
Solar rotation was first accurately measured in the last century (in 1863) by R.C.
Carrington (q.v.) who used the position of prominent spots as marker points to determine a
synodic period of about 27 days. Beginning from the first year of observation the solar
rotations are indentified by "Carrington numbers". The solar surface, however, exhibits
differential rotation, as well as a coherent pattern of activity related to magnetic fields,
and globally coherent oscillation modes. All three phenomena can be employed to shed light
on the structure and dynamics of the Sun. Particularly helioseismology, the study of
solar oscillation, made it possible to measure the depth of the solar convection zone, the
internal rotation profile, the sound speed throughout the Sun, and the solar helium
abundance, (Deubner and Gough 1984; Hill and Kroll 1992). Employing a standard model for the
internal structure of the Sun, it has been shown with linear adiabatic perturbation theory
that smallamplitude oscillations of the solar body about its equilibrium state can be
classified into three types: (i) pressure modes (pmodes), where the pressure is the
dominant restoring force; (ii) gravitymodes (gmodes), where gravity or buoyancy is the
dominant restoring force; and a class of surface or interface modes (fmodes), which are
nearly compressionless surface waves. The existence of all three modes has been confirmed by
solar observations. The solar rotation rate through a large part of the solar interior has
been estimated, utilizing for the most part observations of the pmode frequency splittings.
Each mode is characterized by an eigenfunction with frequency eigenvalue
v_{nlm}, where n, l, and m are integer "quantum" numbers; n
counts the number of radial nodes in the wavefunction, and l and m describe the nodes in
colatitude and longitude, respectively. Rotation breaks the spherical symmetry of the Sun.
Because of that the pmode frequencies are not completely degenerate in m, and the
frequencies v_{nlm} in an nlmultiplet are said to be split in
analogy to the Zeeman splitting of degenerate atomic energy levels. Because of observational
limits it is not yet possible to observe values of splittings for individual m, to be
used for inversion. However, results of observations are available in terms of efficients
a_{j} (j
5) of leastsquares fits of
the splittings
.

(16)

where P_{j}^{(L)} is a polynomial of degree
j and L = (l[l + 1])^{1/2}. The coefficients
a_{j}(n,l) of odd j reveal the
information about the internal rotation of the Sun (Figure 15). The analysis of
observational data reveal that the latitudedependent solar rotation profile as observed at
the solar surface extends down through the convective envelope. In the radiative zone the
rotation seems to have a solidbody profile. (Schou, ChristensenDalsgaard, and Thompson
1992; Hill, Oglesby, and Gu 1992). Todate there exists no obvious theoretical explanation
for this helioseismologically inferred solar rotation profile.

