List of Figures

View Image Figure 1:
A section through the interior of the Sun, showing the contours of constant rotation and the major features of the rotation profile, for a temporal average over about 12 years of MDI data. The cross-hatched areas indicate the regions in which it is difficult or impossible to obtain reliable inversion results with the available data.
View Image Figure 2:
A single Doppler velocity image of the Sun from one GONG [Global Oscillation Network Group] instrument (left), and the difference between that image and one taken a minute earlier (right), with red corresponding to motion away from, and blue to motion towards, the observer. The shading across the first image comes from the solar rotation.
View Image Figure 3:
A segment of an l = 0 time series of Doppler velocity observations, showing the dominant five-minute period and the rich beat structure.
View Image Figure 4:
Typical l − ν spectrum from one day of GONG observations (image courtesy NSO/GONG).
View Image Figure 5:
Lower turning point of acoustic modes as a function of phase speed ν∕L, based on Model S of Christensen-Dalsgaard et al. (1996).
View Image Figure 6:
Locations of modes in the l,ν plane for a typical MDI mode set. The colored shading represents the radial regions in which the modes have their lower turning points; the core, r ≤ 0.2 R⊙, the radiative interior, 0.2 ≤ r∕R ⊙ ≤ 0.65, the tachocline, 0.65 ≤ r∕R ⊙ ≤ 0.75, the bulk of the convection zone, 0.75 ≤ r∕R ⊙ ≤ 0.95, and the near-surface shear layer, r∕R ⊙ ≥ 0.95; the dashed line on the lower right corresponds to r∕R = 0.99 ⊙.
View Image Figure 7:
Spectrum for l = 100 in the ν,m plane (top) and detail (bottom) of a single ridge (radial order) showing the curvature due to differential rotation and the multiple-ridge structure arising from spherical harmonic leakage.
View Image Figure 8:
Spherical harmonic patterns for l = 50: left, m = 0; center, m = 45; right, m = 50.
View Image Figure 9:
a1 (top) and a3 (bottom) coefficients for (left) 1986 BBSO observations, (middle) 108 days of GONG observations in 1996, (right) the mean of 35 consecutive 108-day periods of GONG observations from 1995 – 2005, plotted as a function of phase speed with the turning point radius marked on the upper axis.
View Image Figure 10:
Sections through rotation kernels for selected azimuthal orders for l = 3,n = 9 (top), and l = 20, n = 5 (bottom).
View Image Figure 11:
Averaging kernels for a typical RLS inversion of MDI data, for target latitudes 0 (a), 15 (b), 30 (c), 45 (d), 60 (e), and 75 (f) degrees as marked by the dashed radial lines, and target radii 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.99 R⊙ indicated by colors from blue to red as denoted by the dashed concentric circles. Contour intervals are 5% of the local maximum value closest to the target location, with dashed contours indicating negative values.
View Image Figure 12:
As Figure 11, for a SOLA inversion.
View Image Figure 13:
Schematic time line of helioseismic observations in the last three solar cycles (top panel), with the filled part of each bar representing approximate duty cycle, plotted on the same temporal scale as the butterfly diagram (bottom panel) of the gross magnetic field strength from Kitt Peak observations.
View Image Figure 14:
l = 1 splitting estimates as a function of publication date.
View Image Figure 15:
Power spectrum from 10 years of BiSON data, 1992 – 2002; the insets show the low-frequency end of the five-minute band (blue) and a single, rotationally split l = 1 peak (red).
View Image Figure 16:
Summary of rotation inferences from Brown et al. (1989) (reproduced by permission of the AAS).
View Image Figure 17:
Rotation profile based on analysis of BBSO splittings, (Schou et al., 1992) (reproduced by permission of the AAS).
View Image Figure 18:
Four inferred rotation profiles from the first 144 days of MDI observations (Schou et al., 1998): (a) 2dRLS, (b) 2dSOLA, (c) 1d×1dSOLA, (d) 1.5dRLS, from Schou et al. (1998) (reproduced by permission of the AAS).
View Image Figure 19:
Mean rotation profile from GONG data; contours of constant rotation (left), showing lines at 25° to the rotation axis as dashed lines, after Howe et al. (2005), and cuts at constant latitude as a function of radius (right), after Howe et al. (2000b).
View Image Figure 20:
Idealized rotation profiles for rotation constant on cylinders (left), radial lines (middle), and lines at 25° to the rotation axis (right). The top row shows contours of constant rotation, while the lower row shows rotation rate as a function of radius at constant latitude for latitudes at 15° intervals from the equator (top) to 75° (bottom). The rotation rate is matched to the GONG inferences at 0.99 R ⊙ and smoothed to simulate the broadening effect of inversion resolution on the tachocline; the near-surface shear was not included.
View Image Figure 21:
Three temporally averaged rotation profiles from the spherical-shell simulations of (a) Brun et al. (2004), (b) Browning et al. (2006), and (c) Miesch et al. (2008) (reproduced by permission of the AAS).
View Image Figure 22:
Radial variation of the mean rotation rate after subtraction of the tracking rate, for global inversions (blue) and north – south averaged local inversions of MDI (green) and GONG (red) data at latitudes 0° (a), 15° (b), 30°(c), and 45° (d); similar to Howe et al. (2006a).
View Image Figure 23:
Contour diagrams of constant rotation velocity residuals at 0.98 R⊙, obtained using two dimensional RLS inversion of the GONG data, from Basu and Antia (2003) (reproduced by permission of the AAS).
View Image Figure 24:
Zonal flow pattern derived from MDI f-mode measurements, with smooth profile subtracted. Based on a figure from Schou (1999), updated and used by kind permission of J. Schou (2008, private communication.)
View Image Figure 25:
Rotation rate after subtraction of a temporal mean at each location, as a function of latitude and time at selected depths, for OLA (top) and RLS (middle) inversions of MDI data, and for RLS inversions of GONG data (bottom).
View Image Figure 26:
Rotation rate after subtraction of a temporal mean at each location, as a function of depth and time at selected latitudes. Latitudes are 0, 15, 30, 45, 60° from left to right; inversions are MDI OLA (top), MDI RLS (middle), and GONG RLS (bottom).
View Image Figure 27:
Rotation rates at selected latitudes and depths as a function of time, after subtraction of a temporal mean. The results are from GONG RLS (black), MDI RLS (red), and MDI OLA (blue) inversions.
View Image Figure 28:
Phase (left) and amplitude (right) of 11-year sine functions fitted to temporal variation of the rotation rate for OLA (top) and RLS (middle) inversions of around 11 years of MDI observations and for RLS inversions of GONG data (bottom).
View Image Figure 29:
Local helioseismic inferences of zonal flows close to the surface, from Haber et al. (2002) (left) and Zhao and Kosovichev (2004) (right) (reproduced by permission of the AAS).
View Image Figure 30:
Zonal flows since 1986, from Mount Wilson Doppler measurements (top), global helioseismic measurements from BBSO and MDI (middle) and MDI ring-diagram analysis (bottom). The color scale is in nHz.
View Image Figure 31:
Rotation-rate residuals at the equator at 0.72 R ⊙ (top) and 0.63 R⊙ (bottom), for RLS (filled) and OLA (open) inversions of MDI (red triangles) and GONG (black circles) data.
View Image Figure 32:
Sine-wave power in the rotation rate residuals from RLS inversions of GONG data, at 0.72 R⊙, 0°, plotted as a function of frequency for a) 1995 – 2000, b) 1995 – 2003, c) 1995 – 2005, d) 2000 – 2005.