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Comparing solar internal rotation results
from MDI and GONG
1
Howe ,
2
Christensen-Dalsgaard ,
R.
J.
1
1
3
4
F. Hill , R. W. Komm , J. Schou , M. J. Thompson
1. National Solar Observatory, Tucson, AZ 2, Aarhus University, Denmark 3. Stanford University 4. Imperial College, London, UK
Introduction
The Global Oscillations Network Group (GONG) and the Solar
Oscillations Investigation (SOI) using the Michelson Doppler
Imager (MDI) instrument aboard the SOHO spacecraft have
jointly accumulated more than five years of helioseismic data,
with nearly four years of contemporaneous observations. The
results from the two projects are generally in good agreement;
however, there are differences in detail which need to be
understood. We report here on an ongoing exercise to compare
the data and analysis from the two projects.
Three 108-d periods were chosen, with low, medium and high
levels of solar activity. The GONG and MDI data for each period
were then analyzed using both the algorithm usually used in
Tucson, AZ on GONG data and that usually used in Stanford, CA
on MDI data. For convenience, we denote the analysis pipelines
by AZ and CA respectively.
The GONG project uses a network of six terrestrial
observing stations, each with a 256x256 pixel
camera. Data are collected up to degree l=250, but
routine analysis produces only spectra up to l=200
and frequencies up to l=150. The typical duty cycle
is around 87 per cent. The network has been in
operation since May 1995.
The MDI instrument aboard the SOHO spacecraft
has been collecting medium-l data since May 1996,
using a 1024x1024 pixel camera with the results
binned to 256x256. The data are produced and
analyzed up to l=300.
Low activity
1996-09-22 – 1997-01-07
GONG Months 15-17
MDI days 1360-1467
Mode Coverage
The coverage of successfully fitted multiplets in the
l- plane differs both between data sources and
between algorithms. The MDI instrument accesses
modes up to l=300, while GONG data can only be
analyzed up to l=200. Furthermore, the CA algorithm
is able to fit the spectrum to slightly higher degrees
than AZ, because of the greater stability given by
fitting whole multiplets at one time rather than
individual (n,l,m) modes. In the high-activity set, the
distribution of activity causes problems with the AZ
coefficient fitting around 3mHz.
a coefficient differences
Here we show the locations in the l- plane of a3
coefficients that differ significantly between the
various analyses and data sets. The a3 coefficients
represent the dominant term in the differential
rotation. The most obvious differences in the rotation
coefficients occur between AZ and CA processing in
a frequency band centered around 3.3 mHz. Similar
patterns are seen in higher-order coefficients. This
appears to reflect an anomaly in the CA coefficients,
which is stronger for the MDI data in the latter two
periods but not the first one.
Rotation Inferences
Here we show RLS rotation profiles for the various
sets.The results from all the data sets and methods
agree well at low latitudes within the convection
zone. At higher latitudes, discrepancies appear, both
near the surface where MDI(CA) shows an anomaly
at about 0.95R and CA shows a reversal in the
direction of the near-surface shear layer, and at
greater depths where CA gives faster rotation at high
latitudes than AZ. Notice that this last effect is seen
more strongly in MDI than GONG except for the first
period.
Inversions with restricted data sets
When we remove the modes above 3mHz, which
show systematic anomalies in CA fits, and restrict
the inversion to modes common to all four data sets,
the differences among the inversions are much
reduced. Further numerical experiments have shown
that the downward shift in the CA results at high
latitudes cannot be attributed to the loss of
resolution caused by restricting the data set. These
shifts are therefore clearly associated with the
3.5mHz anomaly in the CA coefficients.
OLA Inversions
The OLA inversions for the CA sets agree well
except at high latitudes. It is more difficult to obtain
satisfactory results from the OLA technique using
the AZ data, because the lack of high-degree modes
makes it hard to localize kernels close to the
surface.
The AZ analysis fits peaks to each (l,m) power
spectrum separately, and does not explicitly take
into account the spatial leakage effects which cause
each spectrum to contain power from neighboring
spectra. Coefficients are obtained by fitting a
polynomial expansion to the frequencies.
The CA analysis fits all the Fourier spectra of each l
simultaneously, deriving a coefficients directly from
the data and using an explicit calculation of the
leakage characteristics.
Medium Activity
High Activity
1998-02-08 – 1998-05-26 1999-05-22 – 1999-09-06
GONG Months 29-31
MDI days 1864-1971
GONG Months 42-44
MDI days 2332-2439
Conclusions
1. Near to solar maximum, nearsectoral modes experience
different activity-related shifts,
which causes problems with the
AZ method of fitting a
coefficients to the frequencies,
resulting in some lost
coefficients when the errors are
small.
(Howe et al 2001)
3. Around 3.5 mHz, CA fitting has
systematic errors in the coefficients,
which in turn cause systematic
errors – an apparent higher rotation
rate at high latitudes – in the
rotation inversions.
4. The highest l values, where the
ridges are partially blended, can
only be accessed by the CA fitting.
They may contain systematic errors
in the coefficients. These
coefficients affect the inferred
rotation rate near the surface.
2. The ‘n-leak gap’ appears in AZ
fits at around l=30. This occurs
when modes of different n from
the target mode, but close to it in
l are not well resolved from the
target mode and cause the fit to
fail.
(Howe and Thompson 1997)
Rotation Profile from Inversion
5. The AZ analysis neglect of mleakage causes under-estimation
of low-degree rotational splittings
and hence of the rotation rate
below the convection zone.
(Howe and Hill 1998)
Summary
•Neither the AZ nor the CA algorithm is perfect!
•The agreement between different data sets analyzed with the same
algorithm is generally good.
•Even with different analyses, the rotation inferences agree well over
much of the Convection Zone.
•The AZ processing drops too many modes.
•The CA fitting seems to introduce systematic errors, particularly at
3.3-3.5 mHz.
•In general, the differences are independent of activity level.
6. MDI data with the CA analysis
show a ‘jet’ at 0.95R, 75 degrees
latitude. (Schou et al. 1997, Howe
et al. 1998). The non-appearance
of this feature in the other
data/analysis combinations, even
when the resolution ought to be
sufficient to show it, suggests that it
may arise from systematic errors,
but this is not yet conclusively
established.
References
Howe, R., Hill, F., 1998 In Structure and Dynamics of the Interior of the Sun and Sun-like Stars
(Eds. S.G. Korzennik & A. Wilson), ESA SP-418, ESA Publications Division, Noordwijk, The
Netherlands, 237-242
Howe, R., Thompson, M.J., 1998 A&AS 131, 539
R. Howe, H. Antia, S. Basu, et al., 1998
In Structure and Dynamics of the Interior of the Sun and Sun-like Stars (Eds. S.G. Korzennik & A.
Wilson), ESA SP-418, ESA Publications Division, Noordwijk, The Netherlands,1998 803-808
Howe, R., Komm, R.W., Landy, D.H. & Hill, F., 2001 In Helio- and Asteroseismology at the Dawn
of the Millennium (Ed. A. Wilson), ESA SP-464, ESA Publications Division, Noordwijk, The
Netherlands, 2001, p. 91
J. Schou, H.M. Antia, S. Basu, et al, 1998, ApJ 505, 390
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.