A stars, axial rotation in, 11, 175, 176

ABCD instability, see Shibahashi oscillatory instability absolute magnitude, effect of rotation on, 169

acceleration of a fluid particle, 26, 29

accretion disks, 15, 86, 198-200

acoustic modes, 4, 8-10, 138

adiabatic exponents, 67

age estimates of open clusters, effect of rotation on, 171

Alfven waves, 132, 192

Am stars, axial rotation in, 12, 13, 173, 178-179 angular momentum diagram, 174-175 angular momentum, transport of, 93, 102, 151 anisotropic eddy diffusivity, see diffusivity anisotropic eddy viscosity, see viscosity Ap stars, axial rotation in, 12, 13, 173, 178-179 associations, see open clusters asteroids, 175 asteroseismology, 246 astrostrophic approximation, 208, 230-237

^-plane approximation, 37, 53 B stars, axial rotation in, 11, 175, 176 baric wind law, see Buys Ballot law barlike modes, 59, 61 barocline, 69

baroclinic instability, 53-54, 81, 86 barotrope, 69

barotropic and baroclinic instabilities, generic, 49-54,

88, 152 barotropic instability, 52, 81 Be and shell stars, axial rotation in, 12, 13, 175-178 bifurcation, 58, 59, 61 black body radiation, 66 boundary conditions, 28-29 boundary layers: thermo-viscous, 101-118, 134, 136, 180 viscous, see Ekman and Munk layers Boussinesq approximation, 50 broken symmetry, 58 Brunt-Vaisala frequency, 50, 78 buoyancy frequency, see Brunt-Vaisala frequency Buys Ballot law, 38

centrifugal acceleration, 29

circulation in stars, see meridional circulation close binaries, early-type: axial rotation, 16 coplanarity, 207, 212

orbital circularization, 17, 19, 214-217, 226-230 reflection effect, 123-126, 238 synchronization (or pseudo-synchronization), 4, 17, 18, 43, 120, 214-217, 226-230 close binaries, late-type: axial rotation, 16 coplanarity, 21, 207, 209, 211 orbital circularization, 17, 20, 208-214 synchronization (or pseudo-synchronization), 17, 43, 208-214 color, effect of rotation on, 169 conservation of:

angular momentum, 56, 210 energy, 27, 66 mass, 26, 66 contact binaries, 230-237, 239 convection, interaction of rotation with, see solar differential rotation convective cores, effect of rotation on, 163 convective equilibrium, 72-73 coplanarity, see close binaries Coriolis acceleration, 29 Coriolis parameter, 37 Cowling point-source model, 98, 99 cup of tea, motions in a, 42

diffusion, microscopic and turbulent:

in the chemically peculiar stars, 178, 179-182 in the Sun's radiative core, 152-154, 248 diffusivity, coefficients of: eddy, 88, 89, 152, 181 microscopic, 153, 181 dissipation function, 27 dynamical instabilities:

axisymmetric motions, 65, 73-80 nonaxisymmetric motions, 65, 81-82 dynamo activity, 184, 193, 202, 203

Earth's atmosphere, 25, 35, 36-43, 245 eclipsing binaries, 3, 4, 17, 229, 230, 231 Eddington-Sweet time, 86, 97 eddy-mean flow interaction, 66, 86-89, 93 effective gravity, 29, 68

effective temperature, effect of rotation on, 166, 169 Ekman layer, 93, 134, 238

at a rigid plane boundary, 38-40 at the ocean-atmosphere interface, 43-45 Ekman number, 30, 218 Ekman pumping:

at a rigid plane boundary, 40-43, 217-220, 238 at atidally distorted stellar surface, 220-225 Ekman spiral, 39, 44 energy principle, 73-76 entropy per unit mass, 27, 28, 94 equatorial break-up, 13, 61, 95, 166, 168, 170, 174, 175

Eulerian variables, 26 Eulerian variations, 51, 73 evolved stars, rotation of, 182-185

F stars, axial rotation in, 11 f -modes, see Kelvin modes f -plane approximation, 37, 50 Ferraro's isorotation law, 129-133 Ferrel law, see Buys Ballot law

G stars, axial rotation in, 14, 15 g-modes, see gravity modes galaxies, clusters of, 175 geopotential, 38

geostrophic approximation, 37-38, 45, 93, 134, 208, 233, 236

giant stars, axial rotation in, 12, 182-185 Goldreich-Schubert-Fricke instability, 85 gravitational potential, 55, 165 gravitational sorting, see diffusion gravity darkening, 170, 232

von Zeipel law, 70, 169, 232 gravity modes, 50, 153, 214, 217, 246 Gray mechanism, 184 Gulf Stream, 46, 48

helioseismology, see solar observations hydrodynamical mechanism, 220-230, 242, 248 hydrostatic approximation, 37, 236

ideal gas, 27, 66

isentropic motions, 28, 67

isobaric surfaces, 68

isopycnic surfaces, 69

isorotation, see Ferraro's isorotation law

Jacobi ellipsoids, 57-60

K stars, axial rotation in, 15 Kelvin modes, 59 Kelvin-Helmholtz instability, 52 Kelvin-Helmholtz time, 86, 97 Kepler's third law, 120, 210

Lagrangian displacement, 9, 73

Lagrangian variables, 26, 32

Lagrangian variations, 73

Legendre polynomials, see spherical harmonics limb darkening, 170

lithium abundance, solar, 152 Lorentz force, 126, 128, 129, 133, 155 low-mass stars, rotational evolution of, 197-204, 247

/-gradients, role of, 82-86, 145-151 M stars, axial rotation in, 15 Maclaurin spheroids, 57-60 magnetic braking in early-type stars, 173, 179 magnetic diffusivity, coefficients of: eddy, 126 microscopic, 128 magnetic fields and isorotation, 129-133, 157, 164 magnetic fields in the Sun's radiative core, 154—158 magneto-rotational instabilities, 86 main-sequence models, 162-169 differential rotation, 168 solid-body rotation, 166, 167 mass-luminosity relation, 232 Maunder sunspot minimum, 7 mechanically driven currents, see hydrodynamical mechanism meridional circulation, theory of: in close binaries, 120-126, 238 in magnetic stars, 126-133

in radiative envelopes, 25, 49, 71, 94-118, 179-182, 246

in the solar convection zone, 72, 73, 139-142 in the Sun's radiative core, 145-151, 158 in white dwarfs, 118-120 meteorites, 152

mixing in stably stratified regions, 88, 152-154,

Navier-Stokes equation, 27 neutron stars, axial rotation in, 175, 198 Newton's second law of action, 26, 29, 66 Newtonian fluids, 27

O stars, axial rotation in, 11, 175, 176 oblique-rotator model, 4, 128 oceans, 25, 35, 43-49, 245 ohmic dissipation, 132 opacity, coefficients of: electron-scattering, 105 Kramers law, 105 open clusters and associations, axial rotation in, 13, 15,

16, 172-173, 193, 194-197, 204 orbital circularization, see close binaries p-modes, see acoustic modes Poincare-Wavre theorem, 67-69, 140 Poisson equation, 66 polytropic index, 60

effective, 97 polytropic models:

differential rotation, 61, 80 solid-body rotation, 60, 61 population II objects, axial rotation in, 12, 13 post-main-sequence phases, 182-185, 214 potential temperature, 28, 50

pre-main-sequence phases, 179, 191, 199,

200-204,214 pre-main-sequence stars, see T Tauri stars pseudo-synchronism, see close binaries pulsars, axial rotation in, 175

r -modes, 217 radiation pressure, 66

radiative conductivity, coefficient of, 66, 94, 119

radiative equilibrium, 70-72

Rayleigh criterion, 79

resonance mechanism, 214-217, 227, 230

Reynolds number, 33, 229

Reynolds stresses, 34, 35, 87, 139

Richardson criterion, 54, 81

Richardson number, 50, 51, 88

Roche model, 230, 232

Rossby number, 30, 52, 194, 218

Rossby waves, 217

rotating frame of reference, 29-30

rotational velocity distributions, 175

Routh-Hurwitz criterion, 84

RS CVn stars, tidal interaction in, 20

Schatzman mechanism, 191-194 secular instability, see bifurcation self-consistent-field method, 165 self-gravitating fluid masses, 55-62 shear-flow instability, 54, 81, 88 Shibahashi oscillatory instability, 85 Skumanich law, 14, 190, 193 solar differential rotation:

global-convection models, 142-144, 158 mean-field models, 139-142, 158 observations, 5-8 solar internal rotation: observations, 8-10, 138 spin-down models, 151-158, 159 solar observations:

Doppler shift of spectral lines, 2, 5 early measurements, 1-5 five-minute oscillations, 4, 5, 8 helioseismology, 5, 8-10, 138, 151, 247 long-term periodic modulation, 8 magnetic fields, 5, 8 meridional currents, 2, 5, 8, 25 sunspot cycles, 7 sunspots and other tracers, 1, 2, 5 torsional oscillation, 7 solar tachocline, 10, 157 Solberg-H0iland conditions, 53, 76-80 spectral lines, effect of differential rotation on, 172 spectroscopic binaries, 18, 19, 20 spherical harmonics, 9, 59

spin-down (or spin-up) time, 42, 219, 220, 224, 239

stellar observations:

early measurements, 1-5 Fourier analysis of spectral lines, 4, 182 rotational broadening of spectral lines, 3,11 rotational discontinuity along the main sequence,

4, 14, 15, 162, 175, 190 rotational discontinuity for the subgiant and giant stars, 13, 182-185 rotational modulation of starspots and plages, 2, 4, 11

stellar winds and episodic mass ejections, 14, 138, 151,

162, 175, 190, 191, 192, 201, 203 stress tensor, 27 stress vector, 29

supergiant stars, axial rotation in, 12, 182-185 Sverdrup relation, 45-46 symmetric instability, 52-53, 80 synchronism, see close binaries

T Tauri stars, axial rotation in, 15, 194-197, 197-200

Taylor-Proudman theorem, 32-33, 38

thermal conductivity, coefficient of, 27, 119

thermal instabilities, 65, 82-86

thermal-wind equation, 38, 50, 77

thermally driven currents, see meridional circulation tidal interaction, 16, 173, 179, 207

tidal-torque mechanism, 208-214, 227, 230

tide:

dynamical, 207 equilibrium, 207 toroidal modes, see barlike modes turbulence, 33

turbulent heat transport, 141, 142 turbulent motions in stars, 25, 82, 86, 245

upper main sequence, axial rotation along the, 3, 172-179

virial equations, 55-56 viscosity, coefficients of: bulk, 27

eddy, 33, 35, 40, 42, 48, 86, 88, 102, 104, 139, 151,

152, 157, 224 kinematic, 30, 36, 40, 42 radiative, 104, 224 shear (dynamical), 27, 151, 157 vorticity: absolute, 30 geostrophic, 41 planetary, 37 relative, 31, 41 vorticity equation, 30-32, 42, 46

western boundary currents, see Munk layer white dwarfs, axial rotation in, 13, 198, 246 wind-driven oceanic circulation, 43-49

Was this article helpful?

## Post a comment