Variations in rotation rate within the solar convection
zone from GONG and MDI 1995-2000
R.
1
Howe ,
J.
2
Christensen-Dalsgaard ,
1
Hill ,
F.
R.W.
4
5
M. J. Thompson , J. Toomre
1
Komm ,
J.
3
Schou ,
1. National Solar Observatory, Tucson, AZ 2. Aarhus University, Denmark 3. Stanford University 4. Imperial College, London, UK 5. JILA, University of Colorado
Introduction
High latitude rotation variations
With nearly 6 years of observations of medium-degree acoustic modes from the GONG network and
the MDI instrument aboard SOHO, we are able to use helioseismology to probe the dynamics of the
convection zone in unprecedented detail.
We have analyzed 52 overlapping 108-day periods of GONG data, starting on dates 36 days apart,
and 22 non-overlapping 72-day periods of MDI data. In addition, the MDI data have been reanalyzed in overlapping 108-day periods matching the cadence of the GONG data. Together, these
data sets cover the period from May 1995 to December 2000, encompassing the end of the previous
solar cycle and most of the rising phase of the current one. Two two-dimensional inversion
techniques – Regularized Least Squares (RLS) and Optimally Localized Averages (OLA) were used
to infer the rotation profiles as a function of latitude and radius. The radial measurements are
expressed as fractions of the solar radius R: 0.01R is equivalent to about 7Mm.
These observations reveal the substantial (60 Mm) penetration into the convection zone of the
banded zonal flows associated with the torsional oscillation. Furthermore, the data show periodic
variations in rotation rate at and below the base of the convection zone with a surprising 1.3 year
period. These discoveries further underscore the complexity of the dynamics within the convection
zone, and offer new challenges for theoretical models.
For more details, see R. Howe et al. 2000, Science 287 2456, and R. Howe et al. 2000, Astrophysical
Journal 533 L163.
Banded Zonal Flows
Above we show the rotation residuals as a function of time at selected latitudes and
depths. The black symbols represent RLS inferences from GONG, the red filled
symbols RLS inferences from MDI, and the red open symbols OLA inferences from
MDI. The high-latitude rotation rate, which is essentially always slower than the smooth
profile, decreases to a minimum in 1998 and then increases again. The offsets between
the different results may be due to differences in the detail of the inversion averages.
Rotation residuals at selected times
We can study the evolution of the rotation over many inversions by subtracting a
smooth, temporally invariant function of latitude from the rotation profiles. The profile
used here was derived by fitting a two-term expansion in cosine(latitude) to the
temporal mean rotation at each radial mesh point. As we have been observing for only
about half of an eleven-year cycle, this representation is probably more useful than
subtracting a simple temporal average.
•We observe coherent bands of faster and slower rotation, migrating towards the equator
as the solar cycle progresses.
•These bands seem to maintain their shape at least as far as radius 0.92R, or about 56
Mm below the surface.
•There is a higher-latitude branch to the flow pattern, with an amplitude that increases
over time during the observations.
•There is some hint that the low-latitude flows are shifted closer to the equator
at 0.92R, but this may be a resolution effect.
•There is some evidence for a different pattern of flows, migrating if anything slowly
poleward, at 0.84R. This needs further investigation.
The plots above show latitudinal cuts through the rotation residuals after subtraction of a
smooth profile, for OLA inversions of MDI data. Successive curves within each panel
are separated by about one year in time and have been displaced by 8nHz/year along the
x axis. Dashed vertical lines represent the 'zero' value for each curve.
Points to note are:
•The lower-latitude torsional-oscillation flows do not change much in amplitude once
they are established.
•However, the higher-latitude branch of the flows, with its maximum amplitude around
60 degrees, becomes stronger with time throughout the period of the observations.
Variations near the tachocline
The Global Picture
Cutaway view (left) and radial cuts (right) of mean rotation, from RLS
inversion of GONG data. The color scale in the cutaway view has red as fast
rotation, blue as slow.
The rotation is approximately constant on radial lines within the convection
zone, with a shear layer in the outer 5% by radius. At the base of the
convection zone (0.71R) is a transition region (the tachocline) below which
rotation is approximately uniform.
The plots above show variations in the rotation-rate residuals at selected radii and
latitudes close to the base of the Convection Zone. Black circles represent GONG and
red triangles MDI data, with RLS inferences shown as filled and OLA as open symbols.
We have now analyzed about a year of data beyond that shown by Howe et al. (2000b),
and both the oscillatory signal at 0.72R at the equator, and the agreement between
GONG and MDI results, appear to persist.
Variations near the tachocline – 108-day sets
With different temporal sampling in the MDI and GONG data, it was difficult to
compare the results directly. The MDI data were therefore re-analyzed in the same 108day cadence used for the GONG data. The agreement at 0.72R at the equator remains
good, at least in the RLS inversions. The more erratic variations at 60 degrees latitude
are less well reproduced.
The periodic nature of the signal can be assessed by fitting sine wave functions,
y=a1 cos(2t)+a2 sin(2t) to the data. The plots above show (A) the best-fit sine wave
(frequency 0.77±0.1 y-1) superimposed on the GONG RLS data, (B) the power spectrum
at 0.72 R, 0º, (C) power at 0.77 y-1 at 0º as a function of radius. Notice the secondary
peak in power at 0.63R.
This work utilizes data obtained by the Global Oscillation Network Group (GONG) project, managed by the National
Solar Observatory, which is operated by AURA, Inc. under a cooperative agreement with the National Science
Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude
Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de AstrofÍsico de Canarias, and
Cerro Tololo Interamerican Observatory.
SOHO is a joint project of ESA and NASA.
This work was supported in part by the UK Particle Physics and Astronomy Research Council. MJT thanks the
Theoretical Astrophysics Center, Denmark, for hospitality and financial support.
Above, we illustrate the continuing difficulty of obtaining the oscillatory signal directly
from the short, interrupted time series of the MDI data. In the top panel, we plot the
RLS rotation residuals at 0.72R at the equator, with black symbols for GONG and red
for MDI. The open symbols represent the GONG data with no corresponding MDI data,
and the dashed line the best sine wave fit to the whole GONG data sequence. The lower
left panel shows the relationship between corresponding residuals for GONG and MDI.
In the lower right panel, the GONG power spectrum for the common data set is plotted
in black and the MDI one in red. With this temporal sampling, neither data set shows a
clean single peak, but the spectra for MDI and GONG are similar, with a slightly
smaller amplitude for MDI.