Comparing solar internal rotation results from MDI and GONG R. Howe 1, J. Christensen-Dalsgaard 2, F. Hill 1, R. W. Komm 1, J. Schou 3, M. J. Thompson 4 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. Low activity – GONG Months MDI days Medium Activity – GONG Months MDI days High Activity – GONG Months MDI days 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 a 3 coefficients that differ significantly between the various analyses and data sets. The a 3 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. 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 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= National Solar Observatory, Tucson, AZ 2, Aarhus University, Denmark 3. Stanford University 4. Imperial College, London, UK

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. 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) 1. Near to solar maximum, near- sectoral 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. 5. The AZ analysis neglect of m- leakage causes under-estimation of low-degree rotational splittings and hence of the rotation rate below the convection zone. (Howe and Hill 1998) 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. Conclusions Rotation Profile from Inversion 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 mHz. In general, the differences are independent of activity level. 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, 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, 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