calculated using the TOP code (Two-dimension Oscillation Program), in fully distorted 2D models based on the self-consistent field (SCF) method. The specific intensities come from a grid of Kurucz atmospheres, thereby taking into account limb and gravity darkening.
Results: We obtain mode visibilities and amplitude ratios for 2 M models with rotation rates ranging from 0 to 80% of the critical rotation rate. Based on these calculations, we confirm a number of results from earlier studies, such as the increased visibility of numerous chaotic modes at sufficient rotation rates, the simpler frequency spectra with dominant island modes for pole-on configurations, or the dependence of amplitude ratios on inclination and azimuthal order in rotating stars. In addition, we explain how the geometric shape of the star leads to a smaller contrast between pole-on and equator-on visibilities of equatorially-focused island modes. We also show that modes with similar (ℓ, |m|) values frequently have similar amplitude ratios, even in the most rapidly rotating models.

Appendices are available in electronic form at http://www.aanda.org Title: Angular Momentum and Mass Loss From Magnetized Solar-Like Winds Authors: Pinsonneault, Marc H.; Matt, S.; MacGregor, K. B. Bibcode: 2013AAS...22125206P Altcode: We investigate angular momentum and mass loss from magnetized solar-like winds in cool stars. We present a physically motivated formulation and investigate two key phenomena: the F star transition from effective to ineffective spin down and the mass dependence of the spin down timescale in lower mass stars. We demonstrate that both phenomena are naturally explained within our framework. Tests of angular momentum loss models from upcoming Kepler data are discussed. Title: Signatures of rotation in oscillation spectra Authors: Reese, D. R.; Prat, V.; Barban, C.; van't Veer-Menneret, C.; MacGregor, K. B. Bibcode: 2012sf2a.conf..211R Altcode: Rotation makes oscillation spectra of rapidly rotating stars much more complicated. Hence, new strategies need to be developed in order to interpret such spectra. In what follows, we describe how multi-colour photometric mode visibilities can be generalised to rapidly rotating stars, while fully taking into account centrifugal deformation and gravity darkening. We then go on to describe some first results as well as a strategy for constraining mode identification. Title: Magnetic Braking Formulation for Sun-like Stars: Dependence on Dipole Field Strength and Rotation Rate Authors: Matt, Sean P.; MacGregor, Keith B.; Pinsonneault, Marc H.; Greene, Thomas P. Bibcode: 2012ApJ...754L..26M Altcode: 2012arXiv1206.2354M We use two-dimensional axisymmetric magnetohydrodynamic simulations to compute steady-state solutions for solar-like stellar winds from rotating stars with dipolar magnetic fields. Our parameter study includes 50 simulations covering a wide range of relative magnetic field strengths and rotation rates, extending from the slow- and approaching the fast-magnetic-rotator regimes. Using the simulations to compute the angular momentum loss, we derive a semi-analytic formulation for the external torque on the star that fits all of the simulations to a precision of a few percent. This formula provides a simple method for computing the magnetic braking of Sun-like stars due to magnetized stellar winds, which properly includes the dependence on the strength of the magnetic field, mass loss rate, stellar radius, surface gravity, and spin rate, and which is valid for both slow and fast rotators. Title: Self-Consistent Field Model Spectra and Images for the Rapid Rotator α Cephei Authors: Aufdenberg, Jason P.; MacGregor, K.; Sola, M. Bibcode: 2012AAS...22013004A Altcode: Non-LTE synthetic radiation fields have been coupled to Self-Consistent Field (SCF) rotating star models to predict images, interferometric observables (visibilities and closure phases), spectral energy distributions (SEDs), and high-resolution spectra for comparison with rapid rotater alpha Cephei (Alderamin). SCF models include differential rotation from the interior to the surface and differ from Roche models that assume a point-mass approximation of the gravitational potential and axially symmetric uniform rotation. SCF models are parametrized by a mass, the ratio of the axial rotation rate to the critical rate, and the degree and kind (solar or anti-solar) of differential rotation. Model spectra have been computed using a parallel interpolation algorithm (coded in Fortran90 with openMPI) which maps a radiation field database onto the rotationally distorted model star. The SCF model describes the surface shape and gravitational field from the pole to the equator. The luminosity and the von Zeipel exponent

specify the variation in effective temperature with stellar latitude. The radiation field is interpolated at each point on the star for each wavelength, emergent angle, local effective, and local surface gravity.

Model images are compared to the reconstructed images of Alderamin (Zhao et al. 2009) from the Michigan InfraRed Combiner (MIRC) at the CHARA Array. Model SEDs are compared to ultraviolet, visual and near-IR spectrophotometry. High-resolution model spectra are compared Alderamin's Mg II 4481 A line from the ELODIE spectral archive. We have found models near 2.2 solar masses with anti-solar differential rotation which match simultaneously the absolute magnitude, B-V color index, and projected axial ratio measured for Alderamin. The model images differ from the observations in brightness-temperature distribution over the projected stellar surface, the strength of the Mg II line profile, and the strength of the ultraviolet continuum. This work is partially funded by the McNair Scholars Program at Embry-Riddle Aeronautical University. Title: Reflection and Ducting of Gravity Waves Inside the Sun Authors: MacGregor, K. B.; Rogers, T. M. Bibcode: 2011SoPh..270..417M Altcode: 2011arXiv1104.4310M; 2011SoPh..tmp..103M Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an α-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection. Title: Quantifying Magnetic Stellar Wind Torques Authors: Matt, Sean; MacGregor, K. B.; Pinsonneault, M. H.; Greene, T. P. Bibcode: 2011AAS...21743420M Altcode: 2011BAAS...4343420M In order to be able to understand the evolution of stellar spin rates and differential rotation, it is necessary to have a rigorous theory for predicting angular momentum loss via magnetic stellar winds that is applicable over a wide range of conditions. Based upon the results of multidimensional, numerical simulations and semi-analytic calculations, we present an improved formulation for predicting the stellar wind torque, which is valid for varying degrees of magnetization in the wind, as well as for stellar spin rates that range from the slow- to the fast-magnetic-rotator regimes. Title: Emission of Alfven Waves by Planets in Close Orbits Authors: MacGregor, Keith B.; Pinsonneault, M. H. Bibcode: 2011AAS...21734323M Altcode: 2011BAAS...4334323M We examine the electrodynamics of a conducting planet orbiting within a magnetized wind that emanates from its parent star. When the orbital motion differs from corotation with the star, an electric field exists in the rest frame of the planet, inducing a charge separation in its ionosphere. Because the planet is immersed in a plasma, this charge can flow away from it along the stellar magnetic field lines it successively contacts in its orbit. For sufficiently rapid orbital motion, a current system can be formed that is closed by Alfvenic disturbances that propagate along field lines away from the planet. Using a simple model for the wind from a Sun-like star, we survey the conditions under which Alfven wave emission can occur, and estimate the power radiated in the form of linear waves for a range of stellar, planetary, and wind properties. For a Jupiter-like planet in a close (a < 0.10 AU) orbit about a solar-type star, the emitted wave power can be as large as 1027 erg/s. While only a small influence on the planet's orbit, a wave power of this magnitude may have consequences for wind dynamics and localized heating of the stellar atmosphere. NCAR is sponsored by the NSF. Title: On the interaction of internal gravity waves with a magnetic field - II. Convective forcing Authors: Rogers, T. M.; MacGregor, K. B. Bibcode: 2011MNRAS.410..946R Altcode: 2010MNRAS.tmp.1507R; 2010arXiv1009.5933R We present results from numerical simulations of the interaction of internal gravity waves (IGW) with magnetic fields in the radiative interior of the Sun. In this second paper, the waves are forced self-consistently by an overlying convection zone and a toroidal magnetic field is imposed in the stably stratified layer just underneath the convection zone. Consistent with the results of previous analytic and simple numerical calculations, we find a strong wave-field interaction, in which waves are reflected in the field region. The wave-field interaction and wave reflection depend on the field strength as well as on the adopted values of the diffusivities. In some cases, wave reflection leads to an increased mean flow in the field region. In addition to reproducing some of the features of our simpler models, we find additional complex behaviours in these more complete and realistic calculations. First, we find that the spectrum of wave generation, both in magnetized and in unmagnetized models, is not generally well described by available analytic models, although some overlap does exist. Similarly, we find that the dissipation of waves is only partially described by the results of linear theory. We find that the distortion of the field by waves and convective overshoot leads to rapid decay and entrainment of the magnetic field which subsequently changes the wave-field interaction. In addition, the field alters the amount of wave energy propagating into the deep radiative interior, at times increasing the wave energy there and at others decreasing it. Because of the complexity of the problem and because the durations of these simulations are shorter than the anticipated time-scale for dynamical adjustment of the deep solar interior, we are unable to draw a definitive conclusion regarding the efficiency of angular momentum transport in the deep radiative interior by IGW in the presence of a magnetic field. Title: Atmospheres for Self-Consistent Field (SCF) Rotating Star Models Authors: Aufdenberg, Jason P.; MacGregor, K. B. Bibcode: 2010AAS...21542708A Altcode: 2010BAAS...42..343A A standard model detailed atmosphere for a rapidly rotating star makes the following assumptions: (1) a point-mass approximation of the gravitational potential (a Roche model) and (2) an axially symmetric uniform (non-differential) rotation. These assumptions are not made in the Self-Consistent Field (SCF) models of Jackson et al. (2004, 2005) and MacGregor et al. (2007). The SCF differentially rotating stellar structures use a mass distribution that is fully self consistent with the effective potential, which is the sum of the gravitational potential from Poisson's equation and the centrifugal potential. We investigate whether a SCF model can match observations of the pole-on rapid rotator and photometric standard Vega. Our first models match Vega's equatorial diameter and projected rotation velocity, but are not a very good match to the observed spectral energy distribution (SED). The photospheric shape under anti-solar conservative differential rotation yields a cool equatorial region which leaves the model SED too line blanketed in the ultraviolet. A further exploration of SCF model parameter space is outlined, including changes in the stellar mass, the rate of rotation and the kind and degree of differential rotation. Title: Reflection and Ducting of Gravity Waves Inside the Sun Authors: MacGregor, Keith B.; Rogers, T. M. Bibcode: 2010AAS...21542208M Altcode: 2010BAAS...42..292M Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an alpha-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.

NCAR is sponsored by the National Science Foundation. Title: On the interaction of internal gravity waves with a magnetic field - I. Artificial wave forcing Authors: Rogers, T. M.; MacGregor, K. B. Bibcode: 2010MNRAS.401..191R Altcode: 2009MNRAS.tmp.1534R We present results from numerical simulations of the interaction of internal gravity waves (IGW) with a magnetic field. In accordance with the dispersion relation governing IGW in the presence of magnetism and rotation, when the IGW frequency is approximately that of the Alfvén frequency, strong reflection of the wave occurs. Such strong reflection markedly changes the angular momentum transport properties of the waves. In these simple models a strong, time-independent shear layer develops, in contrast to the oscillating shear layer that develops in the purely hydrodynamic case. Title: Pulsation Modes with High Azimuthal Orders in Stellar Models Based on the Self-Consistent Field Method Authors: Reese, D. R.; MacGregor, K. B.; Jackson, S.; Skumanich, A.; Metcalfe, T. S. Bibcode: 2009ASPC..416..395R Altcode: We investigate pulsation modes with high azimuthal orders in a uniformly and differentially rotating stellar model based on the SCF method. Our results show a more complicated m dependence of the pulsation frequencies than what was proposed in previous studies. These results allow a more precise determination of the effects of rapid uniform or differential rotation on stellar pulsations

thereby providing a better understanding of the underlying physics. Title: Mode identification in rapidly rotating stars Authors: Reese, D. R.; Thompson, M. J.; MacGregor, K. B.; Jackson, S.; Skumanich, A.; Metcalfe, T. S. Bibcode: 2009A&A...506..183R Altcode: 2009arXiv0905.4889R Context: Recent calculations of pulsation modes in rapidly rotating polytropic models and models based on the Self-Consistent Field method have shown that the frequency spectrum of low degree pulsation modes can be described by an empirical formula similar to Tassoul's asymptotic formula, provided that the underlying rotation profile is not too differential.
Aims: Given the simplicity of this asymptotic formula, we investigate whether it can provide a means by which to identify pulsation modes in rapidly rotating stars.
Methods: We develop a new mode identification scheme which consists in scanning a multidimensional parameter space for the formula coefficients which yield the best-fitting asymptotic spectra. This mode identification scheme is then tested on artificial spectra based on the asymptotic formula, on random frequencies and on spectra based on full numerical eigenmode calculations for which the mode identification is known beforehand. We also investigate the effects of adding random frequencies to mimic the effects of chaotic modes which are also expected to show up in such stars.
Results: In the absence of chaotic modes, it is possible to accurately find a correct mode identification for most of the observed frequencies provided these frequencies are sufficiently close to their asymptotic values. The addition of random frequencies can very quickly become problematic and hinder correct mode identification. Modifying the mode identification scheme to reject the worst fitting modes can bring some improvement but the results still remain poorer than in the case without chaotic modes. Title: Pulsation modes in rapidly rotating stellar models based on the self-consistent field method Authors: Reese, D. R.; MacGregor, K. B.; Jackson, S.; Skumanich, A.; Metcalfe, T. S. Bibcode: 2009A&A...506..189R Altcode: 2009arXiv0903.4854R Context: New observational means such as the space missions CoRoT and Kepler and ground-based networks are and will be collecting stellar pulsation data with unprecedented accuracy. A significant fraction of the stars in which pulsations are observed are rotating rapidly.
Aims: Our aim is to characterise pulsation modes in rapidly rotating stellar models so as to be able to interpret asteroseismic data from such stars.
Methods: A new pulsation code is applied to stellar models based on the self-consistent field (SCF) method.
Results: Pulsation modes in SCF models follow a similar behaviour to those in uniformly rotating polytropic models, provided that the rotation profile is not too differential. Pulsation modes fall into different categories, the three main ones being island, chaotic, and whispering gallery modes, which are rotating counterparts to modes with low, medium, and high l-|m| values, respectively. The frequencies of the island modes follow an asymptotic pattern quite similar to what was found for polytropic models. Extending this asymptotic formula to higher azimuthal orders reveals more subtle behaviour as a function of m and provides a first estimate of the average advection of pulsation modes by rotation. Further calculations based on a variational principle confirm this estimate and provide rotation kernels that could be used in inversion methods. When the rotation profile becomes highly differential, it becomes more and more difficult to find island and whispering gallery modes at low azimuthal orders. At high azimuthal orders, whispering gallery modes, and in some cases island modes, reappear.
Conclusions: The asymptotic formula found for frequencies of island modes can potentially serve as the basis of a mode identification scheme in rapidly rotating stars when the rotation profile is not too differential. Title: RECENT DIRECTIONS IN ASTROPHYSICAL QUANTITATIVE SPECTROSCOPY AND RADIATION HYDRODYNAMICS: Proceedings of the International Conference in Honor of Dimitri Mihalas for His Lifetime Scientific Contributions on the Occasion of His 70th Birthday Authors: Hubeny, Ivan; Stone, James M.; MacGregor, Keith; Werner, Klaus Bibcode: 2009AIPC.1171.....H Altcode: No abstract at ADS Title: Comparison of pulsation modes in rapidly rotating polytropic and SCF models Authors: Reese, D.; MacGregor, K. B.; Jackson, S.; Skumanich, A.; Metcalfe, T. S. Bibcode: 2009CoAst.158..264R Altcode: In this talk, I will show numerical calculations of pulsation modes in rapidly differentially rotating stellar models based on the self-consistent field (SCF) method {(e.g. MacGregor et al. 2007)}. The pulsation calculations are based on the numerical method presented in {Lignières et al. (2006)} and {Reese et al. (2006)}. I will compare these results with previous calculations based on simpler polytropic models, and discuss how the structure of the frequency spectrum is affected by differential rotation and other stellar parameters. In particular, differential rotation can lead to a breakdown of regularities in the frequency spectrum in favour of a more chaotic behaviour. Title: Magneto-Thermohaline Mixing in Red Giants Authors: Denissenkov, Pavel A.; Pinsonneault, Marc; MacGregor, Keith B. Bibcode: 2009ApJ...696.1823D Altcode: 2008arXiv0806.4346D We revise a magnetic buoyancy model that has recently been proposed as a mechanism for extra mixing in the radiative zones of low-mass red giants. The most important revision is our accounting of the heat exchange between rising magnetic flux rings and their surrounding medium. This increases the buoyant rising time by five orders of magnitude; therefore, the number of magnetic flux rings participating in the mixing has to be increased correspondingly. On the other hand, our revised model takes advantage of the fact that the mean molecular weight of the rings formed in the vicinity of the hydrogen burning shell has been reduced by 3He burning. This increases their thermohaline buoyancy (hence, decreases the total ring number) considerably, making it equivalent to the pure magnetic buoyancy produced by a frozen-in toroidal field with B phiv ≈ 10 MG. We emphasize that some toroidal field is still needed for the rings to remain cohesive while rising. Besides, this field prevents the horizontal turbulent diffusion from eroding the μ contrast between the rings and their surrounding medium. We propose that the necessary toroidal magnetic field is generated by differential rotation of the radiative zone that stretches a preexisting poloidal field around the rotation axis, and that magnetic flux rings are formed as a result of its buoyancy-related instability. Title: Structural Models for Stars with Solar-like Differential Rotation Authors: MacGregor, Keith B.; Metcalfe, T. S.; Cameron, M. Bibcode: 2009AAS...21340611M Altcode: 2009BAAS...41..200M Rapid rotation can profoundly affect the structure of stars, changing basic stellar properties like the radiative luminosity and effective temperature and causing the photospheric shape to deviate from sphericity. We have computed a grid of models for chemically homogeneous, uniformly and differentially rotating stars with masses in the range from 1 to 2 solar masses, using a recently developed method for obtaining fully consistent solutions to the equations governing the stellar structure and gravitational potential. A reformulation of the so-called self-consistent field method, this new approach yields two-dimensional, axisymmetric, equilibrium configurations for conservative rotation laws (i.e., internal angular velocity distributions with the property that the associated centrifugal acceleration can be derived from a potential). We present results for 1 and 2 solar-mass models with solar-like differential rotation profiles in which the stellar equator rotates more rapidly than the poles. The models have flattened, oblate shapes with equatorial (polar) radii that are larger (smaller) than the radius of the corresponding non-rotating models. Rotationally induced modifications of the thermodynamic conditions in the deep interior lead to reduced luminosities, and the model surface temperature distributions are latitude-dependent with polar (equatorial) regions that are hotter (cooler) than the effective temperature of a non-rotating model for the same mass. We compare the properties of these models with those of previously computed 1 and 2 solar-mass models having anti-solar differential rotation (MacGregor et al. 2007), and enumerate several possible consequences of the structural changes arising from rapid rotation. NCAR is sponsored by the National Science Foundation. Title: Pulsations of rapidly rotating stellar models based on the Self-Consistent-Field method: numerical aspects and accuracy Authors: Reese, D.; MacGregor, K. B.; Jackson, S.; Skumanich, A.; Metcalfe, T. S. Bibcode: 2008sf2a.conf..531R Altcode: We use the numerical method developed in tet{Lignieres2006} and tet{Reese2006} to calculate pulsation modes in stellar models generated by the Self-Consistent-Field method described in tet{Jackson2005} and tet{MacGregor2007}. A discussion on the numerical method and its accuracy is given, followed by a very brief description of some of the results. Title: What Prevents Internal Gravity Waves from Disturbing the Solar Uniform Rotation? Authors: Denissenkov, Pavel A.; Pinsonneault, Marc; MacGregor, Keith B. Bibcode: 2008ApJ...684..757D Altcode: 2008arXiv0801.3622D Internal gravity waves (IGWs) are naturally produced by convection in stellar envelopes, and they could be an important mechanism for transporting angular momentum in the radiative interiors of stars. Prior work has established that they could operate over a short enough timescale to explain the internal solar rotation as a function of depth. We demonstrate that the natural action of IGWs is to produce large-scale oscillations in the solar rotation as a function of depth, which is in marked contrast to the nearly uniform rotation in the outer radiative envelope of the Sun. An additional angular momentum transport mechanism is therefore required, and neither molecular nor shear-induced turbulent viscosity is sufficient to smooth out the profile. Magnetic processes, such as the Tayler-Spruit dynamo, could flatten the rotation profile. We therefore conclude that IGWs must operate in conjunction with magnetic angular momentum transport processes if they operate at all. Furthermore, both classes of mechanisms must be inhibited to some degree by mean molecular weight gradients in order to explain the recent evidence for a rapidly rotating embedded core in the Sun, should it be confirmed by a further analysis of solar g-mode oscillations. Title: Non-linear dynamics of gravity wave driven flows in the solar radiative interior Authors: Rogers, T. M.; MacGregor, K. B.; Glatzmaier, G. A. Bibcode: 2008MNRAS.387..616R Altcode: 2008arXiv0804.1987R; 2008MNRAS.tmp..615R We present results of non-linear numerical simulations of gravity wave driven shear flow oscillations in the equatorial plane of the solar radiative interior. These results show that many of the assumptions of quasi-linear theory are not valid. When only two waves are forced (prograde and retrograde), oscillatory mean flow is maintained; but critical layers often form and are dynamically important. When a spectrum of waves is forced, the non-linear wave-wave interactions are dynamically important, often acting to decrease the maintenance of a mean flow. The (in)coherence of such wave-wave interactions must be taken into account when describing wave-driven mean flows. Title: Absorption Line Profiles for Differentially Rotating Stellar Models Authors: MacGregor, Keith B.; Casini, R.; Flanagan, W.; Jackson, S.; Skumanich, A. Bibcode: 2007AAS...21110310M Altcode: 2007BAAS...39..921M We have computed absorption line profiles for rapidly rotating 2 solar-mass stars, using structural models of chemically homogeneous, uniformly and differentially rotating stars of this mass to specify photospheric physical conditions. The models were constructed with a recent reformulation of the self-consistent field method, an iterative procedure yielding two-dimensional, axisymmetric, equilibrium configurations that are consistent solutions to the stellar structure equations and Poisson's equation for the gravitational potential, for a specified conservative angular velocity distribution. The simulated line profiles display a variety of shapes, with morphological characteristics that depend on the properties of the surface rotational velocity distribution, the angle of inclination of the line of sight relative to the rotation axis, and on rotational modifications to the structure of the star, including the difference between the surface temperatures of the poles and the equator and deviations of the stellar shape from sphericity. Some features of the Doppler-broadened profiles reflect details of the distribution of the projected rotation speed over the visible surface of the star, and may thus provide the means for distinguishing between uniform and differential rotation of the stellar photosphere. For example, differentially rotating models can exhibit absorption profiles with flat or even convex-upward bottoms, as opposed to the rounded, concave-upward profiles that are indicative of uniform rotation. We present preliminary results from an ongoing effort to use simulated line profiles in conjunction with the techniques of Principal Component Analysis to infer stellar rotational properties from observations. Title: On the Structure and Properties of Differentially Rotating, Main-Sequence Stars in the 1-2 Msolar Range Authors: MacGregor, K. B.; Jackson, Stephen; Skumanich, Andrew; Metcalfe, Travis S. Bibcode: 2007ApJ...663..560M Altcode: 2007arXiv0704.1275M We present models for chemically homogeneous, differentially rotating, main-sequence stars with masses in the range 1-2 Msolar. The models were constructed using a code based on a reformulation of the self-consistent field method of computing the equilibrium stellar structure for a specified conservative internal rotation law. Relative to nonrotating stars of the same mass, these models all have reduced luminosities and effective temperatures, and flattened photospheric shapes (i.e., decreased polar radii) with equatorial radii that can be larger or smaller, depending on the degree of differential rotation. For a fixed ratio of the axial rotation rate to the surface equatorial rotation rate, increasingly rapid rotation generally deepens convective envelopes, shrinks convective cores, and can lead to the presence of a convective core (envelope) in a 1 (2) Msolar model, a feature that is absent in a nonrotating star of the same mass. The positions of differentially rotating models for a given mass in the H-R diagram can be shifted in such a way as to approximate the nonrotating ZAMS for lower mass stars. Implications of these results include (1) possible ambiguities arising from similarities between the properties of rotating and nonrotating models of different masses, (2) a reduced radiative luminosity for a young, rapidly rotating Sun, (3) modified rates of lithium destruction by nuclear processes in the layers beneath an outer convective envelope, and (4) the excitation of solar-like oscillations and the operation of a solar-like hydromagnetic dynamo in some 1.5-2 Msolar stars. Title: Penetration of Dynamo-generated Magnetic Fields into the Sun's Radiative Interior Authors: Dikpati, Mausumi; Gilman, Peter A.; MacGregor, Keith B. Bibcode: 2006ApJ...638..564D Altcode: Any large-scale magnetic fields present in solar/stellar radiative interiors have so far been thought to be primordial or residuals from extinct dynamos. We show that a regular cyclic dynamo can also be the origin of strong magnetic fields in the solar radiative tachocline and interior below. By exploiting a kinematic, mean-field flux-transport dynamo, we show that for a wide range of core-diffusivity values, from 109 cm2 s-1 down to a molecular diffusivity of 103 cm2 s-1, oscillatory dynamo fields penetrate below the tachocline. Amplitudes of these fields are in the range of ~1 kG to 3×103 kG, depending on core diffusivity value, when the dynamo produces ~100 kG peak toroidal fields in the overshoot tachocline. For a low enough core diffusivity (<~107 cm2 s-1), there is also a steady (nonreversing) dynamo in the radiative tachocline and below, which generates strong toroidal field of amplitude ~1 kG to 3×103 kG or more there. The key elements in this dynamo are the low diffusivity, the differential rotation near the bottom of the tachocline, and an assumed tachocline α-effect. The Lorentz force feedback may limit oscillatory dynamo fields to ~30 kG, for which the mean nonreversing toroidal fields is still ~300 kG, for the lowest core diffusivity value. The presence of strong oscillatory and steady toroidal fields in the radiative tachocline implies that there cannot be a slow tachocline; the dynamics should always be fast there, dominated by MHD. These results are obtained using solar parameters, but they should also apply generally to stars with convecting shells and perhaps also with convective cores. Title: Generating Magnetic Fields in Early-type Stars Authors: MacGregor, K. B. Bibcode: 2005ASPC..337...28M Altcode: Although magnetic fields have been detected in many upper main sequence stars, the physical origins of this magnetism are not well understood. After surveying the magnetic properties of these stars and reviewing some of the arguments for and against a fossil origin for the observed fields, we examine the possibility that they are produced by a hydromagnetic dynamo, operating within the central convective core. We describe model results suggesting that dynamo action can take place in such an environment, but that the high electrical conductivity and large spatial extent of the overlying, stably stratified, radiative envelope are significant obstacles to the emergence of the generated fields at the stellar surface. Advection by internal circulatory flows is, by itself, an ineffective transport mechanism, but the buoyant rise of tube-like concentrations of magnetic flux may, under certain conditions, contribute to bringing the fields from the core to the photosphere. We briefly discuss some alternative models, in which these problems are circumvented by field generation processes that take place closer to the stellar surface. Title: Constraints on the Applicability of an Interface Dynamo to the Sun Authors: Dikpati, Mausumi; Gilman, Peter A.; MacGregor, Keith B. Bibcode: 2005ApJ...631..647D Altcode: Taking into account the helioseismically inferred interior structure, we show that a pure interface-type dynamo does not work for the Sun if the skin effect for poloidal fields does not allow them to penetrate the tachocline. Using a simple mean-field kinematic α-Ω dynamo model, we demonstrate that, in the absence of tachocline radial shear participating in the dynamo process, a latitudinal differential rotation can provide the necessary Ω-effect to drive an oscillation in an interface dynamo, but it alone cannot produce the latitudinal migration. We show that to make an interface dynamo work with the constraints of interior structure and skin depth, a meridional circulation is essential. We conclude that a flux-transport dynamo driven by both the Babcock-Leighton and interface/bottom α-effects is a robust large-scale dynamo for the Sun. Title: Comments on "Full-sphere simulations of circulation-dominated solar dynamo: Exploring the parity issue" Authors: Dikpati, M.; Rempel, M.; Gilman, P. A.; MacGregor, K. B. Bibcode: 2005A&A...437..699D Altcode: Using two distinct simulation codes that respectively apply semi-implicit and fully explicit schemes, we perform calculations of a 2D kinematic Babcock-Leighton type flux-transport dynamo with Chatterjee et al.'s parameter settings. We show that their solutions are diffusion-dominated, rather than circulation-dominated as their title implies. We also have been unable to reproduce several properties of their dynamo solutions, namely we obtain a much faster cycle with ~ 4 times shorter period than theirs, with highly overlapping cycles; a polar field value of ∼ 2 kG if one has to produce a ~ 100 kG toroidal field at convection zone base; and quadrupolar parity as opposed to Chatterjee et al.'s dipolar parity solutions. Title: Dynamos with feedback of of j x B force on meridional flow and differential rotation Authors: Rempel, M.; Dikpati, M.; MacGregor, K. Bibcode: 2005ESASP.560..913R Altcode: 2005csss...13..913R No abstract at ADS Title: On the Use of the Self-consistent-Field Method in the Construction of Models for Rapidly Rotating Main-Sequence Stars Authors: Jackson, Stephen; MacGregor, Keith B.; Skumanich, Andrew Bibcode: 2005ApJS..156..245J Altcode: A new formulation of the self-consistent-field (SCF) method for computing models of rapidly, differentially rotating stars is described. The angular velocity is assumed to depend only on the distance from the axis of rotation. In the modified SCF iterative scheme, normalized distributions of two thermodynamic variables-pressure and temperature-are used as trial functions, while the central values of the pressure and temperature are adjusted by a Newton-Raphson iteration. A two-dimensional trial density distribution, which is needed to compute the gravitational potential, is readily obtained from the pressure and temperature through the equation of state in conjunction with a third trial function specifying the two-dimensional shape of the constant-density surfaces. Rotating models of chemically homogeneous main-sequence stars have been computed as necessary in order to illustrate the algorithm and to make comparisons with existing models. Unlike previous implementations of the SCF method, the method described here is not limited to the upper main sequence: it converges for all main-sequence masses, including those well below 9 Msolar. Moreover, the method converges for values of the parameter t=T/|W| (the ratio of rotational kinetic energy to gravitational potential energy) that are at least as high as those obtained by Clement's relaxation technique. The method is also capable of producing models with deep concavities about the poles as well as models with extreme oblateness (far greater than that possible in uniformly rotating stars). For cases with moderate degrees of differential rotation (say for Ω0e<10, where Ω0 and Ωe denote the angular velocity at the center and at the equator, respectively), the method has been found to be remarkably robust. For higher degrees of differential rotation, models are restricted to a portion of parameter space away from two regions of nonconvergence, inside which some of the models evidently develop toroidal level surfaces. Title: Models for the Rapidly Rotating Be Star Achernar Authors: Jackson, Stephen; MacGregor, Keith B.; Skumanich, Andrew Bibcode: 2004ApJ...606.1196J Altcode: We present models for the Be star Achernar (α Eri), which recent interferometric observations have shown has a photospheric shape that is significantly distorted by the effects of rotation. The models are two-dimensional, axisymmetric configurations, constructed using a new version of the self-consistent field (SCF) method for computing the structure of a rapidly, differentially rotating star. Our revised SCF technique does not suffer from the computational difficulties that affected previous implementations of the method, yielding converged stellar models regardless of mass. For models with masses like those of main sequence stars of mid- to early-B spectral type, it is possible to reproduce Achernar's inferred equatorial and polar dimensions through a combination of rotational flattening/distension and suitable inclination of the rotation axis. However, while matching Achernar's apparent shape, these models are discrepant in other respects, being (on average) cooler and more rapidly rotating than observations indicate. Title: Dynamos with feedback of jxB Force on Meridional Flow and Differential Rotation Authors: Rempel, M.; Dikpati, M.; MacGregor, K. Bibcode: 2004AAS...204.8802R Altcode: 2004BAAS...36..819R Recently, flux-transport dynamos have been successful in reproducing various observed features of the large scale solar magnetic fields. However, these studies addressed the transport of magnetic fields by the meridional circulation in a purely kinematic regime. The toroidal field strength at the base of the solar convection zone inferred from studies of rising magnetic flux tubes is around 100 KG and thus orders of magnitude larger than the equipartition field strength estimated from a meridional flow velocity of a few m/s. Therefore it is crucial for flux-transport dynamos to address the feedback of the jxB on the meridional flow. We present a "dynamic" dynamo model, in which we couple a mean-field Reynolds-stress approach for the differential rotation and meridional circulation with the axisymmetric dynamo equations. This provides a self-consistent model that allows to study the back-reaction of the mean-field Lorentz force of the dynamo generated field on differential rotation and meridional circulation. This model gives an estimate of the magnetic field strength up to which a transport of magnetic field by the weak meridional flow and amplification by the shear in the differential rotation is possible. Additional to this the model also provides solar cycle variations in differential rotation and meridional circulation, which can be compared to helioseismic data. We also show that the feedback of the Lorentz-force on the meridional flow can be included into a kinematic dynamo model in terms of a "quenching" of the stream function, which deflects the flow from regions of strong toroidal magnetic field. From both studies we conclude that flux-transport dynamos work even with strong feedback of the jxB force, primarily because of two reasons: 1) The transport of the weak poloidal magnetic field, which is the sources of strong toroidal field, is not affected strongly. 2) The meridional flow results from a small difference between large forces, so that the transport capability is much larger than a simple estimate based on equipartition argument.

This work is partially supported by NASA grants W-10107 and W-10175. The National Center for Atmospheric Research is sponsored by the National Science Foundation. Title: Models for the Rapidly Rotating Be Star Achernar Authors: Skumanich, A.; Macgregor, K. B.; Jackson, S. Bibcode: 2004AAS...204.0704S Altcode: 2004BAAS...36..785S We present models for the Be star Achernar (α Eridani), which recent interferometric observations have shown has a photospheric shape that is significantly distorted by the effects of rotation. The models are two-dimensional, axisymmetric configurations, constructed using a new version of the self-consistent-field (SCF) method for computing the the structure of a rapidly, differentially rotating star, Jackson et al. (2004). Our revised SCF technique does not suffer from the computational difficulties that affected previous implementations of the method, yielding converged stellar models regardless of mass. For models with masses like those of main sequence stars of mid to early B spectral type, it is possible to reproduce Achernar's inferred equatorial and polar dimensions through a combination of rotational flattening/distension and suitable inclination of the rotation axis. However, while matching Achernar's apparent shape, these models are discrepant in other respects, being (on average) cooler and more rapidly rotating than observations indicate.

Jackson, S., Macgregor, K. B. & Skumanich, A., in preparation

The NCAR (National Center for Atmospheric Research) is sponsored by the National Science Foundation. Title: Angular Momentum Transport between a T Tauri Star and an Accretion Disk Authors: Barnes, B.; MacGregor, K. B. Bibcode: 2003csss...12..747B Altcode: We present results from time dependent numerical simulations of the hydromagnetic interaction between a rotating T Tauri star and a magnetically coupled Keplerian accretion disk. For a diffusive disk, we find that most of the toroidal component of the magnetic field is generated within a thin, shearing boundary layer that forms along the interface between the disk and the magnetosphere. We describe the properties of the system when it has attained a rotational equilibrium state in which the stellar spin-up produced by accretion and structural changes is compensated for by the spin-down torque arising from the magnetic connection between the star and the disk. Title: Gravity Wave-driven Flows in the Solar Tachocline. II. Stationary Flows Authors: Kim, Eun-jin; MacGregor, K. B. Bibcode: 2003ApJ...588..645K Altcode: The effects of gravity waves on the mean radial differential rotation profile in the solar tachocline are studied, including the effect of a uniform, toroidal magnetic field. Vertical transport of horizontal momentum arises from the radiative damping of inwardly traveling waves that are generated by low-frequency, convective fluid motions. By considering two-wave and one-wave interactions, the radiatively damped gravity waves are shown to accentuate the shear in the mean radial differential rotation. In the presence of a strong horizontal magnetic field, internal gravity waves become nearly Alfvénic and cannot propagate downward through the tachocline. For a magnetic field that is weak enough to permit wave propagation, the mean shear profile is shown to be smoother than that obtained in the case of purely hydrodynamic waves. The implications of our results for gravity-wave forcing of the internal solar rotation are discussed. Title: Magnetic Fields in Massive Stars. II. The Buoyant Rise of Magnetic Flux Tubes through the Radiative Interior Authors: MacGregor, K. B.; Cassinelli, J. P. Bibcode: 2003ApJ...586..480M Altcode: 2002astro.ph.12224M We present results from an investigation of the dynamical behavior of buoyant magnetic flux rings in the radiative interior of a uniformly rotating, early-type star. Our physical model describes a thin, axisymmetric, toroidal flux tube that is released from the outer boundary of the convective core and is acted on by buoyant, centrifugal, Coriolis, magnetic tension, and aerodynamic drag forces. We find that rings emitted in the equatorial plane can attain a stationary equilibrium state that is stable with respect to small displacements in radius, but is unstable when perturbed in the meridional direction. Rings emitted at other latitudes travel toward the surface along trajectories that largely parallel the rotation axis of the star. Over much of the ascent, the instantaneous rise speed is determined by the rate of heating by the absorption of radiation that diffuses into the tube from the external medium. Since the timescale for this heating varies like the square of the tube cross-sectional radius, for the same field strength, thin rings rise more rapidly than do thick rings. For a reasonable range of assumed ring sizes and field strengths, our results suggest that buoyancy is a viable mechanism for bringing magnetic flux from the core to the surface, being capable of accomplishing this transport in a time that is generally much less than the stellar main-sequence lifetime. Title: Gravity Waves in the Radiative Zone and Tachocline Authors: MacGregor, K. B. Bibcode: 2003PADEU..13....9M Altcode: We review the properties of internal gravity waves under physical conditions like those of the solar radiative interior, and consider a few of the ways in which such disturbances might influence the dynamical structure of the tachocline region. Title: Solar dynamo models Authors: MacGregor, Keith Bibcode: 2002ocnd.confE..19M Altcode: No abstract at ADS Title: Magnetic Fields in Massive Stars. I. Dynamo Models Authors: Charbonneau, Paul; MacGregor, Keith B. Bibcode: 2001ApJ...559.1094C Altcode: Motivated by mounting evidence for the presence of magnetic fields in the atmospheres of ``normal'' early-type main-sequence stars, we investigate the various possible modes of dynamo action in their convective core. Working within the framework of mean field electrodynamics, we compute α2 and α2Ω dynamo models and demonstrate that the transition from the former class to the latter occurs smoothly as internal differential rotation is increased. Our models also include a magnetic diffusivity contrast between the core and radiative envelope. The primary challenge facing such models is to somehow bring the magnetic field generated in the deep interior to the stellar surface. We investigate the degree to which thermally driven meridional circulation can act as a suitable transport agent. In all models with strong core-to-envelope magnetic diffusivity contrast-presumably closest to reality- whenever circulation is strong enough to carry a significant magnetic flux, it is also strong enough to prevent dynamo action. Estimates of typical meridional circulation speeds indicate that this regime is likely not attained in the interior of early-type main-sequence stars. Dynamo action then remains highly probable, but an alternate mechanism must be sought to carry the magnetic field to the surface. Title: Gravity Wave-driven Flows in the Solar Tachocline Authors: Kim, Eun-jin; MacGregor, K. B. Bibcode: 2001ApJ...556L.117K Altcode: We present results from time-dependent hydrodynamic calculations of the interaction between internal gravity waves and the mean radial differential rotation in the solar tachocline. Such waves are thought to be generated by turbulent fluid motions at the base of the convection zone. Our simplified model treats the effects of wave forcing, produced by radiative damping of downward propagating disturbances, on the rotational shear flow in the region immediately below the convection zone. We have used the model to investigate the dependence of the computed flow properties on the values assumed for the wave frequency, the horizontal component of the wavevector, the initial wave velocity amplitude, and the viscosity of the background medium. Our results indicate that if the first three of these quantities are held fixed, stationary shear flow solutions are obtained for viscosities larger than a parameter-dependent critical value. If the viscosity is continuously decreased from this value, the flow undergoes a succession of dramatic transformations, first becoming periodic, then quasi-periodic, and ultimately chaotic when the viscosity is made sufficiently small. We discuss the implications of these results for the recently reported time variability of the angular velocity of rotation within the solar tachocline. Title: Spin-Down of Young Stars: The Role of Magnetic Fields Authors: MacGregor, K. B. Bibcode: 2001ASPC..248..505M Altcode: 2001mfah.conf..505M No abstract at ADS Title: Angular momentum transport by internal gravity waves Authors: Kim, Eun-Jin; MacGregor, Keith B. Bibcode: 2000AIPC..537..256K Altcode: 2000wdss.conf..256K We discuss the effects of internal gravity waves on the mean radial differential rotation profile in the solar tachocline. Vertical transport of horizontal momentum arises from the radiative damping of inwardly traveling waves that are generated by low-frequency, convective fluid motions. For a viscosity typical of the radiative layers below the convection zone, the equilibrium profile of radial differential rotation is demonstrated to be unstable, possibly leading to turbulent mixing in the tachocline. The effect of a uniform, toroidal magnetic field is discussed. . Title: The Rise of a Magnetic Flux Tube through the Radiative Envelope of a 9 M_solar Star Authors: Cassinelli, J. P.; MacGregor, K. B. Bibcode: 2000ASPC..214..337C Altcode: 2000IAUCo.175..337C; 2000bpet.conf..337C No abstract at ADS Title: Magnetic fields and light element depletion in the Sun Authors: Charbonneau, P.; Barnes, G.; MacGregor, K. B. Bibcode: 2000IAUJD...5E..14C Altcode: I will first briefly review some important similarities and differences in models for the spin-down of solar-type stars, with or without internal magnetic fields in their radiative interior. This will be followed by a presentation of some simple calculations for the main-sequence depletion of Lithium and Beryllium in the Sun, in a regime where magnetic fields provide the chief mechanism for the internal redistribution of angular momentum. In this model the transport of light elements still occurs in response to shear-induced small-scale turbulence, following various commonly used prescriptions for the transport coefficients. For some (physically reasonable) values of model parameters, both internal differential rotation and light element abundances end up solar-like at 4.5Gyr. Within this framework light element depletion is a sensitive function of the strength of the assumed internal magnetic field. Title: Angular momentum evolution: a comparison of internal transport mechanisms Authors: MacGregor, K. B. Bibcode: 2000ASPC..198..329M Altcode: 2000scac.conf..329M No abstract at ADS Title: On the magnetohydrodynamics of a conducting fluid between two flat plates Authors: Barnes, G.; MacGregor, K. B. Bibcode: 1999PhPl....6.3030B Altcode: The time-dependent flow of a viscous, electrically conducting fluid contained within the space between two parallel, semi-infinite, perfectly conducting plates is considered. A uniform magnetic field directed perpendicular to the plate surfaces is assumed to pervade the fluid. Oscillatory motion of one of the plates in its own plane is induced through the application of a prescribed acceleration, the magnitude and direction of which vary sinusoidally in time. For a system forced in this manner, the resulting flow and transverse field component are solved for, as well as for the motion of the plate as a function of time. The magnetic and viscous stresses exerted on the boundary plate by the contiguous field and fluid are explicitly incorporated into the treatment of its motion. The physical properties and behavior of this system are investigated by examining analytic and numerical solutions obtained for a range of forcing periods, Reynolds numbers, and plate mass column densities. The relevance of these results to the interpretation of a model for Alfvénic torsional oscillations in the solar interior are discussed. Title: Angular Momentum Transport in Magnetized Stellar Radiative Zones. IV. Ferraro's Theorem and the Solar Tachocline Authors: MacGregor, K. B.; Charbonneau, P. Bibcode: 1999ApJ...519..911M Altcode: We consider the circumstances under which the latitudinal differential rotation of the solar convective envelope can (or cannot) be imprinted on the underlying radiative core through the agency of a hypothetical weak, large-scale poloidal magnetic field threading the solar radiative interior. We do so by constructing steady, two-dimensional axisymmetric solutions to the coupled momentum and induction equations under the assumption of a purely zonal flow and time-independent poloidal magnetic field. Our results show that the structure of the interior solutions is entirely determined by the boundary conditions imposed at the core-envelope interface. Specifically, in the high Reynolds number regime a poloidal field having a nonzero component normal to the core-envelope interface can lead to the transmission of significant differential rotation into the radiative interior. In contrast, for a poloidal field that is contained entirely within the radiative core, any differential rotation is confined to a thin magnetoviscous boundary layer located immediately beneath the interface, as well as along the rotation/magnetic axis. We argue that a magnetically decoupled configuration is more likely to be realized in the solar interior. Consequently, the helioseismically inferred lack of differential rotation in the radiative core does not necessarily preclude the existence of a weak, large-scale poloidal field therein. We suggest that such a field may well be dynamically significant in determining the structure of the solar tachocline. Title: Angular Momentum Transport in Magnetized Stellar Radiative Zones. III. The Solar Light-Element Abundances Authors: Barnes, G.; Charbonneau, P.; MacGregor, K. B. Bibcode: 1999ApJ...511..466B Altcode: We calculate the depletion of the trace elements lithium and beryllium within a solar-mass star during the course of its evolution from the zero-age main sequence to the age of the present-day Sun. In the radiative layers beneath the convection zone, we assume that these elements are transported by the turbulent fluid motions that result from instability of the shear flow associated with internal differential rotation. This turbulent mixing is modeled as a diffusion process, using a diffusion coefficient that is taken to be proportional to the gradient of the angular velocity distribution inside the star. We study the evolution of the light-element abundances produced by rotational mixing for models in which internal angular momentum redistribution takes place either by hydrodynamic or by hydromagnetic means. Since models based on these alternative mechanisms for angular-momentum transport predict similar surface rotation rates late in the evolution, we explore the extent to which light-element abundances make it possible to distinguish between them. In the case of an internally magnetized star, our computations indicate that both the details of the surface abundance evolution and the magnitude of the depletion at solar age can depend sensitively on the assumed strength and configuration of the poloidal magnetic field inside the star. For a configuration with no direct magnetic coupling between the radiative and convective portions of the stellar interior, the depletion of lithium calibrated to the solar lithium depletion at the solar age is similar at all ages to the lithium depletion of a model in which angular-momentum transport occurs solely by hydrodynamical processes. However, the two models can be distinguished on the basis of their respective beryllium depletions, with the depletion of the magnetic model being significantly smaller than that of the nonmagnetic model. Title: Gravity Waves in a Magnetized Shear Layer Authors: Barnes, G.; MacGregor, K. B.; Charbonneau, P. Bibcode: 1998ApJ...498L.169B Altcode: We use the equations governing the propagation of a gravity wave in the presence of a background flow and magnetic field to derive, in the Boussinesq approximation, dispersion relations for plane wave solutions in certain special cases. We show how, under conditions typical of the interior of the Sun, the addition of a magnetic field may prevent certain wavevectors from propagating and alter the existence and position of any critical layer that might absorb the gravity wave. Title: Angular Momentum Transport in Magnetized Stellar Radiative Zones: The Solar Light Element Abundances Authors: Barnes, G.; Charbonneau, P.; MacGregor, K. B. Bibcode: 1998ASPC..154..886B Altcode: 1998csss...10..886B We calculate the depletion of the trace elements lithium and beryllium within a solar mass star, during the course of its evolution from the zero-age main sequence to the age of the present-day Sun. In the radiative layers beneath the convection zone, we assume that these elements are transported by the turbulent fluid motions that result from the instability of the shear flow associated with internal differential rotation. This turbulent mixing is modeled as a diffusive process, using a diffusion coefficient that is taken to be proportional to the gradient of the angular velocity distribution inside the star. We study the evolution of the light element abundances produced by rotational mixing for models in which internal angular momentum redistribution takes place either by hydrodynamic or by hydromagnetic means. Since models based on these alternative mechanisms for angular momentum transport predict similar surface rotation rates late in the evolution, we explore the extent to which light element abundances make it possible to distinguish between them. In the case of an internally magnetized star, our computations indicate that both the details of the surface abundance evolution and the magnitude of the depletion at solar age can depend sensitively on the assumed strength and configuration of the poloidal magnetic field inside the star. For a configuration with no direct magnetic coupling between the radiative and convective portions of the stellar interior, the depletion of lithium as a function of age is similar to that of a model in which angular momentum transport occurs solely by hydrodynamical processes. However, the two models can be distinguished on the basis of their respective beryllium depletions, with the depletion of the magnetic model being significantly smaller than that of the non-magnetic model. Title: Acceleration Mechanisms for Cool Star Winds Authors: MacGregor, K. B. Bibcode: 1998cvsw.conf....3M Altcode: No abstract at ADS Title: Mixing in Low-Mass Stars: The Lithium-Rotation Connection Authors: Balachandran, Suchitra C.; Garcia Lopez, R. J.; Kraft, R. P.; MacGregor, K. B.; Barnes, G.; Martin, E. L.; Pinsonneault, Marc H. Bibcode: 1998ASPC..154..111B Altcode: 1998csss...10..111B We have known for over three decades that the Sun has depleted its surface lithium. During this period it has become increasingly evident that mixing, unaccounted for by the standard models, occurs in the stellar interior. There is some conjecture that this mixing may be driven by rotation and thus be dependent upon the rotational history of the star. In this discussion session, we will examine the observational connection between mixing and rotation and critically evaluate current models. Title: Solar Interface Dynamos. I. Linear, Kinematic Models in Cartesian Geometry Authors: MacGregor, K. B.; Charbonneau, P. Bibcode: 1997ApJ...486..484M Altcode: We describe a simple, kinematic model for a dynamo operating in the vicinity of the interface between the convective and radiative portions of the solar interior. The model dynamo resides within a Cartesian domain, partioned into an upper, convective half and lower, radiative half, with the magnetic diffusivity η of the former region (η2) assumed to exceed that of the latter (η1). The fluid motions that constitute the α-effect are confined to a thin, horizontal layer located entirely within the convective half of the domain; the vertical shear is nonzero only within a second, nonoverlapping layer contained inside the radiative half of the domain. We derive and solve a dispersion relation that describes horizontally propagating dynamo waves. For sufficiently large values of a parameter analogous to the dynamo number of conventional models, growing modes can be found for any ratio of the upper and lower magnetic diffusivities. However, unlike kinematic models in which the shear and α-effect are uniformly distributed throughout the same volume, the present model has wavelike solutions that grow in time only for a finite range of horizontal wavenumbers.

An additional consequence of the assumed dynamo spatial structure is that the strength of the azimuthal magnetic field at the location of the α-effect layer is reduced relative to the azimuthal field strength at the shear layer. When the jump in η occurs close to the α-effect layer, it is found that over one period of the dynamo's operation, the ratio of the maximum strengths of the azimuthal fields at these two positions can vary as the ratio (η12) of the magnetic diffusivities. Title: Solar Interface Dynamos. II. Linear, Kinematic Models in Spherical Geometry Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1997ApJ...486..502C Altcode: Numerical models of interface dynamos are constructed, and their properties discussed in some detail. These models are extensions in spherical geometry of the Cartesian interface models considered by Parker and in the first paper of this series. The models are cast in the framework of classical mean-field electrodynamics and make use of a realistic solar-like internal differential rotation profile. The magnetic diffusivity is assumed to vary discontinously by orders of magnitude across the core-envelope interface. This allows the buildup of very strong toroidal magnetic fields below the interface, as apparently required by recent models of erupting bipolar magnetic regions.

Distinct dynamo modes powered either by the latitudinal or radial shear can coexist and, under certain conditions, interfere destructively with one another. Hybrid modes, relying on the latitudinal shear both in the envelope and below it, are most easily excited in some portions of parameter space, and represent a class of dynamo solutions distinct from the true interface modes previously investigated in Cartesian geometry. Which mode is preferentially excited depends primarily on the assumed ratio of magnetic diffusivities on either side of the core-envelope interface. For an α-effect having a simple cos θ latitudinal dependency, the interface mode associated with the radial shear below the polar regions of the interface is easier to excite than its equatorial counterpart. In analogy with more conventional dynamo models, interface modes propagate equatorward if the product of the radial shear (∂Ω/∂r) and α-effect coefficient (Cα) is negative, and poleward if that product is positive.

Interface dynamo modes powered by the positive radial shear localized below the core-envelope interface in the equatorial regions can be produced by artificially restricting the α-effect to low latitudes. For negative dynamo number, those modes are globally dipolar, propagate toward the equator, and are characterized by a phase relationship between poloidal and toroidal magnetic field components that is in agreement with observations.

While the models discussed in this paper are linear and kinematic, and consequently rather limited in their predictive power, results obtained so far certainly suggest that interface dynamos represent a very attractive alternative to conventional solar mean-field dynamo models. Title: Angular Momentum Evolution in Late-Type Stars Authors: Charbonneau, P.; Schrijver, C. J.; MacGregor, K. B. Bibcode: 1997cwh..conf..677C Altcode: 2006mslp.conf..677C No abstract at ADS Title: ALFVÉN Wave-Driven Winds Authors: MacGregor, K. B.; Charbonneau, P. Bibcode: 1997cwh..conf..327M Altcode: 2006mslp.conf..327M No abstract at ADS Title: On the Generation of Equipartition-Strength Magnetic Fields by Turbulent Hydromagnetic Dynamos Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1996ApJ...473L..59C Altcode: The generation of a mean magnetic field by the action of small-scale turbulent fluid motions, the alpha -effect, is a fundamental ingredient of mean-field dynamo theory. However, recent mathematical models and numerical experiments are providing increasingly strong support to the notion that at high magnetic Reynolds numbers, the alpha -effect is strongly impeded long before the mean magnetic field has reached energy equipartition with the driving fluid motions. Taken at face value, this raises serious doubt as to whether the solar magnetic field is produced by a turbulent hydromagnetic dynamo after all, since it is an observed fact that the Sun does possess a structured, large-scale mean magnetic field of strength comparable to equipartition. In this Letter we demonstrate that the class of mean-field turbulent hydromagnetic models known as interface dynamos can produce equipartition-strength mean magnetic fields even in the presence of strong alpha -quenching. Title: Nonlinear interface dynamos with α-quenching. Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1996BAAS...28..935C Altcode: No abstract at ADS Title: Nonlinear interface dynamos with alpha -quenching Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1996AAS...188.6902C Altcode: 1996BAAS...28Q.935C There exist various mechanisms capable of limiting the magnitude of the (presumably) dynamo-generated, large-scale solar magnetic field. One such mechanism is the so-called ``alpha -quenching''. The underlying idea is that the Lorentz force associated with the dynamo-generated magnetic fields impedes the small scale, turbulent fluid motions giving rise to the so-called ``alpha -effect'' (the production of poloidal from toroidal fields in the framework of mean-field dynamo theory). In mean-field models, a popular ---yet essentially ad hoc--- prescription for alpha -quenching consists in replacing the coefficient (alpha ) of the alpha -effect source term in the dynamo equations by an expression of the form alpha -> alpha (B) =alpha_0 /(1+(|B|/B_eq)(2)) , where alpha_0 is a measure of the strength of the alpha -effect in the linear regime, and B_eq is the equipartition field strength, based on the kinetic energy of the turbulent, convective fluid motions (B_eq ~ 10(4) G at the base of the solar convection zone). In principle, such ``Weak Quenching'' allows the production of magnetic fields of roughly equipartition strength, as demonstrated by the numerous conventional mean-field dynamo models making use of eq. (1), or some close variant, published to date. Vainshtein & Cattaneo (1992, ApJ 393, 165) and Gruzinov & Diamond (1995, Phys. Plasmas 2, 1941) have argued, however, that alpha -quenching should be described by alpha -> alpha (B) =alpha_0 /(R_m(|B|/B_eq)(2)) where R_m is a magnetic Reynolds number based on the microscopic properties of the flow (R_m>> 1 for solar interior conditions). This now describes a much stronger form of alpha -quenching, and, with R_m>> 1, could be fatal to large-scale dynamo action, in the sense that the dynamo could only produce magnetic fields of strength << B_eq. This is in marked contradiction with the demands set by recent models of bipolar magnetic region emergence, which require field strengths of order 10x B_eq ~ 10(5) G for the observed latitudes and tilt of emergence to be adequately reproduced. In this contribution, we investigate the circumstances under which interface dynamos can avoid alpha -quenching, either in the ``Weak'' or ``Strong'' forms defined above. In interface dynamos the alpha -effect is assumed to operate within the solar convective envelope, while the strongest magnetic fields are generated by shearing below the core-envelope interface (Parker 1993, ApJ 408, 707; Charbonneau & MacGregor, submitted to ApJ). This spatial segregation of the alpha -effect source region is the key to avoiding alpha -quenching. This is illustrated using a few nonlinear, kinematic interface dynamo solutions applicable to the Sun. Title: Stellar winds. Authors: MacGregor, K. B. Bibcode: 1996ASIC..481..301M Altcode: The author considers some of the ways in which MHD processes can contribute to the acceleration of wind-type outflows from stars. He first summarizes the measured properties of the "average" solar wind, and reviews the evidence for the existence of analogous flows from solar-type stars in general. The influence of magnetic fields on wind dynamics is then studied by considering how a simple, stationary, thermally driven wind model is modified by the inclusion of several different MHD effects. Specifically, the author examines how the radial acceleration of such a wind is influenced by the incorporation of (1) magnetically controlled, non-spherical expansion, (2) the Lorentz force associated with a large-scale, stellar magnetic field, and (3) the force arising from outwardly propagating, short-wavelength Alfvén waves into the basic model. He subsequently considers how these processes might affect the dynamical structure of a radiatively driven wind from a luminous, hot, OB star. Title: Waves in Radiating Fluids Authors: Bogdan, T. J.; Knoelker, M.; MacGregor, K. B.; Kim, E. -J. Bibcode: 1996ApJ...456..879B Altcode: We derive from first principles the equations which govern the behavior of small-amplitude fluctuations in a homogeneous and isotropic radiating fluid. Products of the fluctuating quantities are shown to obey a wave-energy conservation law from which it follows that all perturbations must ultimately decay in time. Under fairly general circumstances the governing equations may be solved through the use of integral transforms which affords an accounting of the various wave modes supported by the radiating fluid. In addition to the familiar radiatively modified acoustic mode, the radiation-diffusion mode, the radiative-relaxation mode, and the isotropization and exchange modes which constitute the discrete spectrum of the differential equation, we find a continuous spectrum of wave modes associated with the "collisionless" nature of the photons on timescales short compared to the photon lifetime. This continuous spectrum is eliminated if an Eddington approximation is used to close the hierarchy of equations that relate the fluctuating angular moments of the radiation field. Quantitative results are obtained for the simple case in which the opacity may be regarded as being independent of the frequency of the photon and the source function may be approximated by the (local) Planck function. Title: Stellar Winds with Non-WKB Alfven Waves. II. Wind Models for Cool, Evolved Stars Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1995ApJ...454..901C Altcode: We construct Alfvén wave-driven wind models for physical conditions appropriate to the expanding envelopes of cool, evolved stars. To derive wind properties, we assume steady, isothermal, spherically symmetric flow, but do not use the WKB (i.e., short-wavelength) approximation to calculate the wave amplitudes. Instead, we make use of the formalism developed in the first paper of this series (MacGregor & Charbonneau 1994), which describes wave reflection and associated modifications to the wave force, and consistently incorporates these effects into the treatment of wind dynamics.

For flows containing undamped Alfvén waves of arbitrarily long wavelength we find that the occurrence of wave reflection has profound consequences for wind acceleration and mass loss. Specifically, in all of our computed models, the outward-directed wave force near the base of the flow is significantly reduced relative to that in comparable WKB models. As a result, the initial expansion speeds and mass flux densities of model winds that include non-WKB effects are smaller than those of corresponding WKB winds. Moreover, at large distances from the star, wave reflection leads to an enhancement of the wave force relative to models in which all waves are presumed to be outwardly propagating. This tendency, when combined with the previously noted reduction in mass flux, produces winds with higher asymptotic flow speeds than those driven by high-frequency, short-wavelength Alfvén waves. Given that the challenge of modeling winds from cool evolved stars is to produce winds with high mass fluxes and low asymptotic flow speeds, we argue that Alfvén waves provide an acceptable driving mechanism only if their wavelengths are sufficiently short that minimal reflection occurs near the base of the flow. For stellar parameters characteristic of a supergiant star with spectral type ∼K5, this translates into an upper bound on Alfvén wave periods of ∼1 day. Title: On the evolution of rotational velocity distributions for solar-type stars. Authors: Keppens, R.; MacGregor, K. B.; Charbonneau, P. Bibcode: 1995A&A...294..469K Altcode: We investigate how the distribution of rotational velocities for late-type stars of a given mass evolves with age, both before and during residence on the main sequence. Starting from an age ~10^6^years, an assumed pre-main sequence rotational velocity/period distribution is evolved forward in time using the model described by MacGregor & Brenner (1991) to trace the rotational histories of single, constituent stars. This model treats: (i) stellar angular momentum loss as a result of the torque applied to the convection zone by a magnetically coupled wind; (ii) angular momentum transport from the radiative interior to the convective envelope in response to the rotational deceleration of the stellar surface layers; and (iii), angular momentum redistribution associated with changes in internal structure during the process of contraction to the main sequence. We ascertain how the evolution of a specified, initial rotational velocity/period distribution is affected by such things as: (i) the dependence of the coronal magnetic field strength on rotation rate through a prescribed, phenomenological dynamo relation; (ii) the magnitude of the timescale τ_c_ characterizing the transfer of angular momentum from the core to the envelope; (ii) differences in the details and duration of pre-main sequence structural evolution for stars with masses in the range 0.8<=M_*_/Msun_<=1.0 and (iv), the exchange of angular momentum between a star and a surrounding, magnetized accretion disk during the first few million years of pre-main sequence evolution following the development of a radiative core. The results of this extensive parameter study are compared with the distributions derived from measurements of rotational velocities of solar-type stars in open clusters with known ages. Starting from an initial distribution compiled from observations of rotation among T Tauri stars, we find that reasonable agreement with the distribution evolution inferred from cluster observations is obtained for: (i) a dynamo law in which the strength of the coronal field increases linearly with surface angular velocity for rotation rates <=20 times the present solar rate, and becomes saturated for more rapid rotation; (ii) a coupling timescale ~10^7^years; (iii) a mix of stellar masses consisting of roughly equal numbers of 0.8Msun_ and 1.0Msun_ stars; and (iv), disk regulation of the surface rotation up to an age ~6x10^6^years for stars with initial rotation periods longer than 5days. A number of discrepancies remain, however: even with the most favorable choice of model parameters, the present calculations fail to produce a sufficiently large proportion of slow (equatorial velocities less than 10km/s) rotators on the Zero-Age Main Sequence. Title: Stellar Winds with Non-WKB Alfven Waves. I. Wind Models for Solar Coronal Conditions Authors: MacGregor, K. B.; Charbonneau, P. Bibcode: 1994ApJ...430..387M Altcode: We have constructed numerical models for stationary, wind-type outflows that include treatment of the force produced by propagating Alfven waves. We make no assumptions regarding the relative sizes of the wavelengths of such disturbances and the scale lengths that characterize the variation of the physical properties of the expanding stellar atmosphere. Consequently, our models take account the process of Alfven wave reflection, and provide for dynamical effects arising from the simultaneous presence of outward and inward traveling waves in the wind. For physical conditions like those prevailing in the outer solar corona and wind, we find that even relatively high frequency, short wavelength waves can suffer some reflection from the gradient in Alfven speed at the vase of the flow. Among the consequences of the interaction between outward and inward directed perturbations in the sub-Alfvenic portion of the wind is a reduction in the magnitude of the time-averaged wave force relative to its value in the Wentzel-Kramer-Brillouin (WKB) (i.e., short-wavelenght) limit. As a result, the flow velocities of our models interior to the Alfven radius are smaller than those of corresponding WKB models. For models containing very low frequency, long wavelength waves, a substantial amount of wave reflection can also take place in the super-Alvenic portion of the wind. The resulting modifications to the spatial dependences of the eave magnetic and velocity amplitudes can lead to a wave force whose magnitude at large distances exceeds that of an equivalent WKB solution. Title: Angular Momentum Evolution of Late-Type Stars: A Theoretical Perspective (Invited Review) Authors: MacGregor, K. B.; Charbonneau, P. Bibcode: 1994ASPC...64..174M Altcode: 1994csss....8..174M No abstract at ADS Title: Angular Momentum Loss from the Young Sun: Improved Wind and Dynamo Models Authors: Keppens, R.; Charbonneau, P.; MacGregor, K. B.; Brandenburg, A. Bibcode: 1994ASPC...64..193K Altcode: 1994csss....8..193K No abstract at ADS Title: Solar wind with non-WKB Alfvén waves Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1994smf..conf..405C Altcode: No abstract at ADS Title: Angular Momentum Transport in Magnetized Stellar Radiative Zones. II. The Solar Spin-down Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1993ApJ...417..762C Altcode: We present a large set of numerical calculations describing the rotational evolution of a solar-type star, in response to the torque exerted on it by a magnetically coupled wind emanating from its surface. We consider a situation where the internal redistribution of angular momentum in the radiative part of the envelope is dominated by magnetic stresses arising from the shearing of a preexisting, large-scale, poloidal magnetic field.

By assuming a time-independent poloidal magnetic field, neglecting fluid motions in meridional planes, and restricting our attention to axisymmetric systems, we reduce the spin-down problem to solving the (coupled) ψ-components of the momentum and induction equations. Nevertheless, our computations remain dynamical, in that they take into account both the generation of a toroidal magnetic field by shearing of the preexisting poloidal field, and the back-reaction of the resulting Lorentz force on the differential rotation. It becomes possible to draw, for the first time, a reasonably realistic and quantitative picture of the effects of large-scale internal magnetic fields on the main-sequence rotational evolution of solar-type stars.

We perform spin-down calculations for a standard solar model, starting from the ZAMS and extending all the way to the solar age. The wind-induced surface torque is computed using the axisymmetric formulation of Weber & Davis (1967). We consider a number of poloidal magnetic field configurations which differ both in the degree of magnetic coupling between the convective envelope and radiative core and in average strength.

The rotational evolution can be divided into three more or less distinct phases: an initial phase of toroidal field buildup in the radiative zone, lasting from a few times 104 to a few times 106 yr; a second period in which oscillations set up in the radiative zone during the first phase are damped; and a third period, lasting from an age of about 107 yr onward, characterized by a state of dynamical balance between the total stresses (magnetic + viscous) at the core-envelope interface and the wind-induced surface torque, leading to a quasistatic internal magnetic and rotational evolution.

Our results also demonstrate (1) the existence of classes of large-scale internal magnetic fields that can accommodate rapid spin-down near the ZAMS and yield a weak internal differential rotation by the solar age, (2) the importance of phase mixing in efficiently damping large-scale toroidal oscillations pervading the radiative interior at early times, (3) the near-independence of the present solar surface angular velocity on the strength and geometry (past and present) of any internal large-scale magnetic field pervading the radiative interior, and (4) the greater dependence of the present solar internal differential rotation on the overall morphology (but not on the strength) of the internal magnetic field. Title: A Numerical Simulation of Two-dimensional Radiative Equilibrium in Magnetostatic Flux Tubes. II. Computational Results Authors: Pizzo, V. J.; MacGregor, K. B.; Kunasz, P. B. Bibcode: 1993ApJ...413..764P Altcode: We apply a recently developed numerical procedure for obtaining self-consistent radiative and mechanical equilibria of solar magnetostatic flux tubes. The tubes are modeled as localized but continuous field concentrations in a 2D slab geometry, and the radiation is treated in the LTE limit. The reduced opacities in the tube lead to the lateral intrusion of radiative flux into the tube, with subsequent modification of the internal atmosphere. Our calculations show that the effect is negligible, however, when the diameter of the tube exceeds the scale height of the atmosphere in the surface layers or if convective energy transport in the tube is itself sufficient to produce a thermal stratification close to that in the surrounding photosphere. That is, 2D radiative effects are likely to be important only in small tubes in which the upward convective energy flux is strongly suppressed. The treatment of the underlying convective layers appears to be of paramount importance in determining the computed surface properties. Title: The Evolution of Angular Momentum among Zero-Age Main-Sequence Solar-Type Stars Authors: Soderblom, David R.; Stauffer, John R.; MacGregor, Keith B.; Jones, Burton F. Bibcode: 1993ApJ...409..624S Altcode: We consider a survey of rotation among F, G, and K dwarfs of the Pleiades in the context of other young clusters (Alpha Persei and the Hyades) and pre-main-sequence (PMS) stars (in Taurus-Auriga and Orion) in order to examine how the angular momentum of a star like the sun evolves during its early life on the main sequence. The rotation of PMS stars can be evolved into distributions like those seen in the young clusters if there is only modest, rotation-independent angular momentum loss prior to the ZAMS. Even then, the ultrafast rotators (UFRs, or ZAMS G and K dwarfs with v sin i equal to or greater than 30 km/s) must owe their extra angular momentum to their conditions of formation and to different angular momentum loss rates above a threshold velocity, for it is unlikely that these stars had angular momentum added as they neared the ZAMS, nor can a spread in ages within a cluster account for the range of rotation seen. Only a fraction of solar-type stars are thus capable of becoming UFRs, and it is not a phase that all stars experience. Simple scaling relations (like the Skumanich relation) applied to the observed surface rotation rates of young solar-type stars cannot reproduce the way in which the Pleiades evolve into the Hyades. We argue that invoking internal differential rotation in these ZAMS stars can explain several aspects of the observations and thus can provide a consistent picture of ZAMS angular momentum evolution. Title: Solar Spin-down with Internal Magnetic Fields: Erratum Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1993ApJ...403L..87C Altcode: No abstract at ADS Title: A Numerical Simulation of Two-dimensional Radiative Equilibrium in Magnetostatic Flux Tubes. I. The Model Authors: Pizzo, V. J.; MacGregor, K. B.; Kunasz, P. B. Bibcode: 1993ApJ...404..788P Altcode: We describe an efficient numerical procedure for obtaining self-consistent radiative and mechanical equilibria of solar magnetostatic flux tubes. The flux tube is treated as a localized but continuous concentration of magnetic flux in a two-dimensional slab geometry. Starting from some given initial atmosphere, we compute a preliminary magnetostatic equilibrium state by a nonlinear iterative technique, subject to certain boundary conditions on the magnetic field. Given the resulting spatial distribution of opacities (derived from the initial run of temperature and density along each field line), and with knowledge of a distant radiation field incident upon the magnetic region, the radiative state of the atmosphere is computed by the short-characteristics method assuming gray, LTE conditions. The new temperature derived from the angle-averaged radiation field is used to update the hydrostatic atmosphere for the magnetostatic calculation, and so on, until both mechanical and radiative balance is attained. Title: Spin down of solar-type stars with internal magnetic fields Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1993ASPC...40..464C Altcode: 1993IAUCo.137..464C; 1993ist..proc..464C No abstract at ADS Title: Winds. Authors: MacGregor, K. B. Bibcode: 1993ASPC...40..620M Altcode: 1993IAUCo.137..620M; 1993ist..proc..620M It is by now well known that most main sequence stars continuously lose mass as a consequence of the winds they emit. In addition to affecting the thermal and dynamical state of the stellar atmosphere, such mass loss can also induce changes in the interiors of stars. In the present review, the author considers a few of the ways in which sustained, wind-like mass loss can alter the physical state of main sequence stellar interiors by examining the differences in internal structure, composition, and rotation between mass-losing and conservatively evolving stars. Title: On the Interaction between Dust and Gas in Late-Type Stellar Atmospheres and Winds Authors: MacGregor, K. B.; Stencel, R. E. Bibcode: 1992ApJ...397..644M Altcode: An assumption inherent to most models of dust-driven winds from cool, evolved stars is that the radiative and collisional drag forces acting on an individual dust grain are in balance throughout the flow. We have checked the validity of this supposition of 'complete momentum coupling' by comparing the grain motion obtained from such a model with that derived from solution of the full grain equation of motion. For physical conditions typical of the circumstellar envelopes of oxygen-rich red giants, we find that silicate grains with initial radii smaller than about 5 x 10 exp -6 cm decouple from the ambient gas near the base of the outflow. The implications of these results for models of dust-driven mass loss from late-type giants and supergiants are discussed. Title: Solar Spin-down with Internal Magnetic Fields Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1992ApJ...397L..63C Altcode: We investigate the rotational evolution of a solar-type star containing a large-scale poloidal magnetic field in its radiative core, in response to the torque applied to it by magnetically coupled wind. Our model takes into account both the generation of a toroidal magnetic component via shearing of the existing poloidal component by differential rotation, as well as the back-reaction on the differential rotation due to Lorentz forces associated with the toroidal field. Our computations demonstrate the existence of classes of large-scale poloidal magnetic fields allowing rapid spin-down of the surface layers shortly after the arrival on the zero-age main sequence, while producing weak internal differential rotation in the radiative core by the solar age. This indicates that the constraints brought about by rotational evolution of solar analogs in young clusters and by helioseismology are not incompatible with the existence of large-scale magnetic fields in stellar radiative interiors. The present surface solar rotation rate is also shown to be a poor indicator of the strength and geometry of hypothetical poloidal magnetic fields pervading the solar radiative interior. Title: Angular Momentum Transport in Magnetized Stellar Radiative Zones. I. Numerical Solutions to the Core Spin-up Model Problem Authors: Charbonneau, P.; MacGregor, K. B. Bibcode: 1992ApJ...387..639C Altcode: The present paper investigates the time evolution of the angular momentum and induced toroidal magnetic field distribution in an initially nonrotating radiative stellar envelope containing a large-scale poloidal magnetic field, following the impulsive spin-up of the underlying core. A large set of numerical calculations pertaining to monopolar, dipolar, and quadrupolar magnetic configurations, with and without density gradients across the envelope, as well as a set of solutions for which the poloidal field is only partially anchored on the core is presented. It is demonstrated that in moderate to high Reynolds-number systems, any global magnetic dissipation time scale constructed using length scales of order of the stellar radius greatly overestimates the true dissipation time scale of the toroidal magnetic component. Title: Winds from rotating, magnetic, hot stars: consequences for the rotational evolution of O and B stars. Authors: MacGregor, K. B.; Friend, D. B.; Gilliland, R. L. Bibcode: 1992A&A...256..141M Altcode: In an effort to obtain estimates of magnetic field strengths in hot stars, the authors have computed the evolution of rigidly rotating 15 and 30 Msun stars, including the effects of magnetically coupled, line-driven mass loss as described by the model of Friend and Mac-Gregor (1984). Using mean rotational velocities (i.e. v sin i values) derived from observations of main-sequence stars of these masses to specify the initial state, they followed the variations in time of the surface rotation rate due to internal structural changes and wind-related breaking. In each case the initial magnetic field strength was varied until the calculated rotational velocity at the onset of the blue supergiant phase was in resonable agreement with the corresponding mean v sin i value derived from observations. For both evolutionary models, it is found that the computed rotational velocity decrease in the presence of a magnetic field of even modest strength (⪉100 G) exceeds the limits set by observations. The limitations of this study and its implications for both the magnetic fields and winds of hot stars are discussed. Title: Wind-Driven Dust: The Interaction Between Dust; Gas in Late-Type Stellar Atmospheres; Winds Authors: MacGregor, K. B.; Stencel, R. E. Bibcode: 1992ASPC...26..484M Altcode: 1992csss....7..484M No abstract at ADS Title: Rotational Evolution of Solar-Type Stars. I. Main-Sequence Evolution Authors: MacGregor, K. B.; Brenner, M. Bibcode: 1991ApJ...376..204M Altcode: A simple, parameterized model for the redistribution of angular momentum within the interiors of solar-type stars is presented. By incorporating it with a description of angular momentum loss through the action of a magnetically coupled wind, tracing the rotational histories of low-mass dwarf stars for a variety of initial conditions and parameter specifications is accomplished. The results of calculations are discussed for the rotational evolution of a 1 solar mass star, from the time of its arrival on the zero-age main sequence to the age of the present-day sun. Best agreement is with observational constraints for (1) a surface magnetic field strength which is largely independent of surface angular velocity omega for rapid rotation, and approximately linearly dependent on omega for approximately solar values, and (2), a time scale for angular momentum transfer from the core to the convection zone which remains essentially constant throughout the evolution, with magnitude of a about 10 million yr. This value is approximately equal to the initial wind braking time. These results are discussed in the context of a qualitative description of angluar momentum redistribution by magnetic fields in the radiative interiors of solar-type stars. Title: A Numerical Simulation of Two-Dimensional Radiative Equilibrium in Magnetostatic Flux Tubes Authors: Pizzo, V. J.; MacGregor, K. B.; Kunasz, P. Bibcode: 1991BAAS...23Q1051P Altcode: No abstract at ADS Title: Pre-Main Sequence and Main Sequence Rotational Evolution - Constraints on Models Derived from Observations Authors: MacGregor, K. B. Bibcode: 1991ASIC..340..315M Altcode: 1991amey.conf..315M No abstract at ADS Title: A Numerical Simulation of Two-Dimensional Radiative Equilibrium in Magnetostatic Flux Tubes Authors: Pizzo, V. J.; MacGregor, K. B.; Kunasz, P. Bibcode: 1990BAAS...22R1198P Altcode: No abstract at ADS Title: Pre-Main Sequence Rotational Evolution of Solar-Type Stars Authors: MacGregor, K. B.; Cohen, P. Bibcode: 1990BAAS...22.1207M Altcode: No abstract at ADS Title: Lower Solar Chromosphere-Corona Transition Region. II. Wave Pressure Effects for a Specific Form of the Heating Function Authors: Woods, D. Tod; Holzer, Thomas E.; MacGregor, Keith B. Bibcode: 1990ApJS...73..489W Altcode: Lower transition region models with a balance between mechanical heating and radiative losses are expanded to include wave pressure effects. The models are used to study the simple damping length form of the heating function. The results are compared to the results obtained by Woods et al. (1990) for solutions in the lower transition region. The results suggest that a mixture of fast-mode and slow-mode waves may provide the appropriate heating mechanism in the lower transition region, with the decline in effective vertical wave speed caused by the refraction and eventual total reflection of the fast-mode wave resulting from the decreasing atmospheric density. Title: Lower Solar Chromosphere-Corona Transition Region. I. Theoretical Models with Small Temperature Gradients Authors: Woods, D. Tod; Holzer, Thomas E.; MacGregor, Keith B. Bibcode: 1990ApJ...355..295W Altcode: A study of transition region models including the effects of classical thermal conduction, heating, and radiative cooling is carried out with attention directed toward the problem of understanding the observed emission in the lower transition region. It is found that the observationally inferred emission measure curve implies a near-balance between heating and radiative cooling in the lower transition region, and that the presence of strong hydrogen Ly-alpha cooling leads to the existence of singularities in the solutions of the force balance and energy balance equations when such a near-balance between heating and cooling is assumed. These singularities place strong constraints on the nature of viable models of the lower transition region and must be considered when Ly-alpha cooling is important. Previously suggested explanations of the observed emission from the lower transition region are considered in the context of the results of the present study, and conditions for the applicability of these suggested explanations are discussed. Title: Lower Solar Chromosphere-Corona Transition Region. III. Implications of the Observed Quiet-Sun Emission Measure Including Wave Pressure Effects Authors: Woods, D. Tod; Holzer, Thomas E.; MacGregor, Keith B. Bibcode: 1990ApJ...355..309W Altcode: The observed form of the emission measure (EM) is used as a function of temperature to infer the wave energy flux density and pressure throughout the lower transition region (TR). This procedure eliminates the need for specifying how the wave energy flux density is damped and addresses the question of whether there is any form of the mechanical heating associated with the degradation of an upward traveling wave energy flux density which is consistent with the observed EM and other observational constraints for the quiet sun. It is found that the observed form of the EM curve is incompatible with waves traveling vertically at the sound speed, regardless of any filling factor arguments. The same conclusion also applies to waves traveling at the Alfven speed, unless it is assumed that the emission in lower TR lines originates solely from small, spatially unresolved regions of large magnetic field strength (100 G), which cover a small fraction (filling factors of 1 percent) of the solar surface. Title: High-Latitude SPOT and Plage Activity on the Rapidly Rotating M Dwarf Star Gliese 890 Authors: Young, Arthur; Skumanich, Andrew; MacGregor, Keith B.; Temple, Scott Bibcode: 1990ApJ...349..608Y Altcode: Simultaneous time-resolved observations in broadband photometry and in H-alpha and near-UV spectroscopy are presented of Gliese 890, a single M dwarf of the BY Draconis type with the shortest known period of rotation among field stars of its type. The continuum light curves exhibit modulations characteristic of the presence of localized dark spot regions, and the spectra show corresponding modulations of the intensity of H-alpha emission, with the latter being substantially in phase with the former. Secular changes in the continuum light curve indicate that the geometry of the spots changes appreciably over time scales of the order of 60 rotation periods. The overall chromospheric activity is not significantly greater than that found in similar stars which rotate much more slowly. The principal active region present on the visible disk of the star during the observations appear to be at a remarkably high latitude compared to the occurrence of such regions on the sun. Title: Rotational Evolution of Solar-Type Stars Authors: MacGregor, K. B.; Brenner, M. Bibcode: 1989BAAS...21.1078M Altcode: No abstract at ADS Title: On the Structure of Radiating Shocks Authors: Halvorson, C. M.; MacGregor, K. B. Bibcode: 1989BAAS...21.1114H Altcode: No abstract at ADS Title: Nonspherical Expansion of Radiation-driven Winds Authors: MacGregor, K. B. Bibcode: 1988ApJ...327..794M Altcode: The line-driven wind theory of Castor et al. (1975) is extended to include effects arising from nonspherical expansion. Specifically, isothermal flow along the central streamline of a flow tube whose cross-sectional area increases outward faster than r-squared near the stellar surface is considered. Using the area function of Kopp and Holzer (1976), it is found that rapid flow tube divergence causes the critical point to occur closer to the stellar photosphere. Even modest departures from spherically symmetric expansion can significantly enhance the radiative force, and lead to large increases in the asymptotic flow speed of the wind. For models in which the region of rapid geometrical divergence is located more than a few tenths of a stellar radius from the photosphere, the mass flux density at the base of the wind is essentially unchanged from that of the spherical case. These results may have implications for the occurrence and structure of streams and corotating interaction regions in the winds of hot stars. Title: Shallow Temperature Gradient Solutions and Wave Pressure Effects in the Lower Transition Region Authors: Woods, D. T.; MacGregor, K. B.; Holzer, T. E. Bibcode: 1987BAAS...19Q.937W Altcode: No abstract at ADS Title: Winds from Rotating, Magnetic, Hot Stars. III. The Azimuthal Velocity and Magnetic Force Authors: MacGregor, K. B.; Friend, D. B. Bibcode: 1987ApJ...312..659M Altcode: The model of Friend and MacGregor (1984) is used to study the dynamical interplay between the azimuthal velocity and the Lorentz force in the line-driven wind from a rotating, magnetic, hot star. It is found that strong, outward acceleration by the radiative force can cause the azimuthal component of the magnetic force to reverse direction and act counter to the sense of the stellar rotation. One manifestation of this behavior is a faster than 1/r decrease in V(phi) over a limited spatial region near the base of the flow. By consideration of the wind momentum equation in the corotating reference frame, such a magnetic force reversal is shown to be a consequence of the required force balance perpendicular to the magnetic field. Title: Stars with Thin and Thick Convection Zones: M Giants (Invited review) Authors: MacGregor, K. B. Bibcode: 1987LNP...291..250M Altcode: 1987LNP87.291..250M; 1987csss....5..250M Observational results pertaining to the thermal and dynamical structure of the atmospheres of cool, evolved stars are summarized. It is noted that the inferred atmospheric properties of a given star of this type appear to depend on its position relative to the various dividing lines which have been identified in the HR diagram. Using computed evolutionary models, changes in the internal structure of an intermediate mass star are followed as its redward motion in the HR diagram carries it across the transition region dividing line. It is suggested that this boundary may reflect the onset of deep envelope convection during post main sequence evolution. Title: On the Size of Convective Cores in Rotating, Upper--Main-Sequence Stars Authors: MacGregor, K. B.; Gilliland, Ronald L. Bibcode: 1986ApJ...310..273M Altcode: The effects of rotation on the structure of upper main sequence stars are reviewed, and the effects resulting from alterations of the convective-radiative stability criterion due to changes in the radiative gradient are explicitly modeled and analyzed. It is found that rotation leads to a smaller convective core and reduced luminosity, the coupled effects of which lead to little change in the main sequence lifetime. It is noted that the rotational modification to the Schwarzschild criterion suggested by Sreenivasan and Wilson (1985) has in fact been included in the computations conducted by previous authors. Title: Radiation-Driven Winds in Non-Spherical Geometries Authors: MacGregor, K. B. Bibcode: 1986BAAS...18..954M Altcode: No abstract at ADS Title: The Effect of Extremely Rapid Rotation on Stellar Activity: The Case of Gliese 890 Authors: Young, Arthur; Skumanich, Andrew; MacGregor, Keith; Temple, Scott Bibcode: 1986LNP...254..127Y Altcode: 1986csss....4..127Y We present an analysis of broad-band photometry and of the H-alpha emission line profile of the active, rapidly rotating (P = 0.43 days) single M-dwarf star Gleise 890. Our analysis suggests that the (presumed dark) spots and the bright emission regions are confined to high latitudes on the star. We combine our results with published work on other rapidly rotating single stars which indicate that such activity is generally confined to the polar regions of such stars, and we contrast that to rapidly rotating active components in binary systems where the active regions do not appear to be confined to the polar latitudes. Noting that solar activity is confined to lower latitudes and seems unable to affect polar latitudes, we suggest that extremely rapid rotation may ater the convective turnover time in the equatorial latitudes, and that strong tidal coupling may restore it to normal values in spite of rapid rotation. The evidence suggests that even though radiative power losses due to activity may be comparable in single and binary stars, the driving mechanisms may differ appreciably. Title: Stellar chromospheres, coronae, and winds. Authors: Cassinelli, J. P.; MacGregor, K. B. Bibcode: 1986psun....3...47C Altcode: Contents: Late-type stars: observational evidence for the presence of chromospheres in late-type stellar atmospheres (spectral diagnostics and line formation, observational summary and location in the H-R diagram, the Wilson-Bappu effect), observational evidence for the presence of regions and coronae in late-type stellar atmospheres, chromospheric and coronal heating mechanisms, observational evidence for mass loss from late-type stars (main sequence stars, circumstellar absorption lines, chromospheric emission line asymmetries, circumstellar dust shells), mass loss mechanisms for late-type giants and supergiants. The winds and coronae of early-type stars: the velocity and mass loss rates derived from line and continuum observations (the formation of P Cygni profiles, the free-free continuum energy distribution of hot stars), coronal gas in early-type stars (superionization of the winds, X-ray observation of early-type stars), wind dynamics (radiation forces on line opacity: momentum deposition considerations, radiative acceleration, instability of line driven winds and the consequences, hybrid models with a base coronal zone, magnetically driven winds and magnetically dominated coronae). Title: Evolution of activity signatures during the main sequence phase Authors: Skumanich, A.; MacGregor, K. Bibcode: 1986AdSpR...6h.151S Altcode: 1986AdSpR...6Q.151S We review recent work on the decay of magnetic activity signatures, such as chromospheric/transition region/coronal emission as well as mean flare emission, with age for solar and later type stars. Both implicit and explicit evolutionary representations are discussed. In terms of magnetic flux, as measured by excess chromospheric CaII luminosity, we show that a simple dynamo-rotation relation that incorporates both a saturated state with its characteristic critical rotation (or scale factor) as well as an asymptotic linear power law, i.e. a scale free relation, fits the extant data that includes the dMe stars. Introducing the saturated dynamo state, as exemplified by the dMe stars, into activity power-power diagrams, allows us to not only specify the saturated state, but to define evolutionary tracks that represent the decay from the saturated state. Using the quiescent coronal X-ray power (luminosity) as a basic measure of magnetic activity, we find simple monomial relations for both the saturated state (linear) and for the evolutionary tracks governing both quiescent activity and mean flare activity. In particular, the coronal power loss is found to vary quadratically with the chromospheric power loss, hence with magnetic flux.

NCAR is sponsored by the National Science Foundation. Title: The Development of Thermally Driven Winds Around Low Mass Protostars Authors: Terebey, S.; MacGregor, K. B. Bibcode: 1985BAAS...17..862T Altcode: No abstract at ADS Title: Mass Loss Mechanisms for Cool, Low-Gravity Stars (Review) Authors: Holzer, T. E.; MacGregor, K. B. Bibcode: 1985ASSL..117..229H Altcode: 1985mlrg.proc..229H A number of physical effects relevant to mass loss from cool, low-gravity stars is explored in order to provide a basis for understanding the various mechanisms proposed to explain such quasi-steady and non-steady mass loss. After considering a few general implications of the requirements of mass, momentum, and energy balance, four specific mass loss mechanisms are examined in some detail. Emphasis is placed on the basic physical constraints imposed uniformly on all these mechanisms by inferences drawn from observations of a broad range of stars. It is suggested that these physical constraints, rather than the techniques used to observe particular objects should serve as the dominant factor in organizing thinking about massive, low speed, late type stellar winds. Title: Rotational Evolution of Hot Stars Authors: MacGregor, K. B.; Friend, D. B.; Gilliland, R. L. Bibcode: 1984BAAS...16..996M Altcode: No abstract at ADS Title: The Extremely Rapidly Rotating M-Dwarf Star Gliese 890 Authors: Young, A.; Skumanich, A.; MacGregor, K.; Temple, S. Bibcode: 1984BAAS...16.1014Y Altcode: No abstract at ADS Title: The Role of Diamagnetic Material in the Solar Atmosphere Authors: Cargill, P. J.; MacGregor, K. B.; Pneuman, G. W. Bibcode: 1984BAAS...16.1005C Altcode: No abstract at ADS Title: A Non-Radial Radiation Force in Hot Star Winds Authors: Friend, D. B.; MacGregor, K. B. Bibcode: 1984BAAS...16..899F Altcode: No abstract at ADS Title: Winds from rotating, magnetic, hot stars. I. General model results. Authors: Friend, D. B.; MacGregor, K. B. Bibcode: 1984ApJ...282..591F Altcode: It is generally thought that the winds of hot stars are driven by the force arising from the absorption and scattering of photospheric continuum radiation by ultraviolet resonance lines of abundant ions in the flow. However, puzzling discrepancies were found in a comparison of observational data with the predictions of theoretical models for line-driven mass loss. It is pointed out that part of the apparent disagreement between theory and observation might result from the existence of additional, nonradiative forces which contribute to the acceleration of hot star winds, but which are omitted from the model considered by Castor et al. (1975). The present investigation takes, therefore, into account the dynamics of winds which are predominantly radiation driven, but which are also acted upon by the forces due to rapid rotation in the presence of a stellar magnetic field. Title: Theory of winds in late-type evolved and pre-main-sequence stars. Authors: MacGregor, K. B. Bibcode: 1983NASCP.2280.241M Altcode: 1983sowi.conf..241M Recent observational results confirm that many of the physical processes which are known to occur in the Sun also occur among late-type stars in general. One such process is the continuous loss of mass from a star in the form of a wind. There now exists an abundance of either direct or circumstantial evidence which suggests that most (if not all) stars in the cool portion of the HR diagram possess winds. An attempt is made to assess the current state of theoretical understanding of mass loss from two distinctly different classes of late-type stars: the post-main-sequence giant/supergiant stars and the pre-main-sequence T Tauri stars. Toward this end, the observationally inferred properties of the wind associated with each of the two stellar classes under consideration are summarized and compared against the predictions of existing theoretical models. Although considerable progress has been made in attempting to identify the mechanisms responsible for mass loss from cool stars, many fundamental problems remain to be solved. Title: Winds from Rotating, Magnetic, Hot Stars Authors: Friend, D. B.; MacGregor, K. B. Bibcode: 1983BAAS...15..970F Altcode: No abstract at ADS Title: Mass loss from rotating magnetic stars - Weber and Davis re-revisited Authors: MacGregor, K. B.; Pizzo, V. J. Bibcode: 1983ApJ...267..340M Altcode: The criticisms by Barker and Marlborough (BM, 1982) concerning the model of Weber and Davis (WD, 1967) for the flow of a magnetically coupled wind from a rotating star are critically examined and the assumptions inherent to both approaches are compared. It is shown that when differences in the respective definitions of the stellar angular velocity are reconciled, the extended theory proposed by BM is equivalent to the original description of WD. In addition, the conditions under which the azimuthal velocity of a WD-type solar wind initial decreases outward from the surface of the star are determined and it is shown that such behavior is in no way contingent upon the modifications proposed by BM. Title: Future Prospects for the Theory of Solar-Stellar Winds Authors: MacGregor, K. B. Bibcode: 1982BAAS...14..946M Altcode: No abstract at ADS Title: Protostellar mass and angular momentum loss Authors: Hartmann, L.; MacGregor, K. B. Bibcode: 1982ApJ...259..180H Altcode: Recent radio observations have indicated that appreciable, continuing mass loss is occurring from regions of star formation. The conditions under which massive protostellar objects may exhibit strong, rotationally driven winds are investigated. For plausible rotational velocities and magnetic field strengths, ejection of about 10,000 solar masses a year at speeds of 10-100 km/s can be maintained for time scales of about 0.0001 yr; these values are insensitive to the protostellar luminosity. An evolutionary scenario is sketched which suggests that protostellar clouds may be expected to be rapidly rotating and to possess substantial magnetic fields when the clouds have contracted to radii of about 10 to the 14th cm. The centrifugally driven winds proposed present an alternative to fragmentation for providing the angular momentum loss required in the phase of rapid cloud contraction. Title: Stellar winds in binary X-ray systems. Authors: MacGregor, K. B.; Vitello, P. A. J. Bibcode: 1982ApJ...259..267M Altcode: It is thought that accretion from a strong stellar wind by a compact object may be responsible for the X-ray emission from binary systems containing a massive early-type primary. To investigate the effect of X-ray heating and ionization on the mass transfer process in systems of this type, an idealized model is constructed for the flow of a radiation-driven wind in the presence of an X-ray source of specified luminosity, Lx. It is noted that for low values of Lx, X-ray photoionization gives rise to additional ions having spectral lines with wavelengths situated near the peak of the primary continuum flux distribution. As a consequence, the radiation force acting on the gas increases in relation to its value in the absence of X-rays, and the wind is accelerated to higher velocities. As Lx is increased, the degree of ionization of the wind increases, and the magnitude of the radiation force is diminished in comparison with the case in which Lx = 0. This reduction leads at first to a decrease in the wind velocity and ultimately (for Lx sufficiently large) to the termination of radiatively driven mass loss. Title: Wave-driven winds from cool stars. I - Some effects of magnetic field geometry Authors: Hartmann, L.; MacGregor, K. B. Bibcode: 1982ApJ...257..264H Altcode: The wave-driven wind theory of Hartmann and MacGregor (1980) is extended to include effects due to non-radial divergence of the flow. Specifically, isothermal expansion within a flow tube whose cross-sectional area increases outward faster than the square of the radius near the stellar surface is considered. It is found that the qualitative conclusions of Hartmann and MacGregor concerning the physical properties of Alfven wave-driven winds are largely unaffected. In particular, mass fluxes of similar magnitude are obtained, and wave dissipation is still necessary to produce acceptably small terminal velocities. Increasingly divergent flow geometries generally lead to higher initial wind speeds and slightly lower terminal velocities. For some cases of extremely rapid flow tube divergence, steady supersonic wind solutions which extend to infinity with vanishing gas pressure cannot be obtained. In addition, departures from spherical symmetry can cause the relative Alfven wave amplitude delta-B/B to become approximately greater than 1 within several stellar radii of the base of the wind, suggesting that nonlinear processes may contribute to the wave dissipation required by the theory. Title: Momentum and energy balance in late-type stellar winds. Authors: MacGregor, K. B. Bibcode: 1982SAOSR.392A..83M Altcode: 1982csss....2...83M Observations at ultraviolet and X-ray wavelengths indicate that the classical picture of a static stellar atmosphere containing a radiative equilibrium temperature distribution is inapplicable to the majority of late type stars. Mass loss and the presence of atmospheric regions characterized by gas temperatures in excess of the stellar effective temperature appear to be almost ubiquitous throughout the HR diagram. Evidence pertaining to the thermal and dynamical structure of the outer envelopes of cool stars is summarized. These results are compared with the predictions of several theoretical models which were proposed to account for mass loss from latetype stars. Models in which the outflow is thermally radiatively, or wave driven are considered for identification of the physical processes responsible for the observed wind properties. The observed variation of both the wind, thermal and dynamical structure as one proceeds from the supergiant branch toward the main sequence in the cool portion of the HR diagram give consideration to potential mechanisms for heating and cooling the flow from low gravity stars. Title: Protostellar Mass and Angular Momentum Loss Authors: MacGregor, K. B.; Hartmann, L. Bibcode: 1981BAAS...13R.855M Altcode: No abstract at ADS Title: Momentum and energy deposition in late-type stellar atmospheres and winds. Authors: Hartmann, L.; MacGregor, K. B. Bibcode: 1980ApJ...242..260H Altcode: The present study calculates the response of the outer atmospheres of cool low-gravity stars to the passage of the mechanical energy fluxes of solar magnitude in the form of acoustic waves and Alfven waves. It is shown that Alfven waves are efficient in generating outflow, and can account for the order of magnitude of observed mass loss in late-type luminous stars. However, unless these magnetic waves undergo some dissipation within several stellar radii of the surface, the predicted terminal velocities of the resulting stellar winds are far too high. Alfven wave dissipation should give rise to extended warm chromospheres in low-gravity late-type stars, a prediction which can be observationally tested. Title: Radiative amplification of sound waves in the winds of O and B stars. Authors: MacGregor, K. B.; Hartmann, L.; Raymond, J. C. Bibcode: 1979ApJ...231..514M Altcode: The velocity perturbation associated with an outwardly propagating sound wave in a radiation-driven stellar wind gives rise to a periodic Doppler shifting of absorption lines formed in the flow. A linearized theory applicable to optically thin waves is used to show that the resulting fluctuation in the absorption-line force can cause the wave amplitude to grow. Detailed calculations of the acceleration due to a large number of lines indicate that significant amplification can occur throughout the high-velocity portion of winds in which the dominant force-producing lines have appreciable optical depths. In the particular case of the wind of Zeta Pup (O4f), it is found that the e-folding distance for wave growth is considerably shorter than the scale lengths over which the physical properties of the flow vary. A qualitative estimate of the rate at which mechanical energy due to nonlinear waves can be dissipated suggests that this mechanism may be important in heating the supersonic portion of winds of early-type stars. Title: Model Winds and Chromospheres for Late-Type Giants and Supergiants Authors: MacGregor, K. B.; Hartmann, L. Bibcode: 1979BAAS...11..448M Altcode: No abstract at ADS Title: Radiation-Driven Winds in Binary X-Ray Source Systems Authors: MacGregor, K.; Vitello, P. A. J. Bibcode: 1979xras.proc..267M Altcode: No abstract at ADS Title: Radiation-driven winds in binary X-ray source systems Authors: MacGregor, K.; Vitello, P. A. J. Bibcode: 1978cosp.meetS....M Altcode: The hydrodynamics of line-driven stellar winds in binary systems containing a weak X-ray source is investigated. The gravitational, ionization, and heating effects due to the secondary on the acceleration of the wind are taken into account. It is found that the changes in the acceleration which result from the presence of even a weak X-ray source can profoundly alter the wind velocity profile. Title: Coronal Regions in the Winds of Early-type Stars. Authors: MacGregor, K. B. Bibcode: 1978BAAS...10..412M Altcode: No abstract at ADS Title: The Effects of Centrifugal, Magnetic, and Radiative Forces on the Dynamics of Stellar Wind Flow. Authors: MacGregor, Keith Bruce Bibcode: 1977PhDT.......129M Altcode: No abstract at ADS Title: Magnetic acceleration of winds from solar-type stars. Authors: Belcher, J. W.; MacGregor, K. B. Bibcode: 1976ApJ...210..498B Altcode: The spin-down of solar type stars (F5 V to G3 V) is generally ascribed to the outflow of magnetized plasma in the form of a wind. Magnetically coupled stellar winds are thought to provide the dominant mechanism for angular momentum loss over the entire main-sequence lifetime of stars possessing hydrogen convective zones. The associated loss in rotational kinetic energy can strongly affect the energetics of winds emanating from such stars, for sufficiently high rotation rates and magnetic field strengths. In the present paper, an attempt is made to describe qualitatively how MHD plasma outflow from a rotating star adjusts itself to a broad range of stellar conditions, including fast, intermediate, and slow magnetic rotator configurations. Using the Weber and Davis (1967) model of MHD winds, it is shown that the magnetic deceleration of an MHD wind is of importance when the loss of rotational kinetic energy due to magnetic braking exceeds the energy flux due to thermal processes alone. Title: Magnetic Acceleration of Winds from Solar-Type Stars Authors: Belcher, J. W.; MacGregor, K. B. Bibcode: 1976BAAS....8..307B Altcode: No abstract at ADS