P1253037271zpjqM

1
Variations in rotation rate within the solar
convection zone from GONG and MDI 1995-2000 R.
Howe1, J. Christensen-Dalsgaard2, F. Hill1, R.W.
Komm1, J. Schou3, M. J. Thompson4, J. Toomre5
1. National Solar Observatory, Tucson, AZ 2.
Aarhus University, Denmark 3. Stanford University
4. Imperial College, London, UK 5. JILA,
University of Colorado
Introduction 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
re-analyzed 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.
High latitude rotation variations
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.

2
The Global Picture
Variations near the tachocline
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.
Variations near the tachocline 108-day sets
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.
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 108-day 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, ya1
cos(2??t)a2 sin(2??t) to the data. The plots
above show (A) the best-fit sine wave (frequency
0.770.1 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.
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.
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.