Preliminary Results from Plane-Wave Analysis of Helioseismic Data

Richard S. Bogart & Luiz A. D. Sá,

Center for Space Science & Astrophysics, Stanford Univerity

Deborah Haber

Joint Institute for Laboratory Astrophysics, University of Colorado

Frank Hill

National Solar Observatory, National Optical Astronomy Observatories

Table of contents


Using the techniques described in Bogart et al., 1995 (Paper I), we have analyzed the p-mode spectra in four consecutive days of Ca-K filtergram data from the High-l Helioseismometer at Kitt Peak. Although the mode frequencies have not been inverted, the amplitude and phase of the frequency shifts analyzed this way demonstrate consistent behaviour that appears to be tied to solar features. These results are compared with results from a separate plane-wave (ring-diagram) analysis of the same data.


In the process of developing plane-wave mode analysis techniques for application to data from the Solar Oscillations Investigation (SOI) on SOHO, we have begun to analyze data from a four-day series of Ca-K filtergrams made with the High-l Helioseismometer at the National Solar Observatory. Some very preliminary estimates of velocities in the region sampled are presented here, and compared with other results obtained with similar data.

Data Analysis

The Ca-K filtergrams are taken at a cadence of one per minute, with a spatial sampling of 2 arcsec per pixel, so that the entire solar disc is contained within a 1024*1024 pixel frame. We have analyzed data from the four days Jun 22-25, 1993. On each of these days there were approximately eleven hours of data, with very few gaps. For each day we have analyzed 512 minutes of data centered on local noon. Data for the first day were available with corrections for scattered light, but our results do not seem to be particularly sensitive to this correction. The data were mapped and power spectra determined using the techniques described in Paper 1, and the acoustic-mode frequency shifts corresponding to the field motions estimated using both the techniques described in that paper and in Haber et al. 1995.

The average velocities were estimated by averaging together, in the case of the Fourier technique, values from 28 cylindrical cuts along a single surface (n = 2) at values of k separated by the spatial Nyquist frequency. With the Ring diagram technique, rings corresponding to the same surface from 28 frequency-plane cuts were used, at values of w separated by the temporal Nyquist frequency. Results for one data sample, the nine-hour time series of data from Jun 22, 1993 used in the ``hound & hare exercise'' described in Paper 1, are shown in Table 1. This region is centered at Carrington longitude 135, approaching central meridian at the end of the day, and at latitude -25. The region has an extent of about 30 degrees (256*256 pixels with a scale at the map center of 0.12 heliographic degree/pixel). In Paper 1 we used the differences between this and other deliberately mistracked fields to demonstrate the linearity of both methods and establish the agreement of the constant of proportionality relating the determined frequency variations to velocities. The present result seems to establish that whatever constant offset may exist between the real and the inferred velocity at least does not differ in the two techniques. This is important to demonstrate, since the typical average velocities inferred are several hundred meters per second relative to the supposedly stationary photosphere.

Using the Fourier technique we have explored multiple regions on the solar disc concurrently and extended the analysis over the full 4 days' of data. These data are presented in Table 2. Typically the averaged velocities are in the 50-200 m/s range, with statistical uncertainties of 30-60 m/s, so the results are statistically significant. It can be seen that there is often good agreement between the velocities of adjacent regions and between the velocities of the same region on successive days, but that there are sometimes significant discontinuities in these patterns. Also, large uncertainies in direction are often, but not always, correlated with small absolute velocities.


The comparatively large absolute value of the velocities we infer is a matter of some concern, as it is unusual to have consistent surface flows of this magnitude. However, it should be remembered that the flows are averaged in depth, with significant weighting from regions well below the photosphere. Furthermore, the values we find are similar in amplitude to those that have been found independently with Ring-diagram analysis of comparable data (Hill, 1988; Patrón, 1994).

The consistency of the velocities in both time and space with occasional discontinuities is what would be expected if we are detecting large-scale organized, slowly-evolving flow fields, such as giant cells. It is important to extend these measurements to observations covering a large fraction of a solar rotation in order to determine that they are not related to systematic errors having to do with either disc location or contamination of the signal by active regions. It would also be useful to compare estimates for overlapping regions of different sizes.

It should be remembered that these results are preliminary. More careful calibration is required, we need to investigate sources of systematic errors, and we also need to verify the appropriate tracking rates to use in mapping. The most glaring deficiency in the present estimates, however, and one that commands urgent attention, is the lack of any inversion. The results presented are merely based on averages of frequency shifts over a fairly large set of modes. There are cases where there is quite large uncertainty in the velocity direction (based on the standard deviation of the contributing modes) even though the average velocities are quite high. These cases in particular are suggestive of the possibility of shear flows with depth.


Bogart R. S., Sá, L., Duvall, T., Haber, D., Toomre, J., & Hill, F. 1995. ``Plane-Wave Analysis of Solar Acoustic-Gravity Waves: a (Slightly) New Approach'' 4th SOHO Workshop on Helioseismology, Pacific Grove, California, Apr. 2-6, 1995
Haber, D., Toomre, J., Hill, F., & Gough D. 1995. ``Local Area Analysis of High-Degree Solar Oscillations: New Ring Fitting Procedures'' 4th SOHO Workshop on Helioseismology, Pacific Grove, California, Apr. 2-6, 1995
Hill, F. 1988. Ap. J., 333, 996.
Patrón Recio, D. J. 1994. ``Tridimensional Distribution of Horizontal Velocity Flows Under the Solar Surface'' Doctoral dissertation, Instituto de Astrofísica de Canarias.