List of Symbols A Vector potential A 1. Amplitude of light wave 2. Astronomical unit 3. Atomic weight 4. 1012 times element abundance relative to hydrogen 5. Azimuthal component of vector potential 6. Constant in law of differential rotation 7. Area of sunspot AUL Einstein coefficient for spontaneous emission A z Mean atomic weight of atoms heavier than helium B Magnetic field vector Bp Poloidal magnetic field vector Bt Toroidal magnetic field vector B 1. Kirchhoff-Planck function 2. Magnitude (or component) of magnetic field 3. Constant in law of differential rotation BLU Einstein coefficient for radiative excitation Bp Field in equilibrium with pressure BUL Einstein coefficient for induced emission Be Critical magnetic field strength Be Equipartition field strength Bm Central field strength in sunspot Bo 1. Heliographic latitude of disc center 2. Initial magnetic field strength C 1. Intensity contrast of granulation 2. Constant in law of differential rotation Cij Rate of collisional transition D 1. Aperture (diameter) of telescope 2. Diameter of granule 3. Dynamo number Ds Aperture of spectrograph E Electric field vector E 1. Number fraction electrons/all other particles 2. Energy of nuclear reaction Iff =(uxb), vector of mean electric field EES Electrostatic energy of charged particles Eij Energy of jth state of ith atom Ej Energy of jth atomic state Emax Energy of Gamow peak 362 List of Symbols F 1. Vector of energy flux density 2. Volume force Vector of convective energy flux density Vector of heating energy flux density Vector of radiative energy flux density 1. Magnitude of energy flux 2. Cross section of flux tube G Gravitational constant H 1. Voigt function 2. Density scale height 3. Specific enthalpy Hp Pressure scale height I Stokes vector I Intensity of radiation Ie Continuum intensity J 1. Birefringence of Lyot filter 2. Mean (over solid angle) of intensity 3. Quantum number of angular momentum 4. Total angular momentum of Sun Total initial angular momentum of Sun Solar quadrupole moment Second moment of intensity Rotational splitting kernel 1. Luminosity 2. Quantum number of orbital angular momentum 3. Linear operator of solar oscillation equations 4. Ecliptic heliographic longitude 5. Constant of integration for magnetic braking Ls Luminosity at surface of solar model Lo Heliographic (ecliptic) longitude of disc center L0 Luminosity of present Sun L2 - r2 times angular part of Laplacian operator LSF Line spread function M Absolute magnitude of a star MA AJfven Mach number M J Magnetic quantum number MTF Modulation transfer function MTFn Modulation transfer function due to diffraction MTFs Modulation transfer function due to seeing N 1. j/D, focal ratio 2. Brunt-Vaisala frequency 3. Truncation index of spherical harmonic expansion NA Avogadro number O(x) Term of first order in x p 1. Pressure 2. Degree of polarization 3. Power spectrum 4. Position angle of northern direction on Sun List of Symbols 363 Electrostatic correction to pressure Gas pressure Ion contribution to gas pressure Perfect gas pressure Radiation pressure 1. Electron pressure 2. Pressure external to flux tube Associated Legendre function Pressure at surface of solar model 1. Equilibrium pressure 2. Pressure on the axis of flux tube Pj Eulerian pressure perturbation PSF Point spread function PSFD Point spread function of diffraction PSFs Point spread function of seeing Q 1. Energy release per nuclear reaction 2. Stokes parameter of linear polarized light 3. =vILlv, quality factor 4. Energy gain per volume for granular flow Reynolds stress Energy of neutrino Energy release exclusive of neutrino energy Sunspot relative number Gas constant Radius of flux tube Rate of transition from ith to jth state Magnetic Reynolds number Rossby number 1. Irradiance (energy flux) at mean solar distance 2. Quantum number of spin angular momentum 3. Source function 4. Specific entropy 1. Line source function 2. Limit frequency for acoustic oscillations T 1. Orbital period 2. Absolute temperature 3. Period of solar oscillation TB Brightness temperature Ts Sidereal period of Carrington rotation Te Electron temperature Teff Effective temperature Tp Proton temperature Ts Temperature at surface of solar model To 1. Time constant for internal g-mode oscillations 2. Coronal temperature at radius TO u 1. Internal energy, or specific internal energy 2. Stokes parameter of linear polarized light Electrostatic correction to specific internal energy 364 List of Symbols V Velocity vector of center of gravity V 1. Electrostatic potential 2. Volume, or specific volume 3. Stokes parameter of circular polarized light Vmac Parameter (velocity) of macroturbulence X Mass fraction of hydrogen X CN Combined mass fraction of carbon and nitrogen Xi Mass fraction of element i Y Mass fraction of 4He Yi Spherical harmonic function Yo Initial mass fraction of helium Y08 Value of Yo adapted to reproduce present Sun Y3 Mass fraction of 3He Y 30 Initial mass fraction of 3He Z 1. Mass fraction of elements heavier than helium 2. Charge number of a particle a 1. Grating constant 2. =4o/C, radiation constant 3. Semi-major axis of elliptical orbit b Fluctuating part of magnetic field b Binormal vector of thin flux tube c 1. Velocity of light 2. Velocity of sound 3. Oblateness parameter CA Alfven velocity Cp Specific heat at constant pressure CT Tube speed Cv Specific heat at constant volume C2 =hclk, radiation constant d 1. Diameter of solar image 2. Distance between centers of granules 3. Width of magnetic flux sheet or tube d Deuteron e 1. Elementary charge 2. Thickness of first crystal in Lyot filter e Electron e+ Positron 1 1. Focal length of telescope 2. Oscillator strength 3. Filling factor for convecting parcels Is Focal length of spectrograph leff Effective focal length g Vector of gravitational acceleration g 1. Gravitational acceleration 2. Lande factor of atomic state gL Statistical weight of lower state List of Symbols 365 gu Statistical weight of upper state geff Vector of effective gravitational acceleration gij Statistical weight of jth state of ith atom g'{' Coefficient of multipole expansion g* g factor for atomic transition g8 Gravitational acceleration at present Sun's surface h 1. Planck constant 2. Height in solar atmosphere above the level where <500 = 1 h'{' Coefficient of multipole expansion Inclination between ecliptic and solar equator j Vector of electric current density k VVave vector k 1. Gaussian gravitational constant 2. Boltzmann constant 3. VVave number kNy Nyquist wave number kh Horizontal wave number k m Largest wave number transmitted by telescope kr Radial wave number ko VVave number for separation of granulation and oscillation f Tangent vector of thin flux tube I 1. Mixing length 2. Typical size of convection cell, or length scale of fluctuation 3. Degree of spherical harmonic m 1. Mass 2. Reduced mass 3. Apparent magnitude of a star 4. Order of spectrum 5. Longitudinal order of spherical harmonic mH Atomic mass of hydrogen me Electron mass m8 Mass of present Sun Ii Principal normal vector of thin flux tube n 1. Number of grooves in a diffraction grating 2. Principal quantum number 3. Index of refraction 4. Order (radial node number) of oscillations 5. Co-ordinate in normal direction n Neutron nH Number density of hydrogen nL Number density of atoms in lower state nu Number density of atoms in upper state nz Number density of particles with charge Ze ne 1. Electron density 2. Index of refraction for extraordinary ray 3. Polytropic index ni Number density of particle species i nij Number density of ith particle in jth ionization state 366 List of Symbols nijk Number density of ith particle in jth ionization and kth excitation state n/ Number density which would obtain in LTE no Index of refraction for ordinary ray P Momentum of a particle p Proton Po Impact parameter for 90° collision r Radius vector r 1. Line depression 2. Radius rA Alfven radius rD Debye radius rv Radius where v = 0, i.e., base of convection zone rc 1. Reflection coefficient of retroreflector 2. Critical radius for coronal expansion re External reflection coefficient of glass plate rik Nuclear reaction rate per mass of species i and k rs Surface radius of solar model rt Radius of reflection for an acoustic oscillation rw Radius of solar wind source surface ro 1. Central line depression 2. Classical electron radius 3. Fried parameter 4. Radius of heat input in corona r iJT Radius where LIT reverses sign riJV Radius where LtV reverses sign r(') Radius of present Sun S 1. Co-ordinate along ray 2. =r sin e, distance from axis So Seeing parameter s Anisotropy parameter of turbulent diffusivity t time tD Dynamical time scale tKH Kelvin-Helmholtz time tff Time scale of free fall t(') Age of the Sun u Fluctuating part of velocity vector u 1. =hvlkT 2. Energy of particle 3. Partition function 4. Typical velocity in convection cell, typical fluctuating velocity, or wave amplitude v Velocity vector vrn Vector of meridional circulation vp Poloidal velocity vector vt Toroidal velocity vector Vo Vector of rotational velocity List of Symbols 367 v 1. Magnitude (or component) of velocity 2. =(A - AO)/LlAo, normalized distance from line center 3. Mean velocity of convection VA Alfven velocity in solar wind VB Normalized Zeeman splitting Wo Angular radius of usable field F t Adiabatic exponent LI 1. Focus tolerance 2. Laplacian operator LI S Total entropy change over convection zone LIT 1. Temperature difference between granules and intergranular space 2. Temperature excess of displaced parcel Llr Difference between equatorial and polar solar radii LI t 1. Time delay in Doppler spectroheliogram 2. Time resolution of observed oscillation LlA Wavelength distance to line center LlAB Zeeman splitting LlAo Doppler width of line (in wavelength) LlAG Gravitational redshift LI v 1.